%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LAT310+3 : 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 : n007.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 01:04:50 PM UTC 2026
% Result : Theorem 114.13s 17.75s
% Output : CNFRefutation 114.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 90 ( 33 unt; 0 def)
% Number of atoms : 388 ( 15 equ)
% Maximal formula atoms : 45 ( 4 avg)
% Number of connectives : 470 ( 172 ~; 163 |; 78 &)
% ( 10 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 140 ( 3 sgn 90 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t39_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)))
& ~ v1_xboole_0(X2) )
=> ! [X3] :
( ( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
& ~ v1_xboole_0(X3) )
=> ! [X4] :
( ( m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X1)))
& ~ v1_xboole_0(X4) )
=> ( r1_tarski(k19_filter_2(X1,k19_filter_2(X1,X2)),k19_filter_2(X1,X2))
& ( r1_tarski(X3,X4)
=> r1_tarski(k19_filter_2(X1,X3),k19_filter_2(X1,X4)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_filter_2) ).
fof(dt_k19_filter_2,axiom,
! [X1,X2] :
( ( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
& ~ v1_xboole_0(X2)
& l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> m2_filter_2(k19_filter_2(X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k19_filter_2) ).
fof(dt_m2_filter_2,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( m2_lattice4(X2,X1)
& ~ v1_xboole_0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_filter_2) ).
fof(dt_m2_lattice4,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_lattice4(X2,X1)
=> m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+375.ax',dt_m2_lattice4) ).
fof(t3_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,k1_zfmisc_1(X2))
<=> r1_tarski(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+9.ax',t3_subset) ).
fof(d2_subset_1,axiom,
! [X1,X2] :
( ( v1_xboole_0(X1)
=> ( m1_subset_1(X2,X1)
<=> v1_xboole_0(X2) ) )
& ( ~ v1_xboole_0(X1)
=> ( m1_subset_1(X2,X1)
<=> r2_hidden(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+7.ax',d2_subset_1) ).
fof(d11_filter_2,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) )
=> ! [X3] :
( m2_filter_2(X3,X1)
=> ( X3 = k19_filter_2(X1,X2)
<=> ( ! [X4] :
( m2_filter_2(X4,X1)
=> ( r1_tarski(X2,X4)
=> r1_tarski(X3,X4) ) )
& r1_tarski(X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_filter_2) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( r1_tarski(X1,X2)
<=> ! [X3] :
( r2_hidden(X3,X1)
=> r2_hidden(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+1.ax',d3_tarski) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : m1_subset_1(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+7.ax',existence_m1_subset_1) ).
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(t38_filter_2,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> r1_filter_2(u1_struct_0(X1),k19_filter_2(X1,X2),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_filter_2) ).
fof(redefinition_r1_filter_2,axiom,
! [X1,X2,X3] :
( ( m1_subset_1(X3,k1_zfmisc_1(X1))
& m1_subset_1(X2,k1_zfmisc_1(X1))
& ~ v1_xboole_0(X1) )
=> ( r1_filter_2(X1,X2,X3)
<=> X2 = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_filter_2) ).
fof(t1_xboole_1,axiom,
! [X1,X2,X3] :
( ( r1_tarski(X2,X3)
& r1_tarski(X1,X2) )
=> r1_tarski(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t1_xboole_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : r1_tarski(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+1.ax',reflexivity_r1_tarski) ).
fof(c_0_14,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)))
& ~ v1_xboole_0(X2) )
=> ! [X3] :
( ( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
& ~ v1_xboole_0(X3) )
=> ! [X4] :
( ( m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X1)))
& ~ v1_xboole_0(X4) )
=> ( r1_tarski(k19_filter_2(X1,k19_filter_2(X1,X2)),k19_filter_2(X1,X2))
& ( r1_tarski(X3,X4)
=> r1_tarski(k19_filter_2(X1,X3),k19_filter_2(X1,X4)) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[t39_filter_2]) ).
fof(c_0_15,plain,
! [X1,X2] :
( ( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
& ~ v1_xboole_0(X2)
& l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> m2_filter_2(k19_filter_2(X1,X2),X1) ),
inference(fof_simplification,[status(thm)],[dt_k19_filter_2]) ).
