%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT312+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 : n015.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 04:38:03 PM UTC 2026
% Result : Theorem 19.01s 11.71s
% Output : CNFRefutation 19.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 28
% Syntax : Number of formulae : 176 ( 46 unt; 0 def)
% Number of atoms : 733 ( 89 equ)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 850 ( 293 ~; 304 |; 171 &)
% ( 2 <=>; 80 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 3 con; 0-2 aty)
% Number of variables : 230 ( 3 sgn 155 !; 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(t41_filter_2,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( ( ~ v1_xboole_0(X3)
& m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1))) )
=> ( r1_filter_2(u1_struct_0(X1),X3,k6_domain_1(u1_struct_0(X1),X2))
=> r1_filter_2(u1_struct_0(X1),k19_filter_2(X1,X3),k18_filter_2(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_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(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/sandbox2/benchmark/theBenchmark.p',dt_m2_lattice4) ).
fof(d6_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> k7_filter_2(X1,X2) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_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(rc1_subset_1,axiom,
! [X1] :
( ~ v1_xboole_0(X1)
=> ? [X2] :
( m1_subset_1(X2,k1_zfmisc_1(X1))
& ~ v1_xboole_0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(dt_k7_filter_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
=> m1_subset_1(k7_filter_2(X1,X2),k1_zfmisc_1(u1_struct_0(k1_lattice2(X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_filter_2) ).
fof(dt_k6_domain_1,axiom,
! [X1,X2] :
( ( ~ v1_xboole_0(X1)
& m1_subset_1(X2,X1) )
=> m1_subset_1(k6_domain_1(X1,X2),k1_zfmisc_1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_domain_1) ).
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/sandbox2/benchmark/theBenchmark.p',d4_filter_2) ).
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/sandbox2/benchmark/theBenchmark.p',dt_k5_filter_2) ).
fof(redefinition_r1_filter_2,axiom,
! [X1,X2,X3] :
( ( ~ v1_xboole_0(X1)
& m1_subset_1(X2,k1_zfmisc_1(X1))
& m1_subset_1(X3,k1_zfmisc_1(X1)) )
=> ( r1_filter_2(X1,X2,X3)
<=> X2 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_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(d7_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k1_lattice2(X1))))
=> k8_filter_2(X1,X2) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_filter_2) ).
fof(fc1_filter_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& ~ v1_xboole_0(X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
=> ~ v1_xboole_0(k7_filter_2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_filter_2) ).
fof(d9_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> k18_filter_2(X1,X2) = a_2_0_filter_2(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_filter_2) ).
fof(redefinition_k3_filter_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& ~ v1_xboole_0(X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
=> k3_filter_2(X1,X2) = k3_filter_0(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_filter_2) ).
fof(t37_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( ( ~ v1_xboole_0(X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
=> ! [X3] :
( ( ~ v1_xboole_0(X3)
& m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(k1_lattice2(X1)))) )
=> ( k3_filter_2(k1_lattice2(X1),k7_filter_2(X1,X2)) = k19_filter_2(X1,X2)
& k3_filter_2(X1,X2) = k19_filter_2(k1_lattice2(X1),k7_filter_2(X1,X2))
& k3_filter_2(X1,k8_filter_2(X1,X3)) = k19_filter_2(k1_lattice2(X1),X3)
& k3_filter_2(k1_lattice2(X1),X3) = k19_filter_2(X1,k8_filter_2(X1,X3)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_filter_2) ).
fof(dt_k8_filter_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k1_lattice2(X1)))) )
=> m1_subset_1(k8_filter_2(X1,X2),k1_zfmisc_1(u1_struct_0(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_filter_2) ).
fof(t30_filter_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( ( ~ v1_xboole_0(X3)
& m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1))) )
=> ( X3 = k6_domain_1(u1_struct_0(X1),X2)
=> k3_filter_0(X1,X3) = k2_filter_0(X1,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_filter_0) ).
fof(dt_k19_filter_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& ~ v1_xboole_0(X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
=> m2_filter_2(k19_filter_2(X1,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k19_filter_2) ).
fof(t30_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ( k18_filter_2(X1,X2) = k2_filter_2(k1_lattice2(X1),k5_filter_2(X1,X2))
& k18_filter_2(k1_lattice2(X1),k5_filter_2(X1,X2)) = k2_filter_2(X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_filter_2) ).
fof(redefinition_k2_filter_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1)) )
=> k2_filter_2(X1,X2) = k2_filter_0(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_filter_2) ).
