%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LAT327+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : 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 01:59:20 PM UTC 2026
% Result : Theorem 2.73s 1.27s
% Output : CNFRefutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 75 ( 21 unt; 1 def)
% Number of atoms : 382 ( 4 equ)
% Maximal formula atoms : 13 ( 5 avg)
% Number of connectives : 482 ( 201 ~; 204 |; 58 &)
% ( 3 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 5 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 107 ( 0 sgn 101 !; 6 ?; 53 :)
% 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] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ( r3_lattices(X0,X1,X2)
=> ( r2_hidden(X2,k22_filter_2(X0,X1,X2))
& r2_hidden(X1,k22_filter_2(X0,X1,X2)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_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] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ( r3_lattices(X0,X1,X2)
=> ( r2_hidden(X2,k22_filter_2(X0,X1,X2))
& r2_hidden(X1,k22_filter_2(X0,X1,X2)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f33,axiom,
! [X0,X1,X2] :
( ( m1_subset_1(X2,u1_struct_0(X0))
& m1_subset_1(X1,u1_struct_0(X0))
& l3_lattices(X0)
& v9_lattices(X0)
& v8_lattices(X0)
& v6_lattices(X0)
& ~ v3_struct_0(X0) )
=> r3_lattices(X0,X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r3_lattices) ).
fof(f41,axiom,
! [X0] :
( l3_lattices(X0)
=> ( ( v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ( v9_lattices(X0)
& v8_lattices(X0)
& v7_lattices(X0)
& v6_lattices(X0)
& v5_lattices(X0)
& v4_lattices(X0)
& ~ v3_struct_0(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_lattices) ).
fof(f44,axiom,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X0))
=> ( r3_lattices(X0,X1,X2)
=> ( r2_hidden(X3,k22_filter_2(X0,X1,X2))
<=> ( r3_lattices(X0,X3,X2)
& r3_lattices(X0,X1,X3) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_filter_2) ).
fof(f48,plain,
? [X0] :
( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
& ? [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
& r3_lattices(X0,X1,X2)
& ( ~ r2_hidden(X2,k22_filter_2(X0,X1,X2))
| ~ r2_hidden(X1,k22_filter_2(X0,X1,X2)) ) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f49,plain,
? [X0] :
( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
& ? [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
& r3_lattices(X0,X1,X2)
& ( ~ r2_hidden(X2,k22_filter_2(X0,X1,X2))
| ~ r2_hidden(X1,k22_filter_2(X0,X1,X2)) ) ) ) ),
inference(flattening,[],[f48]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v9_lattices(X0)
| ~ v8_lattices(X0)
| ~ v6_lattices(X0)
| v3_struct_0(X0)
| r3_lattices(X0,X1,X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v9_lattices(X0)
| ~ v8_lattices(X0)
| ~ v6_lattices(X0)
| v3_struct_0(X0)
| r3_lattices(X0,X1,X1) ),
inference(flattening,[],[f74]) ).
fof(f81,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ( v9_lattices(X0)
& v8_lattices(X0)
& v7_lattices(X0)
& v6_lattices(X0)
& v5_lattices(X0)
& v4_lattices(X0)
& ~ v3_struct_0(X0) ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f82,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ( v9_lattices(X0)
& v8_lattices(X0)
& v7_lattices(X0)
& v6_lattices(X0)
& v5_lattices(X0)
& v4_lattices(X0)
& ~ v3_struct_0(X0) ) ),
inference(flattening,[],[f81]) ).
fof(f85,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ! [X3] :
( ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ r3_lattices(X0,X1,X2)
| ( r2_hidden(X3,k22_filter_2(X0,X1,X2))
<=> ( r3_lattices(X0,X3,X2)
& r3_lattices(X0,X1,X3) ) ) ) ) ) ),
inference(ennf_transformation,[],[f44]) ).
fof(f86,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ! [X3] :
( ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ r3_lattices(X0,X1,X2)
| ( r2_hidden(X3,k22_filter_2(X0,X1,X2))
<=> ( r3_lattices(X0,X3,X2)
& r3_lattices(X0,X1,X3) ) ) ) ) ) ),
inference(flattening,[],[f85]) ).
fof(f87,plain,
( l3_lattices(sK0)
& v10_lattices(sK0)
& ~ v3_struct_0(sK0)
& m1_subset_1(sK1,u1_struct_0(sK0))
& m1_subset_1(sK2,u1_struct_0(sK0))
& r3_lattices(sK0,sK1,sK2)
& ( ~ r2_hidden(sK2,k22_filter_2(sK0,sK1,sK2))
| ~ r2_hidden(sK1,k22_filter_2(sK0,sK1,sK2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f49]) ).
