%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT303+1 : TPTP v9.2.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n021.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 1.42s 1.78s
% Output : CNFRefutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 20
% Syntax : Number of formulae : 103 ( 21 unt; 0 def)
% Number of atoms : 419 ( 12 equ)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 487 ( 171 ~; 168 |; 96 &)
% ( 6 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-2 aty)
% Number of variables : 124 ( 2 sgn 85 !; 3 ?)
% 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/sandbox/benchmark/theBenchmark.p',existence_m2_filter_2) ).
fof(t27_filter_2,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ( m2_filter_2(k6_domain_1(u1_struct_0(X1),X2),X1)
=> v13_lattices(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_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/sandbox/benchmark/theBenchmark.p',dt_m2_filter_2) ).
fof(dt_m2_lattice4,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(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(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/sandbox/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/sandbox/benchmark/theBenchmark.p',fc6_lattice2) ).
fof(d4_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(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(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/sandbox/benchmark/theBenchmark.p',redefinition_m1_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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : m1_subset_1(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(dt_k5_filter_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,u1_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(fc1_struct_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(dt_k1_lattice2,axiom,
! [X1] :
( l3_lattices(X1)
=> ( v3_lattices(k1_lattice2(X1))
& l3_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattice2) ).
fof(dt_l1_lattices,axiom,
! [X1] :
( l1_lattices(X1)
=> l1_struct_0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
fof(t14_filter_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ( m1_filter_0(k6_domain_1(u1_struct_0(X1),X2),X1)
=> v14_lattices(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_filter_0) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( l1_lattices(X1)
& l2_lattices(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
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/sandbox/benchmark/theBenchmark.p',t63_lattice2) ).
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/sandbox/benchmark/theBenchmark.p',fc1_lattice2) ).
fof(c_0_20,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_21,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ( m2_filter_2(k6_domain_1(u1_struct_0(X1),X2),X1)
=> v13_lattices(X1) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t27_filter_2])]) ).
fof(c_0_22,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_23,plain,
! [X196] :
( v3_struct_0(X196)
| ~ v10_lattices(X196)
| ~ l3_lattices(X196)
| m2_filter_2(esk11_1(X196),X196) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).
fof(c_0_24,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v10_lattices(esk1_0)
& l3_lattices(esk1_0)
& m1_subset_1(esk2_0,u1_struct_0(esk1_0))
& m2_filter_2(k6_domain_1(u1_struct_0(esk1_0),esk2_0),esk1_0)
& ~ v13_lattices(esk1_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
fof(c_0_25,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(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_26,plain,
! [X174,X175] :
( ( ~ v1_xboole_0(X175)
| ~ m2_filter_2(X175,X174)
| v3_struct_0(X174)
| ~ v10_lattices(X174)
| ~ l3_lattices(X174) )
& ( m2_lattice4(X175,X174)
| ~ m2_filter_2(X175,X174)
| v3_struct_0(X174)
| ~ v10_lattices(X174)
| ~ l3_lattices(X174) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])])]) ).
cnf(c_0_27,plain,
( v3_struct_0(X1)
| m2_filter_2(esk11_1(X1),X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_31,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_32,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_33,plain,
! [X176,X177] :
( v3_struct_0(X176)
| ~ v10_lattices(X176)
| ~ l3_lattices(X176)
| ~ m2_lattice4(X177,X176)
| m1_subset_1(X177,k1_zfmisc_1(u1_struct_0(X176))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])]) ).
cnf(c_0_34,plain,
( m2_lattice4(X1,X2)
| v3_struct_0(X2)
| ~ m2_filter_2(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,negated_conjecture,
m2_filter_2(esk11_1(esk1_0),esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]),c_0_30]) ).
fof(c_0_36,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(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_37,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_38,plain,
! [X256,X257] :
( ( ~ m2_filter_2(X257,X256)
| m1_filter_2(X257,k1_lattice2(X256))
| v3_struct_0(X256)
| ~ v10_lattices(X256)
| ~ l3_lattices(X256) )
& ( ~ m1_filter_2(X257,k1_lattice2(X256))
| m2_filter_2(X257,X256)
| v3_struct_0(X256)
| ~ v10_lattices(X256)
| ~ l3_lattices(X256) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])]) ).
fof(c_0_39,plain,
! [X217] :
( ( ~ v3_struct_0(k1_lattice2(X217))
| v3_struct_0(X217)
| ~ v10_lattices(X217)
| ~ l3_lattices(X217) )
& ( v3_lattices(k1_lattice2(X217))
| v3_struct_0(X217)
| ~ v10_lattices(X217)
| ~ l3_lattices(X217) )
& ( v4_lattices(k1_lattice2(X217))
| v3_struct_0(X217)
| ~ v10_lattices(X217)
| ~ l3_lattices(X217) )
& ( v5_lattices(k1_lattice2(X217))
| v3_struct_0(X217)
| ~ v10_lattices(X217)
| ~ l3_lattices(X217) )
& ( v6_lattices(k1_lattice2(X217))
| v3_struct_0(X217)
| ~ v10_lattices(X217)
| ~ l3_lattices(X217) )
& ( v7_lattices(k1_lattice2(X217))
| v3_struct_0(X217)
| ~ v10_lattices(X217)
| ~ l3_lattices(X217) )
& ( v8_lattices(k1_lattice2(X217))
| v3_struct_0(X217)
| ~ v10_lattices(X217)
| ~ l3_lattices(X217) )
& ( v9_lattices(k1_lattice2(X217))
| v3_struct_0(X217)
| ~ v10_lattices(X217)
| ~ l3_lattices(X217) )
& ( v10_lattices(k1_lattice2(X217))
| v3_struct_0(X217)
| ~ v10_lattices(X217)
| ~ l3_lattices(X217) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])]) ).
