%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LAT303+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 : n020.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 01:59:11 PM UTC 2026
% Result : Theorem 8.17s 1.72s
% Output : CNFRefutation 8.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 26
% Syntax : Number of formulae : 193 ( 42 unt; 5 def)
% Number of atoms : 736 ( 42 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 789 ( 316 ~; 336 |; 101 &)
% ( 9 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 32 ( 30 usr; 6 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 198 ( 0 sgn 189 !; 9 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ( m2_filter_2(k6_domain_1(u1_struct_0(X0),X1),X0)
=> v13_lattices(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_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))
=> ( m2_filter_2(k6_domain_1(u1_struct_0(X0),X1),X0)
=> v13_lattices(X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f14,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/sandbox/benchmark/theBenchmark.p',d4_filter_2) ).
fof(f16,axiom,
! [X0] :
( l3_lattices(X0)
=> ( l3_lattices(k1_lattice2(X0))
& v3_lattices(k1_lattice2(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattice2) ).
fof(f21,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/sandbox/benchmark/theBenchmark.p',dt_k5_filter_2) ).
fof(f23,axiom,
! [X0] :
( l1_lattices(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
fof(f26,axiom,
! [X0] :
( l3_lattices(X0)
=> ( l2_lattices(X0)
& l1_lattices(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(f32,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(f44,axiom,
! [X0] :
? [X1] : m1_subset_1(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f48,axiom,
! [X0] :
( ( l3_lattices(X0)
& ~ v3_struct_0(X0) )
=> ( v3_lattices(k1_lattice2(X0))
& ~ v3_struct_0(k1_lattice2(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_lattice2) ).
fof(f49,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(f60,axiom,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(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/sandbox/benchmark/theBenchmark.p',fc6_lattice2) ).
fof(f64,axiom,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ? [X1] :
( ~ v1_xboole_0(X1)
& m2_lattice4(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_lattice4) ).
fof(f68,axiom,
? [X0] :
( v1_funct_1(X0)
& v1_xboole_0(X0)
& v1_relat_1(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f78,axiom,
! [X0,X1] :
( ( m1_subset_1(X1,X0)
& ~ v1_xboole_0(X0) )
=> k6_domain_1(X0,X1) = k1_tarski(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_domain_1) ).
fof(f79,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/sandbox/benchmark/theBenchmark.p',redefinition_m1_filter_2) ).
fof(f82,axiom,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ( m1_filter_0(k6_domain_1(u1_struct_0(X0),X1),X0)
=> v14_lattices(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_filter_0) ).
fof(f84,axiom,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m2_filter_2(X1,X0)
<=> m1_filter_2(X1,k1_lattice2(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_filter_2) ).
fof(f85,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(f88,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(f89,axiom,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ( v13_lattices(X0)
<=> v14_lattices(k1_lattice2(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_lattice2) ).
fof(f90,axiom,
! [X0] :
( v1_xboole_0(X0)
=> X0 = k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f106,plain,
? [X0] :
( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
& m2_filter_2(k6_domain_1(u1_struct_0(X0),X1),X0)
& ~ v13_lattices(X0) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f107,plain,
? [X0] :
( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
& m2_filter_2(k6_domain_1(u1_struct_0(X0),X1),X0)
& ~ v13_lattices(X0) ) ),
inference(flattening,[],[f106]) ).
fof(f125,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,[],[f14]) ).
fof(f126,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,[],[f125]) ).
fof(f129,plain,
! [X0] :
( ~ l3_lattices(X0)
| ( l3_lattices(k1_lattice2(X0))
& v3_lattices(k1_lattice2(X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f130,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,[],[f21]) ).
fof(f131,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,[],[f130]) ).
fof(f134,plain,
! [X0] :
( ~ l1_lattices(X0)
| l1_struct_0(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f136,plain,
! [X0] :
( ~ l3_lattices(X0)
| ( l2_lattices(X0)
& l1_lattices(X0) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f143,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,[],[f32]) ).
fof(f144,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,[],[f143]) ).
