%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LAT297+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 : Thu Sep 24 01:04:45 PM UTC 2026
% Result : Theorem 4.17s 1.24s
% Output : CNFRefutation 4.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 79 ( 20 unt; 0 def)
% Number of atoms : 408 ( 18 equ)
% Maximal formula atoms : 51 ( 5 avg)
% Number of connectives : 506 ( 177 ~; 196 |; 81 &)
% ( 7 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-3 aty)
% Number of variables : 135 ( 1 sgn 85 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t13_filter_2,conjecture,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> ( ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( ( r2_hidden(X4,X2)
& r2_hidden(X3,X2) )
<=> r2_hidden(k4_lattices(X1,X3,X4),X2) ) ) )
=> m2_lattice4(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_filter_2) ).
fof(d10_lattice4,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> ( m2_lattice4(X2,X1)
<=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( ( r2_hidden(X4,X2)
& r2_hidden(X3,X2) )
=> ( r2_hidden(k3_lattices(X1,X3,X4),X2)
& r2_hidden(k4_lattices(X1,X3,X4),X2) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_lattice4) ).
fof(cc1_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( ( v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( v9_lattices(X1)
& v8_lattices(X1)
& v7_lattices(X1)
& v6_lattices(X1)
& v5_lattices(X1)
& v4_lattices(X1)
& ~ v3_struct_0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_lattices) ).
fof(d9_lattices,axiom,
! [X1] :
( ( l3_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( v9_lattices(X1)
<=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> k2_lattices(X1,X2,k1_lattices(X1,X2,X3)) = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_lattices) ).
fof(redefinition_k3_lattices,axiom,
! [X1,X2,X3] :
( ( m1_subset_1(X3,u1_struct_0(X1))
& m1_subset_1(X2,u1_struct_0(X1))
& l2_lattices(X1)
& v4_lattices(X1)
& ~ v3_struct_0(X1) )
=> k3_lattices(X1,X2,X3) = k1_lattices(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_lattices) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( l2_lattices(X1)
& l1_lattices(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(dt_k1_lattices,axiom,
! [X1,X2,X3] :
( ( m1_subset_1(X3,u1_struct_0(X1))
& m1_subset_1(X2,u1_struct_0(X1))
& l2_lattices(X1)
& ~ v3_struct_0(X1) )
=> m1_subset_1(k1_lattices(X1,X2,X3),u1_struct_0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattices) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( m1_subset_1(X2,k1_zfmisc_1(X3))
& r2_hidden(X1,X2) )
=> m1_subset_1(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(redefinition_k4_lattices,axiom,
! [X1,X2,X3] :
( ( m1_subset_1(X3,u1_struct_0(X1))
& m1_subset_1(X2,u1_struct_0(X1))
& l1_lattices(X1)
& v6_lattices(X1)
& ~ v3_struct_0(X1) )
=> k4_lattices(X1,X2,X3) = k2_lattices(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_lattices) ).
fof(t2_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,X2)
=> ( r2_hidden(X1,X2)
| v1_xboole_0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( v1_xboole_0(X2)
& r2_hidden(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(t1_subset,axiom,
! [X1,X2] :
( r2_hidden(X1,X2)
=> m1_subset_1(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(c_0_12,negated_conjecture,
~ ! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> ( ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( ( r2_hidden(X4,X2)
& r2_hidden(X3,X2) )
<=> r2_hidden(k4_lattices(X1,X3,X4),X2) ) ) )
=> m2_lattice4(X2,X1) ) ) ),
inference(assume_negation,[status(cth)],[t13_filter_2]) ).
fof(c_0_13,negated_conjecture,
~ ! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> ( ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( ( r2_hidden(X4,X2)
& r2_hidden(X3,X2) )
<=> r2_hidden(k4_lattices(X1,X3,X4),X2) ) ) )
=> m2_lattice4(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_14,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> ( m2_lattice4(X2,X1)
<=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( ( r2_hidden(X4,X2)
& r2_hidden(X3,X2) )
=> ( r2_hidden(k3_lattices(X1,X3,X4),X2)
& r2_hidden(k4_lattices(X1,X3,X4),X2) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d10_lattice4]) ).
