%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LAT323+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 : n016.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 01:59:18 PM UTC 2026
% Result : Theorem 7.41s 2.00s
% Output : CNFRefutation 8.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 21
% Syntax : Number of formulae : 194 ( 42 unt; 7 def)
% Number of atoms : 987 ( 59 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 1128 ( 432 ~; 482 |; 170 &)
% ( 11 <=>; 31 =>; 0 <=; 2 <~>)
% Maximal formula depth : 18 ( 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 : 37 ( 35 usr; 9 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 211 ( 0 sgn 199 !; 12 ?; 77 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( l3_lattices(X0)
& v17_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m2_filter_2(X1,X0)
=> ( r2_filter_2(X0,X1)
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ( r2_hidden(X2,X1)
<=> ~ r2_hidden(k7_lattices(X0,X2),X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_filter_2) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( l3_lattices(X0)
& v17_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m2_filter_2(X1,X0)
=> ( r2_filter_2(X0,X1)
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ( r2_hidden(X2,X1)
<=> ~ r2_hidden(k7_lattices(X0,X2),X1) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f16,axiom,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> k5_filter_2(X0,X1) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_filter_2) ).
fof(f17,axiom,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
=> k7_filter_2(X0,X1) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_filter_2) ).
fof(f19,axiom,
! [X0,X1] :
( ( m2_filter_2(X1,X0)
& l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> m1_filter_2(k15_filter_2(X0,X1),k1_lattice2(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k15_filter_2) ).
fof(f20,axiom,
! [X0] :
( l3_lattices(X0)
=> ( l3_lattices(k1_lattice2(X0))
& v3_lattices(k1_lattice2(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattice2) ).
fof(f24,axiom,
! [X0,X1] :
( ( m1_subset_1(X1,u1_struct_0(X0))
& l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> m1_subset_1(k5_filter_2(X0,X1),u1_struct_0(k1_lattice2(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_filter_2) ).
fof(f35,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(f36,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(f60,axiom,
! [X0] :
( ( l3_lattices(X0)
& v17_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ( v17_lattices(k1_lattice2(X0))
& v16_lattices(k1_lattice2(X0))
& v15_lattices(k1_lattice2(X0))
& v14_lattices(k1_lattice2(X0))
& v13_lattices(k1_lattice2(X0))
& v12_lattices(k1_lattice2(X0))
& v11_lattices(k1_lattice2(X0))
& v10_lattices(k1_lattice2(X0))
& v9_lattices(k1_lattice2(X0))
& v8_lattices(k1_lattice2(X0))
& v7_lattices(k1_lattice2(X0))
& v6_lattices(k1_lattice2(X0))
& v5_lattices(k1_lattice2(X0))
& v4_lattices(k1_lattice2(X0))
& v3_lattices(k1_lattice2(X0))
& ~ v3_struct_0(k1_lattice2(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_filter_2) ).
fof(f66,axiom,
! [X0] :
( ( l3_lattices(X0)
& v17_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> k7_lattices(k1_lattice2(X0),k5_filter_2(X0,X1)) = k7_lattices(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l70_filter_2) ).
fof(f84,axiom,
! [X0,X1] :
( ( m2_filter_2(X1,X0)
& l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> k15_filter_2(X0,X1) = k7_filter_2(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k15_filter_2) ).
fof(f85,axiom,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_filter_2(X1,X0)
<=> m1_filter_0(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m1_filter_2) ).
fof(f90,axiom,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m2_filter_2(X1,X0)
=> ( r2_filter_2(X0,X1)
<=> v1_filter_0(k15_filter_2(X0,X1),k1_lattice2(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_filter_2) ).
fof(f93,axiom,
! [X0] :
( ( l3_lattices(X0)
& v17_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_filter_0(X1,X0)
=> ( v1_filter_0(X1,X0)
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ( r2_hidden(X2,X1)
<=> ~ r2_hidden(k7_lattices(X0,X2),X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_filter_0) ).
fof(f109,plain,
! [X0] :
( ( l3_lattices(X0)
& v17_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ( v17_lattices(k1_lattice2(X0))
& v16_lattices(k1_lattice2(X0))
& v15_lattices(k1_lattice2(X0))
& v14_lattices(k1_lattice2(X0))
& v13_lattices(k1_lattice2(X0))
& v11_lattices(k1_lattice2(X0))
& v10_lattices(k1_lattice2(X0))
& v9_lattices(k1_lattice2(X0))
& v8_lattices(k1_lattice2(X0))
& v7_lattices(k1_lattice2(X0))
& v6_lattices(k1_lattice2(X0))
& v5_lattices(k1_lattice2(X0))
& v4_lattices(k1_lattice2(X0))
& v3_lattices(k1_lattice2(X0))
& ~ v3_struct_0(k1_lattice2(X0)) ) ),
inference(pure_predicate_removal,[],[f60]) ).
fof(f113,plain,
? [X0] :
( l3_lattices(X0)
& v17_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m2_filter_2(X1,X0)
& r2_filter_2(X0,X1)
& ? [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
& ( r2_hidden(X2,X1)
<~> ~ r2_hidden(k7_lattices(X0,X2),X1) ) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f114,plain,
? [X0] :
( l3_lattices(X0)
& v17_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m2_filter_2(X1,X0)
& r2_filter_2(X0,X1)
& ? [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
& ( r2_hidden(X2,X1)
<~> ~ r2_hidden(k7_lattices(X0,X2),X1) ) ) ) ),
inference(flattening,[],[f113]) ).
fof(f137,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| k5_filter_2(X0,X1) = X1 ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f138,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| k5_filter_2(X0,X1) = X1 ) ),
inference(flattening,[],[f137]) ).
fof(f139,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| k7_filter_2(X0,X1) = X1 ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f140,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| k7_filter_2(X0,X1) = X1 ) ),
inference(flattening,[],[f139]) ).
fof(f143,plain,
! [X0,X1] :
( ~ m2_filter_2(X1,X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| m1_filter_2(k15_filter_2(X0,X1),k1_lattice2(X0)) ),
inference(ennf_transformation,[],[f19]) ).
fof(f144,plain,
! [X0,X1] :
( ~ m2_filter_2(X1,X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| m1_filter_2(k15_filter_2(X0,X1),k1_lattice2(X0)) ),
inference(flattening,[],[f143]) ).
