%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LAT301+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 : n013.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 01:59:10 PM UTC 2026
% Result : Theorem 4.82s 1.40s
% Output : CNFRefutation 4.82s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f398ERROR: Could not build tree for root c_7500ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m2_filter_2(X1,X0)
=> ( v13_lattices(X0)
=> r2_hidden(k5_lattices(X0),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_filter_2) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m2_filter_2(X1,X0)
=> ( v13_lattices(X0)
=> r2_hidden(k5_lattices(X0),X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f13,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(f15,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(f16,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(f31,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(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/sandbox2/benchmark/theBenchmark.p',dt_m2_lattice4) ).
fof(f49,axiom,
! [X0] :
( ( l3_lattices(X0)
& ~ v3_struct_0(X0) )
=> ( v3_lattices(k1_lattice2(X0))
& ~ v3_struct_0(k1_lattice2(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_lattice2) ).
fof(f59,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/sandbox2/benchmark/theBenchmark.p',fc6_lattice2) ).
fof(f75,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(f76,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(f85,axiom,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ( v13_lattices(X0)
<=> v14_lattices(k1_lattice2(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_lattice2) ).
fof(f87,axiom,
! [X0] :
( ( l3_lattices(X0)
& v13_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> k5_lattices(X0) = k6_lattices(k1_lattice2(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_lattice2) ).
fof(f102,plain,
? [X0] :
( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m2_filter_2(X1,X0)
& v13_lattices(X0)
& ~ r2_hidden(k5_lattices(X0),X1) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f103,plain,
? [X0] :
( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m2_filter_2(X1,X0)
& v13_lattices(X0)
& ~ r2_hidden(k5_lattices(X0),X1) ) ),
inference(flattening,[],[f102]) ).
fof(f120,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,[],[f13]) ).
fof(f121,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,[],[f120]) ).
fof(f124,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,[],[f15]) ).
fof(f125,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,[],[f124]) ).
fof(f126,plain,
! [X0] :
( ~ l3_lattices(X0)
| ( l3_lattices(k1_lattice2(X0))
& v3_lattices(k1_lattice2(X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f140,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,[],[f31]) ).
fof(f141,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,[],[f140]) ).
fof(f142,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(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(flattening,[],[f142]) ).
fof(f157,plain,
! [X0] :
( ~ l3_lattices(X0)
| v3_struct_0(X0)
| ( v3_lattices(k1_lattice2(X0))
& ~ v3_struct_0(k1_lattice2(X0)) ) ),
inference(ennf_transformation,[],[f49]) ).
fof(f158,plain,
! [X0] :
( ~ l3_lattices(X0)
| v3_struct_0(X0)
| ( v3_lattices(k1_lattice2(X0))
& ~ v3_struct_0(k1_lattice2(X0)) ) ),
inference(flattening,[],[f157]) ).
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(ennf_transformation,[],[f59]) ).
fof(f174,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,[],[f173]) ).
fof(f182,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,[],[f75]) ).
fof(f183,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,[],[f182]) ).
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(ennf_transformation,[],[f76]) ).
fof(f185,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,[],[f184]) ).
fof(f195,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ( v13_lattices(X0)
<=> v14_lattices(k1_lattice2(X0)) ) ),
inference(ennf_transformation,[],[f85]) ).
fof(f196,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ( v13_lattices(X0)
<=> v14_lattices(k1_lattice2(X0)) ) ),
inference(flattening,[],[f195]) ).
fof(f198,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v13_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| k5_lattices(X0) = k6_lattices(k1_lattice2(X0)) ),
inference(ennf_transformation,[],[f87]) ).
fof(f199,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v13_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| k5_lattices(X0) = k6_lattices(k1_lattice2(X0)) ),
inference(flattening,[],[f198]) ).
fof(f204,plain,
( l3_lattices(sK1)
& v10_lattices(sK1)
& ~ v3_struct_0(sK1)
& m2_filter_2(sK2,sK1)
& v13_lattices(sK1)
& ~ r2_hidden(k5_lattices(sK1),sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f103]) ).
fof(f231,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,[],[f185]) ).
fof(f233,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,[],[f196]) ).
fof(f234,plain,
l3_lattices(sK1),
inference(cnf_transformation,[],[f204]) ).
