%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT302+1 : TPTP v9.2.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:38:00 PM UTC 2026
% Result : Theorem 1.39s 1.76s
% Output : CNFRefutation 1.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 21
% Syntax : Number of formulae : 122 ( 24 unt; 0 def)
% Number of atoms : 495 ( 12 equ)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 578 ( 205 ~; 209 |; 113 &)
% ( 6 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 1 con; 0-2 aty)
% Number of variables : 127 ( 3 sgn 81 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(existence_m2_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ? [X2] : m2_filter_2(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_filter_2) ).
fof(t26_filter_2,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( v13_lattices(X1)
=> m2_filter_2(k6_domain_1(u1_struct_0(X1),k5_lattices(X1)),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_filter_2) ).
fof(t21_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
<=> m1_filter_2(X2,k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_filter_2) ).
fof(fc6_lattice2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( ~ v3_struct_0(k1_lattice2(X1))
& v3_lattices(k1_lattice2(X1))
& v4_lattices(k1_lattice2(X1))
& v5_lattices(k1_lattice2(X1))
& v6_lattices(k1_lattice2(X1))
& v7_lattices(k1_lattice2(X1))
& v8_lattices(k1_lattice2(X1))
& v9_lattices(k1_lattice2(X1))
& v10_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_lattice2) ).
fof(redefinition_m1_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_2(X2,X1)
<=> m1_filter_0(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m1_filter_2) ).
fof(existence_m1_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ? [X2] : m1_filter_2(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_filter_2) ).
fof(t13_filter_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v14_lattices(X1)
& l3_lattices(X1) )
=> m1_filter_0(k6_domain_1(u1_struct_0(X1),k6_lattices(X1)),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_filter_0) ).
fof(t63_lattice2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( v13_lattices(X1)
<=> v14_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_lattice2) ).
fof(t78_lattice2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v13_lattices(X1)
& l3_lattices(X1) )
=> k5_lattices(X1) = k6_lattices(k1_lattice2(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_lattice2) ).
fof(dt_m1_filter_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_0(X2,X1)
=> ( ~ v1_xboole_0(X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_filter_0) ).
fof(dt_k1_lattice2,axiom,
! [X1] :
( l3_lattices(X1)
=> ( v3_lattices(k1_lattice2(X1))
& l3_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattice2) ).
fof(dt_k5_lattices,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_lattices(X1) )
=> m1_subset_1(k5_lattices(X1),u1_struct_0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_lattices) ).
fof(dt_k6_lattices,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l2_lattices(X1) )
=> m1_subset_1(k6_lattices(X1),u1_struct_0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_lattices) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( l1_lattices(X1)
& l2_lattices(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(dt_m1_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_2(X2,X1)
=> ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_filter_2) ).
fof(dt_m2_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_filter_2) ).
fof(redefinition_k6_domain_1,axiom,
! [X1,X2] :
( ( ~ v1_xboole_0(X1)
& m1_subset_1(X2,X1) )
=> k6_domain_1(X1,X2) = k1_tarski(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_domain_1) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( r2_hidden(X1,X2)
& m1_subset_1(X2,k1_zfmisc_1(X3))
& v1_xboole_0(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(t2_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,X2)
=> ( v1_xboole_0(X2)
| r2_hidden(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : m1_subset_1(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(fc1_lattice2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l3_lattices(X1) )
=> ( ~ v3_struct_0(k1_lattice2(X1))
& v3_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_lattice2) ).
fof(c_0_21,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ? [X2] : m2_filter_2(X2,X1) ),
inference(fof_simplification,[status(thm)],[existence_m2_filter_2]) ).
fof(c_0_22,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( v13_lattices(X1)
=> m2_filter_2(k6_domain_1(u1_struct_0(X1),k5_lattices(X1)),X1) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t26_filter_2])]) ).
fof(c_0_23,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
<=> m1_filter_2(X2,k1_lattice2(X1)) ) ),
inference(fof_simplification,[status(thm)],[t21_filter_2]) ).