fof(f145,plain,
! [X0] :
( ~ l3_lattices(X0)
| ( l3_lattices(k1_lattice2(X0))
& v3_lattices(k1_lattice2(X0)) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f146,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| m1_subset_1(k5_filter_2(X0,X1),u1_struct_0(k1_lattice2(X0))) ),
inference(ennf_transformation,[],[f24]) ).
fof(f147,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| m1_subset_1(k5_filter_2(X0,X1),u1_struct_0(k1_lattice2(X0))) ),
inference(flattening,[],[f146]) ).
fof(f159,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,[],[f35]) ).
fof(f160,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,[],[f159]) ).
fof(f161,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,[],[f36]) ).
fof(f162,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,[],[f161]) ).
fof(f186,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ( v17_lattices(k1_lattice2(X0))
& v16_lattices(k1_lattice2(X0))
& v15_lattices(k1_lattice2(X0))
& v14_lattices(k1_lattice2(X0))
& v13_lattices(k1_lattice2(X0))
& v11_lattices(k1_lattice2(X0))
& v10_lattices(k1_lattice2(X0))
& v9_lattices(k1_lattice2(X0))
& v8_lattices(k1_lattice2(X0))
& v7_lattices(k1_lattice2(X0))
& v6_lattices(k1_lattice2(X0))
& v5_lattices(k1_lattice2(X0))
& v4_lattices(k1_lattice2(X0))
& v3_lattices(k1_lattice2(X0))
& ~ v3_struct_0(k1_lattice2(X0)) ) ),
inference(ennf_transformation,[],[f109]) ).
fof(f187,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ( v17_lattices(k1_lattice2(X0))
& v16_lattices(k1_lattice2(X0))
& v15_lattices(k1_lattice2(X0))
& v14_lattices(k1_lattice2(X0))
& v13_lattices(k1_lattice2(X0))
& v11_lattices(k1_lattice2(X0))
& v10_lattices(k1_lattice2(X0))
& v9_lattices(k1_lattice2(X0))
& v8_lattices(k1_lattice2(X0))
& v7_lattices(k1_lattice2(X0))
& v6_lattices(k1_lattice2(X0))
& v5_lattices(k1_lattice2(X0))
& v4_lattices(k1_lattice2(X0))
& v3_lattices(k1_lattice2(X0))
& ~ v3_struct_0(k1_lattice2(X0)) ) ),
inference(flattening,[],[f186]) ).
fof(f198,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| k7_lattices(k1_lattice2(X0),k5_filter_2(X0,X1)) = k7_lattices(X0,X1) ) ),
inference(ennf_transformation,[],[f66]) ).
fof(f199,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| k7_lattices(k1_lattice2(X0),k5_filter_2(X0,X1)) = k7_lattices(X0,X1) ) ),
inference(flattening,[],[f198]) ).
fof(f205,plain,
! [X0,X1] :
( ~ m2_filter_2(X1,X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| k15_filter_2(X0,X1) = k7_filter_2(X0,X1) ),
inference(ennf_transformation,[],[f84]) ).
fof(f206,plain,
! [X0,X1] :
( ~ m2_filter_2(X1,X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| k15_filter_2(X0,X1) = k7_filter_2(X0,X1) ),
inference(flattening,[],[f205]) ).
fof(f207,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( m1_filter_2(X1,X0)
<=> m1_filter_0(X1,X0) ) ),
inference(ennf_transformation,[],[f85]) ).
fof(f208,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( m1_filter_2(X1,X0)
<=> m1_filter_0(X1,X0) ) ),
inference(flattening,[],[f207]) ).
fof(f212,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_filter_2(X1,X0)
| ( r2_filter_2(X0,X1)
<=> v1_filter_0(k15_filter_2(X0,X1),k1_lattice2(X0)) ) ) ),
inference(ennf_transformation,[],[f90]) ).
fof(f213,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_filter_2(X1,X0)
| ( r2_filter_2(X0,X1)
<=> v1_filter_0(k15_filter_2(X0,X1),k1_lattice2(X0)) ) ) ),
inference(flattening,[],[f212]) ).
fof(f217,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_filter_0(X1,X0)
| ~ v1_filter_0(X1,X0)
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ( r2_hidden(X2,X1)
<=> ~ r2_hidden(k7_lattices(X0,X2),X1) ) ) ) ),
inference(ennf_transformation,[],[f93]) ).
fof(f218,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_filter_0(X1,X0)
| ~ v1_filter_0(X1,X0)
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ( r2_hidden(X2,X1)
<=> ~ r2_hidden(k7_lattices(X0,X2),X1) ) ) ) ),
inference(flattening,[],[f217]) ).
fof(f227,plain,
? [X0] :
( l3_lattices(X0)
& v17_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m2_filter_2(X1,X0)
& r2_filter_2(X0,X1)
& ? [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
& ( r2_hidden(X2,X1)
| ~ r2_hidden(k7_lattices(X0,X2),X1) )
& ( ~ r2_hidden(X2,X1)
| r2_hidden(k7_lattices(X0,X2),X1) ) ) ) ),
inference(nnf_transformation,[],[f114]) ).
fof(f228,plain,
? [X0] :
( l3_lattices(X0)
& v17_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m2_filter_2(X1,X0)
& r2_filter_2(X0,X1)
& ? [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
& ( r2_hidden(X2,X1)
| ~ r2_hidden(k7_lattices(X0,X2),X1) )
& ( ~ r2_hidden(X2,X1)
| r2_hidden(k7_lattices(X0,X2),X1) ) ) ) ),
inference(flattening,[],[f227]) ).
fof(f229,plain,
( l3_lattices(sK2)
& v17_lattices(sK2)
& v10_lattices(sK2)
& ~ v3_struct_0(sK2)
& m2_filter_2(sK3,sK2)
& r2_filter_2(sK2,sK3)
& m1_subset_1(sK4,u1_struct_0(sK2))
& ( r2_hidden(sK4,sK3)
| ~ r2_hidden(k7_lattices(sK2,sK4),sK3) )
& ( ~ r2_hidden(sK4,sK3)
| r2_hidden(k7_lattices(sK2,sK4),sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f228]) ).
