%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT286+1 : TPTP v9.2.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n012.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 04:37:54 PM UTC 2026
% Result : Theorem 90.46s 51.54s
% Output : CNFRefutation 90.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 92 ( 25 unt; 0 def)
% Number of atoms : 372 ( 42 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 457 ( 177 ~; 172 |; 82 &)
% ( 3 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 1 con; 0-3 aty)
% Number of variables : 124 ( 19 sgn 61 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k4_lopclset,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v2_pre_topc(X1)
& l1_pre_topc(X1) )
=> ( v1_funct_1(k4_lopclset(X1))
& v1_funct_2(k4_lopclset(X1),k2_zfmisc_1(k1_lopclset(X1),k1_lopclset(X1)),k1_lopclset(X1))
& m2_relset_1(k4_lopclset(X1),k2_zfmisc_1(k1_lopclset(X1),k1_lopclset(X1)),k1_lopclset(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_lopclset) ).
fof(t15_lopclset,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v2_pre_topc(X1)
& l1_pre_topc(X1) )
=> m1_subset_1(k2_pre_topc(X1),u1_struct_0(k6_lopclset(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_lopclset) ).
fof(dt_k5_lopclset,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v2_pre_topc(X1)
& l1_pre_topc(X1) )
=> ( v1_funct_1(k5_lopclset(X1))
& v1_funct_2(k5_lopclset(X1),k2_zfmisc_1(k1_lopclset(X1),k1_lopclset(X1)),k1_lopclset(X1))
& m2_relset_1(k5_lopclset(X1),k2_zfmisc_1(k1_lopclset(X1),k1_lopclset(X1)),k1_lopclset(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_lopclset) ).
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
<=> m1_relset_1(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(d4_lopclset,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v2_pre_topc(X1)
& l1_pre_topc(X1) )
=> k6_lopclset(X1) = g3_lattices(k1_lopclset(X1),k4_lopclset(X1),k5_lopclset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_lopclset) ).
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/sandbox/benchmark/theBenchmark.p',free_g3_lattices) ).
fof(dt_k6_lopclset,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v2_pre_topc(X1)
& l1_pre_topc(X1) )
=> ( ~ v3_struct_0(k6_lopclset(X1))
& v10_lattices(k6_lopclset(X1))
& l3_lattices(k6_lopclset(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_lopclset) ).
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/sandbox/benchmark/theBenchmark.p',abstractness_v3_lattices) ).
fof(dt_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) )
=> ( v3_lattices(g3_lattices(X1,X2,X3))
& l3_lattices(g3_lattices(X1,X2,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_g3_lattices) ).
fof(dt_k1_lopclset,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_pre_topc(X1) )
=> m1_subset_1(k1_lopclset(X1),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(X1)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lopclset) ).
fof(redefinition_m2_subset_1,axiom,
! [X1,X2] :
( ( ~ v1_xboole_0(X1)
& ~ v1_xboole_0(X2)
& m1_subset_1(X2,k1_zfmisc_1(X1)) )
=> ! [X3] :
( m2_subset_1(X3,X1,X2)
<=> m1_subset_1(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_subset_1) ).
fof(fc1_finsub_1,axiom,
! [X1] :
( ~ v1_xboole_0(k1_zfmisc_1(X1))
& v1_finsub_1(k1_zfmisc_1(X1))
& v3_finsub_1(k1_zfmisc_1(X1))
& v4_finsub_1(k1_zfmisc_1(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_finsub_1) ).
fof(t8_lopclset,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v2_pre_topc(X1)
& l1_pre_topc(X1) )
=> m2_subset_1(k2_pre_topc(X1),k1_zfmisc_1(u1_struct_0(X1)),k1_lopclset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_lopclset) ).
fof(fc1_lopclset,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v2_pre_topc(X1)
& l1_pre_topc(X1) )
=> ~ v1_xboole_0(k1_lopclset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_lopclset) ).
fof(c_0_14,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v2_pre_topc(X1)
& l1_pre_topc(X1) )
=> ( v1_funct_1(k4_lopclset(X1))
& v1_funct_2(k4_lopclset(X1),k2_zfmisc_1(k1_lopclset(X1),k1_lopclset(X1)),k1_lopclset(X1))
& m2_relset_1(k4_lopclset(X1),k2_zfmisc_1(k1_lopclset(X1),k1_lopclset(X1)),k1_lopclset(X1)) ) ),
inference(fof_simplification,[status(thm)],[dt_k4_lopclset]) ).
