%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LAT305+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 : n015.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 01:59:12 PM UTC 2026
% Result : Theorem 8.06s 1.89s
% Output : CNFRefutation 8.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 10
% Syntax : Number of formulae : 122 ( 13 unt; 0 def)
% Number of atoms : 693 ( 51 equ)
% Maximal formula atoms : 17 ( 5 avg)
% Number of connectives : 981 ( 410 ~; 458 |; 88 &)
% ( 6 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 8 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 : 19 ( 17 usr; 3 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 260 ( 0 sgn 249 !; 11 ?; 135 :)
% 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))
=> ( r2_hidden(k4_lattices(X0,X2,X1),k18_filter_2(X0,X1))
& r2_hidden(k4_lattices(X0,X1,X2),k18_filter_2(X0,X1))
& r2_hidden(X1,k18_filter_2(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_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))
=> ( r2_hidden(k4_lattices(X0,X2,X1),k18_filter_2(X0,X1))
& r2_hidden(k4_lattices(X0,X1,X2),k18_filter_2(X0,X1))
& r2_hidden(X1,k18_filter_2(X0,X1)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f5,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(f11,axiom,
! [X0,X1,X2] :
( ( m1_subset_1(X2,u1_struct_0(X0))
& m1_subset_1(X1,u1_struct_0(X0))
& l1_lattices(X0)
& v6_lattices(X0)
& ~ v3_struct_0(X0) )
=> k4_lattices(X0,X1,X2) = k4_lattices(X0,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k4_lattices) ).
fof(f15,axiom,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> k18_filter_2(X0,X1) = a_2_0_filter_2(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_filter_2) ).
fof(f26,axiom,
! [X0,X1,X2] :
( ( m1_subset_1(X2,u1_struct_0(X0))
& m1_subset_1(X1,u1_struct_0(X0))
& l1_lattices(X0)
& v6_lattices(X0)
& ~ v3_struct_0(X0) )
=> m1_subset_1(k4_lattices(X0,X1,X2),u1_struct_0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_lattices) ).
fof(f31,axiom,
! [X0] :
( l3_lattices(X0)
=> ( l2_lattices(X0)
& l1_lattices(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(f57,axiom,
! [X0,X1,X2] :
( ( m1_subset_1(X2,u1_struct_0(X1))
& l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( r2_hidden(X0,a_2_0_filter_2(X1,X2))
<=> ? [X3] :
( r3_lattices(X1,X3,X2)
& X0 = X3
& m1_subset_1(X3,u1_struct_0(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_filter_2) ).
fof(f73,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,X2)
<=> r1_lattices(X0,X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r3_lattices) ).
fof(f75,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(f77,axiom,
! [X0] :
( ( l3_lattices(X0)
& v8_lattices(X0)
& v6_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> r1_lattices(X0,k4_lattices(X0,X1,X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_lattices) ).
fof(f95,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))
& ( ~ r2_hidden(k4_lattices(X0,X2,X1),k18_filter_2(X0,X1))
| ~ r2_hidden(k4_lattices(X0,X1,X2),k18_filter_2(X0,X1))
| ~ r2_hidden(X1,k18_filter_2(X0,X1)) ) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f96,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))
& ( ~ r2_hidden(k4_lattices(X0,X2,X1),k18_filter_2(X0,X1))
| ~ r2_hidden(k4_lattices(X0,X1,X2),k18_filter_2(X0,X1))
| ~ r2_hidden(X1,k18_filter_2(X0,X1)) ) ) ) ),
inference(flattening,[],[f95]) ).
fof(f99,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,[],[f5]) ).
fof(f100,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,[],[f99]) ).
fof(f107,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_lattices(X0)
| ~ v6_lattices(X0)
| v3_struct_0(X0)
| k4_lattices(X0,X1,X2) = k4_lattices(X0,X2,X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f108,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_lattices(X0)
| ~ v6_lattices(X0)
| v3_struct_0(X0)
| k4_lattices(X0,X1,X2) = k4_lattices(X0,X2,X1) ),
inference(flattening,[],[f107]) ).