fof(c_0_24,plain,
! [X190] :
( v3_struct_0(X190)
| ~ v10_lattices(X190)
| ~ l3_lattices(X190)
| m2_filter_2(esk10_1(X190),X190) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
fof(c_0_25,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v10_lattices(esk1_0)
& l3_lattices(esk1_0)
& v13_lattices(esk1_0)
& ~ m2_filter_2(k6_domain_1(u1_struct_0(esk1_0),k5_lattices(esk1_0)),esk1_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])]) ).
fof(c_0_26,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( ~ v3_struct_0(k1_lattice2(X1))
& v3_lattices(k1_lattice2(X1))
& v4_lattices(k1_lattice2(X1))
& v5_lattices(k1_lattice2(X1))
& v6_lattices(k1_lattice2(X1))
& v7_lattices(k1_lattice2(X1))
& v8_lattices(k1_lattice2(X1))
& v9_lattices(k1_lattice2(X1))
& v10_lattices(k1_lattice2(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc6_lattice2]) ).
fof(c_0_27,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_2(X2,X1)
<=> m1_filter_0(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[redefinition_m1_filter_2]) ).
fof(c_0_28,plain,
! [X249,X250] :
( ( ~ m2_filter_2(X250,X249)
| m1_filter_2(X250,k1_lattice2(X249))
| v3_struct_0(X249)
| ~ v10_lattices(X249)
| ~ l3_lattices(X249) )
& ( ~ m1_filter_2(X250,k1_lattice2(X249))
| m2_filter_2(X250,X249)
| v3_struct_0(X249)
| ~ v10_lattices(X249)
| ~ l3_lattices(X249) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])]) ).
cnf(c_0_29,plain,
( v3_struct_0(X1)
| m2_filter_2(esk10_1(X1),X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_33,plain,
! [X211] :
( ( ~ v3_struct_0(k1_lattice2(X211))
| v3_struct_0(X211)
| ~ v10_lattices(X211)
| ~ l3_lattices(X211) )
& ( v3_lattices(k1_lattice2(X211))
| v3_struct_0(X211)
| ~ v10_lattices(X211)
| ~ l3_lattices(X211) )
& ( v4_lattices(k1_lattice2(X211))
| v3_struct_0(X211)
| ~ v10_lattices(X211)
| ~ l3_lattices(X211) )
& ( v5_lattices(k1_lattice2(X211))
| v3_struct_0(X211)
| ~ v10_lattices(X211)
| ~ l3_lattices(X211) )
& ( v6_lattices(k1_lattice2(X211))
| v3_struct_0(X211)
| ~ v10_lattices(X211)
| ~ l3_lattices(X211) )
& ( v7_lattices(k1_lattice2(X211))
| v3_struct_0(X211)
| ~ v10_lattices(X211)
| ~ l3_lattices(X211) )
& ( v8_lattices(k1_lattice2(X211))
| v3_struct_0(X211)
| ~ v10_lattices(X211)
| ~ l3_lattices(X211) )
& ( v9_lattices(k1_lattice2(X211))
| v3_struct_0(X211)
| ~ v10_lattices(X211)
| ~ l3_lattices(X211) )
& ( v10_lattices(k1_lattice2(X211))
| v3_struct_0(X211)
| ~ v10_lattices(X211)
| ~ l3_lattices(X211) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])]) ).
fof(c_0_34,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ? [X2] : m1_filter_2(X2,X1) ),
inference(fof_simplification,[status(thm)],[existence_m1_filter_2]) ).
fof(c_0_35,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v14_lattices(X1)
& l3_lattices(X1) )
=> m1_filter_0(k6_domain_1(u1_struct_0(X1),k6_lattices(X1)),X1) ) ),
inference(fof_simplification,[status(thm)],[t13_filter_0]) ).
fof(c_0_36,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( v13_lattices(X1)
<=> v14_lattices(k1_lattice2(X1)) ) ),
inference(fof_simplification,[status(thm)],[t63_lattice2]) ).
fof(c_0_37,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v13_lattices(X1)
& l3_lattices(X1) )
=> k5_lattices(X1) = k6_lattices(k1_lattice2(X1)) ),
inference(fof_simplification,[status(thm)],[t78_lattice2]) ).
