%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LAT306+1 : 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 : n017.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 5.97s 1.43s
% Output : CNFRefutation 5.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 26
% Syntax : Number of formulae : 150 ( 38 unt; 0 def)
% Number of atoms : 601 ( 73 equ)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 696 ( 245 ~; 242 |; 143 &)
% ( 5 <=>; 61 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 1 con; 0-3 aty)
% Number of variables : 166 ( 4 sgn 111 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t32_filter_2,conjecture,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( v14_lattices(X1)
=> r1_filter_2(u1_struct_0(X1),k17_filter_2(X1),k18_filter_2(X1,k6_lattices(X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_filter_2) ).
fof(dt_k6_lattices,axiom,
! [X1] :
( ( l2_lattices(X1)
& ~ v3_struct_0(X1) )
=> m1_subset_1(k6_lattices(X1),u1_struct_0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_lattices) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( l2_lattices(X1)
& l1_lattices(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_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/sandbox/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/sandbox/benchmark/theBenchmark.p',d9_filter_2) ).
fof(d8_filter_2,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> k17_filter_2(X1) = u1_struct_0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_filter_2) ).
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/sandbox/benchmark/theBenchmark.p',dt_k5_filter_2) ).
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/sandbox/benchmark/theBenchmark.p',fc6_lattice2) ).
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/sandbox/benchmark/theBenchmark.p',t30_filter_2) ).
fof(t20_filter_0,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( ( l3_lattices(X1)
& v13_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> k1_filter_0(X1) = k2_filter_0(X1,k5_lattices(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_filter_0) ).
fof(t64_lattice2,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( v14_lattices(X1)
<=> v13_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_lattice2) ).
fof(t79_lattice2,axiom,
! [X1] :
( ( l3_lattices(X1)
& v14_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> k6_lattices(X1) = k5_lattices(k1_lattice2(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_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/sandbox/benchmark/theBenchmark.p',redefinition_k2_filter_2) ).
fof(dt_k1_lattice2,axiom,
! [X1] :
( l3_lattices(X1)
=> ( l3_lattices(k1_lattice2(X1))
& v3_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattice2) ).
fof(dt_k17_filter_2,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> m2_filter_2(k17_filter_2(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k17_filter_2) ).
fof(dt_u2_lattices,axiom,
! [X1] :
( l2_lattices(X1)
=> ( m2_relset_1(u2_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
& v1_funct_2(u2_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
& v1_funct_1(u2_lattices(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u2_lattices) ).
fof(dt_u1_lattices,axiom,
! [X1] :
( l1_lattices(X1)
=> ( m2_relset_1(u1_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
& v1_funct_2(u1_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
& v1_funct_1(u1_lattices(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_lattices) ).
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(d2_filter_0,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> k1_filter_0(X1) = u1_struct_0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_filter_0) ).
fof(d2_lattice2,axiom,
! [X1] :
( l3_lattices(X1)
=> k1_lattice2(X1) = g3_lattices(u1_struct_0(X1),u1_lattices(X1),u2_lattices(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_lattice2) ).
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
<=> m1_relset_1(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
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(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/theBenchmark.p',dt_m2_lattice4) ).
fof(free_g3_lattices,axiom,
! [X1,X2,X3] :
( ( m1_relset_1(X3,k2_zfmisc_1(X1,X1),X1)
& v1_funct_2(X3,k2_zfmisc_1(X1,X1),X1)
& v1_funct_1(X3)
& m1_relset_1(X2,k2_zfmisc_1(X1,X1),X1)
& v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)
& v1_funct_1(X2) )
=> ! [X4,X5,X6] :
( g3_lattices(X1,X2,X3) = g3_lattices(X4,X5,X6)
=> ( X3 = X6
& X2 = X5
& X1 = X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g3_lattices) ).
fof(abstractness_v3_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( v3_lattices(X1)
=> X1 = g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v3_lattices) ).
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/sandbox/benchmark/theBenchmark.p',fc1_lattice2) ).
fof(c_0_26,negated_conjecture,
~ ! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( v14_lattices(X1)
=> r1_filter_2(u1_struct_0(X1),k17_filter_2(X1),k18_filter_2(X1,k6_lattices(X1))) ) ),
inference(assume_negation,[status(cth)],[t32_filter_2]) ).
fof(c_0_27,negated_conjecture,
~ ! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( v14_lattices(X1)
=> r1_filter_2(u1_struct_0(X1),k17_filter_2(X1),k18_filter_2(X1,k6_lattices(X1))) ) ),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_28,plain,
! [X1] :
( ( l2_lattices(X1)
& ~ v3_struct_0(X1) )
=> m1_subset_1(k6_lattices(X1),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k6_lattices]) ).
