%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LAT309+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 : n003.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 01:59:13 PM UTC 2026
% Result : Theorem 115.26s 39.17s
% Output : CNFRefutation 115.26s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f436ERROR: Could not build tree for root c_89433ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ~ ( ! [X2] :
( m2_filter_2(X2,X0)
=> ~ ( r2_filter_2(X0,X2)
& r2_hidden(X1,X2) ) )
& X1 != k6_lattices(X0)
& v14_lattices(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_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))
=> ~ ( ! [X2] :
( m2_filter_2(X2,X0)
=> ~ ( r2_filter_2(X0,X2)
& r2_hidden(X1,X2) ) )
& X1 != k6_lattices(X0)
& v14_lattices(X0) ) ) ),
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,u1_struct_0(X0))
=> k5_filter_2(X0,X1) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_filter_2) ).
fof(f14,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] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k1_lattice2(X0))))
=> k8_filter_2(X0,X1) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_filter_2) ).
fof(f17,axiom,
! [X0,X1] :
( ( m1_filter_0(X1,k1_lattice2(X0))
& l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> m2_filter_2(k14_filter_2(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k14_filter_2) ).
fof(f19,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(f23,axiom,
! [X0,X1] :
( ( m1_subset_1(X1,u1_struct_0(X0))
& l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> m1_subset_1(k5_filter_2(X0,X1),u1_struct_0(k1_lattice2(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_filter_2) ).
fof(f27,axiom,
! [X0,X1] :
( ( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k1_lattice2(X0))))
& l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> m1_subset_1(k8_filter_2(X0,X1),k1_zfmisc_1(u1_struct_0(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_filter_2) ).
fof(f32,axiom,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_filter_0(X1,X0)
=> ( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
& ~ v1_xboole_0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_filter_0) ).
fof(f54,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(f65,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(f81,axiom,
! [X0,X1] :
( ( m1_filter_0(X1,k1_lattice2(X0))
& l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> k14_filter_2(X0,X1) = k8_filter_2(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k14_filter_2) ).
fof(f82,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(f89,axiom,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m2_filter_2(X1,X0)
=> ( r2_filter_2(X0,X1)
<=> v1_filter_0(k15_filter_2(X0,X1),k1_lattice2(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_filter_2) ).
fof(f93,axiom,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ( v14_lattices(X0)
<=> v13_lattices(k1_lattice2(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_lattice2) ).
fof(f95,axiom,
! [X0] :
( ( l3_lattices(X0)
& v14_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> k6_lattices(X0) = k5_lattices(k1_lattice2(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_lattice2) ).
fof(f110,plain,
? [X0] :
( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
& ! [X2] :
( ~ m2_filter_2(X2,X0)
| ~ r2_filter_2(X0,X2)
| ~ r2_hidden(X1,X2) )
& X1 != k6_lattices(X0)
& v14_lattices(X0) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f111,plain,
? [X0] :
( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
& ! [X2] :
( ~ m2_filter_2(X2,X0)
| ~ r2_filter_2(X0,X2)
| ~ r2_hidden(X1,X2) )
& X1 != k6_lattices(X0)
& v14_lattices(X0) ) ),
inference(flattening,[],[f110]) ).
fof(f128,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,[],[f13]) ).
fof(f129,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,[],[f128]) ).
fof(f130,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,[],[f14]) ).
fof(f131,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,[],[f130]) ).
fof(f132,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k1_lattice2(X0))))
| k8_filter_2(X0,X1) = X1 ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f133,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k1_lattice2(X0))))
| k8_filter_2(X0,X1) = X1 ) ),
inference(flattening,[],[f132]) ).
fof(f136,plain,
! [X0,X1] :
( ~ m1_filter_0(X1,k1_lattice2(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| m2_filter_2(k14_filter_2(X0,X1),X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f137,plain,
! [X0,X1] :
( ~ m1_filter_0(X1,k1_lattice2(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| m2_filter_2(k14_filter_2(X0,X1),X0) ),
inference(flattening,[],[f136]) ).
fof(f140,plain,
! [X0] :
( ~ l3_lattices(X0)
| ( l3_lattices(k1_lattice2(X0))
& v3_lattices(k1_lattice2(X0)) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f141,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,[],[f23]) ).
fof(f142,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,[],[f141]) ).
fof(f149,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k1_lattice2(X0))))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| m1_subset_1(k8_filter_2(X0,X1),k1_zfmisc_1(u1_struct_0(X0))) ),
inference(ennf_transformation,[],[f27]) ).
fof(f150,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k1_lattice2(X0))))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| m1_subset_1(k8_filter_2(X0,X1),k1_zfmisc_1(u1_struct_0(X0))) ),
inference(flattening,[],[f149]) ).
fof(f154,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_filter_0(X1,X0)
| ( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
& ~ v1_xboole_0(X1) ) ) ),
inference(ennf_transformation,[],[f32]) ).
fof(f155,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_filter_0(X1,X0)
| ( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
& ~ v1_xboole_0(X1) ) ) ),
inference(flattening,[],[f154]) ).
fof(f175,plain,
! [X0] :
( ~ l3_lattices(X0)
| v3_struct_0(X0)
| ( v3_lattices(k1_lattice2(X0))
& ~ v3_struct_0(k1_lattice2(X0)) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f176,plain,
! [X0] :
( ~ l3_lattices(X0)
| v3_struct_0(X0)
| ( v3_lattices(k1_lattice2(X0))
& ~ v3_struct_0(k1_lattice2(X0)) ) ),
inference(flattening,[],[f175]) ).
fof(f193,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,[],[f65]) ).
fof(f194,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,[],[f193]) ).
fof(f202,plain,
! [X0,X1] :
( ~ m1_filter_0(X1,k1_lattice2(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| k14_filter_2(X0,X1) = k8_filter_2(X0,X1) ),
inference(ennf_transformation,[],[f81]) ).
fof(f203,plain,
! [X0,X1] :
( ~ m1_filter_0(X1,k1_lattice2(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| k14_filter_2(X0,X1) = k8_filter_2(X0,X1) ),
inference(flattening,[],[f202]) ).
fof(f204,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,[],[f82]) ).