fof(f235,plain,
v10_lattices(sK1),
inference(cnf_transformation,[],[f204]) ).
fof(f236,plain,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f204]) ).
fof(f237,plain,
m2_filter_2(sK2,sK1),
inference(cnf_transformation,[],[f204]) ).
fof(f238,plain,
v13_lattices(sK1),
inference(cnf_transformation,[],[f204]) ).
fof(f239,plain,
~ r2_hidden(k5_lattices(sK1),sK2),
inference(cnf_transformation,[],[f204]) ).
fof(f261,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,[],[f121]) ).
fof(f264,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,[],[f125]) ).
fof(f265,plain,
! [X0] :
( ~ l3_lattices(X0)
| l3_lattices(k1_lattice2(X0)) ),
inference(cnf_transformation,[],[f126]) ).
fof(f278,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,[],[f141]) ).
fof(f280,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,[],[f143]) ).
fof(f301,plain,
! [X0] :
( ~ l3_lattices(X0)
| v3_struct_0(X0)
| ~ v3_struct_0(k1_lattice2(X0)) ),
inference(cnf_transformation,[],[f158]) ).
fof(f329,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| sP0(X0) ),
inference(cnf_transformation,[],[f203]) ).
fof(f380,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,[],[f183]) ).
fof(f381,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,[],[f231]) ).
fof(f392,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ v13_lattices(X0)
| v14_lattices(k1_lattice2(X0)) ),
inference(cnf_transformation,[],[f233]) ).
fof(f395,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v13_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| k5_lattices(X0) = k6_lattices(k1_lattice2(X0)) ),
inference(cnf_transformation,[],[f199]) ).
tcf(c_49,negated_conjecture,
~ r2_hidden(k5_lattices(sK1),sK2),
inference(cnf_transformation,[],[f239]) ).
tcf(c_50,negated_conjecture,
v13_lattices(sK1),
inference(cnf_transformation,[],[f238]) ).
tcf(c_51,negated_conjecture,
m2_filter_2(sK2,sK1),
inference(cnf_transformation,[],[f237]) ).
tcf(c_52,negated_conjecture,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f236]) ).
tcf(c_53,negated_conjecture,
v10_lattices(sK1),
inference(cnf_transformation,[],[f235]) ).
tcf(c_54,negated_conjecture,
l3_lattices(sK1),
inference(cnf_transformation,[],[f234]) ).
tcf(c_70,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,[],[f261]) ).
tcf(c_73,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,[],[f264]) ).
tcf(c_75,plain,
! [X0: $i] :
( l3_lattices(k1_lattice2(X0))
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f265]) ).
tcf(c_88,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,[],[f278]) ).
tcf(c_89,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,[],[f280]) ).
tcf(c_109,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v3_struct_0(k1_lattice2(X0)) ),
inference(cnf_transformation,[],[f301]) ).
tcf(c_138,plain,
! [X0: $i] :
( sP0(X0)
| v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0) ),
inference(cnf_transformation,[],[f329]) ).
tcf(c_189,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,[],[f380]) ).
tcf(c_191,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,[],[f381]) ).
tcf(c_195,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| r2_hidden(k6_lattices(X1),X0)
| ~ v14_lattices(X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_filter_0(X0,X1) ),
inference(cnf_transformation,[],[f398]) ).
tcf(c_202,plain,
! [X0: $i] :
( v3_struct_0(X0)
| v14_lattices(k1_lattice2(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ v13_lattices(X0) ),
inference(cnf_transformation,[],[f392]) ).
tcf(c_204,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ( k6_lattices(k1_lattice2(X0)) = k5_lattices(X0) )
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ v13_lattices(X0) ),
inference(cnf_transformation,[],[f395]) ).
tcf(c_2609,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_88,c_89]) ).
tcf(c_2610,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_2609]) ).
tcf(c_2713,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ( k6_lattices(k1_lattice2(X0)) = k5_lattices(X0) )
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_204]) ).
tcf(c_2714,plain,
( v3_struct_0(sK1)
| ( k6_lattices(k1_lattice2(sK1)) = k5_lattices(sK1) )
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1) ),
inference(unflattening,[status(thm)],[c_2713]) ).