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(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_28,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_29,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( ( ~ v1_xboole_0(X3)
& m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1))) )
=> ( r1_filter_2(u1_struct_0(X1),X3,k6_domain_1(u1_struct_0(X1),X2))
=> r1_filter_2(u1_struct_0(X1),k19_filter_2(X1,X3),k18_filter_2(X1,X2)) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t41_filter_2])]) ).
fof(c_0_30,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_31,plain,
! [X278] :
( v3_struct_0(X278)
| ~ v10_lattices(X278)
| ~ l3_lattices(X278)
| m2_filter_2(esk12_1(X278),X278) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])]) ).
fof(c_0_32,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))
& ~ v1_xboole_0(esk3_0)
& m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk1_0)))
& r1_filter_2(u1_struct_0(esk1_0),esk3_0,k6_domain_1(u1_struct_0(esk1_0),esk2_0))
& ~ r1_filter_2(u1_struct_0(esk1_0),k19_filter_2(esk1_0,esk3_0),k18_filter_2(esk1_0,esk2_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])]) ).
fof(c_0_33,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_34,plain,
! [X256,X257] :
( ( ~ v1_xboole_0(X257)
| ~ m2_filter_2(X257,X256)
| v3_struct_0(X256)
| ~ v10_lattices(X256)
| ~ l3_lattices(X256) )
& ( m2_lattice4(X257,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_30])])])]) ).
cnf(c_0_35,plain,
( v3_struct_0(X1)
| m2_filter_2(esk12_1(X1),X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_37,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_39,plain,
! [X258,X259] :
( v3_struct_0(X258)
| ~ v10_lattices(X258)
| ~ l3_lattices(X258)
| ~ m2_lattice4(X259,X258)
| m1_subset_1(X259,k1_zfmisc_1(u1_struct_0(X258))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])]) ).
cnf(c_0_40,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_34]) ).
cnf(c_0_41,negated_conjecture,
m2_filter_2(esk12_1(esk1_0),esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]),c_0_38]) ).
fof(c_0_42,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> k7_filter_2(X1,X2) = X2 ) ),
inference(fof_simplification,[status(thm)],[d6_filter_2]) ).
fof(c_0_43,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_44,plain,
! [X386,X387,X388] :
( ~ r2_hidden(X386,X387)
| ~ m1_subset_1(X387,k1_zfmisc_1(X388))
| ~ v1_xboole_0(X388) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
cnf(c_0_45,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_39]) ).
cnf(c_0_46,negated_conjecture,
m2_lattice4(esk12_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_40,c_0_41]),c_0_36]),c_0_37])]),c_0_38]) ).
fof(c_0_47,plain,
! [X368,X369] :
( ~ m1_subset_1(X368,X369)
| v1_xboole_0(X369)
| r2_hidden(X368,X369) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(c_0_48,plain,
! [X276] : m1_subset_1(esk11_1(X276),X276),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(c_0_49,plain,
! [X1] :
( ~ v1_xboole_0(X1)
=> ? [X2] :
( m1_subset_1(X2,k1_zfmisc_1(X1))
& ~ v1_xboole_0(X2) ) ),
inference(fof_simplification,[status(thm)],[rc1_subset_1]) ).
fof(c_0_50,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
=> m1_subset_1(k7_filter_2(X1,X2),k1_zfmisc_1(u1_struct_0(k1_lattice2(X1)))) ),
inference(fof_simplification,[status(thm)],[dt_k7_filter_2]) ).
fof(c_0_51,plain,
! [X219,X220] :
( v3_struct_0(X219)
| ~ v10_lattices(X219)
| ~ l3_lattices(X219)
| ~ m1_subset_1(X220,k1_zfmisc_1(u1_struct_0(X219)))
| k7_filter_2(X219,X220) = X220 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])]) ).
fof(c_0_52,plain,
! [X1,X2] :
( ( ~ v1_xboole_0(X1)
& m1_subset_1(X2,X1) )
=> m1_subset_1(k6_domain_1(X1,X2),k1_zfmisc_1(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k6_domain_1]) ).
fof(c_0_53,plain,
! [X343,X344] :
( v1_xboole_0(X343)
| ~ m1_subset_1(X344,X343)
| k6_domain_1(X343,X344) = k1_tarski(X344) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])]) ).
cnf(c_0_54,plain,
( ~ r2_hidden(X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X3))
| ~ v1_xboole_0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_55,negated_conjecture,
m1_subset_1(esk12_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_45,c_0_46]),c_0_36]),c_0_37])]),c_0_38]) ).
cnf(c_0_56,plain,
( v1_xboole_0(X2)
| r2_hidden(X1,X2)
| ~ m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_57,plain,
m1_subset_1(esk11_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_58,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_34]) ).
fof(c_0_59,plain,
! [X324] :
( ( m1_subset_1(esk20_1(X324),k1_zfmisc_1(X324))
| v1_xboole_0(X324) )
& ( ~ v1_xboole_0(esk20_1(X324))
| v1_xboole_0(X324) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])])]) ).
fof(c_0_60,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_61,plain,
! [X245,X246] :
( v3_struct_0(X245)
| ~ v10_lattices(X245)
| ~ l3_lattices(X245)
| ~ m1_subset_1(X246,k1_zfmisc_1(u1_struct_0(X245)))
| m1_subset_1(k7_filter_2(X245,X246),k1_zfmisc_1(u1_struct_0(k1_lattice2(X245)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_50])]) ).