fof(f260,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ( ~ m1_filter_2(X1,X0)
| m1_filter_0(X1,X0) )
& ( ~ m1_filter_0(X1,X0)
| m1_filter_2(X1,X0) ) ) ),
inference(nnf_transformation,[],[f208]) ).
fof(f262,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_filter_2(X1,X0)
| ( ( ~ r2_filter_2(X0,X1)
| v1_filter_0(k15_filter_2(X0,X1),k1_lattice2(X0)) )
& ( ~ v1_filter_0(k15_filter_2(X0,X1),k1_lattice2(X0))
| r2_filter_2(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f213]) ).
fof(f263,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_filter_0(X1,X0)
| ~ v1_filter_0(X1,X0)
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ( ( ~ r2_hidden(X2,X1)
| ~ r2_hidden(k7_lattices(X0,X2),X1) )
& ( r2_hidden(k7_lattices(X0,X2),X1)
| r2_hidden(X2,X1) ) ) ) ) ),
inference(nnf_transformation,[],[f218]) ).
fof(f264,plain,
l3_lattices(sK2),
inference(cnf_transformation,[],[f229]) ).
fof(f265,plain,
v17_lattices(sK2),
inference(cnf_transformation,[],[f229]) ).
fof(f266,plain,
v10_lattices(sK2),
inference(cnf_transformation,[],[f229]) ).
fof(f267,plain,
~ v3_struct_0(sK2),
inference(cnf_transformation,[],[f229]) ).
fof(f268,plain,
m2_filter_2(sK3,sK2),
inference(cnf_transformation,[],[f229]) ).
fof(f269,plain,
r2_filter_2(sK2,sK3),
inference(cnf_transformation,[],[f229]) ).
fof(f270,plain,
m1_subset_1(sK4,u1_struct_0(sK2)),
inference(cnf_transformation,[],[f229]) ).
fof(f271,plain,
( r2_hidden(sK4,sK3)
| ~ r2_hidden(k7_lattices(sK2,sK4),sK3) ),
inference(cnf_transformation,[],[f229]) ).
fof(f272,plain,
( ~ r2_hidden(sK4,sK3)
| r2_hidden(k7_lattices(sK2,sK4),sK3) ),
inference(cnf_transformation,[],[f229]) ).
fof(f310,plain,
! [X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| k5_filter_2(X0,X1) = X1 ),
inference(cnf_transformation,[],[f138]) ).
fof(f311,plain,
! [X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| k7_filter_2(X0,X1) = X1 ),
inference(cnf_transformation,[],[f140]) ).
fof(f314,plain,
! [X0,X1] :
( ~ m2_filter_2(X1,X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| m1_filter_2(k15_filter_2(X0,X1),k1_lattice2(X0)) ),
inference(cnf_transformation,[],[f144]) ).
fof(f315,plain,
! [X0] :
( ~ l3_lattices(X0)
| l3_lattices(k1_lattice2(X0)) ),
inference(cnf_transformation,[],[f145]) ).
fof(f317,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| m1_subset_1(k5_filter_2(X0,X1),u1_struct_0(k1_lattice2(X0))) ),
inference(cnf_transformation,[],[f147]) ).
fof(f328,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,[],[f160]) ).
fof(f330,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,[],[f162]) ).
fof(f378,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| sP0(X0) ),
inference(cnf_transformation,[],[f224]) ).
fof(f399,plain,
! [X0,X1] :
( ~ l3_lattices(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| k7_lattices(X0,X1) = k7_lattices(k1_lattice2(X0),k5_filter_2(X0,X1)) ),
inference(cnf_transformation,[],[f199]) ).
fof(f490,plain,
! [X0,X1] :
( ~ m2_filter_2(X1,X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| k7_filter_2(X0,X1) = k15_filter_2(X0,X1) ),
inference(cnf_transformation,[],[f206]) ).
fof(f491,plain,
! [X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_filter_2(X1,X0)
| m1_filter_0(X1,X0) ),
inference(cnf_transformation,[],[f260]) ).
fof(f498,plain,
! [X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m2_filter_2(X1,X0)
| ~ r2_filter_2(X0,X1)
| v1_filter_0(k15_filter_2(X0,X1),k1_lattice2(X0)) ),
inference(cnf_transformation,[],[f262]) ).
fof(f502,plain,
! [X2,X0,X1] :
( ~ l3_lattices(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_filter_0(X1,X0)
| ~ v1_filter_0(X1,X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ r2_hidden(X2,X1)
| ~ r2_hidden(k7_lattices(X0,X2),X1) ),
inference(cnf_transformation,[],[f263]) ).
fof(f503,plain,
! [X2,X0,X1] :
( ~ l3_lattices(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_filter_0(X1,X0)
| ~ v1_filter_0(X1,X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| r2_hidden(k7_lattices(X0,X2),X1)
| r2_hidden(X2,X1) ),
inference(cnf_transformation,[],[f263]) ).
tcf(c_49,negated_conjecture,
( r2_hidden(k7_lattices(sK2,sK4),sK3)
| ~ r2_hidden(sK4,sK3) ),
inference(cnf_transformation,[],[f272]) ).
tcf(c_50,negated_conjecture,
( r2_hidden(sK4,sK3)
| ~ r2_hidden(k7_lattices(sK2,sK4),sK3) ),
inference(cnf_transformation,[],[f271]) ).
tcf(c_51,negated_conjecture,
m1_subset_1(sK4,u1_struct_0(sK2)),
inference(cnf_transformation,[],[f270]) ).
tcf(c_52,negated_conjecture,
r2_filter_2(sK2,sK3),
inference(cnf_transformation,[],[f269]) ).
tcf(c_53,negated_conjecture,
m2_filter_2(sK3,sK2),
inference(cnf_transformation,[],[f268]) ).
tcf(c_54,negated_conjecture,
~ v3_struct_0(sK2),
inference(cnf_transformation,[],[f267]) ).
tcf(c_55,negated_conjecture,
v10_lattices(sK2),
inference(cnf_transformation,[],[f266]) ).
tcf(c_56,negated_conjecture,
v17_lattices(sK2),
inference(cnf_transformation,[],[f265]) ).