fof(f205,plain,
! [X0,X1] :
( ~ m2_filter_2(X1,X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| k15_filter_2(X0,X1) = k7_filter_2(X0,X1) ),
inference(flattening,[],[f204]) ).
fof(f213,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_filter_2(X1,X0)
| ( r2_filter_2(X0,X1)
<=> v1_filter_0(k15_filter_2(X0,X1),k1_lattice2(X0)) ) ) ),
inference(ennf_transformation,[],[f89]) ).
fof(f214,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_filter_2(X1,X0)
| ( r2_filter_2(X0,X1)
<=> v1_filter_0(k15_filter_2(X0,X1),k1_lattice2(X0)) ) ) ),
inference(flattening,[],[f213]) ).
fof(f219,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ( v14_lattices(X0)
<=> v13_lattices(k1_lattice2(X0)) ) ),
inference(ennf_transformation,[],[f93]) ).
fof(f220,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ( v14_lattices(X0)
<=> v13_lattices(k1_lattice2(X0)) ) ),
inference(flattening,[],[f219]) ).
fof(f222,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v14_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| k6_lattices(X0) = k5_lattices(k1_lattice2(X0)) ),
inference(ennf_transformation,[],[f95]) ).
fof(f223,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v14_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| k6_lattices(X0) = k5_lattices(k1_lattice2(X0)) ),
inference(flattening,[],[f222]) ).
fof(f228,plain,
( l3_lattices(sK1)
& v10_lattices(sK1)
& ~ v3_struct_0(sK1)
& m1_subset_1(sK2,u1_struct_0(sK1))
& ! [X2] :
( ~ m2_filter_2(X2,sK1)
| ~ r2_filter_2(sK1,X2)
| ~ r2_hidden(sK2,X2) )
& sK2 != k6_lattices(sK1)
& v14_lattices(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f111]) ).
fof(f258,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_filter_2(X1,X0)
| ( ( ~ r2_filter_2(X0,X1)
| v1_filter_0(k15_filter_2(X0,X1),k1_lattice2(X0)) )
& ( ~ v1_filter_0(k15_filter_2(X0,X1),k1_lattice2(X0))
| r2_filter_2(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f214]) ).
fof(f259,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ( ( ~ v14_lattices(X0)
| v13_lattices(k1_lattice2(X0)) )
& ( ~ v13_lattices(k1_lattice2(X0))
| v14_lattices(X0) ) ) ),
inference(nnf_transformation,[],[f220]) ).
fof(f260,plain,
l3_lattices(sK1),
inference(cnf_transformation,[],[f228]) ).
fof(f261,plain,
v10_lattices(sK1),
inference(cnf_transformation,[],[f228]) ).
fof(f262,plain,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f228]) ).
fof(f263,plain,
m1_subset_1(sK2,u1_struct_0(sK1)),
inference(cnf_transformation,[],[f228]) ).
fof(f264,plain,
! [X2] :
( ~ m2_filter_2(X2,sK1)
| ~ r2_filter_2(sK1,X2)
| ~ r2_hidden(sK2,X2) ),
inference(cnf_transformation,[],[f228]) ).
fof(f265,plain,
sK2 != k6_lattices(sK1),
inference(cnf_transformation,[],[f228]) ).
fof(f266,plain,
v14_lattices(sK1),
inference(cnf_transformation,[],[f228]) ).
fof(f288,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,[],[f129]) ).
fof(f289,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,[],[f131]) ).
fof(f290,plain,
! [X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k1_lattice2(X0))))
| k8_filter_2(X0,X1) = X1 ),
inference(cnf_transformation,[],[f133]) ).
fof(f293,plain,
! [X0,X1] :
( ~ m1_filter_0(X1,k1_lattice2(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| m2_filter_2(k14_filter_2(X0,X1),X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f295,plain,
! [X0] :
( ~ l3_lattices(X0)
| l3_lattices(k1_lattice2(X0)) ),
inference(cnf_transformation,[],[f140]) ).
fof(f297,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,[],[f142]) ).
fof(f301,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k1_lattice2(X0))))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| m1_subset_1(k8_filter_2(X0,X1),k1_zfmisc_1(u1_struct_0(X0))) ),
inference(cnf_transformation,[],[f150]) ).
fof(f306,plain,
! [X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_filter_0(X1,X0)
| m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ),
inference(cnf_transformation,[],[f155]) ).
fof(f333,plain,
! [X0] :
( ~ l3_lattices(X0)
| v3_struct_0(X0)
| ~ v3_struct_0(k1_lattice2(X0)) ),
inference(cnf_transformation,[],[f176]) ).
fof(f362,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| sP0(X0) ),
inference(cnf_transformation,[],[f227]) ).
fof(f413,plain,
! [X0,X1] :
( ~ m1_filter_0(X1,k1_lattice2(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| k8_filter_2(X0,X1) = k14_filter_2(X0,X1) ),
inference(cnf_transformation,[],[f203]) ).
fof(f414,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,[],[f205]) ).
fof(f426,plain,
! [X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m2_filter_2(X1,X0)
| ~ v1_filter_0(k15_filter_2(X0,X1),k1_lattice2(X0))
| r2_filter_2(X0,X1) ),
inference(cnf_transformation,[],[f258]) ).
fof(f430,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ v14_lattices(X0)
| v13_lattices(k1_lattice2(X0)) ),
inference(cnf_transformation,[],[f259]) ).
fof(f433,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v14_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| k6_lattices(X0) = k5_lattices(k1_lattice2(X0)) ),
inference(cnf_transformation,[],[f223]) ).
tcf(c_49,negated_conjecture,
v14_lattices(sK1),
inference(cnf_transformation,[],[f266]) ).
tcf(c_50,negated_conjecture,
k6_lattices(sK1) != sK2,
inference(cnf_transformation,[],[f265]) ).
tcf(c_51,negated_conjecture,
! [X0: $i] :
( ~ m2_filter_2(X0,sK1)
| ~ r2_filter_2(sK1,X0)
| ~ r2_hidden(sK2,X0) ),
inference(cnf_transformation,[],[f264]) ).
tcf(c_52,negated_conjecture,
m1_subset_1(sK2,u1_struct_0(sK1)),
inference(cnf_transformation,[],[f263]) ).
tcf(c_53,negated_conjecture,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f262]) ).
tcf(c_54,negated_conjecture,
v10_lattices(sK1),
inference(cnf_transformation,[],[f261]) ).
tcf(c_55,negated_conjecture,
l3_lattices(sK1),
inference(cnf_transformation,[],[f260]) ).
