%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT337+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 : n001.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 04:38:11 PM UTC 2026
% Result : Theorem 1.29s 1.75s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 60 ( 12 unt; 0 def)
% Number of atoms : 539 ( 0 equ)
% Maximal formula atoms : 65 ( 8 avg)
% Number of connectives : 780 ( 301 ~; 316 |; 127 &)
% ( 0 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 20 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 82 ( 0 sgn 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t87_filter_2,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v17_lattices(X1)
& l3_lattices(X1)
& r3_lattices(X1,X2,X3) )
=> ( ~ v3_struct_0(k23_filter_2(X1,k22_filter_2(X1,X2,X3)))
& v10_lattices(k23_filter_2(X1,k22_filter_2(X1,X2,X3)))
& v17_lattices(k23_filter_2(X1,k22_filter_2(X1,X2,X3)))
& l3_lattices(k23_filter_2(X1,k22_filter_2(X1,X2,X3))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_filter_2) ).
fof(cc6_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( ( ~ v3_struct_0(X1)
& v11_lattices(X1)
& v15_lattices(X1)
& v16_lattices(X1) )
=> ( ~ v3_struct_0(X1)
& v17_lattices(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_lattices) ).
fof(t86_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v15_lattices(X1)
& v16_lattices(X1)
& l3_lattices(X1)
& v12_lattices(X1)
& r3_lattices(X1,X2,X3) )
=> ( ~ v3_struct_0(k23_filter_2(X1,k22_filter_2(X1,X2,X3)))
& v10_lattices(k23_filter_2(X1,k22_filter_2(X1,X2,X3)))
& v15_lattices(k23_filter_2(X1,k22_filter_2(X1,X2,X3)))
& v16_lattices(k23_filter_2(X1,k22_filter_2(X1,X2,X3)))
& l3_lattices(k23_filter_2(X1,k22_filter_2(X1,X2,X3))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_filter_2) ).
fof(cc5_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( ( ~ v3_struct_0(X1)
& v17_lattices(X1) )
=> ( ~ v3_struct_0(X1)
& v11_lattices(X1)
& v13_lattices(X1)
& v14_lattices(X1)
& v15_lattices(X1)
& v16_lattices(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_lattices) ).
fof(t78_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) )
=> ( v11_lattices(X1)
=> v11_lattices(k23_filter_2(X1,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_filter_2) ).
fof(dt_k22_filter_2,axiom,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> ( ~ v1_xboole_0(k22_filter_2(X1,X2,X3))
& m2_lattice4(k22_filter_2(X1,X2,X3),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k22_filter_2) ).
fof(cc7_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v11_lattices(X1) )
=> ( ~ v3_struct_0(X1)
& v4_lattices(X1)
& v5_lattices(X1)
& v6_lattices(X1)
& v7_lattices(X1)
& v8_lattices(X1)
& v9_lattices(X1)
& v10_lattices(X1)
& v12_lattices(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc7_lattices) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v17_lattices(X1)
& l3_lattices(X1)
& r3_lattices(X1,X2,X3) )
=> ( ~ v3_struct_0(k23_filter_2(X1,k22_filter_2(X1,X2,X3)))
& v10_lattices(k23_filter_2(X1,k22_filter_2(X1,X2,X3)))
& v17_lattices(k23_filter_2(X1,k22_filter_2(X1,X2,X3)))
& l3_lattices(k23_filter_2(X1,k22_filter_2(X1,X2,X3))) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t87_filter_2])]) ).
fof(c_0_8,plain,
! [X1] :
( l3_lattices(X1)
=> ( ( ~ v3_struct_0(X1)
& v11_lattices(X1)
& v15_lattices(X1)
& v16_lattices(X1) )
=> ( ~ v3_struct_0(X1)
& v17_lattices(X1) ) ) ),
inference(fof_simplification,[status(thm)],[cc6_lattices]) ).