fof(c_0_29,plain,
! [X48] :
( ( ~ l3_lattices(X48)
| l2_lattices(X48) )
& ( ~ l3_lattices(X48)
| l1_lattices(X48) ) ),
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_30,negated_conjecture,
( ~ r1_filter_2(u1_struct_0(esk1_0),k17_filter_2(esk1_0),k18_filter_2(esk1_0,k6_lattices(esk1_0)))
& v14_lattices(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_27])])])]) ).
fof(c_0_31,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_32,plain,
! [X45] :
( m1_subset_1(k6_lattices(X45),u1_struct_0(X45))
| ~ l2_lattices(X45)
| v3_struct_0(X45) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])]) ).
cnf(c_0_33,plain,
( ~ l3_lattices(X1)
| l2_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_34,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_35,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]) ).
fof(c_0_36,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> k17_filter_2(X1) = u1_struct_0(X1) ),
inference(fof_simplification,[status(thm)],[d8_filter_2]) ).
fof(c_0_37,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_38,plain,
! [X24,X25] :
( k5_filter_2(X24,X25) = X25
| ~ m1_subset_1(X25,u1_struct_0(X24))
| ~ l3_lattices(X24)
| ~ v10_lattices(X24)
| v3_struct_0(X24) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])]) ).
cnf(c_0_39,plain,
( ~ l2_lattices(X1)
| m1_subset_1(k6_lattices(X1),u1_struct_0(X1))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,negated_conjecture,
l2_lattices(esk1_0),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_41,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_42,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_43,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_44,plain,
! [X27,X28] :
( k18_filter_2(X27,X28) = a_2_0_filter_2(X27,X28)
| ~ m1_subset_1(X28,u1_struct_0(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_35])])])]) ).
fof(c_0_45,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( ( l3_lattices(X1)
& v13_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> k1_filter_0(X1) = k2_filter_0(X1,k5_lattices(X1)) ) ),
inference(fof_simplification,[status(thm)],[t20_filter_0]) ).
fof(c_0_46,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( v14_lattices(X1)
<=> v13_lattices(k1_lattice2(X1)) ) ),
inference(fof_simplification,[status(thm)],[t64_lattice2]) ).
fof(c_0_47,plain,
! [X1] :
( ( l3_lattices(X1)
& v14_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> k6_lattices(X1) = k5_lattices(k1_lattice2(X1)) ),
inference(fof_simplification,[status(thm)],[t79_lattice2]) ).
fof(c_0_48,plain,
! [X26] :
( k17_filter_2(X26) = u1_struct_0(X26)
| ~ l3_lattices(X26)
| ~ v10_lattices(X26)
| v3_struct_0(X26) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])]) ).
fof(c_0_49,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_50,plain,
! [X42,X43] :
( m1_subset_1(k5_filter_2(X42,X43),u1_struct_0(k1_lattice2(X42)))
| ~ m1_subset_1(X43,u1_struct_0(X42))
| ~ l3_lattices(X42)
| ~ v10_lattices(X42)
| v3_struct_0(X42) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])]) ).
cnf(c_0_51,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_38]) ).
cnf(c_0_52,negated_conjecture,
m1_subset_1(k6_lattices(esk1_0),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_53,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_54,plain,
! [X37] :
( ( ~ l3_lattices(X37)
| l3_lattices(k1_lattice2(X37)) )
& ( ~ l3_lattices(X37)
| v3_lattices(k1_lattice2(X37)) ) ),
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_55,plain,
! [X94] :
( ( ~ l3_lattices(X94)
| ~ v10_lattices(X94)
| v3_struct_0(X94)
| v10_lattices(k1_lattice2(X94)) )
& ( ~ l3_lattices(X94)
| ~ v10_lattices(X94)
| v3_struct_0(X94)
| v9_lattices(k1_lattice2(X94)) )
& ( ~ l3_lattices(X94)
| ~ v10_lattices(X94)
| v3_struct_0(X94)
| v8_lattices(k1_lattice2(X94)) )
& ( ~ l3_lattices(X94)
| ~ v10_lattices(X94)
| v3_struct_0(X94)
| v7_lattices(k1_lattice2(X94)) )
& ( ~ l3_lattices(X94)
| ~ v10_lattices(X94)
| v3_struct_0(X94)
| v6_lattices(k1_lattice2(X94)) )
& ( ~ l3_lattices(X94)
| ~ v10_lattices(X94)
| v3_struct_0(X94)
| v5_lattices(k1_lattice2(X94)) )
& ( ~ l3_lattices(X94)
| ~ v10_lattices(X94)
| v3_struct_0(X94)
| v4_lattices(k1_lattice2(X94)) )
& ( ~ l3_lattices(X94)
| ~ v10_lattices(X94)
| v3_struct_0(X94)
| v3_lattices(k1_lattice2(X94)) )
& ( ~ l3_lattices(X94)
| ~ v10_lattices(X94)
| v3_struct_0(X94)
| ~ v3_struct_0(k1_lattice2(X94)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])])]) ).