fof(c_0_16,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)))
& ~ v1_xboole_0(X2) )
=> ! [X3] :
( ( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
& ~ v1_xboole_0(X3) )
=> ! [X4] :
( ( m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X1)))
& ~ v1_xboole_0(X4) )
=> ( r1_tarski(k19_filter_2(X1,k19_filter_2(X1,X2)),k19_filter_2(X1,X2))
& ( r1_tarski(X3,X4)
=> r1_tarski(k19_filter_2(X1,X3),k19_filter_2(X1,X4)) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_17,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( m2_lattice4(X2,X1)
& ~ v1_xboole_0(X2) ) ) ),
inference(fof_simplification,[status(thm)],[dt_m2_filter_2]) ).
fof(c_0_18,plain,
! [X94,X95] :
( m2_filter_2(k19_filter_2(X94,X95),X94)
| ~ m1_subset_1(X95,k1_zfmisc_1(u1_struct_0(X94)))
| v1_xboole_0(X95)
| ~ l3_lattices(X94)
| ~ v10_lattices(X94)
| v3_struct_0(X94) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
fof(c_0_19,negated_conjecture,
( ( ~ r1_tarski(k19_filter_2(esk1_0,k19_filter_2(esk1_0,esk2_0)),k19_filter_2(esk1_0,esk2_0))
| ~ r1_tarski(k19_filter_2(esk1_0,esk3_0),k19_filter_2(esk1_0,esk4_0)) )
& ( ~ r1_tarski(k19_filter_2(esk1_0,k19_filter_2(esk1_0,esk2_0)),k19_filter_2(esk1_0,esk2_0))
| r1_tarski(esk3_0,esk4_0) )
& m1_subset_1(esk4_0,k1_zfmisc_1(u1_struct_0(esk1_0)))
& ~ v1_xboole_0(esk4_0)
& m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk1_0)))
& ~ v1_xboole_0(esk3_0)
& m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0)))
& ~ v1_xboole_0(esk2_0)
& l3_lattices(esk1_0)
& v10_lattices(esk1_0)
& ~ v3_struct_0(esk1_0) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])])]) ).
fof(c_0_20,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_lattice4(X2,X1)
=> m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ) ),
inference(fof_simplification,[status(thm)],[dt_m2_lattice4]) ).
fof(c_0_21,plain,
! [X251,X252] :
( ( ~ l3_lattices(X251)
| ~ v10_lattices(X251)
| v3_struct_0(X251)
| ~ m2_filter_2(X252,X251)
| m2_lattice4(X252,X251) )
& ( ~ l3_lattices(X251)
| ~ v10_lattices(X251)
| v3_struct_0(X251)
| ~ m2_filter_2(X252,X251)
| ~ v1_xboole_0(X252) ) ),
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_17])])])])]) ).
cnf(c_0_22,plain,
( ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| m2_filter_2(k19_filter_2(X1,X2),X1)
| v1_xboole_0(X2)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,negated_conjecture,
~ v1_xboole_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_28,plain,
! [X515,X516] :
( m1_subset_1(X516,k1_zfmisc_1(u1_struct_0(X515)))
| ~ m2_lattice4(X516,X515)
| ~ l3_lattices(X515)
| ~ v10_lattices(X515)
| v3_struct_0(X515) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).
cnf(c_0_29,plain,
( ~ l3_lattices(X2)
| ~ v10_lattices(X2)
| ~ m2_filter_2(X1,X2)
| v3_struct_0(X2)
| m2_lattice4(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,negated_conjecture,
m2_filter_2(k19_filter_2(esk1_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_22,c_0_23]),c_0_24]),c_0_25])]),c_0_26]),c_0_27]) ).
fof(c_0_31,plain,
! [X50,X51] :
( ( m1_subset_1(X50,k1_zfmisc_1(X51))
| ~ r1_tarski(X50,X51) )
& ( r1_tarski(X50,X51)
| ~ m1_subset_1(X50,k1_zfmisc_1(X51)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])]) ).
