%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LAT305+2 : 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 : n013.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 01:04:49 PM UTC 2026
% Result : Theorem 197.20s 29.54s
% Output : CNFRefutation 197.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 21
% Syntax : Number of formulae : 131 ( 35 unt; 0 def)
% Number of atoms : 558 ( 16 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 677 ( 250 ~; 241 |; 110 &)
% ( 10 <=>; 66 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 194 ( 4 sgn 129 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t31_filter_2,conjecture,
! [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))
=> ( r2_hidden(k4_lattices(X1,X3,X2),k18_filter_2(X1,X2))
& r2_hidden(k4_lattices(X1,X2,X3),k18_filter_2(X1,X2))
& r2_hidden(X2,k18_filter_2(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_filter_2) ).
fof(dt_m1_filter_0,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_filter_0(X2,X1)
=> ( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
& ~ v1_xboole_0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+242.ax',dt_m1_filter_0) ).
fof(t15_filter_0,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> m1_filter_0(u1_struct_0(X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+242.ax',t15_filter_0) ).
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(d1_xboole_0,axiom,
! [X1] :
( X1 = k1_xboole_0
<=> ! [X2] : ~ r2_hidden(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+2.ax',d1_xboole_0) ).
fof(reflexivity_r3_lattices,axiom,
! [X1,X2,X3] :
( ( m1_subset_1(X3,u1_struct_0(X1))
& m1_subset_1(X2,u1_struct_0(X1))
& l3_lattices(X1)
& v9_lattices(X1)
& v8_lattices(X1)
& v6_lattices(X1)
& ~ v3_struct_0(X1) )
=> r3_lattices(X1,X2,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+205.ax',reflexivity_r3_lattices) ).
fof(t1_subset,axiom,
! [X1,X2] :
( r2_hidden(X1,X2)
=> m1_subset_1(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+9.ax',t1_subset) ).
fof(t49_zfmisc_1,axiom,
! [X1,X2] : k2_xboole_0(k1_tarski(X1),X2) != k1_xboole_0,
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+6.ax',t49_zfmisc_1) ).
fof(t46_zfmisc_1,axiom,
! [X1,X2] :
( r2_hidden(X1,X2)
=> k2_xboole_0(k1_tarski(X1),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+6.ax',t46_zfmisc_1) ).
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/sandbox/benchmark/Axioms/SET007/SET007+205.ax',cc1_lattices) ).
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(dt_k18_filter_2,axiom,
! [X1,X2] :
( ( m1_subset_1(X2,u1_struct_0(X1))
& l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> m2_filter_2(k18_filter_2(X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k18_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(t23_filter_2,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] :
( m2_filter_2(X4,X1)
=> ( r2_hidden(X2,X4)
=> ( r2_hidden(k4_lattices(X1,X3,X2),X4)
& r2_hidden(k4_lattices(X1,X2,X3),X4) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_filter_2) ).
fof(t29_filter_2,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))
=> ( r2_hidden(X2,k18_filter_2(X1,X3))
<=> r3_lattices(X1,X2,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_filter_2) ).
fof(t2_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_subset_1(X4,u1_struct_0(X1))
=> ( r3_lattices(X1,X2,X3)
=> ( r3_lattices(X1,k4_lattices(X1,X4,X2),X3)
& r3_lattices(X1,k4_lattices(X1,X2,X4),X3) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+242.ax',t2_filter_0) ).
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(t28_filter_2,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> m2_filter_2(u1_struct_0(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_filter_2) ).
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(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(c_0_21,negated_conjecture,
~ ! [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))
=> ( r2_hidden(k4_lattices(X1,X3,X2),k18_filter_2(X1,X2))
& r2_hidden(k4_lattices(X1,X2,X3),k18_filter_2(X1,X2))
& r2_hidden(X2,k18_filter_2(X1,X2)) ) ) ) ),
inference(assume_negation,[status(cth)],[t31_filter_2]) ).
fof(c_0_22,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_filter_0(X2,X1)
=> ( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
& ~ v1_xboole_0(X2) ) ) ),
inference(fof_simplification,[status(thm)],[dt_m1_filter_0]) ).
fof(c_0_23,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> m1_filter_0(u1_struct_0(X1),X1) ),
inference(fof_simplification,[status(thm)],[t15_filter_0]) ).
