%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LAT295+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 : n001.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 01:59:08 PM UTC 2026
% Result : Theorem 32.01s 5.34s
% Output : CNFRefutation 32.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 9
% Syntax : Number of formulae : 160 ( 38 unt; 0 def)
% Number of atoms : 577 ( 155 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 709 ( 292 ~; 302 |; 77 &)
% ( 4 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-6 aty)
% Number of variables : 223 ( 0 sgn 211 !; 12 ?; 98 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( l3_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( ( l3_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( g3_lattices(u1_struct_0(X0),u2_lattices(X0),u1_lattices(X0)) = g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1))
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X0))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ! [X5] :
( m1_subset_1(X5,u1_struct_0(X1))
=> ( ( X3 = X5
& X2 = X4 )
=> ( ( r1_lattices(X1,X4,X5)
=> r1_lattices(X0,X2,X3) )
& ( r1_lattices(X0,X2,X3)
=> r1_lattices(X1,X4,X5) )
& k2_lattices(X0,X2,X3) = k2_lattices(X1,X4,X5)
& k1_lattices(X0,X2,X3) = k1_lattices(X1,X4,X5) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_filter_2) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( l3_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( ( l3_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( g3_lattices(u1_struct_0(X0),u2_lattices(X0),u1_lattices(X0)) = g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1))
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X0))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ! [X5] :
( m1_subset_1(X5,u1_struct_0(X1))
=> ( ( X3 = X5
& X2 = X4 )
=> ( ( r1_lattices(X1,X4,X5)
=> r1_lattices(X0,X2,X3) )
& ( r1_lattices(X0,X2,X3)
=> r1_lattices(X1,X4,X5) )
& k2_lattices(X0,X2,X3) = k2_lattices(X1,X4,X5)
& k1_lattices(X0,X2,X3) = k1_lattices(X1,X4,X5) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f11,axiom,
! [X0] :
( ( l2_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> k1_lattices(X0,X1,X2) = k2_binop_1(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),u2_lattices(X0),X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_lattices) ).
fof(f12,axiom,
! [X0] :
( ( l1_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> k2_lattices(X0,X1,X2) = k2_binop_1(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),u1_lattices(X0),X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_lattices) ).
fof(f13,axiom,
! [X0] :
( ( l2_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ( r1_lattices(X0,X1,X2)
<=> k1_lattices(X0,X1,X2) = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattices) ).
fof(f30,axiom,
! [X0] :
( l3_lattices(X0)
=> ( l2_lattices(X0)
& l1_lattices(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(f34,axiom,
! [X0] :
( l1_lattices(X0)
=> ( m2_relset_1(u1_lattices(X0),k2_zfmisc_1(u1_struct_0(X0),u1_struct_0(X0)),u1_struct_0(X0))
& v1_funct_2(u1_lattices(X0),k2_zfmisc_1(u1_struct_0(X0),u1_struct_0(X0)),u1_struct_0(X0))
& v1_funct_1(u1_lattices(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_lattices) ).
fof(f36,axiom,
! [X0] :
( l2_lattices(X0)
=> ( m2_relset_1(u2_lattices(X0),k2_zfmisc_1(u1_struct_0(X0),u1_struct_0(X0)),u1_struct_0(X0))
& v1_funct_2(u2_lattices(X0),k2_zfmisc_1(u1_struct_0(X0),u1_struct_0(X0)),u1_struct_0(X0))
& v1_funct_1(u2_lattices(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u2_lattices) ).
fof(f52,axiom,
! [X0,X1,X2] :
( ( m1_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
& v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
& v1_funct_1(X2)
& m1_relset_1(X1,k2_zfmisc_1(X0,X0),X0)
& v1_funct_2(X1,k2_zfmisc_1(X0,X0),X0)
& v1_funct_1(X1) )
=> ! [X3,X4,X5] :
( g3_lattices(X0,X1,X2) = g3_lattices(X3,X4,X5)
=> ( X2 = X5
& X1 = X4
& X0 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g3_lattices) ).
fof(f67,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
<=> m1_relset_1(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f82,plain,
? [X0] :
( l3_lattices(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( l3_lattices(X1)
& ~ v3_struct_0(X1)
& g3_lattices(u1_struct_0(X0),u2_lattices(X0),u1_lattices(X0)) = g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1))
& ? [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
& ? [X3] :
( m1_subset_1(X3,u1_struct_0(X0))
& ? [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
& ? [X5] :
( m1_subset_1(X5,u1_struct_0(X1))
& X3 = X5
& X2 = X4
& ( ( r1_lattices(X1,X4,X5)
& ~ r1_lattices(X0,X2,X3) )
| ( r1_lattices(X0,X2,X3)
& ~ r1_lattices(X1,X4,X5) )
| k2_lattices(X0,X2,X3) != k2_lattices(X1,X4,X5)
| k1_lattices(X0,X2,X3) != k1_lattices(X1,X4,X5) ) ) ) ) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f83,plain,
? [X0] :
( l3_lattices(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( l3_lattices(X1)
& ~ v3_struct_0(X1)
& g3_lattices(u1_struct_0(X0),u2_lattices(X0),u1_lattices(X0)) = g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1))
& ? [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
& ? [X3] :
( m1_subset_1(X3,u1_struct_0(X0))
& ? [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
& ? [X5] :
( m1_subset_1(X5,u1_struct_0(X1))
& X3 = X5
& X2 = X4
& ( ( r1_lattices(X1,X4,X5)
& ~ r1_lattices(X0,X2,X3) )
| ( r1_lattices(X0,X2,X3)
& ~ r1_lattices(X1,X4,X5) )
| k2_lattices(X0,X2,X3) != k2_lattices(X1,X4,X5)
| k1_lattices(X0,X2,X3) != k1_lattices(X1,X4,X5) ) ) ) ) ) ) ),
inference(flattening,[],[f82]) ).
fof(f94,plain,
! [X0] :
( ~ l2_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| k1_lattices(X0,X1,X2) = k2_binop_1(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),u2_lattices(X0),X1,X2) ) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f95,plain,
! [X0] :
( ~ l2_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| k1_lattices(X0,X1,X2) = k2_binop_1(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),u2_lattices(X0),X1,X2) ) ) ),
inference(flattening,[],[f94]) ).
