%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LAT311+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 01:04:51 PM UTC 2026
% Result : Theorem 265.24s 38.95s
% Output : CNFRefutation 265.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 20
% Syntax : Number of formulae : 110 ( 19 unt; 0 def)
% Number of atoms : 527 ( 59 equ)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 632 ( 215 ~; 221 |; 132 &)
% ( 0 <=>; 64 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 3 con; 0-2 aty)
% Number of variables : 152 ( 1 sgn 106 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t40_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,k1_zfmisc_1(u1_struct_0(X1)))
& ~ v1_xboole_0(X3) )
=> ( r2_hidden(X2,X3)
=> r1_tarski(k18_filter_2(X1,X2),k19_filter_2(X1,X3)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_filter_2) ).
fof(d6_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)))
=> k7_filter_2(X1,X2) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_filter_2) ).
fof(dt_k7_filter_2,axiom,
! [X1,X2] :
( ( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
& l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> m1_subset_1(k7_filter_2(X1,X2),k1_zfmisc_1(u1_struct_0(k1_lattice2(X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_filter_2) ).
fof(t37_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] :
( ( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(k1_lattice2(X1))))
& ~ v1_xboole_0(X3) )
=> ( k3_filter_2(k1_lattice2(X1),X3) = k19_filter_2(X1,k8_filter_2(X1,X3))
& k3_filter_2(X1,k8_filter_2(X1,X3)) = k19_filter_2(k1_lattice2(X1),X3)
& k3_filter_2(X1,X2) = k19_filter_2(k1_lattice2(X1),k7_filter_2(X1,X2))
& k3_filter_2(k1_lattice2(X1),k7_filter_2(X1,X2)) = k19_filter_2(X1,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_filter_2) ).
fof(rc5_struct_0,axiom,
! [X1] :
( ( l1_struct_0(X1)
& ~ v3_struct_0(X1) )
=> ? [X2] :
( ~ v1_xboole_0(X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).
fof(d7_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(k1_lattice2(X1))))
=> k8_filter_2(X1,X2) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_filter_2) ).
fof(t29_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,k1_zfmisc_1(u1_struct_0(X1)))
& ~ v1_xboole_0(X3) )
=> ( r2_hidden(X2,X3)
=> r1_tarski(k2_filter_0(X1,X2),k3_filter_0(X1,X3)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_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/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( v1_xboole_0(X2)
& r2_hidden(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(dt_l1_lattices,axiom,
! [X1] :
( l1_lattices(X1)
=> l1_struct_0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).
fof(d4_filter_2,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> k5_filter_2(X1,X2) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_filter_2) ).
fof(d9_filter_2,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> k18_filter_2(X1,X2) = a_2_0_filter_2(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_filter_2) ).
fof(redefinition_k3_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) )
=> k3_filter_2(X1,X2) = k3_filter_0(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_filter_2) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( l2_lattices(X1)
& l1_lattices(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(dt_k5_filter_2,axiom,
! [X1,X2] :
( ( m1_subset_1(X2,u1_struct_0(X1))
& l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> m1_subset_1(k5_filter_2(X1,X2),u1_struct_0(k1_lattice2(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_filter_2) ).
fof(t30_filter_2,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ( k18_filter_2(k1_lattice2(X1),k5_filter_2(X1,X2)) = k2_filter_2(X1,X2)
& k18_filter_2(X1,X2) = k2_filter_2(k1_lattice2(X1),k5_filter_2(X1,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_filter_2) ).
fof(dt_k1_lattice2,axiom,
! [X1] :
( l3_lattices(X1)
=> ( l3_lattices(k1_lattice2(X1))
& v3_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattice2) ).
fof(fc6_lattice2,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( v10_lattices(k1_lattice2(X1))
& v9_lattices(k1_lattice2(X1))
& v8_lattices(k1_lattice2(X1))
& v7_lattices(k1_lattice2(X1))
& v6_lattices(k1_lattice2(X1))
& v5_lattices(k1_lattice2(X1))
& v4_lattices(k1_lattice2(X1))
& v3_lattices(k1_lattice2(X1))
& ~ v3_struct_0(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_lattice2) ).
fof(redefinition_k2_filter_2,axiom,
! [X1,X2] :
( ( m1_subset_1(X2,u1_struct_0(X1))
& l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> k2_filter_2(X1,X2) = k2_filter_0(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_filter_2) ).