fof(f113,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| k18_filter_2(X0,X1) = a_2_0_filter_2(X0,X1) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f114,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| k18_filter_2(X0,X1) = a_2_0_filter_2(X0,X1) ) ),
inference(flattening,[],[f113]) ).
fof(f121,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_lattices(X0)
| ~ v6_lattices(X0)
| v3_struct_0(X0)
| m1_subset_1(k4_lattices(X0,X1,X2),u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f26]) ).
fof(f122,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_lattices(X0)
| ~ v6_lattices(X0)
| v3_struct_0(X0)
| m1_subset_1(k4_lattices(X0,X1,X2),u1_struct_0(X0)) ),
inference(flattening,[],[f121]) ).
fof(f125,plain,
! [X0] :
( ~ l3_lattices(X0)
| ( l2_lattices(X0)
& l1_lattices(X0) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f144,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ( r2_hidden(X0,a_2_0_filter_2(X1,X2))
<=> ? [X3] :
( r3_lattices(X1,X3,X2)
& X0 = X3
& m1_subset_1(X3,u1_struct_0(X1)) ) ) ),
inference(ennf_transformation,[],[f57]) ).
fof(f145,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ( r2_hidden(X0,a_2_0_filter_2(X1,X2))
<=> ? [X3] :
( r3_lattices(X1,X3,X2)
& X0 = X3
& m1_subset_1(X3,u1_struct_0(X1)) ) ) ),
inference(flattening,[],[f144]) ).
fof(f155,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,X2)
<=> r1_lattices(X0,X1,X2) ) ),
inference(ennf_transformation,[],[f73]) ).
fof(f156,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,X2)
<=> r1_lattices(X0,X1,X2) ) ),
inference(flattening,[],[f155]) ).
fof(f157,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,[],[f75]) ).
fof(f158,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,[],[f157]) ).
fof(f160,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v8_lattices(X0)
| ~ v6_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| r1_lattices(X0,k4_lattices(X0,X1,X2),X1) ) ) ),
inference(ennf_transformation,[],[f77]) ).
fof(f161,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v8_lattices(X0)
| ~ v6_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| r1_lattices(X0,k4_lattices(X0,X1,X2),X1) ) ) ),
inference(flattening,[],[f160]) ).
fof(f172,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))
& ( ~ r2_hidden(k4_lattices(sK0,sK2,sK1),k18_filter_2(sK0,sK1))
| ~ r2_hidden(k4_lattices(sK0,sK1,sK2),k18_filter_2(sK0,sK1))
| ~ r2_hidden(sK1,k18_filter_2(sK0,sK1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f96]) ).
fof(f182,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ( ( ~ r2_hidden(X0,a_2_0_filter_2(X1,X2))
| ? [X3] :
( r3_lattices(X1,X3,X2)
& X0 = X3
& m1_subset_1(X3,u1_struct_0(X1)) ) )
& ( ! [X3] :
( ~ r3_lattices(X1,X3,X2)
| X0 != X3
| ~ m1_subset_1(X3,u1_struct_0(X1)) )
| r2_hidden(X0,a_2_0_filter_2(X1,X2)) ) ) ),
inference(nnf_transformation,[],[f145]) ).
fof(f183,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ( ( ~ r2_hidden(X0,a_2_0_filter_2(X1,X2))
| ? [X4] :
( r3_lattices(X1,X4,X2)
& X0 = X4
& m1_subset_1(X4,u1_struct_0(X1)) ) )
& ( ! [X3] :
( ~ r3_lattices(X1,X3,X2)
| X0 != X3
| ~ m1_subset_1(X3,u1_struct_0(X1)) )
| r2_hidden(X0,a_2_0_filter_2(X1,X2)) ) ) ),
inference(rectify,[],[f182]) ).
fof(f184,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ( ( ~ r2_hidden(X0,a_2_0_filter_2(X1,X2))
| ( r3_lattices(X1,sK12(X0,X1,X2),X2)
& sK12(X0,X1,X2) = X0
& m1_subset_1(sK12(X0,X1,X2),u1_struct_0(X1)) ) )
& ( ! [X3] :
( ~ r3_lattices(X1,X3,X2)
| X0 != X3
| ~ m1_subset_1(X3,u1_struct_0(X1)) )
| r2_hidden(X0,a_2_0_filter_2(X1,X2)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X4,sK12(X0,X1,X2))],[f183]) ).