fof(c_0_15,plain,
! [X1] :
( l3_lattices(X1)
=> ( ( v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( v9_lattices(X1)
& v8_lattices(X1)
& v7_lattices(X1)
& v6_lattices(X1)
& v5_lattices(X1)
& v4_lattices(X1)
& ~ v3_struct_0(X1) ) ) ),
inference(fof_simplification,[status(thm)],[cc1_lattices]) ).
fof(c_0_16,plain,
! [X1] :
( ( l3_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( v9_lattices(X1)
<=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> k2_lattices(X1,X2,k1_lattices(X1,X2,X3)) = X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[d9_lattices]) ).
fof(c_0_17,negated_conjecture,
! [X9,X10] :
( ~ m2_lattice4(esk2_0,esk1_0)
& ( ~ m1_subset_1(X9,u1_struct_0(esk1_0))
| ~ m1_subset_1(X10,u1_struct_0(esk1_0))
| ~ r2_hidden(k4_lattices(esk1_0,X9,X10),esk2_0)
| r2_hidden(X10,esk2_0) )
& ( ~ m1_subset_1(X9,u1_struct_0(esk1_0))
| ~ m1_subset_1(X10,u1_struct_0(esk1_0))
| ~ r2_hidden(k4_lattices(esk1_0,X9,X10),esk2_0)
| r2_hidden(X9,esk2_0) )
& ( ~ m1_subset_1(X9,u1_struct_0(esk1_0))
| ~ m1_subset_1(X10,u1_struct_0(esk1_0))
| r2_hidden(k4_lattices(esk1_0,X9,X10),esk2_0)
| ~ r2_hidden(X10,esk2_0)
| ~ r2_hidden(X9,esk2_0) )
& m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0)))
& l3_lattices(esk1_0)
& v10_lattices(esk1_0)
& ~ v3_struct_0(esk1_0) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])])])]) ).
fof(c_0_18,plain,
! [X29,X30,X31,X32] :
( ( ~ l3_lattices(X29)
| ~ v10_lattices(X29)
| v3_struct_0(X29)
| ~ m1_subset_1(X30,k1_zfmisc_1(u1_struct_0(X29)))
| m2_lattice4(X30,X29)
| ~ r2_hidden(k3_lattices(X29,esk3_2(X29,X30),esk4_2(X29,X30)),X30)
| ~ r2_hidden(k4_lattices(X29,esk3_2(X29,X30),esk4_2(X29,X30)),X30) )
& ( ~ l3_lattices(X29)
| ~ v10_lattices(X29)
| v3_struct_0(X29)
| ~ m1_subset_1(X30,k1_zfmisc_1(u1_struct_0(X29)))
| m2_lattice4(X30,X29)
| r2_hidden(esk4_2(X29,X30),X30) )
& ( ~ l3_lattices(X29)
| ~ v10_lattices(X29)
| v3_struct_0(X29)
| ~ m1_subset_1(X30,k1_zfmisc_1(u1_struct_0(X29)))
| m2_lattice4(X30,X29)
| r2_hidden(esk3_2(X29,X30),X30) )
& ( ~ l3_lattices(X29)
| ~ v10_lattices(X29)
| v3_struct_0(X29)
| ~ m1_subset_1(X30,k1_zfmisc_1(u1_struct_0(X29)))
| m2_lattice4(X30,X29)
| m1_subset_1(esk4_2(X29,X30),u1_struct_0(X29)) )
& ( ~ l3_lattices(X29)
| ~ v10_lattices(X29)
| v3_struct_0(X29)
| ~ m1_subset_1(X30,k1_zfmisc_1(u1_struct_0(X29)))
| m2_lattice4(X30,X29)
| m1_subset_1(esk3_2(X29,X30),u1_struct_0(X29)) )
& ( ~ l3_lattices(X29)
| ~ v10_lattices(X29)
| v3_struct_0(X29)
| ~ m1_subset_1(X30,k1_zfmisc_1(u1_struct_0(X29)))
| ~ m2_lattice4(X30,X29)
| ~ m1_subset_1(X31,u1_struct_0(X29))
| ~ m1_subset_1(X32,u1_struct_0(X29))
| ~ r2_hidden(X32,X30)
| ~ r2_hidden(X31,X30)
| r2_hidden(k3_lattices(X29,X31,X32),X30) )
& ( ~ l3_lattices(X29)
| ~ v10_lattices(X29)
| v3_struct_0(X29)
| ~ m1_subset_1(X30,k1_zfmisc_1(u1_struct_0(X29)))
| ~ m2_lattice4(X30,X29)
| ~ m1_subset_1(X31,u1_struct_0(X29))
| ~ m1_subset_1(X32,u1_struct_0(X29))
| ~ r2_hidden(X32,X30)
| ~ r2_hidden(X31,X30)
| r2_hidden(k4_lattices(X29,X31,X32),X30) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])])])]) ).
