%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT343+1 : TPTP v9.2.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:38:13 PM UTC 2026
% Result : Theorem 6.05s 4.45s
% Output : CNFRefutation 6.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 23
% Syntax : Number of formulae : 163 ( 31 unt; 0 def)
% Number of atoms : 583 ( 37 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 680 ( 260 ~; 268 |; 105 &)
% ( 3 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 3 con; 0-4 aty)
% Number of variables : 196 ( 13 sgn 95 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k10_conlat_1,axiom,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ( v1_funct_1(k10_conlat_1(X1))
& v1_funct_2(k10_conlat_1(X1),k2_zfmisc_1(k8_conlat_1(X1),k8_conlat_1(X1)),k8_conlat_1(X1))
& m2_relset_1(k10_conlat_1(X1),k2_zfmisc_1(k8_conlat_1(X1),k8_conlat_1(X1)),k8_conlat_1(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_conlat_1) ).
fof(t11_conlat_2,conjecture,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_conlat_1(X1))
=> ! [X3] :
( m1_subset_1(X3,u2_conlat_1(X1))
=> ( ~ v7_conlat_1(k8_funct_2(u1_conlat_1(X1),u1_struct_0(k11_conlat_1(X1)),k4_conlat_2(X1),X2),X1)
& v9_conlat_1(k8_funct_2(u1_conlat_1(X1),u1_struct_0(k11_conlat_1(X1)),k4_conlat_2(X1),X2),X1)
& l3_conlat_1(k8_funct_2(u1_conlat_1(X1),u1_struct_0(k11_conlat_1(X1)),k4_conlat_2(X1),X2),X1)
& ~ v7_conlat_1(k8_funct_2(u2_conlat_1(X1),u1_struct_0(k11_conlat_1(X1)),k5_conlat_2(X1),X3),X1)
& v9_conlat_1(k8_funct_2(u2_conlat_1(X1),u1_struct_0(k11_conlat_1(X1)),k5_conlat_2(X1),X3),X1)
& l3_conlat_1(k8_funct_2(u2_conlat_1(X1),u1_struct_0(k11_conlat_1(X1)),k5_conlat_2(X1),X3),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_conlat_2) ).
fof(dt_k9_conlat_1,axiom,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ( v1_funct_1(k9_conlat_1(X1))
& v1_funct_2(k9_conlat_1(X1),k2_zfmisc_1(k8_conlat_1(X1),k8_conlat_1(X1)),k8_conlat_1(X1))
& m2_relset_1(k9_conlat_1(X1),k2_zfmisc_1(k8_conlat_1(X1),k8_conlat_1(X1)),k8_conlat_1(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_conlat_1) ).
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
<=> m1_relset_1(X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(d23_conlat_1,axiom,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> k11_conlat_1(X1) = g3_lattices(k8_conlat_1(X1),k10_conlat_1(X1),k9_conlat_1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d23_conlat_1) ).
fof(free_g3_lattices,axiom,
! [X1,X2,X3] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)
& m1_relset_1(X2,k2_zfmisc_1(X1,X1),X1)
& v1_funct_1(X3)
& v1_funct_2(X3,k2_zfmisc_1(X1,X1),X1)
& m1_relset_1(X3,k2_zfmisc_1(X1,X1),X1) )
=> ! [X4,X5,X6] :
( g3_lattices(X1,X2,X3) = g3_lattices(X4,X5,X6)
=> ( X1 = X4
& X2 = X5
& X3 = X6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g3_lattices) ).
fof(dt_k11_conlat_1,axiom,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ( ~ v3_struct_0(k11_conlat_1(X1))
& v3_lattices(k11_conlat_1(X1))
& l3_lattices(k11_conlat_1(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_conlat_1) ).
fof(dt_u1_lattices,axiom,
! [X1] :
( l1_lattices(X1)
=> ( v1_funct_1(u1_lattices(X1))
& v1_funct_2(u1_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
& m2_relset_1(u1_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_lattices) ).
fof(dt_u2_lattices,axiom,
! [X1] :
( l2_lattices(X1)
=> ( v1_funct_1(u2_lattices(X1))
& v1_funct_2(u2_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
& m2_relset_1(u2_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u2_lattices) ).
fof(abstractness_v3_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( v3_lattices(X1)
=> X1 = g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v3_lattices) ).
fof(d18_conlat_1,axiom,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ! [X2] :
( ~ v1_xboole_0(X2)
=> ( m1_conlat_1(X2,X1)
<=> ! [X3] :
( r2_hidden(X3,X2)
=> ( ~ v7_conlat_1(X3,X1)
& v9_conlat_1(X3,X1)
& l3_conlat_1(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d18_conlat_1) ).
fof(dt_k8_conlat_1,axiom,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> m1_conlat_1(k8_conlat_1(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_conlat_1) ).
fof(dt_k5_conlat_2,axiom,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ( v1_funct_1(k5_conlat_2(X1))
& v1_funct_2(k5_conlat_2(X1),u2_conlat_1(X1),u1_struct_0(k11_conlat_1(X1)))
& m2_relset_1(k5_conlat_2(X1),u2_conlat_1(X1),u1_struct_0(k11_conlat_1(X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_conlat_2) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( r2_hidden(X1,X2)
& v1_xboole_0(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( l1_lattices(X1)
& l2_lattices(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(fc1_struct_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(dt_k4_conlat_2,axiom,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ( v1_funct_1(k4_conlat_2(X1))
& v1_funct_2(k4_conlat_2(X1),u1_conlat_1(X1),u1_struct_0(k11_conlat_1(X1)))
& m2_relset_1(k4_conlat_2(X1),u1_conlat_1(X1),u1_struct_0(k11_conlat_1(X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_conlat_2) ).
fof(dt_k8_funct_2,axiom,
! [X1,X2,X3,X4] :
( ( ~ v1_xboole_0(X1)
& v1_funct_1(X3)
& v1_funct_2(X3,X1,X2)
& m1_relset_1(X3,X1,X2)
& m1_subset_1(X4,X1) )
=> m1_subset_1(k8_funct_2(X1,X2,X3,X4),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_funct_2) ).
fof(dt_l1_lattices,axiom,
! [X1] :
( l1_lattices(X1)
=> l1_struct_0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).