cnf(c_0_62,plain,
( v3_struct_0(X1)
| k7_filter_2(X1,X2) = X2
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
fof(c_0_63,plain,
! [X243,X244] :
( v1_xboole_0(X243)
| ~ m1_subset_1(X244,X243)
| m1_subset_1(k6_domain_1(X243,X244),k1_zfmisc_1(X243)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])]) ).
cnf(c_0_64,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_53]) ).
cnf(c_0_65,negated_conjecture,
m1_subset_1(esk2_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_66,negated_conjecture,
( ~ r2_hidden(X1,esk12_1(esk1_0))
| ~ v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_67,plain,
( r2_hidden(esk11_1(X1),X1)
| v1_xboole_0(X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_68,negated_conjecture,
~ v1_xboole_0(esk12_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_58,c_0_41]),c_0_36]),c_0_37])]),c_0_38]) ).
cnf(c_0_69,plain,
( m1_subset_1(esk20_1(X1),k1_zfmisc_1(X1))
| v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
fof(c_0_70,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_71,plain,
! [X217,X218] :
( v3_struct_0(X217)
| ~ v10_lattices(X217)
| ~ l3_lattices(X217)
| ~ m1_subset_1(X218,u1_struct_0(X217))
| k5_filter_2(X217,X218) = X218 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_60])])]) ).
cnf(c_0_72,plain,
( v3_struct_0(X1)
| m1_subset_1(k7_filter_2(X1,X2),k1_zfmisc_1(u1_struct_0(k1_lattice2(X1))))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_73,negated_conjecture,
k7_filter_2(esk1_0,esk12_1(esk1_0)) = esk12_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_62,c_0_55]),c_0_36]),c_0_37])]),c_0_38]) ).
fof(c_0_74,plain,
! [X1,X2,X3] :
( ( ~ v1_xboole_0(X1)
& m1_subset_1(X2,k1_zfmisc_1(X1))
& m1_subset_1(X3,k1_zfmisc_1(X1)) )
=> ( r1_filter_2(X1,X2,X3)
<=> X2 = X3 ) ),
inference(fof_simplification,[status(thm)],[redefinition_r1_filter_2]) ).
cnf(c_0_75,plain,
( v1_xboole_0(X1)
| m1_subset_1(k6_domain_1(X1,X2),k1_zfmisc_1(X1))
| ~ m1_subset_1(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_76,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_64,c_0_65]) ).
cnf(c_0_77,negated_conjecture,
~ v1_xboole_0(u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]) ).
fof(c_0_78,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_79,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k1_lattice2(X1))))
=> k8_filter_2(X1,X2) = X2 ) ),
inference(fof_simplification,[status(thm)],[d7_filter_2]) ).
cnf(c_0_80,negated_conjecture,
m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_81,plain,
( k7_filter_2(X1,esk20_1(u1_struct_0(X1))) = esk20_1(u1_struct_0(X1))
| v1_xboole_0(u1_struct_0(X1))
| v3_struct_0(X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_69]) ).
fof(c_0_82,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& ~ v1_xboole_0(X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
=> ~ v1_xboole_0(k7_filter_2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[fc1_filter_2]) ).
fof(c_0_83,plain,
! [X241,X242] :
( v3_struct_0(X241)
| ~ v10_lattices(X241)
| ~ l3_lattices(X241)
| ~ m1_subset_1(X242,u1_struct_0(X241))
| m1_subset_1(k5_filter_2(X241,X242),u1_struct_0(k1_lattice2(X241))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_70])]) ).
cnf(c_0_84,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_71]) ).
cnf(c_0_85,negated_conjecture,
m1_subset_1(esk12_1(esk1_0),k1_zfmisc_1(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_72,c_0_55]),c_0_73]),c_0_36]),c_0_37])]),c_0_38]) ).
fof(c_0_86,plain,
! [X350,X351,X352] :
( ( ~ r1_filter_2(X350,X351,X352)
| X351 = X352
| v1_xboole_0(X350)
| ~ m1_subset_1(X351,k1_zfmisc_1(X350))
| ~ m1_subset_1(X352,k1_zfmisc_1(X350)) )
& ( X351 != X352
| r1_filter_2(X350,X351,X352)
| v1_xboole_0(X350)
| ~ m1_subset_1(X351,k1_zfmisc_1(X350))
| ~ m1_subset_1(X352,k1_zfmisc_1(X350)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_74])])]) ).
cnf(c_0_87,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk1_0))
| m1_subset_1(k6_domain_1(u1_struct_0(esk1_0),esk2_0),k1_zfmisc_1(u1_struct_0(esk1_0))) ),
inference(spm,[status(thm)],[c_0_75,c_0_65]) ).