tcf(c_57,negated_conjecture,
l3_lattices(sK2),
inference(cnf_transformation,[],[f264]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| ( k5_filter_2(X1,X0) = X0 )
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f310]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| ( k7_filter_2(X1,X0) = X0 )
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(cnf_transformation,[],[f311]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m1_filter_2(k15_filter_2(X1,X0),k1_lattice2(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m2_filter_2(X0,X1) ),
inference(cnf_transformation,[],[f314]) ).
tcf(c_91,plain,
! [X0: $i] :
( l3_lattices(k1_lattice2(X0))
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f315]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m1_subset_1(k5_filter_2(X1,X0),u1_struct_0(k1_lattice2(X1)))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f317]) ).
tcf(c_104,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,[],[f328]) ).
tcf(c_105,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,[],[f330]) ).
tcf(c_153,plain,
! [X0: $i] :
( sP0(X0)
| v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0) ),
inference(cnf_transformation,[],[f378]) ).
tcf(c_174,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| ( k7_lattices(k1_lattice2(X1),k5_filter_2(X1,X0)) = k7_lattices(X1,X0) )
| ~ l3_lattices(X1)
| ~ v17_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f399]) ).
tcf(c_265,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| ( k7_filter_2(X1,X0) = k15_filter_2(X1,X0) )
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m2_filter_2(X0,X1) ),
inference(cnf_transformation,[],[f490]) ).
tcf(c_267,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m1_filter_0(X0,X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_filter_2(X0,X1) ),
inference(cnf_transformation,[],[f491]) ).
tcf(c_274,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| v1_filter_0(k15_filter_2(X0,X1),k1_lattice2(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m2_filter_2(X1,X0)
| ~ r2_filter_2(X0,X1) ),
inference(cnf_transformation,[],[f498]) ).
tcf(c_277,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| r2_hidden(X0,X2)
| r2_hidden(k7_lattices(X1,X0),X2)
| ~ l3_lattices(X1)
| ~ v17_lattices(X1)
| ~ v10_lattices(X1)
| ~ v1_filter_0(X2,X1)
| ~ m1_filter_0(X2,X1)
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f503]) ).
tcf(c_278,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| ~ v1_filter_0(X2,X0)
| ~ m1_filter_0(X2,X0)
| ~ r2_hidden(X1,X2)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ r2_hidden(k7_lattices(X0,X1),X2) ),
inference(cnf_transformation,[],[f502]) ).
tcf(c_2935,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| v1_filter_0(k15_filter_2(X0,X1),k1_lattice2(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m2_filter_2(X1,X0)
| ( X1 != sK3 )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_274]) ).
tcf(c_2936,plain,
( v3_struct_0(sK2)
| v1_filter_0(k15_filter_2(sK2,sK3),k1_lattice2(sK2))
| ~ l3_lattices(sK2)
| ~ v10_lattices(sK2)
| ~ m2_filter_2(sK3,sK2) ),
inference(unflattening,[status(thm)],[c_2935]) ).
tcf(c_2937,plain,
v1_filter_0(k15_filter_2(sK2,sK3),k1_lattice2(sK2)),
inference(global_subsumption_just,[status(thm)],[c_2936,c_57,c_55,c_54,c_53,c_2936]) ).
tcf(c_2943,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| r2_hidden(X2,X1)
| r2_hidden(k7_lattices(X0,X2),X1)
| ~ l3_lattices(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| ~ m1_filter_0(X1,X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ( k1_lattice2(sK2) != X0 )
| ( k15_filter_2(sK2,sK3) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_277,c_2937]) ).
tcf(c_2944,plain,
! [X0: $i] :
( v3_struct_0(k1_lattice2(sK2))
| r2_hidden(X0,k15_filter_2(sK2,sK3))
| r2_hidden(k7_lattices(k1_lattice2(sK2),X0),k15_filter_2(sK2,sK3))
| ~ l3_lattices(k1_lattice2(sK2))
| ~ v17_lattices(k1_lattice2(sK2))
| ~ v10_lattices(k1_lattice2(sK2))
| ~ m1_subset_1(X0,u1_struct_0(k1_lattice2(sK2)))
| ~ m1_filter_0(k15_filter_2(sK2,sK3),k1_lattice2(sK2)) ),
inference(unflattening,[status(thm)],[c_2943]) ).
tcf(c_2970,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| ~ m1_filter_0(X1,X0)
| ~ r2_hidden(X2,X1)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ r2_hidden(k7_lattices(X0,X2),X1)
| ( k1_lattice2(sK2) != X0 )
| ( k15_filter_2(sK2,sK3) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_278,c_2937]) ).
tcf(c_2971,plain,
! [X0: $i] :
( v3_struct_0(k1_lattice2(sK2))
| ~ l3_lattices(k1_lattice2(sK2))
| ~ v17_lattices(k1_lattice2(sK2))
| ~ v10_lattices(k1_lattice2(sK2))
| ~ m1_subset_1(X0,u1_struct_0(k1_lattice2(sK2)))
| ~ r2_hidden(X0,k15_filter_2(sK2,sK3))
| ~ m1_filter_0(k15_filter_2(sK2,sK3),k1_lattice2(sK2))
| ~ r2_hidden(k7_lattices(k1_lattice2(sK2),X0),k15_filter_2(sK2,sK3)) ),
inference(unflattening,[status(thm)],[c_2970]) ).
tcf(c_3178,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_104,c_105]) ).
tcf(c_3179,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_3178]) ).
tcf(c_3723,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ( X1 != sK3 )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_3179]) ).
tcf(c_3724,plain,
( v3_struct_0(sK2)
| m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK2)))
| ~ l3_lattices(sK2)
| ~ v10_lattices(sK2) ),
inference(unflattening,[status(thm)],[c_3723]) ).
tcf(c_3725,plain,
m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK2))),
inference(global_subsumption_just,[status(thm)],[c_3724,c_57,c_55,c_54,c_3724]) ).
tcf(c_3730,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| ( k7_filter_2(X0,X1) = k15_filter_2(X0,X1) )
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ( X1 != sK3 )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_265]) ).