fof(f96,plain,
! [X0] :
( ~ l1_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| k2_lattices(X0,X1,X2) = k2_binop_1(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),u1_lattices(X0),X1,X2) ) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f97,plain,
! [X0] :
( ~ l1_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| k2_lattices(X0,X1,X2) = k2_binop_1(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),u1_lattices(X0),X1,X2) ) ) ),
inference(flattening,[],[f96]) ).
fof(f98,plain,
! [X0] :
( ~ l2_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ( r1_lattices(X0,X1,X2)
<=> k1_lattices(X0,X1,X2) = X2 ) ) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f99,plain,
! [X0] :
( ~ l2_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ( r1_lattices(X0,X1,X2)
<=> k1_lattices(X0,X1,X2) = X2 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f110,plain,
! [X0] :
( ~ l3_lattices(X0)
| ( l2_lattices(X0)
& l1_lattices(X0) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f112,plain,
! [X0] :
( ~ l1_lattices(X0)
| ( m2_relset_1(u1_lattices(X0),k2_zfmisc_1(u1_struct_0(X0),u1_struct_0(X0)),u1_struct_0(X0))
& v1_funct_2(u1_lattices(X0),k2_zfmisc_1(u1_struct_0(X0),u1_struct_0(X0)),u1_struct_0(X0))
& v1_funct_1(u1_lattices(X0)) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f113,plain,
! [X0] :
( ~ l2_lattices(X0)
| ( m2_relset_1(u2_lattices(X0),k2_zfmisc_1(u1_struct_0(X0),u1_struct_0(X0)),u1_struct_0(X0))
& v1_funct_2(u2_lattices(X0),k2_zfmisc_1(u1_struct_0(X0),u1_struct_0(X0)),u1_struct_0(X0))
& v1_funct_1(u2_lattices(X0)) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f120,plain,
! [X0,X1,X2] :
( ~ m1_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X2)
| ~ m1_relset_1(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X1)
| ! [X3,X4,X5] :
( g3_lattices(X0,X1,X2) != g3_lattices(X3,X4,X5)
| ( X2 = X5
& X1 = X4
& X0 = X3 ) ) ),
inference(ennf_transformation,[],[f52]) ).
fof(f121,plain,
! [X0,X1,X2] :
( ~ m1_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X2)
| ~ m1_relset_1(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X1)
| ! [X3,X4,X5] :
( g3_lattices(X0,X1,X2) != g3_lattices(X3,X4,X5)
| ( X2 = X5
& X1 = X4
& X0 = X3 ) ) ),
inference(flattening,[],[f120]) ).
fof(f137,plain,
( l3_lattices(sK0)
& ~ v3_struct_0(sK0)
& l3_lattices(sK1)
& ~ v3_struct_0(sK1)
& g3_lattices(u1_struct_0(sK0),u2_lattices(sK0),u1_lattices(sK0)) = g3_lattices(u1_struct_0(sK1),u2_lattices(sK1),u1_lattices(sK1))
& m1_subset_1(sK2,u1_struct_0(sK0))
& m1_subset_1(sK3,u1_struct_0(sK0))
& m1_subset_1(sK4,u1_struct_0(sK1))
& m1_subset_1(sK5,u1_struct_0(sK1))
& sK3 = sK5
& sK2 = sK4
& ( ( r1_lattices(sK1,sK4,sK5)
& ~ r1_lattices(sK0,sK2,sK3) )
| ( r1_lattices(sK0,sK2,sK3)
& ~ r1_lattices(sK1,sK4,sK5) )
| k2_lattices(sK0,sK2,sK3) != k2_lattices(sK1,sK4,sK5)
| k1_lattices(sK0,sK2,sK3) != k1_lattices(sK1,sK4,sK5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f83]) ).
fof(f138,plain,
! [X0] :
( ~ l2_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ( ( ~ r1_lattices(X0,X1,X2)
| k1_lattices(X0,X1,X2) = X2 )
& ( k1_lattices(X0,X1,X2) != X2
| r1_lattices(X0,X1,X2) ) ) ) ) ),
inference(nnf_transformation,[],[f99]) ).
fof(f159,plain,
! [X0,X1,X2] :
( ( ~ m2_relset_1(X2,X0,X1)
| m1_relset_1(X2,X0,X1) )
& ( ~ m1_relset_1(X2,X0,X1)
| m2_relset_1(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f67]) ).
fof(f160,plain,
l3_lattices(sK0),
inference(cnf_transformation,[],[f137]) ).
fof(f161,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f137]) ).
fof(f162,plain,
l3_lattices(sK1),
inference(cnf_transformation,[],[f137]) ).
fof(f163,plain,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f137]) ).
fof(f164,plain,
g3_lattices(u1_struct_0(sK0),u2_lattices(sK0),u1_lattices(sK0)) = g3_lattices(u1_struct_0(sK1),u2_lattices(sK1),u1_lattices(sK1)),
inference(cnf_transformation,[],[f137]) ).
fof(f165,plain,
m1_subset_1(sK2,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f137]) ).
fof(f166,plain,
m1_subset_1(sK3,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f137]) ).
fof(f167,plain,
m1_subset_1(sK4,u1_struct_0(sK1)),
inference(cnf_transformation,[],[f137]) ).
fof(f168,plain,
m1_subset_1(sK5,u1_struct_0(sK1)),
inference(cnf_transformation,[],[f137]) ).
fof(f169,plain,
sK3 = sK5,
inference(cnf_transformation,[],[f137]) ).
fof(f170,plain,
sK2 = sK4,
inference(cnf_transformation,[],[f137]) ).
fof(f171,plain,
( r1_lattices(sK1,sK4,sK5)
| r1_lattices(sK0,sK2,sK3)
| k2_lattices(sK0,sK2,sK3) != k2_lattices(sK1,sK4,sK5)
| k1_lattices(sK0,sK2,sK3) != k1_lattices(sK1,sK4,sK5) ),
inference(cnf_transformation,[],[f137]) ).
