%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LAT302+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:59:11 PM UTC 2026
% Result : Theorem 7.85s 1.63s
% Output : CNFRefutation 7.85s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f409ERROR: Could not build tree for root c_13609ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ( v13_lattices(X0)
=> m2_filter_2(k6_domain_1(u1_struct_0(X0),k5_lattices(X0)),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_filter_2) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ( v13_lattices(X0)
=> m2_filter_2(k6_domain_1(u1_struct_0(X0),k5_lattices(X0)),X0) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f15,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(f20,axiom,
! [X0] :
( ( l1_lattices(X0)
& ~ v3_struct_0(X0) )
=> m1_subset_1(k5_lattices(X0),u1_struct_0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_lattices) ).
fof(f22,axiom,
! [X0] :
( ( l2_lattices(X0)
& ~ v3_struct_0(X0) )
=> m1_subset_1(k6_lattices(X0),u1_struct_0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_lattices) ).
fof(f23,axiom,
! [X0] :
( l1_lattices(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).
fof(f26,axiom,
! [X0] :
( l3_lattices(X0)
=> ( l2_lattices(X0)
& l1_lattices(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fc6_lattice2) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',redefinition_m1_filter_2) ).
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/sandbox2/benchmark/theBenchmark.p',t21_filter_2) ).
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/sandbox2/benchmark/theBenchmark.p',t63_lattice2) ).
fof(f91,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(f107,plain,
? [X0] :
( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0)
& v13_lattices(X0)
& ~ m2_filter_2(k6_domain_1(u1_struct_0(X0),k5_lattices(X0)),X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f108,plain,
? [X0] :
( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0)
& v13_lattices(X0)
& ~ m2_filter_2(k6_domain_1(u1_struct_0(X0),k5_lattices(X0)),X0) ),
inference(flattening,[],[f107]) ).
fof(f128,plain,
! [X0] :
( ~ l3_lattices(X0)
| ( l3_lattices(k1_lattice2(X0))
& v3_lattices(k1_lattice2(X0)) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f129,plain,
! [X0] :
( ~ l1_lattices(X0)
| v3_struct_0(X0)
| m1_subset_1(k5_lattices(X0),u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f20]) ).
fof(f130,plain,
! [X0] :
( ~ l1_lattices(X0)
| v3_struct_0(X0)
| m1_subset_1(k5_lattices(X0),u1_struct_0(X0)) ),
inference(flattening,[],[f129]) ).
fof(f133,plain,
! [X0] :
( ~ l2_lattices(X0)
| v3_struct_0(X0)
| m1_subset_1(k6_lattices(X0),u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f22]) ).
fof(f134,plain,
! [X0] :
( ~ l2_lattices(X0)
| v3_struct_0(X0)
| m1_subset_1(k6_lattices(X0),u1_struct_0(X0)) ),
inference(flattening,[],[f133]) ).
fof(f135,plain,
! [X0] :
( ~ l1_lattices(X0)
| l1_struct_0(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f137,plain,
! [X0] :
( ~ l3_lattices(X0)
| ( l2_lattices(X0)
& l1_lattices(X0) ) ),
inference(ennf_transformation,[],[f26]) ).
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,[],[f48]) ).
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(f159,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f49]) ).
fof(f160,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(flattening,[],[f159]) ).
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,[],[f60]) ).
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] :
( ~ m1_subset_1(X1,X0)
| v1_xboole_0(X0)
| k6_domain_1(X0,X1) = k1_tarski(X1) ),
inference(ennf_transformation,[],[f78]) ).
fof(f183,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,X0)
| v1_xboole_0(X0)
| k6_domain_1(X0,X1) = k1_tarski(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,[],[f79]) ).