tcf(c_3731,plain,
( v3_struct_0(sK2)
| ( k7_filter_2(sK2,sK3) = k15_filter_2(sK2,sK3) )
| ~ l3_lattices(sK2)
| ~ v10_lattices(sK2) ),
inference(unflattening,[status(thm)],[c_3730]) ).
tcf(c_3732,plain,
k7_filter_2(sK2,sK3) = k15_filter_2(sK2,sK3),
inference(global_subsumption_just,[status(thm)],[c_3731,c_57,c_55,c_54,c_3731]) ).
tcf(c_3744,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| m1_filter_2(k15_filter_2(X0,X1),k1_lattice2(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ( X1 != sK3 )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_89]) ).
tcf(c_3745,plain,
( v3_struct_0(sK2)
| m1_filter_2(k15_filter_2(sK2,sK3),k1_lattice2(sK2))
| ~ l3_lattices(sK2)
| ~ v10_lattices(sK2) ),
inference(unflattening,[status(thm)],[c_3744]) ).
tcf(c_3746,plain,
m1_filter_2(k15_filter_2(sK2,sK3),k1_lattice2(sK2)),
inference(global_subsumption_just,[status(thm)],[c_3745,c_57,c_55,c_54,c_3745]) ).
tcf(c_4317,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m1_filter_0(X0,X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ( k1_lattice2(sK2) != X1 )
| ( k15_filter_2(sK2,sK3) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_267,c_3746]) ).
tcf(c_4318,plain,
( v3_struct_0(k1_lattice2(sK2))
| m1_filter_0(k15_filter_2(sK2,sK3),k1_lattice2(sK2))
| ~ l3_lattices(k1_lattice2(sK2))
| ~ v10_lattices(k1_lattice2(sK2)) ),
inference(unflattening,[status(thm)],[c_4317]) ).
tcf(c_4418,plain,
! [X0: $i] :
( v3_struct_0(k1_lattice2(sK2))
| r2_hidden(X0,k15_filter_2(sK2,sK3))
| r2_hidden(k7_lattices(k1_lattice2(sK2),X0),k15_filter_2(sK2,sK3))
| ~ l3_lattices(k1_lattice2(sK2))
| ~ v17_lattices(k1_lattice2(sK2))
| ~ v10_lattices(k1_lattice2(sK2))
| ~ m1_subset_1(X0,u1_struct_0(k1_lattice2(sK2))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2944,c_4318]) ).
tcf(c_4419,plain,
! [X0: $i] :
( v3_struct_0(k1_lattice2(sK2))
| ~ l3_lattices(k1_lattice2(sK2))
| ~ v17_lattices(k1_lattice2(sK2))
| ~ v10_lattices(k1_lattice2(sK2))
| ~ m1_subset_1(X0,u1_struct_0(k1_lattice2(sK2)))
| ~ r2_hidden(X0,k15_filter_2(sK2,sK3))
| ~ r2_hidden(k7_lattices(k1_lattice2(sK2),X0),k15_filter_2(sK2,sK3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2971,c_4318]) ).
tcf(c_4493,plain,
! [X0: $i] :
( sP0(X0)
| v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_153]) ).
tcf(c_4494,plain,
( sP0(sK2)
| v3_struct_0(sK2)
| ~ l3_lattices(sK2)
| ~ v10_lattices(sK2) ),
inference(unflattening,[status(thm)],[c_4493]) ).
tcf(c_6479,plain,
! [X0: $i] :
( v3_struct_0(k1_lattice2(sK2))
| r2_hidden(X0,k7_filter_2(sK2,sK3))
| r2_hidden(k7_lattices(k1_lattice2(sK2),X0),k7_filter_2(sK2,sK3))
| ~ l3_lattices(k1_lattice2(sK2))
| ~ v17_lattices(k1_lattice2(sK2))
| ~ v10_lattices(k1_lattice2(sK2))
| ~ m1_subset_1(X0,u1_struct_0(k1_lattice2(sK2))) ),
inference(light_normalisation,[status(thm)],[c_4418,c_3732]) ).
tcf(c_6501,plain,
! [X0: $i] :
( v3_struct_0(k1_lattice2(sK2))
| ~ l3_lattices(k1_lattice2(sK2))
| ~ v17_lattices(k1_lattice2(sK2))
| ~ v10_lattices(k1_lattice2(sK2))
| ~ m1_subset_1(X0,u1_struct_0(k1_lattice2(sK2)))
| ~ r2_hidden(X0,k7_filter_2(sK2,sK3))
| ~ r2_hidden(k7_lattices(k1_lattice2(sK2),X0),k7_filter_2(sK2,sK3)) ),
inference(light_normalisation,[status(thm)],[c_4419,c_3732]) ).
tcf(c_7382,plain,
! [X0: $i] :
( ~ iPr_def_10
| ~ r2_hidden(k7_lattices(k1_lattice2(sK2),X0),k7_filter_2(sK2,sK3))
| ~ r2_hidden(X0,k7_filter_2(sK2,sK3))
| ~ m1_subset_1(X0,u1_struct_0(k1_lattice2(sK2))) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_6501]) ).
tcf(c_7383,plain,
( iPr_def_10
| v3_struct_0(k1_lattice2(sK2))
| ~ l3_lattices(k1_lattice2(sK2))
| ~ v17_lattices(k1_lattice2(sK2))
| ~ v10_lattices(k1_lattice2(sK2)) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_6501]) ).
tcf(c_7384,plain,
! [X0: $i] :
( ~ iPr_def_11
| r2_hidden(k7_lattices(k1_lattice2(sK2),X0),k7_filter_2(sK2,sK3))
| r2_hidden(X0,k7_filter_2(sK2,sK3))
| ~ m1_subset_1(X0,u1_struct_0(k1_lattice2(sK2))) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_6479]) ).
tcf(c_7385,plain,
( iPr_def_11
| v3_struct_0(k1_lattice2(sK2))
| ~ l3_lattices(k1_lattice2(sK2))
| ~ v17_lattices(k1_lattice2(sK2))
| ~ v10_lattices(k1_lattice2(sK2)) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_6479]) ).