fof(c_0_15,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v2_pre_topc(X1)
& l1_pre_topc(X1) )
=> m1_subset_1(k2_pre_topc(X1),u1_struct_0(k6_lopclset(X1))) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t15_lopclset])]) ).
fof(c_0_16,plain,
! [X264] :
( ( v1_funct_1(k4_lopclset(X264))
| v3_struct_0(X264)
| ~ v2_pre_topc(X264)
| ~ l1_pre_topc(X264) )
& ( v1_funct_2(k4_lopclset(X264),k2_zfmisc_1(k1_lopclset(X264),k1_lopclset(X264)),k1_lopclset(X264))
| v3_struct_0(X264)
| ~ v2_pre_topc(X264)
| ~ l1_pre_topc(X264) )
& ( m2_relset_1(k4_lopclset(X264),k2_zfmisc_1(k1_lopclset(X264),k1_lopclset(X264)),k1_lopclset(X264))
| v3_struct_0(X264)
| ~ v2_pre_topc(X264)
| ~ l1_pre_topc(X264) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
fof(c_0_17,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v2_pre_topc(esk1_0)
& l1_pre_topc(esk1_0)
& ~ m1_subset_1(k2_pre_topc(esk1_0),u1_struct_0(k6_lopclset(esk1_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
fof(c_0_18,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v2_pre_topc(X1)
& l1_pre_topc(X1) )
=> ( v1_funct_1(k5_lopclset(X1))
& v1_funct_2(k5_lopclset(X1),k2_zfmisc_1(k1_lopclset(X1),k1_lopclset(X1)),k1_lopclset(X1))
& m2_relset_1(k5_lopclset(X1),k2_zfmisc_1(k1_lopclset(X1),k1_lopclset(X1)),k1_lopclset(X1)) ) ),
inference(fof_simplification,[status(thm)],[dt_k5_lopclset]) ).
fof(c_0_19,plain,
! [X186,X187,X188] :
( ( ~ m2_relset_1(X188,X186,X187)
| m1_relset_1(X188,X186,X187) )
& ( ~ m1_relset_1(X188,X186,X187)
| m2_relset_1(X188,X186,X187) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
cnf(c_0_20,plain,
( m2_relset_1(k4_lopclset(X1),k2_zfmisc_1(k1_lopclset(X1),k1_lopclset(X1)),k1_lopclset(X1))
| v3_struct_0(X1)
| ~ v2_pre_topc(X1)
| ~ l1_pre_topc(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
l1_pre_topc(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
v2_pre_topc(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_24,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v2_pre_topc(X1)
& l1_pre_topc(X1) )
=> k6_lopclset(X1) = g3_lattices(k1_lopclset(X1),k4_lopclset(X1),k5_lopclset(X1)) ),
inference(fof_simplification,[status(thm)],[d4_lopclset]) ).
fof(c_0_25,plain,
! [X265] :
( ( v1_funct_1(k5_lopclset(X265))
| v3_struct_0(X265)
| ~ v2_pre_topc(X265)
| ~ l1_pre_topc(X265) )
& ( v1_funct_2(k5_lopclset(X265),k2_zfmisc_1(k1_lopclset(X265),k1_lopclset(X265)),k1_lopclset(X265))
| v3_struct_0(X265)
| ~ v2_pre_topc(X265)
| ~ l1_pre_topc(X265) )
& ( m2_relset_1(k5_lopclset(X265),k2_zfmisc_1(k1_lopclset(X265),k1_lopclset(X265)),k1_lopclset(X265))
| v3_struct_0(X265)
| ~ v2_pre_topc(X265)
| ~ l1_pre_topc(X265) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
fof(c_0_26,plain,
! [X252,X253,X254,X255,X256,X257] :
( ( X252 = X255
| g3_lattices(X252,X253,X254) != g3_lattices(X255,X256,X257)
| ~ v1_funct_1(X253)
| ~ v1_funct_2(X253,k2_zfmisc_1(X252,X252),X252)
| ~ m1_relset_1(X253,k2_zfmisc_1(X252,X252),X252)
| ~ v1_funct_1(X254)
| ~ v1_funct_2(X254,k2_zfmisc_1(X252,X252),X252)
| ~ m1_relset_1(X254,k2_zfmisc_1(X252,X252),X252) )
& ( X253 = X256
| g3_lattices(X252,X253,X254) != g3_lattices(X255,X256,X257)
| ~ v1_funct_1(X253)
| ~ v1_funct_2(X253,k2_zfmisc_1(X252,X252),X252)
| ~ m1_relset_1(X253,k2_zfmisc_1(X252,X252),X252)
| ~ v1_funct_1(X254)
| ~ v1_funct_2(X254,k2_zfmisc_1(X252,X252),X252)
| ~ m1_relset_1(X254,k2_zfmisc_1(X252,X252),X252) )