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(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(ennf_transformation,[],[f84]) ).
fof(f190,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,[],[f189]) ).
fof(f197,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(f198,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ( v13_lattices(X0)
<=> v14_lattices(k1_lattice2(X0)) ) ),
inference(flattening,[],[f197]) ).
fof(f200,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,[],[f91]) ).
fof(f201,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,[],[f200]) ).
fof(f206,plain,
( l3_lattices(sK1)
& v10_lattices(sK1)
& ~ v3_struct_0(sK1)
& v13_lattices(sK1)
& ~ m2_filter_2(k6_domain_1(u1_struct_0(sK1),k5_lattices(sK1)),sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f108]) ).
fof(f235,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(f237,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,[],[f190]) ).
fof(f238,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,[],[f198]) ).
fof(f239,plain,
l3_lattices(sK1),
inference(cnf_transformation,[],[f206]) ).
fof(f240,plain,
v10_lattices(sK1),
inference(cnf_transformation,[],[f206]) ).
fof(f241,plain,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f206]) ).
fof(f242,plain,
v13_lattices(sK1),
inference(cnf_transformation,[],[f206]) ).
fof(f243,plain,
~ m2_filter_2(k6_domain_1(u1_struct_0(sK1),k5_lattices(sK1)),sK1),
inference(cnf_transformation,[],[f206]) ).
fof(f268,plain,
! [X0] :
( ~ l3_lattices(X0)
| l3_lattices(k1_lattice2(X0)) ),
inference(cnf_transformation,[],[f128]) ).
fof(f270,plain,
! [X0] :
( ~ l1_lattices(X0)
| v3_struct_0(X0)
| m1_subset_1(k5_lattices(X0),u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f130]) ).
fof(f272,plain,
! [X0] :
( ~ l2_lattices(X0)
| v3_struct_0(X0)
| m1_subset_1(k6_lattices(X0),u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f134]) ).
fof(f273,plain,
! [X0] :
( ~ l1_lattices(X0)
| l1_struct_0(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f275,plain,
! [X0] :
( ~ l3_lattices(X0)
| l2_lattices(X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f276,plain,
! [X0] :
( ~ l3_lattices(X0)
| l1_lattices(X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f303,plain,
! [X0] :
( ~ l3_lattices(X0)
| v3_struct_0(X0)
| ~ v3_struct_0(k1_lattice2(X0)) ),
inference(cnf_transformation,[],[f158]) ).
fof(f304,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f160]) ).
fof(f334,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| sP0(X0) ),
inference(cnf_transformation,[],[f205]) ).
fof(f389,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,X0)
| v1_xboole_0(X0)
| k6_domain_1(X0,X1) = k1_tarski(X1) ),
inference(cnf_transformation,[],[f183]) ).
fof(f391,plain,
! [X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_filter_0(X1,X0)
| m1_filter_2(X1,X0) ),
inference(cnf_transformation,[],[f235]) ).
fof(f398,plain,
! [X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_filter_2(X1,k1_lattice2(X0))
| m2_filter_2(X1,X0) ),
inference(cnf_transformation,[],[f237]) ).
fof(f403,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ v13_lattices(X0)
| v14_lattices(k1_lattice2(X0)) ),
inference(cnf_transformation,[],[f238]) ).
fof(f406,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,[],[f201]) ).
tcf(c_49,negated_conjecture,
~ m2_filter_2(k6_domain_1(u1_struct_0(sK1),k5_lattices(sK1)),sK1),
inference(cnf_transformation,[],[f243]) ).
tcf(c_50,negated_conjecture,
v13_lattices(sK1),
inference(cnf_transformation,[],[f242]) ).
tcf(c_51,negated_conjecture,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f241]) ).
tcf(c_52,negated_conjecture,
v10_lattices(sK1),
inference(cnf_transformation,[],[f240]) ).
tcf(c_53,negated_conjecture,
l3_lattices(sK1),
inference(cnf_transformation,[],[f239]) ).
tcf(c_73,plain,
! [X0: $i] :
( l3_lattices(k1_lattice2(X0))
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f268]) ).
tcf(c_74,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m1_subset_1(k5_lattices(X0),u1_struct_0(X0))
| ~ l1_lattices(X0) ),
inference(cnf_transformation,[],[f270]) ).
tcf(c_76,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m1_subset_1(k6_lattices(X0),u1_struct_0(X0))
| ~ l2_lattices(X0) ),
inference(cnf_transformation,[],[f272]) ).
tcf(c_77,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l1_lattices(X0) ),
inference(cnf_transformation,[],[f273]) ).