fof(f174,plain,
( ~ r1_lattices(sK0,sK2,sK3)
| ~ r1_lattices(sK1,sK4,sK5)
| k2_lattices(sK0,sK2,sK3) != k2_lattices(sK1,sK4,sK5)
| k1_lattices(sK0,sK2,sK3) != k1_lattices(sK1,sK4,sK5) ),
inference(cnf_transformation,[],[f137]) ).
fof(f184,plain,
! [X2,X0,X1] :
( ~ l2_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| k1_lattices(X0,X1,X2) = k2_binop_1(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),u2_lattices(X0),X1,X2) ),
inference(cnf_transformation,[],[f95]) ).
fof(f185,plain,
! [X2,X0,X1] :
( ~ l1_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| k2_lattices(X0,X1,X2) = k2_binop_1(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),u1_lattices(X0),X1,X2) ),
inference(cnf_transformation,[],[f97]) ).
fof(f186,plain,
! [X2,X0,X1] :
( ~ l2_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ r1_lattices(X0,X1,X2)
| k1_lattices(X0,X1,X2) = X2 ),
inference(cnf_transformation,[],[f138]) ).
fof(f187,plain,
! [X2,X0,X1] :
( ~ l2_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| k1_lattices(X0,X1,X2) != X2
| r1_lattices(X0,X1,X2) ),
inference(cnf_transformation,[],[f138]) ).
fof(f196,plain,
! [X0] :
( ~ l3_lattices(X0)
| l2_lattices(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f197,plain,
! [X0] :
( ~ l3_lattices(X0)
| l1_lattices(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f199,plain,
! [X0] :
( ~ l1_lattices(X0)
| m2_relset_1(u1_lattices(X0),k2_zfmisc_1(u1_struct_0(X0),u1_struct_0(X0)),u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f112]) ).
fof(f200,plain,
! [X0] :
( ~ l1_lattices(X0)
| v1_funct_2(u1_lattices(X0),k2_zfmisc_1(u1_struct_0(X0),u1_struct_0(X0)),u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f112]) ).
fof(f201,plain,
! [X0] :
( ~ l1_lattices(X0)
| v1_funct_1(u1_lattices(X0)) ),
inference(cnf_transformation,[],[f112]) ).
fof(f202,plain,
! [X0] :
( ~ l2_lattices(X0)
| m2_relset_1(u2_lattices(X0),k2_zfmisc_1(u1_struct_0(X0),u1_struct_0(X0)),u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f113]) ).
fof(f203,plain,
! [X0] :
( ~ l2_lattices(X0)
| v1_funct_2(u2_lattices(X0),k2_zfmisc_1(u1_struct_0(X0),u1_struct_0(X0)),u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f113]) ).
fof(f204,plain,
! [X0] :
( ~ l2_lattices(X0)
| v1_funct_1(u2_lattices(X0)) ),
inference(cnf_transformation,[],[f113]) ).
fof(f222,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ m1_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X2)
| ~ m1_relset_1(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X1)
| g3_lattices(X0,X1,X2) != g3_lattices(X3,X4,X5)
| X2 = X5 ),
inference(cnf_transformation,[],[f121]) ).
fof(f223,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ m1_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X2)
| ~ m1_relset_1(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X1)
| g3_lattices(X0,X1,X2) != g3_lattices(X3,X4,X5)
| X1 = X4 ),
inference(cnf_transformation,[],[f121]) ).
fof(f224,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ m1_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X2)
| ~ m1_relset_1(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X1)
| g3_lattices(X0,X1,X2) != g3_lattices(X3,X4,X5)
| X0 = X3 ),
inference(cnf_transformation,[],[f121]) ).
fof(f252,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f159]) ).
fof(f263,plain,
( ~ r1_lattices(sK0,sK4,sK5)
| ~ r1_lattices(sK1,sK4,sK5)
| k2_lattices(sK1,sK4,sK5) != k2_lattices(sK0,sK4,sK5)
| k1_lattices(sK1,sK4,sK5) != k1_lattices(sK0,sK4,sK5) ),
inference(definition_unfolding,[],[f174,f170,f169,f170,f169,f170,f169]) ).
fof(f266,plain,
( r1_lattices(sK1,sK4,sK5)
| r1_lattices(sK0,sK4,sK5)
| k2_lattices(sK1,sK4,sK5) != k2_lattices(sK0,sK4,sK5)
| k1_lattices(sK1,sK4,sK5) != k1_lattices(sK0,sK4,sK5) ),
inference(definition_unfolding,[],[f171,f170,f169,f170,f169,f170,f169]) ).
fof(f267,plain,
m1_subset_1(sK5,u1_struct_0(sK0)),
inference(definition_unfolding,[],[f166,f169]) ).
fof(f268,plain,
m1_subset_1(sK4,u1_struct_0(sK0)),
inference(definition_unfolding,[],[f165,f170]) ).
tcf(c_49,negated_conjecture,
( ~ r1_lattices(sK0,sK4,sK5)
| ~ r1_lattices(sK1,sK4,sK5)
| ( k2_lattices(sK1,sK4,sK5) != k2_lattices(sK0,sK4,sK5) )
| ( k1_lattices(sK1,sK4,sK5) != k1_lattices(sK0,sK4,sK5) ) ),
inference(cnf_transformation,[],[f263]) ).
tcf(c_50,negated_conjecture,
( r1_lattices(sK0,sK4,sK5)
| r1_lattices(sK1,sK4,sK5)
| ( k2_lattices(sK1,sK4,sK5) != k2_lattices(sK0,sK4,sK5) )
| ( k1_lattices(sK1,sK4,sK5) != k1_lattices(sK0,sK4,sK5) ) ),
inference(cnf_transformation,[],[f266]) ).
tcf(c_51,negated_conjecture,
m1_subset_1(sK5,u1_struct_0(sK1)),
inference(cnf_transformation,[],[f168]) ).
tcf(c_52,negated_conjecture,
m1_subset_1(sK4,u1_struct_0(sK1)),
inference(cnf_transformation,[],[f167]) ).
tcf(c_53,negated_conjecture,
m1_subset_1(sK5,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f267]) ).
tcf(c_54,negated_conjecture,
m1_subset_1(sK4,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f268]) ).