fof(c_0_24,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_25,negated_conjecture,
~ ! [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))
=> ( r2_hidden(k4_lattices(X1,X3,X2),k18_filter_2(X1,X2))
& r2_hidden(k4_lattices(X1,X2,X3),k18_filter_2(X1,X2))
& r2_hidden(X2,k18_filter_2(X1,X2)) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_26,plain,
! [X291,X292] :
( ( ~ l3_lattices(X291)
| ~ v10_lattices(X291)
| v3_struct_0(X291)
| ~ m1_filter_0(X292,X291)
| m1_subset_1(X292,k1_zfmisc_1(u1_struct_0(X291))) )
& ( ~ l3_lattices(X291)
| ~ v10_lattices(X291)
| v3_struct_0(X291)
| ~ m1_filter_0(X292,X291)
| ~ v1_xboole_0(X292) ) ),
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_22])])])])]) ).
fof(c_0_27,plain,
! [X290] :
( m1_filter_0(u1_struct_0(X290),X290)
| ~ l3_lattices(X290)
| ~ v10_lattices(X290)
| v3_struct_0(X290) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])]) ).
fof(c_0_28,plain,
! [X34,X35] :
( ( ~ v1_xboole_0(X34)
| m1_subset_1(X35,X34)
| ~ v1_xboole_0(X35) )
& ( ~ v1_xboole_0(X34)
| v1_xboole_0(X35)
| ~ m1_subset_1(X35,X34) )
& ( v1_xboole_0(X34)
| m1_subset_1(X35,X34)
| ~ r2_hidden(X35,X34) )
& ( v1_xboole_0(X34)
| r2_hidden(X35,X34)
| ~ m1_subset_1(X35,X34) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])]) ).
fof(c_0_29,negated_conjecture,
( ( ~ r2_hidden(k4_lattices(esk1_0,esk3_0,esk2_0),k18_filter_2(esk1_0,esk2_0))
| ~ r2_hidden(k4_lattices(esk1_0,esk2_0,esk3_0),k18_filter_2(esk1_0,esk2_0))
| ~ r2_hidden(esk2_0,k18_filter_2(esk1_0,esk2_0)) )
& m1_subset_1(esk3_0,u1_struct_0(esk1_0))
& m1_subset_1(esk2_0,u1_struct_0(esk1_0))
& l3_lattices(esk1_0)
& v10_lattices(esk1_0)
& ~ v3_struct_0(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])])]) ).
fof(c_0_30,plain,
! [X1] :
( X1 = k1_xboole_0
<=> ! [X2] : ~ r2_hidden(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
cnf(c_0_31,plain,
( ~ l3_lattices(X2)
| ~ v10_lattices(X2)
| ~ m1_filter_0(X1,X2)
| ~ v1_xboole_0(X1)
| v3_struct_0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| m1_filter_0(u1_struct_0(X1),X1)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
( ~ m1_subset_1(X1,X2)
| v1_xboole_0(X2)
| r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,negated_conjecture,
m1_subset_1(esk3_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_35,plain,
! [X1,X2,X3] :
( ( m1_subset_1(X3,u1_struct_0(X1))
& m1_subset_1(X2,u1_struct_0(X1))
& l3_lattices(X1)
& v9_lattices(X1)
& v8_lattices(X1)
& v6_lattices(X1)
& ~ v3_struct_0(X1) )
=> r3_lattices(X1,X2,X2) ),
inference(fof_simplification,[status(thm)],[reflexivity_r3_lattices]) ).
fof(c_0_36,plain,
! [X36,X37] :
( m1_subset_1(X36,X37)
| ~ r2_hidden(X36,X37) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])])]) ).
fof(c_0_37,plain,
! [X324,X325,X326] :
( ( X326 = k1_xboole_0
| r2_hidden(esk46_1(X326),X326) )
& ( ~ r2_hidden(X325,X324)
| X324 != k1_xboole_0 ) ),
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)],[c_0_30])])])])])]) ).
fof(c_0_38,plain,
! [X1,X2] : k2_xboole_0(k1_tarski(X1),X2) != k1_xboole_0,
inference(fof_simplification,[status(thm)],[t49_zfmisc_1]) ).
fof(c_0_39,plain,
! [X491,X492] :
( k2_xboole_0(k1_tarski(X491),X492) = X492
| ~ r2_hidden(X491,X492) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t46_zfmisc_1])])]) ).