cnf(c_0_88,negated_conjecture,
k6_domain_1(u1_struct_0(esk1_0),esk2_0) = k1_tarski(esk2_0),
inference(sr,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_89,negated_conjecture,
r1_filter_2(u1_struct_0(esk1_0),esk3_0,k6_domain_1(u1_struct_0(esk1_0),esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_90,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> k18_filter_2(X1,X2) = a_2_0_filter_2(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[d9_filter_2]) ).
fof(c_0_91,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& ~ v1_xboole_0(X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
=> k3_filter_2(X1,X2) = k3_filter_0(X1,X2) ),
inference(fof_simplification,[status(thm)],[redefinition_k3_filter_2]) ).
fof(c_0_92,plain,
! [X303] :
( ( ~ v3_struct_0(k1_lattice2(X303))
| v3_struct_0(X303)
| ~ v10_lattices(X303)
| ~ l3_lattices(X303) )
& ( v3_lattices(k1_lattice2(X303))
| v3_struct_0(X303)
| ~ v10_lattices(X303)
| ~ l3_lattices(X303) )
& ( v4_lattices(k1_lattice2(X303))
| v3_struct_0(X303)
| ~ v10_lattices(X303)
| ~ l3_lattices(X303) )
& ( v5_lattices(k1_lattice2(X303))
| v3_struct_0(X303)
| ~ v10_lattices(X303)
| ~ l3_lattices(X303) )
& ( v6_lattices(k1_lattice2(X303))
| v3_struct_0(X303)
| ~ v10_lattices(X303)
| ~ l3_lattices(X303) )
& ( v7_lattices(k1_lattice2(X303))
| v3_struct_0(X303)
| ~ v10_lattices(X303)
| ~ l3_lattices(X303) )
& ( v8_lattices(k1_lattice2(X303))
| v3_struct_0(X303)
| ~ v10_lattices(X303)
| ~ l3_lattices(X303) )
& ( v9_lattices(k1_lattice2(X303))
| v3_struct_0(X303)
| ~ v10_lattices(X303)
| ~ l3_lattices(X303) )
& ( v10_lattices(k1_lattice2(X303))
| v3_struct_0(X303)
| ~ v10_lattices(X303)
| ~ l3_lattices(X303) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_78])])]) ).
fof(c_0_93,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( ( ~ v1_xboole_0(X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
=> ! [X3] :
( ( ~ v1_xboole_0(X3)
& m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(k1_lattice2(X1)))) )
=> ( k3_filter_2(k1_lattice2(X1),k7_filter_2(X1,X2)) = k19_filter_2(X1,X2)
& k3_filter_2(X1,X2) = k19_filter_2(k1_lattice2(X1),k7_filter_2(X1,X2))
& k3_filter_2(X1,k8_filter_2(X1,X3)) = k19_filter_2(k1_lattice2(X1),X3)
& k3_filter_2(k1_lattice2(X1),X3) = k19_filter_2(X1,k8_filter_2(X1,X3)) ) ) ) ),
inference(fof_simplification,[status(thm)],[t37_filter_2]) ).
fof(c_0_94,plain,
! [X221,X222] :
( v3_struct_0(X221)
| ~ v10_lattices(X221)
| ~ l3_lattices(X221)
| ~ m1_subset_1(X222,k1_zfmisc_1(u1_struct_0(k1_lattice2(X221))))
| k8_filter_2(X221,X222) = X222 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_79])])]) ).
cnf(c_0_95,negated_conjecture,
k7_filter_2(esk1_0,esk3_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_62,c_0_80]),c_0_36]),c_0_37])]),c_0_38]) ).
fof(c_0_96,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k1_lattice2(X1)))) )
=> m1_subset_1(k8_filter_2(X1,X2),k1_zfmisc_1(u1_struct_0(X1))) ),
inference(fof_simplification,[status(thm)],[dt_k8_filter_2]) ).
cnf(c_0_97,plain,
( v1_xboole_0(u1_struct_0(X1))
| m1_subset_1(k7_filter_2(X1,esk20_1(u1_struct_0(X1))),k1_zfmisc_1(u1_struct_0(k1_lattice2(X1))))
| v3_struct_0(X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(spm,[status(thm)],[c_0_72,c_0_69]) ).
cnf(c_0_98,negated_conjecture,
k7_filter_2(esk1_0,esk20_1(u1_struct_0(esk1_0))) = esk20_1(u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_36]),c_0_37])]),c_0_77]),c_0_38]) ).
fof(c_0_99,plain,
! [X285,X286] :
( v3_struct_0(X285)
| ~ v10_lattices(X285)
| ~ l3_lattices(X285)
| v1_xboole_0(X286)
| ~ m1_subset_1(X286,k1_zfmisc_1(u1_struct_0(X285)))
| ~ v1_xboole_0(k7_filter_2(X285,X286)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_82])]) ).
fof(c_0_100,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( ( ~ v1_xboole_0(X3)
& m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1))) )
=> ( X3 = k6_domain_1(u1_struct_0(X1),X2)
=> k3_filter_0(X1,X3) = k2_filter_0(X1,X2) ) ) ) ),
inference(fof_simplification,[status(thm)],[t30_filter_0]) ).