fof(c_0_56,plain,
! [X161,X162] :
( ( ~ l3_lattices(X161)
| ~ v10_lattices(X161)
| v3_struct_0(X161)
| ~ m1_subset_1(X162,u1_struct_0(X161))
| k18_filter_2(k1_lattice2(X161),k5_filter_2(X161,X162)) = k2_filter_2(X161,X162) )
& ( ~ l3_lattices(X161)
| ~ v10_lattices(X161)
| v3_struct_0(X161)
| ~ m1_subset_1(X162,u1_struct_0(X161))
| k18_filter_2(X161,X162) = k2_filter_2(k1_lattice2(X161),k5_filter_2(X161,X162)) ) ),
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_43])])])])]) ).
cnf(c_0_57,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_44]) ).
fof(c_0_58,plain,
! [X155] :
( k1_filter_0(X155) = k2_filter_0(X155,k5_lattices(X155))
| ~ l3_lattices(X155)
| ~ v13_lattices(X155)
| ~ v10_lattices(X155)
| v3_struct_0(X155)
| ~ l3_lattices(X155)
| ~ v10_lattices(X155)
| v3_struct_0(X155) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])]) ).
fof(c_0_59,plain,
! [X171] :
( ( ~ l3_lattices(X171)
| ~ v10_lattices(X171)
| v3_struct_0(X171)
| v14_lattices(X171)
| ~ v13_lattices(k1_lattice2(X171)) )
& ( ~ l3_lattices(X171)
| ~ v10_lattices(X171)
| v3_struct_0(X171)
| v13_lattices(k1_lattice2(X171))
| ~ v14_lattices(X171) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_46])])])]) ).
fof(c_0_60,plain,
! [X173] :
( k6_lattices(X173) = k5_lattices(k1_lattice2(X173))
| ~ l3_lattices(X173)
| ~ v14_lattices(X173)
| ~ v10_lattices(X173)
| v3_struct_0(X173) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])])]) ).
fof(c_0_61,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> m2_filter_2(k17_filter_2(X1),X1) ),
inference(fof_simplification,[status(thm)],[dt_k17_filter_2]) ).
cnf(c_0_62,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| k17_filter_2(X1) = u1_struct_0(X1)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
fof(c_0_63,plain,
! [X130,X131] :
( k2_filter_2(X130,X131) = k2_filter_0(X130,X131)
| ~ m1_subset_1(X131,u1_struct_0(X130))
| ~ l3_lattices(X130)
| ~ v10_lattices(X130)
| v3_struct_0(X130) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])]) ).
cnf(c_0_64,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_50]) ).
cnf(c_0_65,negated_conjecture,
k5_filter_2(esk1_0,k6_lattices(esk1_0)) = k6_lattices(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_34]),c_0_53])]),c_0_41]) ).
cnf(c_0_66,plain,
( ~ l3_lattices(X1)
| l3_lattices(k1_lattice2(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_67,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| v10_lattices(k1_lattice2(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_68,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_56]) ).
cnf(c_0_69,negated_conjecture,
k18_filter_2(esk1_0,k6_lattices(esk1_0)) = a_2_0_filter_2(esk1_0,k6_lattices(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_52]),c_0_34]),c_0_53])]),c_0_41]) ).
cnf(c_0_70,plain,
( ~ l3_lattices(X1)
| ~ v13_lattices(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| k1_filter_0(X1) = k2_filter_0(X1,k5_lattices(X1))
| v3_struct_0(X1)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_71,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ v14_lattices(X1)
| v3_struct_0(X1)
| v13_lattices(k1_lattice2(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_72,negated_conjecture,
v14_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_73,plain,
( ~ l3_lattices(X1)
| ~ v14_lattices(X1)
| ~ v10_lattices(X1)
| k6_lattices(X1) = k5_lattices(k1_lattice2(X1))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
fof(c_0_74,plain,
! [X61] :
( ( ~ l2_lattices(X61)
| m2_relset_1(u2_lattices(X61),k2_zfmisc_1(u1_struct_0(X61),u1_struct_0(X61)),u1_struct_0(X61)) )
& ( ~ l2_lattices(X61)
| v1_funct_2(u2_lattices(X61),k2_zfmisc_1(u1_struct_0(X61),u1_struct_0(X61)),u1_struct_0(X61)) )
& ( ~ l2_lattices(X61)
| v1_funct_1(u2_lattices(X61)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u2_lattices])])])]) ).