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,[],[f288]) ).
tcf(c_72,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,[],[f289]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| ( k8_filter_2(X1,X0) = X0 )
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(k1_lattice2(X1)))) ),
inference(cnf_transformation,[],[f290]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m2_filter_2(k14_filter_2(X1,X0),X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_filter_0(X0,k1_lattice2(X1)) ),
inference(cnf_transformation,[],[f293]) ).
tcf(c_79,plain,
! [X0: $i] :
( l3_lattices(k1_lattice2(X0))
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f295]) ).
tcf(c_80,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,[],[f297]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m1_subset_1(k8_filter_2(X1,X0),k1_zfmisc_1(u1_struct_0(X1)))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(k1_lattice2(X1)))) ),
inference(cnf_transformation,[],[f301]) ).
tcf(c_90,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)
| ~ m1_filter_0(X0,X1) ),
inference(cnf_transformation,[],[f306]) ).
tcf(c_115,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v3_struct_0(k1_lattice2(X0)) ),
inference(cnf_transformation,[],[f333]) ).
tcf(c_145,plain,
! [X0: $i] :
( sP0(X0)
| v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0) ),
inference(cnf_transformation,[],[f362]) ).
tcf(c_196,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| ( k8_filter_2(X1,X0) = k14_filter_2(X1,X0) )
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_filter_0(X0,k1_lattice2(X1)) ),
inference(cnf_transformation,[],[f413]) ).
tcf(c_197,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,[],[f414]) ).
tcf(c_204,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| r2_hidden(X0,sK28(X1,X0))
| ( k5_lattices(X1) = X0 )
| ~ v13_lattices(X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f436]) ).
tcf(c_205,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v1_filter_0(sK28(X1,X0),X1)
| ( k5_lattices(X1) = X0 )
| ~ v13_lattices(X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f437]) ).
tcf(c_206,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m1_filter_0(sK28(X1,X0),X1)
| ( k5_lattices(X1) = X0 )
| ~ v13_lattices(X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f438]) ).
tcf(c_208,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| r2_filter_2(X0,X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m2_filter_2(X1,X0)
| ~ v1_filter_0(k15_filter_2(X0,X1),k1_lattice2(X0)) ),
inference(cnf_transformation,[],[f426]) ).
tcf(c_214,plain,
! [X0: $i] :
( v3_struct_0(X0)
| v13_lattices(k1_lattice2(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ v14_lattices(X0) ),
inference(cnf_transformation,[],[f430]) ).
tcf(c_216,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ( k5_lattices(k1_lattice2(X0)) = k6_lattices(X0) )
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ v14_lattices(X0) ),
inference(cnf_transformation,[],[f433]) ).
tcf(c_1705,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X2)
| ~ l3_lattices(X2)
| ~ v10_lattices(X2)
| ~ m2_filter_2(X0,sK1)
| ~ r2_hidden(sK2,X0)
| ~ m2_filter_2(X1,X2)
| ~ v1_filter_0(k15_filter_2(X2,X1),k1_lattice2(X2))
| ( X2 != sK1 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_208]) ).
tcf(c_1706,plain,
! [X0: $i] :
( v3_struct_0(sK1)
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| ~ m2_filter_2(X0,sK1)
| ~ r2_hidden(sK2,X0)
| ~ v1_filter_0(k15_filter_2(sK1,X0),k1_lattice2(sK1)) ),
inference(unflattening,[status(thm)],[c_1705]) ).
tcf(c_1708,plain,
! [X0: $i] :
( ~ v1_filter_0(k15_filter_2(sK1,X0),k1_lattice2(sK1))
| ~ r2_hidden(sK2,X0)
| ~ m2_filter_2(X0,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_1706,c_55,c_54,c_53,c_1706]) ).
tcf(c_1709,plain,
! [X0: $i] :
( ~ m2_filter_2(X0,sK1)
| ~ r2_hidden(sK2,X0)
| ~ v1_filter_0(k15_filter_2(sK1,X0),k1_lattice2(sK1)) ),
inference(renaming,[status(thm)],[c_1708]) ).
tcf(c_1723,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| ( k5_lattices(X0) = X1 )
| ~ v13_lattices(X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m2_filter_2(X2,sK1)
| ~ r2_hidden(sK2,X2)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ( k1_lattice2(sK1) != X0 )
| ( sK28(X0,X1) != k15_filter_2(sK1,X2) ) ),
inference(resolution_lifted,[status(thm)],[c_205,c_1709]) ).
tcf(c_1724,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(k1_lattice2(sK1))
| ( k5_lattices(k1_lattice2(sK1)) = X0 )
| ~ v13_lattices(k1_lattice2(sK1))
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1))
| ~ m2_filter_2(X1,sK1)
| ~ r2_hidden(sK2,X1)
| ~ m1_subset_1(X0,u1_struct_0(k1_lattice2(sK1)))
| ( sK28(k1_lattice2(sK1),X0) != k15_filter_2(sK1,X1) ) ),
inference(unflattening,[status(thm)],[c_1723]) ).
tcf(c_2181,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ( k5_lattices(k1_lattice2(X0)) = k6_lattices(X0) )
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_216]) ).
tcf(c_2182,plain,
( v3_struct_0(sK1)
| ( k5_lattices(k1_lattice2(sK1)) = k6_lattices(sK1) )
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1) ),
inference(unflattening,[status(thm)],[c_2181]) ).
tcf(c_2183,plain,
k5_lattices(k1_lattice2(sK1)) = k6_lattices(sK1),
inference(global_subsumption_just,[status(thm)],[c_2182,c_55,c_54,c_53,c_2182]) ).
tcf(c_2188,plain,
! [X0: $i] :
( v3_struct_0(X0)
| v13_lattices(k1_lattice2(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_214]) ).
tcf(c_2189,plain,
( v3_struct_0(sK1)
| v13_lattices(k1_lattice2(sK1))
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1) ),
inference(unflattening,[status(thm)],[c_2188]) ).