& ( X254 = X257
| g3_lattices(X252,X253,X254) != g3_lattices(X255,X256,X257)
| ~ v1_funct_1(X253)
| ~ v1_funct_2(X253,k2_zfmisc_1(X252,X252),X252)
| ~ m1_relset_1(X253,k2_zfmisc_1(X252,X252),X252)
| ~ v1_funct_1(X254)
| ~ v1_funct_2(X254,k2_zfmisc_1(X252,X252),X252)
| ~ m1_relset_1(X254,k2_zfmisc_1(X252,X252),X252) ) ),
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_27,plain,
( m1_relset_1(X1,X2,X3)
| ~ m2_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,negated_conjecture,
m2_relset_1(k4_lopclset(esk1_0),k2_zfmisc_1(k1_lopclset(esk1_0),k1_lopclset(esk1_0)),k1_lopclset(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_29,plain,
( v1_funct_2(k4_lopclset(X1),k2_zfmisc_1(k1_lopclset(X1),k1_lopclset(X1)),k1_lopclset(X1))
| v3_struct_0(X1)
| ~ v2_pre_topc(X1)
| ~ l1_pre_topc(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_30,plain,
( v1_funct_1(k4_lopclset(X1))
| v3_struct_0(X1)
| ~ v2_pre_topc(X1)
| ~ l1_pre_topc(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_31,plain,
! [X317] :
( v3_struct_0(X317)
| ~ v2_pre_topc(X317)
| ~ l1_pre_topc(X317)
| k6_lopclset(X317) = g3_lattices(k1_lopclset(X317),k4_lopclset(X317),k5_lopclset(X317)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])]) ).
cnf(c_0_32,plain,
( m2_relset_1(k5_lopclset(X1),k2_zfmisc_1(k1_lopclset(X1),k1_lopclset(X1)),k1_lopclset(X1))
| v3_struct_0(X1)
| ~ v2_pre_topc(X1)
| ~ l1_pre_topc(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_33,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v2_pre_topc(X1)
& l1_pre_topc(X1) )
=> ( ~ v3_struct_0(k6_lopclset(X1))
& v10_lattices(k6_lopclset(X1))
& l3_lattices(k6_lopclset(X1)) ) ),
inference(fof_simplification,[status(thm)],[dt_k6_lopclset]) ).
cnf(c_0_34,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_26]) ).
cnf(c_0_35,negated_conjecture,
m1_relset_1(k4_lopclset(esk1_0),k2_zfmisc_1(k1_lopclset(esk1_0),k1_lopclset(esk1_0)),k1_lopclset(esk1_0)),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_36,negated_conjecture,
v1_funct_2(k4_lopclset(esk1_0),k2_zfmisc_1(k1_lopclset(esk1_0),k1_lopclset(esk1_0)),k1_lopclset(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_37,negated_conjecture,
v1_funct_1(k4_lopclset(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_38,plain,
( v3_struct_0(X1)
| k6_lopclset(X1) = g3_lattices(k1_lopclset(X1),k4_lopclset(X1),k5_lopclset(X1))
| ~ v2_pre_topc(X1)
| ~ l1_pre_topc(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_39,negated_conjecture,
m2_relset_1(k5_lopclset(esk1_0),k2_zfmisc_1(k1_lopclset(esk1_0),k1_lopclset(esk1_0)),k1_lopclset(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_40,plain,
( v1_funct_2(k5_lopclset(X1),k2_zfmisc_1(k1_lopclset(X1),k1_lopclset(X1)),k1_lopclset(X1))
| v3_struct_0(X1)
| ~ v2_pre_topc(X1)
| ~ l1_pre_topc(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_41,plain,
( v1_funct_1(k5_lopclset(X1))
| v3_struct_0(X1)
| ~ v2_pre_topc(X1)
| ~ l1_pre_topc(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_42,plain,
! [X306] :
( ( ~ v3_struct_0(k6_lopclset(X306))
| v3_struct_0(X306)
| ~ v2_pre_topc(X306)
| ~ l1_pre_topc(X306) )
& ( v10_lattices(k6_lopclset(X306))
| v3_struct_0(X306)
| ~ v2_pre_topc(X306)
| ~ l1_pre_topc(X306) )
& ( l3_lattices(k6_lopclset(X306))
| v3_struct_0(X306)
| ~ v2_pre_topc(X306)
| ~ l1_pre_topc(X306) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])]) ).