cnf(c_0_40,plain,
( ~ v1_xboole_0(u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_41,negated_conjecture,
( r2_hidden(esk3_0,u1_struct_0(esk1_0))
| v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_42,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_43,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_44,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_45,plain,
! [X222,X223,X224] :
( r3_lattices(X222,X223,X223)
| ~ m1_subset_1(X224,u1_struct_0(X222))
| ~ m1_subset_1(X223,u1_struct_0(X222))
| ~ l3_lattices(X222)
| ~ v9_lattices(X222)
| ~ v8_lattices(X222)
| ~ v6_lattices(X222)
| v3_struct_0(X222) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])]) ).
cnf(c_0_46,plain,
( ~ r2_hidden(X1,X2)
| m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_47,plain,
( X1 = k1_xboole_0
| r2_hidden(esk46_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_48,plain,
! [X493,X494] : k2_xboole_0(k1_tarski(X493),X494) != k1_xboole_0,
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_38])]) ).
cnf(c_0_49,plain,
( ~ r2_hidden(X1,X2)
| k2_xboole_0(k1_tarski(X1),X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_50,negated_conjecture,
r2_hidden(esk3_0,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_40,c_0_41]),c_0_42]),c_0_43])]),c_0_44]) ).
cnf(c_0_51,plain,
( ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v9_lattices(X1)
| ~ v8_lattices(X1)
| ~ v6_lattices(X1)
| r3_lattices(X1,X2,X2)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_52,plain,
( m1_subset_1(esk46_1(X1),X1)
| X1 = k1_xboole_0 ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_53,plain,
k2_xboole_0(k1_tarski(X1),X2) != k1_xboole_0,
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_54,negated_conjecture,
k2_xboole_0(k1_tarski(esk3_0),u1_struct_0(esk1_0)) = u1_struct_0(esk1_0),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
fof(c_0_55,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_56,plain,
! [X104] : m1_subset_1(esk15_1(X104),X104),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(c_0_57,plain,
! [X1,X2] :
( ( m1_subset_1(X2,u1_struct_0(X1))
& l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> m2_filter_2(k18_filter_2(X1,X2),X1) ),
inference(fof_simplification,[status(thm)],[dt_k18_filter_2]) ).
cnf(c_0_58,plain,
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v6_lattices(X1)
| ~ v8_lattices(X1)
| ~ v9_lattices(X1)
| v3_struct_0(X1)
| r3_lattices(X1,X2,X2)
| u1_struct_0(X1) = k1_xboole_0 ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_59,negated_conjecture,
u1_struct_0(esk1_0) != k1_xboole_0,
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
fof(c_0_60,plain,
! [X438] :
( ( ~ l3_lattices(X438)
| ~ v10_lattices(X438)
| v3_struct_0(X438)
| v9_lattices(X438) )
& ( ~ l3_lattices(X438)
| ~ v10_lattices(X438)
| v3_struct_0(X438)
| v8_lattices(X438) )
& ( ~ l3_lattices(X438)
| ~ v10_lattices(X438)
| v3_struct_0(X438)
| v7_lattices(X438) )
& ( ~ l3_lattices(X438)
| ~ v10_lattices(X438)
| v3_struct_0(X438)
| v6_lattices(X438) )
& ( ~ l3_lattices(X438)
| ~ v10_lattices(X438)
| v3_struct_0(X438)
| v5_lattices(X438) )
& ( ~ l3_lattices(X438)
| ~ v10_lattices(X438)
| v3_struct_0(X438)
| v4_lattices(X438) )
& ( ~ l3_lattices(X438)
| ~ v10_lattices(X438)
| v3_struct_0(X438)
| ~ v3_struct_0(X438) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])])]) ).
cnf(c_0_61,plain,
m1_subset_1(esk15_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
fof(c_0_62,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_63,plain,
! [X60,X61] :
( m2_filter_2(k18_filter_2(X60,X61),X60)
| ~ m1_subset_1(X61,u1_struct_0(X60))
| ~ l3_lattices(X60)
| ~ v10_lattices(X60)
| v3_struct_0(X60) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])]) ).
cnf(c_0_64,negated_conjecture,
( ~ v6_lattices(esk1_0)
| ~ v8_lattices(esk1_0)
| ~ v9_lattices(esk1_0)
| r3_lattices(esk1_0,esk3_0,esk3_0) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_34]),c_0_43])]),c_0_59]),c_0_44]) ).