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(fc1_conlat_1,axiom,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l1_conlat_1(X1) )
=> ~ v1_xboole_0(u2_conlat_1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_conlat_1) ).
fof(fc2_conlat_1,axiom,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l1_conlat_1(X1) )
=> ~ v1_xboole_0(u1_conlat_1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_conlat_1) ).
fof(dt_l2_conlat_1,axiom,
! [X1] :
( l2_conlat_1(X1)
=> l1_conlat_1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_conlat_1) ).
fof(c_0_23,plain,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ( v1_funct_1(k10_conlat_1(X1))
& v1_funct_2(k10_conlat_1(X1),k2_zfmisc_1(k8_conlat_1(X1),k8_conlat_1(X1)),k8_conlat_1(X1))
& m2_relset_1(k10_conlat_1(X1),k2_zfmisc_1(k8_conlat_1(X1),k8_conlat_1(X1)),k8_conlat_1(X1)) ) ),
inference(fof_simplification,[status(thm)],[dt_k10_conlat_1]) ).
fof(c_0_24,negated_conjecture,
~ ! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_conlat_1(X1))
=> ! [X3] :
( m1_subset_1(X3,u2_conlat_1(X1))
=> ( ~ v7_conlat_1(k8_funct_2(u1_conlat_1(X1),u1_struct_0(k11_conlat_1(X1)),k4_conlat_2(X1),X2),X1)
& v9_conlat_1(k8_funct_2(u1_conlat_1(X1),u1_struct_0(k11_conlat_1(X1)),k4_conlat_2(X1),X2),X1)
& l3_conlat_1(k8_funct_2(u1_conlat_1(X1),u1_struct_0(k11_conlat_1(X1)),k4_conlat_2(X1),X2),X1)
& ~ v7_conlat_1(k8_funct_2(u2_conlat_1(X1),u1_struct_0(k11_conlat_1(X1)),k5_conlat_2(X1),X3),X1)
& v9_conlat_1(k8_funct_2(u2_conlat_1(X1),u1_struct_0(k11_conlat_1(X1)),k5_conlat_2(X1),X3),X1)
& l3_conlat_1(k8_funct_2(u2_conlat_1(X1),u1_struct_0(k11_conlat_1(X1)),k5_conlat_2(X1),X3),X1) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t11_conlat_2])]) ).
fof(c_0_25,plain,
! [X185] :
( ( v1_funct_1(k10_conlat_1(X185))
| v3_conlat_1(X185)
| ~ l2_conlat_1(X185) )
& ( v1_funct_2(k10_conlat_1(X185),k2_zfmisc_1(k8_conlat_1(X185),k8_conlat_1(X185)),k8_conlat_1(X185))
| v3_conlat_1(X185)
| ~ l2_conlat_1(X185) )
& ( m2_relset_1(k10_conlat_1(X185),k2_zfmisc_1(k8_conlat_1(X185),k8_conlat_1(X185)),k8_conlat_1(X185))
| v3_conlat_1(X185)
| ~ l2_conlat_1(X185) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])]) ).
fof(c_0_26,negated_conjecture,
( ~ v3_conlat_1(esk1_0)
& l2_conlat_1(esk1_0)
& m1_subset_1(esk2_0,u1_conlat_1(esk1_0))
& m1_subset_1(esk3_0,u2_conlat_1(esk1_0))
& ( v7_conlat_1(k8_funct_2(u1_conlat_1(esk1_0),u1_struct_0(k11_conlat_1(esk1_0)),k4_conlat_2(esk1_0),esk2_0),esk1_0)
| ~ v9_conlat_1(k8_funct_2(u1_conlat_1(esk1_0),u1_struct_0(k11_conlat_1(esk1_0)),k4_conlat_2(esk1_0),esk2_0),esk1_0)
| ~ l3_conlat_1(k8_funct_2(u1_conlat_1(esk1_0),u1_struct_0(k11_conlat_1(esk1_0)),k4_conlat_2(esk1_0),esk2_0),esk1_0)
| v7_conlat_1(k8_funct_2(u2_conlat_1(esk1_0),u1_struct_0(k11_conlat_1(esk1_0)),k5_conlat_2(esk1_0),esk3_0),esk1_0)
| ~ v9_conlat_1(k8_funct_2(u2_conlat_1(esk1_0),u1_struct_0(k11_conlat_1(esk1_0)),k5_conlat_2(esk1_0),esk3_0),esk1_0)
| ~ l3_conlat_1(k8_funct_2(u2_conlat_1(esk1_0),u1_struct_0(k11_conlat_1(esk1_0)),k5_conlat_2(esk1_0),esk3_0),esk1_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])]) ).
fof(c_0_27,plain,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ( v1_funct_1(k9_conlat_1(X1))
& v1_funct_2(k9_conlat_1(X1),k2_zfmisc_1(k8_conlat_1(X1),k8_conlat_1(X1)),k8_conlat_1(X1))
& m2_relset_1(k9_conlat_1(X1),k2_zfmisc_1(k8_conlat_1(X1),k8_conlat_1(X1)),k8_conlat_1(X1)) ) ),
inference(fof_simplification,[status(thm)],[dt_k9_conlat_1]) ).
fof(c_0_28,plain,
! [X278,X279,X280] :
( ( ~ m2_relset_1(X280,X278,X279)
| m1_relset_1(X280,X278,X279) )
& ( ~ m1_relset_1(X280,X278,X279)
| m2_relset_1(X280,X278,X279) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
cnf(c_0_29,plain,
( m2_relset_1(k10_conlat_1(X1),k2_zfmisc_1(k8_conlat_1(X1),k8_conlat_1(X1)),k8_conlat_1(X1))
| v3_conlat_1(X1)
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,negated_conjecture,
l2_conlat_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,negated_conjecture,
~ v3_conlat_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_32,plain,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> k11_conlat_1(X1) = g3_lattices(k8_conlat_1(X1),k10_conlat_1(X1),k9_conlat_1(X1)) ),
inference(fof_simplification,[status(thm)],[d23_conlat_1]) ).