fof(f198,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,X2)
| r1_lattices(X0,X1,X2) )
& ( ~ r1_lattices(X0,X1,X2)
| r3_lattices(X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f156]) ).
fof(f201,plain,
l3_lattices(sK0),
inference(cnf_transformation,[],[f172]) ).
fof(f202,plain,
v10_lattices(sK0),
inference(cnf_transformation,[],[f172]) ).
fof(f203,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f172]) ).
fof(f204,plain,
m1_subset_1(sK1,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f172]) ).
fof(f205,plain,
m1_subset_1(sK2,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f172]) ).
fof(f206,plain,
( ~ r2_hidden(k4_lattices(sK0,sK2,sK1),k18_filter_2(sK0,sK1))
| ~ r2_hidden(k4_lattices(sK0,sK1,sK2),k18_filter_2(sK0,sK1))
| ~ r2_hidden(sK1,k18_filter_2(sK0,sK1)) ),
inference(cnf_transformation,[],[f172]) ).
fof(f209,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| v9_lattices(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f210,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| v8_lattices(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f212,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| v6_lattices(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f223,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_lattices(X0)
| ~ v6_lattices(X0)
| v3_struct_0(X0)
| k4_lattices(X0,X1,X2) = k4_lattices(X0,X2,X1) ),
inference(cnf_transformation,[],[f108]) ).
fof(f227,plain,
! [X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| k18_filter_2(X0,X1) = a_2_0_filter_2(X0,X1) ),
inference(cnf_transformation,[],[f114]) ).
fof(f231,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_lattices(X0)
| ~ v6_lattices(X0)
| v3_struct_0(X0)
| m1_subset_1(k4_lattices(X0,X1,X2),u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f122]) ).
fof(f235,plain,
! [X0] :
( ~ l3_lattices(X0)
| l1_lattices(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f269,plain,
! [X2,X3,X0,X1] :
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ~ r3_lattices(X1,X3,X2)
| X0 != X3
| ~ m1_subset_1(X3,u1_struct_0(X1))
| r2_hidden(X0,a_2_0_filter_2(X1,X2)) ),
inference(cnf_transformation,[],[f184]) ).
fof(f298,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)
| ~ r1_lattices(X0,X1,X2)
| r3_lattices(X0,X1,X2) ),
inference(cnf_transformation,[],[f198]) ).
fof(f300,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,[],[f158]) ).
fof(f302,plain,
! [X2,X0,X1] :
( ~ l3_lattices(X0)
| ~ v8_lattices(X0)
| ~ v6_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| r1_lattices(X0,k4_lattices(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f161]) ).
fof(f313,plain,
! [X2,X3,X1] :
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ~ r3_lattices(X1,X3,X2)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| r2_hidden(X3,a_2_0_filter_2(X1,X2)) ),
inference(equality_resolution,[],[f269]) ).
tcf(c_49,negated_conjecture,
( ~ r2_hidden(sK1,k18_filter_2(sK0,sK1))
| ~ r2_hidden(k4_lattices(sK0,sK2,sK1),k18_filter_2(sK0,sK1))
| ~ r2_hidden(k4_lattices(sK0,sK1,sK2),k18_filter_2(sK0,sK1)) ),
inference(cnf_transformation,[],[f206]) ).
tcf(c_50,negated_conjecture,
m1_subset_1(sK2,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f205]) ).
tcf(c_51,negated_conjecture,
m1_subset_1(sK1,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f204]) ).
tcf(c_52,negated_conjecture,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f203]) ).
tcf(c_53,negated_conjecture,
v10_lattices(sK0),
inference(cnf_transformation,[],[f202]) ).
tcf(c_54,negated_conjecture,
l3_lattices(sK0),
inference(cnf_transformation,[],[f201]) ).