cnf(c_0_65,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| v9_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_66,plain,
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v6_lattices(X1)
| ~ v8_lattices(X1)
| ~ v9_lattices(X1)
| v3_struct_0(X1)
| r3_lattices(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_61]) ).
cnf(c_0_67,negated_conjecture,
m1_subset_1(esk2_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_68,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_69,plain,
! [X193,X194] :
( ( ~ l3_lattices(X193)
| ~ v10_lattices(X193)
| v3_struct_0(X193)
| ~ m2_filter_2(X194,X193)
| m2_lattice4(X194,X193) )
& ( ~ l3_lattices(X193)
| ~ v10_lattices(X193)
| v3_struct_0(X193)
| ~ m2_filter_2(X194,X193)
| ~ v1_xboole_0(X194) ) ),
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_62])])])])]) ).
cnf(c_0_70,plain,
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| m2_filter_2(k18_filter_2(X1,X2),X1)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
fof(c_0_71,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] :
( m2_filter_2(X4,X1)
=> ( r2_hidden(X2,X4)
=> ( r2_hidden(k4_lattices(X1,X3,X2),X4)
& r2_hidden(k4_lattices(X1,X2,X3),X4) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[t23_filter_2]) ).
fof(c_0_72,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))
=> ( r2_hidden(X2,k18_filter_2(X1,X3))
<=> r3_lattices(X1,X2,X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[t29_filter_2]) ).
cnf(c_0_73,negated_conjecture,
( ~ v6_lattices(esk1_0)
| ~ v8_lattices(esk1_0)
| r3_lattices(esk1_0,esk3_0,esk3_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_42]),c_0_43])]),c_0_44]) ).
cnf(c_0_74,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| v8_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_75,negated_conjecture,
( ~ v6_lattices(esk1_0)
| ~ v8_lattices(esk1_0)
| ~ v9_lattices(esk1_0)
| r3_lattices(esk1_0,esk2_0,esk2_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_43])]),c_0_44]) ).
fof(c_0_76,plain,
! [X385,X386] :
( m1_subset_1(X386,k1_zfmisc_1(u1_struct_0(X385)))
| ~ m2_lattice4(X386,X385)
| ~ l3_lattices(X385)
| ~ v10_lattices(X385)
| v3_struct_0(X385) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_68])])])]) ).
cnf(c_0_77,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_69]) ).
cnf(c_0_78,negated_conjecture,
m2_filter_2(k18_filter_2(esk1_0,esk3_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_70,c_0_34]),c_0_42]),c_0_43])]),c_0_44]) ).
fof(c_0_79,plain,
! [X212,X213,X214,X215] :
( ( ~ l3_lattices(X212)
| ~ v10_lattices(X212)
| v3_struct_0(X212)
| ~ m1_subset_1(X213,u1_struct_0(X212))
| ~ m1_subset_1(X214,u1_struct_0(X212))
| ~ m2_filter_2(X215,X212)
| ~ r2_hidden(X213,X215)
| r2_hidden(k4_lattices(X212,X214,X213),X215) )
& ( ~ l3_lattices(X212)
| ~ v10_lattices(X212)
| v3_struct_0(X212)
| ~ m1_subset_1(X213,u1_struct_0(X212))
| ~ m1_subset_1(X214,u1_struct_0(X212))
| ~ m2_filter_2(X215,X212)
| ~ r2_hidden(X213,X215)
| r2_hidden(k4_lattices(X212,X213,X214),X215) ) ),
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_71])])])])]) ).
fof(c_0_80,plain,
! [X62,X63,X64] :
( ( ~ l3_lattices(X62)
| ~ v10_lattices(X62)
| v3_struct_0(X62)
| ~ m1_subset_1(X63,u1_struct_0(X62))
| ~ m1_subset_1(X64,u1_struct_0(X62))
| r2_hidden(X63,k18_filter_2(X62,X64))
| ~ r3_lattices(X62,X63,X64) )
& ( ~ l3_lattices(X62)
| ~ v10_lattices(X62)
| v3_struct_0(X62)
| ~ m1_subset_1(X63,u1_struct_0(X62))
| ~ m1_subset_1(X64,u1_struct_0(X62))
| r3_lattices(X62,X63,X64)
| ~ r2_hidden(X63,k18_filter_2(X62,X64)) ) ),
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_72])])])])]) ).
cnf(c_0_81,negated_conjecture,
( ~ v6_lattices(esk1_0)
| r3_lattices(esk1_0,esk3_0,esk3_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_42]),c_0_43])]),c_0_44]) ).