fof(f156,plain,
! [X0] :
( ~ l3_lattices(X0)
| v3_struct_0(X0)
| ( v3_lattices(k1_lattice2(X0))
& ~ v3_struct_0(k1_lattice2(X0)) ) ),
inference(ennf_transformation,[],[f48]) ).
fof(f157,plain,
! [X0] :
( ~ l3_lattices(X0)
| v3_struct_0(X0)
| ( v3_lattices(k1_lattice2(X0))
& ~ v3_struct_0(k1_lattice2(X0)) ) ),
inference(flattening,[],[f156]) ).
fof(f158,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f49]) ).
fof(f159,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(flattening,[],[f158]) ).
fof(f172,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(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,[],[f60]) ).
fof(f173,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(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,[],[f172]) ).
fof(f176,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ? [X1] :
( ~ v1_xboole_0(X1)
& m2_lattice4(X1,X0) ) ),
inference(ennf_transformation,[],[f64]) ).
fof(f177,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ? [X1] :
( ~ v1_xboole_0(X1)
& m2_lattice4(X1,X0) ) ),
inference(flattening,[],[f176]) ).
fof(f181,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,X0)
| v1_xboole_0(X0)
| k6_domain_1(X0,X1) = k1_tarski(X1) ),
inference(ennf_transformation,[],[f78]) ).
fof(f182,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,X0)
| v1_xboole_0(X0)
| k6_domain_1(X0,X1) = k1_tarski(X1) ),
inference(flattening,[],[f181]) ).
fof(f183,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,[],[f79]) ).
fof(f184,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,[],[f183]) ).
fof(f185,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_filter_0(k6_domain_1(u1_struct_0(X0),X1),X0)
| v14_lattices(X0) ) ),
inference(ennf_transformation,[],[f82]) ).
fof(f186,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_filter_0(k6_domain_1(u1_struct_0(X0),X1),X0)
| v14_lattices(X0) ) ),
inference(flattening,[],[f185]) ).
fof(f188,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( m2_filter_2(X1,X0)
<=> m1_filter_2(X1,k1_lattice2(X0)) ) ),
inference(ennf_transformation,[],[f84]) ).
fof(f189,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( m2_filter_2(X1,X0)
<=> m1_filter_2(X1,k1_lattice2(X0)) ) ),
inference(flattening,[],[f188]) ).
fof(f190,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(ennf_transformation,[],[f85]) ).
fof(f191,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(flattening,[],[f190]) ).
fof(f195,plain,
! [X0,X1,X2] :
( ~ v1_xboole_0(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f88]) ).
fof(f196,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ( v13_lattices(X0)
<=> v14_lattices(k1_lattice2(X0)) ) ),
inference(ennf_transformation,[],[f89]) ).
fof(f197,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ( v13_lattices(X0)
<=> v14_lattices(k1_lattice2(X0)) ) ),
inference(flattening,[],[f196]) ).
fof(f198,plain,
! [X0] :
( ~ v1_xboole_0(X0)
| X0 = k1_xboole_0 ),
inference(ennf_transformation,[],[f90]) ).
fof(f203,plain,
( l3_lattices(sK1)
& v10_lattices(sK1)
& ~ v3_struct_0(sK1)
& m1_subset_1(sK2,u1_struct_0(sK1))
& m2_filter_2(k6_domain_1(u1_struct_0(sK1),sK2),sK1)
& ~ v13_lattices(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f107]) ).
fof(f211,plain,
! [X0] : m1_subset_1(sK10(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X1,sK10(X0))],[f44]) ).
fof(f218,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ( ~ v1_xboole_0(sK16(X0))
& m2_lattice4(sK16(X0),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X1,sK16(X0))],[f177]) ).
fof(f222,plain,
( v1_funct_1(sK20)
& v1_xboole_0(sK20)
& v1_relat_1(sK20) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(X0,sK20)],[f68]) ).
fof(f232,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,[],[f184]) ).