fof(c_0_32,plain,
! [X1,X2] :
( ( v1_xboole_0(X1)
=> ( m1_subset_1(X2,X1)
<=> v1_xboole_0(X2) ) )
& ( ~ v1_xboole_0(X1)
=> ( m1_subset_1(X2,X1)
<=> r2_hidden(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[d2_subset_1]) ).
fof(c_0_33,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) )
=> ! [X3] :
( m2_filter_2(X3,X1)
=> ( X3 = k19_filter_2(X1,X2)
<=> ( ! [X4] :
( m2_filter_2(X4,X1)
=> ( r1_tarski(X2,X4)
=> r1_tarski(X3,X4) ) )
& r1_tarski(X2,X3) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d11_filter_2]) ).
cnf(c_0_34,plain,
( ~ m2_lattice4(X2,X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,negated_conjecture,
m2_lattice4(k19_filter_2(esk1_0,esk2_0),esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_36,plain,
( ~ l3_lattices(X2)
| ~ v10_lattices(X2)
| ~ m2_filter_2(X1,X2)
| ~ v1_xboole_0(X1)
| v3_struct_0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_37,plain,
! [X19,X20,X21,X22,X23] :
( ( r1_tarski(X22,X23)
| ~ r2_hidden(esk5_2(X22,X23),X23) )
& ( r1_tarski(X22,X23)
| r2_hidden(esk5_2(X22,X23),X22) )
& ( r2_hidden(X21,X20)
| ~ r2_hidden(X21,X19)
| ~ r1_tarski(X19,X20) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])])]) ).
cnf(c_0_38,plain,
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| r1_tarski(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_39,negated_conjecture,
m1_subset_1(esk4_0,k1_zfmisc_1(u1_struct_0(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_40,plain,
! [X140,X141] :
( ( ~ v1_xboole_0(X140)
| m1_subset_1(X141,X140)
| ~ v1_xboole_0(X141) )
& ( ~ v1_xboole_0(X140)
| v1_xboole_0(X141)
| ~ m1_subset_1(X141,X140) )
& ( v1_xboole_0(X140)
| m1_subset_1(X141,X140)
| ~ r2_hidden(X141,X140) )
& ( v1_xboole_0(X140)
| r2_hidden(X141,X140)
| ~ m1_subset_1(X141,X140) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])])]) ).
fof(c_0_41,plain,
! [X110] : m1_subset_1(esk10_1(X110),X110),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(c_0_42,plain,
! [X96,X97,X98,X99] :
( ( ~ l3_lattices(X96)
| ~ v10_lattices(X96)
| v3_struct_0(X96)
| ~ m1_subset_1(X97,k1_zfmisc_1(u1_struct_0(X96)))
| v1_xboole_0(X97)
| ~ m2_filter_2(X98,X96)
| X98 = k19_filter_2(X96,X97)
| ~ r1_tarski(X97,X98)
| ~ r1_tarski(X98,esk9_3(X96,X97,X98)) )
& ( ~ l3_lattices(X96)
| ~ v10_lattices(X96)
| v3_struct_0(X96)
| ~ m1_subset_1(X97,k1_zfmisc_1(u1_struct_0(X96)))
| v1_xboole_0(X97)
| ~ m2_filter_2(X98,X96)
| X98 = k19_filter_2(X96,X97)
| ~ r1_tarski(X97,X98)
| r1_tarski(X97,esk9_3(X96,X97,X98)) )
& ( ~ l3_lattices(X96)
| ~ v10_lattices(X96)
| v3_struct_0(X96)
| ~ m1_subset_1(X97,k1_zfmisc_1(u1_struct_0(X96)))
| v1_xboole_0(X97)
| ~ m2_filter_2(X98,X96)
| X98 = k19_filter_2(X96,X97)
| ~ r1_tarski(X97,X98)
| m2_filter_2(esk9_3(X96,X97,X98),X96) )
& ( ~ l3_lattices(X96)
| ~ v10_lattices(X96)
| v3_struct_0(X96)
| ~ m1_subset_1(X97,k1_zfmisc_1(u1_struct_0(X96)))
| v1_xboole_0(X97)
| ~ m2_filter_2(X98,X96)
| X98 != k19_filter_2(X96,X97)
| r1_tarski(X98,X99)
| ~ r1_tarski(X97,X99)
| ~ m2_filter_2(X99,X96) )
& ( ~ l3_lattices(X96)
| ~ v10_lattices(X96)
| v3_struct_0(X96)
| ~ m1_subset_1(X97,k1_zfmisc_1(u1_struct_0(X96)))
| v1_xboole_0(X97)
| ~ m2_filter_2(X98,X96)
| X98 != k19_filter_2(X96,X97)
| r1_tarski(X97,X98) ) ),
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_33])])])])])]) ).