tcf(c_2190,plain,
v13_lattices(k1_lattice2(sK1)),
inference(global_subsumption_just,[status(thm)],[c_2189,c_55,c_54,c_53,c_2189]) ).
tcf(c_2216,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(k1_lattice2(sK1))
| ( k5_lattices(k1_lattice2(sK1)) = X0 )
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1))
| ~ m2_filter_2(X1,sK1)
| ~ r2_hidden(sK2,X1)
| ~ m1_subset_1(X0,u1_struct_0(k1_lattice2(sK1)))
| ( sK28(k1_lattice2(sK1),X0) != k15_filter_2(sK1,X1) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1724,c_2190]) ).
tcf(c_2553,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| m1_filter_0(sK28(X0,X1),X0)
| ( k5_lattices(X0) = X1 )
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ( k1_lattice2(sK1) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_206,c_2190]) ).
tcf(c_2554,plain,
! [X0: $i] :
( v3_struct_0(k1_lattice2(sK1))
| m1_filter_0(sK28(k1_lattice2(sK1),X0),k1_lattice2(sK1))
| ( k5_lattices(k1_lattice2(sK1)) = X0 )
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1))
| ~ m1_subset_1(X0,u1_struct_0(k1_lattice2(sK1))) ),
inference(unflattening,[status(thm)],[c_2553]) ).
tcf(c_2574,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| r2_hidden(X1,sK28(X0,X1))
| ( k5_lattices(X0) = X1 )
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ( k1_lattice2(sK1) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_204,c_2190]) ).
tcf(c_2575,plain,
! [X0: $i] :
( v3_struct_0(k1_lattice2(sK1))
| r2_hidden(X0,sK28(k1_lattice2(sK1),X0))
| ( k5_lattices(k1_lattice2(sK1)) = X0 )
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1))
| ~ m1_subset_1(X0,u1_struct_0(k1_lattice2(sK1))) ),
inference(unflattening,[status(thm)],[c_2574]) ).
tcf(c_4441,plain,
! [X0: $i] :
( v3_struct_0(k1_lattice2(sK1))
| r2_hidden(X0,sK28(k1_lattice2(sK1),X0))
| ( k6_lattices(sK1) = X0 )
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1))
| ~ m1_subset_1(X0,u1_struct_0(k1_lattice2(sK1))) ),
inference(light_normalisation,[status(thm)],[c_2575,c_2183]) ).
tcf(c_4442,plain,
! [X0: $i] :
( v3_struct_0(k1_lattice2(sK1))
| m1_filter_0(sK28(k1_lattice2(sK1),X0),k1_lattice2(sK1))
| ( k6_lattices(sK1) = X0 )
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1))
| ~ m1_subset_1(X0,u1_struct_0(k1_lattice2(sK1))) ),
inference(light_normalisation,[status(thm)],[c_2554,c_2183]) ).
tcf(c_4443,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(k1_lattice2(sK1))
| ( k6_lattices(sK1) = X0 )
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1))
| ~ m2_filter_2(X1,sK1)
| ~ r2_hidden(sK2,X1)
| ~ m1_subset_1(X0,u1_struct_0(k1_lattice2(sK1)))
| ( sK28(k1_lattice2(sK1),X0) != k15_filter_2(sK1,X1) ) ),
inference(light_normalisation,[status(thm)],[c_2216,c_2183]) ).
tcf(c_5400,plain,
! [X0: $i,X1: $i] :
( ~ iPr_def_10
| ( k6_lattices(sK1) = X0 )
| ( sK28(k1_lattice2(sK1),X0) != k15_filter_2(sK1,X1) )
| ~ r2_hidden(sK2,X1)
| ~ m2_filter_2(X1,sK1)
| ~ m1_subset_1(X0,u1_struct_0(k1_lattice2(sK1))) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_4443]) ).
tcf(c_5401,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_4443]) ).
tcf(c_5402,plain,
! [X0: $i] :
( ~ iPr_def_11
| ( k6_lattices(sK1) = X0 )
| ~ m1_subset_1(X0,u1_struct_0(k1_lattice2(sK1)))
| m1_filter_0(sK28(k1_lattice2(sK1),X0),k1_lattice2(sK1)) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_4442]) ).
tcf(c_5403,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_4442]) ).
tcf(c_5404,plain,
! [X0: $i] :
( ~ iPr_def_12
| ( k6_lattices(sK1) = X0 )
| r2_hidden(X0,sK28(k1_lattice2(sK1),X0))
| ~ m1_subset_1(X0,u1_struct_0(k1_lattice2(sK1))) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_4441]) ).
tcf(c_5405,plain,
( iPr_def_12
| v3_struct_0(k1_lattice2(sK1))
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1)) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_4441]) ).
tcf(c_87241,plain,
( v3_struct_0(sK1)
| ( k5_filter_2(sK1,sK2) = sK2 )
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1) ),
inference(superposition,[status(thm)],[c_52,c_71]) ).
tcf(c_87246,plain,
k5_filter_2(sK1,sK2) = sK2,
inference(forward_subsumption_resolution,[status(thm)],[c_87241,c_53,c_55,c_54]) ).
tcf(c_87265,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_87246,c_80]) ).
tcf(c_87268,plain,
m1_subset_1(sK2,u1_struct_0(k1_lattice2(sK1))),
inference(forward_subsumption_resolution,[status(thm)],[c_87265,c_53,c_55,c_54,c_52]) ).
tcf(c_87458,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v3_struct_0(k1_lattice2(X1))
| ( k8_filter_2(X1,X0) = X0 )
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(k1_lattice2(X1))
| ~ v10_lattices(k1_lattice2(X1))
| ~ m1_filter_0(X0,k1_lattice2(X1)) ),
inference(superposition,[status(thm)],[c_90,c_73]) ).
fof(f226,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(f227,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| sP0(X0) ),
inference(definition_folding,[],[f194,f226]) ).
fof(f240,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,[],[f226]) ).
fof(f353,plain,
! [X0] :
( ~ sP0(X0)
| v10_lattices(k1_lattice2(X0)) ),
inference(cnf_transformation,[],[f240]) ).