fof(f234,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ( ~ m2_filter_2(X1,X0)
| m1_filter_2(X1,k1_lattice2(X0)) )
& ( ~ m1_filter_2(X1,k1_lattice2(X0))
| m2_filter_2(X1,X0) ) ) ),
inference(nnf_transformation,[],[f189]) ).
fof(f235,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ( ( ~ v13_lattices(X0)
| v14_lattices(k1_lattice2(X0)) )
& ( ~ v14_lattices(k1_lattice2(X0))
| v13_lattices(X0) ) ) ),
inference(nnf_transformation,[],[f197]) ).
fof(f236,plain,
l3_lattices(sK1),
inference(cnf_transformation,[],[f203]) ).
fof(f237,plain,
v10_lattices(sK1),
inference(cnf_transformation,[],[f203]) ).
fof(f238,plain,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f203]) ).
fof(f239,plain,
m1_subset_1(sK2,u1_struct_0(sK1)),
inference(cnf_transformation,[],[f203]) ).
fof(f240,plain,
m2_filter_2(k6_domain_1(u1_struct_0(sK1),sK2),sK1),
inference(cnf_transformation,[],[f203]) ).
fof(f241,plain,
~ v13_lattices(sK1),
inference(cnf_transformation,[],[f203]) ).
fof(f264,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,[],[f126]) ).
fof(f267,plain,
! [X0] :
( ~ l3_lattices(X0)
| l3_lattices(k1_lattice2(X0)) ),
inference(cnf_transformation,[],[f129]) ).
fof(f269,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,[],[f131]) ).
fof(f271,plain,
! [X0] :
( ~ l1_lattices(X0)
| l1_struct_0(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f274,plain,
! [X0] :
( ~ l3_lattices(X0)
| l1_lattices(X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f281,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,[],[f144]) ).
fof(f296,plain,
! [X0] : m1_subset_1(sK10(X0),X0),
inference(cnf_transformation,[],[f211]) ).
fof(f301,plain,
! [X0] :
( ~ l3_lattices(X0)
| v3_struct_0(X0)
| ~ v3_struct_0(k1_lattice2(X0)) ),
inference(cnf_transformation,[],[f157]) ).
fof(f302,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f159]) ).
fof(f332,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| sP0(X0) ),
inference(cnf_transformation,[],[f202]) ).
fof(f351,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(sK16(X0)) ),
inference(cnf_transformation,[],[f218]) ).
fof(f352,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| m2_lattice4(sK16(X0),X0) ),
inference(cnf_transformation,[],[f218]) ).
fof(f359,plain,
v1_xboole_0(sK20),
inference(cnf_transformation,[],[f222]) ).
fof(f387,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,X0)
| v1_xboole_0(X0)
| k6_domain_1(X0,X1) = k1_tarski(X1) ),
inference(cnf_transformation,[],[f182]) ).
fof(f388,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,[],[f232]) ).
fof(f393,plain,
! [X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_filter_0(k6_domain_1(u1_struct_0(X0),X1),X0)
| v14_lattices(X0) ),
inference(cnf_transformation,[],[f186]) ).
fof(f395,plain,
! [X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m2_filter_2(X1,X0)
| m1_filter_2(X1,k1_lattice2(X0)) ),
inference(cnf_transformation,[],[f234]) ).
fof(f397,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f191]) ).
fof(f400,plain,
! [X2,X0,X1] :
( ~ v1_xboole_0(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f195]) ).
fof(f402,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ v14_lattices(k1_lattice2(X0))
| v13_lattices(X0) ),
inference(cnf_transformation,[],[f235]) ).
fof(f403,plain,
! [X0] :
( ~ v1_xboole_0(X0)
| k1_xboole_0 = X0 ),
inference(cnf_transformation,[],[f198]) ).
tcf(c_49,negated_conjecture,
~ v13_lattices(sK1),
inference(cnf_transformation,[],[f241]) ).
tcf(c_50,negated_conjecture,
m2_filter_2(k6_domain_1(u1_struct_0(sK1),sK2),sK1),
inference(cnf_transformation,[],[f240]) ).