tcf(c_55,negated_conjecture,
g3_lattices(u1_struct_0(sK1),u2_lattices(sK1),u1_lattices(sK1)) = g3_lattices(u1_struct_0(sK0),u2_lattices(sK0),u1_lattices(sK0)),
inference(cnf_transformation,[],[f164]) ).
tcf(c_56,negated_conjecture,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f163]) ).
tcf(c_57,negated_conjecture,
l3_lattices(sK1),
inference(cnf_transformation,[],[f162]) ).
tcf(c_58,negated_conjecture,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f161]) ).
tcf(c_59,negated_conjecture,
l3_lattices(sK0),
inference(cnf_transformation,[],[f160]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| ( k2_binop_1(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),u2_lattices(X1),X0,X2) = k1_lattices(X1,X0,X2) )
| ~ l2_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| ( k2_binop_1(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),u1_lattices(X1),X0,X2) = k2_lattices(X1,X0,X2) )
| ~ l1_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| r1_lattices(X0,X1,X2)
| ~ l2_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ( k1_lattices(X0,X1,X2) != X2 ) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| ( k1_lattices(X0,X1,X2) = X2 )
| ~ l2_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ r1_lattices(X0,X1,X2) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_78,plain,
! [X0: $i] :
( l1_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f197]) ).
tcf(c_79,plain,
! [X0: $i] :
( l2_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f196]) ).
tcf(c_81,plain,
! [X0: $i] :
( v1_funct_1(u1_lattices(X0))
| ~ l1_lattices(X0) ),
inference(cnf_transformation,[],[f201]) ).
tcf(c_82,plain,
! [X0: $i] :
( v1_funct_2(u1_lattices(X0),k2_zfmisc_1(u1_struct_0(X0),u1_struct_0(X0)),u1_struct_0(X0))
| ~ l1_lattices(X0) ),
inference(cnf_transformation,[],[f200]) ).
tcf(c_83,plain,
! [X0: $i] :
( m2_relset_1(u1_lattices(X0),k2_zfmisc_1(u1_struct_0(X0),u1_struct_0(X0)),u1_struct_0(X0))
| ~ l1_lattices(X0) ),
inference(cnf_transformation,[],[f199]) ).
tcf(c_84,plain,
! [X0: $i] :
( v1_funct_1(u2_lattices(X0))
| ~ l2_lattices(X0) ),
inference(cnf_transformation,[],[f204]) ).
tcf(c_85,plain,
! [X0: $i] :
( v1_funct_2(u2_lattices(X0),k2_zfmisc_1(u1_struct_0(X0),u1_struct_0(X0)),u1_struct_0(X0))
| ~ l2_lattices(X0) ),
inference(cnf_transformation,[],[f203]) ).
tcf(c_86,plain,
! [X0: $i] :
( m2_relset_1(u2_lattices(X0),k2_zfmisc_1(u1_struct_0(X0),u1_struct_0(X0)),u1_struct_0(X0))
| ~ l2_lattices(X0) ),
inference(cnf_transformation,[],[f202]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X0 = X3 )
| ~ v1_funct_1(X2)
| ~ v1_funct_1(X1)
| ~ m1_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
| ~ m1_relset_1(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X1,k2_zfmisc_1(X0,X0),X0)
| ( g3_lattices(X0,X1,X2) != g3_lattices(X3,X4,X5) ) ),
inference(cnf_transformation,[],[f224]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X1 = X4 )
| ~ v1_funct_1(X2)
| ~ v1_funct_1(X1)
| ~ m1_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
| ~ m1_relset_1(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X1,k2_zfmisc_1(X0,X0),X0)
| ( g3_lattices(X0,X1,X2) != g3_lattices(X3,X4,X5) ) ),
inference(cnf_transformation,[],[f223]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X2 = X5 )
| ~ v1_funct_1(X2)
| ~ v1_funct_1(X1)
| ~ m1_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
| ~ m1_relset_1(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X1,k2_zfmisc_1(X0,X0),X0)
| ( g3_lattices(X0,X1,X2) != g3_lattices(X3,X4,X5) ) ),
inference(cnf_transformation,[],[f222]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i,X2: $i] :
( m1_relset_1(X0,X1,X2)
| ~ m2_relset_1(X0,X1,X2) ),
inference(cnf_transformation,[],[f252]) ).
tcf(c_360,plain,
( l1_lattices(sK1)
| ~ l3_lattices(sK1) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_361,plain,
( l1_lattices(sK0)
| ~ l3_lattices(sK0) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_365,plain,
( l2_lattices(sK1)
| ~ l3_lattices(sK1) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_366,plain,
( l2_lattices(sK0)
| ~ l3_lattices(sK0) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_698,plain,
( m2_relset_1(u1_lattices(sK0),k2_zfmisc_1(u1_struct_0(sK0),u1_struct_0(sK0)),u1_struct_0(sK0))
| ~ l1_lattices(sK0) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_699,plain,
( v1_funct_2(u1_lattices(sK0),k2_zfmisc_1(u1_struct_0(sK0),u1_struct_0(sK0)),u1_struct_0(sK0))
| ~ l1_lattices(sK0) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_700,plain,
( v1_funct_1(u1_lattices(sK0))
| ~ l1_lattices(sK0) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_744,plain,
( m2_relset_1(u2_lattices(sK0),k2_zfmisc_1(u1_struct_0(sK0),u1_struct_0(sK0)),u1_struct_0(sK0))
| ~ l2_lattices(sK0) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_745,plain,
( v1_funct_2(u2_lattices(sK0),k2_zfmisc_1(u1_struct_0(sK0),u1_struct_0(sK0)),u1_struct_0(sK0))
| ~ l2_lattices(sK0) ),
inference(instantiation,[status(thm)],[c_85]) ).
tcf(c_746,plain,
( v1_funct_1(u2_lattices(sK0))
| ~ l2_lattices(sK0) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_1057,plain,
! [X0: $i] :
( v3_struct_0(sK1)
| ( k2_binop_1(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),u2_lattices(sK1),sK4,X0) = k1_lattices(sK1,sK4,X0) )
| ~ l2_lattices(sK1)
| ~ m1_subset_1(X0,u1_struct_0(sK1)) ),
inference(superposition,[status(thm)],[c_52,c_67]) ).
