%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT337+2 : 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 : 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 51.13s 30.56s
% Output : CNFRefutation 51.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 75 ( 22 unt; 0 def)
% Number of atoms : 624 ( 6 equ)
% Maximal formula atoms : 65 ( 8 avg)
% Number of connectives : 850 ( 301 ~; 310 |; 187 &)
% ( 0 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 98 ( 0 sgn 66 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/theBenchmark.p',dt_k22_filter_2) ).
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/sandbox2/benchmark/theBenchmark.p',t87_filter_2) ).
fof(fc5_filter_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) )
=> ( ~ v3_struct_0(k23_filter_2(X1,X2))
& v3_lattices(k23_filter_2(X1,X2))
& v4_lattices(k23_filter_2(X1,X2))
& v5_lattices(k23_filter_2(X1,X2))
& v6_lattices(k23_filter_2(X1,X2))
& v7_lattices(k23_filter_2(X1,X2))
& v8_lattices(k23_filter_2(X1,X2))
& v9_lattices(k23_filter_2(X1,X2))
& v10_lattices(k23_filter_2(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_filter_2) ).
fof(dt_k23_filter_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) )
=> m2_nat_lat(k23_filter_2(X1,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k23_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/sandbox2/benchmark/Axioms/SET007/SET007+205.ax',cc5_lattices) ).
fof(dt_m2_nat_lat,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_nat_lat(X2,X1)
=> ( ~ v3_struct_0(X2)
& v10_lattices(X2)
& l3_lattices(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+297.ax',dt_m2_nat_lat) ).
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/sandbox2/benchmark/theBenchmark.p',t78_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/sandbox2/benchmark/Axioms/SET007/SET007+205.ax',cc6_lattices) ).
fof(t84_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))
=> ( r3_lattices(X1,X2,X3)
=> ( v15_lattices(k23_filter_2(X1,k22_filter_2(X1,X2,X3)))
& k6_lattices(k23_filter_2(X1,k22_filter_2(X1,X2,X3))) = X3
& k5_lattices(k23_filter_2(X1,k22_filter_2(X1,X2,X3))) = X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_filter_2) ).
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/sandbox2/benchmark/theBenchmark.p',t86_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/sandbox2/benchmark/Axioms/SET007/SET007+205.ax',cc7_lattices) ).
fof(c_0_11,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]) ).
fof(c_0_12,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_13,plain,
! [X6489,X6490,X6491] :
( ( ~ v1_xboole_0(k22_filter_2(X6489,X6490,X6491))
| v3_struct_0(X6489)
| ~ v10_lattices(X6489)
| ~ l3_lattices(X6489)
| ~ m1_subset_1(X6490,u1_struct_0(X6489))
| ~ m1_subset_1(X6491,u1_struct_0(X6489)) )
& ( m2_lattice4(k22_filter_2(X6489,X6490,X6491),X6489)
| v3_struct_0(X6489)
| ~ v10_lattices(X6489)
| ~ l3_lattices(X6489)
| ~ m1_subset_1(X6490,u1_struct_0(X6489))
| ~ m1_subset_1(X6491,u1_struct_0(X6489)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_14,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_12])])]) ).
fof(c_0_15,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) )
=> ( ~ v3_struct_0(k23_filter_2(X1,X2))
& v3_lattices(k23_filter_2(X1,X2))
& v4_lattices(k23_filter_2(X1,X2))
& v5_lattices(k23_filter_2(X1,X2))
& v6_lattices(k23_filter_2(X1,X2))
& v7_lattices(k23_filter_2(X1,X2))
& v8_lattices(k23_filter_2(X1,X2))
& v9_lattices(k23_filter_2(X1,X2))
& v10_lattices(k23_filter_2(X1,X2)) ) ),
inference(fof_simplification,[status(thm)],[fc5_filter_2]) ).
cnf(c_0_16,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_13]) ).
cnf(c_0_17,negated_conjecture,
m1_subset_1(esk3_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,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_13]) ).
fof(c_0_22,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) )
=> m2_nat_lat(k23_filter_2(X1,X2),X1) ),
inference(fof_simplification,[status(thm)],[dt_k23_filter_2]) ).