tcf(c_144,plain,
! [X0: $i] :
( v10_lattices(k1_lattice2(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f353]) ).
tcf(c_417,plain,
! [X0: $i] :
( v10_lattices(k1_lattice2(X0))
| ~ sP0(X0) ),
inference(prop_impl_just,[status(thm)],[c_144]) ).
tcf(c_2389,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_145,c_417]) ).
tcf(c_2390,plain,
! [X0: $i] :
( v3_struct_0(X0)
| v10_lattices(k1_lattice2(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0) ),
inference(unflattening,[status(thm)],[c_2389]) ).
tcf(c_79475,plain,
( iPr_def_11
| v3_struct_0(sK1)
| v3_struct_0(k1_lattice2(sK1))
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| ~ l3_lattices(k1_lattice2(sK1)) ),
inference(superposition,[status(thm)],[c_2390,c_5403]) ).
tcf(c_79491,plain,
( iPr_def_11
| v3_struct_0(k1_lattice2(sK1))
| ~ l3_lattices(k1_lattice2(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_79475,c_53,c_55,c_54]) ).
tcf(c_80167,plain,
( iPr_def_11
| v3_struct_0(k1_lattice2(sK1))
| ~ l3_lattices(sK1) ),
inference(superposition,[status(thm)],[c_79,c_79491]) ).
tcf(c_80168,plain,
( iPr_def_11
| v3_struct_0(k1_lattice2(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_80167,c_55]) ).
tcf(c_80169,plain,
( iPr_def_11
| v3_struct_0(sK1)
| ~ l3_lattices(sK1) ),
inference(superposition,[status(thm)],[c_80168,c_115]) ).
tcf(c_80170,plain,
iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_80169,c_53,c_55]) ).
tcf(c_87157,plain,
! [X0: $i] :
( m1_filter_0(sK28(k1_lattice2(sK1),X0),k1_lattice2(sK1))
| ( k6_lattices(sK1) = X0 )
| ~ m1_subset_1(X0,u1_struct_0(k1_lattice2(sK1))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_5402,c_80170]) ).
tcf(c_87164,plain,
! [X0: $i] :
( v3_struct_0(sK1)
| ( k6_lattices(sK1) = X0 )
| ( k8_filter_2(sK1,sK28(k1_lattice2(sK1),X0)) = k14_filter_2(sK1,sK28(k1_lattice2(sK1),X0)) )
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| ~ m1_subset_1(X0,u1_struct_0(k1_lattice2(sK1))) ),
inference(superposition,[status(thm)],[c_87157,c_196]) ).
tcf(c_87165,plain,
! [X0: $i] :
( ( k6_lattices(sK1) = X0 )
| ( k8_filter_2(sK1,sK28(k1_lattice2(sK1),X0)) = k14_filter_2(sK1,sK28(k1_lattice2(sK1),X0)) )
| ~ m1_subset_1(X0,u1_struct_0(k1_lattice2(sK1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_87164,c_53,c_55,c_54]) ).
tcf(c_87214,plain,
! [X0: $i] :
( v3_struct_0(sK1)
| ( k5_filter_2(sK1,X0) = k6_lattices(sK1) )
| ( k8_filter_2(sK1,sK28(k1_lattice2(sK1),k5_filter_2(sK1,X0))) = k14_filter_2(sK1,sK28(k1_lattice2(sK1),k5_filter_2(sK1,X0))) )
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| ~ m1_subset_1(X0,u1_struct_0(sK1)) ),
inference(superposition,[status(thm)],[c_80,c_87165]) ).
tcf(c_87216,plain,
! [X0: $i] :
( ( k5_filter_2(sK1,X0) = k6_lattices(sK1) )
| ( k8_filter_2(sK1,sK28(k1_lattice2(sK1),k5_filter_2(sK1,X0))) = k14_filter_2(sK1,sK28(k1_lattice2(sK1),k5_filter_2(sK1,X0))) )
| ~ m1_subset_1(X0,u1_struct_0(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_87214,c_53,c_55,c_54]) ).
tcf(c_87226,plain,
( ( k5_filter_2(sK1,sK2) = k6_lattices(sK1) )
| ( k8_filter_2(sK1,sK28(k1_lattice2(sK1),k5_filter_2(sK1,sK2))) = k14_filter_2(sK1,sK28(k1_lattice2(sK1),k5_filter_2(sK1,sK2))) ) ),
inference(superposition,[status(thm)],[c_52,c_87216]) ).
tcf(c_87228,plain,
( v3_struct_0(sK1)
| m2_filter_2(k8_filter_2(sK1,sK28(k1_lattice2(sK1),k5_filter_2(sK1,sK2))),sK1)
| ( k5_filter_2(sK1,sK2) = k6_lattices(sK1) )
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| ~ m1_filter_0(sK28(k1_lattice2(sK1),k5_filter_2(sK1,sK2)),k1_lattice2(sK1)) ),
inference(superposition,[status(thm)],[c_87226,c_76]) ).
tcf(c_87229,plain,
( m2_filter_2(k8_filter_2(sK1,sK28(k1_lattice2(sK1),k5_filter_2(sK1,sK2))),sK1)
| ( k5_filter_2(sK1,sK2) = k6_lattices(sK1) )
| ~ m1_filter_0(sK28(k1_lattice2(sK1),k5_filter_2(sK1,sK2)),k1_lattice2(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_87228,c_53,c_55,c_54]) ).
tcf(c_87248,plain,
( m2_filter_2(k8_filter_2(sK1,sK28(k1_lattice2(sK1),sK2)),sK1)
| ( k6_lattices(sK1) = sK2 )
| ~ m1_filter_0(sK28(k1_lattice2(sK1),sK2),k1_lattice2(sK1)) ),
inference(demodulation,[status(thm)],[c_87229,c_87246]) ).
tcf(c_87251,plain,
( m2_filter_2(k8_filter_2(sK1,sK28(k1_lattice2(sK1),sK2)),sK1)
| ~ m1_filter_0(sK28(k1_lattice2(sK1),sK2),k1_lattice2(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_87248,c_50]) ).
