%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LAT297+4 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 01:04:46 PM UTC 2026
% Result : Theorem 60.75s 11.22s
% Output : CNFRefutation 60.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 60 ( 18 unt; 0 def)
% Number of atoms : 400 ( 0 equ)
% Maximal formula atoms : 70 ( 6 avg)
% Number of connectives : 532 ( 192 ~; 233 |; 54 &)
% ( 9 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 103 ( 1 sgn 60 !; 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/sandbox/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/sandbox/benchmark/Axioms/SET007/SET007+375.ax',d10_lattice4) ).
fof(t10_filter_0,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_filter_0(X4,X1)
=> ( r2_hidden(X2,X4)
=> ( r2_hidden(k3_lattices(X1,X3,X2),X4)
& r2_hidden(k3_lattices(X1,X2,X3),X4) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+242.ax',t10_filter_0) ).
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/sandbox/benchmark/Axioms/SET007/SET007+9.ax',t4_subset) ).
fof(d1_filter_0,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
& ~ v1_xboole_0(X2) )
=> ( m1_filter_0(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(k4_lattices(X1,X3,X4),X2) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+242.ax',d1_filter_0) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( v1_xboole_0(X2)
& r2_hidden(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+3.ax',t7_boole) ).
fof(c_0_6,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_7,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_8,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_6]) ).
fof(c_0_9,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_filter_0(X4,X1)
=> ( r2_hidden(X2,X4)
=> ( r2_hidden(k3_lattices(X1,X3,X2),X4)
& r2_hidden(k3_lattices(X1,X2,X3),X4) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[t10_filter_0]) ).
fof(c_0_10,plain,
! [X58,X59,X60,X61] :
( ( ~ l3_lattices(X58)
| ~ v10_lattices(X58)
| v3_struct_0(X58)
| ~ m1_subset_1(X59,k1_zfmisc_1(u1_struct_0(X58)))
| m2_lattice4(X59,X58)
| ~ r2_hidden(k3_lattices(X58,esk4_2(X58,X59),esk5_2(X58,X59)),X59)
| ~ r2_hidden(k4_lattices(X58,esk4_2(X58,X59),esk5_2(X58,X59)),X59) )
& ( ~ l3_lattices(X58)
| ~ v10_lattices(X58)
| v3_struct_0(X58)
| ~ m1_subset_1(X59,k1_zfmisc_1(u1_struct_0(X58)))
| m2_lattice4(X59,X58)
| r2_hidden(esk5_2(X58,X59),X59) )
& ( ~ l3_lattices(X58)
| ~ v10_lattices(X58)
| v3_struct_0(X58)
| ~ m1_subset_1(X59,k1_zfmisc_1(u1_struct_0(X58)))
| m2_lattice4(X59,X58)
| r2_hidden(esk4_2(X58,X59),X59) )
& ( ~ l3_lattices(X58)
| ~ v10_lattices(X58)
| v3_struct_0(X58)
| ~ m1_subset_1(X59,k1_zfmisc_1(u1_struct_0(X58)))
| m2_lattice4(X59,X58)
| m1_subset_1(esk5_2(X58,X59),u1_struct_0(X58)) )
& ( ~ l3_lattices(X58)
| ~ v10_lattices(X58)
| v3_struct_0(X58)
| ~ m1_subset_1(X59,k1_zfmisc_1(u1_struct_0(X58)))
| m2_lattice4(X59,X58)
| m1_subset_1(esk4_2(X58,X59),u1_struct_0(X58)) )
& ( ~ l3_lattices(X58)
| ~ v10_lattices(X58)
| v3_struct_0(X58)
| ~ m1_subset_1(X59,k1_zfmisc_1(u1_struct_0(X58)))
| ~ m2_lattice4(X59,X58)
| ~ m1_subset_1(X60,u1_struct_0(X58))
| ~ m1_subset_1(X61,u1_struct_0(X58))
| ~ r2_hidden(X61,X59)
| ~ r2_hidden(X60,X59)
| r2_hidden(k3_lattices(X58,X60,X61),X59) )
& ( ~ l3_lattices(X58)
| ~ v10_lattices(X58)
| v3_struct_0(X58)
| ~ m1_subset_1(X59,k1_zfmisc_1(u1_struct_0(X58)))
| ~ m2_lattice4(X59,X58)
| ~ m1_subset_1(X60,u1_struct_0(X58))
| ~ m1_subset_1(X61,u1_struct_0(X58))
| ~ r2_hidden(X61,X59)
| ~ r2_hidden(X60,X59)
| r2_hidden(k4_lattices(X58,X60,X61),X59) ) ),
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_7])])])])])]) ).