tcf(c_79,plain,
! [X0: $i] :
( l1_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f276]) ).
tcf(c_80,plain,
! [X0: $i] :
( l2_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f275]) ).
tcf(c_106,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v3_struct_0(k1_lattice2(X0)) ),
inference(cnf_transformation,[],[f303]) ).
tcf(c_108,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ l1_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f304]) ).
tcf(c_138,plain,
! [X0: $i] :
( sP0(X0)
| v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0) ),
inference(cnf_transformation,[],[f334]) ).
tcf(c_193,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,[],[f389]) ).
tcf(c_194,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m1_filter_2(X0,X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_filter_0(X0,X1) ),
inference(cnf_transformation,[],[f391]) ).
tcf(c_199,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m1_filter_0(k6_domain_1(u1_struct_0(X0),k6_lattices(X0)),X0)
| ~ v14_lattices(X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0) ),
inference(cnf_transformation,[],[f409]) ).
tcf(c_201,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m2_filter_2(X0,X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_filter_2(X0,k1_lattice2(X1)) ),
inference(cnf_transformation,[],[f398]) ).
tcf(c_208,plain,
! [X0: $i] :
( v3_struct_0(X0)
| v14_lattices(k1_lattice2(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ v13_lattices(X0) ),
inference(cnf_transformation,[],[f403]) ).
tcf(c_210,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,[],[f406]) ).
tcf(c_329,plain,
! [X0: $i] :
( l1_lattices(X0)
| ~ l3_lattices(X0) ),
inference(prop_impl_just,[status(thm)],[c_79]) ).
tcf(c_331,plain,
! [X0: $i] :
( l2_lattices(X0)
| ~ l3_lattices(X0) ),
inference(prop_impl_just,[status(thm)],[c_80]) ).
tcf(c_357,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l1_lattices(X0) ),
inference(prop_impl_just,[status(thm)],[c_77]) ).
tcf(c_2234,plain,
! [X0: $i,X1: $i] :
( l1_struct_0(X1)
| ~ l3_lattices(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_329,c_357]) ).
tcf(c_2235,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l3_lattices(X0) ),
inference(unflattening,[status(thm)],[c_2234]) ).
tcf(c_2243,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m1_subset_1(k5_lattices(X1),u1_struct_0(X1))
| ~ l3_lattices(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_329,c_74]) ).
tcf(c_2244,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m1_subset_1(k5_lattices(X0),u1_struct_0(X0))
| ~ l3_lattices(X0) ),
inference(unflattening,[status(thm)],[c_2243]) ).
tcf(c_2346,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m1_subset_1(k6_lattices(X1),u1_struct_0(X1))
| ~ l3_lattices(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_331,c_76]) ).
tcf(c_2347,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m1_subset_1(k6_lattices(X0),u1_struct_0(X0))
| ~ l3_lattices(X0) ),
inference(unflattening,[status(thm)],[c_2346]) ).
tcf(c_2700,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_210]) ).
tcf(c_2701,plain,
( v3_struct_0(sK1)
| ( k6_lattices(k1_lattice2(sK1)) = k5_lattices(sK1) )
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1) ),
inference(unflattening,[status(thm)],[c_2700]) ).
tcf(c_2702,plain,
k6_lattices(k1_lattice2(sK1)) = k5_lattices(sK1),
inference(global_subsumption_just,[status(thm)],[c_2701,c_53,c_52,c_51,c_2701]) ).
tcf(c_2707,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_208]) ).
tcf(c_2708,plain,
( v3_struct_0(sK1)
| v14_lattices(k1_lattice2(sK1))
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1) ),
inference(unflattening,[status(thm)],[c_2707]) ).
tcf(c_2709,plain,
v14_lattices(k1_lattice2(sK1)),
inference(global_subsumption_just,[status(thm)],[c_2708,c_53,c_52,c_51,c_2708]) ).
tcf(c_2858,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_2235,c_108]) ).
tcf(c_2859,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(unflattening,[status(thm)],[c_2858]) ).