tcf(c_1059,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| ( k2_binop_1(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),u2_lattices(sK0),sK4,X0) = k1_lattices(sK0,sK4,X0) )
| ~ l2_lattices(sK0)
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(superposition,[status(thm)],[c_54,c_67]) ).
tcf(c_1166,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,u1_struct_0(sK1))
| ( k2_binop_1(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),u2_lattices(sK1),sK4,X0) = k1_lattices(sK1,sK4,X0) ) ),
inference(global_subsumption_just,[status(thm)],[c_1057,c_57,c_56,c_365,c_1057]) ).
tcf(c_1167,plain,
! [X0: $i] :
( ( k2_binop_1(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),u2_lattices(sK1),sK4,X0) = k1_lattices(sK1,sK4,X0) )
| ~ m1_subset_1(X0,u1_struct_0(sK1)) ),
inference(renaming,[status(thm)],[c_1166]) ).
tcf(c_1211,plain,
! [X0: $i] :
( v3_struct_0(sK1)
| ( k2_binop_1(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),u1_lattices(sK1),sK4,X0) = k2_lattices(sK1,sK4,X0) )
| ~ l1_lattices(sK1)
| ~ m1_subset_1(X0,u1_struct_0(sK1)) ),
inference(superposition,[status(thm)],[c_52,c_68]) ).
tcf(c_1213,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| ( k2_binop_1(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),u1_lattices(sK0),sK4,X0) = k2_lattices(sK0,sK4,X0) )
| ~ l1_lattices(sK0)
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(superposition,[status(thm)],[c_54,c_68]) ).
tcf(c_1485,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,u1_struct_0(sK0))
| ( k2_binop_1(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),u2_lattices(sK0),sK4,X0) = k1_lattices(sK0,sK4,X0) ) ),
inference(global_subsumption_just,[status(thm)],[c_1059,c_59,c_58,c_366,c_1059]) ).
tcf(c_1486,plain,
! [X0: $i] :
( ( k2_binop_1(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),u2_lattices(sK0),sK4,X0) = k1_lattices(sK0,sK4,X0) )
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(renaming,[status(thm)],[c_1485]) ).
tcf(c_1758,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( u1_struct_0(sK0) = X0 )
| ~ v1_funct_1(u1_lattices(sK0))
| ~ v1_funct_1(u2_lattices(sK0))
| ~ m1_relset_1(u1_lattices(sK0),k2_zfmisc_1(u1_struct_0(sK0),u1_struct_0(sK0)),u1_struct_0(sK0))
| ~ m1_relset_1(u2_lattices(sK0),k2_zfmisc_1(u1_struct_0(sK0),u1_struct_0(sK0)),u1_struct_0(sK0))
| ~ v1_funct_2(u1_lattices(sK0),k2_zfmisc_1(u1_struct_0(sK0),u1_struct_0(sK0)),u1_struct_0(sK0))
| ~ v1_funct_2(u2_lattices(sK0),k2_zfmisc_1(u1_struct_0(sK0),u1_struct_0(sK0)),u1_struct_0(sK0))
| ( g3_lattices(u1_struct_0(sK1),u2_lattices(sK1),u1_lattices(sK1)) != g3_lattices(X0,X1,X2) ) ),
inference(superposition,[status(thm)],[c_55,c_104]) ).
tcf(c_1780,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( u2_lattices(sK0) = X1 )
| ~ v1_funct_1(u1_lattices(sK0))
| ~ v1_funct_1(u2_lattices(sK0))
| ~ m1_relset_1(u1_lattices(sK0),k2_zfmisc_1(u1_struct_0(sK0),u1_struct_0(sK0)),u1_struct_0(sK0))
| ~ m1_relset_1(u2_lattices(sK0),k2_zfmisc_1(u1_struct_0(sK0),u1_struct_0(sK0)),u1_struct_0(sK0))
| ~ v1_funct_2(u1_lattices(sK0),k2_zfmisc_1(u1_struct_0(sK0),u1_struct_0(sK0)),u1_struct_0(sK0))
| ~ v1_funct_2(u2_lattices(sK0),k2_zfmisc_1(u1_struct_0(sK0),u1_struct_0(sK0)),u1_struct_0(sK0))
| ( g3_lattices(u1_struct_0(sK1),u2_lattices(sK1),u1_lattices(sK1)) != g3_lattices(X0,X1,X2) ) ),
inference(superposition,[status(thm)],[c_55,c_105]) ).
tcf(c_1872,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,u1_struct_0(sK1))
| ( k2_binop_1(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),u1_lattices(sK1),sK4,X0) = k2_lattices(sK1,sK4,X0) ) ),
inference(global_subsumption_just,[status(thm)],[c_1211,c_57,c_56,c_360,c_1211]) ).
tcf(c_1873,plain,
! [X0: $i] :
( ( k2_binop_1(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),u1_lattices(sK1),sK4,X0) = k2_lattices(sK1,sK4,X0) )
| ~ m1_subset_1(X0,u1_struct_0(sK1)) ),
inference(renaming,[status(thm)],[c_1872]) ).
tcf(c_2035,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( u1_lattices(sK0) = X2 )
| ~ v1_funct_1(u1_lattices(sK0))
| ~ v1_funct_1(u2_lattices(sK0))
| ~ m1_relset_1(u1_lattices(sK0),k2_zfmisc_1(u1_struct_0(sK0),u1_struct_0(sK0)),u1_struct_0(sK0))
| ~ m1_relset_1(u2_lattices(sK0),k2_zfmisc_1(u1_struct_0(sK0),u1_struct_0(sK0)),u1_struct_0(sK0))
| ~ v1_funct_2(u1_lattices(sK0),k2_zfmisc_1(u1_struct_0(sK0),u1_struct_0(sK0)),u1_struct_0(sK0))
| ~ v1_funct_2(u2_lattices(sK0),k2_zfmisc_1(u1_struct_0(sK0),u1_struct_0(sK0)),u1_struct_0(sK0))
| ( g3_lattices(u1_struct_0(sK1),u2_lattices(sK1),u1_lattices(sK1)) != g3_lattices(X0,X1,X2) ) ),
inference(superposition,[status(thm)],[c_55,c_106]) ).