fof(c_0_11,negated_conjecture,
! [X54,X55] :
( ~ m2_lattice4(esk2_0,esk1_0)
& ( ~ m1_subset_1(X54,u1_struct_0(esk1_0))
| ~ m1_subset_1(X55,u1_struct_0(esk1_0))
| ~ r2_hidden(k4_lattices(esk1_0,X54,X55),esk2_0)
| r2_hidden(X55,esk2_0) )
& ( ~ m1_subset_1(X54,u1_struct_0(esk1_0))
| ~ m1_subset_1(X55,u1_struct_0(esk1_0))
| ~ r2_hidden(k4_lattices(esk1_0,X54,X55),esk2_0)
| r2_hidden(X54,esk2_0) )
& ( ~ m1_subset_1(X54,u1_struct_0(esk1_0))
| ~ m1_subset_1(X55,u1_struct_0(esk1_0))
| r2_hidden(k4_lattices(esk1_0,X54,X55),esk2_0)
| ~ r2_hidden(X55,esk2_0)
| ~ r2_hidden(X54,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_8])])])])])]) ).
fof(c_0_12,plain,
! [X99,X100,X101] :
( m1_subset_1(X99,X101)
| ~ m1_subset_1(X100,k1_zfmisc_1(X101))
| ~ r2_hidden(X99,X100) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])])]) ).
fof(c_0_13,plain,
! [X220,X221,X222,X223] :
( ( ~ l3_lattices(X220)
| ~ v10_lattices(X220)
| v3_struct_0(X220)
| ~ m1_subset_1(X221,u1_struct_0(X220))
| ~ m1_subset_1(X222,u1_struct_0(X220))
| ~ m1_filter_0(X223,X220)
| ~ r2_hidden(X221,X223)
| r2_hidden(k3_lattices(X220,X222,X221),X223) )
& ( ~ l3_lattices(X220)
| ~ v10_lattices(X220)
| v3_struct_0(X220)
| ~ m1_subset_1(X221,u1_struct_0(X220))
| ~ m1_subset_1(X222,u1_struct_0(X220))
| ~ m1_filter_0(X223,X220)
| ~ r2_hidden(X221,X223)
| r2_hidden(k3_lattices(X220,X221,X222),X223) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])])]) ).
cnf(c_0_14,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(esk5_2(X1,X2),u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
~ m2_lattice4(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,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_12]) ).
cnf(c_0_21,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_filter_0(X4,X1)
| ~ r2_hidden(X3,X4)
| v3_struct_0(X1)
| r2_hidden(k3_lattices(X1,X2,X3),X4) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,negated_conjecture,
m1_subset_1(esk5_2(esk1_0,esk2_0),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17])]),c_0_18]),c_0_19]) ).
cnf(c_0_23,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(esk5_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_24,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_11]) ).
cnf(c_0_25,negated_conjecture,
( ~ r2_hidden(X1,esk2_0)
| m1_subset_1(X1,u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_20,c_0_15]) ).
cnf(c_0_26,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_10]) ).
fof(c_0_27,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
& ~ v1_xboole_0(X2) )
=> ( m1_filter_0(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(k4_lattices(X1,X3,X4),X2) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d1_filter_0]) ).
fof(c_0_28,plain,
! [X80,X81] :
( ~ v1_xboole_0(X81)
| ~ r2_hidden(X80,X81) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])])]) ).
cnf(c_0_29,negated_conjecture,
( ~ r2_hidden(esk5_2(esk1_0,esk2_0),X2)
| ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ m1_filter_0(X2,esk1_0)
| r2_hidden(k3_lattices(esk1_0,X1,esk5_2(esk1_0,esk2_0)),X2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_16]),c_0_17])]),c_0_19]) ).
cnf(c_0_30,negated_conjecture,
r2_hidden(esk5_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(spm,[status(thm)],[c_0_23,c_0_15]),c_0_16]),c_0_17])]),c_0_18]),c_0_19]) ).
cnf(c_0_31,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_10]) ).