tcf(c_59,plain,
! [X0: $i] :
( v6_lattices(X0)
| v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0) ),
inference(cnf_transformation,[],[f212]) ).
tcf(c_61,plain,
! [X0: $i] :
( v8_lattices(X0)
| v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0) ),
inference(cnf_transformation,[],[f210]) ).
tcf(c_62,plain,
! [X0: $i] :
( v9_lattices(X0)
| v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0) ),
inference(cnf_transformation,[],[f209]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| ( k4_lattices(X1,X0,X2) = k4_lattices(X1,X2,X0) )
| ~ l1_lattices(X1)
| ~ v6_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f223]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| ( k18_filter_2(X1,X0) = a_2_0_filter_2(X1,X0) )
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f227]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| m1_subset_1(k4_lattices(X1,X0,X2),u1_struct_0(X1))
| ~ l1_lattices(X1)
| ~ v6_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f231]) ).
tcf(c_77,plain,
! [X0: $i] :
( l1_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f235]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| r2_hidden(X1,a_2_0_filter_2(X0,X2))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ r3_lattices(X0,X1,X2) ),
inference(cnf_transformation,[],[f313]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| r3_lattices(X0,X1,X2)
| ~ v9_lattices(X0)
| ~ v8_lattices(X0)
| ~ v6_lattices(X0)
| ~ l3_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ r1_lattices(X0,X1,X2) ),
inference(cnf_transformation,[],[f298]) ).
tcf(c_143,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,[],[f300]) ).
tcf(c_145,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| r1_lattices(X1,k4_lattices(X1,X0,X2),X0)
| ~ 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,[],[f302]) ).
tcf(c_260,plain,
! [X0: $i] :
( l1_lattices(X0)
| ~ l3_lattices(X0) ),
inference(prop_impl_just,[status(thm)],[c_77]) ).
tcf(c_1559,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( v3_struct_0(X1)
| v3_struct_0(X0)
| r3_lattices(X0,X4,X5)
| ~ v9_lattices(X0)
| ~ v8_lattices(X1)
| ~ v8_lattices(X0)
| ~ v6_lattices(X1)
| ~ v6_lattices(X0)
| ~ l3_lattices(X1)
| ~ l3_lattices(X0)
| ~ m1_subset_1(X5,u1_struct_0(X0))
| ~ m1_subset_1(X4,u1_struct_0(X0))
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ( X2 != X5 )
| ( X0 != X1 )
| ( k4_lattices(X1,X2,X3) != X4 ) ),
inference(resolution_lifted,[status(thm)],[c_140,c_145]) ).
tcf(c_1560,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| r3_lattices(X0,k4_lattices(X0,X1,X2),X1)
| ~ v9_lattices(X0)
| ~ v8_lattices(X0)
| ~ v6_lattices(X0)
| ~ l3_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(k4_lattices(X0,X1,X2),u1_struct_0(X0)) ),
inference(unflattening,[status(thm)],[c_1559]) ).
tcf(c_1598,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X1)
| v3_struct_0(X0)
| r3_lattices(X1,k4_lattices(X1,X2,X3),X2)
| ~ v9_lattices(X1)
| ~ v6_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))
| ~ m1_subset_1(k4_lattices(X1,X2,X3),u1_struct_0(X1))
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_61,c_1560]) ).
tcf(c_1599,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| r3_lattices(X0,k4_lattices(X0,X1,X2),X1)
| ~ v9_lattices(X0)
| ~ v6_lattices(X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(k4_lattices(X0,X1,X2),u1_struct_0(X0)) ),
inference(unflattening,[status(thm)],[c_1598]) ).
tcf(c_1601,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| r3_lattices(X0,k4_lattices(X0,X1,X2),X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(k4_lattices(X0,X1,X2),u1_struct_0(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_1599,c_62,c_61,c_59,c_1560]) ).
tcf(c_1625,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X1)
| v3_struct_0(X0)
| r3_lattices(X0,X2,X2)
| ~ v9_lattices(X0)
| ~ v6_lattices(X0)
| ~ l3_lattices(X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_143,c_61]) ).