cnf(c_0_101,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_83]) ).
cnf(c_0_102,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_84,c_0_65]),c_0_36]),c_0_37])]),c_0_38]) ).
cnf(c_0_103,negated_conjecture,
( ~ r2_hidden(X1,esk12_1(esk1_0))
| ~ v1_xboole_0(u1_struct_0(k1_lattice2(esk1_0))) ),
inference(spm,[status(thm)],[c_0_54,c_0_85]) ).
cnf(c_0_104,plain,
( X2 = X3
| v1_xboole_0(X1)
| ~ r1_filter_2(X1,X2,X3)
| ~ m1_subset_1(X2,k1_zfmisc_1(X1))
| ~ m1_subset_1(X3,k1_zfmisc_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_105,negated_conjecture,
m1_subset_1(k1_tarski(esk2_0),k1_zfmisc_1(u1_struct_0(esk1_0))),
inference(rw,[status(thm)],[inference(sr,[status(thm)],[c_0_87,c_0_77]),c_0_88]) ).
cnf(c_0_106,negated_conjecture,
( r1_filter_2(u1_struct_0(esk1_0),esk3_0,k1_tarski(esk2_0))
| v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_89,c_0_76]) ).
fof(c_0_107,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& ~ v1_xboole_0(X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
=> m2_filter_2(k19_filter_2(X1,X2),X1) ),
inference(fof_simplification,[status(thm)],[dt_k19_filter_2]) ).
fof(c_0_108,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ( k18_filter_2(X1,X2) = k2_filter_2(k1_lattice2(X1),k5_filter_2(X1,X2))
& k18_filter_2(k1_lattice2(X1),k5_filter_2(X1,X2)) = k2_filter_2(X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[t30_filter_2]) ).
fof(c_0_109,plain,
! [X223,X224] :
( v3_struct_0(X223)
| ~ v10_lattices(X223)
| ~ l3_lattices(X223)
| ~ m1_subset_1(X224,u1_struct_0(X223))
| k18_filter_2(X223,X224) = a_2_0_filter_2(X223,X224) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_90])])]) ).
fof(c_0_110,plain,
! [X341,X342] :
( v3_struct_0(X341)
| ~ v10_lattices(X341)
| ~ l3_lattices(X341)
| v1_xboole_0(X342)
| ~ m1_subset_1(X342,k1_zfmisc_1(u1_struct_0(X341)))
| k3_filter_2(X341,X342) = k3_filter_0(X341,X342) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_91])]) ).
cnf(c_0_111,plain,
( v10_lattices(k1_lattice2(X1))
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
fof(c_0_112,plain,
! [X378,X379,X380] :
( ( k3_filter_2(k1_lattice2(X378),k7_filter_2(X378,X379)) = k19_filter_2(X378,X379)
| v1_xboole_0(X380)
| ~ m1_subset_1(X380,k1_zfmisc_1(u1_struct_0(k1_lattice2(X378))))
| v1_xboole_0(X379)
| ~ m1_subset_1(X379,k1_zfmisc_1(u1_struct_0(X378)))
| v3_struct_0(X378)
| ~ v10_lattices(X378)
| ~ l3_lattices(X378) )
& ( k3_filter_2(X378,X379) = k19_filter_2(k1_lattice2(X378),k7_filter_2(X378,X379))
| v1_xboole_0(X380)
| ~ m1_subset_1(X380,k1_zfmisc_1(u1_struct_0(k1_lattice2(X378))))
| v1_xboole_0(X379)
| ~ m1_subset_1(X379,k1_zfmisc_1(u1_struct_0(X378)))
| v3_struct_0(X378)
| ~ v10_lattices(X378)
| ~ l3_lattices(X378) )
& ( k3_filter_2(X378,k8_filter_2(X378,X380)) = k19_filter_2(k1_lattice2(X378),X380)
| v1_xboole_0(X380)
| ~ m1_subset_1(X380,k1_zfmisc_1(u1_struct_0(k1_lattice2(X378))))
| v1_xboole_0(X379)
| ~ m1_subset_1(X379,k1_zfmisc_1(u1_struct_0(X378)))
| v3_struct_0(X378)
| ~ v10_lattices(X378)
| ~ l3_lattices(X378) )
& ( k3_filter_2(k1_lattice2(X378),X380) = k19_filter_2(X378,k8_filter_2(X378,X380))
| v1_xboole_0(X380)
| ~ m1_subset_1(X380,k1_zfmisc_1(u1_struct_0(k1_lattice2(X378))))
| v1_xboole_0(X379)
| ~ m1_subset_1(X379,k1_zfmisc_1(u1_struct_0(X378)))
| v3_struct_0(X378)
| ~ v10_lattices(X378)
| ~ l3_lattices(X378) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_93])])])]) ).