cnf(c_0_32,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ r2_hidden(k3_lattices(X1,esk4_2(X1,X2),esk5_2(X1,X2)),X2)
| ~ r2_hidden(k4_lattices(X1,esk4_2(X1,X2),esk5_2(X1,X2)),X2)
| v3_struct_0(X1)
| m2_lattice4(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_33,negated_conjecture,
( ~ r2_hidden(X1,esk2_0)
| ~ r2_hidden(X2,esk2_0)
| r2_hidden(k4_lattices(esk1_0,X1,X2),esk2_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_24,c_0_25]),c_0_25]) ).
cnf(c_0_34,negated_conjecture,
r2_hidden(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(spm,[status(thm)],[c_0_26,c_0_15]),c_0_16]),c_0_17])]),c_0_18]),c_0_19]) ).
fof(c_0_35,plain,
! [X168,X169,X170,X171] :
( ( ~ l3_lattices(X168)
| ~ v10_lattices(X168)
| v3_struct_0(X168)
| ~ m1_subset_1(X169,k1_zfmisc_1(u1_struct_0(X168)))
| v1_xboole_0(X169)
| m1_filter_0(X169,X168)
| r2_hidden(k4_lattices(X168,esk22_2(X168,X169),esk23_2(X168,X169)),X169)
| r2_hidden(esk23_2(X168,X169),X169) )
& ( ~ l3_lattices(X168)
| ~ v10_lattices(X168)
| v3_struct_0(X168)
| ~ m1_subset_1(X169,k1_zfmisc_1(u1_struct_0(X168)))
| v1_xboole_0(X169)
| m1_filter_0(X169,X168)
| r2_hidden(k4_lattices(X168,esk22_2(X168,X169),esk23_2(X168,X169)),X169)
| r2_hidden(esk22_2(X168,X169),X169) )
& ( ~ l3_lattices(X168)
| ~ v10_lattices(X168)
| v3_struct_0(X168)
| ~ m1_subset_1(X169,k1_zfmisc_1(u1_struct_0(X168)))
| v1_xboole_0(X169)
| m1_filter_0(X169,X168)
| ~ r2_hidden(k4_lattices(X168,esk22_2(X168,X169),esk23_2(X168,X169)),X169)
| ~ r2_hidden(esk23_2(X168,X169),X169)
| ~ r2_hidden(esk22_2(X168,X169),X169) )
& ( ~ l3_lattices(X168)
| ~ v10_lattices(X168)
| v3_struct_0(X168)
| ~ m1_subset_1(X169,k1_zfmisc_1(u1_struct_0(X168)))
| v1_xboole_0(X169)
| m1_filter_0(X169,X168)
| m1_subset_1(esk23_2(X168,X169),u1_struct_0(X168)) )
& ( ~ l3_lattices(X168)
| ~ v10_lattices(X168)
| v3_struct_0(X168)
| ~ m1_subset_1(X169,k1_zfmisc_1(u1_struct_0(X168)))
| v1_xboole_0(X169)
| m1_filter_0(X169,X168)
| m1_subset_1(esk22_2(X168,X169),u1_struct_0(X168)) )
& ( ~ l3_lattices(X168)
| ~ v10_lattices(X168)
| v3_struct_0(X168)
| ~ m1_subset_1(X169,k1_zfmisc_1(u1_struct_0(X168)))
| v1_xboole_0(X169)
| ~ m1_filter_0(X169,X168)
| ~ m1_subset_1(X170,u1_struct_0(X168))
| ~ m1_subset_1(X171,u1_struct_0(X168))
| ~ r2_hidden(k4_lattices(X168,X170,X171),X169)
| r2_hidden(X171,X169) )
& ( ~ l3_lattices(X168)
| ~ v10_lattices(X168)
| v3_struct_0(X168)
| ~ m1_subset_1(X169,k1_zfmisc_1(u1_struct_0(X168)))
| v1_xboole_0(X169)
| ~ m1_filter_0(X169,X168)
| ~ m1_subset_1(X170,u1_struct_0(X168))
| ~ m1_subset_1(X171,u1_struct_0(X168))
| ~ r2_hidden(k4_lattices(X168,X170,X171),X169)
| r2_hidden(X170,X169) )
& ( ~ l3_lattices(X168)
| ~ v10_lattices(X168)
| v3_struct_0(X168)
| ~ m1_subset_1(X169,k1_zfmisc_1(u1_struct_0(X168)))
| v1_xboole_0(X169)
| ~ m1_filter_0(X169,X168)
| ~ m1_subset_1(X170,u1_struct_0(X168))
| ~ m1_subset_1(X171,u1_struct_0(X168))
| r2_hidden(k4_lattices(X168,X170,X171),X169)
| ~ r2_hidden(X171,X169)
| ~ r2_hidden(X170,X169) ) ),
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_27])])])])])]) ).