fof(c_0_38,plain,
! [X240,X241] :
( ( ~ m1_filter_2(X241,X240)
| m1_filter_0(X241,X240)
| v3_struct_0(X240)
| ~ v10_lattices(X240)
| ~ l3_lattices(X240) )
& ( ~ m1_filter_0(X241,X240)
| m1_filter_2(X241,X240)
| v3_struct_0(X240)
| ~ v10_lattices(X240)
| ~ l3_lattices(X240) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])])]) ).
cnf(c_0_39,plain,
( m1_filter_2(X1,k1_lattice2(X2))
| v3_struct_0(X2)
| ~ m2_filter_2(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_40,negated_conjecture,
m2_filter_2(esk10_1(esk1_0),esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]),c_0_32]) ).
cnf(c_0_41,plain,
( v10_lattices(k1_lattice2(X1))
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_42,plain,
! [X183] :
( v3_struct_0(X183)
| ~ v10_lattices(X183)
| ~ l3_lattices(X183)
| m1_filter_2(esk7_1(X183),X183) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])]) ).
fof(c_0_43,plain,
! [X246] :
( v3_struct_0(X246)
| ~ v10_lattices(X246)
| ~ l3_lattices(X246)
| v3_struct_0(X246)
| ~ v10_lattices(X246)
| ~ v14_lattices(X246)
| ~ l3_lattices(X246)
| m1_filter_0(k6_domain_1(u1_struct_0(X246),k6_lattices(X246)),X246) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])]) ).
fof(c_0_44,plain,
! [X261] :
( ( ~ v13_lattices(X261)
| v14_lattices(k1_lattice2(X261))
| v3_struct_0(X261)
| ~ v10_lattices(X261)
| ~ l3_lattices(X261) )
& ( ~ v14_lattices(k1_lattice2(X261))
| v13_lattices(X261)
| v3_struct_0(X261)
| ~ v10_lattices(X261)
| ~ l3_lattices(X261) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])]) ).
fof(c_0_45,plain,
! [X263] :
( v3_struct_0(X263)
| ~ v10_lattices(X263)
| ~ v13_lattices(X263)
| ~ l3_lattices(X263)
| k5_lattices(X263) = k6_lattices(k1_lattice2(X263)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])]) ).
fof(c_0_46,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_0(X2,X1)
=> ( ~ v1_xboole_0(X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ) ) ),
inference(fof_simplification,[status(thm)],[dt_m1_filter_0]) ).
cnf(c_0_47,plain,
( m1_filter_0(X1,X2)
| v3_struct_0(X2)
| ~ m1_filter_2(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_48,negated_conjecture,
m1_filter_2(esk10_1(esk1_0),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_39,c_0_40]),c_0_30]),c_0_31])]),c_0_32]) ).
cnf(c_0_49,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_41,c_0_30]),c_0_31])]),c_0_32]) ).
fof(c_0_50,plain,
! [X156] :
( ( v3_lattices(k1_lattice2(X156))
| ~ l3_lattices(X156) )
& ( l3_lattices(k1_lattice2(X156))
| ~ l3_lattices(X156) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_lattice2])])]) ).
fof(c_0_51,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_lattices(X1) )
=> m1_subset_1(k5_lattices(X1),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k5_lattices]) ).
cnf(c_0_52,plain,
( v3_struct_0(X1)
| m1_filter_2(esk7_1(X1),X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_53,plain,
( v3_struct_0(X1)
| v3_struct_0(X1)
| m1_filter_0(k6_domain_1(u1_struct_0(X1),k6_lattices(X1)),X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ v14_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_54,plain,
( v14_lattices(k1_lattice2(X1))
| v3_struct_0(X1)
| ~ v13_lattices(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_55,negated_conjecture,
v13_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_56,plain,
( v3_struct_0(X1)
| k5_lattices(X1) = k6_lattices(k1_lattice2(X1))
| ~ v10_lattices(X1)
| ~ v13_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
fof(c_0_57,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l2_lattices(X1) )
=> m1_subset_1(k6_lattices(X1),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k6_lattices]) ).