tcf(c_51,negated_conjecture,
m1_subset_1(sK2,u1_struct_0(sK1)),
inference(cnf_transformation,[],[f239]) ).
tcf(c_52,negated_conjecture,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f238]) ).
tcf(c_53,negated_conjecture,
v10_lattices(sK1),
inference(cnf_transformation,[],[f237]) ).
tcf(c_54,negated_conjecture,
l3_lattices(sK1),
inference(cnf_transformation,[],[f236]) ).
tcf(c_71,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,[],[f264]) ).
tcf(c_75,plain,
! [X0: $i] :
( l3_lattices(k1_lattice2(X0))
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f267]) ).
tcf(c_76,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,[],[f269]) ).
tcf(c_78,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l1_lattices(X0) ),
inference(cnf_transformation,[],[f271]) ).
tcf(c_80,plain,
! [X0: $i] :
( l1_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f274]) ).
tcf(c_88,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,[],[f281]) ).
tcf(c_103,plain,
! [X0: $i] : m1_subset_1(sK10(X0),X0),
inference(cnf_transformation,[],[f296]) ).
tcf(c_107,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v3_struct_0(k1_lattice2(X0)) ),
inference(cnf_transformation,[],[f301]) ).
tcf(c_109,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ l1_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f302]) ).
tcf(c_139,plain,
! [X0: $i] :
( sP0(X0)
| v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0) ),
inference(cnf_transformation,[],[f332]) ).
tcf(c_158,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m2_lattice4(sK16(X0),X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0) ),
inference(cnf_transformation,[],[f352]) ).
tcf(c_159,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ v1_xboole_0(sK16(X0)) ),
inference(cnf_transformation,[],[f351]) ).
tcf(c_166,plain,
v1_xboole_0(sK20),
inference(cnf_transformation,[],[f359]) ).
tcf(c_194,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X1)
| ( k6_domain_1(X1,X0) = k1_tarski(X0) )
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f387]) ).
tcf(c_196,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,[],[f388]) ).
tcf(c_200,plain,
! [X0: $i,X1: $i] :
( v14_lattices(X0)
| v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_filter_0(k6_domain_1(u1_struct_0(X0),X1),X0) ),
inference(cnf_transformation,[],[f393]) ).
tcf(c_203,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m1_filter_2(X0,k1_lattice2(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m2_filter_2(X0,X1) ),
inference(cnf_transformation,[],[f395]) ).
tcf(c_204,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X1)
| r2_hidden(X0,X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f397]) ).
tcf(c_207,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,[],[f400]) ).
tcf(c_208,plain,
! [X0: $i] :
( v3_struct_0(X0)
| v13_lattices(X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ v14_lattices(k1_lattice2(X0)) ),
inference(cnf_transformation,[],[f402]) ).
tcf(c_210,plain,
! [X0: $i] :
( ( X0 = k1_xboole_0 )
| ~ v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f403]) ).
tcf(c_327,plain,
! [X0: $i] :
( l1_lattices(X0)
| ~ l3_lattices(X0) ),
inference(prop_impl_just,[status(thm)],[c_80]) ).
tcf(c_359,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l1_lattices(X0) ),
inference(prop_impl_just,[status(thm)],[c_78]) ).
tcf(c_2146,plain,
! [X0: $i,X1: $i] :
( l1_struct_0(X1)
| ~ l3_lattices(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_327,c_359]) ).
tcf(c_2147,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l3_lattices(X0) ),
inference(unflattening,[status(thm)],[c_2146]) ).
tcf(c_2351,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ v14_lattices(k1_lattice2(X0))
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_208]) ).
tcf(c_2352,plain,
( v3_struct_0(sK1)
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| ~ v14_lattices(k1_lattice2(sK1)) ),
inference(unflattening,[status(thm)],[c_2351]) ).
tcf(c_2353,plain,
~ v14_lattices(k1_lattice2(sK1)),
inference(global_subsumption_just,[status(thm)],[c_2352,c_54,c_53,c_52,c_2352]) ).