cnf(c_0_82,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| v6_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
fof(c_0_83,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_subset_1(X4,u1_struct_0(X1))
=> ( r3_lattices(X1,X2,X3)
=> ( r3_lattices(X1,k4_lattices(X1,X4,X2),X3)
& r3_lattices(X1,k4_lattices(X1,X2,X4),X3) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[t2_filter_0]) ).
cnf(c_0_84,negated_conjecture,
( ~ v6_lattices(esk1_0)
| ~ v8_lattices(esk1_0)
| r3_lattices(esk1_0,esk2_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_75,c_0_65]),c_0_42]),c_0_43])]),c_0_44]) ).
fof(c_0_85,plain,
! [X132,X133] :
( ( m1_subset_1(X132,k1_zfmisc_1(X133))
| ~ r1_tarski(X132,X133) )
& ( r1_tarski(X132,X133)
| ~ m1_subset_1(X132,k1_zfmisc_1(X133)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])]) ).
cnf(c_0_86,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_76]) ).
cnf(c_0_87,negated_conjecture,
m2_lattice4(k18_filter_2(esk1_0,esk3_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_77,c_0_78]),c_0_42]),c_0_43])]),c_0_44]) ).
cnf(c_0_88,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m2_filter_2(X4,X1)
| ~ r2_hidden(X3,X4)
| v3_struct_0(X1)
| r2_hidden(k4_lattices(X1,X2,X3),X4) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_89,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ r3_lattices(X1,X2,X3)
| v3_struct_0(X1)
| r2_hidden(X2,k18_filter_2(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_90,negated_conjecture,
r3_lattices(esk1_0,esk3_0,esk3_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_42]),c_0_43])]),c_0_44]) ).
fof(c_0_91,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> m2_filter_2(u1_struct_0(X1),X1) ),
inference(fof_simplification,[status(thm)],[t28_filter_2]) ).
fof(c_0_92,plain,
! [X32,X33] :
( ~ v1_xboole_0(X33)
| ~ r2_hidden(X32,X33) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])])]) ).
fof(c_0_93,plain,
! [X78,X79,X80,X81] :
( ( ~ l3_lattices(X78)
| ~ v10_lattices(X78)
| v3_struct_0(X78)
| ~ m1_subset_1(X79,u1_struct_0(X78))
| ~ m1_subset_1(X80,u1_struct_0(X78))
| ~ m1_subset_1(X81,u1_struct_0(X78))
| ~ r3_lattices(X78,X79,X80)
| r3_lattices(X78,k4_lattices(X78,X81,X79),X80) )
& ( ~ l3_lattices(X78)
| ~ v10_lattices(X78)
| v3_struct_0(X78)
| ~ m1_subset_1(X79,u1_struct_0(X78))
| ~ m1_subset_1(X80,u1_struct_0(X78))
| ~ m1_subset_1(X81,u1_struct_0(X78))
| ~ r3_lattices(X78,X79,X80)
| r3_lattices(X78,k4_lattices(X78,X79,X81),X80) ) ),
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_83])])])])]) ).
cnf(c_0_94,negated_conjecture,
( ~ v6_lattices(esk1_0)
| r3_lattices(esk1_0,esk2_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_84,c_0_74]),c_0_42]),c_0_43])]),c_0_44]) ).
fof(c_0_95,plain,
! [X22,X23,X24,X25,X26] :
( ( r1_tarski(X25,X26)
| ~ r2_hidden(esk5_2(X25,X26),X26) )
& ( r1_tarski(X25,X26)
| r2_hidden(esk5_2(X25,X26),X25) )
& ( r2_hidden(X24,X23)
| ~ r2_hidden(X24,X22)
| ~ r1_tarski(X22,X23) ) ),
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_96,plain,
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| r1_tarski(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_97,negated_conjecture,
m1_subset_1(k18_filter_2(esk1_0,esk3_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_86,c_0_87]),c_0_42]),c_0_43])]),c_0_44]) ).
cnf(c_0_98,negated_conjecture,
( ~ r2_hidden(X2,k18_filter_2(esk1_0,esk3_0))
| ~ 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),k18_filter_2(esk1_0,esk3_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_78]),c_0_42]),c_0_43])]),c_0_44]) ).
cnf(c_0_99,negated_conjecture,
r2_hidden(esk3_0,k18_filter_2(esk1_0,esk3_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_89,c_0_90]),c_0_42]),c_0_43]),c_0_34])]),c_0_44]) ).