fof(f102,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ! [X3] :
( ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ r3_lattices(X0,X1,X2)
| ( ( ~ r2_hidden(X3,k22_filter_2(X0,X1,X2))
| ( r3_lattices(X0,X3,X2)
& r3_lattices(X0,X1,X3) ) )
& ( ~ r3_lattices(X0,X3,X2)
| ~ r3_lattices(X0,X1,X3)
| r2_hidden(X3,k22_filter_2(X0,X1,X2)) ) ) ) ) ) ),
inference(nnf_transformation,[],[f86]) ).
fof(f103,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ! [X3] :
( ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ r3_lattices(X0,X1,X2)
| ( ( ~ r2_hidden(X3,k22_filter_2(X0,X1,X2))
| ( r3_lattices(X0,X3,X2)
& r3_lattices(X0,X1,X3) ) )
& ( ~ r3_lattices(X0,X3,X2)
| ~ r3_lattices(X0,X1,X3)
| r2_hidden(X3,k22_filter_2(X0,X1,X2)) ) ) ) ) ) ),
inference(flattening,[],[f102]) ).
fof(f104,plain,
l3_lattices(sK0),
inference(cnf_transformation,[],[f87]) ).
fof(f105,plain,
v10_lattices(sK0),
inference(cnf_transformation,[],[f87]) ).
fof(f106,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f87]) ).
fof(f107,plain,
m1_subset_1(sK1,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f87]) ).
fof(f108,plain,
m1_subset_1(sK2,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f87]) ).
fof(f109,plain,
r3_lattices(sK0,sK1,sK2),
inference(cnf_transformation,[],[f87]) ).
fof(f110,plain,
( ~ r2_hidden(sK2,k22_filter_2(sK0,sK1,sK2))
| ~ r2_hidden(sK1,k22_filter_2(sK0,sK1,sK2)) ),
inference(cnf_transformation,[],[f87]) ).
fof(f143,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v9_lattices(X0)
| ~ v8_lattices(X0)
| ~ v6_lattices(X0)
| v3_struct_0(X0)
| r3_lattices(X0,X1,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f152,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| v9_lattices(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f153,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| v8_lattices(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f155,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| v6_lattices(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f163,plain,
! [X2,X3,X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ r3_lattices(X0,X1,X2)
| ~ r3_lattices(X0,X3,X2)
| ~ r3_lattices(X0,X1,X3)
| r2_hidden(X3,k22_filter_2(X0,X1,X2)) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_49,negated_conjecture,
( ~ r2_hidden(sK2,k22_filter_2(sK0,sK1,sK2))
| ~ r2_hidden(sK1,k22_filter_2(sK0,sK1,sK2)) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_50,negated_conjecture,
r3_lattices(sK0,sK1,sK2),
inference(cnf_transformation,[],[f109]) ).
tcf(c_51,negated_conjecture,
m1_subset_1(sK2,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f108]) ).
tcf(c_52,negated_conjecture,
m1_subset_1(sK1,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f107]) ).
tcf(c_53,negated_conjecture,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f106]) ).
tcf(c_54,negated_conjecture,
v10_lattices(sK0),
inference(cnf_transformation,[],[f105]) ).
tcf(c_55,negated_conjecture,
l3_lattices(sK0),
inference(cnf_transformation,[],[f104]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| r3_lattices(X1,X0,X0)
| ~ v9_lattices(X1)
| ~ v8_lattices(X1)
| ~ v6_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_98,plain,
! [X0: $i] :
( v6_lattices(X0)
| v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0) ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_100,plain,
! [X0: $i] :
( v8_lattices(X0)
| v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0) ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_101,plain,
! [X0: $i] :
( v9_lattices(X0)
| v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X0)
| r2_hidden(X3,k22_filter_2(X0,X1,X2))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ r3_lattices(X0,X3,X2)
| ~ r3_lattices(X0,X1,X3)
| ~ r3_lattices(X0,X1,X2) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_878,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X1)
| v3_struct_0(X0)
| r3_lattices(X1,X2,X2)
| ~ v9_lattices(X1)
| ~ v8_lattices(X1)
| ~ l3_lattices(X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_98,c_87]) ).
tcf(c_879,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| r3_lattices(X1,X0,X0)
| ~ v9_lattices(X1)
| ~ v8_lattices(X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(unflattening,[status(thm)],[c_878]) ).
tcf(c_897,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| r3_lattices(X1,X0,X0)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_879,c_101,c_100]) ).
tcf(c_1149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X0)
| r2_hidden(X3,k22_filter_2(X0,X1,X2))
| ~ l3_lattices(X0)
| ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ r3_lattices(X0,X3,X2)
| ~ r3_lattices(X0,X1,X3)
| ~ r3_lattices(X0,X1,X2)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_104]) ).