fof(c_0_75,plain,
! [X60] :
( ( ~ l1_lattices(X60)
| m2_relset_1(u1_lattices(X60),k2_zfmisc_1(u1_struct_0(X60),u1_struct_0(X60)),u1_struct_0(X60)) )
& ( ~ l1_lattices(X60)
| v1_funct_2(u1_lattices(X60),k2_zfmisc_1(u1_struct_0(X60),u1_struct_0(X60)),u1_struct_0(X60)) )
& ( ~ l1_lattices(X60)
| v1_funct_1(u1_lattices(X60)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_lattices])])])]) ).
cnf(c_0_76,plain,
( ~ l3_lattices(X1)
| l1_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_77,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_78,plain,
! [X32] :
( m2_filter_2(k17_filter_2(X32),X32)
| ~ l3_lattices(X32)
| ~ v10_lattices(X32)
| v3_struct_0(X32) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_61])])]) ).
cnf(c_0_79,negated_conjecture,
~ r1_filter_2(u1_struct_0(esk1_0),k17_filter_2(esk1_0),k18_filter_2(esk1_0,k6_lattices(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_80,negated_conjecture,
k17_filter_2(esk1_0) = u1_struct_0(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_34]),c_0_53])]),c_0_41]) ).
cnf(c_0_81,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_63]) ).
cnf(c_0_82,negated_conjecture,
m1_subset_1(k6_lattices(esk1_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_64,c_0_52]),c_0_34]),c_0_53])]),c_0_41]),c_0_65]) ).
cnf(c_0_83,negated_conjecture,
l3_lattices(k1_lattice2(esk1_0)),
inference(spm,[status(thm)],[c_0_66,c_0_34]) ).
cnf(c_0_84,negated_conjecture,
v10_lattices(k1_lattice2(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_34]),c_0_53])]),c_0_41]) ).
cnf(c_0_85,negated_conjecture,
k2_filter_2(k1_lattice2(esk1_0),k6_lattices(esk1_0)) = a_2_0_filter_2(esk1_0,k6_lattices(esk1_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_68,c_0_52]),c_0_34]),c_0_53])]),c_0_41]),c_0_65]),c_0_69]) ).
cnf(c_0_86,plain,
( ~ v13_lattices(X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| k1_filter_0(X1) = k2_filter_0(X1,k5_lattices(X1)) ),
inference(cn,[status(thm)],[c_0_70]) ).
cnf(c_0_87,negated_conjecture,
v13_lattices(k1_lattice2(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_34]),c_0_53])]),c_0_41]) ).
cnf(c_0_88,negated_conjecture,
k5_lattices(k1_lattice2(esk1_0)) = k6_lattices(esk1_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_72]),c_0_34]),c_0_53])]),c_0_41]) ).
fof(c_0_89,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> k1_filter_0(X1) = u1_struct_0(X1) ),
inference(fof_simplification,[status(thm)],[d2_filter_0]) ).
fof(c_0_90,plain,
! [X21] :
( k1_lattice2(X21) = g3_lattices(u1_struct_0(X21),u1_lattices(X21),u2_lattices(X21))
| ~ l3_lattices(X21) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_lattice2])])]) ).
fof(c_0_91,plain,
! [X134,X135,X136] :
( ( m2_relset_1(X136,X134,X135)
| ~ m1_relset_1(X136,X134,X135) )
& ( m1_relset_1(X136,X134,X135)
| ~ m2_relset_1(X136,X134,X135) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])])]) ).
cnf(c_0_92,plain,
( ~ l2_lattices(X1)
| m2_relset_1(u2_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_93,plain,
( ~ l1_lattices(X1)
| m2_relset_1(u1_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_94,negated_conjecture,
l1_lattices(esk1_0),
inference(spm,[status(thm)],[c_0_76,c_0_34]) ).
fof(c_0_95,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_96,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_97,plain,
! [X53,X54] :
( ( ~ l3_lattices(X53)
| ~ v10_lattices(X53)
| v3_struct_0(X53)
| ~ m2_filter_2(X54,X53)
| m2_lattice4(X54,X53) )
& ( ~ l3_lattices(X53)
| ~ v10_lattices(X53)
| v3_struct_0(X53)
| ~ m2_filter_2(X54,X53)
| ~ v1_xboole_0(X54) ) ),
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_77])])])])]) ).