cnf(c_0_113,plain,
( v3_struct_0(X1)
| k8_filter_2(X1,X2) = X2
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k1_lattice2(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_114,negated_conjecture,
m1_subset_1(esk3_0,k1_zfmisc_1(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_72,c_0_80]),c_0_95]),c_0_36]),c_0_37])]),c_0_38]) ).
fof(c_0_115,plain,
! [X247,X248] :
( v3_struct_0(X247)
| ~ v10_lattices(X247)
| ~ l3_lattices(X247)
| ~ m1_subset_1(X248,k1_zfmisc_1(u1_struct_0(k1_lattice2(X247))))
| m1_subset_1(k8_filter_2(X247,X248),k1_zfmisc_1(u1_struct_0(X247))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_96])]) ).
cnf(c_0_116,negated_conjecture,
m1_subset_1(esk20_1(u1_struct_0(esk1_0)),k1_zfmisc_1(u1_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_36]),c_0_98]),c_0_37])]),c_0_77]),c_0_38]) ).
cnf(c_0_117,plain,
( v3_struct_0(X1)
| v1_xboole_0(X2)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ v1_xboole_0(k7_filter_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_118,plain,
( v1_xboole_0(X1)
| ~ v1_xboole_0(esk20_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
fof(c_0_119,plain,
! [X373,X374,X375] :
( v3_struct_0(X373)
| ~ v10_lattices(X373)
| ~ l3_lattices(X373)
| ~ m1_subset_1(X374,u1_struct_0(X373))
| v1_xboole_0(X375)
| ~ m1_subset_1(X375,k1_zfmisc_1(u1_struct_0(X373)))
| X375 != k6_domain_1(u1_struct_0(X373),X374)
| k3_filter_0(X373,X375) = k2_filter_0(X373,X374) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_100])])]) ).
cnf(c_0_120,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_101,c_0_65]),c_0_102]),c_0_36]),c_0_37])]),c_0_38]) ).
cnf(c_0_121,negated_conjecture,
~ v1_xboole_0(u1_struct_0(k1_lattice2(esk1_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_67]),c_0_68]) ).
cnf(c_0_122,negated_conjecture,
( X1 = k1_tarski(esk2_0)
| ~ r1_filter_2(u1_struct_0(esk1_0),X1,k1_tarski(esk2_0))
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(esk1_0))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_77]) ).
cnf(c_0_123,negated_conjecture,
r1_filter_2(u1_struct_0(esk1_0),esk3_0,k1_tarski(esk2_0)),
inference(sr,[status(thm)],[c_0_106,c_0_77]) ).
fof(c_0_124,plain,
! [X230,X231] :
( v3_struct_0(X230)
| ~ v10_lattices(X230)
| ~ l3_lattices(X230)
| v1_xboole_0(X231)
| ~ m1_subset_1(X231,k1_zfmisc_1(u1_struct_0(X230)))
| m2_filter_2(k19_filter_2(X230,X231),X230) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_107])]) ).
fof(c_0_125,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1)) )
=> k2_filter_2(X1,X2) = k2_filter_0(X1,X2) ),
inference(fof_simplification,[status(thm)],[redefinition_k2_filter_2]) ).
fof(c_0_126,plain,
! [X376,X377] :
( ( k18_filter_2(X376,X377) = k2_filter_2(k1_lattice2(X376),k5_filter_2(X376,X377))
| ~ m1_subset_1(X377,u1_struct_0(X376))
| v3_struct_0(X376)
| ~ v10_lattices(X376)
| ~ l3_lattices(X376) )
& ( k18_filter_2(k1_lattice2(X376),k5_filter_2(X376,X377)) = k2_filter_2(X376,X377)
| ~ m1_subset_1(X377,u1_struct_0(X376))
| v3_struct_0(X376)
| ~ v10_lattices(X376)
| ~ l3_lattices(X376) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_108])])])]) ).
cnf(c_0_127,plain,
( v3_struct_0(X1)
| k18_filter_2(X1,X2) = a_2_0_filter_2(X1,X2)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_128,plain,
( v3_struct_0(X1)
| v1_xboole_0(X2)
| k3_filter_2(X1,X2) = k3_filter_0(X1,X2)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_129,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_111,c_0_36]),c_0_37])]),c_0_38]) ).
cnf(c_0_130,negated_conjecture,
~ v1_xboole_0(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_131,plain,
! [X232] :
( ( v3_lattices(k1_lattice2(X232))
| ~ l3_lattices(X232) )
& ( l3_lattices(k1_lattice2(X232))
| ~ l3_lattices(X232) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_lattice2])])]) ).
cnf(c_0_132,plain,
( k3_filter_2(k1_lattice2(X1),X2) = k19_filter_2(X1,k8_filter_2(X1,X2))
| v1_xboole_0(X2)
| v1_xboole_0(X3)
| v3_struct_0(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k1_lattice2(X1))))
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_133,negated_conjecture,
k8_filter_2(esk1_0,esk3_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_113,c_0_114]),c_0_36]),c_0_37])]),c_0_38]) ).