fof(c_0_19,plain,
! [X14] :
( ( ~ l3_lattices(X14)
| ~ v10_lattices(X14)
| v3_struct_0(X14)
| v9_lattices(X14) )
& ( ~ l3_lattices(X14)
| ~ v10_lattices(X14)
| v3_struct_0(X14)
| v8_lattices(X14) )
& ( ~ l3_lattices(X14)
| ~ v10_lattices(X14)
| v3_struct_0(X14)
| v7_lattices(X14) )
& ( ~ l3_lattices(X14)
| ~ v10_lattices(X14)
| v3_struct_0(X14)
| v6_lattices(X14) )
& ( ~ l3_lattices(X14)
| ~ v10_lattices(X14)
| v3_struct_0(X14)
| v5_lattices(X14) )
& ( ~ l3_lattices(X14)
| ~ v10_lattices(X14)
| v3_struct_0(X14)
| v4_lattices(X14) )
& ( ~ l3_lattices(X14)
| ~ v10_lattices(X14)
| v3_struct_0(X14)
| ~ v3_struct_0(X14) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
fof(c_0_20,plain,
! [X1,X2,X3] :
( ( m1_subset_1(X3,u1_struct_0(X1))
& m1_subset_1(X2,u1_struct_0(X1))
& l2_lattices(X1)
& v4_lattices(X1)
& ~ v3_struct_0(X1) )
=> k3_lattices(X1,X2,X3) = k1_lattices(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[redefinition_k3_lattices]) ).
fof(c_0_21,plain,
! [X71] :
( ( ~ l3_lattices(X71)
| l2_lattices(X71) )
& ( ~ l3_lattices(X71)
| l1_lattices(X71) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])])]) ).
fof(c_0_22,plain,
! [X46,X47,X48] :
( ( ~ l3_lattices(X46)
| v3_struct_0(X46)
| v9_lattices(X46)
| k2_lattices(X46,esk5_1(X46),k1_lattices(X46,esk5_1(X46),esk6_1(X46))) != esk5_1(X46) )
& ( ~ l3_lattices(X46)
| v3_struct_0(X46)
| v9_lattices(X46)
| m1_subset_1(esk6_1(X46),u1_struct_0(X46)) )
& ( ~ l3_lattices(X46)
| v3_struct_0(X46)
| v9_lattices(X46)
| m1_subset_1(esk5_1(X46),u1_struct_0(X46)) )
& ( ~ l3_lattices(X46)
| v3_struct_0(X46)
| k2_lattices(X46,X47,k1_lattices(X46,X47,X48)) = X47
| ~ m1_subset_1(X48,u1_struct_0(X46))
| ~ m1_subset_1(X47,u1_struct_0(X46))
| ~ v9_lattices(X46) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])])])]) ).
cnf(c_0_23,negated_conjecture,
~ m2_lattice4(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| v3_struct_0(X1)
| m2_lattice4(X2,X1)
| m1_subset_1(esk4_2(X1,X2),u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,negated_conjecture,
m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_28,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_29,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| v9_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_30,plain,
! [X127,X128,X129] :
( k3_lattices(X127,X128,X129) = k1_lattices(X127,X128,X129)
| ~ m1_subset_1(X129,u1_struct_0(X127))
| ~ m1_subset_1(X128,u1_struct_0(X127))
| ~ l2_lattices(X127)
| ~ v4_lattices(X127)
| v3_struct_0(X127) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).