tcf(c_2372,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_filter_0(k6_domain_1(u1_struct_0(X0),X1),X0)
| ( k1_lattice2(sK1) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_200,c_2353]) ).
tcf(c_2373,plain,
! [X0: $i] :
( v3_struct_0(k1_lattice2(sK1))
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1))
| ~ m1_subset_1(X0,u1_struct_0(k1_lattice2(sK1)))
| ~ m1_filter_0(k6_domain_1(u1_struct_0(k1_lattice2(sK1)),X0),k1_lattice2(sK1)) ),
inference(unflattening,[status(thm)],[c_2372]) ).
tcf(c_2551,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X2)
| v3_struct_0(X0)
| m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))
| ~ l3_lattices(X2)
| ~ l3_lattices(X0)
| ~ v10_lattices(X2)
| ~ v10_lattices(X0)
| ( X0 != X2 )
| ( sK16(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_88,c_158]) ).
tcf(c_2552,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m1_subset_1(sK16(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0) ),
inference(unflattening,[status(thm)],[c_2551]) ).
tcf(c_2608,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_2147,c_109]) ).
tcf(c_2609,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(unflattening,[status(thm)],[c_2608]) ).
tcf(c_2900,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m1_filter_2(X0,k1_lattice2(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ( X1 != sK1 )
| ( k6_domain_1(u1_struct_0(sK1),sK2) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_203]) ).
tcf(c_2901,plain,
( v3_struct_0(sK1)
| m1_filter_2(k6_domain_1(u1_struct_0(sK1),sK2),k1_lattice2(sK1))
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1) ),
inference(unflattening,[status(thm)],[c_2900]) ).
tcf(c_2902,plain,
m1_filter_2(k6_domain_1(u1_struct_0(sK1),sK2),k1_lattice2(sK1)),
inference(global_subsumption_just,[status(thm)],[c_2901,c_54,c_53,c_52,c_2901]) ).
tcf(c_3035,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X2)
| v3_struct_0(k1_lattice2(sK1))
| ~ l3_lattices(X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1))
| ~ m1_filter_2(X1,X2)
| ~ m1_subset_1(X0,u1_struct_0(k1_lattice2(sK1)))
| ( k1_lattice2(sK1) != X2 )
| ( k6_domain_1(u1_struct_0(k1_lattice2(sK1)),X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_196,c_2373]) ).
tcf(c_3036,plain,
! [X0: $i] :
( v3_struct_0(k1_lattice2(sK1))
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1))
| ~ m1_subset_1(X0,u1_struct_0(k1_lattice2(sK1)))
| ~ m1_filter_2(k6_domain_1(u1_struct_0(k1_lattice2(sK1)),X0),k1_lattice2(sK1)) ),
inference(unflattening,[status(thm)],[c_3035]) ).
tcf(c_4829,plain,
! [X0: $i] :
( ~ iPr_def_11
| ~ m1_subset_1(X0,u1_struct_0(k1_lattice2(sK1)))
| ~ m1_filter_2(k6_domain_1(u1_struct_0(k1_lattice2(sK1)),X0),k1_lattice2(sK1)) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_3036]) ).
tcf(c_4830,plain,
( iPr_def_11
| v3_struct_0(k1_lattice2(sK1))
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1)) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_3036]) ).
tcf(c_4831,definition,
iPr_def_12 = k1_lattice2(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_4832,definition,
iPr_def_13 = u1_struct_0(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_4834,definition,
iPr_def_15 = u1_struct_0(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_4835,definition,
iPr_def_16 = k6_domain_1(iPr_def_15,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_4840,plain,
( iPr_def_11
| v3_struct_0(iPr_def_12)
| ~ l3_lattices(iPr_def_12)
| ~ v10_lattices(iPr_def_12) ),
inference(demodulation,[status(thm)],[c_4830]) ).
tcf(c_4841,plain,
! [X0: $i] :
( ~ iPr_def_11
| ~ m1_subset_1(X0,iPr_def_13)
| ~ m1_filter_2(k6_domain_1(iPr_def_13,X0),iPr_def_12) ),
inference(demodulation,[status(thm)],[c_4829]) ).