tcf(c_87280,plain,
( v3_struct_0(sK1)
| ( k7_filter_2(sK1,k8_filter_2(sK1,sK28(k1_lattice2(sK1),sK2))) = k15_filter_2(sK1,k8_filter_2(sK1,sK28(k1_lattice2(sK1),sK2))) )
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| ~ m1_filter_0(sK28(k1_lattice2(sK1),sK2),k1_lattice2(sK1)) ),
inference(superposition,[status(thm)],[c_87251,c_197]) ).
tcf(c_87282,plain,
( ( k7_filter_2(sK1,k8_filter_2(sK1,sK28(k1_lattice2(sK1),sK2))) = k15_filter_2(sK1,k8_filter_2(sK1,sK28(k1_lattice2(sK1),sK2))) )
| ~ m1_filter_0(sK28(k1_lattice2(sK1),sK2),k1_lattice2(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_87280,c_53,c_55,c_54]) ).
tcf(c_87308,plain,
( ( k6_lattices(sK1) = sK2 )
| ( k7_filter_2(sK1,k8_filter_2(sK1,sK28(k1_lattice2(sK1),sK2))) = k15_filter_2(sK1,k8_filter_2(sK1,sK28(k1_lattice2(sK1),sK2))) )
| ~ m1_subset_1(sK2,u1_struct_0(k1_lattice2(sK1))) ),
inference(superposition,[status(thm)],[c_87157,c_87282]) ).
tcf(c_87309,plain,
k7_filter_2(sK1,k8_filter_2(sK1,sK28(k1_lattice2(sK1),sK2))) = k15_filter_2(sK1,k8_filter_2(sK1,sK28(k1_lattice2(sK1),sK2))),
inference(forward_subsumption_resolution,[status(thm)],[c_87308,c_50,c_87268]) ).
tcf(c_87975,plain,
! [X0: $i] :
( v3_struct_0(sK1)
| v3_struct_0(k1_lattice2(sK1))
| ( k6_lattices(sK1) = X0 )
| ( k8_filter_2(sK1,sK28(k1_lattice2(sK1),X0)) = sK28(k1_lattice2(sK1),X0) )
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1))
| ~ m1_subset_1(X0,u1_struct_0(k1_lattice2(sK1))) ),
inference(superposition,[status(thm)],[c_87157,c_87458]) ).
tcf(c_87976,plain,
! [X0: $i] :
( v3_struct_0(k1_lattice2(sK1))
| ( k6_lattices(sK1) = X0 )
| ( k8_filter_2(sK1,sK28(k1_lattice2(sK1),X0)) = sK28(k1_lattice2(sK1),X0) )
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1))
| ~ m1_subset_1(X0,u1_struct_0(k1_lattice2(sK1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_87975,c_53,c_55,c_54]) ).
tcf(c_87983,plain,
( v3_struct_0(k1_lattice2(sK1))
| ( k6_lattices(sK1) = sK2 )
| ( k8_filter_2(sK1,sK28(k1_lattice2(sK1),sK2)) = sK28(k1_lattice2(sK1),sK2) )
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1)) ),
inference(superposition,[status(thm)],[c_87268,c_87976]) ).
tcf(c_87987,plain,
( v3_struct_0(k1_lattice2(sK1))
| ( k8_filter_2(sK1,sK28(k1_lattice2(sK1),sK2)) = sK28(k1_lattice2(sK1),sK2) )
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_87983,c_50]) ).
tcf(c_88097,plain,
( v3_struct_0(sK1)
| v3_struct_0(k1_lattice2(sK1))
| ( k8_filter_2(sK1,sK28(k1_lattice2(sK1),sK2)) = sK28(k1_lattice2(sK1),sK2) )
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| ~ l3_lattices(k1_lattice2(sK1)) ),
inference(superposition,[status(thm)],[c_2390,c_87987]) ).
tcf(c_88108,plain,
( iPr_def_12
| v3_struct_0(sK1)
| v3_struct_0(k1_lattice2(sK1))
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| ~ l3_lattices(k1_lattice2(sK1)) ),
inference(superposition,[status(thm)],[c_2390,c_5405]) ).
tcf(c_88109,plain,
( iPr_def_10
| v3_struct_0(sK1)
| v3_struct_0(k1_lattice2(sK1))
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| ~ l3_lattices(k1_lattice2(sK1)) ),
inference(superposition,[status(thm)],[c_2390,c_5401]) ).
tcf(c_88110,plain,
( iPr_def_10
| v3_struct_0(k1_lattice2(sK1))
| ~ l3_lattices(k1_lattice2(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_88109,c_53,c_55,c_54]) ).
tcf(c_88111,plain,
( iPr_def_12
| v3_struct_0(k1_lattice2(sK1))
| ~ l3_lattices(k1_lattice2(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_88108,c_53,c_55,c_54]) ).
tcf(c_88114,plain,
( v3_struct_0(k1_lattice2(sK1))
| ( k8_filter_2(sK1,sK28(k1_lattice2(sK1),sK2)) = sK28(k1_lattice2(sK1),sK2) )
| ~ l3_lattices(k1_lattice2(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_88097,c_53,c_55,c_54]) ).
tcf(c_88151,plain,
( iPr_def_10
| v3_struct_0(k1_lattice2(sK1))
| ~ l3_lattices(sK1) ),
inference(superposition,[status(thm)],[c_79,c_88110]) ).
tcf(c_88152,plain,
( iPr_def_10
| v3_struct_0(k1_lattice2(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_88151,c_55]) ).
tcf(c_88153,plain,
( iPr_def_10
| v3_struct_0(sK1)
| ~ l3_lattices(sK1) ),
inference(superposition,[status(thm)],[c_88152,c_115]) ).
tcf(c_88154,plain,
iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_88153,c_53,c_55]) ).
tcf(c_88168,plain,
! [X0: $i,X1: $i] :
( ( k6_lattices(sK1) = X0 )
| ~ m2_filter_2(X1,sK1)
| ~ r2_hidden(sK2,X1)
| ~ m1_subset_1(X0,u1_struct_0(k1_lattice2(sK1)))
| ( sK28(k1_lattice2(sK1),X0) != k15_filter_2(sK1,X1) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_5400,c_88154]) ).