tcf(c_2715,plain,
k6_lattices(k1_lattice2(sK1)) = k5_lattices(sK1),
inference(global_subsumption_just,[status(thm)],[c_2714,c_54,c_53,c_52,c_2714]) ).
tcf(c_2720,plain,
! [X0: $i] :
( v3_struct_0(X0)
| v14_lattices(k1_lattice2(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_202]) ).
tcf(c_2721,plain,
( v3_struct_0(sK1)
| v14_lattices(k1_lattice2(sK1))
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1) ),
inference(unflattening,[status(thm)],[c_2720]) ).
tcf(c_2722,plain,
v14_lattices(k1_lattice2(sK1)),
inference(global_subsumption_just,[status(thm)],[c_2721,c_54,c_53,c_52,c_2721]) ).
tcf(c_3133,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 != sK2 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_2610]) ).
tcf(c_3134,plain,
( v3_struct_0(sK1)
| m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1) ),
inference(unflattening,[status(thm)],[c_3133]) ).
tcf(c_3135,plain,
m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1))),
inference(global_subsumption_just,[status(thm)],[c_3134,c_54,c_53,c_52,c_3134]) ).
tcf(c_3140,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 != sK2 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_189]) ).
tcf(c_3141,plain,
( v3_struct_0(sK1)
| ( k7_filter_2(sK1,sK2) = k15_filter_2(sK1,sK2) )
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1) ),
inference(unflattening,[status(thm)],[c_3140]) ).
tcf(c_3142,plain,
k7_filter_2(sK1,sK2) = k15_filter_2(sK1,sK2),
inference(global_subsumption_just,[status(thm)],[c_3141,c_54,c_53,c_52,c_3141]) ).
tcf(c_3154,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 != sK2 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_73]) ).
tcf(c_3155,plain,
( v3_struct_0(sK1)
| m1_filter_2(k15_filter_2(sK1,sK2),k1_lattice2(sK1))
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1) ),
inference(unflattening,[status(thm)],[c_3154]) ).
tcf(c_3156,plain,
m1_filter_2(k15_filter_2(sK1,sK2),k1_lattice2(sK1)),
inference(global_subsumption_just,[status(thm)],[c_3155,c_54,c_53,c_52,c_3155]) ).
tcf(c_3241,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X3)
| v3_struct_0(X2)
| r2_hidden(k6_lattices(X3),X1)
| ~ v14_lattices(X3)
| ~ l3_lattices(X3)
| ~ l3_lattices(X2)
| ~ v10_lattices(X3)
| ~ v10_lattices(X2)
| ~ m1_filter_2(X0,X2)
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_191,c_195]) ).
tcf(c_3242,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| r2_hidden(k6_lattices(X1),X0)
| ~ v14_lattices(X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_filter_2(X0,X1) ),
inference(unflattening,[status(thm)],[c_3241]) ).
tcf(c_3422,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| r2_hidden(k6_lattices(X0),X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m1_filter_2(X1,X0)
| ( k1_lattice2(sK1) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_3242,c_2722]) ).
tcf(c_3423,plain,
! [X0: $i] :
( v3_struct_0(k1_lattice2(sK1))
| r2_hidden(k6_lattices(k1_lattice2(sK1)),X0)
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1))
| ~ m1_filter_2(X0,k1_lattice2(sK1)) ),
inference(unflattening,[status(thm)],[c_3422]) ).
tcf(c_4452,plain,
m1_filter_2(k7_filter_2(sK1,sK2),k1_lattice2(sK1)),
inference(demodulation,[status(thm)],[c_3156,c_3142]) ).
tcf(c_4719,plain,
! [X0: $i] :
( v3_struct_0(k1_lattice2(sK1))
| r2_hidden(k5_lattices(sK1),X0)
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1))
| ~ m1_filter_2(X0,k1_lattice2(sK1)) ),
inference(light_normalisation,[status(thm)],[c_3423,c_2715]) ).
tcf(c_5258,plain,
! [X0: $i] :
( ~ iPr_def_10
| r2_hidden(k5_lattices(sK1),X0)
| ~ m1_filter_2(X0,k1_lattice2(sK1)) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_4719]) ).