tcf(c_7386,definition,
iPr_def_12 = k1_lattice2(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_7387,definition,
iPr_def_13 = u1_struct_0(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_7388,definition,
iPr_def_14 = k7_filter_2(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_7391,definition,
iPr_def_17 = u1_struct_0(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_7392,definition,
iPr_def_18 = k1_zfmisc_1(iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_7393,definition,
iPr_def_19 = k7_lattices(sK2,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_7394,plain,
( iPr_def_10
| v3_struct_0(iPr_def_12)
| ~ l3_lattices(iPr_def_12)
| ~ v17_lattices(iPr_def_12)
| ~ v10_lattices(iPr_def_12) ),
inference(demodulation,[status(thm)],[c_7383,c_7386]) ).
tcf(c_7395,plain,
! [X0: $i] :
( ~ iPr_def_10
| ~ m1_subset_1(X0,iPr_def_13)
| ~ r2_hidden(X0,iPr_def_14)
| ~ r2_hidden(k7_lattices(iPr_def_12,X0),iPr_def_14) ),
inference(demodulation,[status(thm)],[c_7382,c_7388,c_7387]) ).
tcf(c_7396,plain,
( iPr_def_11
| v3_struct_0(iPr_def_12)
| ~ l3_lattices(iPr_def_12)
| ~ v17_lattices(iPr_def_12)
| ~ v10_lattices(iPr_def_12) ),
inference(demodulation,[status(thm)],[c_7385]) ).
tcf(c_7397,plain,
! [X0: $i] :
( r2_hidden(X0,iPr_def_14)
| r2_hidden(k7_lattices(iPr_def_12,X0),iPr_def_14)
| ~ iPr_def_11
| ~ m1_subset_1(X0,iPr_def_13) ),
inference(demodulation,[status(thm)],[c_7384]) ).
tcf(c_7402,plain,
m1_subset_1(sK3,iPr_def_18),
inference(demodulation,[status(thm)],[c_3725,c_7391,c_7392]) ).
tcf(c_7403,negated_conjecture,
l3_lattices(sK2),
inference(demodulation,[status(thm)],[c_57]) ).
tcf(c_7404,negated_conjecture,
v17_lattices(sK2),
inference(demodulation,[status(thm)],[c_56]) ).
tcf(c_7405,negated_conjecture,
v10_lattices(sK2),
inference(demodulation,[status(thm)],[c_55]) ).
tcf(c_7406,negated_conjecture,
~ v3_struct_0(sK2),
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_7407,negated_conjecture,
m1_subset_1(sK4,iPr_def_17),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_7408,negated_conjecture,
( r2_hidden(sK4,sK3)
| ~ r2_hidden(iPr_def_19,sK3) ),
inference(demodulation,[status(thm)],[c_50,c_7393]) ).
tcf(c_7409,negated_conjecture,
( r2_hidden(iPr_def_19,sK3)
| ~ r2_hidden(sK4,sK3) ),
inference(demodulation,[status(thm)],[c_49]) ).
tcf(c_9961,plain,
( l3_lattices(iPr_def_12)
| ~ l3_lattices(sK2) ),
inference(superposition,[status(thm)],[c_7386,c_91]) ).
tcf(c_9962,plain,
l3_lattices(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_9961,c_7403]) ).
tcf(c_9965,plain,
( iPr_def_11
| v3_struct_0(iPr_def_12)
| ~ v17_lattices(iPr_def_12)
| ~ v10_lattices(iPr_def_12) ),
inference(backward_subsumption_resolution,[status(thm)],[c_7396,c_9962]) ).
tcf(c_9966,plain,
( iPr_def_10
| v3_struct_0(iPr_def_12)
| ~ v17_lattices(iPr_def_12)
| ~ v10_lattices(iPr_def_12) ),
inference(backward_subsumption_resolution,[status(thm)],[c_7394,c_9962]) ).
tcf(c_10953,plain,
! [X0: $i] :
( v3_struct_0(sK2)
| ( k5_filter_2(sK2,X0) = X0 )
| ~ l3_lattices(sK2)
| ~ v10_lattices(sK2)
| ~ m1_subset_1(X0,iPr_def_17) ),
inference(superposition,[status(thm)],[c_7391,c_85]) ).
tcf(c_10958,plain,
! [X0: $i] :
( ( k5_filter_2(sK2,X0) = X0 )
| ~ m1_subset_1(X0,iPr_def_17) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10953,c_7406,c_7403,c_7405]) ).
tcf(c_11010,plain,
! [X0: $i] :
( v3_struct_0(sK2)
| ( k7_filter_2(sK2,X0) = X0 )
| ~ l3_lattices(sK2)
| ~ v10_lattices(sK2)
| ~ m1_subset_1(X0,k1_zfmisc_1(iPr_def_17)) ),
inference(superposition,[status(thm)],[c_7391,c_86]) ).
tcf(c_11044,plain,
! [X0: $i] :
( v3_struct_0(sK2)
| ( k7_filter_2(sK2,X0) = X0 )
| ~ l3_lattices(sK2)
| ~ v10_lattices(sK2)
| ~ m1_subset_1(X0,iPr_def_18) ),
inference(light_normalisation,[status(thm)],[c_11010,c_7392]) ).
tcf(c_11045,plain,
! [X0: $i] :
( ( k7_filter_2(sK2,X0) = X0 )
| ~ m1_subset_1(X0,iPr_def_18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11044,c_7406,c_7403,c_7405]) ).
tcf(c_11077,plain,
! [X0: $i] :
( v3_struct_0(sK2)
| m1_subset_1(k5_filter_2(sK2,X0),u1_struct_0(iPr_def_12))
| ~ l3_lattices(sK2)
| ~ v10_lattices(sK2)
| ~ m1_subset_1(X0,u1_struct_0(sK2)) ),
inference(superposition,[status(thm)],[c_7386,c_92]) ).
tcf(c_11080,plain,
! [X0: $i] :
( v3_struct_0(sK2)
| m1_subset_1(k5_filter_2(sK2,X0),iPr_def_13)
| ~ l3_lattices(sK2)
| ~ v10_lattices(sK2)
| ~ m1_subset_1(X0,iPr_def_17) ),
inference(light_normalisation,[status(thm)],[c_11077,c_7387,c_7391]) ).
tcf(c_11081,plain,
! [X0: $i] :
( m1_subset_1(k5_filter_2(sK2,X0),iPr_def_13)
| ~ m1_subset_1(X0,iPr_def_17) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11080,c_7406,c_7403,c_7405]) ).