cnf(c_0_36,plain,
( ~ v1_xboole_0(X2)
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_37,negated_conjecture,
( ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ m1_filter_0(esk2_0,esk1_0)
| r2_hidden(k3_lattices(esk1_0,X1,esk5_2(esk1_0,esk2_0)),esk2_0) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_38,negated_conjecture,
m1_subset_1(esk4_2(esk1_0,esk2_0),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_15]),c_0_16]),c_0_17])]),c_0_18]),c_0_19]) ).
cnf(c_0_39,negated_conjecture,
~ r2_hidden(k3_lattices(esk1_0,esk4_2(esk1_0,esk2_0),esk5_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_32,c_0_33]),c_0_16]),c_0_17]),c_0_15]),c_0_30]),c_0_34])]),c_0_18]),c_0_19]) ).
cnf(c_0_40,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| v3_struct_0(X1)
| v1_xboole_0(X2)
| m1_filter_0(X2,X1)
| m1_subset_1(esk23_2(X1,X2),u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_41,negated_conjecture,
~ v1_xboole_0(esk2_0),
inference(spm,[status(thm)],[c_0_36,c_0_34]) ).
cnf(c_0_42,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| v3_struct_0(X1)
| v1_xboole_0(X2)
| m1_filter_0(X2,X1)
| m1_subset_1(esk22_2(X1,X2),u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ r2_hidden(k4_lattices(X1,esk22_2(X1,X2),esk23_2(X1,X2)),X2)
| ~ r2_hidden(esk23_2(X1,X2),X2)
| ~ r2_hidden(esk22_2(X1,X2),X2)
| v3_struct_0(X1)
| v1_xboole_0(X2)
| m1_filter_0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_44,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| v3_struct_0(X1)
| v1_xboole_0(X2)
| m1_filter_0(X2,X1)
| r2_hidden(k4_lattices(X1,esk22_2(X1,X2),esk23_2(X1,X2)),X2)
| r2_hidden(esk22_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_45,negated_conjecture,
~ m1_filter_0(esk2_0,esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_46,negated_conjecture,
( m1_subset_1(esk23_2(esk1_0,esk2_0),u1_struct_0(esk1_0))
| m1_filter_0(esk2_0,esk1_0) ),
inference(sr,[status(thm)],[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_15]),c_0_16]),c_0_17])]),c_0_19]),c_0_41]) ).
cnf(c_0_47,negated_conjecture,
( m1_subset_1(esk22_2(esk1_0,esk2_0),u1_struct_0(esk1_0))
| m1_filter_0(esk2_0,esk1_0) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_15]),c_0_16]),c_0_17])]),c_0_19]),c_0_41]) ).
cnf(c_0_48,plain,
( ~ r2_hidden(esk23_2(X2,X1),X1)
| ~ r2_hidden(esk22_2(X2,X1),X1)
| ~ r2_hidden(k4_lattices(X2,esk22_2(X2,X1),esk23_2(X2,X1)),X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))
| ~ l3_lattices(X2)
| ~ v10_lattices(X2)
| v3_struct_0(X2)
| m1_filter_0(X1,X2) ),
inference(csr,[status(thm)],[c_0_43,c_0_36]) ).
cnf(c_0_49,negated_conjecture,
( ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ m1_subset_1(X2,u1_struct_0(esk1_0))
| ~ r2_hidden(k4_lattices(esk1_0,X1,X2),esk2_0)
| r2_hidden(X1,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_50,negated_conjecture,
( r2_hidden(esk22_2(esk1_0,esk2_0),esk2_0)
| r2_hidden(k4_lattices(esk1_0,esk22_2(esk1_0,esk2_0),esk23_2(esk1_0,esk2_0)),esk2_0) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_15]),c_0_16]),c_0_17])]),c_0_19]),c_0_41]),c_0_45]) ).