cnf(c_0_98,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| m2_filter_2(k17_filter_2(X1),X1)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_99,negated_conjecture,
~ r1_filter_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),k18_filter_2(esk1_0,k6_lattices(esk1_0))),
inference(rw,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_100,negated_conjecture,
( v3_struct_0(k1_lattice2(esk1_0))
| k2_filter_0(k1_lattice2(esk1_0),k6_lattices(esk1_0)) = a_2_0_filter_2(esk1_0,k6_lattices(esk1_0)) ),
inference(rw,[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_83]),c_0_84])]),c_0_85]) ).
cnf(c_0_101,negated_conjecture,
( v3_struct_0(k1_lattice2(esk1_0))
| k2_filter_0(k1_lattice2(esk1_0),k6_lattices(esk1_0)) = k1_filter_0(k1_lattice2(esk1_0)) ),
inference(rw,[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_83]),c_0_84])]),c_0_88]) ).
fof(c_0_102,plain,
! [X20] :
( k1_filter_0(X20) = u1_struct_0(X20)
| ~ l3_lattices(X20)
| ~ v10_lattices(X20)
| v3_struct_0(X20) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_89])])]) ).
fof(c_0_103,plain,
! [X105,X106,X107,X108,X109,X110] :
( ( ~ m1_relset_1(X107,k2_zfmisc_1(X105,X105),X105)
| ~ v1_funct_2(X107,k2_zfmisc_1(X105,X105),X105)
| ~ v1_funct_1(X107)
| ~ m1_relset_1(X106,k2_zfmisc_1(X105,X105),X105)
| ~ v1_funct_2(X106,k2_zfmisc_1(X105,X105),X105)
| ~ v1_funct_1(X106)
| g3_lattices(X105,X106,X107) != g3_lattices(X108,X109,X110)
| X107 = X110 )
& ( ~ m1_relset_1(X107,k2_zfmisc_1(X105,X105),X105)
| ~ v1_funct_2(X107,k2_zfmisc_1(X105,X105),X105)
| ~ v1_funct_1(X107)
| ~ m1_relset_1(X106,k2_zfmisc_1(X105,X105),X105)
| ~ v1_funct_2(X106,k2_zfmisc_1(X105,X105),X105)
| ~ v1_funct_1(X106)
| g3_lattices(X105,X106,X107) != g3_lattices(X108,X109,X110)
| X106 = X109 )
& ( ~ m1_relset_1(X107,k2_zfmisc_1(X105,X105),X105)
| ~ v1_funct_2(X107,k2_zfmisc_1(X105,X105),X105)
| ~ v1_funct_1(X107)
| ~ m1_relset_1(X106,k2_zfmisc_1(X105,X105),X105)
| ~ v1_funct_2(X106,k2_zfmisc_1(X105,X105),X105)
| ~ v1_funct_1(X106)
| g3_lattices(X105,X106,X107) != g3_lattices(X108,X109,X110)
| X105 = X108 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[free_g3_lattices])])])])]) ).
cnf(c_0_104,plain,
( ~ l3_lattices(X1)
| k1_lattice2(X1) = g3_lattices(u1_struct_0(X1),u1_lattices(X1),u2_lattices(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_105,plain,
( ~ m2_relset_1(X1,X2,X3)
| m1_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_106,negated_conjecture,
m2_relset_1(u2_lattices(esk1_0),k2_zfmisc_1(u1_struct_0(esk1_0),u1_struct_0(esk1_0)),u1_struct_0(esk1_0)),
inference(spm,[status(thm)],[c_0_92,c_0_40]) ).
cnf(c_0_107,negated_conjecture,
m2_relset_1(u1_lattices(esk1_0),k2_zfmisc_1(u1_struct_0(esk1_0),u1_struct_0(esk1_0)),u1_struct_0(esk1_0)),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_108,plain,
( ~ l2_lattices(X1)
| v1_funct_2(u2_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_109,plain,
( ~ l1_lattices(X1)
| v1_funct_2(u1_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_110,plain,
( ~ l2_lattices(X1)
| v1_funct_1(u2_lattices(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_111,plain,
( ~ l1_lattices(X1)
| v1_funct_1(u1_lattices(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
fof(c_0_112,plain,
! [X8] :
( X8 = g3_lattices(u1_struct_0(X8),u2_lattices(X8),u1_lattices(X8))
| ~ v3_lattices(X8)
| ~ l3_lattices(X8) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[abstractness_v3_lattices])])]) ).