fof(c_0_9,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v15_lattices(X1)
& v16_lattices(X1)
& l3_lattices(X1)
& v12_lattices(X1)
& r3_lattices(X1,X2,X3) )
=> ( ~ v3_struct_0(k23_filter_2(X1,k22_filter_2(X1,X2,X3)))
& v10_lattices(k23_filter_2(X1,k22_filter_2(X1,X2,X3)))
& v15_lattices(k23_filter_2(X1,k22_filter_2(X1,X2,X3)))
& v16_lattices(k23_filter_2(X1,k22_filter_2(X1,X2,X3)))
& l3_lattices(k23_filter_2(X1,k22_filter_2(X1,X2,X3))) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[t86_filter_2]) ).
fof(c_0_10,plain,
! [X1] :
( l3_lattices(X1)
=> ( ( ~ v3_struct_0(X1)
& v17_lattices(X1) )
=> ( ~ v3_struct_0(X1)
& v11_lattices(X1)
& v13_lattices(X1)
& v14_lattices(X1)
& v15_lattices(X1)
& v16_lattices(X1) ) ) ),
inference(fof_simplification,[status(thm)],[cc5_lattices]) ).
fof(c_0_11,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))
& m1_subset_1(esk3_0,u1_struct_0(esk1_0))
& ~ v3_struct_0(esk1_0)
& v10_lattices(esk1_0)
& v17_lattices(esk1_0)
& l3_lattices(esk1_0)
& r3_lattices(esk1_0,esk2_0,esk3_0)
& ( v3_struct_0(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0)))
| ~ v10_lattices(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0)))
| ~ v17_lattices(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0)))
| ~ l3_lattices(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0))) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_12,plain,
! [X152] :
( ( ~ v3_struct_0(X152)
| v3_struct_0(X152)
| ~ v11_lattices(X152)
| ~ v15_lattices(X152)
| ~ v16_lattices(X152)
| ~ l3_lattices(X152) )
& ( v17_lattices(X152)
| v3_struct_0(X152)
| ~ v11_lattices(X152)
| ~ v15_lattices(X152)
| ~ v16_lattices(X152)
| ~ l3_lattices(X152) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_13,plain,
! [X259,X260,X261] :
( ( ~ v3_struct_0(k23_filter_2(X259,k22_filter_2(X259,X260,X261)))
| v3_struct_0(X259)
| ~ v10_lattices(X259)
| ~ v15_lattices(X259)
| ~ v16_lattices(X259)
| ~ l3_lattices(X259)
| ~ v12_lattices(X259)
| ~ r3_lattices(X259,X260,X261)
| ~ m1_subset_1(X261,u1_struct_0(X259))
| ~ m1_subset_1(X260,u1_struct_0(X259))
| v3_struct_0(X259)
| ~ v10_lattices(X259)
| ~ l3_lattices(X259) )
& ( v10_lattices(k23_filter_2(X259,k22_filter_2(X259,X260,X261)))
| v3_struct_0(X259)
| ~ v10_lattices(X259)
| ~ v15_lattices(X259)
| ~ v16_lattices(X259)
| ~ l3_lattices(X259)
| ~ v12_lattices(X259)
| ~ r3_lattices(X259,X260,X261)
| ~ m1_subset_1(X261,u1_struct_0(X259))
| ~ m1_subset_1(X260,u1_struct_0(X259))
| v3_struct_0(X259)
| ~ v10_lattices(X259)
| ~ l3_lattices(X259) )
& ( v15_lattices(k23_filter_2(X259,k22_filter_2(X259,X260,X261)))
| v3_struct_0(X259)
| ~ v10_lattices(X259)
| ~ v15_lattices(X259)
| ~ v16_lattices(X259)
| ~ l3_lattices(X259)
| ~ v12_lattices(X259)
| ~ r3_lattices(X259,X260,X261)
| ~ m1_subset_1(X261,u1_struct_0(X259))
| ~ m1_subset_1(X260,u1_struct_0(X259))
| v3_struct_0(X259)
| ~ v10_lattices(X259)
| ~ l3_lattices(X259) )
& ( v16_lattices(k23_filter_2(X259,k22_filter_2(X259,X260,X261)))
| v3_struct_0(X259)
| ~ v10_lattices(X259)
| ~ v15_lattices(X259)
| ~ v16_lattices(X259)
| ~ l3_lattices(X259)
| ~ v12_lattices(X259)
| ~ r3_lattices(X259,X260,X261)
| ~ m1_subset_1(X261,u1_struct_0(X259))
| ~ m1_subset_1(X260,u1_struct_0(X259))