fof(c_0_40,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]) ).
fof(c_0_41,plain,
! [X265,X266,X267] :
( ~ r2_hidden(X265,X266)
| ~ m1_subset_1(X266,k1_zfmisc_1(X267))
| ~ v1_xboole_0(X267) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
cnf(c_0_42,plain,
( v3_struct_0(X1)
| m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m2_lattice4(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_43,negated_conjecture,
m2_lattice4(esk11_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_34,c_0_35]),c_0_28]),c_0_29])]),c_0_30]) ).
fof(c_0_44,plain,
! [X258,X259] :
( ~ m1_subset_1(X258,X259)
| v1_xboole_0(X259)
| r2_hidden(X258,X259) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(c_0_45,plain,
! [X194] : m1_subset_1(esk10_1(X194),X194),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(c_0_46,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,u1_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_47,plain,
! [X157,X158] :
( v3_struct_0(X157)
| ~ v10_lattices(X157)
| ~ l3_lattices(X157)
| ~ m1_subset_1(X158,u1_struct_0(X157))
| k5_filter_2(X157,X158) = X158 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])]) ).
fof(c_0_48,plain,
! [X246,X247] :
( ( ~ m1_filter_2(X247,X246)
| m1_filter_0(X247,X246)
| v3_struct_0(X246)
| ~ v10_lattices(X246)
| ~ l3_lattices(X246) )
& ( ~ m1_filter_0(X247,X246)
| m1_filter_2(X247,X246)
| v3_struct_0(X246)
| ~ v10_lattices(X246)
| ~ l3_lattices(X246) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])])]) ).
cnf(c_0_49,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_38]) ).
cnf(c_0_50,negated_conjecture,
m2_filter_2(k6_domain_1(u1_struct_0(esk1_0),esk2_0),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_51,plain,
( v10_lattices(k1_lattice2(X1))
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_52,plain,
! [X244,X245] :
( v1_xboole_0(X244)
| ~ m1_subset_1(X245,X244)
| k6_domain_1(X244,X245) = k1_tarski(X245) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])]) ).
cnf(c_0_53,plain,
( ~ r2_hidden(X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X3))
| ~ v1_xboole_0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_54,negated_conjecture,
m1_subset_1(esk11_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_42,c_0_43]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_55,plain,
( v1_xboole_0(X2)
| r2_hidden(X1,X2)
| ~ m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_56,plain,
m1_subset_1(esk10_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_57,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_26]) ).
fof(c_0_58,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).
fof(c_0_59,plain,
! [X163,X164] :
( v3_struct_0(X163)
| ~ v10_lattices(X163)
| ~ l3_lattices(X163)
| ~ m1_subset_1(X164,u1_struct_0(X163))
| m1_subset_1(k5_filter_2(X163,X164),u1_struct_0(k1_lattice2(X163))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_46])]) ).
cnf(c_0_60,plain,
( v3_struct_0(X1)
| k5_filter_2(X1,X2) = X2
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_61,negated_conjecture,
m1_subset_1(esk2_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_62,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_48]) ).
cnf(c_0_63,negated_conjecture,
m1_filter_2(k6_domain_1(u1_struct_0(esk1_0),esk2_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_49,c_0_50]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_64,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_51,c_0_28]),c_0_29])]),c_0_30]) ).
fof(c_0_65,plain,
! [X162] :
( ( v3_lattices(k1_lattice2(X162))
| ~ l3_lattices(X162) )
& ( l3_lattices(k1_lattice2(X162))
| ~ l3_lattices(X162) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_lattice2])])]) ).
cnf(c_0_66,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_52]) ).
cnf(c_0_67,negated_conjecture,
( ~ v1_xboole_0(u1_struct_0(esk1_0))
| ~ r2_hidden(X1,esk11_1(esk1_0)) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_68,plain,
( v1_xboole_0(X1)
| r2_hidden(esk10_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_69,negated_conjecture,
~ v1_xboole_0(esk11_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_57,c_0_35]),c_0_28]),c_0_29])]),c_0_30]) ).
fof(c_0_70,plain,
! [X204] :
( v3_struct_0(X204)
| ~ l1_struct_0(X204)
| ~ v1_xboole_0(u1_struct_0(X204)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_58])]) ).
fof(c_0_71,plain,
! [X167] :
( ~ l1_lattices(X167)
| l1_struct_0(X167) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_lattices])]) ).
fof(c_0_72,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ( m1_filter_0(k6_domain_1(u1_struct_0(X1),X2),X1)
=> v14_lattices(X1) ) ) ),
inference(fof_simplification,[status(thm)],[t14_filter_0]) ).