fof(c_0_58,plain,
! [X164,X165] :
( ( ~ v1_xboole_0(X165)
| ~ m1_filter_0(X165,X164)
| v3_struct_0(X164)
| ~ v10_lattices(X164)
| ~ l3_lattices(X164) )
& ( m1_subset_1(X165,k1_zfmisc_1(u1_struct_0(X164)))
| ~ m1_filter_0(X165,X164)
| v3_struct_0(X164)
| ~ v10_lattices(X164)
| ~ l3_lattices(X164) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_46])])])]) ).
cnf(c_0_59,negated_conjecture,
( m1_filter_0(esk10_1(esk1_0),k1_lattice2(esk1_0))
| v3_struct_0(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49])]) ).
cnf(c_0_60,plain,
( l3_lattices(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
fof(c_0_61,plain,
! [X157] :
( v3_struct_0(X157)
| ~ l1_lattices(X157)
| m1_subset_1(k5_lattices(X157),u1_struct_0(X157)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_51])]) ).
fof(c_0_62,plain,
! [X163] :
( ( l1_lattices(X163)
| ~ l3_lattices(X163) )
& ( l2_lattices(X163)
| ~ l3_lattices(X163) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
cnf(c_0_63,negated_conjecture,
m1_filter_2(esk7_1(esk1_0),esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_30]),c_0_31])]),c_0_32]) ).
fof(c_0_64,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_2(X2,X1)
=> ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[dt_m1_filter_2]) ).
cnf(c_0_65,plain,
( v3_struct_0(X1)
| m1_filter_0(k6_domain_1(u1_struct_0(X1),k6_lattices(X1)),X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ v14_lattices(X1) ),
inference(cn,[status(thm)],[c_0_53]) ).
cnf(c_0_66,negated_conjecture,
v14_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_54,c_0_55]),c_0_30]),c_0_31])]),c_0_32]) ).
cnf(c_0_67,negated_conjecture,
k6_lattices(k1_lattice2(esk1_0)) = k5_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_56,c_0_55]),c_0_30]),c_0_31])]),c_0_32]) ).
fof(c_0_68,plain,
! [X160] :
( v3_struct_0(X160)
| ~ l2_lattices(X160)
| m1_subset_1(k6_lattices(X160),u1_struct_0(X160)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])]) ).
cnf(c_0_69,plain,
( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))
| v3_struct_0(X2)
| ~ m1_filter_0(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_70,negated_conjecture,
( m1_filter_0(esk10_1(esk1_0),k1_lattice2(esk1_0))
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_30])]) ).
fof(c_0_71,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[dt_m2_filter_2]) ).
fof(c_0_72,plain,
! [X1,X2] :
( ( ~ v1_xboole_0(X1)
& m1_subset_1(X2,X1) )
=> k6_domain_1(X1,X2) = k1_tarski(X2) ),
inference(fof_simplification,[status(thm)],[redefinition_k6_domain_1]) ).
cnf(c_0_73,plain,
( v3_struct_0(X1)
| m1_subset_1(k5_lattices(X1),u1_struct_0(X1))
| ~ l1_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_74,plain,
( l1_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
fof(c_0_75,plain,
! [X258,X259,X260] :
( ~ r2_hidden(X258,X259)
| ~ m1_subset_1(X259,k1_zfmisc_1(X260))
| ~ v1_xboole_0(X260) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
cnf(c_0_76,negated_conjecture,
m1_filter_0(esk7_1(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_47,c_0_63]),c_0_30]),c_0_31])]),c_0_32]) ).
fof(c_0_77,plain,
! [X251,X252] :
( ~ m1_subset_1(X251,X252)
| v1_xboole_0(X252)
| r2_hidden(X251,X252) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(c_0_78,plain,
! [X188] : m1_subset_1(esk9_1(X188),X188),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(c_0_79,plain,
! [X166,X167] :
( ( ~ v1_xboole_0(X167)
| ~ m1_filter_2(X167,X166)
| v3_struct_0(X166)
| ~ v10_lattices(X166)
| ~ l3_lattices(X166) )
& ( m2_lattice4(X167,X166)
| ~ m1_filter_2(X167,X166)
| v3_struct_0(X166)
| ~ v10_lattices(X166)
| ~ l3_lattices(X166) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_64])])])]) ).