fof(c_0_23,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_24,plain,
! [X6446,X6447] :
( ( ~ v3_struct_0(k23_filter_2(X6446,X6447))
| v3_struct_0(X6446)
| ~ v10_lattices(X6446)
| ~ l3_lattices(X6446)
| v1_xboole_0(X6447)
| ~ m2_lattice4(X6447,X6446) )
& ( v3_lattices(k23_filter_2(X6446,X6447))
| v3_struct_0(X6446)
| ~ v10_lattices(X6446)
| ~ l3_lattices(X6446)
| v1_xboole_0(X6447)
| ~ m2_lattice4(X6447,X6446) )
& ( v4_lattices(k23_filter_2(X6446,X6447))
| v3_struct_0(X6446)
| ~ v10_lattices(X6446)
| ~ l3_lattices(X6446)
| v1_xboole_0(X6447)
| ~ m2_lattice4(X6447,X6446) )
& ( v5_lattices(k23_filter_2(X6446,X6447))
| v3_struct_0(X6446)
| ~ v10_lattices(X6446)
| ~ l3_lattices(X6446)
| v1_xboole_0(X6447)
| ~ m2_lattice4(X6447,X6446) )
& ( v6_lattices(k23_filter_2(X6446,X6447))
| v3_struct_0(X6446)
| ~ v10_lattices(X6446)
| ~ l3_lattices(X6446)
| v1_xboole_0(X6447)
| ~ m2_lattice4(X6447,X6446) )
& ( v7_lattices(k23_filter_2(X6446,X6447))
| v3_struct_0(X6446)
| ~ v10_lattices(X6446)
| ~ l3_lattices(X6446)
| v1_xboole_0(X6447)
| ~ m2_lattice4(X6447,X6446) )
& ( v8_lattices(k23_filter_2(X6446,X6447))
| v3_struct_0(X6446)
| ~ v10_lattices(X6446)
| ~ l3_lattices(X6446)
| v1_xboole_0(X6447)
| ~ m2_lattice4(X6447,X6446) )
& ( v9_lattices(k23_filter_2(X6446,X6447))
| v3_struct_0(X6446)
| ~ v10_lattices(X6446)
| ~ l3_lattices(X6446)
| v1_xboole_0(X6447)
| ~ m2_lattice4(X6447,X6446) )
& ( v10_lattices(k23_filter_2(X6446,X6447))
| v3_struct_0(X6446)
| ~ v10_lattices(X6446)
| ~ l3_lattices(X6446)
| v1_xboole_0(X6447)
| ~ m2_lattice4(X6447,X6446) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
cnf(c_0_25,negated_conjecture,
( m2_lattice4(k22_filter_2(esk1_0,X1,esk3_0),esk1_0)
| ~ m1_subset_1(X1,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_16,c_0_17]),c_0_18]),c_0_19])]),c_0_20]) ).
cnf(c_0_26,negated_conjecture,
m1_subset_1(esk2_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_27,negated_conjecture,
( ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ v1_xboole_0(k22_filter_2(esk1_0,X1,esk3_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_17]),c_0_18]),c_0_19])]),c_0_20]) ).
fof(c_0_28,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_nat_lat(X2,X1)
=> ( ~ v3_struct_0(X2)
& v10_lattices(X2)
& l3_lattices(X2) ) ) ),
inference(fof_simplification,[status(thm)],[dt_m2_nat_lat]) ).
fof(c_0_29,plain,
! [X6437,X6438] :
( v3_struct_0(X6437)
| ~ v10_lattices(X6437)
| ~ l3_lattices(X6437)
| v1_xboole_0(X6438)
| ~ m2_lattice4(X6438,X6437)
| m2_nat_lat(k23_filter_2(X6437,X6438),X6437) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])]) ).
fof(c_0_30,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]) ).
fof(c_0_31,plain,
! [X6505] :
( ( ~ v3_struct_0(X6505)
| v3_struct_0(X6505)
| ~ v17_lattices(X6505)
| ~ l3_lattices(X6505) )
& ( v11_lattices(X6505)
| v3_struct_0(X6505)
| ~ v17_lattices(X6505)
| ~ l3_lattices(X6505) )
& ( v13_lattices(X6505)
| v3_struct_0(X6505)
| ~ v17_lattices(X6505)
| ~ l3_lattices(X6505) )
& ( v14_lattices(X6505)
| v3_struct_0(X6505)
| ~ v17_lattices(X6505)
| ~ l3_lattices(X6505) )
& ( v15_lattices(X6505)
| v3_struct_0(X6505)
| ~ v17_lattices(X6505)
| ~ l3_lattices(X6505) )
& ( v16_lattices(X6505)
| v3_struct_0(X6505)
| ~ v17_lattices(X6505)
| ~ l3_lattices(X6505) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])]) ).