fof(fc1_lattice2,axiom,
! [X1] :
( ( l3_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( v3_lattices(k1_lattice2(X1))
& ~ v3_struct_0(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_lattice2) ).
fof(c_0_20,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,k1_zfmisc_1(u1_struct_0(X1)))
& ~ v1_xboole_0(X3) )
=> ( r2_hidden(X2,X3)
=> r1_tarski(k18_filter_2(X1,X2),k19_filter_2(X1,X3)) ) ) ) ),
inference(assume_negation,[status(cth)],[t40_filter_2]) ).
fof(c_0_21,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> k7_filter_2(X1,X2) = X2 ) ),
inference(fof_simplification,[status(thm)],[d6_filter_2]) ).
fof(c_0_22,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,k1_zfmisc_1(u1_struct_0(X1)))
& ~ v1_xboole_0(X3) )
=> ( r2_hidden(X2,X3)
=> r1_tarski(k18_filter_2(X1,X2),k19_filter_2(X1,X3)) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_23,plain,
! [X1,X2] :
( ( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
& l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> m1_subset_1(k7_filter_2(X1,X2),k1_zfmisc_1(u1_struct_0(k1_lattice2(X1)))) ),
inference(fof_simplification,[status(thm)],[dt_k7_filter_2]) ).
fof(c_0_24,plain,
! [X25,X26] :
( k7_filter_2(X25,X26) = X26
| ~ m1_subset_1(X26,k1_zfmisc_1(u1_struct_0(X25)))
| ~ l3_lattices(X25)
| ~ v10_lattices(X25)
| v3_struct_0(X25) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])]) ).
fof(c_0_25,negated_conjecture,
( ~ r1_tarski(k18_filter_2(esk1_0,esk2_0),k19_filter_2(esk1_0,esk3_0))
& r2_hidden(esk2_0,esk3_0)
& m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk1_0)))
& ~ v1_xboole_0(esk3_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_22])])])]) ).
fof(c_0_26,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] :
( ( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(k1_lattice2(X1))))
& ~ v1_xboole_0(X3) )
=> ( k3_filter_2(k1_lattice2(X1),X3) = k19_filter_2(X1,k8_filter_2(X1,X3))
& k3_filter_2(X1,k8_filter_2(X1,X3)) = k19_filter_2(k1_lattice2(X1),X3)
& k3_filter_2(X1,X2) = k19_filter_2(k1_lattice2(X1),k7_filter_2(X1,X2))
& k3_filter_2(k1_lattice2(X1),k7_filter_2(X1,X2)) = k19_filter_2(X1,X2) ) ) ) ),
inference(fof_simplification,[status(thm)],[t37_filter_2]) ).
fof(c_0_27,plain,
! [X1] :
( ( l1_struct_0(X1)
& ~ v3_struct_0(X1) )
=> ? [X2] :
( ~ v1_xboole_0(X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ) ),
inference(fof_simplification,[status(thm)],[rc5_struct_0]) ).
fof(c_0_28,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k1_lattice2(X1))))
=> k8_filter_2(X1,X2) = X2 ) ),
inference(fof_simplification,[status(thm)],[d7_filter_2]) ).
fof(c_0_29,plain,
! [X49,X50] :
( m1_subset_1(k7_filter_2(X49,X50),k1_zfmisc_1(u1_struct_0(k1_lattice2(X49))))
| ~ m1_subset_1(X50,k1_zfmisc_1(u1_struct_0(X49)))
| ~ l3_lattices(X49)
| ~ v10_lattices(X49)
| v3_struct_0(X49) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])]) ).