cnf(c_0_31,plain,
( ~ l3_lattices(X1)
| l2_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_32,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| v4_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_33,plain,
! [X1,X2,X3] :
( ( m1_subset_1(X3,u1_struct_0(X1))
& m1_subset_1(X2,u1_struct_0(X1))
& l2_lattices(X1)
& ~ v3_struct_0(X1) )
=> m1_subset_1(k1_lattices(X1,X2,X3),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k1_lattices]) ).
fof(c_0_34,plain,
! [X143,X144,X145] :
( m1_subset_1(X143,X145)
| ~ m1_subset_1(X144,k1_zfmisc_1(X145))
| ~ r2_hidden(X143,X144) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])])]) ).
fof(c_0_35,plain,
! [X1,X2,X3] :
( ( m1_subset_1(X3,u1_struct_0(X1))
& m1_subset_1(X2,u1_struct_0(X1))
& l1_lattices(X1)
& v6_lattices(X1)
& ~ v3_struct_0(X1) )
=> k4_lattices(X1,X2,X3) = k2_lattices(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[redefinition_k4_lattices]) ).
cnf(c_0_36,plain,
( ~ l3_lattices(X1)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ v9_lattices(X1)
| v3_struct_0(X1)
| k2_lattices(X1,X2,k1_lattices(X1,X2,X3)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_37,negated_conjecture,
m1_subset_1(esk4_2(esk1_0,esk2_0),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26]),c_0_27])]),c_0_28]) ).
cnf(c_0_38,negated_conjecture,
v9_lattices(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_27]),c_0_26])]),c_0_28]) ).
cnf(c_0_39,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| v3_struct_0(X1)
| m2_lattice4(X2,X1)
| m1_subset_1(esk3_2(X1,X2),u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_40,plain,
( ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l2_lattices(X1)
| ~ v4_lattices(X1)
| k3_lattices(X1,X2,X3) = k1_lattices(X1,X2,X3)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_41,negated_conjecture,
l2_lattices(esk1_0),
inference(spm,[status(thm)],[c_0_31,c_0_26]) ).
cnf(c_0_42,negated_conjecture,
v4_lattices(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_27]),c_0_26])]),c_0_28]) ).
fof(c_0_43,plain,
! [X51,X52,X53] :
( m1_subset_1(k1_lattices(X51,X52,X53),u1_struct_0(X51))
| ~ m1_subset_1(X53,u1_struct_0(X51))
| ~ m1_subset_1(X52,u1_struct_0(X51))
| ~ l2_lattices(X51)
| v3_struct_0(X51) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])]) ).
fof(c_0_44,plain,
! [X139,X140] :
( r2_hidden(X139,X140)
| v1_xboole_0(X140)
| ~ m1_subset_1(X139,X140) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])])]) ).
fof(c_0_45,plain,
! [X150,X151] :
( ~ v1_xboole_0(X151)
| ~ r2_hidden(X150,X151) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])])]) ).
fof(c_0_46,plain,
! [X137,X138] :
( m1_subset_1(X137,X138)
| ~ r2_hidden(X137,X138) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])])]) ).
cnf(c_0_47,plain,
( ~ m1_subset_1(X2,k1_zfmisc_1(X3))
| ~ r2_hidden(X1,X2)
| m1_subset_1(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_48,plain,
! [X130,X131,X132] :
( k4_lattices(X130,X131,X132) = k2_lattices(X130,X131,X132)
| ~ m1_subset_1(X132,u1_struct_0(X130))
| ~ m1_subset_1(X131,u1_struct_0(X130))
| ~ l1_lattices(X130)
| ~ v6_lattices(X130)
| v3_struct_0(X130) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])]) ).
cnf(c_0_49,plain,
( ~ l3_lattices(X1)
| l1_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_50,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| v6_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_51,negated_conjecture,
( ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| k2_lattices(esk1_0,X1,k1_lattices(esk1_0,X1,esk4_2(esk1_0,esk2_0))) = X1 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_26])]),c_0_28]) ).