tcf(c_88169,plain,
( iPr_def_12
| v3_struct_0(k1_lattice2(sK1))
| ~ l3_lattices(sK1) ),
inference(superposition,[status(thm)],[c_79,c_88111]) ).
tcf(c_88170,plain,
( iPr_def_12
| v3_struct_0(k1_lattice2(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_88169,c_55]) ).
tcf(c_88171,plain,
( iPr_def_12
| v3_struct_0(sK1)
| ~ l3_lattices(sK1) ),
inference(superposition,[status(thm)],[c_88170,c_115]) ).
tcf(c_88172,plain,
iPr_def_12,
inference(forward_subsumption_resolution,[status(thm)],[c_88171,c_53,c_55]) ).
tcf(c_88182,plain,
! [X0: $i] :
( r2_hidden(X0,sK28(k1_lattice2(sK1),X0))
| ( k6_lattices(sK1) = X0 )
| ~ m1_subset_1(X0,u1_struct_0(k1_lattice2(sK1))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_5404,c_88172]) ).
tcf(c_88208,plain,
( v3_struct_0(k1_lattice2(sK1))
| ( k8_filter_2(sK1,sK28(k1_lattice2(sK1),sK2)) = sK28(k1_lattice2(sK1),sK2) )
| ~ l3_lattices(sK1) ),
inference(superposition,[status(thm)],[c_79,c_88114]) ).
tcf(c_88209,plain,
( v3_struct_0(k1_lattice2(sK1))
| ( k8_filter_2(sK1,sK28(k1_lattice2(sK1),sK2)) = sK28(k1_lattice2(sK1),sK2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_88208,c_55]) ).
tcf(c_88210,plain,
( v3_struct_0(sK1)
| ( k8_filter_2(sK1,sK28(k1_lattice2(sK1),sK2)) = sK28(k1_lattice2(sK1),sK2) )
| ~ l3_lattices(sK1) ),
inference(superposition,[status(thm)],[c_88209,c_115]) ).
tcf(c_88211,plain,
k8_filter_2(sK1,sK28(k1_lattice2(sK1),sK2)) = sK28(k1_lattice2(sK1),sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_88210,c_53,c_55]) ).
tcf(c_88214,plain,
k7_filter_2(sK1,sK28(k1_lattice2(sK1),sK2)) = k15_filter_2(sK1,sK28(k1_lattice2(sK1),sK2)),
inference(demodulation,[status(thm)],[c_87309,c_88211]) ).
tcf(c_88216,plain,
( m2_filter_2(sK28(k1_lattice2(sK1),sK2),sK1)
| ~ m1_filter_0(sK28(k1_lattice2(sK1),sK2),k1_lattice2(sK1)) ),
inference(demodulation,[status(thm)],[c_87251,c_88211]) ).
tcf(c_88218,plain,
( v3_struct_0(sK1)
| m1_subset_1(sK28(k1_lattice2(sK1),sK2),k1_zfmisc_1(u1_struct_0(sK1)))
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| ~ m1_subset_1(sK28(k1_lattice2(sK1),sK2),k1_zfmisc_1(u1_struct_0(k1_lattice2(sK1)))) ),
inference(superposition,[status(thm)],[c_88211,c_84]) ).
tcf(c_88220,plain,
( m1_subset_1(sK28(k1_lattice2(sK1),sK2),k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m1_subset_1(sK28(k1_lattice2(sK1),sK2),k1_zfmisc_1(u1_struct_0(k1_lattice2(sK1)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_88218,c_53,c_55,c_54]) ).
tcf(c_88252,plain,
( v3_struct_0(k1_lattice2(sK1))
| m1_subset_1(sK28(k1_lattice2(sK1),sK2),k1_zfmisc_1(u1_struct_0(sK1)))
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1))
| ~ m1_filter_0(sK28(k1_lattice2(sK1),sK2),k1_lattice2(sK1)) ),
inference(superposition,[status(thm)],[c_90,c_88220]) ).
tcf(c_88457,plain,
( m2_filter_2(sK28(k1_lattice2(sK1),sK2),sK1)
| ( k6_lattices(sK1) = sK2 )
| ~ m1_subset_1(sK2,u1_struct_0(k1_lattice2(sK1))) ),
inference(superposition,[status(thm)],[c_87157,c_88216]) ).
tcf(c_88458,plain,
m2_filter_2(sK28(k1_lattice2(sK1),sK2),sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_88457,c_50,c_87268]) ).
tcf(c_88530,plain,
( v3_struct_0(sK1)
| v3_struct_0(k1_lattice2(sK1))
| ( k7_filter_2(sK1,sK28(k1_lattice2(sK1),sK2)) = sK28(k1_lattice2(sK1),sK2) )
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1))
| ~ m1_filter_0(sK28(k1_lattice2(sK1),sK2),k1_lattice2(sK1)) ),
inference(superposition,[status(thm)],[c_88252,c_72]) ).
tcf(c_88535,plain,
( v3_struct_0(k1_lattice2(sK1))
| ( k7_filter_2(sK1,sK28(k1_lattice2(sK1),sK2)) = sK28(k1_lattice2(sK1),sK2) )
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1))
| ~ m1_filter_0(sK28(k1_lattice2(sK1),sK2),k1_lattice2(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_88530,c_53,c_55,c_54]) ).
tcf(c_88539,plain,
( v3_struct_0(k1_lattice2(sK1))
| ( k6_lattices(sK1) = sK2 )
| ( k7_filter_2(sK1,sK28(k1_lattice2(sK1),sK2)) = sK28(k1_lattice2(sK1),sK2) )
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1))
| ~ m1_subset_1(sK2,u1_struct_0(k1_lattice2(sK1))) ),
inference(superposition,[status(thm)],[c_87157,c_88535]) ).
tcf(c_88540,plain,
( v3_struct_0(k1_lattice2(sK1))
| ( k7_filter_2(sK1,sK28(k1_lattice2(sK1),sK2)) = sK28(k1_lattice2(sK1),sK2) )
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_88539,c_50,c_87268]) ).
tcf(c_88541,plain,
( v3_struct_0(sK1)
| v3_struct_0(k1_lattice2(sK1))
| ( k7_filter_2(sK1,sK28(k1_lattice2(sK1),sK2)) = sK28(k1_lattice2(sK1),sK2) )
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| ~ l3_lattices(k1_lattice2(sK1)) ),
inference(superposition,[status(thm)],[c_2390,c_88540]) ).