cnf(c_0_30,plain,
( ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| k7_filter_2(X1,X2) = X2
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,negated_conjecture,
m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_33,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_34,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_35,plain,
! [X167,X168,X169] :
( ( ~ l3_lattices(X167)
| ~ v10_lattices(X167)
| v3_struct_0(X167)
| ~ m1_subset_1(X168,k1_zfmisc_1(u1_struct_0(X167)))
| v1_xboole_0(X168)
| ~ m1_subset_1(X169,k1_zfmisc_1(u1_struct_0(k1_lattice2(X167))))
| v1_xboole_0(X169)
| k3_filter_2(k1_lattice2(X167),X169) = k19_filter_2(X167,k8_filter_2(X167,X169)) )
& ( ~ l3_lattices(X167)
| ~ v10_lattices(X167)
| v3_struct_0(X167)
| ~ m1_subset_1(X168,k1_zfmisc_1(u1_struct_0(X167)))
| v1_xboole_0(X168)
| ~ m1_subset_1(X169,k1_zfmisc_1(u1_struct_0(k1_lattice2(X167))))
| v1_xboole_0(X169)
| k3_filter_2(X167,k8_filter_2(X167,X169)) = k19_filter_2(k1_lattice2(X167),X169) )
& ( ~ l3_lattices(X167)
| ~ v10_lattices(X167)
| v3_struct_0(X167)
| ~ m1_subset_1(X168,k1_zfmisc_1(u1_struct_0(X167)))
| v1_xboole_0(X168)
| ~ m1_subset_1(X169,k1_zfmisc_1(u1_struct_0(k1_lattice2(X167))))
| v1_xboole_0(X169)
| k3_filter_2(X167,X168) = k19_filter_2(k1_lattice2(X167),k7_filter_2(X167,X168)) )
& ( ~ l3_lattices(X167)
| ~ v10_lattices(X167)
| v3_struct_0(X167)
| ~ m1_subset_1(X168,k1_zfmisc_1(u1_struct_0(X167)))
| v1_xboole_0(X168)
| ~ m1_subset_1(X169,k1_zfmisc_1(u1_struct_0(k1_lattice2(X167))))
| v1_xboole_0(X169)
| k3_filter_2(k1_lattice2(X167),k7_filter_2(X167,X168)) = k19_filter_2(X167,X168) ) ),
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_26])])])])]) ).
fof(c_0_36,plain,
! [X135] :
( ( ~ l1_struct_0(X135)
| v3_struct_0(X135)
| ~ v1_xboole_0(esk27_1(X135)) )
& ( ~ l1_struct_0(X135)
| v3_struct_0(X135)
| m1_subset_1(esk27_1(X135),k1_zfmisc_1(u1_struct_0(X135))) ) ),
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_27])])])])]) ).
fof(c_0_37,plain,
! [X27,X28] :
( k8_filter_2(X27,X28) = X28
| ~ m1_subset_1(X28,k1_zfmisc_1(u1_struct_0(k1_lattice2(X27))))
| ~ l3_lattices(X27)
| ~ v10_lattices(X27)
| v3_struct_0(X27) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])])]) ).
cnf(c_0_38,plain,
( ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| m1_subset_1(k7_filter_2(X1,X2),k1_zfmisc_1(u1_struct_0(k1_lattice2(X1))))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,negated_conjecture,
k7_filter_2(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_30,c_0_31]),c_0_32]),c_0_33])]),c_0_34]) ).
fof(c_0_40,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,k1_zfmisc_1(u1_struct_0(X1)))
& ~ v1_xboole_0(X3) )
=> ( r2_hidden(X2,X3)
=> r1_tarski(k2_filter_0(X1,X2),k3_filter_0(X1,X3)) ) ) ) ),
inference(fof_simplification,[status(thm)],[t29_filter_0]) ).
cnf(c_0_41,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k1_lattice2(X1))))
| v3_struct_0(X1)
| v1_xboole_0(X3)
| v1_xboole_0(X2)
| k3_filter_2(k1_lattice2(X1),X2) = k19_filter_2(X1,k8_filter_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_42,plain,
( ~ l1_struct_0(X1)
| v3_struct_0(X1)
| m1_subset_1(esk27_1(X1),k1_zfmisc_1(u1_struct_0(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_43,plain,
( ~ l1_struct_0(X1)
| ~ v1_xboole_0(esk27_1(X1))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_44,plain,
( ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k1_lattice2(X1))))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| k8_filter_2(X1,X2) = X2
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_45,negated_conjecture,
m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(k1_lattice2(esk1_0)))),
inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_31]),c_0_32]),c_0_33])]),c_0_34]),c_0_39]) ).
fof(c_0_46,plain,
! [X157,X158,X159] :
( r1_tarski(k2_filter_0(X157,X158),k3_filter_0(X157,X159))
| ~ r2_hidden(X158,X159)
| ~ m1_subset_1(X159,k1_zfmisc_1(u1_struct_0(X157)))
| v1_xboole_0(X159)
| ~ m1_subset_1(X158,u1_struct_0(X157))
| ~ l3_lattices(X157)
| ~ v10_lattices(X157)
| v3_struct_0(X157) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])])]) ).