tcf(c_2127,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,u1_struct_0(sK0))
| ( k2_binop_1(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),u1_lattices(sK0),sK4,X0) = k2_lattices(sK0,sK4,X0) ) ),
inference(global_subsumption_just,[status(thm)],[c_1213,c_59,c_58,c_361,c_1213]) ).
tcf(c_2128,plain,
! [X0: $i] :
( ( k2_binop_1(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),u1_lattices(sK0),sK4,X0) = k2_lattices(sK0,sK4,X0) )
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(renaming,[status(thm)],[c_2127]) ).
tcf(c_2279,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( u1_struct_0(sK0) = X0 )
| ~ m1_relset_1(u1_lattices(sK0),k2_zfmisc_1(u1_struct_0(sK0),u1_struct_0(sK0)),u1_struct_0(sK0))
| ~ m1_relset_1(u2_lattices(sK0),k2_zfmisc_1(u1_struct_0(sK0),u1_struct_0(sK0)),u1_struct_0(sK0))
| ( g3_lattices(u1_struct_0(sK1),u2_lattices(sK1),u1_lattices(sK1)) != g3_lattices(X0,X1,X2) ) ),
inference(global_subsumption_just,[status(thm)],[c_1758,c_59,c_361,c_366,c_700,c_699,c_746,c_745,c_1758]) ).
tcf(c_2284,plain,
( m1_relset_1(u1_lattices(sK0),k2_zfmisc_1(u1_struct_0(sK0),u1_struct_0(sK0)),u1_struct_0(sK0))
| ~ m2_relset_1(u1_lattices(sK0),k2_zfmisc_1(u1_struct_0(sK0),u1_struct_0(sK0)),u1_struct_0(sK0)) ),
inference(instantiation,[status(thm)],[c_135]) ).
tcf(c_2355,plain,
( m1_relset_1(u2_lattices(sK0),k2_zfmisc_1(u1_struct_0(sK0),u1_struct_0(sK0)),u1_struct_0(sK0))
| ~ m2_relset_1(u2_lattices(sK0),k2_zfmisc_1(u1_struct_0(sK0),u1_struct_0(sK0)),u1_struct_0(sK0)) ),
inference(instantiation,[status(thm)],[c_135]) ).
tcf(c_2458,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( u2_lattices(sK0) = X1 )
| ( g3_lattices(u1_struct_0(sK1),u2_lattices(sK1),u1_lattices(sK1)) != g3_lattices(X0,X1,X2) ) ),
inference(global_subsumption_just,[status(thm)],[c_1780,c_59,c_361,c_366,c_700,c_699,c_698,c_746,c_745,c_744,c_1780,c_2284,c_2355]) ).
tcf(c_6289,plain,
! [X0: $i] :
( v3_struct_0(sK1)
| ( k2_binop_1(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),u2_lattices(sK1),sK4,X0) = k1_lattices(sK1,sK4,X0) )
| ~ l2_lattices(sK1)
| ~ m1_subset_1(X0,u1_struct_0(sK1)) ),
inference(superposition,[status(thm)],[c_52,c_67]) ).
tcf(c_6291,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| ( k2_binop_1(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),u2_lattices(sK0),sK4,X0) = k1_lattices(sK0,sK4,X0) )
| ~ l2_lattices(sK0)
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(superposition,[status(thm)],[c_54,c_67]) ).
tcf(c_6308,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,u1_struct_0(sK1))
| ( k2_binop_1(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),u2_lattices(sK1),sK4,X0) = k1_lattices(sK1,sK4,X0) ) ),
inference(global_subsumption_just,[status(thm)],[c_6289,c_1167]) ).
tcf(c_6309,plain,
! [X0: $i] :
( ( k2_binop_1(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),u2_lattices(sK1),sK4,X0) = k1_lattices(sK1,sK4,X0) )
| ~ m1_subset_1(X0,u1_struct_0(sK1)) ),
inference(renaming,[status(thm)],[c_6308]) ).
tcf(c_6310,plain,
k2_binop_1(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),u2_lattices(sK1),sK4,sK5) = k1_lattices(sK1,sK4,sK5),
inference(superposition,[status(thm)],[c_51,c_6309]) ).
tcf(c_6323,plain,
! [X0: $i] :
( v3_struct_0(sK1)
| ( k2_binop_1(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),u1_lattices(sK1),sK4,X0) = k2_lattices(sK1,sK4,X0) )
| ~ l1_lattices(sK1)
| ~ m1_subset_1(X0,u1_struct_0(sK1)) ),
inference(superposition,[status(thm)],[c_52,c_68]) ).
tcf(c_6325,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| ( k2_binop_1(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),u1_lattices(sK0),sK4,X0) = k2_lattices(sK0,sK4,X0) )
| ~ l1_lattices(sK0)
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(superposition,[status(thm)],[c_54,c_68]) ).
tcf(c_6365,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,u1_struct_0(sK0))
| ( k2_binop_1(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),u2_lattices(sK0),sK4,X0) = k1_lattices(sK0,sK4,X0) ) ),
inference(global_subsumption_just,[status(thm)],[c_6291,c_1486]) ).
tcf(c_6366,plain,
! [X0: $i] :
( ( k2_binop_1(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),u2_lattices(sK0),sK4,X0) = k1_lattices(sK0,sK4,X0) )
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(renaming,[status(thm)],[c_6365]) ).
tcf(c_6367,plain,
k2_binop_1(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),u2_lattices(sK0),sK4,sK5) = k1_lattices(sK0,sK4,sK5),
inference(superposition,[status(thm)],[c_53,c_6366]) ).
tcf(c_6391,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( u1_struct_0(sK0) = X0 )
| ~ v1_funct_1(X2)
| ~ v1_funct_1(X1)
| ~ m1_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
| ~ m1_relset_1(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X1,k2_zfmisc_1(X0,X0),X0)
| ( g3_lattices(u1_struct_0(sK1),u2_lattices(sK1),u1_lattices(sK1)) != g3_lattices(X0,X1,X2) ) ),
inference(superposition,[status(thm)],[c_55,c_104]) ).