cnf(c_0_134,plain,
( v3_struct_0(X1)
| m1_subset_1(k8_filter_2(X1,X2),k1_zfmisc_1(u1_struct_0(X1)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k1_lattice2(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_135,negated_conjecture,
k8_filter_2(esk1_0,esk20_1(u1_struct_0(esk1_0))) = esk20_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_113,c_0_116]),c_0_36]),c_0_37])]),c_0_38]) ).
cnf(c_0_136,plain,
( v1_xboole_0(u1_struct_0(X1))
| v3_struct_0(X1)
| ~ v1_xboole_0(k7_filter_2(X1,esk20_1(u1_struct_0(X1))))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_69]),c_0_118]) ).
cnf(c_0_137,plain,
( v3_struct_0(X1)
| v1_xboole_0(X3)
| k3_filter_0(X1,X3) = k2_filter_0(X1,X2)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
| X3 != k6_domain_1(u1_struct_0(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_138,negated_conjecture,
k6_domain_1(u1_struct_0(k1_lattice2(esk1_0)),esk2_0) = k1_tarski(esk2_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_120]),c_0_121]) ).
cnf(c_0_139,negated_conjecture,
k1_tarski(esk2_0) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_80])]) ).
cnf(c_0_140,plain,
( v3_struct_0(X1)
| v1_xboole_0(X2)
| m2_filter_2(k19_filter_2(X1,X2),X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
fof(c_0_141,plain,
! [X339,X340] :
( v3_struct_0(X339)
| ~ v10_lattices(X339)
| ~ l3_lattices(X339)
| ~ m1_subset_1(X340,u1_struct_0(X339))
| k2_filter_2(X339,X340) = k2_filter_0(X339,X340) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_125])]) ).
cnf(c_0_142,plain,
( k18_filter_2(X1,X2) = k2_filter_2(k1_lattice2(X1),k5_filter_2(X1,X2))
| v3_struct_0(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_143,negated_conjecture,
k18_filter_2(esk1_0,esk2_0) = a_2_0_filter_2(esk1_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_127,c_0_65]),c_0_36]),c_0_37])]),c_0_38]) ).
cnf(c_0_144,negated_conjecture,
( k3_filter_0(k1_lattice2(esk1_0),esk3_0) = k3_filter_2(k1_lattice2(esk1_0),esk3_0)
| v3_struct_0(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_114]),c_0_129])]),c_0_130]) ).
cnf(c_0_145,plain,
( l3_lattices(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_131]) ).
cnf(c_0_146,negated_conjecture,
( k3_filter_2(k1_lattice2(esk1_0),esk3_0) = k19_filter_2(esk1_0,esk3_0)
| v1_xboole_0(X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(esk1_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_132,c_0_114]),c_0_133]),c_0_36]),c_0_37])]),c_0_130]),c_0_38]) ).
cnf(c_0_147,negated_conjecture,
m1_subset_1(esk20_1(u1_struct_0(esk1_0)),k1_zfmisc_1(u1_struct_0(esk1_0))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_116]),c_0_36]),c_0_37])]),c_0_38]) ).
cnf(c_0_148,negated_conjecture,
~ v1_xboole_0(esk20_1(u1_struct_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_136,c_0_98]),c_0_36]),c_0_37])]),c_0_77]),c_0_38]) ).
cnf(c_0_149,plain,
( k3_filter_0(X1,k6_domain_1(u1_struct_0(X1),X2)) = k2_filter_0(X1,X2)
| v1_xboole_0(k6_domain_1(u1_struct_0(X1),X2))
| v3_struct_0(X1)
| ~ m1_subset_1(k6_domain_1(u1_struct_0(X1),X2),k1_zfmisc_1(u1_struct_0(X1)))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(er,[status(thm)],[c_0_137]) ).
cnf(c_0_150,negated_conjecture,
k6_domain_1(u1_struct_0(k1_lattice2(esk1_0)),esk2_0) = esk3_0,
inference(rw,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_151,negated_conjecture,
m2_filter_2(k19_filter_2(esk1_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_140,c_0_80]),c_0_36]),c_0_37])]),c_0_130]),c_0_38]) ).
cnf(c_0_152,plain,
( v3_struct_0(X1)
| k2_filter_2(X1,X2) = k2_filter_0(X1,X2)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_141]) ).
cnf(c_0_153,negated_conjecture,
k2_filter_2(k1_lattice2(esk1_0),esk2_0) = a_2_0_filter_2(esk1_0,esk2_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_142,c_0_65]),c_0_102]),c_0_143]),c_0_36]),c_0_37])]),c_0_38]) ).
cnf(c_0_154,negated_conjecture,
( k3_filter_0(k1_lattice2(esk1_0),esk3_0) = k3_filter_2(k1_lattice2(esk1_0),esk3_0)
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_36])]) ).