fof(c_0_33,plain,
! [X195] :
( ( v1_funct_1(k9_conlat_1(X195))
| v3_conlat_1(X195)
| ~ l2_conlat_1(X195) )
& ( v1_funct_2(k9_conlat_1(X195),k2_zfmisc_1(k8_conlat_1(X195),k8_conlat_1(X195)),k8_conlat_1(X195))
| v3_conlat_1(X195)
| ~ l2_conlat_1(X195) )
& ( m2_relset_1(k9_conlat_1(X195),k2_zfmisc_1(k8_conlat_1(X195),k8_conlat_1(X195)),k8_conlat_1(X195))
| v3_conlat_1(X195)
| ~ l2_conlat_1(X195) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])]) ).
fof(c_0_34,plain,
! [X242,X243,X244,X245,X246,X247] :
( ( X242 = X245
| g3_lattices(X242,X243,X244) != g3_lattices(X245,X246,X247)
| ~ v1_funct_1(X243)
| ~ v1_funct_2(X243,k2_zfmisc_1(X242,X242),X242)
| ~ m1_relset_1(X243,k2_zfmisc_1(X242,X242),X242)
| ~ v1_funct_1(X244)
| ~ v1_funct_2(X244,k2_zfmisc_1(X242,X242),X242)
| ~ m1_relset_1(X244,k2_zfmisc_1(X242,X242),X242) )
& ( X243 = X246
| g3_lattices(X242,X243,X244) != g3_lattices(X245,X246,X247)
| ~ v1_funct_1(X243)
| ~ v1_funct_2(X243,k2_zfmisc_1(X242,X242),X242)
| ~ m1_relset_1(X243,k2_zfmisc_1(X242,X242),X242)
| ~ v1_funct_1(X244)
| ~ v1_funct_2(X244,k2_zfmisc_1(X242,X242),X242)
| ~ m1_relset_1(X244,k2_zfmisc_1(X242,X242),X242) )
& ( X244 = X247
| g3_lattices(X242,X243,X244) != g3_lattices(X245,X246,X247)
| ~ v1_funct_1(X243)
| ~ v1_funct_2(X243,k2_zfmisc_1(X242,X242),X242)
| ~ m1_relset_1(X243,k2_zfmisc_1(X242,X242),X242)
| ~ v1_funct_1(X244)
| ~ v1_funct_2(X244,k2_zfmisc_1(X242,X242),X242)
| ~ m1_relset_1(X244,k2_zfmisc_1(X242,X242),X242) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[free_g3_lattices])])])]) ).
cnf(c_0_35,plain,
( v1_funct_2(k10_conlat_1(X1),k2_zfmisc_1(k8_conlat_1(X1),k8_conlat_1(X1)),k8_conlat_1(X1))
| v3_conlat_1(X1)
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_36,plain,
( v1_funct_1(k10_conlat_1(X1))
| v3_conlat_1(X1)
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_37,plain,
( m1_relset_1(X1,X2,X3)
| ~ m2_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,negated_conjecture,
m2_relset_1(k10_conlat_1(esk1_0),k2_zfmisc_1(k8_conlat_1(esk1_0),k8_conlat_1(esk1_0)),k8_conlat_1(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
fof(c_0_39,plain,
! [X181] :
( v3_conlat_1(X181)
| ~ l2_conlat_1(X181)
| k11_conlat_1(X181) = g3_lattices(k8_conlat_1(X181),k10_conlat_1(X181),k9_conlat_1(X181)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])]) ).
cnf(c_0_40,plain,
( m2_relset_1(k9_conlat_1(X1),k2_zfmisc_1(k8_conlat_1(X1),k8_conlat_1(X1)),k8_conlat_1(X1))
| v3_conlat_1(X1)
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_41,plain,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ( ~ v3_struct_0(k11_conlat_1(X1))
& v3_lattices(k11_conlat_1(X1))
& l3_lattices(k11_conlat_1(X1)) ) ),
inference(fof_simplification,[status(thm)],[dt_k11_conlat_1]) ).
fof(c_0_42,plain,
! [X205] :
( ( v1_funct_1(u1_lattices(X205))
| ~ l1_lattices(X205) )
& ( v1_funct_2(u1_lattices(X205),k2_zfmisc_1(u1_struct_0(X205),u1_struct_0(X205)),u1_struct_0(X205))
| ~ l1_lattices(X205) )
& ( m2_relset_1(u1_lattices(X205),k2_zfmisc_1(u1_struct_0(X205),u1_struct_0(X205)),u1_struct_0(X205))
| ~ l1_lattices(X205) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_lattices])])]) ).
cnf(c_0_43,plain,
( X1 = X2
| g3_lattices(X3,X4,X1) != g3_lattices(X5,X6,X2)
| ~ v1_funct_1(X4)
| ~ v1_funct_2(X4,k2_zfmisc_1(X3,X3),X3)
| ~ m1_relset_1(X4,k2_zfmisc_1(X3,X3),X3)
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k2_zfmisc_1(X3,X3),X3)
| ~ m1_relset_1(X1,k2_zfmisc_1(X3,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_44,negated_conjecture,
v1_funct_2(k10_conlat_1(esk1_0),k2_zfmisc_1(k8_conlat_1(esk1_0),k8_conlat_1(esk1_0)),k8_conlat_1(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_30]),c_0_31]) ).
cnf(c_0_45,negated_conjecture,
v1_funct_1(k10_conlat_1(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_30]),c_0_31]) ).