tcf(c_6398,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( u2_lattices(sK0) = X1 )
| ~ v1_funct_1(X2)
| ~ v1_funct_1(X1)
| ~ m1_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
| ~ m1_relset_1(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X1,k2_zfmisc_1(X0,X0),X0)
| ( g3_lattices(u1_struct_0(sK1),u2_lattices(sK1),u1_lattices(sK1)) != g3_lattices(X0,X1,X2) ) ),
inference(superposition,[status(thm)],[c_55,c_105]) ).
tcf(c_6419,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,u1_struct_0(sK1))
| ( k2_binop_1(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),u1_lattices(sK1),sK4,X0) = k2_lattices(sK1,sK4,X0) ) ),
inference(global_subsumption_just,[status(thm)],[c_6323,c_1873]) ).
tcf(c_6420,plain,
! [X0: $i] :
( ( k2_binop_1(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),u1_lattices(sK1),sK4,X0) = k2_lattices(sK1,sK4,X0) )
| ~ m1_subset_1(X0,u1_struct_0(sK1)) ),
inference(renaming,[status(thm)],[c_6419]) ).
tcf(c_6421,plain,
k2_binop_1(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),u1_lattices(sK1),sK4,sK5) = k2_lattices(sK1,sK4,sK5),
inference(superposition,[status(thm)],[c_51,c_6420]) ).
tcf(c_6439,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,u1_struct_0(sK0))
| ( k2_binop_1(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),u1_lattices(sK0),sK4,X0) = k2_lattices(sK0,sK4,X0) ) ),
inference(global_subsumption_just,[status(thm)],[c_6325,c_2128]) ).
tcf(c_6440,plain,
! [X0: $i] :
( ( k2_binop_1(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),u1_lattices(sK0),sK4,X0) = k2_lattices(sK0,sK4,X0) )
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(renaming,[status(thm)],[c_6439]) ).
tcf(c_6441,plain,
k2_binop_1(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),u1_lattices(sK0),sK4,sK5) = k2_lattices(sK0,sK4,sK5),
inference(superposition,[status(thm)],[c_53,c_6440]) ).
tcf(c_6450,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( u1_lattices(sK0) = X2 )
| ~ v1_funct_1(X2)
| ~ v1_funct_1(X1)
| ~ m1_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
| ~ m1_relset_1(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X1,k2_zfmisc_1(X0,X0),X0)
| ( g3_lattices(u1_struct_0(sK1),u2_lattices(sK1),u1_lattices(sK1)) != g3_lattices(X0,X1,X2) ) ),
inference(superposition,[status(thm)],[c_55,c_106]) ).
tcf(c_6477,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( u1_struct_0(sK0) = X0 )
| ( g3_lattices(u1_struct_0(sK1),u2_lattices(sK1),u1_lattices(sK1)) != g3_lattices(X0,X1,X2) ) ),
inference(global_subsumption_just,[status(thm)],[c_6391,c_59,c_361,c_366,c_698,c_744,c_2279,c_2284,c_2355]) ).
tcf(c_6482,plain,
u1_struct_0(sK1) = u1_struct_0(sK0),
inference(equality_resolution,[status(thm)],[c_6477]) ).
tcf(c_6483,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( u2_lattices(sK0) = X1 )
| ( g3_lattices(u1_struct_0(sK1),u2_lattices(sK1),u1_lattices(sK1)) != g3_lattices(X0,X1,X2) ) ),
inference(global_subsumption_just,[status(thm)],[c_6398,c_2458]) ).
tcf(c_6488,plain,
u2_lattices(sK1) = u2_lattices(sK0),
inference(equality_resolution,[status(thm)],[c_6483]) ).
tcf(c_6489,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( u1_lattices(sK0) = X2 )
| ( g3_lattices(u1_struct_0(sK1),u2_lattices(sK1),u1_lattices(sK1)) != g3_lattices(X0,X1,X2) ) ),
inference(global_subsumption_just,[status(thm)],[c_6450,c_59,c_361,c_366,c_700,c_699,c_698,c_746,c_745,c_744,c_2035,c_2284,c_2355]) ).
tcf(c_6494,plain,
u1_lattices(sK1) = u1_lattices(sK0),
inference(equality_resolution,[status(thm)],[c_6489]) ).
tcf(c_6543,plain,
k2_binop_1(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),u1_lattices(sK0),sK4,sK5) = k2_lattices(sK0,sK4,sK5),
inference(superposition,[status(thm)],[c_6482,c_6441]) ).
tcf(c_6549,plain,
k2_binop_1(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),u2_lattices(sK0),sK4,sK5) = k1_lattices(sK0,sK4,sK5),
inference(superposition,[status(thm)],[c_6482,c_6367]) ).
tcf(c_6780,plain,
k2_binop_1(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),u1_lattices(sK1),sK4,sK5) = k2_lattices(sK0,sK4,sK5),
inference(superposition,[status(thm)],[c_6494,c_6543]) ).
tcf(c_6788,plain,
k2_binop_1(u1_struct_0(sK1),u1_struct_0(sK1),u1_struct_0(sK1),u2_lattices(sK1),sK4,sK5) = k1_lattices(sK0,sK4,sK5),
inference(superposition,[status(thm)],[c_6488,c_6549]) ).
tcf(c_7223,plain,
k2_lattices(sK1,sK4,sK5) = k2_lattices(sK0,sK4,sK5),
inference(superposition,[status(thm)],[c_6780,c_6421]) ).
tcf(c_7357,plain,
k1_lattices(sK1,sK4,sK5) = k1_lattices(sK0,sK4,sK5),
inference(superposition,[status(thm)],[c_6788,c_6310]) ).
tcf(c_7381,plain,
( ~ r1_lattices(sK0,sK4,sK5)
| ~ r1_lattices(sK1,sK4,sK5)
| ( k2_lattices(sK1,sK4,sK5) != k2_lattices(sK0,sK4,sK5) ) ),
inference(superposition,[status(thm)],[c_7357,c_49]) ).