tcf(c_1626,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| r3_lattices(X1,X0,X0)
| ~ v9_lattices(X1)
| ~ v6_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_1625]) ).
tcf(c_1644,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_1626,c_62,c_59]) ).
tcf(c_1694,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X1)
| v3_struct_0(X0)
| m1_subset_1(k4_lattices(X0,X2,X3),u1_struct_0(X0))
| ~ l1_lattices(X0)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_74,c_59]) ).
tcf(c_1695,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| m1_subset_1(k4_lattices(X1,X0,X2),u1_struct_0(X1))
| ~ l1_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_1694]) ).
tcf(c_1711,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| m1_subset_1(k4_lattices(X1,X0,X2),u1_struct_0(X1))
| ~ 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_1695,c_260]) ).
tcf(c_1719,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X1)
| v3_struct_0(X0)
| ( k4_lattices(X0,X2,X3) = k4_lattices(X0,X3,X2) )
| ~ l1_lattices(X0)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_67,c_59]) ).
tcf(c_1720,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| ( k4_lattices(X1,X0,X2) = k4_lattices(X1,X2,X0) )
| ~ l1_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_1719]) ).
tcf(c_1736,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| ( k4_lattices(X1,X0,X2) = k4_lattices(X1,X2,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_1720,c_260]) ).
tcf(c_1755,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| r3_lattices(X1,k4_lattices(X1,X0,X2),X0)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1601,c_1711]) ).
tcf(c_1846,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( v3_struct_0(X1)
| v3_struct_0(X0)
| r2_hidden(X2,a_2_0_filter_2(X0,X4))
| ~ l3_lattices(X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X1)
| ~ v10_lattices(X0)
| ~ m1_subset_1(X5,u1_struct_0(X1))
| ~ m1_subset_1(X4,u1_struct_0(X0))
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ( X3 != X4 )
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_109,c_1644]) ).
tcf(c_1847,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| r2_hidden(X0,a_2_0_filter_2(X1,X0))
| ~ 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_1846]) ).
tcf(c_1867,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( v3_struct_0(X1)
| v3_struct_0(X0)
| r2_hidden(X4,a_2_0_filter_2(X0,X5))
| ~ l3_lattices(X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X1)
| ~ v10_lattices(X0)
| ~ m1_subset_1(X5,u1_struct_0(X0))
| ~ m1_subset_1(X4,u1_struct_0(X0))
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ( X2 != X5 )
| ( X0 != X1 )
| ( k4_lattices(X1,X2,X3) != X4 ) ),
inference(resolution_lifted,[status(thm)],[c_109,c_1755]) ).
tcf(c_1868,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| r2_hidden(k4_lattices(X0,X1,X2),a_2_0_filter_2(X0,X1))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(k4_lattices(X0,X1,X2),u1_struct_0(X0)) ),
inference(unflattening,[status(thm)],[c_1867]) ).
tcf(c_1884,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| r2_hidden(k4_lattices(X1,X0,X2),a_2_0_filter_2(X1,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_1868,c_1711]) ).
tcf(c_2580,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| r2_hidden(k4_lattices(X0,X1,X2),a_2_0_filter_2(X0,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_53,c_1884]) ).
tcf(c_2581,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| r2_hidden(k4_lattices(sK0,X0,X1),a_2_0_filter_2(sK0,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_2580]) ).
tcf(c_2583,plain,
! [X0: $i,X1: $i] :
( ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| r2_hidden(k4_lattices(sK0,X0,X1),a_2_0_filter_2(sK0,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_2581,c_54,c_52,c_2581]) ).
tcf(c_2584,plain,
! [X0: $i,X1: $i] :
( r2_hidden(k4_lattices(sK0,X0,X1),a_2_0_filter_2(sK0,X0))
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(renaming,[status(thm)],[c_2583]) ).
tcf(c_2595,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| r2_hidden(X1,a_2_0_filter_2(X0,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_53,c_1847]) ).
tcf(c_2596,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| r2_hidden(X0,a_2_0_filter_2(sK0,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_2595]) ).