fof(c_0_100,plain,
! [X221] :
( m2_filter_2(u1_struct_0(X221),X221)
| ~ l3_lattices(X221)
| ~ v10_lattices(X221)
| v3_struct_0(X221) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_91])])]) ).
cnf(c_0_101,plain,
( ~ v1_xboole_0(X2)
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_102,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X4,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ r3_lattices(X1,X2,X4)
| v3_struct_0(X1)
| r3_lattices(X1,k4_lattices(X1,X2,X3),X4) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_103,negated_conjecture,
r3_lattices(esk1_0,esk2_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_94,c_0_82]),c_0_42]),c_0_43])]),c_0_44]) ).
cnf(c_0_104,plain,
( ~ r2_hidden(X3,X1)
| ~ r1_tarski(X1,X2)
| r2_hidden(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_105,negated_conjecture,
r1_tarski(k18_filter_2(esk1_0,esk3_0),u1_struct_0(esk1_0)),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_106,negated_conjecture,
( ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| r2_hidden(k4_lattices(esk1_0,X1,esk3_0),k18_filter_2(esk1_0,esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_34])]) ).
cnf(c_0_107,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| m2_filter_2(u1_struct_0(X1),X1)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_108,negated_conjecture,
~ v1_xboole_0(u1_struct_0(esk1_0)),
inference(spm,[status(thm)],[c_0_101,c_0_50]) ).
cnf(c_0_109,negated_conjecture,
( ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| r3_lattices(esk1_0,k4_lattices(esk1_0,esk2_0,X1),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_102,c_0_103]),c_0_42]),c_0_43]),c_0_67])]),c_0_44]) ).
cnf(c_0_110,negated_conjecture,
( ~ r2_hidden(X1,k18_filter_2(esk1_0,esk3_0))
| r2_hidden(X1,u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_111,negated_conjecture,
r2_hidden(k4_lattices(esk1_0,esk2_0,esk3_0),k18_filter_2(esk1_0,esk3_0)),
inference(spm,[status(thm)],[c_0_106,c_0_67]) ).
cnf(c_0_112,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X4,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ r3_lattices(X1,X3,X4)
| v3_struct_0(X1)
| r3_lattices(X1,k4_lattices(X1,X2,X3),X4) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_113,plain,
( ~ r2_hidden(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| r2_hidden(k4_lattices(X1,X2,X3),u1_struct_0(X1))
| v3_struct_0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_107]),c_0_46]) ).
cnf(c_0_114,negated_conjecture,
r2_hidden(esk2_0,u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_67]),c_0_108]) ).
cnf(c_0_115,negated_conjecture,
r3_lattices(esk1_0,k4_lattices(esk1_0,esk2_0,esk3_0),esk2_0),
inference(spm,[status(thm)],[c_0_109,c_0_34]) ).
cnf(c_0_116,negated_conjecture,
r2_hidden(k4_lattices(esk1_0,esk2_0,esk3_0),u1_struct_0(esk1_0)),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_117,negated_conjecture,
( ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| r3_lattices(esk1_0,k4_lattices(esk1_0,X1,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_112,c_0_103]),c_0_42]),c_0_43]),c_0_67])]),c_0_44]) ).
cnf(c_0_118,negated_conjecture,
( ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| r2_hidden(k4_lattices(esk1_0,X1,esk2_0),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_113,c_0_114]),c_0_42]),c_0_43])]),c_0_44]) ).
cnf(c_0_119,negated_conjecture,
( ~ r2_hidden(k4_lattices(esk1_0,esk3_0,esk2_0),k18_filter_2(esk1_0,esk2_0))
| ~ r2_hidden(k4_lattices(esk1_0,esk2_0,esk3_0),k18_filter_2(esk1_0,esk2_0))
| ~ r2_hidden(esk2_0,k18_filter_2(esk1_0,esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_120,negated_conjecture,
r2_hidden(esk2_0,k18_filter_2(esk1_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_89,c_0_103]),c_0_42]),c_0_43]),c_0_67])]),c_0_44]) ).
cnf(c_0_121,negated_conjecture,
( ~ m1_subset_1(k4_lattices(esk1_0,esk2_0,esk3_0),u1_struct_0(esk1_0))
| r2_hidden(k4_lattices(esk1_0,esk2_0,esk3_0),k18_filter_2(esk1_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_89,c_0_115]),c_0_42]),c_0_43]),c_0_67])]),c_0_44]) ).