cnf(c_0_43,negated_conjecture,
( X1 = X2
| g3_lattices(k1_lopclset(esk1_0),k4_lopclset(esk1_0),X1) != g3_lattices(X3,X4,X2)
| ~ m1_relset_1(X1,k2_zfmisc_1(k1_lopclset(esk1_0),k1_lopclset(esk1_0)),k1_lopclset(esk1_0))
| ~ v1_funct_2(X1,k2_zfmisc_1(k1_lopclset(esk1_0),k1_lopclset(esk1_0)),k1_lopclset(esk1_0))
| ~ v1_funct_1(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_37])]) ).
cnf(c_0_44,negated_conjecture,
g3_lattices(k1_lopclset(esk1_0),k4_lopclset(esk1_0),k5_lopclset(esk1_0)) = k6_lopclset(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_45,negated_conjecture,
m1_relset_1(k5_lopclset(esk1_0),k2_zfmisc_1(k1_lopclset(esk1_0),k1_lopclset(esk1_0)),k1_lopclset(esk1_0)),
inference(spm,[status(thm)],[c_0_27,c_0_39]) ).
cnf(c_0_46,negated_conjecture,
v1_funct_2(k5_lopclset(esk1_0),k2_zfmisc_1(k1_lopclset(esk1_0),k1_lopclset(esk1_0)),k1_lopclset(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_47,negated_conjecture,
v1_funct_1(k5_lopclset(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_21]),c_0_22])]),c_0_23]) ).
fof(c_0_48,plain,
! [X177] :
( ~ l3_lattices(X177)
| ~ v3_lattices(X177)
| X177 = g3_lattices(u1_struct_0(X177),u2_lattices(X177),u1_lattices(X177)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[abstractness_v3_lattices])]) ).
cnf(c_0_49,plain,
( l3_lattices(k6_lopclset(X1))
| v3_struct_0(X1)
| ~ v2_pre_topc(X1)
| ~ l1_pre_topc(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
fof(c_0_50,plain,
! [X261,X262,X263] :
( ( v3_lattices(g3_lattices(X261,X262,X263))
| ~ v1_funct_1(X262)
| ~ v1_funct_2(X262,k2_zfmisc_1(X261,X261),X261)
| ~ m1_relset_1(X262,k2_zfmisc_1(X261,X261),X261)
| ~ v1_funct_1(X263)
| ~ v1_funct_2(X263,k2_zfmisc_1(X261,X261),X261)
| ~ m1_relset_1(X263,k2_zfmisc_1(X261,X261),X261) )
& ( l3_lattices(g3_lattices(X261,X262,X263))
| ~ v1_funct_1(X262)
| ~ v1_funct_2(X262,k2_zfmisc_1(X261,X261),X261)
| ~ m1_relset_1(X262,k2_zfmisc_1(X261,X261),X261)
| ~ v1_funct_1(X263)
| ~ v1_funct_2(X263,k2_zfmisc_1(X261,X261),X261)
| ~ m1_relset_1(X263,k2_zfmisc_1(X261,X261),X261) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_g3_lattices])])]) ).
cnf(c_0_51,negated_conjecture,
( k5_lopclset(esk1_0) = X1
| k6_lopclset(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_43,c_0_44]),c_0_45]),c_0_46]),c_0_47])]) ).
cnf(c_0_52,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_48]) ).