tcf(c_3143,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_filter_2(X0,k1_lattice2(X1))
| ( X1 != sK1 )
| ( k6_domain_1(u1_struct_0(sK1),k5_lattices(sK1)) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_201]) ).
tcf(c_3144,plain,
( v3_struct_0(sK1)
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| ~ m1_filter_2(k6_domain_1(u1_struct_0(sK1),k5_lattices(sK1)),k1_lattice2(sK1)) ),
inference(unflattening,[status(thm)],[c_3143]) ).
tcf(c_3145,plain,
~ m1_filter_2(k6_domain_1(u1_struct_0(sK1),k5_lattices(sK1)),k1_lattice2(sK1)),
inference(global_subsumption_just,[status(thm)],[c_3144,c_53,c_52,c_51,c_3144]) ).
tcf(c_3277,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X2)
| v3_struct_0(X0)
| m1_filter_2(X1,X2)
| ~ v14_lattices(X0)
| ~ l3_lattices(X2)
| ~ l3_lattices(X0)
| ~ v10_lattices(X2)
| ~ v10_lattices(X0)
| ( X0 != X2 )
| ( k6_domain_1(u1_struct_0(X0),k6_lattices(X0)) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_194,c_199]) ).
tcf(c_3278,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m1_filter_2(k6_domain_1(u1_struct_0(X0),k6_lattices(X0)),X0)
| ~ v14_lattices(X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0) ),
inference(unflattening,[status(thm)],[c_3277]) ).
tcf(c_3428,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m1_filter_2(k6_domain_1(u1_struct_0(X0),k6_lattices(X0)),X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ( k1_lattice2(sK1) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_3278,c_2709]) ).
tcf(c_3429,plain,
( v3_struct_0(k1_lattice2(sK1))
| m1_filter_2(k6_domain_1(u1_struct_0(k1_lattice2(sK1)),k6_lattices(k1_lattice2(sK1))),k1_lattice2(sK1))
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1)) ),
inference(unflattening,[status(thm)],[c_3428]) ).
tcf(c_4858,plain,
( v3_struct_0(k1_lattice2(sK1))
| m1_filter_2(k6_domain_1(u1_struct_0(k1_lattice2(sK1)),k5_lattices(sK1)),k1_lattice2(sK1))
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1)) ),
inference(light_normalisation,[status(thm)],[c_3429,c_2702]) ).
tcf(c_5484,definition,
iPr_def_10 = k1_lattice2(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_5485,definition,
iPr_def_11 = u1_struct_0(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_5486,definition,
iPr_def_12 = k5_lattices(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_5487,definition,
iPr_def_13 = k6_domain_1(iPr_def_11,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_5489,definition,
iPr_def_15 = u1_struct_0(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_5490,definition,
iPr_def_16 = k6_domain_1(iPr_def_15,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_5492,definition,
iPr_def_18 = k6_lattices(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_5494,plain,
( v3_struct_0(iPr_def_10)
| m1_filter_2(iPr_def_13,iPr_def_10)
| ~ l3_lattices(iPr_def_10)
| ~ v10_lattices(iPr_def_10) ),
inference(demodulation,[status(thm)],[c_4858]) ).
tcf(c_5497,plain,
~ m1_filter_2(iPr_def_16,iPr_def_10),
inference(demodulation,[status(thm)],[c_3145]) ).
tcf(c_5499,plain,
iPr_def_18 = iPr_def_12,
inference(demodulation,[status(thm)],[c_2702,c_5492]) ).
tcf(c_5500,negated_conjecture,
l3_lattices(sK1),
inference(demodulation,[status(thm)],[c_53]) ).
tcf(c_5501,negated_conjecture,
v10_lattices(sK1),
inference(demodulation,[status(thm)],[c_52]) ).
tcf(c_5502,negated_conjecture,
~ v3_struct_0(sK1),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_7128,plain,
k6_lattices(iPr_def_10) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_5492,c_5499]) ).
tcf(c_7139,plain,
( l3_lattices(iPr_def_10)
| ~ l3_lattices(sK1) ),
inference(superposition,[status(thm)],[c_5484,c_73]) ).
tcf(c_7140,plain,
l3_lattices(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_7139,c_5500]) ).