tcf(c_4843,plain,
m1_filter_2(iPr_def_16,iPr_def_12),
inference(demodulation,[status(thm)],[c_2902]) ).
tcf(c_4848,negated_conjecture,
l3_lattices(sK1),
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_4849,negated_conjecture,
v10_lattices(sK1),
inference(demodulation,[status(thm)],[c_53]) ).
tcf(c_4850,negated_conjecture,
~ v3_struct_0(sK1),
inference(demodulation,[status(thm)],[c_52]) ).
tcf(c_4851,negated_conjecture,
m1_subset_1(sK2,iPr_def_15),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_6352,plain,
( l3_lattices(iPr_def_12)
| ~ l3_lattices(sK1) ),
inference(superposition,[status(thm)],[c_4831,c_75]) ).
tcf(c_6353,plain,
l3_lattices(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_6352,c_4848]) ).
tcf(c_6355,plain,
( iPr_def_11
| v3_struct_0(iPr_def_12)
| ~ v10_lattices(iPr_def_12) ),
inference(backward_subsumption_resolution,[status(thm)],[c_4840,c_6353]) ).
tcf(c_6396,plain,
k1_xboole_0 = sK20,
inference(superposition,[status(thm)],[c_166,c_210]) ).
tcf(c_6400,plain,
! [X0: $i] :
( ( X0 = sK20 )
| ~ v1_xboole_0(X0) ),
inference(demodulation,[status(thm)],[c_210,c_6396]) ).
tcf(c_6472,plain,
( v3_struct_0(sK1)
| ~ l3_lattices(sK1)
| ~ v3_struct_0(iPr_def_12) ),
inference(superposition,[status(thm)],[c_4831,c_107]) ).
tcf(c_6473,plain,
~ v3_struct_0(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_6472,c_4850,c_4848]) ).
tcf(c_6476,plain,
( iPr_def_11
| ~ v10_lattices(iPr_def_12) ),
inference(backward_subsumption_resolution,[status(thm)],[c_6355,c_6473]) ).
tcf(c_6535,plain,
( v3_struct_0(iPr_def_12)
| m1_subset_1(sK16(iPr_def_12),k1_zfmisc_1(iPr_def_13))
| ~ l3_lattices(iPr_def_12)
| ~ v10_lattices(iPr_def_12) ),
inference(superposition,[status(thm)],[c_4832,c_2552]) ).
tcf(c_6536,plain,
( m1_subset_1(sK16(iPr_def_12),k1_zfmisc_1(iPr_def_13))
| ~ v10_lattices(iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6535,c_6473,c_6353]) ).
tcf(c_6547,plain,
! [X0: $i] :
( v1_xboole_0(X0)
| r2_hidden(sK10(X0),X0) ),
inference(superposition,[status(thm)],[c_103,c_204]) ).
tcf(c_6824,plain,
! [X0: $i] :
( ~ v1_xboole_0(iPr_def_13)
| ~ v10_lattices(iPr_def_12)
| ~ r2_hidden(X0,sK16(iPr_def_12)) ),
inference(superposition,[status(thm)],[c_6536,c_207]) ).
tcf(c_6888,plain,
( v1_xboole_0(iPr_def_15)
| ( k6_domain_1(iPr_def_15,sK2) = k1_tarski(sK2) ) ),
inference(superposition,[status(thm)],[c_4851,c_194]) ).
tcf(c_6899,plain,
( v1_xboole_0(iPr_def_15)
| ( k1_tarski(sK2) = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_6888,c_4835]) ).
tcf(c_6989,plain,
( ( sK20 = iPr_def_15 )
| ( k1_tarski(sK2) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_6899,c_6400]) ).
tcf(c_7094,plain,
! [X0: $i] :
( v3_struct_0(sK1)
| ( k5_filter_2(sK1,X0) = X0 )
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| ~ m1_subset_1(X0,iPr_def_15) ),
inference(superposition,[status(thm)],[c_4834,c_71]) ).