cnf(c_0_122,negated_conjecture,
m1_subset_1(k4_lattices(esk1_0,esk2_0,esk3_0),u1_struct_0(esk1_0)),
inference(spm,[status(thm)],[c_0_46,c_0_116]) ).
cnf(c_0_123,negated_conjecture,
r3_lattices(esk1_0,k4_lattices(esk1_0,esk3_0,esk2_0),esk2_0),
inference(spm,[status(thm)],[c_0_117,c_0_34]) ).
cnf(c_0_124,negated_conjecture,
r2_hidden(k4_lattices(esk1_0,esk3_0,esk2_0),u1_struct_0(esk1_0)),
inference(spm,[status(thm)],[c_0_118,c_0_34]) ).
cnf(c_0_125,negated_conjecture,
( ~ r2_hidden(k4_lattices(esk1_0,esk3_0,esk2_0),k18_filter_2(esk1_0,esk2_0))
| ~ r2_hidden(k4_lattices(esk1_0,esk2_0,esk3_0),k18_filter_2(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_119,c_0_120])]) ).
cnf(c_0_126,negated_conjecture,
r2_hidden(k4_lattices(esk1_0,esk2_0,esk3_0),k18_filter_2(esk1_0,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_121,c_0_122])]) ).
cnf(c_0_127,negated_conjecture,
( ~ m1_subset_1(k4_lattices(esk1_0,esk3_0,esk2_0),u1_struct_0(esk1_0))
| r2_hidden(k4_lattices(esk1_0,esk3_0,esk2_0),k18_filter_2(esk1_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_89,c_0_123]),c_0_42]),c_0_43]),c_0_67])]),c_0_44]) ).
cnf(c_0_128,negated_conjecture,
m1_subset_1(k4_lattices(esk1_0,esk3_0,esk2_0),u1_struct_0(esk1_0)),
inference(spm,[status(thm)],[c_0_46,c_0_124]) ).
cnf(c_0_129,negated_conjecture,
~ r2_hidden(k4_lattices(esk1_0,esk3_0,esk2_0),k18_filter_2(esk1_0,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_125,c_0_126])]) ).
cnf(c_0_130,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_127,c_0_128])]),c_0_129]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT305+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 23:30:52 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 197.20/29.54 % Version: 3.5.1
% 197.20/29.54 % Preprocessing class: FMLMSMSLSSSNFFN.
% 197.20/29.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 197.20/29.54 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 197.20/29.54 % Starting new_bool_3 with 600s (2) cores
% 197.20/29.54 % Starting new_bool_1 with 600s (2) cores
% 197.20/29.54 % Starting sh5l with 300s (1) cores
% 197.20/29.54 % new_bool_3 with pid 3639860 completed with status 0
% 197.20/29.54 % Result found by new_bool_3
% 197.20/29.54 % Preprocessing class: FMLMSMSLSSSNFFN.
% 197.20/29.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 197.20/29.54 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 197.20/29.54 % Starting new_bool_3 with 600s (2) cores
% 197.20/29.54 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 197.20/29.54 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 197.20/29.54 % Search class: FGHSM-FSLM31-MFFFFFNN
% 197.20/29.54 % Scheduled 8 strats onto 2 cores with 600 seconds (600 total)
% 197.20/29.54 % Starting SubtermCWHack with 55s (1) cores
% 197.20/29.54 % Starting new_bool_3 with 61s (1) cores
% 197.20/29.54 % new_bool_3 with pid 3639866 completed with status 0
% 197.20/29.54 % Result found by new_bool_3
% 197.20/29.54 % Preprocessing class: FMLMSMSLSSSNFFN.
% 197.20/29.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 197.20/29.54 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 197.20/29.54 % Starting new_bool_3 with 600s (2) cores
% 197.20/29.54 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 197.20/29.54 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 197.20/29.54 % Search class: FGHSM-FSLM31-MFFFFFNN
% 197.20/29.54 % Scheduled 8 strats onto 2 cores with 600 seconds (600 total)
% 197.20/29.54 % Starting SubtermCWHack with 55s (1) cores
% 197.20/29.54 % Starting new_bool_3 with 61s (1) cores
% 197.20/29.54 % Preprocessing time : 0.007 s
% 197.20/29.54 % Presaturation interreduction done
% 197.20/29.54
% 197.20/29.54 % Proof found!