tcf(c_2598,plain,
! [X0: $i,X1: $i] :
( ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| r2_hidden(X0,a_2_0_filter_2(sK0,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_2596,c_54,c_52,c_2596]) ).
tcf(c_2599,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X0,a_2_0_filter_2(sK0,X0))
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(renaming,[status(thm)],[c_2598]) ).
tcf(c_2625,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| ( k4_lattices(X0,X1,X2) = k4_lattices(X0,X2,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_53,c_1736]) ).
tcf(c_2626,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| ( k4_lattices(sK0,X0,X1) = k4_lattices(sK0,X1,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_2625]) ).
tcf(c_2628,plain,
! [X0: $i,X1: $i] :
( ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ( k4_lattices(sK0,X0,X1) = k4_lattices(sK0,X1,X0) ) ),
inference(global_subsumption_just,[status(thm)],[c_2626,c_54,c_52,c_2626]) ).
tcf(c_2629,plain,
! [X0: $i,X1: $i] :
( ( k4_lattices(sK0,X0,X1) = k4_lattices(sK0,X1,X0) )
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(renaming,[status(thm)],[c_2628]) ).
tcf(c_2724,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| ( k18_filter_2(X0,X1) = a_2_0_filter_2(X0,X1) )
| ~ l3_lattices(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_70]) ).
tcf(c_2725,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| ( k18_filter_2(sK0,X0) = a_2_0_filter_2(sK0,X0) )
| ~ l3_lattices(sK0)
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(unflattening,[status(thm)],[c_2724]) ).
tcf(c_2727,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,u1_struct_0(sK0))
| ( k18_filter_2(sK0,X0) = a_2_0_filter_2(sK0,X0) ) ),
inference(global_subsumption_just,[status(thm)],[c_2725,c_54,c_52,c_2725]) ).
tcf(c_2728,plain,
! [X0: $i] :
( ( k18_filter_2(sK0,X0) = a_2_0_filter_2(sK0,X0) )
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(renaming,[status(thm)],[c_2727]) ).
tcf(c_3354,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_2599]) ).
tcf(c_3355,plain,
! [X0: $i] :
( ~ iPr_def_11
| r2_hidden(X0,a_2_0_filter_2(sK0,X0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_2599]) ).
tcf(c_3356,plain,
( iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_2599]) ).
tcf(c_3403,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,u1_struct_0(sK0))
| r2_hidden(X0,a_2_0_filter_2(sK0,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_3355,c_3354,c_3355,c_3356]) ).
tcf(c_3404,plain,
! [X0: $i] :
( r2_hidden(X0,a_2_0_filter_2(sK0,X0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(renaming,[status(thm)],[c_3403]) ).
tcf(c_3861,plain,
! [X0: $i] :
( ( k4_lattices(sK0,X0,sK2) = k4_lattices(sK0,sK2,X0) )
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(superposition,[status(thm)],[c_50,c_2629]) ).
tcf(c_3916,plain,
k18_filter_2(sK0,sK1) = a_2_0_filter_2(sK0,sK1),
inference(superposition,[status(thm)],[c_51,c_2728]) ).
tcf(c_3930,plain,
( ~ r2_hidden(sK1,k18_filter_2(sK0,sK1))
| ~ r2_hidden(k4_lattices(sK0,sK2,sK1),k18_filter_2(sK0,sK1))
| ~ r2_hidden(k4_lattices(sK0,sK1,sK2),a_2_0_filter_2(sK0,sK1)) ),
inference(superposition,[status(thm)],[c_3916,c_49]) ).
tcf(c_3937,plain,
( ~ r2_hidden(sK1,a_2_0_filter_2(sK0,sK1))
| ~ r2_hidden(k4_lattices(sK0,sK2,sK1),a_2_0_filter_2(sK0,sK1))
| ~ r2_hidden(k4_lattices(sK0,sK1,sK2),a_2_0_filter_2(sK0,sK1)) ),
inference(light_normalisation,[status(thm)],[c_3930,c_3916]) ).