cnf(c_0_51,negated_conjecture,
m1_subset_1(esk23_2(esk1_0,esk2_0),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[c_0_46,c_0_45]) ).
cnf(c_0_52,negated_conjecture,
m1_subset_1(esk22_2(esk1_0,esk2_0),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[c_0_47,c_0_45]) ).
cnf(c_0_53,negated_conjecture,
( ~ r2_hidden(esk23_2(esk1_0,esk2_0),esk2_0)
| ~ r2_hidden(esk22_2(esk1_0,esk2_0),esk2_0)
| m1_filter_0(esk2_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_48,c_0_33]),c_0_16]),c_0_17]),c_0_15])]),c_0_19]) ).
cnf(c_0_54,negated_conjecture,
r2_hidden(esk22_2(esk1_0,esk2_0),esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_52])]) ).
cnf(c_0_55,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| v3_struct_0(X1)
| v1_xboole_0(X2)
| m1_filter_0(X2,X1)
| r2_hidden(k4_lattices(X1,esk22_2(X1,X2),esk23_2(X1,X2)),X2)
| r2_hidden(esk23_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_56,negated_conjecture,
~ r2_hidden(esk23_2(esk1_0,esk2_0),esk2_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_54])]),c_0_45]) ).
cnf(c_0_57,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_11]) ).
cnf(c_0_58,negated_conjecture,
r2_hidden(k4_lattices(esk1_0,esk22_2(esk1_0,esk2_0),esk23_2(esk1_0,esk2_0)),esk2_0),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_15]),c_0_16]),c_0_17])]),c_0_19]),c_0_41]),c_0_45]),c_0_56]) ).
cnf(c_0_59,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_52]),c_0_51])]),c_0_56]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT297+4 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.34 % Computer : n019.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sun Sep 20 23:30:14 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 60.75/11.22 % Version: 3.5.1
% 60.75/11.22 % Preprocessing class: FMLLMLLLSSSNFFN.
% 60.75/11.22 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 60.75/11.22 % Starting new_bool_3 with 897s (3) cores
% 60.75/11.22 % Starting new_bool_1 with 897s (3) cores
% 60.75/11.22 % Starting sh5l with 299s (1) cores
% 60.75/11.22 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 299s (1) cores
% 60.75/11.22 % new_bool_1 with pid 1156764 completed with status 0
% 60.75/11.22 % Result found by new_bool_1
% 60.75/11.22 % Preprocessing class: FMLLMLLLSSSNFFN.
% 60.75/11.22 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 60.75/11.22 % Starting new_bool_3 with 897s (3) cores
% 60.75/11.22 % Starting new_bool_1 with 897s (3) cores
% 60.75/11.22 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 60.75/11.22 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 60.75/11.22 % Search class: FGHSS-FSLM31-MFFFFFNN
% 60.75/11.22 % partial match(1): FGHSM-FSLM31-MFFFFFNN
% 60.75/11.22 % Scheduled 8 strats onto 3 cores with 897 seconds (897 total)
% 60.75/11.22 % Starting SubtermCWHack with 81s (1) cores
% 60.75/11.22 % Starting new_bool_1 with 90s (1) cores
% 60.75/11.22 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN with 81s (1) cores
% 60.75/11.22 % G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN with pid 1156772 completed with status 0
% 60.75/11.22 % Result found by G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN
% 60.75/11.22 % Preprocessing class: FMLLMLLLSSSNFFN.
% 60.75/11.22 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 60.75/11.22 % Starting new_bool_3 with 897s (3) cores
% 60.75/11.22 % Starting new_bool_1 with 897s (3) cores
% 60.75/11.22 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 60.75/11.22 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 60.75/11.22 % Search class: FGHSS-FSLM31-MFFFFFNN
% 60.75/11.22 % partial match(1): FGHSM-FSLM31-MFFFFFNN
% 60.75/11.22 % Scheduled 8 strats onto 3 cores with 897 seconds (897 total)
% 60.75/11.22 % Starting SubtermCWHack with 81s (1) cores
% 60.75/11.22 % Starting new_bool_1 with 90s (1) cores
% 60.75/11.22 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN with 81s (1) cores
% 60.75/11.22 % Preprocessing time : 0.350 s
% 60.75/11.22 % Presaturation interreduction done
% 60.75/11.22
% 60.75/11.22 % Proof found!