| v3_struct_0(X259)
| ~ v10_lattices(X259)
| ~ l3_lattices(X259) )
& ( l3_lattices(k23_filter_2(X259,k22_filter_2(X259,X260,X261)))
| v3_struct_0(X259)
| ~ v10_lattices(X259)
| ~ v15_lattices(X259)
| ~ v16_lattices(X259)
| ~ l3_lattices(X259)
| ~ v12_lattices(X259)
| ~ r3_lattices(X259,X260,X261)
| ~ m1_subset_1(X261,u1_struct_0(X259))
| ~ m1_subset_1(X260,u1_struct_0(X259))
| v3_struct_0(X259)
| ~ v10_lattices(X259)
| ~ l3_lattices(X259) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
fof(c_0_14,plain,
! [X151] :
( ( ~ v3_struct_0(X151)
| v3_struct_0(X151)
| ~ v17_lattices(X151)
| ~ l3_lattices(X151) )
& ( v11_lattices(X151)
| v3_struct_0(X151)
| ~ v17_lattices(X151)
| ~ l3_lattices(X151) )
& ( v13_lattices(X151)
| v3_struct_0(X151)
| ~ v17_lattices(X151)
| ~ l3_lattices(X151) )
& ( v14_lattices(X151)
| v3_struct_0(X151)
| ~ v17_lattices(X151)
| ~ l3_lattices(X151) )
& ( v15_lattices(X151)
| v3_struct_0(X151)
| ~ v17_lattices(X151)
| ~ l3_lattices(X151) )
& ( v16_lattices(X151)
| v3_struct_0(X151)
| ~ v17_lattices(X151)
| ~ l3_lattices(X151) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
cnf(c_0_15,negated_conjecture,
( v3_struct_0(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0)))
| ~ v10_lattices(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0)))
| ~ v17_lattices(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0)))
| ~ l3_lattices(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0))) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( v17_lattices(X1)
| v3_struct_0(X1)
| ~ v11_lattices(X1)
| ~ v15_lattices(X1)
| ~ v16_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( v16_lattices(k23_filter_2(X1,k22_filter_2(X1,X2,X3)))
| v3_struct_0(X1)
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ v15_lattices(X1)
| ~ v16_lattices(X1)
| ~ l3_lattices(X1)
| ~ v12_lattices(X1)
| ~ r3_lattices(X1,X2,X3)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( v16_lattices(X1)
| v3_struct_0(X1)
| ~ v17_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,negated_conjecture,
v17_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_22,plain,
( v15_lattices(X1)
| v3_struct_0(X1)
| ~ v17_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_23,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) )
=> ( v11_lattices(X1)
=> v11_lattices(k23_filter_2(X1,X2)) ) ) ),
inference(fof_simplification,[status(thm)],[t78_filter_2]) ).
cnf(c_0_24,negated_conjecture,
( v3_struct_0(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0)))
| ~ v16_lattices(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0)))
| ~ v11_lattices(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0)))
| ~ v15_lattices(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0)))
| ~ l3_lattices(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0)))
| ~ v10_lattices(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0))) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_25,plain,
( v3_struct_0(X1)
| v16_lattices(k23_filter_2(X1,k22_filter_2(X1,X2,X3)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ v15_lattices(X1)
| ~ v16_lattices(X1)
| ~ v12_lattices(X1)
| ~ r3_lattices(X1,X2,X3)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(cn,[status(thm)],[c_0_17]) ).