fof(c_0_43,plain,
! [X136,X137] :
( ~ v1_xboole_0(X137)
| ~ r2_hidden(X136,X137) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])])]) ).
fof(c_0_44,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> r1_filter_2(u1_struct_0(X1),k19_filter_2(X1,X2),X2) ) ),
inference(fof_simplification,[status(thm)],[t38_filter_2]) ).
cnf(c_0_45,negated_conjecture,
m1_subset_1(k19_filter_2(esk1_0,esk2_0),k1_zfmisc_1(u1_struct_0(esk1_0))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_46,negated_conjecture,
~ v1_xboole_0(k19_filter_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_36,c_0_30]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_47,plain,
( ~ r2_hidden(X3,X1)
| ~ r1_tarski(X1,X2)
| r2_hidden(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_48,negated_conjecture,
r1_tarski(esk4_0,u1_struct_0(esk1_0)),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_49,plain,
( ~ m1_subset_1(X1,X2)
| v1_xboole_0(X2)
| r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_50,plain,
m1_subset_1(esk10_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_51,plain,
( ~ l3_lattices(X3)
| ~ v10_lattices(X3)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X3)))
| ~ m2_filter_2(X2,X3)
| X2 != k19_filter_2(X3,X1)
| v3_struct_0(X3)
| v1_xboole_0(X1)
| r1_tarski(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_52,plain,
( ~ v1_xboole_0(X2)
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_53,plain,
( r1_tarski(X1,X2)
| r2_hidden(esk5_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_54,plain,
! [X1,X2,X3] :
( ( m1_subset_1(X3,k1_zfmisc_1(X1))
& m1_subset_1(X2,k1_zfmisc_1(X1))
& ~ v1_xboole_0(X1) )
=> ( r1_filter_2(X1,X2,X3)
<=> X2 = X3 ) ),
inference(fof_simplification,[status(thm)],[redefinition_r1_filter_2]) ).
fof(c_0_55,plain,
! [X108,X109] :
( r1_filter_2(u1_struct_0(X108),k19_filter_2(X108,X109),X109)
| ~ m2_filter_2(X109,X108)
| ~ l3_lattices(X108)
| ~ v10_lattices(X108)
| v3_struct_0(X108) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])])]) ).
cnf(c_0_56,negated_conjecture,
m2_filter_2(k19_filter_2(esk1_0,k19_filter_2(esk1_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_22,c_0_45]),c_0_24]),c_0_25])]),c_0_26]),c_0_46]) ).
cnf(c_0_57,negated_conjecture,
( ~ r2_hidden(X1,esk4_0)
| r2_hidden(X1,u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_58,plain,
( r2_hidden(esk10_1(X1),X1)
| v1_xboole_0(X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_59,negated_conjecture,
~ v1_xboole_0(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_60,plain,
( ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| r1_tarski(X2,k19_filter_2(X1,X2))
| v1_xboole_0(X2)
| v3_struct_0(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_51]),c_0_22]) ).
cnf(c_0_61,plain,
( ~ v1_xboole_0(X1)
| r1_tarski(X1,X2) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
fof(c_0_62,plain,
! [X356,X357,X358] :
( ( ~ m1_subset_1(X358,k1_zfmisc_1(X356))
| ~ m1_subset_1(X357,k1_zfmisc_1(X356))
| v1_xboole_0(X356)
| r1_filter_2(X356,X357,X358)
| X357 != X358 )
& ( ~ m1_subset_1(X358,k1_zfmisc_1(X356))
| ~ m1_subset_1(X357,k1_zfmisc_1(X356))
| v1_xboole_0(X356)
| X357 = X358
| ~ r1_filter_2(X356,X357,X358) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_54])])])]) ).