fof(c_0_47,plain,
! [X172,X173,X174] :
( m1_subset_1(X172,X174)
| ~ m1_subset_1(X173,k1_zfmisc_1(X174))
| ~ r2_hidden(X172,X173) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])])]) ).
fof(c_0_48,plain,
! [X179,X180] :
( ~ v1_xboole_0(X180)
| ~ r2_hidden(X179,X180) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])])]) ).
cnf(c_0_49,plain,
( ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k1_lattice2(X1))))
| ~ l1_struct_0(X1)
| v3_struct_0(X1)
| v1_xboole_0(X2)
| k19_filter_2(X1,k8_filter_2(X1,X2)) = k3_filter_2(k1_lattice2(X1),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
cnf(c_0_50,negated_conjecture,
k8_filter_2(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_44,c_0_45]),c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_51,negated_conjecture,
~ v1_xboole_0(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_52,plain,
! [X53] :
( l1_struct_0(X53)
| ~ l1_lattices(X53) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_lattices])])]) ).
fof(c_0_53,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> k5_filter_2(X1,X2) = X2 ) ),
inference(fof_simplification,[status(thm)],[d4_filter_2]) ).
fof(c_0_54,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> k18_filter_2(X1,X2) = a_2_0_filter_2(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[d9_filter_2]) ).
cnf(c_0_55,plain,
( ~ r2_hidden(X2,X3)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| r1_tarski(k2_filter_0(X1,X2),k3_filter_0(X1,X3))
| v1_xboole_0(X3)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_56,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_47]) ).
cnf(c_0_57,plain,
( ~ v1_xboole_0(X2)
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
fof(c_0_58,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) )
=> k3_filter_2(X1,X2) = k3_filter_0(X1,X2) ),
inference(fof_simplification,[status(thm)],[redefinition_k3_filter_2]) ).
cnf(c_0_59,negated_conjecture,
( ~ l1_struct_0(esk1_0)
| k3_filter_2(k1_lattice2(esk1_0),esk3_0) = k19_filter_2(esk1_0,esk3_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(spm,[status(thm)],[c_0_49,c_0_45]),c_0_50]),c_0_32]),c_0_33])]),c_0_51]),c_0_34]) ).
cnf(c_0_60,plain,
( ~ l1_lattices(X1)
| l1_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
fof(c_0_61,plain,
! [X55] :
( ( ~ l3_lattices(X55)
| l2_lattices(X55) )
& ( ~ l3_lattices(X55)
| l1_lattices(X55) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])])]) ).
fof(c_0_62,plain,
! [X1,X2] :
( ( m1_subset_1(X2,u1_struct_0(X1))
& l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> m1_subset_1(k5_filter_2(X1,X2),u1_struct_0(k1_lattice2(X1))) ),
inference(fof_simplification,[status(thm)],[dt_k5_filter_2]) ).
fof(c_0_63,plain,
! [X23,X24] :
( k5_filter_2(X23,X24) = X24
| ~ m1_subset_1(X24,u1_struct_0(X23))
| ~ l3_lattices(X23)
| ~ v10_lattices(X23)
| v3_struct_0(X23) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_53])])])]) ).
fof(c_0_64,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ( k18_filter_2(k1_lattice2(X1),k5_filter_2(X1,X2)) = k2_filter_2(X1,X2)
& k18_filter_2(X1,X2) = k2_filter_2(k1_lattice2(X1),k5_filter_2(X1,X2)) ) ) ),
inference(fof_simplification,[status(thm)],[t30_filter_2]) ).
fof(c_0_65,plain,
! [X29,X30] :
( k18_filter_2(X29,X30) = a_2_0_filter_2(X29,X30)
| ~ m1_subset_1(X30,u1_struct_0(X29))
| ~ l3_lattices(X29)
| ~ v10_lattices(X29)
| v3_struct_0(X29) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_54])])])]) ).
cnf(c_0_66,plain,
( ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
| ~ r2_hidden(X2,X3)
| v3_struct_0(X1)
| r1_tarski(k2_filter_0(X1,X2),k3_filter_0(X1,X3)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_55,c_0_56]),c_0_57]) ).
fof(c_0_67,plain,
! [X38] :
( ( ~ l3_lattices(X38)
| l3_lattices(k1_lattice2(X38)) )
& ( ~ l3_lattices(X38)
| v3_lattices(k1_lattice2(X38)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_lattice2])])])]) ).