tcf(c_3944,plain,
( ~ m1_subset_1(sK2,u1_struct_0(sK0))
| ~ m1_subset_1(sK1,u1_struct_0(sK0))
| ~ r2_hidden(sK1,a_2_0_filter_2(sK0,sK1))
| ~ r2_hidden(k4_lattices(sK0,sK2,sK1),a_2_0_filter_2(sK0,sK1)) ),
inference(superposition,[status(thm)],[c_2584,c_3937]) ).
tcf(c_3945,plain,
( ~ r2_hidden(sK1,a_2_0_filter_2(sK0,sK1))
| ~ r2_hidden(k4_lattices(sK0,sK2,sK1),a_2_0_filter_2(sK0,sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_3944,c_51,c_50,c_3944]) ).
tcf(c_3980,plain,
k4_lattices(sK0,sK1,sK2) = k4_lattices(sK0,sK2,sK1),
inference(superposition,[status(thm)],[c_51,c_3861]) ).
tcf(c_3992,plain,
( r2_hidden(k4_lattices(sK0,sK2,sK1),a_2_0_filter_2(sK0,sK1))
| ~ m1_subset_1(sK2,u1_struct_0(sK0))
| ~ m1_subset_1(sK1,u1_struct_0(sK0)) ),
inference(superposition,[status(thm)],[c_3980,c_2584]) ).
tcf(c_4024,plain,
( r2_hidden(sK1,a_2_0_filter_2(sK0,sK1))
| ~ m1_subset_1(sK1,u1_struct_0(sK0)) ),
inference(instantiation,[status(thm)],[c_3404]) ).
tcf(c_4025,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4024,c_3992,c_3945,c_50,c_51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LAT305+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/0.43 % Computer : n015.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Wed Sep 23 21:01:24 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/0.48 Running first-order theorem proving
% 0.15/0.48 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
% 0.15/0.50
% 0.15/0.50 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.50
% 0.15/0.50 % Detected problem language: tptp
% 0.23/0.51 % Proving...
% 8.06/1.89 % SZS status Started for theBenchmark.p
% 8.06/1.89 % SZS status Theorem for theBenchmark.p
% 8.06/1.89
% 8.06/1.89 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.06/1.89
% 8.06/1.89 % ------ iProver source info
% 8.06/1.89
% 8.06/1.89 % git: date: 2026-07-19 20:42:38 +0200
% 8.06/1.89 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.06/1.89 % git: non_committed_changes: false
% 8.06/1.89
% 8.06/1.89 % ------ Parsing...
% 8.06/1.89 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.06/1.89
% 8.06/1.89 % ------ 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:16:0s pe_e %
% 8.06/1.89
% 8.06/1.89 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.06/1.89
% 8.06/1.89 % ------ Preprocessing... sf_s rm: 3 0s sf_e
% 8.06/1.89 % ------ Proving...
% 8.06/1.89 % ------ Problem Properties
% 8.06/1.89
% 8.06/1.89 %
% 8.06/1.89 % clauses 82
% 8.06/1.89 % conjectures 3
% 8.06/1.89 % EPR 24
% 8.06/1.89 % Horn 75
% 8.06/1.89 % unary 42
% 8.06/1.89 % binary 17
% 8.06/1.89 % lits 157
% 8.06/1.89 % lits eq 17
% 8.06/1.89 % fd_pure 0
% 8.06/1.89 % fd_pseudo 0
% 8.06/1.89 % fd_cond 1
% 8.06/1.89 % fd_pseudo_cond 3
% 8.06/1.89 % AC symbols 0
% 8.06/1.89
% 8.06/1.89 % ------ Input Options Time Limit: Unbounded
% 8.06/1.89
% 8.06/1.89
% 8.06/1.89 % ------
% 8.06/1.89 % Current options:
% 8.06/1.89 % ------
% 8.06/1.89
% 8.06/1.89
% 8.06/1.89 %
% 8.06/1.89
% 8.06/1.89 % ------ Proving...
% 8.06/1.89 %
% 8.06/1.89
% 8.06/1.89 % SZS status Theorem for theBenchmark.p
% 8.06/1.89
% 8.06/1.89 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.06/1.89
% 8.06/1.89
%------------------------------------------------------------------------------