cnf(c_0_73,plain,
( v3_struct_0(X1)
| m1_subset_1(k5_filter_2(X1,X2),u1_struct_0(k1_lattice2(X1)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_74,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_60,c_0_61]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_75,negated_conjecture,
( m1_filter_0(k6_domain_1(u1_struct_0(esk1_0),esk2_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_62,c_0_63]),c_0_64])]) ).
cnf(c_0_76,plain,
( l3_lattices(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_77,negated_conjecture,
( k6_domain_1(u1_struct_0(esk1_0),esk2_0) = k1_tarski(esk2_0)
| v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_66,c_0_61]) ).
cnf(c_0_78,negated_conjecture,
~ v1_xboole_0(u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69]) ).
cnf(c_0_79,plain,
( v3_struct_0(X1)
| ~ l1_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_80,plain,
( l1_struct_0(X1)
| ~ l1_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
fof(c_0_81,plain,
! [X169] :
( ( l1_lattices(X169)
| ~ l3_lattices(X169) )
& ( l2_lattices(X169)
| ~ l3_lattices(X169) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
fof(c_0_82,plain,
! [X252,X253] :
( v3_struct_0(X252)
| ~ v10_lattices(X252)
| ~ l3_lattices(X252)
| ~ m1_subset_1(X253,u1_struct_0(X252))
| ~ m1_filter_0(k6_domain_1(u1_struct_0(X252),X253),X252)
| v14_lattices(X252) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_72])])]) ).
cnf(c_0_83,negated_conjecture,
m1_subset_1(esk2_0,u1_struct_0(k1_lattice2(esk1_0))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_61]),c_0_74]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_84,negated_conjecture,
( m1_filter_0(k6_domain_1(u1_struct_0(esk1_0),esk2_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_75,c_0_76]),c_0_28])]) ).
cnf(c_0_85,negated_conjecture,
k6_domain_1(u1_struct_0(esk1_0),esk2_0) = k1_tarski(esk2_0),
inference(sr,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_86,plain,
( v3_struct_0(X1)
| ~ l1_lattices(X1)
| ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_87,plain,
( l1_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
fof(c_0_88,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]) ).
cnf(c_0_89,plain,
( v3_struct_0(X1)
| v14_lattices(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_filter_0(k6_domain_1(u1_struct_0(X1),X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_90,negated_conjecture,
( k6_domain_1(u1_struct_0(k1_lattice2(esk1_0)),esk2_0) = k1_tarski(esk2_0)
| v1_xboole_0(u1_struct_0(k1_lattice2(esk1_0))) ),
inference(spm,[status(thm)],[c_0_66,c_0_83]) ).
cnf(c_0_91,negated_conjecture,
( m1_filter_0(k1_tarski(esk2_0),k1_lattice2(esk1_0))
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(rw,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_92,plain,
( v3_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1))
| ~ l3_lattices(X1) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
fof(c_0_93,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]) ).
fof(c_0_94,plain,
! [X268] :
( ( ~ v13_lattices(X268)
| v14_lattices(k1_lattice2(X268))
| v3_struct_0(X268)
| ~ v10_lattices(X268)
| ~ l3_lattices(X268) )
& ( ~ v14_lattices(k1_lattice2(X268))
| v13_lattices(X268)
| v3_struct_0(X268)
| ~ v10_lattices(X268)
| ~ l3_lattices(X268) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_88])])]) ).
cnf(c_0_95,negated_conjecture,
( v14_lattices(k1_lattice2(esk1_0))
| v3_struct_0(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_83]),c_0_64])]),c_0_91]),c_0_92]) ).
fof(c_0_96,plain,
! [X203] :
( ( ~ v3_struct_0(k1_lattice2(X203))
| v3_struct_0(X203)
| ~ l3_lattices(X203) )
& ( v3_lattices(k1_lattice2(X203))
| v3_struct_0(X203)
| ~ l3_lattices(X203) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_93])])]) ).
cnf(c_0_97,plain,
( v13_lattices(X1)
| v3_struct_0(X1)
| ~ v14_lattices(k1_lattice2(X1))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_98,negated_conjecture,
( v14_lattices(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_95,c_0_76]),c_0_28])]) ).
cnf(c_0_99,negated_conjecture,
~ v13_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_100,plain,
( v3_struct_0(X1)
| ~ v3_struct_0(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_101,negated_conjecture,
v3_struct_0(k1_lattice2(esk1_0)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_28]),c_0_29])]),c_0_99]),c_0_30]) ).
cnf(c_0_102,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_28])]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT303+1 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.13/0.32 % Computer : n021.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Mon May 4 21:09:40 EDT 2026
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % start to proof: theBenchmark
% 1.42/1.78 % Version : CSE_E---1.7
% 1.42/1.78 % Problem : theBenchmark.p
% 1.42/1.78 % SZS status Theorem for theBenchmark.p
% 1.42/1.78 % SZS output start CNFRefutation
% See solution above
% 1.42/1.79 % Total time : 1.372s
%------------------------------------------------------------------------------