tcf(c_7254,plain,
( v3_struct_0(sK1)
| ~ l3_lattices(sK1)
| ~ v3_struct_0(iPr_def_10) ),
inference(superposition,[status(thm)],[c_5484,c_106]) ).
tcf(c_7255,plain,
~ v3_struct_0(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_7254,c_5502,c_5500]) ).
tcf(c_7459,plain,
( v3_struct_0(sK1)
| m1_subset_1(k5_lattices(sK1),iPr_def_15)
| ~ l3_lattices(sK1) ),
inference(superposition,[status(thm)],[c_5489,c_2244]) ).
tcf(c_7463,plain,
( v3_struct_0(sK1)
| m1_subset_1(iPr_def_12,iPr_def_15)
| ~ l3_lattices(sK1) ),
inference(light_normalisation,[status(thm)],[c_7459,c_5486]) ).
tcf(c_7464,plain,
m1_subset_1(iPr_def_12,iPr_def_15),
inference(forward_subsumption_resolution,[status(thm)],[c_7463,c_5502,c_5500]) ).
tcf(c_7580,plain,
( v1_xboole_0(iPr_def_15)
| ( k6_domain_1(iPr_def_15,iPr_def_12) = k1_tarski(iPr_def_12) ) ),
inference(superposition,[status(thm)],[c_7464,c_193]) ).
tcf(c_7584,plain,
( v1_xboole_0(iPr_def_15)
| ( k1_tarski(iPr_def_12) = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_7580,c_5490]) ).
tcf(c_9639,plain,
( v3_struct_0(sK1)
| ~ v1_xboole_0(iPr_def_15)
| ~ l3_lattices(sK1) ),
inference(superposition,[status(thm)],[c_5489,c_2859]) ).
tcf(c_9640,plain,
( v3_struct_0(iPr_def_10)
| ~ v1_xboole_0(iPr_def_11)
| ~ l3_lattices(iPr_def_10) ),
inference(superposition,[status(thm)],[c_5485,c_2859]) ).
tcf(c_9641,plain,
~ v1_xboole_0(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_9640,c_7255,c_7140]) ).
tcf(c_9642,plain,
~ v1_xboole_0(iPr_def_15),
inference(forward_subsumption_resolution,[status(thm)],[c_9639,c_5502,c_5500]) ).
tcf(c_9653,plain,
k1_tarski(iPr_def_12) = iPr_def_16,
inference(backward_subsumption_resolution,[status(thm)],[c_7584,c_9642]) ).
tcf(c_13538,plain,
( v3_struct_0(iPr_def_10)
| m1_subset_1(k6_lattices(iPr_def_10),iPr_def_11)
| ~ l3_lattices(iPr_def_10) ),
inference(superposition,[status(thm)],[c_5485,c_2347]) ).
tcf(c_13541,plain,
( v3_struct_0(iPr_def_10)
| m1_subset_1(iPr_def_12,iPr_def_11)
| ~ l3_lattices(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_13538,c_7128]) ).
tcf(c_13542,plain,
m1_subset_1(iPr_def_12,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_13541,c_7255,c_7140]) ).
tcf(c_13578,plain,
( v1_xboole_0(iPr_def_11)
| ( k6_domain_1(iPr_def_11,iPr_def_12) = k1_tarski(iPr_def_12) ) ),
inference(superposition,[status(thm)],[c_13542,c_193]) ).
tcf(c_13581,plain,
( v1_xboole_0(iPr_def_11)
| ( iPr_def_13 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_13578,c_5487,c_9653]) ).
tcf(c_13582,plain,
iPr_def_13 = iPr_def_16,
inference(forward_subsumption_resolution,[status(thm)],[c_13581,c_9641]) ).
tcf(c_13608,plain,
~ m1_filter_2(iPr_def_13,iPr_def_10),
inference(demodulation,[status(thm)],[c_5497,c_13582]) ).
fof(f204,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(f205,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| sP0(X0) ),
inference(definition_folding,[],[f174,f204]) ).
fof(f218,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,[],[f204]) ).