cnf(c_0_113,plain,
( ~ l3_lattices(X1)
| v3_lattices(k1_lattice2(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
fof(c_0_114,plain,
! [X137,X138,X139] :
( ( ~ m1_subset_1(X139,k1_zfmisc_1(X137))
| ~ m1_subset_1(X138,k1_zfmisc_1(X137))
| v1_xboole_0(X137)
| r1_filter_2(X137,X138,X139)
| X138 != X139 )
& ( ~ m1_subset_1(X139,k1_zfmisc_1(X137))
| ~ m1_subset_1(X138,k1_zfmisc_1(X137))
| v1_xboole_0(X137)
| X138 = X139
| ~ r1_filter_2(X137,X138,X139) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_95])])])]) ).
fof(c_0_115,plain,
! [X55,X56] :
( m1_subset_1(X56,k1_zfmisc_1(u1_struct_0(X55)))
| ~ m2_lattice4(X56,X55)
| ~ l3_lattices(X55)
| ~ v10_lattices(X55)
| v3_struct_0(X55) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_96])])])]) ).
cnf(c_0_116,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_97]) ).
cnf(c_0_117,negated_conjecture,
m2_filter_2(u1_struct_0(esk1_0),esk1_0),
inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_34]),c_0_53])]),c_0_41]),c_0_80]) ).
cnf(c_0_118,negated_conjecture,
~ r1_filter_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),a_2_0_filter_2(esk1_0,k6_lattices(esk1_0))),
inference(rw,[status(thm)],[c_0_99,c_0_69]) ).
cnf(c_0_119,negated_conjecture,
( v3_struct_0(k1_lattice2(esk1_0))
| a_2_0_filter_2(esk1_0,k6_lattices(esk1_0)) = k1_filter_0(k1_lattice2(esk1_0)) ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_120,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| k1_filter_0(X1) = u1_struct_0(X1)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_121,plain,
( ~ m1_relset_1(X4,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(X4,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_1(X4)
| ~ m1_relset_1(X3,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(X3,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_1(X3)
| g3_lattices(X1,X3,X4) != g3_lattices(X2,X5,X6)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_122,negated_conjecture,
g3_lattices(u1_struct_0(esk1_0),u1_lattices(esk1_0),u2_lattices(esk1_0)) = k1_lattice2(esk1_0),
inference(spm,[status(thm)],[c_0_104,c_0_34]) ).
cnf(c_0_123,negated_conjecture,
m1_relset_1(u2_lattices(esk1_0),k2_zfmisc_1(u1_struct_0(esk1_0),u1_struct_0(esk1_0)),u1_struct_0(esk1_0)),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_124,negated_conjecture,
m1_relset_1(u1_lattices(esk1_0),k2_zfmisc_1(u1_struct_0(esk1_0),u1_struct_0(esk1_0)),u1_struct_0(esk1_0)),
inference(spm,[status(thm)],[c_0_105,c_0_107]) ).
cnf(c_0_125,negated_conjecture,
v1_funct_2(u2_lattices(esk1_0),k2_zfmisc_1(u1_struct_0(esk1_0),u1_struct_0(esk1_0)),u1_struct_0(esk1_0)),
inference(spm,[status(thm)],[c_0_108,c_0_40]) ).
cnf(c_0_126,negated_conjecture,
v1_funct_2(u1_lattices(esk1_0),k2_zfmisc_1(u1_struct_0(esk1_0),u1_struct_0(esk1_0)),u1_struct_0(esk1_0)),
inference(spm,[status(thm)],[c_0_109,c_0_94]) ).
cnf(c_0_127,negated_conjecture,
v1_funct_1(u2_lattices(esk1_0)),
inference(spm,[status(thm)],[c_0_110,c_0_40]) ).
cnf(c_0_128,negated_conjecture,
v1_funct_1(u1_lattices(esk1_0)),
inference(spm,[status(thm)],[c_0_111,c_0_94]) ).
cnf(c_0_129,plain,
( ~ v3_lattices(X1)
| ~ l3_lattices(X1)
| X1 = g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_130,negated_conjecture,
v3_lattices(k1_lattice2(esk1_0)),
inference(spm,[status(thm)],[c_0_113,c_0_34]) ).
cnf(c_0_131,plain,
( ~ m1_subset_1(X2,k1_zfmisc_1(X3))
| ~ m1_subset_1(X1,k1_zfmisc_1(X3))
| X1 != X2
| v1_xboole_0(X3)
| r1_filter_2(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_132,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_115]) ).
cnf(c_0_133,negated_conjecture,
m2_lattice4(u1_struct_0(esk1_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_116,c_0_117]),c_0_34]),c_0_53])]),c_0_41]) ).
cnf(c_0_134,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_97]) ).