cnf(c_0_63,plain,
( ~ m2_filter_2(X2,X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| r1_filter_2(u1_struct_0(X1),k19_filter_2(X1,X2),X2)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_64,negated_conjecture,
m2_lattice4(k19_filter_2(esk1_0,k19_filter_2(esk1_0,esk2_0)),esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_56]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_65,negated_conjecture,
r2_hidden(esk10_1(esk4_0),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]) ).
fof(c_0_66,plain,
! [X28,X29,X30] :
( r1_tarski(X28,X30)
| ~ r1_tarski(X29,X30)
| ~ r1_tarski(X28,X29) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])])]) ).
cnf(c_0_67,plain,
( ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| r1_tarski(X2,k19_filter_2(X1,X2))
| v3_struct_0(X1) ),
inference(csr,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_68,plain,
( ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ m1_subset_1(X2,k1_zfmisc_1(X1))
| ~ r1_filter_2(X1,X2,X3)
| v1_xboole_0(X1)
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_69,negated_conjecture,
r1_filter_2(u1_struct_0(esk1_0),k19_filter_2(esk1_0,k19_filter_2(esk1_0,esk2_0)),k19_filter_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_63,c_0_30]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_70,negated_conjecture,
m1_subset_1(k19_filter_2(esk1_0,k19_filter_2(esk1_0,esk2_0)),k1_zfmisc_1(u1_struct_0(esk1_0))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_64]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_71,negated_conjecture,
~ v1_xboole_0(u1_struct_0(esk1_0)),
inference(spm,[status(thm)],[c_0_52,c_0_65]) ).
fof(c_0_72,plain,
! [X25] : r1_tarski(X25,X25),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_73,plain,
( ~ l3_lattices(X2)
| ~ v10_lattices(X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
| ~ m2_filter_2(X4,X2)
| X4 != k19_filter_2(X2,X3)
| ~ r1_tarski(X3,X1)
| ~ m2_filter_2(X1,X2)
| v3_struct_0(X2)
| v1_xboole_0(X3)
| r1_tarski(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_74,plain,
( ~ r1_tarski(X2,X3)
| ~ r1_tarski(X1,X2)
| r1_tarski(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_75,negated_conjecture,
r1_tarski(esk4_0,k19_filter_2(esk1_0,esk4_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_39]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_76,negated_conjecture,
( ~ r1_tarski(k19_filter_2(esk1_0,k19_filter_2(esk1_0,esk2_0)),k19_filter_2(esk1_0,esk2_0))
| r1_tarski(esk3_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_77,negated_conjecture,
k19_filter_2(esk1_0,k19_filter_2(esk1_0,esk2_0)) = k19_filter_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_68,c_0_69]),c_0_45]),c_0_70])]),c_0_71]) ).
cnf(c_0_78,plain,
r1_tarski(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_79,plain,
( ~ r1_tarski(X2,X3)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m2_filter_2(X3,X1)
| r1_tarski(k19_filter_2(X1,X2),X3)
| v1_xboole_0(X2)
| v3_struct_0(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_73]),c_0_22]) ).
cnf(c_0_80,negated_conjecture,
m2_filter_2(k19_filter_2(esk1_0,esk4_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_22,c_0_39]),c_0_24]),c_0_25])]),c_0_26]),c_0_59]) ).
cnf(c_0_81,negated_conjecture,
( ~ r1_tarski(k19_filter_2(esk1_0,k19_filter_2(esk1_0,esk2_0)),k19_filter_2(esk1_0,esk2_0))
| ~ r1_tarski(k19_filter_2(esk1_0,esk3_0),k19_filter_2(esk1_0,esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_82,negated_conjecture,
( ~ r1_tarski(X1,esk4_0)
| r1_tarski(X1,k19_filter_2(esk1_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_83,negated_conjecture,
r1_tarski(esk3_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_77]),c_0_78])]) ).