tcf(c_7100,plain,
! [X0: $i] :
( ( k5_filter_2(sK1,X0) = X0 )
| ~ m1_subset_1(X0,iPr_def_15) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7094,c_4850,c_4848,c_4849]) ).
tcf(c_7124,plain,
k5_filter_2(sK1,sK2) = sK2,
inference(superposition,[status(thm)],[c_4851,c_7100]) ).
tcf(c_7188,plain,
( v3_struct_0(sK1)
| m1_subset_1(sK2,u1_struct_0(k1_lattice2(sK1)))
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| ~ m1_subset_1(sK2,u1_struct_0(sK1)) ),
inference(superposition,[status(thm)],[c_7124,c_76]) ).
tcf(c_7194,plain,
( v3_struct_0(sK1)
| m1_subset_1(sK2,iPr_def_13)
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| ~ m1_subset_1(sK2,iPr_def_15) ),
inference(light_normalisation,[status(thm)],[c_7188,c_4831,c_4832,c_4834]) ).
tcf(c_7195,plain,
m1_subset_1(sK2,iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_7194,c_4850,c_4848,c_4849,c_4851]) ).
tcf(c_7288,plain,
( v1_xboole_0(iPr_def_13)
| ( k6_domain_1(iPr_def_13,sK2) = k1_tarski(sK2) ) ),
inference(superposition,[status(thm)],[c_7195,c_194]) ).
tcf(c_10406,plain,
( v3_struct_0(sK1)
| ~ v1_xboole_0(iPr_def_15)
| ~ l3_lattices(sK1) ),
inference(superposition,[status(thm)],[c_4834,c_2609]) ).
fof(f201,definition,
! [X0] :
( ~ sP0(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(f202,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| sP0(X0) ),
inference(definition_folding,[],[f173,f201]) ).
fof(f215,plain,
! [X0] :
( ~ sP0(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,[],[f201]) ).
fof(f323,plain,
! [X0] :
( ~ sP0(X0)
| v10_lattices(k1_lattice2(X0)) ),
inference(cnf_transformation,[],[f215]) ).
tcf(c_138,plain,
! [X0: $i] :
( v10_lattices(k1_lattice2(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f323]) ).
tcf(c_403,plain,
! [X0: $i] :
( v10_lattices(k1_lattice2(X0))
| ~ sP0(X0) ),
inference(prop_impl_just,[status(thm)],[c_138]) ).
tcf(c_2753,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| v10_lattices(k1_lattice2(X1))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_139,c_403]) ).
tcf(c_2754,plain,
! [X0: $i] :
( v3_struct_0(X0)
| v10_lattices(k1_lattice2(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0) ),
inference(unflattening,[status(thm)],[c_2753]) ).
tcf(c_8303,plain,
( v10_lattices(iPr_def_12)
| v3_struct_0(sK1)
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1) ),
inference(superposition,[status(thm)],[c_4831,c_2754]) ).
tcf(c_8304,plain,
v10_lattices(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_8303,c_4850,c_4848,c_4849]) ).
tcf(c_8311,plain,
! [X0: $i] :
( ~ v1_xboole_0(iPr_def_13)
| ~ r2_hidden(X0,sK16(iPr_def_12)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_6824,c_8304]) ).
tcf(c_8318,plain,
iPr_def_11,
inference(backward_subsumption_resolution,[status(thm)],[c_6476,c_8304]) ).
tcf(c_8335,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,iPr_def_13)
| ~ m1_filter_2(k6_domain_1(iPr_def_13,X0),iPr_def_12) ),
inference(backward_subsumption_resolution,[status(thm)],[c_4841,c_8318]) ).
tcf(c_8445,plain,
( v1_xboole_0(sK16(iPr_def_12))
| ~ v1_xboole_0(iPr_def_13) ),
inference(superposition,[status(thm)],[c_6547,c_8311]) ).