cnf(c_0_26,negated_conjecture,
v16_lattices(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]),c_0_21]) ).
cnf(c_0_27,negated_conjecture,
v15_lattices(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_19]),c_0_20])]),c_0_21]) ).
cnf(c_0_28,negated_conjecture,
r3_lattices(esk1_0,esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_29,negated_conjecture,
m1_subset_1(esk3_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_30,negated_conjecture,
m1_subset_1(esk2_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_31,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_32,plain,
! [X255,X256] :
( v3_struct_0(X255)
| ~ v10_lattices(X255)
| ~ l3_lattices(X255)
| v1_xboole_0(X256)
| ~ m2_lattice4(X256,X255)
| ~ v11_lattices(X255)
| v11_lattices(k23_filter_2(X255,X256)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])]) ).
cnf(c_0_33,plain,
( v11_lattices(X1)
| v3_struct_0(X1)
| ~ v17_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_34,negated_conjecture,
( v3_struct_0(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0)))
| ~ v12_lattices(esk1_0)
| ~ v11_lattices(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0)))
| ~ v15_lattices(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0)))
| ~ l3_lattices(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0)))
| ~ v10_lattices(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0))) ),
inference(sr,[status(thm)],[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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27]),c_0_28]),c_0_29]),c_0_30]),c_0_20]),c_0_31])]),c_0_21]) ).
cnf(c_0_35,plain,
( v3_struct_0(X1)
| v1_xboole_0(X2)
| v11_lattices(k23_filter_2(X1,X2))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m2_lattice4(X2,X1)
| ~ v11_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_36,negated_conjecture,
v11_lattices(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_19]),c_0_20])]),c_0_21]) ).
cnf(c_0_37,plain,
( v15_lattices(k23_filter_2(X1,k22_filter_2(X1,X2,X3)))
| v3_struct_0(X1)
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ v15_lattices(X1)
| ~ v16_lattices(X1)
| ~ l3_lattices(X1)
| ~ v12_lattices(X1)
| ~ r3_lattices(X1,X2,X3)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_38,plain,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> ( ~ v1_xboole_0(k22_filter_2(X1,X2,X3))
& m2_lattice4(k22_filter_2(X1,X2,X3),X1) ) ),
inference(fof_simplification,[status(thm)],[dt_k22_filter_2]) ).
cnf(c_0_39,negated_conjecture,
( v1_xboole_0(k22_filter_2(esk1_0,esk2_0,esk3_0))
| v3_struct_0(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0)))
| ~ m2_lattice4(k22_filter_2(esk1_0,esk2_0,esk3_0),esk1_0)
| ~ v12_lattices(esk1_0)
| ~ v15_lattices(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0)))
| ~ l3_lattices(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0)))
| ~ v10_lattices(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_20]),c_0_31])]),c_0_21]) ).
cnf(c_0_40,plain,
( v3_struct_0(X1)
| v15_lattices(k23_filter_2(X1,k22_filter_2(X1,X2,X3)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ v15_lattices(X1)
| ~ v16_lattices(X1)
| ~ v12_lattices(X1)
| ~ r3_lattices(X1,X2,X3)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(cn,[status(thm)],[c_0_37]) ).
fof(c_0_41,plain,
! [X157,X158,X159] :
( ( ~ v1_xboole_0(k22_filter_2(X157,X158,X159))
| v3_struct_0(X157)
| ~ v10_lattices(X157)
| ~ l3_lattices(X157)
| ~ m1_subset_1(X158,u1_struct_0(X157))
| ~ m1_subset_1(X159,u1_struct_0(X157)) )
& ( m2_lattice4(k22_filter_2(X157,X158,X159),X157)
| v3_struct_0(X157)
| ~ v10_lattices(X157)
| ~ l3_lattices(X157)
| ~ m1_subset_1(X158,u1_struct_0(X157))
| ~ m1_subset_1(X159,u1_struct_0(X157)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])]) ).