cnf(c_0_84,negated_conjecture,
( ~ r1_tarski(X1,k19_filter_2(esk1_0,esk4_0))
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(esk1_0)))
| r1_tarski(k19_filter_2(esk1_0,X1),k19_filter_2(esk1_0,esk4_0))
| v1_xboole_0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_85,negated_conjecture,
~ r1_tarski(k19_filter_2(esk1_0,esk3_0),k19_filter_2(esk1_0,esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_77]),c_0_78])]) ).
cnf(c_0_86,negated_conjecture,
~ v1_xboole_0(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_87,negated_conjecture,
r1_tarski(esk3_0,k19_filter_2(esk1_0,esk4_0)),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_88,negated_conjecture,
m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_89,plain,
$false,
inference(cdclpropres,[status(thm)],[c_0_84,c_0_85,c_0_86,c_0_87,c_0_88]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT310+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.55 % Computer : n007.cluster.edu
% 0.11/0.55 % Model : x86_64 x86_64
% 0.11/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.55 % Memory : 8046.5625MB
% 0.11/0.55 % OS : Linux 6.8.0-71-generic
% 0.11/0.55 % CPULimit : 300
% 0.11/0.55 % WCLimit : 300
% 0.11/0.55 % DateTime : Sun Sep 20 23:31:40 UTC 2026
% 0.11/0.55 % CPUTime :
% 0.11/0.55 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.59 Running first-order theorem proving
% 0.16/0.59 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
% 114.13/17.75 % Version: 3.5.1
% 114.13/17.75 % Preprocessing class: FMLLSMLLSSSNFFN.
% 114.13/17.75 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 114.13/17.75 % Starting new_bool_3 with 900s (3) cores
% 114.13/17.75 % Starting new_bool_1 with 900s (3) cores
% 114.13/17.75 % Starting sh5l with 300s (1) cores
% 114.13/17.75 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 300s (1) cores
% 114.13/17.75 % new_bool_1 with pid 3834421 completed with status 0
% 114.13/17.75 % Result found by new_bool_1
% 114.13/17.75 % Preprocessing class: FMLLSMLLSSSNFFN.
% 114.13/17.75 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 114.13/17.75 % Starting new_bool_3 with 900s (3) cores
% 114.13/17.75 % Starting new_bool_1 with 900s (3) cores
% 114.13/17.75 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 114.13/17.75 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 114.13/17.75 % Search class: FGHSM-FSLM32-MFFFFFNN
% 114.13/17.75 % Scheduled 12 strats onto 3 cores with 900 seconds (900 total)
% 114.13/17.75 % Starting SubtermCWHack with 82s (1) cores
% 114.13/17.75 % Starting new_bool_1 with 91s (1) cores
% 114.13/17.75 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with 74s (1) cores
% 114.13/17.75 % new_bool_1 with pid 3834445 completed with status 0
% 114.13/17.75 % Result found by new_bool_1
% 114.13/17.75 % Preprocessing class: FMLLSMLLSSSNFFN.
% 114.13/17.75 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 114.13/17.75 % Starting new_bool_3 with 900s (3) cores
% 114.13/17.75 % Starting new_bool_1 with 900s (3) cores
% 114.13/17.75 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 114.13/17.75 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 114.13/17.75 % Search class: FGHSM-FSLM32-MFFFFFNN
% 114.13/17.75 % Scheduled 12 strats onto 3 cores with 900 seconds (900 total)
% 114.13/17.75 % Starting SubtermCWHack with 82s (1) cores
% 114.13/17.75 % Starting new_bool_1 with 91s (1) cores
% 114.13/17.75 % Preprocessing time : 0.031 s
% 114.13/17.75 % Presaturation interreduction done
% 114.13/17.75 % SatCheck found unsatisfiable ground set
% 114.13/17.75
% 114.13/17.75 % Proof found!