fof(c_0_68,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( v10_lattices(k1_lattice2(X1))
& v9_lattices(k1_lattice2(X1))
& v8_lattices(k1_lattice2(X1))
& v7_lattices(k1_lattice2(X1))
& v6_lattices(k1_lattice2(X1))
& v5_lattices(k1_lattice2(X1))
& v4_lattices(k1_lattice2(X1))
& v3_lattices(k1_lattice2(X1))
& ~ v3_struct_0(k1_lattice2(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc6_lattice2]) ).
fof(c_0_69,plain,
! [X141,X142] :
( k3_filter_2(X141,X142) = k3_filter_0(X141,X142)
| ~ m1_subset_1(X142,k1_zfmisc_1(u1_struct_0(X141)))
| v1_xboole_0(X142)
| ~ l3_lattices(X141)
| ~ v10_lattices(X141)
| v3_struct_0(X141) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_58])])]) ).
cnf(c_0_70,negated_conjecture,
( ~ l1_lattices(esk1_0)
| k3_filter_2(k1_lattice2(esk1_0),esk3_0) = k19_filter_2(esk1_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_71,plain,
( ~ l3_lattices(X1)
| l1_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
fof(c_0_72,plain,
! [X1,X2] :
( ( m1_subset_1(X2,u1_struct_0(X1))
& l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> k2_filter_2(X1,X2) = k2_filter_0(X1,X2) ),
inference(fof_simplification,[status(thm)],[redefinition_k2_filter_2]) ).
fof(c_0_73,plain,
! [X47,X48] :
( m1_subset_1(k5_filter_2(X47,X48),u1_struct_0(k1_lattice2(X47)))
| ~ m1_subset_1(X48,u1_struct_0(X47))
| ~ l3_lattices(X47)
| ~ v10_lattices(X47)
| v3_struct_0(X47) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_62])])]) ).
cnf(c_0_74,plain,
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| k5_filter_2(X1,X2) = X2
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_75,negated_conjecture,
m1_subset_1(esk2_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_76,plain,
! [X165,X166] :
( ( ~ l3_lattices(X165)
| ~ v10_lattices(X165)
| v3_struct_0(X165)
| ~ m1_subset_1(X166,u1_struct_0(X165))
| k18_filter_2(k1_lattice2(X165),k5_filter_2(X165,X166)) = k2_filter_2(X165,X166) )
& ( ~ l3_lattices(X165)
| ~ v10_lattices(X165)
| v3_struct_0(X165)
| ~ m1_subset_1(X166,u1_struct_0(X165))
| k18_filter_2(X165,X166) = k2_filter_2(k1_lattice2(X165),k5_filter_2(X165,X166)) ) ),
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_64])])])])]) ).
cnf(c_0_77,plain,
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| k18_filter_2(X1,X2) = a_2_0_filter_2(X1,X2)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_78,negated_conjecture,
( ~ v10_lattices(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0))
| ~ r2_hidden(X1,esk3_0)
| v3_struct_0(k1_lattice2(esk1_0))
| r1_tarski(k2_filter_0(k1_lattice2(esk1_0),X1),k3_filter_0(k1_lattice2(esk1_0),esk3_0)) ),
inference(spm,[status(thm)],[c_0_66,c_0_45]) ).
cnf(c_0_79,plain,
( ~ l3_lattices(X1)
| l3_lattices(k1_lattice2(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
fof(c_0_80,plain,
! [X105] :
( ( ~ l3_lattices(X105)
| ~ v10_lattices(X105)
| v3_struct_0(X105)
| v10_lattices(k1_lattice2(X105)) )
& ( ~ l3_lattices(X105)
| ~ v10_lattices(X105)
| v3_struct_0(X105)
| v9_lattices(k1_lattice2(X105)) )
& ( ~ l3_lattices(X105)
| ~ v10_lattices(X105)
| v3_struct_0(X105)
| v8_lattices(k1_lattice2(X105)) )
& ( ~ l3_lattices(X105)
| ~ v10_lattices(X105)
| v3_struct_0(X105)
| v7_lattices(k1_lattice2(X105)) )
& ( ~ l3_lattices(X105)
| ~ v10_lattices(X105)
| v3_struct_0(X105)
| v6_lattices(k1_lattice2(X105)) )
& ( ~ l3_lattices(X105)
| ~ v10_lattices(X105)
| v3_struct_0(X105)
| v5_lattices(k1_lattice2(X105)) )
& ( ~ l3_lattices(X105)
| ~ v10_lattices(X105)
| v3_struct_0(X105)
| v4_lattices(k1_lattice2(X105)) )
& ( ~ l3_lattices(X105)
| ~ v10_lattices(X105)
| v3_struct_0(X105)
| v3_lattices(k1_lattice2(X105)) )
& ( ~ l3_lattices(X105)
| ~ v10_lattices(X105)
| v3_struct_0(X105)
| ~ v3_struct_0(k1_lattice2(X105)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_68])])])]) ).