cnf(c_0_46,negated_conjecture,
m1_relset_1(k10_conlat_1(esk1_0),k2_zfmisc_1(k8_conlat_1(esk1_0),k8_conlat_1(esk1_0)),k8_conlat_1(esk1_0)),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_47,plain,
( v1_funct_2(k9_conlat_1(X1),k2_zfmisc_1(k8_conlat_1(X1),k8_conlat_1(X1)),k8_conlat_1(X1))
| v3_conlat_1(X1)
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_48,plain,
( v3_conlat_1(X1)
| k11_conlat_1(X1) = g3_lattices(k8_conlat_1(X1),k10_conlat_1(X1),k9_conlat_1(X1))
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_49,plain,
( v1_funct_1(k9_conlat_1(X1))
| v3_conlat_1(X1)
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_50,negated_conjecture,
m2_relset_1(k9_conlat_1(esk1_0),k2_zfmisc_1(k8_conlat_1(esk1_0),k8_conlat_1(esk1_0)),k8_conlat_1(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_30]),c_0_31]) ).
fof(c_0_51,plain,
! [X186] :
( ( ~ v3_struct_0(k11_conlat_1(X186))
| v3_conlat_1(X186)
| ~ l2_conlat_1(X186) )
& ( v3_lattices(k11_conlat_1(X186))
| v3_conlat_1(X186)
| ~ l2_conlat_1(X186) )
& ( l3_lattices(k11_conlat_1(X186))
| v3_conlat_1(X186)
| ~ l2_conlat_1(X186) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])]) ).
cnf(c_0_52,plain,
( m2_relset_1(u1_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ l1_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
fof(c_0_53,plain,
! [X206] :
( ( v1_funct_1(u2_lattices(X206))
| ~ l2_lattices(X206) )
& ( v1_funct_2(u2_lattices(X206),k2_zfmisc_1(u1_struct_0(X206),u1_struct_0(X206)),u1_struct_0(X206))
| ~ l2_lattices(X206) )
& ( m2_relset_1(u2_lattices(X206),k2_zfmisc_1(u1_struct_0(X206),u1_struct_0(X206)),u1_struct_0(X206))
| ~ l2_lattices(X206) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u2_lattices])])]) ).
cnf(c_0_54,negated_conjecture,
( X1 = X2
| g3_lattices(k8_conlat_1(esk1_0),k10_conlat_1(esk1_0),X1) != g3_lattices(X3,X4,X2)
| ~ v1_funct_2(X1,k2_zfmisc_1(k8_conlat_1(esk1_0),k8_conlat_1(esk1_0)),k8_conlat_1(esk1_0))
| ~ v1_funct_1(X1)
| ~ m1_relset_1(X1,k2_zfmisc_1(k8_conlat_1(esk1_0),k8_conlat_1(esk1_0)),k8_conlat_1(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]),c_0_46])]) ).
cnf(c_0_55,negated_conjecture,
v1_funct_2(k9_conlat_1(esk1_0),k2_zfmisc_1(k8_conlat_1(esk1_0),k8_conlat_1(esk1_0)),k8_conlat_1(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_30]),c_0_31]) ).
cnf(c_0_56,negated_conjecture,
g3_lattices(k8_conlat_1(esk1_0),k10_conlat_1(esk1_0),k9_conlat_1(esk1_0)) = k11_conlat_1(esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_30]),c_0_31]) ).
cnf(c_0_57,negated_conjecture,
v1_funct_1(k9_conlat_1(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_30]),c_0_31]) ).
cnf(c_0_58,negated_conjecture,
m1_relset_1(k9_conlat_1(esk1_0),k2_zfmisc_1(k8_conlat_1(esk1_0),k8_conlat_1(esk1_0)),k8_conlat_1(esk1_0)),
inference(spm,[status(thm)],[c_0_37,c_0_50]) ).
fof(c_0_59,plain,
! [X156] :
( ~ l3_lattices(X156)
| ~ v3_lattices(X156)
| X156 = g3_lattices(u1_struct_0(X156),u2_lattices(X156),u1_lattices(X156)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[abstractness_v3_lattices])]) ).
cnf(c_0_60,plain,
( v3_lattices(k11_conlat_1(X1))
| v3_conlat_1(X1)
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_61,plain,
( l3_lattices(k11_conlat_1(X1))
| v3_conlat_1(X1)
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_62,plain,
( X1 = X2
| g3_lattices(X1,X3,X4) != g3_lattices(X2,X5,X6)
| ~ v1_funct_1(X3)
| ~ v1_funct_2(X3,k2_zfmisc_1(X1,X1),X1)
| ~ m1_relset_1(X3,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_1(X4)
| ~ v1_funct_2(X4,k2_zfmisc_1(X1,X1),X1)
| ~ m1_relset_1(X4,k2_zfmisc_1(X1,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_63,plain,
( v1_funct_2(u1_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ l1_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_64,plain,
( m1_relset_1(u1_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ l1_lattices(X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_52]) ).
cnf(c_0_65,plain,
( v1_funct_1(u1_lattices(X1))
| ~ l1_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_66,plain,
( m2_relset_1(u2_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ l2_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_67,negated_conjecture,
( k9_conlat_1(esk1_0) = X1
| k11_conlat_1(esk1_0) != g3_lattices(X2,X3,X1) ),
inference(cn,[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_56]),c_0_57]),c_0_58])]) ).
cnf(c_0_68,plain,
( X1 = g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1))
| ~ l3_lattices(X1)
| ~ v3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_69,negated_conjecture,
v3_lattices(k11_conlat_1(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_30]),c_0_31]) ).
cnf(c_0_70,negated_conjecture,
l3_lattices(k11_conlat_1(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_30]),c_0_31]) ).
cnf(c_0_71,plain,
( u1_struct_0(X1) = X2
| g3_lattices(u1_struct_0(X1),X3,u1_lattices(X1)) != g3_lattices(X2,X4,X5)
| ~ l1_lattices(X1)
| ~ v1_funct_2(X3,k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ v1_funct_1(X3)
| ~ m1_relset_1(X3,k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]),c_0_65]) ).
cnf(c_0_72,plain,
( v1_funct_2(u2_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ l2_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_73,plain,
( m1_relset_1(u2_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ l2_lattices(X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_66]) ).
cnf(c_0_74,plain,
( v1_funct_1(u2_lattices(X1))
| ~ l2_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_75,negated_conjecture,
k9_conlat_1(esk1_0) = u1_lattices(k11_conlat_1(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68])]),c_0_69]),c_0_70])]) ).