cnf(c_0_32,plain,
( v10_lattices(k23_filter_2(X1,X2))
| v3_struct_0(X1)
| v1_xboole_0(X2)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m2_lattice4(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,negated_conjecture,
m2_lattice4(k22_filter_2(esk1_0,esk2_0,esk3_0),esk1_0),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_34,negated_conjecture,
~ v1_xboole_0(k22_filter_2(esk1_0,esk2_0,esk3_0)),
inference(spm,[status(thm)],[c_0_27,c_0_26]) ).
cnf(c_0_35,plain,
( v3_struct_0(X1)
| v1_xboole_0(X2)
| ~ v3_struct_0(k23_filter_2(X1,X2))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m2_lattice4(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_36,plain,
! [X6792,X6793] :
( ( ~ v3_struct_0(X6793)
| ~ m2_nat_lat(X6793,X6792)
| v3_struct_0(X6792)
| ~ v10_lattices(X6792)
| ~ l3_lattices(X6792) )
& ( v10_lattices(X6793)
| ~ m2_nat_lat(X6793,X6792)
| v3_struct_0(X6792)
| ~ v10_lattices(X6792)
| ~ l3_lattices(X6792) )
& ( l3_lattices(X6793)
| ~ m2_nat_lat(X6793,X6792)
| v3_struct_0(X6792)
| ~ v10_lattices(X6792)
| ~ l3_lattices(X6792) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])])]) ).
cnf(c_0_37,plain,
( v3_struct_0(X1)
| v1_xboole_0(X2)
| m2_nat_lat(k23_filter_2(X1,X2),X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m2_lattice4(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_38,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_39,plain,
! [X6468,X6469] :
( v3_struct_0(X6468)
| ~ v10_lattices(X6468)
| ~ l3_lattices(X6468)
| v1_xboole_0(X6469)
| ~ m2_lattice4(X6469,X6468)
| ~ v11_lattices(X6468)
| v11_lattices(k23_filter_2(X6468,X6469)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])]) ).
cnf(c_0_40,plain,
( v11_lattices(X1)
| v3_struct_0(X1)
| ~ v17_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_41,negated_conjecture,
v17_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_42,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_14]) ).
cnf(c_0_43,negated_conjecture,
v10_lattices(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_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_32,c_0_33]),c_0_18]),c_0_19])]),c_0_20]),c_0_34]) ).
cnf(c_0_44,negated_conjecture,
~ v3_struct_0(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_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_35,c_0_33]),c_0_18]),c_0_19])]),c_0_20]),c_0_34]) ).
cnf(c_0_45,plain,
( l3_lattices(X1)
| v3_struct_0(X2)
| ~ m2_nat_lat(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_46,negated_conjecture,
m2_nat_lat(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0)),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_37,c_0_33]),c_0_18]),c_0_19])]),c_0_20]),c_0_34]) ).
fof(c_0_47,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))
=> ( r3_lattices(X1,X2,X3)
=> ( v15_lattices(k23_filter_2(X1,k22_filter_2(X1,X2,X3)))
& k6_lattices(k23_filter_2(X1,k22_filter_2(X1,X2,X3))) = X3
& k5_lattices(k23_filter_2(X1,k22_filter_2(X1,X2,X3))) = X2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[t84_filter_2]) ).
fof(c_0_48,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_49,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]) ).
fof(c_0_50,plain,
! [X6506] :
( ( ~ v3_struct_0(X6506)
| v3_struct_0(X6506)
| ~ v11_lattices(X6506)
| ~ v15_lattices(X6506)
| ~ v16_lattices(X6506)
| ~ l3_lattices(X6506) )
& ( v17_lattices(X6506)
| v3_struct_0(X6506)
| ~ v11_lattices(X6506)
| ~ v15_lattices(X6506)
| ~ v16_lattices(X6506)
| ~ l3_lattices(X6506) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])]) ).
cnf(c_0_51,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_39]) ).
cnf(c_0_52,negated_conjecture,
v11_lattices(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_19]),c_0_41])]),c_0_20]) ).
cnf(c_0_53,negated_conjecture,
( ~ 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(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]),c_0_44]) ).
cnf(c_0_54,negated_conjecture,
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(spm,[status(thm)],[c_0_45,c_0_46]),c_0_18]),c_0_19])]),c_0_20]) ).