cnf(c_0_42,negated_conjecture,
( v1_xboole_0(k22_filter_2(esk1_0,esk2_0,esk3_0))
| v3_struct_0(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0)))
| ~ m2_lattice4(k22_filter_2(esk1_0,esk2_0,esk3_0),esk1_0)
| ~ v12_lattices(esk1_0)
| ~ l3_lattices(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0)))
| ~ v10_lattices(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0))) ),
inference(sr,[status(thm)],[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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_26]),c_0_27]),c_0_28]),c_0_29]),c_0_30]),c_0_20]),c_0_31])]),c_0_21]) ).
cnf(c_0_43,plain,
( m2_lattice4(k22_filter_2(X1,X2,X3),X1)
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_44,plain,
( v10_lattices(k23_filter_2(X1,k22_filter_2(X1,X2,X3)))
| v3_struct_0(X1)
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ v15_lattices(X1)
| ~ v16_lattices(X1)
| ~ l3_lattices(X1)
| ~ v12_lattices(X1)
| ~ r3_lattices(X1,X2,X3)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_45,negated_conjecture,
( v1_xboole_0(k22_filter_2(esk1_0,esk2_0,esk3_0))
| v3_struct_0(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0)))
| ~ v12_lattices(esk1_0)
| ~ l3_lattices(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0)))
| ~ v10_lattices(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_29]),c_0_30]),c_0_20]),c_0_31])]),c_0_21]) ).
cnf(c_0_46,plain,
( v3_struct_0(X1)
| v10_lattices(k23_filter_2(X1,k22_filter_2(X1,X2,X3)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ v15_lattices(X1)
| ~ v16_lattices(X1)
| ~ v12_lattices(X1)
| ~ r3_lattices(X1,X2,X3)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(cn,[status(thm)],[c_0_44]) ).
cnf(c_0_47,plain,
( l3_lattices(k23_filter_2(X1,k22_filter_2(X1,X2,X3)))
| v3_struct_0(X1)
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ v15_lattices(X1)
| ~ v16_lattices(X1)
| ~ l3_lattices(X1)
| ~ v12_lattices(X1)
| ~ r3_lattices(X1,X2,X3)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_48,plain,
( v3_struct_0(X1)
| v3_struct_0(X1)
| ~ v3_struct_0(k23_filter_2(X1,k22_filter_2(X1,X2,X3)))
| ~ v10_lattices(X1)
| ~ v15_lattices(X1)
| ~ v16_lattices(X1)
| ~ l3_lattices(X1)
| ~ v12_lattices(X1)
| ~ r3_lattices(X1,X2,X3)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_49,negated_conjecture,
( v1_xboole_0(k22_filter_2(esk1_0,esk2_0,esk3_0))
| v3_struct_0(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0)))
| ~ v12_lattices(esk1_0)
| ~ l3_lattices(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0))) ),
inference(sr,[status(thm)],[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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_26]),c_0_27]),c_0_28]),c_0_29]),c_0_30]),c_0_20]),c_0_31])]),c_0_21]) ).
cnf(c_0_50,plain,
( v3_struct_0(X1)
| l3_lattices(k23_filter_2(X1,k22_filter_2(X1,X2,X3)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ v15_lattices(X1)
| ~ v16_lattices(X1)
| ~ v12_lattices(X1)
| ~ r3_lattices(X1,X2,X3)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(cn,[status(thm)],[c_0_47]) ).
cnf(c_0_51,plain,
( v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ v15_lattices(X1)
| ~ v16_lattices(X1)
| ~ v12_lattices(X1)
| ~ r3_lattices(X1,X2,X3)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ v3_struct_0(k23_filter_2(X1,k22_filter_2(X1,X2,X3))) ),
inference(cn,[status(thm)],[c_0_48]) ).