fof(c_0_76,plain,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ! [X2] :
( ~ v1_xboole_0(X2)
=> ( m1_conlat_1(X2,X1)
<=> ! [X3] :
( r2_hidden(X3,X2)
=> ( ~ v7_conlat_1(X3,X1)
& v9_conlat_1(X3,X1)
& l3_conlat_1(X3,X1) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d18_conlat_1]) ).
fof(c_0_77,plain,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> m1_conlat_1(k8_conlat_1(X1),X1) ),
inference(fof_simplification,[status(thm)],[dt_k8_conlat_1]) ).
cnf(c_0_78,plain,
( u1_struct_0(X1) = X2
| g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1)) != g3_lattices(X2,X3,X4)
| ~ l2_lattices(X1)
| ~ l1_lattices(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]),c_0_74]) ).
cnf(c_0_79,negated_conjecture,
g3_lattices(k8_conlat_1(esk1_0),k10_conlat_1(esk1_0),u1_lattices(k11_conlat_1(esk1_0))) = k11_conlat_1(esk1_0),
inference(rw,[status(thm)],[c_0_56,c_0_75]) ).
fof(c_0_80,plain,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ( v1_funct_1(k5_conlat_2(X1))
& v1_funct_2(k5_conlat_2(X1),u2_conlat_1(X1),u1_struct_0(k11_conlat_1(X1)))
& m2_relset_1(k5_conlat_2(X1),u2_conlat_1(X1),u1_struct_0(k11_conlat_1(X1))) ) ),
inference(fof_simplification,[status(thm)],[dt_k5_conlat_2]) ).
fof(c_0_81,plain,
! [X177,X178,X179] :
( ( ~ v7_conlat_1(X179,X177)
| ~ r2_hidden(X179,X178)
| ~ m1_conlat_1(X178,X177)
| v1_xboole_0(X178)
| v3_conlat_1(X177)
| ~ l2_conlat_1(X177) )
& ( v9_conlat_1(X179,X177)
| ~ r2_hidden(X179,X178)
| ~ m1_conlat_1(X178,X177)
| v1_xboole_0(X178)
| v3_conlat_1(X177)
| ~ l2_conlat_1(X177) )
& ( l3_conlat_1(X179,X177)
| ~ r2_hidden(X179,X178)
| ~ m1_conlat_1(X178,X177)
| v1_xboole_0(X178)
| v3_conlat_1(X177)
| ~ l2_conlat_1(X177) )
& ( r2_hidden(esk4_2(X177,X178),X178)
| m1_conlat_1(X178,X177)
| v1_xboole_0(X178)
| v3_conlat_1(X177)
| ~ l2_conlat_1(X177) )
& ( v7_conlat_1(esk4_2(X177,X178),X177)
| ~ v9_conlat_1(esk4_2(X177,X178),X177)
| ~ l3_conlat_1(esk4_2(X177,X178),X177)
| m1_conlat_1(X178,X177)
| v1_xboole_0(X178)
| v3_conlat_1(X177)
| ~ l2_conlat_1(X177) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_76])])])])]) ).
fof(c_0_82,plain,
! [X295,X296] :
( ~ r2_hidden(X295,X296)
| ~ v1_xboole_0(X296) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(c_0_83,plain,
! [X190] :
( v3_conlat_1(X190)
| ~ l2_conlat_1(X190)
| m1_conlat_1(k8_conlat_1(X190),X190) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_77])]) ).
cnf(c_0_84,negated_conjecture,
( u1_struct_0(X1) = k8_conlat_1(esk1_0)
| g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1)) != k11_conlat_1(esk1_0)
| ~ l2_lattices(X1)
| ~ l1_lattices(X1) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
fof(c_0_85,plain,
! [X199] :
( ( l1_lattices(X199)
| ~ l3_lattices(X199) )
& ( l2_lattices(X199)
| ~ l3_lattices(X199) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
fof(c_0_86,plain,
! [X188] :
( ( v1_funct_1(k5_conlat_2(X188))
| v3_conlat_1(X188)
| ~ l2_conlat_1(X188) )
& ( v1_funct_2(k5_conlat_2(X188),u2_conlat_1(X188),u1_struct_0(k11_conlat_1(X188)))
| v3_conlat_1(X188)
| ~ l2_conlat_1(X188) )
& ( m2_relset_1(k5_conlat_2(X188),u2_conlat_1(X188),u1_struct_0(k11_conlat_1(X188)))
| v3_conlat_1(X188)
| ~ l2_conlat_1(X188) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_80])])]) ).
fof(c_0_87,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).
fof(c_0_88,plain,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ( v1_funct_1(k4_conlat_2(X1))
& v1_funct_2(k4_conlat_2(X1),u1_conlat_1(X1),u1_struct_0(k11_conlat_1(X1)))
& m2_relset_1(k4_conlat_2(X1),u1_conlat_1(X1),u1_struct_0(k11_conlat_1(X1))) ) ),
inference(fof_simplification,[status(thm)],[dt_k4_conlat_2]) ).
cnf(c_0_89,plain,
( l3_conlat_1(X1,X2)
| v1_xboole_0(X3)
| v3_conlat_1(X2)
| ~ r2_hidden(X1,X3)
| ~ m1_conlat_1(X3,X2)
| ~ l2_conlat_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_90,plain,
( ~ r2_hidden(X1,X2)
| ~ v1_xboole_0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_91,plain,
( v3_conlat_1(X1)
| m1_conlat_1(k8_conlat_1(X1),X1)
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_92,negated_conjecture,
( k8_conlat_1(esk1_0) = u1_struct_0(k11_conlat_1(esk1_0))
| ~ l2_lattices(k11_conlat_1(esk1_0))
| ~ l1_lattices(k11_conlat_1(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_68])]),c_0_69]),c_0_70])]) ).