fof(c_0_55,plain,
! [X6481,X6482,X6483] :
( ( v15_lattices(k23_filter_2(X6481,k22_filter_2(X6481,X6482,X6483)))
| ~ r3_lattices(X6481,X6482,X6483)
| ~ m1_subset_1(X6483,u1_struct_0(X6481))
| ~ m1_subset_1(X6482,u1_struct_0(X6481))
| v3_struct_0(X6481)
| ~ v10_lattices(X6481)
| ~ l3_lattices(X6481) )
& ( k6_lattices(k23_filter_2(X6481,k22_filter_2(X6481,X6482,X6483))) = X6483
| ~ r3_lattices(X6481,X6482,X6483)
| ~ m1_subset_1(X6483,u1_struct_0(X6481))
| ~ m1_subset_1(X6482,u1_struct_0(X6481))
| v3_struct_0(X6481)
| ~ v10_lattices(X6481)
| ~ l3_lattices(X6481) )
& ( k5_lattices(k23_filter_2(X6481,k22_filter_2(X6481,X6482,X6483))) = X6482
| ~ r3_lattices(X6481,X6482,X6483)
| ~ m1_subset_1(X6483,u1_struct_0(X6481))
| ~ m1_subset_1(X6482,u1_struct_0(X6481))
| v3_struct_0(X6481)
| ~ v10_lattices(X6481)
| ~ l3_lattices(X6481) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])])])]) ).
fof(c_0_56,plain,
! [X6486,X6487,X6488] :
( ( ~ v3_struct_0(k23_filter_2(X6486,k22_filter_2(X6486,X6487,X6488)))
| v3_struct_0(X6486)
| ~ v10_lattices(X6486)
| ~ v15_lattices(X6486)
| ~ v16_lattices(X6486)
| ~ l3_lattices(X6486)
| ~ v12_lattices(X6486)
| ~ r3_lattices(X6486,X6487,X6488)
| ~ m1_subset_1(X6488,u1_struct_0(X6486))
| ~ m1_subset_1(X6487,u1_struct_0(X6486))
| v3_struct_0(X6486)
| ~ v10_lattices(X6486)
| ~ l3_lattices(X6486) )
& ( v10_lattices(k23_filter_2(X6486,k22_filter_2(X6486,X6487,X6488)))
| v3_struct_0(X6486)
| ~ v10_lattices(X6486)
| ~ v15_lattices(X6486)
| ~ v16_lattices(X6486)
| ~ l3_lattices(X6486)
| ~ v12_lattices(X6486)
| ~ r3_lattices(X6486,X6487,X6488)
| ~ m1_subset_1(X6488,u1_struct_0(X6486))
| ~ m1_subset_1(X6487,u1_struct_0(X6486))
| v3_struct_0(X6486)
| ~ v10_lattices(X6486)
| ~ l3_lattices(X6486) )
& ( v15_lattices(k23_filter_2(X6486,k22_filter_2(X6486,X6487,X6488)))
| v3_struct_0(X6486)
| ~ v10_lattices(X6486)
| ~ v15_lattices(X6486)
| ~ v16_lattices(X6486)
| ~ l3_lattices(X6486)
| ~ v12_lattices(X6486)
| ~ r3_lattices(X6486,X6487,X6488)
| ~ m1_subset_1(X6488,u1_struct_0(X6486))
| ~ m1_subset_1(X6487,u1_struct_0(X6486))
| v3_struct_0(X6486)
| ~ v10_lattices(X6486)
| ~ l3_lattices(X6486) )
& ( v16_lattices(k23_filter_2(X6486,k22_filter_2(X6486,X6487,X6488)))
| v3_struct_0(X6486)
| ~ v10_lattices(X6486)
| ~ v15_lattices(X6486)
| ~ v16_lattices(X6486)
| ~ l3_lattices(X6486)
| ~ v12_lattices(X6486)
| ~ r3_lattices(X6486,X6487,X6488)
| ~ m1_subset_1(X6488,u1_struct_0(X6486))
| ~ m1_subset_1(X6487,u1_struct_0(X6486))
| v3_struct_0(X6486)
| ~ v10_lattices(X6486)
| ~ l3_lattices(X6486) )
& ( l3_lattices(k23_filter_2(X6486,k22_filter_2(X6486,X6487,X6488)))
| v3_struct_0(X6486)
| ~ v10_lattices(X6486)
| ~ v15_lattices(X6486)
| ~ v16_lattices(X6486)
| ~ l3_lattices(X6486)
| ~ v12_lattices(X6486)
| ~ r3_lattices(X6486,X6487,X6488)
| ~ m1_subset_1(X6488,u1_struct_0(X6486))
| ~ m1_subset_1(X6487,u1_struct_0(X6486))
| v3_struct_0(X6486)
| ~ v10_lattices(X6486)
| ~ l3_lattices(X6486) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_48])])])]) ).