% 60.75/11.22 % SZS status Theorem
% 60.75/11.22 % SZS output start CNFRefutation
% See solution above
% 60.75/11.22 % Parsed axioms : 34663
% 60.75/11.22 % Removed by relevancy pruning/SinE : 34592
% 60.75/11.22 % Initial clauses : 165
% 60.75/11.22 % Removed in clause preprocessing : 2
% 60.75/11.22 % Initial clauses in saturation : 163
% 60.75/11.22 % Processed clauses : 19563
% 60.75/11.22 % ...of these trivial : 122
% 60.75/11.22 % ...subsumed : 13541
% 60.75/11.22 % ...remaining for further processing : 5900
% 60.75/11.22 % Other redundant clauses eliminated : 0
% 60.75/11.22 % Clauses deleted for lack of memory : 0
% 60.75/11.22 % Backward-subsumed : 321
% 60.75/11.22 % Backward-rewritten : 732
% 60.75/11.22 % Generated clauses : 167625
% 60.75/11.22 % ...of the previous two non-redundant : 161262
% 60.75/11.22 % ...aggressively subsumed : 0
% 60.75/11.22 % Contextual simplify-reflections : 132
% 60.75/11.22 % Paramodulations : 167531
% 60.75/11.22 % Factorizations : 80
% 60.75/11.22 % NegExts : 0
% 60.75/11.22 % Equation resolutions : 3
% 60.75/11.22 % Disequality decompositions : 0
% 60.75/11.22 % Total rewrite steps : 74815
% 60.75/11.22 % ...of those cached : 74333
% 60.75/11.22 % Propositional unsat checks : 1
% 60.75/11.22 % Propositional check models : 0
% 60.75/11.22 % Propositional check unsatisfiable : 0
% 60.75/11.22 % Propositional clauses : 0
% 60.75/11.22 % Propositional clauses after purity: 0
% 60.75/11.22 % Propositional unsat core size : 0
% 60.75/11.22 % Propositional preprocessing time : 0.000
% 60.75/11.22 % Propositional encoding time : 0.219
% 60.75/11.22 % Propositional solver time : 0.212
% 60.75/11.22 % Success case prop preproc time : 0.000
% 60.75/11.22 % Success case prop encoding time : 0.000
% 60.75/11.22 % Success case prop solver time : 0.000
% 60.75/11.22 % Current number of processed clauses : 4675
% 60.75/11.22 % Positive orientable unit clauses : 426
% 60.75/11.22 % Positive unorientable unit clauses: 0
% 60.75/11.22 % Negative unit clauses : 169
% 60.75/11.22 % Non-unit-clauses : 4080
% 60.75/11.22 % Current number of unprocessed clauses: 139900
% 60.75/11.22 % ...number of literals in the above : 694028
% 60.75/11.22 % Current number of archived formulas : 0
% 60.75/11.22 % Current number of archived clauses : 1225
% 60.75/11.22 % Clause-clause subsumption calls (NU) : 3127775
% 60.75/11.22 % Rec. Clause-clause subsumption calls : 1084825
% 60.75/11.22 % Non-unit clause-clause subsumptions : 4874
% 60.75/11.22 % Unit Clause-clause subsumption calls : 201816
% 60.75/11.22 % Rewrite failures with RHS unbound : 0
% 60.75/11.22 % BW rewrite match attempts : 961
% 60.75/11.22 % BW rewrite match successes : 69
% 60.75/11.22 % Condensation attempts : 0
% 60.75/11.22 % Condensation successes : 0
% 60.75/11.22 % Termbank termtop insertions : 6207441
% 60.75/11.22 % Search garbage collected termcells : 344399
% 60.75/11.22
% 60.75/11.22 % -------------------------------------------------
% 60.75/11.22 % User time : 8.195 s
% 60.75/11.22 % System time : 0.375 s
% 60.75/11.22 % Total time : 8.570 s
% 60.75/11.22 % Maximum resident set size: 70056 pages
% 60.75/11.23
% 60.75/11.23 % -------------------------------------------------
% 60.75/11.23 % User time : 25.700 s
% 60.75/11.23 % System time : 1.079 s
% 60.75/11.23 % Total time : 26.778 s
% 60.75/11.23 % Maximum resident set size: 56832 pages
% 60.75/11.23 % E exiting
%------------------------------------------------------------------------------