tcf(c_7382,plain,
( r1_lattices(sK0,sK4,sK5)
| r1_lattices(sK1,sK4,sK5)
| ( k2_lattices(sK1,sK4,sK5) != k2_lattices(sK0,sK4,sK5) ) ),
inference(superposition,[status(thm)],[c_7357,c_50]) ).
tcf(c_7383,plain,
( v3_struct_0(sK0)
| r1_lattices(sK0,sK4,sK5)
| ~ l2_lattices(sK0)
| ~ m1_subset_1(sK5,u1_struct_0(sK0))
| ~ m1_subset_1(sK4,u1_struct_0(sK0))
| ( k1_lattices(sK1,sK4,sK5) != sK5 ) ),
inference(superposition,[status(thm)],[c_7357,c_69]) ).
tcf(c_7385,plain,
( r1_lattices(sK0,sK4,sK5)
| r1_lattices(sK1,sK4,sK5) ),
inference(global_subsumption_just,[status(thm)],[c_7382,c_7223,c_7382]) ).
tcf(c_7387,plain,
( v3_struct_0(sK0)
| r1_lattices(sK1,sK4,sK5)
| ( k1_lattices(sK0,sK4,sK5) = sK5 )
| ~ l2_lattices(sK0)
| ~ m1_subset_1(sK5,u1_struct_0(sK0))
| ~ m1_subset_1(sK4,u1_struct_0(sK0)) ),
inference(superposition,[status(thm)],[c_7385,c_70]) ).
tcf(c_7388,plain,
( ~ r1_lattices(sK0,sK4,sK5)
| ~ r1_lattices(sK1,sK4,sK5) ),
inference(global_subsumption_just,[status(thm)],[c_7381,c_7223,c_7381]) ).
tcf(c_8304,plain,
( ( k1_lattices(sK0,sK4,sK5) = sK5 )
| r1_lattices(sK1,sK4,sK5) ),
inference(global_subsumption_just,[status(thm)],[c_7387,c_59,c_58,c_54,c_53,c_366,c_7387]) ).
tcf(c_8305,plain,
( r1_lattices(sK1,sK4,sK5)
| ( k1_lattices(sK0,sK4,sK5) = sK5 ) ),
inference(renaming,[status(thm)],[c_8304]) ).
tcf(c_8306,plain,
( ( k1_lattices(sK0,sK4,sK5) = sK5 )
| ~ r1_lattices(sK0,sK4,sK5) ),
inference(superposition,[status(thm)],[c_8305,c_7388]) ).
tcf(c_8307,plain,
( v3_struct_0(sK1)
| ( k1_lattices(sK0,sK4,sK5) = sK5 )
| ( k1_lattices(sK1,sK4,sK5) = sK5 )
| ~ l2_lattices(sK1)
| ~ m1_subset_1(sK5,u1_struct_0(sK1))
| ~ m1_subset_1(sK4,u1_struct_0(sK1)) ),
inference(superposition,[status(thm)],[c_8305,c_70]) ).
tcf(c_8308,plain,
k1_lattices(sK0,sK4,sK5) = sK5,
inference(global_subsumption_just,[status(thm)],[c_8306,c_59,c_57,c_58,c_56,c_54,c_53,c_52,c_51,c_365,c_366,c_7383,c_8306,c_8307]) ).
tcf(c_8310,plain,
k1_lattices(sK1,sK4,sK5) = sK5,
inference(superposition,[status(thm)],[c_7357,c_8308]) ).
tcf(c_55634,plain,
( v3_struct_0(sK1)
| r1_lattices(sK1,sK4,sK5)
| ~ l2_lattices(sK1)
| ~ m1_subset_1(sK5,u1_struct_0(sK1))
| ~ m1_subset_1(sK4,u1_struct_0(sK1))
| ( k1_lattices(sK1,sK4,sK5) != sK5 ) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_55635,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_55634,c_8310,c_7388,c_7383,c_366,c_365,c_51,c_52,c_53,c_54,c_56,c_58,c_57,c_59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT295+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.35 % Computer : n001.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Wed Sep 23 20:59:51 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.41 % Proving...
% 32.01/5.34 % SZS status Started for theBenchmark.p
% 32.01/5.34 % SZS status Theorem for theBenchmark.p
% 32.01/5.34
% 32.01/5.34 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 32.01/5.34
% 32.01/5.34 % ------ iProver source info
% 32.01/5.34
% 32.01/5.34 % git: date: 2026-07-19 20:42:38 +0200
% 32.01/5.34 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 32.01/5.34 % git: non_committed_changes: false
% 32.01/5.34
% 32.01/5.34 % ------ Parsing...
% 32.01/5.34 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 32.01/5.34
% 32.01/5.34 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e sup_sim: 0 sf_s rm: 1 0s sf_e %
% 32.01/5.34
% 32.01/5.34 % ------ Preprocessing...%
% 32.01/5.34
% 32.01/5.34 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 32.01/5.34 % ------ Proving...
% 32.01/5.34 % ------ Problem Properties
% 32.01/5.34
% 32.01/5.34 %
% 32.01/5.34 % clauses 94
% 32.01/5.34 % conjectures 23
% 32.01/5.34 % EPR 44
% 32.01/5.34 % Horn 81
% 32.01/5.34 % unary 45
% 32.01/5.34 % binary 23
% 32.01/5.34 % lits 223
% 32.01/5.34 % lits eq 21
% 32.01/5.34 % fd_pure 0
% 32.01/5.34 % fd_pseudo 0
% 32.01/5.34 % fd_cond 1
% 32.01/5.34 % fd_pseudo_cond 4
% 32.01/5.34 % AC symbols 0
% 32.01/5.34
% 32.01/5.34 % ------ Input Options Time Limit: Unbounded
% 32.01/5.34
% 32.01/5.34
% 32.01/5.34 % ------
% 32.01/5.34 % Current options:
% 32.01/5.34 % ------
% 32.01/5.34
% 32.01/5.34
% 32.01/5.34 %
% 32.01/5.34
% 32.01/5.34 % ------ Proving...
% 32.01/5.34 %
% 32.01/5.34
% 32.01/5.34 % SZS status Theorem for theBenchmark.p
% 32.01/5.34
% 32.01/5.34 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 32.01/5.34
% 32.01/5.34
%------------------------------------------------------------------------------