fof(c_0_135,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_136,negated_conjecture,
( ~ r1_filter_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),k1_filter_0(k1_lattice2(esk1_0)))
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_137,negated_conjecture,
( v3_struct_0(k1_lattice2(esk1_0))
| k1_filter_0(k1_lattice2(esk1_0)) = u1_struct_0(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_83]),c_0_84])]) ).
cnf(c_0_138,negated_conjecture,
( g3_lattices(X1,X2,X3) != k1_lattice2(esk1_0)
| u1_struct_0(esk1_0) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_123]),c_0_124]),c_0_125]),c_0_126]),c_0_127]),c_0_128])]) ).
cnf(c_0_139,negated_conjecture,
g3_lattices(u1_struct_0(k1_lattice2(esk1_0)),u2_lattices(k1_lattice2(esk1_0)),u1_lattices(k1_lattice2(esk1_0))) = k1_lattice2(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_83])]) ).
cnf(c_0_140,plain,
( ~ m1_subset_1(X2,k1_zfmisc_1(X1))
| r1_filter_2(X1,X2,X2)
| v1_xboole_0(X1) ),
inference(er,[status(thm)],[c_0_131]) ).
cnf(c_0_141,negated_conjecture,
m1_subset_1(u1_struct_0(esk1_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_132,c_0_133]),c_0_34]),c_0_53])]),c_0_41]) ).
cnf(c_0_142,negated_conjecture,
~ v1_xboole_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_134,c_0_117]),c_0_34]),c_0_53])]),c_0_41]) ).
fof(c_0_143,plain,
! [X82] :
( ( ~ l3_lattices(X82)
| v3_struct_0(X82)
| v3_lattices(k1_lattice2(X82)) )
& ( ~ l3_lattices(X82)
| v3_struct_0(X82)
| ~ v3_struct_0(k1_lattice2(X82)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_135])])])]) ).
cnf(c_0_144,negated_conjecture,
( ~ r1_filter_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(k1_lattice2(esk1_0)))
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_145,negated_conjecture,
u1_struct_0(k1_lattice2(esk1_0)) = u1_struct_0(esk1_0),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_146,negated_conjecture,
r1_filter_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_142]) ).
cnf(c_0_147,plain,
( ~ l3_lattices(X1)
| ~ v3_struct_0(k1_lattice2(X1))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_143]) ).
cnf(c_0_148,negated_conjecture,
v3_struct_0(k1_lattice2(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_144,c_0_145]),c_0_146])]) ).
cnf(c_0_149,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_34])]),c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LAT306+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.49 % Computer : n017.cluster.edu
% 0.21/0.49 % Model : x86_64 x86_64
% 0.21/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.49 % Memory : 8046.5625MB
% 0.21/0.49 % OS : Linux 6.8.0-71-generic
% 0.21/0.49 % CPULimit : 300
% 0.21/0.49 % WCLimit : 300
% 0.21/0.49 % DateTime : Sun Sep 20 23:27:11 UTC 2026
% 0.21/0.50 % CPUTime :
% 0.21/0.50 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.58 Running first-order theorem proving
% 0.25/0.58 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
% 5.97/1.43 % Version: 3.5.1
% 5.97/1.43 % Preprocessing class: FSLSSMSSSSSNFFN.
% 5.97/1.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.97/1.43 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 5.97/1.43 % Starting new_bool_3 with 300s (1) cores
% 5.97/1.43 % Starting new_bool_1 with 300s (1) cores
% 5.97/1.43 % Starting sh5l with 300s (1) cores
% 5.97/1.43 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 871174 completed with status 0
% 5.97/1.43 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 5.97/1.43 % Preprocessing class: FSLSSMSSSSSNFFN.
% 5.97/1.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.97/1.43 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 5.97/1.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.97/1.43 % No SInE strategy applied
% 5.97/1.43 % Search class: FGHSM-FSLM31-SFFFFFNN
% 5.97/1.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 5.97/1.43 % Starting SubtermCWHack with 136s (1) cores
% 5.97/1.43 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 5.97/1.43 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_S0e with 136s (1) cores
% 5.97/1.43 % Starting G-E--_208_C18_F1_AE_CS_SP_PI_S0a with 136s (1) cores
% 5.97/1.43 % Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 5.97/1.43 % G-E--_207_C18_F1_AE_CS_SP_PI_S0e with pid 871181 completed with status 0
% 5.97/1.43 % Result found by G-E--_207_C18_F1_AE_CS_SP_PI_S0e
% 5.97/1.43 % Preprocessing class: FSLSSMSSSSSNFFN.