cnf(c_0_53,negated_conjecture,
l3_lattices(k6_lopclset(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_54,plain,
( v3_lattices(g3_lattices(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) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_55,plain,
( X1 = X2
| g3_lattices(X3,X1,X4) != g3_lattices(X5,X2,X6)
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k2_zfmisc_1(X3,X3),X3)
| ~ m1_relset_1(X1,k2_zfmisc_1(X3,X3),X3)
| ~ v1_funct_1(X4)
| ~ v1_funct_2(X4,k2_zfmisc_1(X3,X3),X3)
| ~ m1_relset_1(X4,k2_zfmisc_1(X3,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_56,negated_conjecture,
( u1_lattices(k6_lopclset(esk1_0)) = k5_lopclset(esk1_0)
| ~ v3_lattices(k6_lopclset(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52])]),c_0_53])]) ).
cnf(c_0_57,negated_conjecture,
( v3_lattices(g3_lattices(k1_lopclset(esk1_0),X1,k5_lopclset(esk1_0)))
| ~ m1_relset_1(X1,k2_zfmisc_1(k1_lopclset(esk1_0),k1_lopclset(esk1_0)),k1_lopclset(esk1_0))
| ~ v1_funct_2(X1,k2_zfmisc_1(k1_lopclset(esk1_0),k1_lopclset(esk1_0)),k1_lopclset(esk1_0))
| ~ v1_funct_1(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_45]),c_0_46]),c_0_47])]) ).
fof(c_0_58,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_pre_topc(X1) )
=> m1_subset_1(k1_lopclset(X1),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(X1)))) ),
inference(fof_simplification,[status(thm)],[dt_k1_lopclset]) ).
cnf(c_0_59,negated_conjecture,
( X1 = X2
| g3_lattices(k1_lopclset(esk1_0),X1,k5_lopclset(esk1_0)) != g3_lattices(X3,X2,X4)
| ~ m1_relset_1(X1,k2_zfmisc_1(k1_lopclset(esk1_0),k1_lopclset(esk1_0)),k1_lopclset(esk1_0))
| ~ v1_funct_2(X1,k2_zfmisc_1(k1_lopclset(esk1_0),k1_lopclset(esk1_0)),k1_lopclset(esk1_0))
| ~ v1_funct_1(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_45]),c_0_46]),c_0_47])]) ).
cnf(c_0_60,negated_conjecture,
( g3_lattices(u1_struct_0(k6_lopclset(esk1_0)),u2_lattices(k6_lopclset(esk1_0)),k5_lopclset(esk1_0)) = k6_lopclset(esk1_0)
| ~ v3_lattices(k6_lopclset(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_56]),c_0_53])]) ).
cnf(c_0_61,negated_conjecture,
v3_lattices(k6_lopclset(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_44]),c_0_35]),c_0_36]),c_0_37])]) ).
fof(c_0_62,plain,
! [X1,X2] :
( ( ~ v1_xboole_0(X1)
& ~ v1_xboole_0(X2)
& m1_subset_1(X2,k1_zfmisc_1(X1)) )
=> ! [X3] :
( m2_subset_1(X3,X1,X2)
<=> m1_subset_1(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[redefinition_m2_subset_1]) ).
fof(c_0_63,plain,
! [X304] :
( v3_struct_0(X304)
| ~ l1_pre_topc(X304)
| m1_subset_1(k1_lopclset(X304),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(X304)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_58])]) ).
fof(c_0_64,plain,
! [X1] :
( ~ v1_xboole_0(k1_zfmisc_1(X1))
& v1_finsub_1(k1_zfmisc_1(X1))
& v3_finsub_1(k1_zfmisc_1(X1))
& v4_finsub_1(k1_zfmisc_1(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_finsub_1]) ).
fof(c_0_65,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v2_pre_topc(X1)
& l1_pre_topc(X1) )
=> m2_subset_1(k2_pre_topc(X1),k1_zfmisc_1(u1_struct_0(X1)),k1_lopclset(X1)) ),
inference(fof_simplification,[status(thm)],[t8_lopclset]) ).
cnf(c_0_66,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_26]) ).
cnf(c_0_67,negated_conjecture,
( k4_lopclset(esk1_0) = X1
| k6_lopclset(esk1_0) != g3_lattices(X2,X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_44]),c_0_35]),c_0_36]),c_0_37])]) ).
cnf(c_0_68,negated_conjecture,
g3_lattices(u1_struct_0(k6_lopclset(esk1_0)),u2_lattices(k6_lopclset(esk1_0)),k5_lopclset(esk1_0)) = k6_lopclset(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_61])]) ).