fof(c_0_57,plain,
! [X7543] :
( ( ~ v3_struct_0(X7543)
| v3_struct_0(X7543)
| ~ v10_lattices(X7543)
| ~ v11_lattices(X7543)
| ~ l3_lattices(X7543) )
& ( v4_lattices(X7543)
| v3_struct_0(X7543)
| ~ v10_lattices(X7543)
| ~ v11_lattices(X7543)
| ~ l3_lattices(X7543) )
& ( v5_lattices(X7543)
| v3_struct_0(X7543)
| ~ v10_lattices(X7543)
| ~ v11_lattices(X7543)
| ~ l3_lattices(X7543) )
& ( v6_lattices(X7543)
| v3_struct_0(X7543)
| ~ v10_lattices(X7543)
| ~ v11_lattices(X7543)
| ~ l3_lattices(X7543) )
& ( v7_lattices(X7543)
| v3_struct_0(X7543)
| ~ v10_lattices(X7543)
| ~ v11_lattices(X7543)
| ~ l3_lattices(X7543) )
& ( v8_lattices(X7543)
| v3_struct_0(X7543)
| ~ v10_lattices(X7543)
| ~ v11_lattices(X7543)
| ~ l3_lattices(X7543) )
& ( v9_lattices(X7543)
| v3_struct_0(X7543)
| ~ v10_lattices(X7543)
| ~ v11_lattices(X7543)
| ~ l3_lattices(X7543) )
& ( v10_lattices(X7543)
| v3_struct_0(X7543)
| ~ v10_lattices(X7543)
| ~ v11_lattices(X7543)
| ~ l3_lattices(X7543) )
& ( v12_lattices(X7543)
| v3_struct_0(X7543)
| ~ v10_lattices(X7543)
| ~ v11_lattices(X7543)
| ~ l3_lattices(X7543) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])]) ).
cnf(c_0_58,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_50]) ).
cnf(c_0_59,negated_conjecture,
v11_lattices(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0))),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_33]),c_0_52]),c_0_18]),c_0_19])]),c_0_20]),c_0_34]) ).
cnf(c_0_60,negated_conjecture,
~ v17_lattices(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_54])]) ).
cnf(c_0_61,plain,
( v15_lattices(k23_filter_2(X1,k22_filter_2(X1,X2,X3)))
| v3_struct_0(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_55]) ).
cnf(c_0_62,negated_conjecture,
r3_lattices(esk1_0,esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_63,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_56]) ).
cnf(c_0_64,plain,
( v16_lattices(X1)
| v3_struct_0(X1)
| ~ v17_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_65,plain,
( v15_lattices(X1)
| v3_struct_0(X1)
| ~ v17_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_66,plain,
( v12_lattices(X1)
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ v11_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_67,negated_conjecture,
( ~ v16_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))) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_54]),c_0_59])]),c_0_44]),c_0_60]) ).
cnf(c_0_68,negated_conjecture,
v15_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_61,c_0_62]),c_0_18]),c_0_19]),c_0_17]),c_0_26])]),c_0_20]) ).
cnf(c_0_69,plain,
( v3_struct_0(X1)
| v16_lattices(k23_filter_2(X1,k22_filter_2(X1,X2,X3)))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ v12_lattices(X1)
| ~ v15_lattices(X1)
| ~ v16_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_63]) ).
cnf(c_0_70,negated_conjecture,
v16_lattices(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_19]),c_0_41])]),c_0_20]) ).
cnf(c_0_71,negated_conjecture,
v15_lattices(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_19]),c_0_41])]),c_0_20]) ).
cnf(c_0_72,negated_conjecture,
v12_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_66,c_0_19]),c_0_52]),c_0_18])]),c_0_20]) ).
cnf(c_0_73,negated_conjecture,
~ v16_lattices(k23_filter_2(esk1_0,k22_filter_2(esk1_0,esk2_0,esk3_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68])]) ).
cnf(c_0_74,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_62]),c_0_70]),c_0_71]),c_0_72]),c_0_18]),c_0_19]),c_0_17]),c_0_26])]),c_0_73]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT337+2 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.12 % 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
% 0.14/0.33 % Computer : n001.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 21:25:34 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 51.13/30.56 % Version : CSE_E---1.7
% 51.13/30.56 % Problem : theBenchmark.p
% 51.13/30.56 % SZS status Theorem for theBenchmark.p
% 51.13/30.56 % SZS output start CNFRefutation
% See solution above
% 51.33/30.73 % Total time : 23.318s
%------------------------------------------------------------------------------