tcf(c_5259,plain,
( iPr_def_10
| v3_struct_0(k1_lattice2(sK1))
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1)) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_4719]) ).
tcf(c_5260,definition,
iPr_def_11 = k1_lattice2(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_5261,definition,
iPr_def_12 = k5_lattices(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_5263,definition,
iPr_def_14 = k7_filter_2(sK1,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_5265,definition,
iPr_def_16 = u1_struct_0(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_5266,definition,
iPr_def_17 = k1_zfmisc_1(iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_5268,plain,
( iPr_def_10
| v3_struct_0(iPr_def_11)
| ~ l3_lattices(iPr_def_11)
| ~ v10_lattices(iPr_def_11) ),
inference(demodulation,[status(thm)],[c_5259,c_5260]) ).
tcf(c_5269,plain,
! [X0: $i] :
( r2_hidden(iPr_def_12,X0)
| ~ iPr_def_10
| ~ m1_filter_2(X0,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_5258,c_5261]) ).
tcf(c_5271,plain,
m1_filter_2(iPr_def_14,iPr_def_11),
inference(demodulation,[status(thm)],[c_4452,c_5263]) ).
tcf(c_5274,plain,
m1_subset_1(sK2,iPr_def_17),
inference(demodulation,[status(thm)],[c_3135,c_5265,c_5266]) ).
tcf(c_5277,negated_conjecture,
l3_lattices(sK1),
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_5278,negated_conjecture,
v10_lattices(sK1),
inference(demodulation,[status(thm)],[c_53]) ).
tcf(c_5279,negated_conjecture,
~ v3_struct_0(sK1),
inference(demodulation,[status(thm)],[c_52]) ).
tcf(c_5280,negated_conjecture,
~ r2_hidden(iPr_def_12,sK2),
inference(demodulation,[status(thm)],[c_49]) ).
tcf(c_6864,plain,
( r2_hidden(iPr_def_12,iPr_def_14)
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_5271,c_5269]) ).
tcf(c_6944,plain,
( l3_lattices(iPr_def_11)
| ~ l3_lattices(sK1) ),
inference(superposition,[status(thm)],[c_5260,c_75]) ).
tcf(c_6945,plain,
l3_lattices(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_6944,c_5277]) ).
tcf(c_7069,plain,
( v3_struct_0(sK1)
| ~ l3_lattices(sK1)
| ~ v3_struct_0(iPr_def_11) ),
inference(superposition,[status(thm)],[c_5260,c_109]) ).
tcf(c_7070,plain,
~ v3_struct_0(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_7069,c_5279,c_5277]) ).
tcf(c_7306,plain,
! [X0: $i] :
( v3_struct_0(sK1)
| ( k7_filter_2(sK1,X0) = X0 )
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| ~ m1_subset_1(X0,k1_zfmisc_1(iPr_def_16)) ),
inference(superposition,[status(thm)],[c_5265,c_70]) ).
tcf(c_7319,plain,
! [X0: $i] :
( v3_struct_0(sK1)
| ( k7_filter_2(sK1,X0) = X0 )
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| ~ m1_subset_1(X0,iPr_def_17) ),
inference(light_normalisation,[status(thm)],[c_7306,c_5266]) ).
tcf(c_7320,plain,
! [X0: $i] :
( ( k7_filter_2(sK1,X0) = X0 )
| ~ m1_subset_1(X0,iPr_def_17) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7319,c_5279,c_5277,c_5278]) ).
tcf(c_7489,plain,
k7_filter_2(sK1,sK2) = sK2,
inference(superposition,[status(thm)],[c_5274,c_7320]) ).
tcf(c_7492,plain,
sK2 = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_7489,c_5263]) ).
tcf(c_7499,plain,
~ r2_hidden(iPr_def_12,iPr_def_14),
inference(demodulation,[status(thm)],[c_5280,c_7492]) ).
fof(f202,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(f203,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| sP0(X0) ),
inference(definition_folding,[],[f174,f202]) ).
fof(f216,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,[],[f202]) ).
fof(f320,plain,
! [X0] :
( ~ sP0(X0)
| v10_lattices(k1_lattice2(X0)) ),
inference(cnf_transformation,[],[f216]) ).
tcf(c_137,plain,
! [X0: $i] :
( v10_lattices(k1_lattice2(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f320]) ).