tcf(c_1150,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(sK0)
| r2_hidden(X2,k22_filter_2(sK0,X0,X1))
| ~ l3_lattices(sK0)
| ~ m1_subset_1(X2,u1_struct_0(sK0))
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r3_lattices(sK0,X2,X1)
| ~ r3_lattices(sK0,X0,X2)
| ~ r3_lattices(sK0,X0,X1) ),
inference(unflattening,[status(thm)],[c_1149]) ).
tcf(c_1152,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ m1_subset_1(X2,u1_struct_0(sK0))
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r3_lattices(sK0,X2,X1)
| ~ r3_lattices(sK0,X0,X2)
| ~ r3_lattices(sK0,X0,X1)
| r2_hidden(X2,k22_filter_2(sK0,X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_1150,c_55,c_53,c_1150]) ).
tcf(c_1153,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(X2,k22_filter_2(sK0,X0,X1))
| ~ m1_subset_1(X2,u1_struct_0(sK0))
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r3_lattices(sK0,X2,X1)
| ~ r3_lattices(sK0,X0,X2)
| ~ r3_lattices(sK0,X0,X1) ),
inference(renaming,[status(thm)],[c_1152]) ).
tcf(c_1213,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| r3_lattices(X0,X1,X1)
| ~ l3_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_897]) ).
tcf(c_1214,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| r3_lattices(sK0,X0,X0)
| ~ l3_lattices(sK0)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(unflattening,[status(thm)],[c_1213]) ).
tcf(c_1216,plain,
! [X0: $i,X1: $i] :
( ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| r3_lattices(sK0,X0,X0) ),
inference(global_subsumption_just,[status(thm)],[c_1214,c_55,c_53,c_1214]) ).
tcf(c_1217,plain,
! [X0: $i,X1: $i] :
( r3_lattices(sK0,X0,X0)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(renaming,[status(thm)],[c_1216]) ).
tcf(c_2157,plain,
! [X0: $i] :
( ~ iPr_def_10
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_1217]) ).
tcf(c_2158,plain,
! [X0: $i] :
( ~ iPr_def_11
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| r3_lattices(sK0,X0,X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_1217]) ).
tcf(c_2159,plain,
( iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_1217]) ).
tcf(c_2165,definition,
iPr_def_17 = k22_filter_2(sK0,sK1,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_2171,plain,
( iPr_def_11
| iPr_def_10 ),
inference(demodulation,[status(thm)],[c_2159]) ).
tcf(c_2172,plain,
! [X0: $i] :
( r3_lattices(sK0,X0,X0)
| ~ iPr_def_11
| ~ m1_subset_1(X0,iPr_def_12) ),
inference(demodulation,[status(thm)],[c_2158]) ).
tcf(c_2173,plain,
! [X0: $i] :
( ~ iPr_def_10
| ~ m1_subset_1(X0,iPr_def_12) ),
inference(demodulation,[status(thm)],[c_2157]) ).
tcf(c_2177,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(X2,k22_filter_2(sK0,X0,X1))
| ~ m1_subset_1(X2,iPr_def_12)
| ~ m1_subset_1(X1,iPr_def_12)
| ~ m1_subset_1(X0,iPr_def_12)
| ~ r3_lattices(sK0,X2,X1)
| ~ r3_lattices(sK0,X0,X2)
| ~ r3_lattices(sK0,X0,X1) ),
inference(demodulation,[status(thm)],[c_1153]) ).
tcf(c_2181,negated_conjecture,
m1_subset_1(sK1,iPr_def_12),
inference(demodulation,[status(thm)],[c_52]) ).
tcf(c_2182,negated_conjecture,
m1_subset_1(sK2,iPr_def_12),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_2183,negated_conjecture,
r3_lattices(sK0,sK1,sK2),
inference(demodulation,[status(thm)],[c_50]) ).
tcf(c_2184,negated_conjecture,
( ~ r2_hidden(sK2,iPr_def_17)
| ~ r2_hidden(sK1,iPr_def_17) ),
inference(demodulation,[status(thm)],[c_49,c_2165]) ).
tcf(c_2212,plain,
! [X0: $i] :
( r3_lattices(sK0,X0,X0)
| ~ m1_subset_1(X0,iPr_def_12) ),
inference(global_subsumption_just,[status(thm)],[c_2172,c_2171,c_2172,c_2173]) ).
tcf(c_2806,plain,
! [X0: $i] :
( r3_lattices(sK0,X0,X0)
| ~ m1_subset_1(X0,iPr_def_12) ),
inference(global_subsumption_just,[status(thm)],[c_2172,c_2212]) ).