cnf(c_0_81,plain,
( ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| k3_filter_2(X1,X2) = k3_filter_0(X1,X2)
| v1_xboole_0(X2)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_82,negated_conjecture,
k3_filter_2(k1_lattice2(esk1_0),esk3_0) = k19_filter_2(esk1_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_32])]) ).
fof(c_0_83,plain,
! [X139,X140] :
( k2_filter_2(X139,X140) = k2_filter_0(X139,X140)
| ~ m1_subset_1(X140,u1_struct_0(X139))
| ~ l3_lattices(X139)
| ~ v10_lattices(X139)
| v3_struct_0(X139) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_72])])]) ).
cnf(c_0_84,plain,
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| m1_subset_1(k5_filter_2(X1,X2),u1_struct_0(k1_lattice2(X1)))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_85,negated_conjecture,
k5_filter_2(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_74,c_0_75]),c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_86,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| v3_struct_0(X1)
| k18_filter_2(X1,X2) = k2_filter_2(k1_lattice2(X1),k5_filter_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_87,negated_conjecture,
k18_filter_2(esk1_0,esk2_0) = a_2_0_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_77,c_0_75]),c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_88,negated_conjecture,
( ~ v10_lattices(k1_lattice2(esk1_0))
| ~ r2_hidden(X1,esk3_0)
| v3_struct_0(k1_lattice2(esk1_0))
| r1_tarski(k2_filter_0(k1_lattice2(esk1_0),X1),k3_filter_0(k1_lattice2(esk1_0),esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_32])]) ).
cnf(c_0_89,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| v10_lattices(k1_lattice2(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_90,negated_conjecture,
( ~ v10_lattices(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0))
| v3_struct_0(k1_lattice2(esk1_0))
| k3_filter_0(k1_lattice2(esk1_0),esk3_0) = k19_filter_2(esk1_0,esk3_0) ),
inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_45]),c_0_51]),c_0_82]) ).
cnf(c_0_91,plain,
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| k2_filter_2(X1,X2) = k2_filter_0(X1,X2)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_92,negated_conjecture,
m1_subset_1(esk2_0,u1_struct_0(k1_lattice2(esk1_0))),
inference(rw,[status(thm)],[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_75]),c_0_32]),c_0_33])]),c_0_34]),c_0_85]) ).
cnf(c_0_93,negated_conjecture,
k2_filter_2(k1_lattice2(esk1_0),esk2_0) = a_2_0_filter_2(esk1_0,esk2_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[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_75]),c_0_32]),c_0_33])]),c_0_34]),c_0_85]),c_0_87]) ).
cnf(c_0_94,negated_conjecture,
( ~ r2_hidden(X1,esk3_0)
| v3_struct_0(k1_lattice2(esk1_0))
| r1_tarski(k2_filter_0(k1_lattice2(esk1_0),X1),k3_filter_0(k1_lattice2(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_89]),c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_95,negated_conjecture,
r2_hidden(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_96,negated_conjecture,
( ~ v10_lattices(k1_lattice2(esk1_0))
| v3_struct_0(k1_lattice2(esk1_0))
| k3_filter_0(k1_lattice2(esk1_0),esk3_0) = k19_filter_2(esk1_0,esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_79]),c_0_32])]) ).
cnf(c_0_97,negated_conjecture,
( ~ v10_lattices(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0))
| v3_struct_0(k1_lattice2(esk1_0))
| k2_filter_0(k1_lattice2(esk1_0),esk2_0) = a_2_0_filter_2(esk1_0,esk2_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93]) ).
fof(c_0_98,plain,
! [X1] :
( ( l3_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( v3_lattices(k1_lattice2(X1))
& ~ v3_struct_0(k1_lattice2(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc1_lattice2]) ).