tcf(c_393,plain,
! [X0: $i] :
( v10_lattices(k1_lattice2(X0))
| ~ sP0(X0) ),
inference(prop_impl_just,[status(thm)],[c_137]) ).
tcf(c_3031,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_138,c_393]) ).
tcf(c_3032,plain,
! [X0: $i] :
( v3_struct_0(X0)
| v10_lattices(k1_lattice2(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0) ),
inference(unflattening,[status(thm)],[c_3031]) ).
tcf(c_6906,plain,
( v10_lattices(iPr_def_11)
| v3_struct_0(sK1)
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1) ),
inference(superposition,[status(thm)],[c_5260,c_3032]) ).
tcf(c_6908,plain,
v10_lattices(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_6906,c_5279,c_5277,c_5278]) ).
tcf(c_6911,plain,
( iPr_def_10
| v3_struct_0(iPr_def_11)
| ~ l3_lattices(iPr_def_11) ),
inference(backward_subsumption_resolution,[status(thm)],[c_5268,c_6908]) ).
tcf(c_6946,plain,
( iPr_def_10
| v3_struct_0(iPr_def_11) ),
inference(backward_subsumption_resolution,[status(thm)],[c_6911,c_6945]) ).
tcf(c_7073,plain,
iPr_def_10,
inference(backward_subsumption_resolution,[status(thm)],[c_6946,c_7070]) ).
tcf(c_7075,plain,
r2_hidden(iPr_def_12,iPr_def_14),
inference(backward_subsumption_resolution,[status(thm)],[c_6864,c_7073]) ).
tcf(c_7500,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_7499,c_7075]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LAT301+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.41 % Computer : n013.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Wed Sep 23 20:55:52 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.47 Running first-order theorem proving
% 0.15/0.47 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
% 0.15/0.49
% 0.15/0.49 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.49
% 0.15/0.49 % Detected problem language: tptp
% 0.23/0.51 % Proving...
% 4.82/1.40 % SZS status Started for theBenchmark.p
% 4.82/1.40 % SZS status Theorem for theBenchmark.p
% 4.82/1.40
% 4.82/1.40 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.82/1.40
% 4.82/1.40 % ------ iProver source info
% 4.82/1.40
% 4.82/1.40 % git: date: 2026-07-19 20:42:38 +0200
% 4.82/1.40 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.82/1.40 % git: non_committed_changes: false
% 4.82/1.40
% 4.82/1.40 % ------ Parsing...
% 4.82/1.40 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.82/1.40
% 4.82/1.40 % ------ 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: 5 sf_s rm: 18 0s sf_e pe_s pe_e %
% 4.82/1.40
% 4.82/1.40 % ------ Preprocessing... gs_s sp: 1 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.82/1.40
% 4.82/1.40 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.82/1.40 % ------ Proving...
% 4.82/1.40 % ------ Problem Properties
% 4.82/1.40
% 4.82/1.40 %
% 4.82/1.40 % clauses 134
% 4.82/1.40 % conjectures 4
% 4.82/1.40 % EPR 42
% 4.82/1.40 % Horn 105
% 4.82/1.40 % unary 61
% 4.82/1.40 % binary 32
% 4.82/1.40 % lits 307
% 4.82/1.40 % lits eq 29
% 4.82/1.40 % fd_pure 0
% 4.82/1.40 % fd_pseudo 0
% 4.82/1.40 % fd_cond 1
% 4.82/1.40 % fd_pseudo_cond 4
% 4.82/1.40 % AC symbols 0
% 4.82/1.40
% 4.82/1.40 % ------ Schedule dynamic 5 is on
% 4.82/1.40
% 4.82/1.40 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.82/1.40
% 4.82/1.40
% 4.82/1.40 % ------
% 4.82/1.40 % Current options:
% 4.82/1.40 % ------
% 4.82/1.40
% 4.82/1.40
% 4.82/1.40 %
% 4.82/1.40
% 4.82/1.40 % ------ Proving...
% 4.82/1.40 %
% 4.82/1.40
% 4.82/1.40 % SZS status Theorem for theBenchmark.p
% 4.82/1.40
% 4.82/1.40 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.82/1.41
% 4.82/1.41
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