cnf(c_0_93,plain,
( l2_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_94,plain,
( v9_conlat_1(X1,X2)
| v1_xboole_0(X3)
| v3_conlat_1(X2)
| ~ r2_hidden(X1,X3)
| ~ m1_conlat_1(X3,X2)
| ~ l2_conlat_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_95,plain,
( v1_xboole_0(X3)
| v3_conlat_1(X2)
| ~ v7_conlat_1(X1,X2)
| ~ r2_hidden(X1,X3)
| ~ m1_conlat_1(X3,X2)
| ~ l2_conlat_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
fof(c_0_96,plain,
! [X1,X2,X3,X4] :
( ( ~ v1_xboole_0(X1)
& v1_funct_1(X3)
& v1_funct_2(X3,X1,X2)
& m1_relset_1(X3,X1,X2)
& m1_subset_1(X4,X1) )
=> m1_subset_1(k8_funct_2(X1,X2,X3,X4),X2) ),
inference(fof_simplification,[status(thm)],[dt_k8_funct_2]) ).
cnf(c_0_97,plain,
( m2_relset_1(k5_conlat_2(X1),u2_conlat_1(X1),u1_struct_0(k11_conlat_1(X1)))
| v3_conlat_1(X1)
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
fof(c_0_98,plain,
! [X227] :
( v3_struct_0(X227)
| ~ l1_struct_0(X227)
| ~ v1_xboole_0(u1_struct_0(X227)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_87])]) ).
fof(c_0_99,plain,
! [X196] :
( ~ l1_lattices(X196)
| l1_struct_0(X196) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_lattices])]) ).
fof(c_0_100,plain,
! [X187] :
( ( v1_funct_1(k4_conlat_2(X187))
| v3_conlat_1(X187)
| ~ l2_conlat_1(X187) )
& ( v1_funct_2(k4_conlat_2(X187),u1_conlat_1(X187),u1_struct_0(k11_conlat_1(X187)))
| v3_conlat_1(X187)
| ~ l2_conlat_1(X187) )
& ( m2_relset_1(k4_conlat_2(X187),u1_conlat_1(X187),u1_struct_0(k11_conlat_1(X187)))
| v3_conlat_1(X187)
| ~ l2_conlat_1(X187) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_88])])]) ).
cnf(c_0_101,plain,
( l3_conlat_1(X1,X2)
| v3_conlat_1(X2)
| ~ m1_conlat_1(X3,X2)
| ~ r2_hidden(X1,X3)
| ~ l2_conlat_1(X2) ),
inference(csr,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_102,negated_conjecture,
m1_conlat_1(k8_conlat_1(esk1_0),esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_30]),c_0_31]) ).
cnf(c_0_103,negated_conjecture,
( k8_conlat_1(esk1_0) = u1_struct_0(k11_conlat_1(esk1_0))
| ~ l1_lattices(k11_conlat_1(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_70])]) ).
cnf(c_0_104,plain,
( l1_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_105,plain,
( v9_conlat_1(X1,X2)
| v3_conlat_1(X2)
| ~ m1_conlat_1(X3,X2)
| ~ r2_hidden(X1,X3)
| ~ l2_conlat_1(X2) ),
inference(csr,[status(thm)],[c_0_94,c_0_90]) ).
cnf(c_0_106,plain,
( v3_conlat_1(X1)
| ~ m1_conlat_1(X2,X1)
| ~ r2_hidden(X3,X2)
| ~ v7_conlat_1(X3,X1)
| ~ l2_conlat_1(X1) ),
inference(csr,[status(thm)],[c_0_95,c_0_90]) ).
fof(c_0_107,plain,
! [X191,X192,X193,X194] :
( v1_xboole_0(X191)
| ~ v1_funct_1(X193)
| ~ v1_funct_2(X193,X191,X192)
| ~ m1_relset_1(X193,X191,X192)
| ~ m1_subset_1(X194,X191)
| m1_subset_1(k8_funct_2(X191,X192,X193,X194),X192) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_96])]) ).
cnf(c_0_108,plain,
( v1_funct_2(k5_conlat_2(X1),u2_conlat_1(X1),u1_struct_0(k11_conlat_1(X1)))
| v3_conlat_1(X1)
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_109,plain,
( v1_funct_1(k5_conlat_2(X1))
| v3_conlat_1(X1)
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_110,negated_conjecture,
m2_relset_1(k5_conlat_2(esk1_0),u2_conlat_1(esk1_0),u1_struct_0(k11_conlat_1(esk1_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_30]),c_0_31]) ).
cnf(c_0_111,plain,
( v3_struct_0(X1)
| ~ l1_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_112,plain,
( l1_struct_0(X1)
| ~ l1_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_113,plain,
( m2_relset_1(k4_conlat_2(X1),u1_conlat_1(X1),u1_struct_0(k11_conlat_1(X1)))
| v3_conlat_1(X1)
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_114,negated_conjecture,
( l3_conlat_1(X1,esk1_0)
| ~ r2_hidden(X1,k8_conlat_1(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_30])]),c_0_31]) ).
cnf(c_0_115,negated_conjecture,
k8_conlat_1(esk1_0) = u1_struct_0(k11_conlat_1(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_70])]) ).
cnf(c_0_116,negated_conjecture,
( v9_conlat_1(X1,esk1_0)
| ~ r2_hidden(X1,k8_conlat_1(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_102]),c_0_30])]),c_0_31]) ).
cnf(c_0_117,negated_conjecture,
( ~ r2_hidden(X1,k8_conlat_1(esk1_0))
| ~ v7_conlat_1(X1,esk1_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_102]),c_0_30])]),c_0_31]) ).
cnf(c_0_118,plain,
( v1_xboole_0(X1)
| m1_subset_1(k8_funct_2(X1,X3,X2,X4),X3)
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,X1,X3)
| ~ m1_relset_1(X2,X1,X3)
| ~ m1_subset_1(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_119,negated_conjecture,
v1_funct_2(k5_conlat_2(esk1_0),u2_conlat_1(esk1_0),u1_struct_0(k11_conlat_1(esk1_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_30]),c_0_31]) ).
cnf(c_0_120,negated_conjecture,
v1_funct_1(k5_conlat_2(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_30]),c_0_31]) ).