cnf(c_0_155,negated_conjecture,
k3_filter_2(k1_lattice2(esk1_0),esk3_0) = k19_filter_2(esk1_0,esk3_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_148]) ).
cnf(c_0_156,negated_conjecture,
( k3_filter_0(k1_lattice2(esk1_0),esk3_0) = k2_filter_0(k1_lattice2(esk1_0),esk2_0)
| v3_struct_0(k1_lattice2(esk1_0))
| ~ l3_lattices(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_149,c_0_150]),c_0_114]),c_0_120]),c_0_129])]),c_0_130]) ).
cnf(c_0_157,plain,
( r1_filter_2(X3,X1,X2)
| v1_xboole_0(X3)
| X1 != X2
| ~ m1_subset_1(X1,k1_zfmisc_1(X3))
| ~ m1_subset_1(X2,k1_zfmisc_1(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_158,negated_conjecture,
m2_lattice4(k19_filter_2(esk1_0,esk3_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_40,c_0_151]),c_0_36]),c_0_37])]),c_0_38]) ).
cnf(c_0_159,negated_conjecture,
( k2_filter_0(k1_lattice2(esk1_0),esk2_0) = a_2_0_filter_2(esk1_0,esk2_0)
| v3_struct_0(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0)) ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_120]),c_0_129])]),c_0_153]) ).
cnf(c_0_160,negated_conjecture,
( k3_filter_0(k1_lattice2(esk1_0),esk3_0) = k19_filter_2(esk1_0,esk3_0)
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(rw,[status(thm)],[c_0_154,c_0_155]) ).
cnf(c_0_161,negated_conjecture,
( k3_filter_0(k1_lattice2(esk1_0),esk3_0) = k2_filter_0(k1_lattice2(esk1_0),esk2_0)
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_145]),c_0_36])]) ).
cnf(c_0_162,plain,
( r1_filter_2(X1,X2,X2)
| v1_xboole_0(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(X1)) ),
inference(er,[status(thm)],[c_0_157]) ).
cnf(c_0_163,negated_conjecture,
m1_subset_1(k19_filter_2(esk1_0,esk3_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_45,c_0_158]),c_0_36]),c_0_37])]),c_0_38]) ).
fof(c_0_164,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_165,negated_conjecture,
~ r1_filter_2(u1_struct_0(esk1_0),k19_filter_2(esk1_0,esk3_0),k18_filter_2(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_166,negated_conjecture,
( k2_filter_0(k1_lattice2(esk1_0),esk2_0) = a_2_0_filter_2(esk1_0,esk2_0)
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_145]),c_0_36])]) ).
cnf(c_0_167,negated_conjecture,
( k2_filter_0(k1_lattice2(esk1_0),esk2_0) = k19_filter_2(esk1_0,esk3_0)
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(spm,[status(thm)],[c_0_160,c_0_161]) ).
cnf(c_0_168,negated_conjecture,
( r1_filter_2(u1_struct_0(esk1_0),k19_filter_2(esk1_0,esk3_0),k19_filter_2(esk1_0,esk3_0))
| v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_162,c_0_163]) ).
fof(c_0_169,plain,
! [X287] :
( ( ~ v3_struct_0(k1_lattice2(X287))
| v3_struct_0(X287)
| ~ l3_lattices(X287) )
& ( v3_lattices(k1_lattice2(X287))
| v3_struct_0(X287)
| ~ l3_lattices(X287) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_164])])]) ).
cnf(c_0_170,negated_conjecture,
~ r1_filter_2(u1_struct_0(esk1_0),k19_filter_2(esk1_0,esk3_0),a_2_0_filter_2(esk1_0,esk2_0)),
inference(rw,[status(thm)],[c_0_165,c_0_143]) ).
cnf(c_0_171,negated_conjecture,
( a_2_0_filter_2(esk1_0,esk2_0) = k19_filter_2(esk1_0,esk3_0)
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(spm,[status(thm)],[c_0_166,c_0_167]) ).
cnf(c_0_172,negated_conjecture,
r1_filter_2(u1_struct_0(esk1_0),k19_filter_2(esk1_0,esk3_0),k19_filter_2(esk1_0,esk3_0)),
inference(sr,[status(thm)],[c_0_168,c_0_77]) ).
cnf(c_0_173,plain,
( v3_struct_0(X1)
| ~ v3_struct_0(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_169]) ).
cnf(c_0_174,negated_conjecture,
v3_struct_0(k1_lattice2(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_171]),c_0_172])]) ).
cnf(c_0_175,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_174]),c_0_36])]),c_0_38]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LAT312+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
% 0.14/0.32 % Computer : n015.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 21:12:32 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 19.01/11.71 % Version : CSE_E---1.7
% 19.01/11.71 % Problem : theBenchmark.p
% 19.01/11.71 % SZS status Theorem for theBenchmark.p
% 19.01/11.71 % SZS output start CNFRefutation
% See solution above
% 19.01/11.79 % Total time : 8.387s
%------------------------------------------------------------------------------