cnf(c_0_99,negated_conjecture,
( v3_struct_0(k1_lattice2(esk1_0))
| r1_tarski(k2_filter_0(k1_lattice2(esk1_0),esk2_0),k3_filter_0(k1_lattice2(esk1_0),esk3_0)) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_100,negated_conjecture,
( v3_struct_0(k1_lattice2(esk1_0))
| k3_filter_0(k1_lattice2(esk1_0),esk3_0) = k19_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_96,c_0_89]),c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_101,negated_conjecture,
( ~ v10_lattices(k1_lattice2(esk1_0))
| v3_struct_0(k1_lattice2(esk1_0))
| k2_filter_0(k1_lattice2(esk1_0),esk2_0) = a_2_0_filter_2(esk1_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_79]),c_0_32])]) ).
cnf(c_0_102,negated_conjecture,
~ r1_tarski(k18_filter_2(esk1_0,esk2_0),k19_filter_2(esk1_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_103,plain,
! [X91] :
( ( ~ l3_lattices(X91)
| v3_struct_0(X91)
| v3_lattices(k1_lattice2(X91)) )
& ( ~ l3_lattices(X91)
| v3_struct_0(X91)
| ~ v3_struct_0(k1_lattice2(X91)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_98])])])]) ).
cnf(c_0_104,negated_conjecture,
( v3_struct_0(k1_lattice2(esk1_0))
| r1_tarski(k2_filter_0(k1_lattice2(esk1_0),esk2_0),k19_filter_2(esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_105,negated_conjecture,
( v3_struct_0(k1_lattice2(esk1_0))
| k2_filter_0(k1_lattice2(esk1_0),esk2_0) = a_2_0_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_101,c_0_89]),c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_106,negated_conjecture,
~ r1_tarski(a_2_0_filter_2(esk1_0,esk2_0),k19_filter_2(esk1_0,esk3_0)),
inference(rw,[status(thm)],[c_0_102,c_0_87]) ).
cnf(c_0_107,plain,
( ~ l3_lattices(X1)
| ~ v3_struct_0(k1_lattice2(X1))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_108,negated_conjecture,
v3_struct_0(k1_lattice2(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_106]) ).
cnf(c_0_109,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_32])]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT311+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 % Computer : n005.cluster.edu
% 0.12/0.41 % Model : x86_64 x86_64
% 0.12/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.41 % Memory : 8046.5625MB
% 0.12/0.41 % OS : Linux 6.8.0-71-generic
% 0.12/0.41 % CPULimit : 300
% 0.12/0.41 % WCLimit : 300
% 0.12/0.41 % DateTime : Sun Sep 20 23:33:34 UTC 2026
% 0.12/0.41 % CPUTime :
% 0.12/0.41 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.47 Running first-order theorem proving
% 0.21/0.47 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 265.24/38.95 % Version: 3.5.1
% 265.24/38.95 % Preprocessing class: FSLSSMSSSSSNFFN.
% 265.24/38.95 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 265.24/38.95 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 265.24/38.95 % Starting new_bool_3 with 300s (1) cores
% 265.24/38.95 % Starting new_bool_1 with 300s (1) cores
% 265.24/38.95 % Starting sh5l with 300s (1) cores
% 265.24/38.95 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2001177 completed with status 0
% 265.24/38.95 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 265.24/38.95 % Preprocessing class: FSLSSMSSSSSNFFN.
% 265.24/38.95 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 265.24/38.95 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 265.24/38.95 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 265.24/38.95 % No SInE strategy applied
% 265.24/38.95 % Search class: FGHSM-FSLM31-MFFFFFNN
% 265.24/38.95 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 265.24/38.95 % Starting SubtermCWHack with 136s (1) cores
% 265.24/38.95 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 265.24/38.95 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN with 136s (1) cores
% 265.24/38.95 % Starting G-E--_207_B07_F1_AE_CS_SP_PI_PS_S0Y with 136s (1) cores
% 265.24/38.95 % Starting U----_116Y_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 265.24/38.95 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2001185 completed with status 0
% 265.24/38.95 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 265.24/38.95 % Preprocessing class: FSLSSMSSSSSNFFN.
% 265.24/38.95 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 265.24/38.95 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 265.24/38.95 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 265.24/38.95 % No SInE strategy applied
% 265.24/38.95 % Search class: FGHSM-FSLM31-MFFFFFNN
% 265.24/38.95 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 265.24/38.95 % Starting SubtermCWHack with 136s (1) cores
% 265.24/38.95 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 265.24/38.95 % Preprocessing time : 0.006 s
% 265.24/38.95 % Presaturation interreduction done
% 265.24/38.95
% 265.24/38.95 % Proof found!