cnf(c_0_121,negated_conjecture,
m1_relset_1(k5_conlat_2(esk1_0),u2_conlat_1(esk1_0),u1_struct_0(k11_conlat_1(esk1_0))),
inference(spm,[status(thm)],[c_0_37,c_0_110]) ).
cnf(c_0_122,plain,
( v3_struct_0(X1)
| ~ l1_lattices(X1)
| ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_123,plain,
( v3_conlat_1(X1)
| ~ v3_struct_0(k11_conlat_1(X1))
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_124,plain,
( v1_funct_2(k4_conlat_2(X1),u1_conlat_1(X1),u1_struct_0(k11_conlat_1(X1)))
| v3_conlat_1(X1)
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_125,plain,
( v1_funct_1(k4_conlat_2(X1))
| v3_conlat_1(X1)
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_126,negated_conjecture,
m2_relset_1(k4_conlat_2(esk1_0),u1_conlat_1(esk1_0),u1_struct_0(k11_conlat_1(esk1_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_30]),c_0_31]) ).
cnf(c_0_127,negated_conjecture,
( v7_conlat_1(k8_funct_2(u1_conlat_1(esk1_0),u1_struct_0(k11_conlat_1(esk1_0)),k4_conlat_2(esk1_0),esk2_0),esk1_0)
| v7_conlat_1(k8_funct_2(u2_conlat_1(esk1_0),u1_struct_0(k11_conlat_1(esk1_0)),k5_conlat_2(esk1_0),esk3_0),esk1_0)
| ~ v9_conlat_1(k8_funct_2(u1_conlat_1(esk1_0),u1_struct_0(k11_conlat_1(esk1_0)),k4_conlat_2(esk1_0),esk2_0),esk1_0)
| ~ l3_conlat_1(k8_funct_2(u1_conlat_1(esk1_0),u1_struct_0(k11_conlat_1(esk1_0)),k4_conlat_2(esk1_0),esk2_0),esk1_0)
| ~ v9_conlat_1(k8_funct_2(u2_conlat_1(esk1_0),u1_struct_0(k11_conlat_1(esk1_0)),k5_conlat_2(esk1_0),esk3_0),esk1_0)
| ~ l3_conlat_1(k8_funct_2(u2_conlat_1(esk1_0),u1_struct_0(k11_conlat_1(esk1_0)),k5_conlat_2(esk1_0),esk3_0),esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_128,negated_conjecture,
( l3_conlat_1(X1,esk1_0)
| ~ r2_hidden(X1,u1_struct_0(k11_conlat_1(esk1_0))) ),
inference(rw,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_129,negated_conjecture,
( v9_conlat_1(X1,esk1_0)
| ~ r2_hidden(X1,u1_struct_0(k11_conlat_1(esk1_0))) ),
inference(rw,[status(thm)],[c_0_116,c_0_115]) ).
cnf(c_0_130,negated_conjecture,
( ~ r2_hidden(X1,u1_struct_0(k11_conlat_1(esk1_0)))
| ~ v7_conlat_1(X1,esk1_0) ),
inference(rw,[status(thm)],[c_0_117,c_0_115]) ).
fof(c_0_131,plain,
! [X284,X285] :
( ~ m1_subset_1(X284,X285)
| v1_xboole_0(X285)
| r2_hidden(X284,X285) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
cnf(c_0_132,negated_conjecture,
( v1_xboole_0(u2_conlat_1(esk1_0))
| m1_subset_1(k8_funct_2(u2_conlat_1(esk1_0),u1_struct_0(k11_conlat_1(esk1_0)),k5_conlat_2(esk1_0),X1),u1_struct_0(k11_conlat_1(esk1_0)))
| ~ m1_subset_1(X1,u2_conlat_1(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_120]),c_0_121])]) ).
cnf(c_0_133,negated_conjecture,
m1_subset_1(esk3_0,u2_conlat_1(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_134,plain,
( v3_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1))
| ~ l3_lattices(X1) ),
inference(spm,[status(thm)],[c_0_122,c_0_104]) ).
cnf(c_0_135,negated_conjecture,
~ v3_struct_0(k11_conlat_1(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_123]),c_0_30])]) ).
cnf(c_0_136,negated_conjecture,
v1_funct_2(k4_conlat_2(esk1_0),u1_conlat_1(esk1_0),u1_struct_0(k11_conlat_1(esk1_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_30]),c_0_31]) ).
cnf(c_0_137,negated_conjecture,
v1_funct_1(k4_conlat_2(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_30]),c_0_31]) ).
cnf(c_0_138,negated_conjecture,
m1_relset_1(k4_conlat_2(esk1_0),u1_conlat_1(esk1_0),u1_struct_0(k11_conlat_1(esk1_0))),
inference(spm,[status(thm)],[c_0_37,c_0_126]) ).
fof(c_0_139,plain,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l1_conlat_1(X1) )
=> ~ v1_xboole_0(u2_conlat_1(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_conlat_1]) ).
cnf(c_0_140,negated_conjecture,
( v7_conlat_1(k8_funct_2(u2_conlat_1(esk1_0),u1_struct_0(k11_conlat_1(esk1_0)),k5_conlat_2(esk1_0),esk3_0),esk1_0)
| ~ r2_hidden(k8_funct_2(u1_conlat_1(esk1_0),u1_struct_0(k11_conlat_1(esk1_0)),k4_conlat_2(esk1_0),esk2_0),u1_struct_0(k11_conlat_1(esk1_0)))
| ~ l3_conlat_1(k8_funct_2(u2_conlat_1(esk1_0),u1_struct_0(k11_conlat_1(esk1_0)),k5_conlat_2(esk1_0),esk3_0),esk1_0)
| ~ v9_conlat_1(k8_funct_2(u2_conlat_1(esk1_0),u1_struct_0(k11_conlat_1(esk1_0)),k5_conlat_2(esk1_0),esk3_0),esk1_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_129]),c_0_130]) ).
cnf(c_0_141,plain,
( v1_xboole_0(X2)
| r2_hidden(X1,X2)
| ~ m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_131]) ).