cnf(c_0_52,negated_conjecture,
( v1_xboole_0(k22_filter_2(esk1_0,esk2_0,esk3_0))
| v3_struct_0(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0)))
| ~ v12_lattices(esk1_0) ),
inference(sr,[status(thm)],[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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_26]),c_0_27]),c_0_28]),c_0_29]),c_0_30]),c_0_20]),c_0_31])]),c_0_21]) ).
fof(c_0_53,plain,
! [X1] :
( l3_lattices(X1)
=> ( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v11_lattices(X1) )
=> ( ~ v3_struct_0(X1)
& v4_lattices(X1)
& v5_lattices(X1)
& v6_lattices(X1)
& v7_lattices(X1)
& v8_lattices(X1)
& v9_lattices(X1)
& v10_lattices(X1)
& v12_lattices(X1) ) ) ),
inference(fof_simplification,[status(thm)],[cc7_lattices]) ).
cnf(c_0_54,plain,
( v3_struct_0(X1)
| ~ v1_xboole_0(k22_filter_2(X1,X2,X3))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_55,negated_conjecture,
( v1_xboole_0(k22_filter_2(esk1_0,esk2_0,esk3_0))
| ~ v12_lattices(esk1_0) ),
inference(sr,[status(thm)],[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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_26]),c_0_27]),c_0_28]),c_0_29]),c_0_30]),c_0_20]),c_0_31])]),c_0_21]) ).
fof(c_0_56,plain,
! [X153] :
( ( ~ v3_struct_0(X153)
| v3_struct_0(X153)
| ~ v10_lattices(X153)
| ~ v11_lattices(X153)
| ~ l3_lattices(X153) )
& ( v4_lattices(X153)
| v3_struct_0(X153)
| ~ v10_lattices(X153)
| ~ v11_lattices(X153)
| ~ l3_lattices(X153) )
& ( v5_lattices(X153)
| v3_struct_0(X153)
| ~ v10_lattices(X153)
| ~ v11_lattices(X153)
| ~ l3_lattices(X153) )
& ( v6_lattices(X153)
| v3_struct_0(X153)
| ~ v10_lattices(X153)
| ~ v11_lattices(X153)
| ~ l3_lattices(X153) )
& ( v7_lattices(X153)
| v3_struct_0(X153)
| ~ v10_lattices(X153)
| ~ v11_lattices(X153)
| ~ l3_lattices(X153) )
& ( v8_lattices(X153)
| v3_struct_0(X153)
| ~ v10_lattices(X153)
| ~ v11_lattices(X153)
| ~ l3_lattices(X153) )
& ( v9_lattices(X153)
| v3_struct_0(X153)
| ~ v10_lattices(X153)
| ~ v11_lattices(X153)
| ~ l3_lattices(X153) )
& ( v10_lattices(X153)
| v3_struct_0(X153)
| ~ v10_lattices(X153)
| ~ v11_lattices(X153)
| ~ l3_lattices(X153) )
& ( v12_lattices(X153)
| v3_struct_0(X153)
| ~ v10_lattices(X153)
| ~ v11_lattices(X153)
| ~ l3_lattices(X153) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_53])])]) ).
cnf(c_0_57,negated_conjecture,
~ v12_lattices(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_29]),c_0_30]),c_0_20]),c_0_31])]),c_0_21]) ).
cnf(c_0_58,plain,
( v12_lattices(X1)
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ v11_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_59,negated_conjecture,
$false,
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_57,c_0_58]),c_0_36]),c_0_20]),c_0_31])]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT337+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
% 0.15/0.33 % Computer : n001.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 21:25:33 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.29/1.75 % Version : CSE_E---1.7
% 1.29/1.75 % Problem : theBenchmark.p
% 1.29/1.75 % SZS status Theorem for theBenchmark.p
% 1.29/1.75 % SZS output start CNFRefutation
% See solution above
% 1.29/1.75 % Total time : 1.371s
%------------------------------------------------------------------------------