% 5.97/1.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.97/1.43 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 5.97/1.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.97/1.43 % No SInE strategy applied
% 5.97/1.43 % Search class: FGHSM-FSLM31-SFFFFFNN
% 5.97/1.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 5.97/1.43 % Starting SubtermCWHack with 136s (1) cores
% 5.97/1.43 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 5.97/1.43 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_S0e with 136s (1) cores
% 5.97/1.43 % Preprocessing time : 0.006 s
% 5.97/1.43
% 5.97/1.43 % Proof found!
% 5.97/1.43 % SZS status Theorem
% 5.97/1.43 % SZS output start CNFRefutation
% See solution above
% 5.97/1.43 % Parsed axioms : 106
% 5.97/1.43 % Removed by relevancy pruning/SinE : 0
% 5.97/1.43 % Initial clauses : 208
% 5.97/1.43 % Removed in clause preprocessing : 13
% 5.97/1.43 % Initial clauses in saturation : 195
% 5.97/1.43 % Processed clauses : 3002
% 5.97/1.43 % ...of these trivial : 113
% 5.97/1.43 % ...subsumed : 534
% 5.97/1.43 % ...remaining for further processing : 2355
% 5.97/1.43 % Other redundant clauses eliminated : 3
% 5.97/1.43 % Clauses deleted for lack of memory : 0
% 5.97/1.43 % Backward-subsumed : 6
% 5.97/1.43 % Backward-rewritten : 337
% 5.97/1.43 % Generated clauses : 7766
% 5.97/1.43 % ...of the previous two non-redundant : 7530
% 5.97/1.43 % ...aggressively subsumed : 0
% 5.97/1.43 % Contextual simplify-reflections : 1
% 5.97/1.43 % Paramodulations : 7758
% 5.97/1.43 % Factorizations : 2
% 5.97/1.43 % NegExts : 0
% 5.97/1.43 % Equation resolutions : 6
% 5.97/1.43 % Disequality decompositions : 0
% 5.97/1.43 % Total rewrite steps : 8243
% 5.97/1.43 % ...of those cached : 7714
% 5.97/1.43 % Propositional unsat checks : 0
% 5.97/1.43 % Propositional check models : 0
% 5.97/1.43 % Propositional check unsatisfiable : 0
% 5.97/1.43 % Propositional clauses : 0
% 5.97/1.43 % Propositional clauses after purity: 0
% 5.97/1.43 % Propositional unsat core size : 0
% 5.97/1.43 % Propositional preprocessing time : 0.000
% 5.97/1.43 % Propositional encoding time : 0.000
% 5.97/1.43 % Propositional solver time : 0.000
% 5.97/1.43 % Success case prop preproc time : 0.000
% 5.97/1.43 % Success case prop encoding time : 0.000
% 5.97/1.43 % Success case prop solver time : 0.000
% 5.97/1.43 % Current number of processed clauses : 2009
% 5.97/1.43 % Positive orientable unit clauses : 952
% 5.97/1.43 % Positive unorientable unit clauses: 0
% 5.97/1.43 % Negative unit clauses : 167
% 5.97/1.43 % Non-unit-clauses : 890
% 5.97/1.43 % Current number of unprocessed clauses: 4652
% 5.97/1.43 % ...number of literals in the above : 14243
% 5.97/1.43 % Current number of archived formulas : 0
% 5.97/1.43 % Current number of archived clauses : 343
% 5.97/1.43 % Clause-clause subsumption calls (NU) : 82871
% 5.97/1.43 % Rec. Clause-clause subsumption calls : 56115
% 5.97/1.43 % Non-unit clause-clause subsumptions : 232
% 5.97/1.43 % Unit Clause-clause subsumption calls : 20430
% 5.97/1.43 % Rewrite failures with RHS unbound : 0
% 5.97/1.43 % BW rewrite match attempts : 2305
% 5.97/1.43 % BW rewrite match successes : 58
% 5.97/1.43 % Condensation attempts : 0
% 5.97/1.43 % Condensation successes : 0
% 5.97/1.43 % Termbank termtop insertions : 199051
% 5.97/1.43 % Search garbage collected termcells : 2325
% 5.97/1.43
% 5.97/1.43 % -------------------------------------------------
% 5.97/1.43 % User time : 0.543 s
% 5.97/1.43 % System time : 0.033 s
% 5.97/1.43 % Total time : 0.576 s
% 5.97/1.43 % Maximum resident set size: 4000 pages
% 5.97/1.43
% 5.97/1.43 % -------------------------------------------------
% 5.97/1.43 % User time : 3.292 s
% 5.97/1.43 % System time : 0.140 s
% 5.97/1.43 % Total time : 3.433 s
% 5.97/1.43 % Maximum resident set size: 4864 pages
% 5.97/1.43 % E exiting
%------------------------------------------------------------------------------