cnf(c_0_80,negated_conjecture,
( m1_filter_0(k6_domain_1(u1_struct_0(k1_lattice2(esk1_0)),k5_lattices(esk1_0)),k1_lattice2(esk1_0))
| v3_struct_0(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]),c_0_49])]) ).
cnf(c_0_81,plain,
( v3_struct_0(X1)
| m1_subset_1(k6_lattices(X1),u1_struct_0(X1))
| ~ l2_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_82,plain,
( l2_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_83,negated_conjecture,
( m1_subset_1(esk10_1(esk1_0),k1_zfmisc_1(u1_struct_0(k1_lattice2(esk1_0))))
| v3_struct_0(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_49])]) ).
fof(c_0_84,plain,
! [X168,X169] :
( ( ~ v1_xboole_0(X169)
| ~ m2_filter_2(X169,X168)
| v3_struct_0(X168)
| ~ v10_lattices(X168)
| ~ l3_lattices(X168) )
& ( m2_lattice4(X169,X168)
| ~ m2_filter_2(X169,X168)
| v3_struct_0(X168)
| ~ v10_lattices(X168)
| ~ l3_lattices(X168) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_71])])])]) ).
fof(c_0_85,plain,
! [X238,X239] :
( v1_xboole_0(X238)
| ~ m1_subset_1(X239,X238)
| k6_domain_1(X238,X239) = k1_tarski(X239) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_72])]) ).
cnf(c_0_86,plain,
( m1_subset_1(k5_lattices(X1),u1_struct_0(X1))
| v3_struct_0(X1)
| ~ l3_lattices(X1) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_87,plain,
( ~ r2_hidden(X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X3))
| ~ v1_xboole_0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_88,negated_conjecture,
m1_subset_1(esk7_1(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_69,c_0_76]),c_0_30]),c_0_31])]),c_0_32]) ).
cnf(c_0_89,plain,
( v1_xboole_0(X2)
| r2_hidden(X1,X2)
| ~ m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_90,plain,
m1_subset_1(esk9_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_91,plain,
( v3_struct_0(X2)
| ~ v1_xboole_0(X1)
| ~ m1_filter_2(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_92,plain,
( m1_filter_2(X1,X2)
| v3_struct_0(X2)
| ~ m1_filter_0(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_93,negated_conjecture,
( m1_filter_0(k6_domain_1(u1_struct_0(k1_lattice2(esk1_0)),k5_lattices(esk1_0)),k1_lattice2(esk1_0))
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_60]),c_0_30])]) ).
cnf(c_0_94,plain,
( m1_subset_1(k6_lattices(X1),u1_struct_0(X1))
| v3_struct_0(X1)
| ~ l3_lattices(X1) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_95,negated_conjecture,
( m1_subset_1(esk10_1(esk1_0),k1_zfmisc_1(u1_struct_0(k1_lattice2(esk1_0))))
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_60]),c_0_30])]) ).
cnf(c_0_96,plain,
( v3_struct_0(X2)
| ~ v1_xboole_0(X1)
| ~ m2_filter_2(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_97,plain,
( v1_xboole_0(X1)
| k6_domain_1(X1,X2) = k1_tarski(X2)
| ~ m1_subset_1(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_98,negated_conjecture,
m1_subset_1(k5_lattices(esk1_0),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_30]),c_0_32]) ).
cnf(c_0_99,negated_conjecture,
( ~ v1_xboole_0(u1_struct_0(esk1_0))
| ~ r2_hidden(X1,esk7_1(esk1_0)) ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_100,plain,
( v1_xboole_0(X1)
| r2_hidden(esk9_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_101,negated_conjecture,
~ v1_xboole_0(esk7_1(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_63]),c_0_30]),c_0_31])]),c_0_32]) ).
cnf(c_0_102,negated_conjecture,
( m1_filter_2(k6_domain_1(u1_struct_0(k1_lattice2(esk1_0)),k5_lattices(esk1_0)),k1_lattice2(esk1_0))
| v3_struct_0(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_49])]) ).
cnf(c_0_103,plain,
( m1_subset_1(k6_lattices(k1_lattice2(X1)),u1_struct_0(k1_lattice2(X1)))
| v3_struct_0(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(spm,[status(thm)],[c_0_94,c_0_60]) ).