cnf(c_0_52,negated_conjecture,
m1_subset_1(esk3_2(esk1_0,esk2_0),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_39]),c_0_25]),c_0_26]),c_0_27])]),c_0_28]) ).
cnf(c_0_53,negated_conjecture,
( ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| k1_lattices(esk1_0,X1,esk4_2(esk1_0,esk2_0)) = k3_lattices(esk1_0,X1,esk4_2(esk1_0,esk2_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_37]),c_0_41]),c_0_42])]),c_0_28]) ).
cnf(c_0_54,plain,
( ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l2_lattices(X1)
| m1_subset_1(k1_lattices(X1,X2,X3),u1_struct_0(X1))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_55,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ r2_hidden(k3_lattices(X1,esk3_2(X1,X2),esk4_2(X1,X2)),X2)
| ~ r2_hidden(k4_lattices(X1,esk3_2(X1,X2),esk4_2(X1,X2)),X2)
| v3_struct_0(X1)
| m2_lattice4(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_56,plain,
( ~ m1_subset_1(X1,X2)
| r2_hidden(X1,X2)
| v1_xboole_0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_57,plain,
( ~ v1_xboole_0(X2)
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_58,plain,
( ~ r2_hidden(X1,X2)
| m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_59,negated_conjecture,
( ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ m1_subset_1(X2,u1_struct_0(esk1_0))
| ~ r2_hidden(X2,esk2_0)
| ~ r2_hidden(X1,esk2_0)
| r2_hidden(k4_lattices(esk1_0,X1,X2),esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_60,negated_conjecture,
( ~ r2_hidden(X1,esk2_0)
| m1_subset_1(X1,u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_47,c_0_25]) ).
cnf(c_0_61,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| v3_struct_0(X1)
| m2_lattice4(X2,X1)
| r2_hidden(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_62,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| v3_struct_0(X1)
| m2_lattice4(X2,X1)
| r2_hidden(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_63,negated_conjecture,
( ~ m1_subset_1(X2,u1_struct_0(esk1_0))
| ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ r2_hidden(k4_lattices(esk1_0,X2,X1),esk2_0)
| r2_hidden(X1,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_64,plain,
( ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l1_lattices(X1)
| ~ v6_lattices(X1)
| k4_lattices(X1,X2,X3) = k2_lattices(X1,X2,X3)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_65,negated_conjecture,
l1_lattices(esk1_0),
inference(spm,[status(thm)],[c_0_49,c_0_26]) ).
cnf(c_0_66,negated_conjecture,
v6_lattices(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_27]),c_0_26])]),c_0_28]) ).
cnf(c_0_67,negated_conjecture,
k2_lattices(esk1_0,esk3_2(esk1_0,esk2_0),k1_lattices(esk1_0,esk3_2(esk1_0,esk2_0),esk4_2(esk1_0,esk2_0))) = esk3_2(esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_68,negated_conjecture,
k1_lattices(esk1_0,esk3_2(esk1_0,esk2_0),esk4_2(esk1_0,esk2_0)) = k3_lattices(esk1_0,esk3_2(esk1_0,esk2_0),esk4_2(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_53,c_0_52]) ).
cnf(c_0_69,negated_conjecture,
( ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| m1_subset_1(k1_lattices(esk1_0,X1,esk4_2(esk1_0,esk2_0)),u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_37]),c_0_41])]),c_0_28]) ).
cnf(c_0_70,plain,
( ~ v10_lattices(X2)
| ~ l3_lattices(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))
| ~ m1_subset_1(k4_lattices(X2,esk3_2(X2,X1),esk4_2(X2,X1)),X1)
| ~ r2_hidden(k3_lattices(X2,esk3_2(X2,X1),esk4_2(X2,X1)),X1)
| v3_struct_0(X2)
| m2_lattice4(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]) ).
cnf(c_0_71,negated_conjecture,
( ~ r2_hidden(X1,esk2_0)
| ~ r2_hidden(X2,esk2_0)
| m1_subset_1(k4_lattices(esk1_0,X1,X2),esk2_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]),c_0_60]) ).