% 114.13/17.75 % SZS status Theorem
% 114.13/17.75 % SZS output start CNFRefutation
% See solution above
% 114.13/17.75 % Parsed axioms : 13627
% 114.13/17.75 % Removed by relevancy pruning/SinE : 13338
% 114.13/17.75 % Initial clauses : 689
% 114.13/17.75 % Removed in clause preprocessing : 31
% 114.13/17.75 % Initial clauses in saturation : 658
% 114.13/17.75 % Processed clauses : 57262
% 114.13/17.75 % ...of these trivial : 351
% 114.13/17.75 % ...subsumed : 46911
% 114.13/17.75 % ...remaining for further processing : 10000
% 114.13/17.75 % Other redundant clauses eliminated : 291
% 114.13/17.75 % Clauses deleted for lack of memory : 0
% 114.13/17.75 % Backward-subsumed : 631
% 114.13/17.75 % Backward-rewritten : 235
% 114.13/17.75 % Generated clauses : 422206
% 114.13/17.75 % ...of the previous two non-redundant : 403654
% 114.13/17.75 % ...aggressively subsumed : 0
% 114.13/17.75 % Contextual simplify-reflections : 228
% 114.13/17.75 % Paramodulations : 421900
% 114.13/17.75 % Factorizations : 2
% 114.13/17.75 % NegExts : 0
% 114.13/17.75 % Equation resolutions : 306
% 114.13/17.75 % Disequality decompositions : 0
% 114.13/17.75 % Total rewrite steps : 56556
% 114.13/17.75 % ...of those cached : 52749
% 114.13/17.75 % Propositional unsat checks : 2
% 114.13/17.75 % Propositional check models : 0
% 114.13/17.75 % Propositional check unsatisfiable : 1
% 114.13/17.75 % Propositional clauses : 353418
% 114.13/17.75 % Propositional clauses after purity: 18844
% 114.13/17.75 % Propositional unsat core size : 5
% 114.13/17.75 % Propositional preprocessing time : 0.000
% 114.13/17.75 % Propositional encoding time : 0.649
% 114.13/17.75 % Propositional solver time : 0.284
% 114.13/17.75 % Success case prop preproc time : 0.000
% 114.13/17.75 % Success case prop encoding time : 0.479
% 114.13/17.75 % Success case prop solver time : 0.061
% 114.13/17.75 % Current number of processed clauses : 8494
% 114.13/17.75 % Positive orientable unit clauses : 2197
% 114.13/17.75 % Positive unorientable unit clauses: 2
% 114.13/17.75 % Negative unit clauses : 1664
% 114.13/17.75 % Non-unit-clauses : 4631
% 114.13/17.75 % Current number of unprocessed clauses: 344924
% 114.13/17.75 % ...number of literals in the above : 1101751
% 114.13/17.75 % Current number of archived formulas : 0
% 114.13/17.75 % Current number of archived clauses : 1467
% 114.13/17.75 % Clause-clause subsumption calls (NU) : 3673494
% 114.13/17.75 % Rec. Clause-clause subsumption calls : 1981538
% 114.13/17.75 % Non-unit clause-clause subsumptions : 11048
% 114.13/17.75 % Unit Clause-clause subsumption calls : 751872
% 114.13/17.75 % Rewrite failures with RHS unbound : 5
% 114.13/17.75 % BW rewrite match attempts : 36262
% 114.13/17.75 % BW rewrite match successes : 50
% 114.13/17.75 % Condensation attempts : 0
% 114.13/17.75 % Condensation successes : 0
% 114.13/17.75 % Termbank termtop insertions : 9047773
% 114.13/17.75 % Search garbage collected termcells : 126899
% 114.13/17.75
% 114.13/17.75 % -------------------------------------------------
% 114.13/17.75 % User time : 15.705 s
% 114.13/17.75 % System time : 0.545 s
% 114.13/17.75 % Total time : 16.250 s
% 114.13/17.75 % Maximum resident set size: 27972 pages
% 114.13/17.75
% 114.13/17.75 % -------------------------------------------------
% 114.13/17.75 % User time : 46.907 s
% 114.13/17.75 % System time : 1.415 s
% 114.13/17.75 % Total time : 48.321 s
% 114.13/17.75 % Maximum resident set size: 23296 pages
% 114.13/17.75 % E exiting
%------------------------------------------------------------------------------