tcf(c_2964,plain,
! [X0: $i] :
( r2_hidden(X0,iPr_def_17)
| ~ m1_subset_1(sK2,iPr_def_12)
| ~ m1_subset_1(sK1,iPr_def_12)
| ~ m1_subset_1(X0,iPr_def_12)
| ~ r3_lattices(sK0,sK1,sK2)
| ~ r3_lattices(sK0,sK1,X0)
| ~ r3_lattices(sK0,X0,sK2) ),
inference(superposition,[status(thm)],[c_2165,c_2177]) ).
tcf(c_2977,plain,
! [X0: $i] :
( r2_hidden(X0,iPr_def_17)
| ~ m1_subset_1(X0,iPr_def_12)
| ~ r3_lattices(sK0,sK1,X0)
| ~ r3_lattices(sK0,X0,sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2964,c_2182,c_2181,c_2183]) ).
tcf(c_3093,plain,
( r2_hidden(sK2,iPr_def_17)
| ~ m1_subset_1(sK2,iPr_def_12)
| ~ r3_lattices(sK0,sK2,sK2) ),
inference(superposition,[status(thm)],[c_2183,c_2977]) ).
tcf(c_3094,plain,
( r2_hidden(sK1,iPr_def_17)
| ~ m1_subset_1(sK1,iPr_def_12)
| ~ r3_lattices(sK0,sK1,sK2) ),
inference(superposition,[status(thm)],[c_2806,c_2977]) ).
tcf(c_3097,plain,
r2_hidden(sK1,iPr_def_17),
inference(forward_subsumption_resolution,[status(thm)],[c_3094,c_2181,c_2183]) ).
tcf(c_3098,plain,
( r2_hidden(sK2,iPr_def_17)
| ~ r3_lattices(sK0,sK2,sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3093,c_2182]) ).
tcf(c_3103,plain,
~ r2_hidden(sK2,iPr_def_17),
inference(backward_subsumption_resolution,[status(thm)],[c_2184,c_3097]) ).
tcf(c_3104,plain,
~ r3_lattices(sK0,sK2,sK2),
inference(backward_subsumption_resolution,[status(thm)],[c_3098,c_3103]) ).
tcf(c_3210,plain,
~ m1_subset_1(sK2,iPr_def_12),
inference(superposition,[status(thm)],[c_2806,c_3104]) ).
tcf(c_3212,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3210,c_2182]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT327+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % 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 21:12:13 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.39 Running first-order theorem proving
% 0.09/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.40
% 0.09/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.40
% 0.09/0.40 % Detected problem language: tptp
% 0.09/0.42 % Proving...
% 2.73/1.27 % SZS status Started for theBenchmark.p
% 2.73/1.27 % SZS status Theorem for theBenchmark.p
% 2.73/1.27
% 2.73/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.73/1.27
% 2.73/1.27 % ------ iProver source info
% 2.73/1.27
% 2.73/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 2.73/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.73/1.27 % git: non_committed_changes: false
% 2.73/1.27
% 2.73/1.27 % ------ Parsing...
% 2.73/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.73/1.27
% 2.73/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 7 0s sf_e pe_s pe_e %
% 2.73/1.27
% 2.73/1.27 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.73/1.27
% 2.73/1.27 % ------ Preprocessing... sf_s rm: 3 0s sf_e sf_s rm: 0 0s sf_e
% 2.73/1.27 % ------ Proving...
% 2.73/1.27 % ------ Problem Properties
% 2.73/1.27
% 2.73/1.27 %
% 2.73/1.27 % clauses 59
% 2.73/1.27 % conjectures 5
% 2.73/1.27 % EPR 24
% 2.73/1.27 % Horn 52
% 2.73/1.27 % unary 28
% 2.73/1.27 % binary 21
% 2.73/1.27 % lits 110
% 2.73/1.27 % lits eq 8
% 2.73/1.27 % fd_pure 0
% 2.73/1.27 % fd_pseudo 0
% 2.73/1.27 % fd_cond 1
% 2.73/1.27 % fd_pseudo_cond 1
% 2.73/1.27 % AC symbols 0
% 2.73/1.27
% 2.73/1.27 % ------ Schedule dynamic 5 is on
% 2.73/1.27
% 2.73/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.73/1.27
% 2.73/1.27
% 2.73/1.27 % ------
% 2.73/1.27 % Current options:
% 2.73/1.27 % ------
% 2.73/1.27
% 2.73/1.27
% 2.73/1.27 %
% 2.73/1.27
% 2.73/1.27 % ------ Proving...
% 2.73/1.27 %
% 2.73/1.27
% 2.73/1.27 % SZS status Theorem for theBenchmark.p
% 2.73/1.27
% 2.73/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.73/1.27
% 2.73/1.27
%------------------------------------------------------------------------------