% 197.20/29.54 % SZS status Theorem
% 197.20/29.54 % SZS output start CNFRefutation
% See solution above
% 197.20/29.54 % Parsed axioms : 2958
% 197.20/29.54 % Removed by relevancy pruning/SinE : 2740
% 197.20/29.54 % Initial clauses : 489
% 197.20/29.54 % Removed in clause preprocessing : 14
% 197.20/29.54 % Initial clauses in saturation : 475
% 197.20/29.54 % Processed clauses : 77150
% 197.20/29.54 % ...of these trivial : 370
% 197.20/29.54 % ...subsumed : 61019
% 197.20/29.54 % ...remaining for further processing : 15761
% 197.20/29.54 % Other redundant clauses eliminated : 789
% 197.20/29.54 % Clauses deleted for lack of memory : 0
% 197.20/29.54 % Backward-subsumed : 516
% 197.20/29.54 % Backward-rewritten : 63
% 197.20/29.54 % Generated clauses : 1181939
% 197.20/29.54 % ...of the previous two non-redundant : 1162066
% 197.20/29.54 % ...aggressively subsumed : 0
% 197.20/29.54 % Contextual simplify-reflections : 150
% 197.20/29.54 % Paramodulations : 1181067
% 197.20/29.54 % Factorizations : 43
% 197.20/29.54 % NegExts : 0
% 197.20/29.54 % Equation resolutions : 801
% 197.20/29.54 % Disequality decompositions : 0
% 197.20/29.54 % Total rewrite steps : 100540
% 197.20/29.54 % ...of those cached : 95980
% 197.20/29.54 % Propositional unsat checks : 3
% 197.20/29.54 % Propositional check models : 0
% 197.20/29.54 % Propositional check unsatisfiable : 0
% 197.20/29.54 % Propositional clauses : 0
% 197.20/29.54 % Propositional clauses after purity: 0
% 197.20/29.54 % Propositional unsat core size : 0
% 197.20/29.54 % Propositional preprocessing time : 0.000
% 197.20/29.54 % Propositional encoding time : 2.769
% 197.20/29.54 % Propositional solver time : 1.961
% 197.20/29.54 % Success case prop preproc time : 0.000
% 197.20/29.54 % Success case prop encoding time : 0.000
% 197.20/29.54 % Success case prop solver time : 0.000
% 197.20/29.54 % Current number of processed clauses : 14690
% 197.20/29.54 % Positive orientable unit clauses : 1484
% 197.20/29.54 % Positive unorientable unit clauses: 2
% 197.20/29.54 % Negative unit clauses : 2943
% 197.20/29.54 % Non-unit-clauses : 10261
% 197.20/29.54 % Current number of unprocessed clauses: 1084372
% 197.20/29.54 % ...number of literals in the above : 4575467
% 197.20/29.54 % Current number of archived formulas : 0
% 197.20/29.54 % Current number of archived clauses : 1051
% 197.20/29.54 % Clause-clause subsumption calls (NU) : 6816573
% 197.20/29.54 % Rec. Clause-clause subsumption calls : 4492250
% 197.20/29.54 % Non-unit clause-clause subsumptions : 12609
% 197.20/29.54 % Unit Clause-clause subsumption calls : 1040575
% 197.20/29.54 % Rewrite failures with RHS unbound : 0
% 197.20/29.54 % BW rewrite match attempts : 2867
% 197.20/29.54 % BW rewrite match successes : 41
% 197.20/29.54 % Condensation attempts : 0
% 197.20/29.54 % Condensation successes : 0
% 197.20/29.54 % Termbank termtop insertions : 35963373
% 197.20/29.54 % Search garbage collected termcells : 27816
% 197.20/29.54
% 197.20/29.54 % -------------------------------------------------
% 197.20/29.54 % User time : 26.443 s
% 197.20/29.54 % System time : 1.038 s
% 197.20/29.54 % Total time : 27.481 s
% 197.20/29.54 % Maximum resident set size: 8924 pages
% 197.20/29.54
% 197.20/29.54 % -------------------------------------------------
% 197.20/29.54 % User time : 54.070 s
% 197.20/29.54 % System time : 1.841 s
% 197.20/29.54 % Total time : 55.912 s
% 197.20/29.54 % Maximum resident set size: 8448 pages
% 197.20/29.54 % E exiting
%------------------------------------------------------------------------------