% 265.24/38.95 % SZS status Theorem
% 265.24/38.95 % SZS output start CNFRefutation
% See solution above
% 265.24/38.95 % Parsed axioms : 101
% 265.24/38.95 % Removed by relevancy pruning/SinE : 0
% 265.24/38.95 % Initial clauses : 192
% 265.24/38.95 % Removed in clause preprocessing : 11
% 265.24/38.95 % Initial clauses in saturation : 181
% 265.24/38.95 % Processed clauses : 76992
% 265.24/38.95 % ...of these trivial : 574
% 265.24/38.95 % ...subsumed : 57916
% 265.24/38.95 % ...remaining for further processing : 18502
% 265.24/38.95 % Other redundant clauses eliminated : 2
% 265.24/38.95 % Clauses deleted for lack of memory : 0
% 265.24/38.95 % Backward-subsumed : 418
% 265.24/38.95 % Backward-rewritten : 1443
% 265.24/38.95 % Generated clauses : 563021
% 265.24/38.95 % ...of the previous two non-redundant : 558642
% 265.24/38.95 % ...aggressively subsumed : 0
% 265.24/38.95 % Contextual simplify-reflections : 587
% 265.24/38.95 % Paramodulations : 562803
% 265.24/38.95 % Factorizations : 216
% 265.24/38.95 % NegExts : 0
% 265.24/38.95 % Equation resolutions : 2
% 265.24/38.95 % Disequality decompositions : 0
% 265.24/38.95 % Total rewrite steps : 82363
% 265.24/38.95 % ...of those cached : 80590
% 265.24/38.95 % Propositional unsat checks : 3
% 265.24/38.95 % Propositional check models : 0
% 265.24/38.95 % Propositional check unsatisfiable : 0
% 265.24/38.95 % Propositional clauses : 0
% 265.24/38.95 % Propositional clauses after purity: 0
% 265.24/38.95 % Propositional unsat core size : 0
% 265.24/38.95 % Propositional preprocessing time : 0.000
% 265.24/38.95 % Propositional encoding time : 1.262
% 265.24/38.95 % Propositional solver time : 1.607
% 265.24/38.95 % Success case prop preproc time : 0.000
% 265.24/38.95 % Success case prop encoding time : 0.000
% 265.24/38.95 % Success case prop solver time : 0.000
% 265.24/38.95 % Current number of processed clauses : 16470
% 265.24/38.95 % Positive orientable unit clauses : 3149
% 265.24/38.95 % Positive unorientable unit clauses: 0
% 265.24/38.95 % Negative unit clauses : 996
% 265.24/38.95 % Non-unit-clauses : 12325
% 265.24/38.95 % Current number of unprocessed clauses: 475336
% 265.24/38.95 % ...number of literals in the above : 2198640
% 265.24/38.95 % Current number of archived formulas : 0
% 265.24/38.95 % Current number of archived clauses : 2030
% 265.24/38.95 % Clause-clause subsumption calls (NU) : 15420968
% 265.24/38.95 % Rec. Clause-clause subsumption calls : 4046730
% 265.24/38.95 % Non-unit clause-clause subsumptions : 20410
% 265.24/38.95 % Unit Clause-clause subsumption calls : 1743679
% 265.24/38.95 % Rewrite failures with RHS unbound : 0
% 265.24/38.95 % BW rewrite match attempts : 55913
% 265.24/38.95 % BW rewrite match successes : 189
% 265.24/38.95 % Condensation attempts : 0
% 265.24/38.95 % Condensation successes : 0
% 265.24/38.95 % Termbank termtop insertions : 21271388
% 265.24/38.95 % Search garbage collected termcells : 2326
% 265.24/38.95
% 265.24/38.95 % -------------------------------------------------
% 265.24/38.95 % User time : 36.968 s
% 265.24/38.95 % System time : 0.812 s
% 265.24/38.95 % Total time : 37.780 s
% 265.24/38.95 % Maximum resident set size: 3744 pages
% 265.24/38.95
% 265.24/38.95 % -------------------------------------------------
% 265.24/38.95 % User time : 183.327 s
% 265.24/38.95 % System time : 4.371 s
% 265.24/38.95 % Total time : 187.698 s
% 265.24/38.95 % Maximum resident set size: 4864 pages
% 265.24/38.95 % E exiting
%------------------------------------------------------------------------------