tcf(c_11150,plain,
k5_filter_2(sK2,sK4) = sK4,
inference(superposition,[status(thm)],[c_7407,c_10958]) ).
tcf(c_11188,plain,
( m1_subset_1(sK4,iPr_def_13)
| ~ m1_subset_1(sK4,iPr_def_17) ),
inference(superposition,[status(thm)],[c_11150,c_11081]) ).
tcf(c_11189,plain,
m1_subset_1(sK4,iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_11188,c_7407]) ).
tcf(c_11200,plain,
k7_filter_2(sK2,sK3) = sK3,
inference(superposition,[status(thm)],[c_7402,c_11045]) ).
tcf(c_11208,plain,
sK3 = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_11200,c_7388]) ).
tcf(c_11217,plain,
( r2_hidden(iPr_def_19,iPr_def_14)
| ~ r2_hidden(sK4,iPr_def_14) ),
inference(demodulation,[status(thm)],[c_7409,c_11208]) ).
tcf(c_11218,plain,
( r2_hidden(sK4,iPr_def_14)
| ~ r2_hidden(iPr_def_19,iPr_def_14) ),
inference(demodulation,[status(thm)],[c_7408,c_11208]) ).
tcf(c_11415,plain,
! [X0: $i] :
( v3_struct_0(sK2)
| ( k7_lattices(k1_lattice2(sK2),k5_filter_2(sK2,X0)) = k7_lattices(sK2,X0) )
| ~ l3_lattices(sK2)
| ~ v17_lattices(sK2)
| ~ v10_lattices(sK2)
| ~ m1_subset_1(X0,iPr_def_17) ),
inference(superposition,[status(thm)],[c_7391,c_174]) ).
tcf(c_11420,plain,
! [X0: $i] :
( v3_struct_0(sK2)
| ( k7_lattices(iPr_def_12,k5_filter_2(sK2,X0)) = k7_lattices(sK2,X0) )
| ~ l3_lattices(sK2)
| ~ v17_lattices(sK2)
| ~ v10_lattices(sK2)
| ~ m1_subset_1(X0,iPr_def_17) ),
inference(light_normalisation,[status(thm)],[c_11415,c_7386]) ).
tcf(c_11421,plain,
! [X0: $i] :
( ( k7_lattices(iPr_def_12,k5_filter_2(sK2,X0)) = k7_lattices(sK2,X0) )
| ~ m1_subset_1(X0,iPr_def_17) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11420,c_7406,c_7403,c_7404,c_7405]) ).
tcf(c_11557,plain,
k7_lattices(iPr_def_12,k5_filter_2(sK2,sK4)) = k7_lattices(sK2,sK4),
inference(superposition,[status(thm)],[c_7407,c_11421]) ).
tcf(c_11561,plain,
k7_lattices(iPr_def_12,sK4) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_11557,c_7393,c_11150]) ).
fof(f223,definition,
! [X0] :
( ~ sP0(X0)
| ( v17_lattices(k1_lattice2(X0))
& v16_lattices(k1_lattice2(X0))
& v15_lattices(k1_lattice2(X0))
& v14_lattices(k1_lattice2(X0))
& v13_lattices(k1_lattice2(X0))
& v11_lattices(k1_lattice2(X0))
& v10_lattices(k1_lattice2(X0))
& v9_lattices(k1_lattice2(X0))
& v8_lattices(k1_lattice2(X0))
& v7_lattices(k1_lattice2(X0))
& v6_lattices(k1_lattice2(X0))
& v5_lattices(k1_lattice2(X0))
& v4_lattices(k1_lattice2(X0))
& v3_lattices(k1_lattice2(X0))
& ~ v3_struct_0(k1_lattice2(X0)) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f224,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| sP0(X0) ),
inference(definition_folding,[],[f187,f223]) ).
fof(f241,plain,
! [X0] :
( ~ sP0(X0)
| ( v17_lattices(k1_lattice2(X0))
& v16_lattices(k1_lattice2(X0))
& v15_lattices(k1_lattice2(X0))
& v14_lattices(k1_lattice2(X0))
& v13_lattices(k1_lattice2(X0))
& v11_lattices(k1_lattice2(X0))
& v10_lattices(k1_lattice2(X0))
& v9_lattices(k1_lattice2(X0))
& v8_lattices(k1_lattice2(X0))
& v7_lattices(k1_lattice2(X0))
& v6_lattices(k1_lattice2(X0))
& v5_lattices(k1_lattice2(X0))
& v4_lattices(k1_lattice2(X0))
& v3_lattices(k1_lattice2(X0))
& ~ v3_struct_0(k1_lattice2(X0)) ) ),
inference(nnf_transformation,[],[f223]) ).
fof(f363,plain,
! [X0] :
( ~ sP0(X0)
| v17_lattices(k1_lattice2(X0)) ),
inference(cnf_transformation,[],[f241]) ).
fof(f369,plain,
! [X0] :
( ~ sP0(X0)
| v10_lattices(k1_lattice2(X0)) ),
inference(cnf_transformation,[],[f241]) ).
fof(f377,plain,
! [X0] :
( ~ sP0(X0)
| ~ v3_struct_0(k1_lattice2(X0)) ),
inference(cnf_transformation,[],[f241]) ).
tcf(c_138,plain,
! [X0: $i] :
( ~ sP0(X0)
| ~ v3_struct_0(k1_lattice2(X0)) ),
inference(cnf_transformation,[],[f377]) ).
tcf(c_146,plain,
! [X0: $i] :
( v10_lattices(k1_lattice2(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f369]) ).
tcf(c_152,plain,
! [X0: $i] :
( v17_lattices(k1_lattice2(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f363]) ).
tcf(c_10018,plain,
( v10_lattices(iPr_def_12)
| ~ sP0(sK2) ),
inference(superposition,[status(thm)],[c_7386,c_146]) ).
tcf(c_10021,plain,
v10_lattices(iPr_def_12),
inference(global_subsumption_just,[status(thm)],[c_10018,c_57,c_55,c_54,c_4494,c_10018]) ).