tcf(c_8553,plain,
( v3_struct_0(iPr_def_12)
| ~ v1_xboole_0(iPr_def_13)
| ~ l3_lattices(iPr_def_12)
| ~ v10_lattices(iPr_def_12) ),
inference(superposition,[status(thm)],[c_8445,c_159]) ).
tcf(c_8558,plain,
~ v1_xboole_0(iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_8553,c_6473,c_6353,c_8304]) ).
tcf(c_8570,plain,
k6_domain_1(iPr_def_13,sK2) = k1_tarski(sK2),
inference(backward_subsumption_resolution,[status(thm)],[c_7288,c_8558]) ).
tcf(c_9343,plain,
( ~ m1_subset_1(sK2,iPr_def_13)
| ~ m1_filter_2(k1_tarski(sK2),iPr_def_12) ),
inference(superposition,[status(thm)],[c_8570,c_8335]) ).
tcf(c_9345,plain,
~ m1_filter_2(k1_tarski(sK2),iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_9343,c_7195]) ).
tcf(c_9347,plain,
( ( sK20 = iPr_def_15 )
| ~ m1_filter_2(iPr_def_16,iPr_def_12) ),
inference(superposition,[status(thm)],[c_6989,c_9345]) ).
tcf(c_9348,plain,
sK20 = iPr_def_15,
inference(forward_subsumption_resolution,[status(thm)],[c_9347,c_4843]) ).
tcf(c_9371,plain,
v1_xboole_0(iPr_def_15),
inference(demodulation,[status(thm)],[c_166,c_9348]) ).
tcf(c_10408,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_10406,c_4850,c_9371,c_4848]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT303+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n020.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Wed Sep 23 20:58:19 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 0.12/0.42
% 0.12/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.42
% 0.12/0.42 % Detected problem language: tptp
% 0.12/0.43 % Proving...
% 8.17/1.72 % SZS status Started for theBenchmark.p
% 8.17/1.72 % SZS status Theorem for theBenchmark.p
% 8.17/1.72
% 8.17/1.72 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.17/1.72
% 8.17/1.72 % ------ iProver source info
% 8.17/1.72
% 8.17/1.72 % git: date: 2026-07-19 20:42:38 +0200
% 8.17/1.72 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.17/1.72 % git: non_committed_changes: false
% 8.17/1.72
% 8.17/1.72 % ------ Parsing...
% 8.17/1.72 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.17/1.72
% 8.17/1.72 % ------ 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: 0 sf_s rm: 19 0s sf_e pe_s pe_e %
% 8.17/1.72
% 8.17/1.72 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.17/1.72
% 8.17/1.72 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 8.17/1.72 % ------ Proving...
% 8.17/1.72 % ------ Problem Properties
% 8.17/1.72
% 8.17/1.72 %
% 8.17/1.72 % clauses 130
% 8.17/1.72 % conjectures 4
% 8.17/1.72 % EPR 45
% 8.17/1.72 % Horn 107
% 8.17/1.72 % unary 63
% 8.17/1.72 % binary 28
% 8.17/1.72 % lits 289
% 8.17/1.72 % lits eq 25
% 8.17/1.72 % fd_pure 0
% 8.17/1.72 % fd_pseudo 0
% 8.17/1.72 % fd_cond 1
% 8.17/1.72 % fd_pseudo_cond 4
% 8.17/1.72 % AC symbols 0
% 8.17/1.72
% 8.17/1.72 % ------ Schedule dynamic 5 is on
% 8.17/1.72
% 8.17/1.72 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 8.17/1.72
% 8.17/1.72
% 8.17/1.72 % ------
% 8.17/1.72 % Current options:
% 8.17/1.72 % ------
% 8.17/1.72
% 8.17/1.72
% 8.17/1.72 %
% 8.17/1.72
% 8.17/1.72 % ------ Proving...
% 8.17/1.72 %
% 8.17/1.72
% 8.17/1.72 % SZS status Theorem for theBenchmark.p
% 8.17/1.72
% 8.17/1.72 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.17/1.72
% 8.17/1.72
%------------------------------------------------------------------------------