cnf(c_0_104,negated_conjecture,
( v3_struct_0(k1_lattice2(esk1_0))
| ~ v1_xboole_0(u1_struct_0(k1_lattice2(esk1_0)))
| ~ r2_hidden(X1,esk10_1(esk1_0)) ),
inference(spm,[status(thm)],[c_0_87,c_0_95]) ).
cnf(c_0_105,negated_conjecture,
~ v1_xboole_0(esk10_1(esk1_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_40]),c_0_30]),c_0_31])]),c_0_32]) ).
cnf(c_0_106,negated_conjecture,
( k6_domain_1(u1_struct_0(esk1_0),k5_lattices(esk1_0)) = k1_tarski(k5_lattices(esk1_0))
| v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_107,negated_conjecture,
~ v1_xboole_0(u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_101]) ).
fof(c_0_108,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l3_lattices(X1) )
=> ( ~ v3_struct_0(k1_lattice2(X1))
& v3_lattices(k1_lattice2(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc1_lattice2]) ).
cnf(c_0_109,plain,
( m2_filter_2(X1,X2)
| v3_struct_0(X2)
| ~ m1_filter_2(X1,k1_lattice2(X2))
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_110,negated_conjecture,
( m1_filter_2(k6_domain_1(u1_struct_0(k1_lattice2(esk1_0)),k5_lattices(esk1_0)),k1_lattice2(esk1_0))
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_60]),c_0_30])]) ).
cnf(c_0_111,negated_conjecture,
( m1_subset_1(k5_lattices(esk1_0),u1_struct_0(k1_lattice2(esk1_0)))
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_30]),c_0_67]) ).
cnf(c_0_112,negated_conjecture,
( v3_struct_0(k1_lattice2(esk1_0))
| ~ v1_xboole_0(u1_struct_0(k1_lattice2(esk1_0))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_100]),c_0_105]) ).
cnf(c_0_113,negated_conjecture,
~ m2_filter_2(k6_domain_1(u1_struct_0(esk1_0),k5_lattices(esk1_0)),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_114,negated_conjecture,
k6_domain_1(u1_struct_0(esk1_0),k5_lattices(esk1_0)) = k1_tarski(k5_lattices(esk1_0)),
inference(sr,[status(thm)],[c_0_106,c_0_107]) ).
fof(c_0_115,plain,
! [X197] :
( ( ~ v3_struct_0(k1_lattice2(X197))
| v3_struct_0(X197)
| ~ l3_lattices(X197) )
& ( v3_lattices(k1_lattice2(X197))
| v3_struct_0(X197)
| ~ l3_lattices(X197) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_108])])]) ).
cnf(c_0_116,negated_conjecture,
( m2_filter_2(k6_domain_1(u1_struct_0(k1_lattice2(esk1_0)),k5_lattices(esk1_0)),esk1_0)
| v3_struct_0(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_109,c_0_110]),c_0_30]),c_0_31])]),c_0_32]) ).
cnf(c_0_117,negated_conjecture,
( k6_domain_1(u1_struct_0(k1_lattice2(esk1_0)),k5_lattices(esk1_0)) = k1_tarski(k5_lattices(esk1_0))
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_111]),c_0_112]) ).
cnf(c_0_118,negated_conjecture,
~ m2_filter_2(k1_tarski(k5_lattices(esk1_0)),esk1_0),
inference(rw,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_119,plain,
( v3_struct_0(X1)
| ~ v3_struct_0(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_120,negated_conjecture,
v3_struct_0(k1_lattice2(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_118]) ).
cnf(c_0_121,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_30])]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LAT302+1 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.32 % Computer : n025.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Mon May 4 21:08:13 EDT 2026
% 0.16/0.32 % CPUTime :
% 0.16/0.33 % start to proof: theBenchmark
% 1.39/1.76 % Version : CSE_E---1.7
% 1.39/1.76 % Problem : theBenchmark.p
% 1.39/1.76 % SZS status Theorem for theBenchmark.p
% 1.39/1.76 % SZS output start CNFRefutation
% See solution above
% 1.39/1.77 % Total time : 1.372s
%------------------------------------------------------------------------------