tcf(c_88542,plain,
( v3_struct_0(k1_lattice2(sK1))
| ( k7_filter_2(sK1,sK28(k1_lattice2(sK1),sK2)) = sK28(k1_lattice2(sK1),sK2) )
| ~ l3_lattices(k1_lattice2(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_88541,c_53,c_55,c_54]) ).
tcf(c_88543,plain,
( v3_struct_0(k1_lattice2(sK1))
| ( k7_filter_2(sK1,sK28(k1_lattice2(sK1),sK2)) = sK28(k1_lattice2(sK1),sK2) )
| ~ l3_lattices(sK1) ),
inference(superposition,[status(thm)],[c_79,c_88542]) ).
tcf(c_88544,plain,
( v3_struct_0(k1_lattice2(sK1))
| ( k7_filter_2(sK1,sK28(k1_lattice2(sK1),sK2)) = sK28(k1_lattice2(sK1),sK2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_88543,c_55]) ).
tcf(c_88557,plain,
( v3_struct_0(sK1)
| ( k7_filter_2(sK1,sK28(k1_lattice2(sK1),sK2)) = sK28(k1_lattice2(sK1),sK2) )
| ~ l3_lattices(sK1) ),
inference(superposition,[status(thm)],[c_88544,c_115]) ).
tcf(c_88558,plain,
k7_filter_2(sK1,sK28(k1_lattice2(sK1),sK2)) = sK28(k1_lattice2(sK1),sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_88557,c_53,c_55]) ).
tcf(c_88566,plain,
k15_filter_2(sK1,sK28(k1_lattice2(sK1),sK2)) = sK28(k1_lattice2(sK1),sK2),
inference(demodulation,[status(thm)],[c_88214,c_88558]) ).
tcf(c_89286,plain,
! [X0: $i] :
( ( k6_lattices(sK1) = X0 )
| ~ m1_subset_1(X0,u1_struct_0(k1_lattice2(sK1)))
| ~ m2_filter_2(sK28(k1_lattice2(sK1),sK2),sK1)
| ~ r2_hidden(sK2,sK28(k1_lattice2(sK1),sK2))
| ( sK28(k1_lattice2(sK1),X0) != sK28(k1_lattice2(sK1),sK2) ) ),
inference(superposition,[status(thm)],[c_88566,c_88168]) ).
tcf(c_89299,plain,
! [X0: $i] :
( ( k6_lattices(sK1) = X0 )
| ~ m1_subset_1(X0,u1_struct_0(k1_lattice2(sK1)))
| ~ r2_hidden(sK2,sK28(k1_lattice2(sK1),sK2))
| ( sK28(k1_lattice2(sK1),X0) != sK28(k1_lattice2(sK1),sK2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89286,c_88458]) ).
tcf(c_89430,plain,
( ( k6_lattices(sK1) = sK2 )
| ~ m1_subset_1(sK2,u1_struct_0(k1_lattice2(sK1)))
| ~ r2_hidden(sK2,sK28(k1_lattice2(sK1),sK2)) ),
inference(equality_resolution,[status(thm)],[c_89299]) ).
tcf(c_89431,plain,
~ r2_hidden(sK2,sK28(k1_lattice2(sK1),sK2)),
inference(forward_subsumption_resolution,[status(thm)],[c_89430,c_50,c_87268]) ).
tcf(c_89432,plain,
( ( k6_lattices(sK1) = sK2 )
| ~ m1_subset_1(sK2,u1_struct_0(k1_lattice2(sK1))) ),
inference(superposition,[status(thm)],[c_88182,c_89431]) ).
tcf(c_89433,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_89432,c_50,c_87268]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT309+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n003.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 21:01:50 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 0.12/0.42
% 0.12/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.42
% 0.12/0.42 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 115.26/39.17 % SZS status Started for theBenchmark.p
% 115.26/39.17 % SZS status Theorem for theBenchmark.p
% 115.26/39.17
% 115.26/39.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 115.26/39.17
% 115.26/39.17 % ------ iProver source info
% 115.26/39.17
% 115.26/39.17 % git: date: 2026-07-19 20:42:38 +0200
% 115.26/39.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 115.26/39.17 % git: non_committed_changes: false
% 115.26/39.17
% 115.26/39.17 % ------ Parsing...
% 115.26/39.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 115.26/39.17
% 115.26/39.17 % ------ 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: 19 0s sf_e pe_s pe_e %
% 115.26/39.17
% 115.26/39.17 % ------ Preprocessing... gs_s sp: 3 0s gs_e snvd_s sp: 0 0s snvd_e %
% 115.26/39.17
% 115.26/39.17 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 115.26/39.17 % ------ Proving...
% 115.26/39.17 % ------ Problem Properties
% 115.26/39.17
% 115.26/39.17 %
% 115.26/39.17 % clauses 136
% 115.26/39.17 % conjectures 5
% 115.26/39.17 % EPR 34
% 115.26/39.17 % Horn 91
% 115.26/39.17 % unary 48
% 115.26/39.17 % binary 30
% 115.26/39.17 % lits 371
% 115.26/39.17 % lits eq 32
% 115.26/39.17 % fd_pure 0
% 115.26/39.17 % fd_pseudo 0
% 115.26/39.17 % fd_cond 8
% 115.26/39.17 % fd_pseudo_cond 4
% 115.26/39.17 % AC symbols 0
% 115.26/39.17
% 115.26/39.17 % ------ Input Options Time Limit: Unbounded
% 115.26/39.17
% 115.26/39.17
% 115.26/39.17 % ------
% 115.26/39.17 % Current options:
% 115.26/39.17 % ------
% 115.26/39.17
% 115.26/39.17
% 115.26/39.17 %
% 115.26/39.17
% 115.26/39.17 % ------ Proving...
% 115.26/39.17 %
% 115.26/39.17
% 115.26/39.17 % SZS status Theorem for theBenchmark.p
% 115.26/39.17
% 115.26/39.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 115.26/39.18
% 115.26/39.18
%------------------------------------------------------------------------------