tcf(c_10023,plain,
( iPr_def_10
| v3_struct_0(iPr_def_12)
| ~ v17_lattices(iPr_def_12) ),
inference(backward_subsumption_resolution,[status(thm)],[c_9966,c_10021]) ).
tcf(c_10024,plain,
( iPr_def_11
| v3_struct_0(iPr_def_12)
| ~ v17_lattices(iPr_def_12) ),
inference(backward_subsumption_resolution,[status(thm)],[c_9965,c_10021]) ).
tcf(c_10065,plain,
( v17_lattices(iPr_def_12)
| ~ sP0(sK2) ),
inference(superposition,[status(thm)],[c_7386,c_152]) ).
tcf(c_10090,plain,
( iPr_def_10
| v3_struct_0(iPr_def_12) ),
inference(global_subsumption_just,[status(thm)],[c_10023,c_57,c_55,c_54,c_4494,c_10023,c_10065]) ).
tcf(c_10096,plain,
( iPr_def_11
| v3_struct_0(iPr_def_12) ),
inference(global_subsumption_just,[status(thm)],[c_10024,c_57,c_55,c_54,c_4494,c_10024,c_10065]) ).
tcf(c_10143,plain,
( ~ sP0(sK2)
| ~ v3_struct_0(iPr_def_12) ),
inference(superposition,[status(thm)],[c_7386,c_138]) ).
tcf(c_10148,plain,
~ v3_struct_0(iPr_def_12),
inference(global_subsumption_just,[status(thm)],[c_10143,c_57,c_55,c_54,c_4494,c_10143]) ).
tcf(c_10150,plain,
iPr_def_11,
inference(backward_subsumption_resolution,[status(thm)],[c_10096,c_10148]) ).
tcf(c_10151,plain,
iPr_def_10,
inference(backward_subsumption_resolution,[status(thm)],[c_10090,c_10148]) ).
tcf(c_10155,plain,
! [X0: $i] :
( r2_hidden(X0,iPr_def_14)
| r2_hidden(k7_lattices(iPr_def_12,X0),iPr_def_14)
| ~ m1_subset_1(X0,iPr_def_13) ),
inference(backward_subsumption_resolution,[status(thm)],[c_7397,c_10150]) ).
tcf(c_10159,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,iPr_def_13)
| ~ r2_hidden(X0,iPr_def_14)
| ~ r2_hidden(k7_lattices(iPr_def_12,X0),iPr_def_14) ),
inference(backward_subsumption_resolution,[status(thm)],[c_7395,c_10151]) ).
tcf(c_11913,plain,
( ~ m1_subset_1(sK4,iPr_def_13)
| ~ r2_hidden(iPr_def_19,iPr_def_14)
| ~ r2_hidden(sK4,iPr_def_14) ),
inference(superposition,[status(thm)],[c_11561,c_10159]) ).
tcf(c_11914,plain,
( r2_hidden(iPr_def_19,iPr_def_14)
| r2_hidden(sK4,iPr_def_14)
| ~ m1_subset_1(sK4,iPr_def_13) ),
inference(superposition,[status(thm)],[c_11561,c_10155]) ).
tcf(c_11915,plain,
( r2_hidden(iPr_def_19,iPr_def_14)
| r2_hidden(sK4,iPr_def_14) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11914,c_11189]) ).
tcf(c_11924,plain,
( ~ r2_hidden(iPr_def_19,iPr_def_14)
| ~ r2_hidden(sK4,iPr_def_14) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11913,c_11189]) ).
tcf(c_11930,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_11924,c_11915,c_11217,c_11218]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LAT323+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.18/0.44 % Computer : n016.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Wed Sep 23 21:10:27 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.22/0.49 Running first-order theorem proving
% 0.22/0.49 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
% 0.22/0.51
% 0.22/0.51 % ======== iProver multi-core TPTP/SMT =========
% 0.22/0.51
% 0.22/0.51 % Detected problem language: tptp
% 0.22/0.52 % Proving...
% 7.41/2.00 % SZS status Started for theBenchmark.p
% 7.41/2.00 % SZS status Theorem for theBenchmark.p
% 7.41/2.00
% 7.41/2.00 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.41/2.00
% 7.41/2.00 % ------ iProver source info
% 7.41/2.00
% 7.41/2.00 % git: date: 2026-07-19 20:42:38 +0200
% 7.41/2.00 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.41/2.00 % git: non_committed_changes: false
% 7.41/2.00
% 7.41/2.00 % ------ Parsing...
% 7.41/2.00 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.41/2.00
% 7.41/2.00 % ------ Preprocessing... sup_sim: 0 sf_s rm: 10 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe_e sup_sim: 4 sf_s rm: 23 0s sf_e pe_s pe_e %
% 7.41/2.00
% 7.41/2.00 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.41/2.00
% 7.41/2.00 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.41/2.00 % ------ Proving...
% 7.41/2.00 % ------ Problem Properties
% 7.41/2.00
% 7.41/2.00 %
% 7.41/2.00 % clauses 150
% 7.41/2.00 % conjectures 7
% 7.41/2.00 % EPR 59
% 7.41/2.00 % Horn 123
% 7.41/2.00 % unary 70
% 7.41/2.00 % binary 36
% 7.41/2.00 % lits 340
% 7.41/2.00 % lits eq 26
% 7.41/2.00 % fd_pure 0
% 7.41/2.00 % fd_pseudo 0
% 7.41/2.00 % fd_cond 1
% 7.41/2.00 % fd_pseudo_cond 4
% 7.41/2.00 % AC symbols 0
% 7.41/2.00
% 7.41/2.00 % ------ Schedule dynamic 5 is on
% 7.41/2.00
% 7.41/2.00 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.41/2.00
% 7.41/2.00
% 7.41/2.00 % ------
% 7.41/2.00 % Current options:
% 7.41/2.00 % ------
% 7.41/2.00
% 7.41/2.00
% 7.41/2.00 %
% 7.41/2.00
% 7.41/2.00 % ------ Proving...
% 7.41/2.00 %
% 7.41/2.00
% 7.41/2.00 % SZS status Theorem for theBenchmark.p
% 7.41/2.00
% 7.41/2.00 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.93/2.00
% 8.93/2.00
%------------------------------------------------------------------------------