fof(f325,plain,
! [X0] :
( ~ sP0(X0)
| v10_lattices(k1_lattice2(X0)) ),
inference(cnf_transformation,[],[f218]) ).
tcf(c_137,plain,
! [X0: $i] :
( v10_lattices(k1_lattice2(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f325]) ).
tcf(c_405,plain,
! [X0: $i] :
( v10_lattices(k1_lattice2(X0))
| ~ sP0(X0) ),
inference(prop_impl_just,[status(thm)],[c_137]) ).
tcf(c_3003,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_405]) ).
tcf(c_3004,plain,
! [X0: $i] :
( v3_struct_0(X0)
| v10_lattices(k1_lattice2(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0) ),
inference(unflattening,[status(thm)],[c_3003]) ).
tcf(c_7083,plain,
( v10_lattices(iPr_def_10)
| v3_struct_0(sK1)
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1) ),
inference(superposition,[status(thm)],[c_5484,c_3004]) ).
tcf(c_7084,plain,
v10_lattices(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_7083,c_5502,c_5500,c_5501]) ).
tcf(c_7087,plain,
( v3_struct_0(iPr_def_10)
| m1_filter_2(iPr_def_13,iPr_def_10)
| ~ l3_lattices(iPr_def_10) ),
inference(backward_subsumption_resolution,[status(thm)],[c_5494,c_7084]) ).
tcf(c_7142,plain,
( v3_struct_0(iPr_def_10)
| m1_filter_2(iPr_def_13,iPr_def_10) ),
inference(backward_subsumption_resolution,[status(thm)],[c_7087,c_7140]) ).
tcf(c_7257,plain,
m1_filter_2(iPr_def_13,iPr_def_10),
inference(backward_subsumption_resolution,[status(thm)],[c_7142,c_7255]) ).
tcf(c_13609,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_13608,c_7257]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT302+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 21:01:58 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.42 % Proving...
% 7.85/1.63 % SZS status Started for theBenchmark.p
% 7.85/1.63 % SZS status Theorem for theBenchmark.p
% 7.85/1.63
% 7.85/1.63 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.85/1.63
% 7.85/1.63 % ------ iProver source info
% 7.85/1.63
% 7.85/1.63 % git: date: 2026-07-19 20:42:38 +0200
% 7.85/1.63 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.85/1.63 % git: non_committed_changes: false
% 7.85/1.63
% 7.85/1.63 % ------ Parsing...
% 7.85/1.63 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.85/1.63
% 7.85/1.63 % ------ 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: 6 sf_s rm: 19 0s sf_e pe_s pe_e %
% 7.85/1.63
% 7.85/1.63 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.85/1.63
% 7.85/1.63 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.85/1.63 % ------ Proving...
% 7.85/1.63 % ------ Problem Properties
% 7.85/1.63
% 7.85/1.63 %
% 7.85/1.63 % clauses 139
% 7.85/1.63 % conjectures 3
% 7.85/1.63 % EPR 42
% 7.85/1.63 % Horn 111
% 7.85/1.63 % unary 68
% 7.85/1.63 % binary 30
% 7.85/1.63 % lits 307
% 7.85/1.63 % lits eq 31
% 7.85/1.63 % fd_pure 0
% 7.85/1.63 % fd_pseudo 0
% 7.85/1.63 % fd_cond 1
% 7.85/1.63 % fd_pseudo_cond 4
% 7.85/1.63 % AC symbols 0
% 7.85/1.63
% 7.85/1.63 % ------ Schedule dynamic 5 is on
% 7.85/1.63
% 7.85/1.63 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.85/1.63
% 7.85/1.63
% 7.85/1.63 % ------
% 7.85/1.63 % Current options:
% 7.85/1.63 % ------
% 7.85/1.63
% 7.85/1.63
% 7.85/1.63 %
% 7.85/1.63
% 7.85/1.63 % ------ Proving...
% 7.85/1.63 %
% 7.85/1.63
% 7.85/1.63 % SZS status Theorem for theBenchmark.p
% 7.85/1.63
% 7.85/1.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.85/1.63
% 7.85/1.63
%------------------------------------------------------------------------------