cnf(c_0_142,negated_conjecture,
( v1_xboole_0(u2_conlat_1(esk1_0))
| m1_subset_1(k8_funct_2(u2_conlat_1(esk1_0),u1_struct_0(k11_conlat_1(esk1_0)),k5_conlat_2(esk1_0),esk3_0),u1_struct_0(k11_conlat_1(esk1_0))) ),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_143,negated_conjecture,
~ v1_xboole_0(u1_struct_0(k11_conlat_1(esk1_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_70]),c_0_135]) ).
cnf(c_0_144,negated_conjecture,
( v1_xboole_0(u1_conlat_1(esk1_0))
| m1_subset_1(k8_funct_2(u1_conlat_1(esk1_0),u1_struct_0(k11_conlat_1(esk1_0)),k4_conlat_2(esk1_0),X1),u1_struct_0(k11_conlat_1(esk1_0)))
| ~ m1_subset_1(X1,u1_conlat_1(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_136]),c_0_137]),c_0_138])]) ).
cnf(c_0_145,negated_conjecture,
m1_subset_1(esk2_0,u1_conlat_1(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_146,plain,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l1_conlat_1(X1) )
=> ~ v1_xboole_0(u1_conlat_1(X1)) ),
inference(fof_simplification,[status(thm)],[fc2_conlat_1]) ).
fof(c_0_147,plain,
! [X225] :
( v3_conlat_1(X225)
| ~ l1_conlat_1(X225)
| ~ v1_xboole_0(u2_conlat_1(X225)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_139])]) ).
cnf(c_0_148,negated_conjecture,
( ~ r2_hidden(k8_funct_2(u2_conlat_1(esk1_0),u1_struct_0(k11_conlat_1(esk1_0)),k5_conlat_2(esk1_0),esk3_0),u1_struct_0(k11_conlat_1(esk1_0)))
| ~ r2_hidden(k8_funct_2(u1_conlat_1(esk1_0),u1_struct_0(k11_conlat_1(esk1_0)),k4_conlat_2(esk1_0),esk2_0),u1_struct_0(k11_conlat_1(esk1_0))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_140]),c_0_129]),c_0_128]) ).
cnf(c_0_149,negated_conjecture,
( v1_xboole_0(u2_conlat_1(esk1_0))
| r2_hidden(k8_funct_2(u2_conlat_1(esk1_0),u1_struct_0(k11_conlat_1(esk1_0)),k5_conlat_2(esk1_0),esk3_0),u1_struct_0(k11_conlat_1(esk1_0))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_143]) ).
cnf(c_0_150,negated_conjecture,
( v1_xboole_0(u1_conlat_1(esk1_0))
| m1_subset_1(k8_funct_2(u1_conlat_1(esk1_0),u1_struct_0(k11_conlat_1(esk1_0)),k4_conlat_2(esk1_0),esk2_0),u1_struct_0(k11_conlat_1(esk1_0))) ),
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
fof(c_0_151,plain,
! [X229] :
( v3_conlat_1(X229)
| ~ l1_conlat_1(X229)
| ~ v1_xboole_0(u1_conlat_1(X229)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_146])]) ).
cnf(c_0_152,plain,
( v3_conlat_1(X1)
| ~ l1_conlat_1(X1)
| ~ v1_xboole_0(u2_conlat_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_147]) ).
cnf(c_0_153,negated_conjecture,
( v1_xboole_0(u2_conlat_1(esk1_0))
| ~ r2_hidden(k8_funct_2(u1_conlat_1(esk1_0),u1_struct_0(k11_conlat_1(esk1_0)),k4_conlat_2(esk1_0),esk2_0),u1_struct_0(k11_conlat_1(esk1_0))) ),
inference(spm,[status(thm)],[c_0_148,c_0_149]) ).
cnf(c_0_154,negated_conjecture,
( v1_xboole_0(u1_conlat_1(esk1_0))
| r2_hidden(k8_funct_2(u1_conlat_1(esk1_0),u1_struct_0(k11_conlat_1(esk1_0)),k4_conlat_2(esk1_0),esk2_0),u1_struct_0(k11_conlat_1(esk1_0))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_150]),c_0_143]) ).
cnf(c_0_155,plain,
( v3_conlat_1(X1)
| ~ l1_conlat_1(X1)
| ~ v1_xboole_0(u1_conlat_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_151]) ).
cnf(c_0_156,negated_conjecture,
( ~ v1_xboole_0(u2_conlat_1(esk1_0))
| ~ l1_conlat_1(esk1_0) ),
inference(spm,[status(thm)],[c_0_31,c_0_152]) ).
cnf(c_0_157,negated_conjecture,
( v1_xboole_0(u1_conlat_1(esk1_0))
| v1_xboole_0(u2_conlat_1(esk1_0)) ),
inference(spm,[status(thm)],[c_0_153,c_0_154]) ).
cnf(c_0_158,negated_conjecture,
( ~ v1_xboole_0(u1_conlat_1(esk1_0))
| ~ l1_conlat_1(esk1_0) ),
inference(spm,[status(thm)],[c_0_31,c_0_155]) ).
fof(c_0_159,plain,
! [X197] :
( ~ l2_conlat_1(X197)
| l1_conlat_1(X197) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_conlat_1])]) ).
cnf(c_0_160,negated_conjecture,
~ l1_conlat_1(esk1_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_157]),c_0_158]) ).
cnf(c_0_161,plain,
( l1_conlat_1(X1)
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_159]) ).
cnf(c_0_162,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : LAT343+1 : TPTP v9.2.1. Released v3.4.0.
% 0.12/0.13 % 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
% 0.17/0.35 % Computer : n025.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Mon May 4 21:26:58 EDT 2026
% 0.17/0.35 % CPUTime :
% 0.22/0.36 % start to proof: theBenchmark
% 6.05/4.45 % Version : CSE_E---1.7
% 6.05/4.45 % Problem : theBenchmark.p
% 6.05/4.45 % SZS status Theorem for theBenchmark.p
% 6.05/4.45 % SZS output start CNFRefutation
% See solution above
% 6.05/4.47 % Total time : 3.378s
%------------------------------------------------------------------------------