cnf(c_0_72,negated_conjecture,
r2_hidden(esk4_2(esk1_0,esk2_0),esk2_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_61]),c_0_25]),c_0_26]),c_0_27])]),c_0_28]) ).
cnf(c_0_73,negated_conjecture,
r2_hidden(esk3_2(esk1_0,esk2_0),esk2_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_62]),c_0_25]),c_0_26]),c_0_27])]),c_0_28]) ).
cnf(c_0_74,negated_conjecture,
( ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ m1_subset_1(X2,u1_struct_0(esk1_0))
| ~ r2_hidden(k2_lattices(esk1_0,X2,X1),esk2_0)
| r2_hidden(X1,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_28]),c_0_65]),c_0_66])]) ).
cnf(c_0_75,negated_conjecture,
k2_lattices(esk1_0,esk3_2(esk1_0,esk2_0),k3_lattices(esk1_0,esk3_2(esk1_0,esk2_0),esk4_2(esk1_0,esk2_0))) = esk3_2(esk1_0,esk2_0),
inference(rw,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_76,negated_conjecture,
m1_subset_1(k3_lattices(esk1_0,esk3_2(esk1_0,esk2_0),esk4_2(esk1_0,esk2_0)),u1_struct_0(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_68]),c_0_52])]) ).
cnf(c_0_77,negated_conjecture,
~ r2_hidden(k3_lattices(esk1_0,esk3_2(esk1_0,esk2_0),esk4_2(esk1_0,esk2_0)),esk2_0),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_25]),c_0_26]),c_0_27]),c_0_72]),c_0_73])]),c_0_23]),c_0_28]) ).
cnf(c_0_78,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_73]),c_0_52]),c_0_76])]),c_0_77]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LAT297+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.44 % Computer : n008.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sun Sep 20 23:30:08 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.51 Running first-order theorem proving
% 0.27/0.51 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.17/1.24 % Version: 3.5.1
% 4.17/1.24 % Preprocessing class: FSLSSMSSSSSNFFN.
% 4.17/1.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.17/1.24 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 4.17/1.24 % Starting new_bool_3 with 300s (1) cores
% 4.17/1.24 % Starting new_bool_1 with 300s (1) cores
% 4.17/1.24 % Starting sh5l with 300s (1) cores
% 4.17/1.24 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 3829958 completed with status 0
% 4.17/1.24 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 4.17/1.24 % Preprocessing class: FSLSSMSSSSSNFFN.
% 4.17/1.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.17/1.24 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 4.17/1.24 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.17/1.24 % No SInE strategy applied
% 4.17/1.24 % Search class: FGHSM-FSMM31-MFFFFFNN
% 4.17/1.24 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 4.17/1.24 % Starting SubtermCWHack with 136s (1) cores
% 4.17/1.24 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 4.17/1.24 % Starting G-E--_208_C18_F1_AE_CS_SP_PI_S0a with 136s (1) cores
% 4.17/1.24 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 4.17/1.24 % Starting new_bool_3 with 136s (1) cores
% 4.17/1.24 % G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y with pid 3829968 completed with status 0
% 4.17/1.24 % Result found by G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y
% 4.17/1.24 % Preprocessing class: FSLSSMSSSSSNFFN.
% 4.17/1.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.17/1.24 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 4.17/1.24 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.17/1.24 % No SInE strategy applied
% 4.17/1.24 % Search class: FGHSM-FSMM31-MFFFFFNN
% 4.17/1.24 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 4.17/1.24 % Starting SubtermCWHack with 136s (1) cores
% 4.17/1.24 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 4.17/1.24 % Starting G-E--_208_C18_F1_AE_CS_SP_PI_S0a with 136s (1) cores
% 4.17/1.24 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 4.17/1.24 % Preprocessing time : 0.003 s
% 4.17/1.24 % Presaturation interreduction done
% 4.17/1.24
% 4.17/1.24 % Proof found!
% 4.17/1.24 % SZS status Theorem
% 4.17/1.24 % SZS output start CNFRefutation
% See solution above
% 4.17/1.24 % Parsed axioms : 85
% 4.17/1.24 % Removed by relevancy pruning/SinE : 0
% 4.17/1.24 % Initial clauses : 147
% 4.17/1.24 % Removed in clause preprocessing : 17
% 4.17/1.24 % Initial clauses in saturation : 130
% 4.17/1.24 % Processed clauses : 1791
% 4.17/1.24 % ...of these trivial : 41
% 4.17/1.24 % ...subsumed : 553
% 4.17/1.24 % ...remaining for further processing : 1197
% 4.17/1.24 % Other redundant clauses eliminated : 0
% 4.17/1.24 % Clauses deleted for lack of memory : 0
% 4.17/1.24 % Backward-subsumed : 18
% 4.17/1.24 % Backward-rewritten : 20
% 4.17/1.24 % Generated clauses : 29563
% 4.17/1.24 % ...of the previous two non-redundant : 29046
% 4.17/1.24 % ...aggressively subsumed : 0
% 4.17/1.24 % Contextual simplify-reflections : 48
% 4.17/1.24 % Paramodulations : 29560
% 4.17/1.24 % Factorizations : 0
% 4.17/1.24 % NegExts : 0
% 4.17/1.24 % Equation resolutions : 0
% 4.17/1.24 % Disequality decompositions : 0
% 4.17/1.24 % Total rewrite steps : 8741
% 4.17/1.24 % ...of those cached : 8615
% 4.17/1.24 % Propositional unsat checks : 0
% 4.17/1.24 % Propositional check models : 0
% 4.17/1.24 % Propositional check unsatisfiable : 0
% 4.17/1.24 % Propositional clauses : 0
% 4.17/1.24 % Propositional clauses after purity: 0
% 4.17/1.24 % Propositional unsat core size : 0
% 4.17/1.24 % Propositional preprocessing time : 0.000
% 4.17/1.24 % Propositional encoding time : 0.000
% 4.17/1.24 % Propositional solver time : 0.000
% 4.17/1.24 % Success case prop preproc time : 0.000
% 4.17/1.24 % Success case prop encoding time : 0.000
% 4.17/1.24 % Success case prop solver time : 0.000
% 4.17/1.24 % Current number of processed clauses : 1037
% 4.17/1.24 % Positive orientable unit clauses : 190
% 4.17/1.24 % Positive unorientable unit clauses: 1
% 4.17/1.24 % Negative unit clauses : 38
% 4.17/1.24 % Non-unit-clauses : 808
% 4.17/1.24 % Current number of unprocessed clauses: 27384
% 4.17/1.24 % ...number of literals in the above : 111334
% 4.17/1.24 % Current number of archived formulas : 0
% 4.17/1.24 % Current number of archived clauses : 160
% 4.17/1.24 % Clause-clause subsumption calls (NU) : 116667
% 4.17/1.24 % Rec. Clause-clause subsumption calls : 45276
% 4.17/1.24 % Non-unit clause-clause subsumptions : 521
% 4.17/1.24 % Unit Clause-clause subsumption calls : 15242
% 4.17/1.24 % Rewrite failures with RHS unbound : 0
% 4.17/1.24 % BW rewrite match attempts : 810
% 4.17/1.24 % BW rewrite match successes : 18
% 4.17/1.24 % Condensation attempts : 0
% 4.17/1.24 % Condensation successes : 0
% 4.17/1.24 % Termbank termtop insertions : 962611
% 4.17/1.24 % Search garbage collected termcells : 1813
% 4.17/1.24
% 4.17/1.24 % -------------------------------------------------
% 4.17/1.24 % User time : 0.657 s
% 4.17/1.24 % System time : 0.032 s
% 4.17/1.24 % Total time : 0.689 s
% 4.17/1.24 % Maximum resident set size: 3972 pages
% 4.17/1.24
% 4.17/1.24 % -------------------------------------------------
% 4.17/1.24 % User time : 3.276 s
% 4.17/1.24 % System time : 0.153 s
% 4.17/1.24 % Total time : 3.429 s
% 4.17/1.24 % Maximum resident set size: 4608 pages
% 4.17/1.24 % E exiting
%------------------------------------------------------------------------------