fof(c_0_69,plain,
! [X301,X302,X303] :
( ( ~ m2_subset_1(X303,X301,X302)
| m1_subset_1(X303,X302)
| v1_xboole_0(X301)
| v1_xboole_0(X302)
| ~ m1_subset_1(X302,k1_zfmisc_1(X301)) )
& ( ~ m1_subset_1(X303,X302)
| m2_subset_1(X303,X301,X302)
| v1_xboole_0(X301)
| v1_xboole_0(X302)
| ~ m1_subset_1(X302,k1_zfmisc_1(X301)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_62])])])]) ).
cnf(c_0_70,plain,
( v3_struct_0(X1)
| m1_subset_1(k1_lopclset(X1),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(X1))))
| ~ l1_pre_topc(X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
fof(c_0_71,plain,
! [X311] :
( ~ v1_xboole_0(k1_zfmisc_1(X311))
& v1_finsub_1(k1_zfmisc_1(X311))
& v3_finsub_1(k1_zfmisc_1(X311))
& v4_finsub_1(k1_zfmisc_1(X311)) ),
inference(variable_rename,[status(thm)],[c_0_64]) ).
fof(c_0_72,plain,
! [X318] :
( v3_struct_0(X318)
| ~ v2_pre_topc(X318)
| ~ l1_pre_topc(X318)
| m2_subset_1(k2_pre_topc(X318),k1_zfmisc_1(u1_struct_0(X318)),k1_lopclset(X318)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_65])]) ).
cnf(c_0_73,negated_conjecture,
( k1_lopclset(esk1_0) = X1
| g3_lattices(k1_lopclset(esk1_0),X2,k5_lopclset(esk1_0)) != g3_lattices(X1,X3,X4)
| ~ m1_relset_1(X2,k2_zfmisc_1(k1_lopclset(esk1_0),k1_lopclset(esk1_0)),k1_lopclset(esk1_0))
| ~ v1_funct_2(X2,k2_zfmisc_1(k1_lopclset(esk1_0),k1_lopclset(esk1_0)),k1_lopclset(esk1_0))
| ~ v1_funct_1(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_45]),c_0_46]),c_0_47])]) ).
cnf(c_0_74,negated_conjecture,
u2_lattices(k6_lopclset(esk1_0)) = k4_lopclset(esk1_0),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_75,plain,
( m1_subset_1(X1,X3)
| v1_xboole_0(X2)
| v1_xboole_0(X3)
| ~ m2_subset_1(X1,X2,X3)
| ~ m1_subset_1(X3,k1_zfmisc_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_76,negated_conjecture,
m1_subset_1(k1_lopclset(esk1_0),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(esk1_0)))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_21]),c_0_23]) ).
cnf(c_0_77,plain,
~ v1_xboole_0(k1_zfmisc_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_78,plain,
( v3_struct_0(X1)
| m2_subset_1(k2_pre_topc(X1),k1_zfmisc_1(u1_struct_0(X1)),k1_lopclset(X1))
| ~ v2_pre_topc(X1)
| ~ l1_pre_topc(X1) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_79,negated_conjecture,
( k1_lopclset(esk1_0) = X1
| k6_lopclset(esk1_0) != g3_lattices(X1,X2,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_44]),c_0_35]),c_0_36]),c_0_37])]) ).
cnf(c_0_80,negated_conjecture,
g3_lattices(u1_struct_0(k6_lopclset(esk1_0)),k4_lopclset(esk1_0),k5_lopclset(esk1_0)) = k6_lopclset(esk1_0),
inference(rw,[status(thm)],[c_0_68,c_0_74]) ).
fof(c_0_81,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v2_pre_topc(X1)
& l1_pre_topc(X1) )
=> ~ v1_xboole_0(k1_lopclset(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_lopclset]) ).
cnf(c_0_82,negated_conjecture,
( v1_xboole_0(k1_lopclset(esk1_0))
| m1_subset_1(X1,k1_lopclset(esk1_0))
| ~ m2_subset_1(X1,k1_zfmisc_1(u1_struct_0(esk1_0)),k1_lopclset(esk1_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77]) ).
cnf(c_0_83,negated_conjecture,
m2_subset_1(k2_pre_topc(esk1_0),k1_zfmisc_1(u1_struct_0(esk1_0)),k1_lopclset(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_84,negated_conjecture,
~ m1_subset_1(k2_pre_topc(esk1_0),u1_struct_0(k6_lopclset(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_85,negated_conjecture,
u1_struct_0(k6_lopclset(esk1_0)) = k1_lopclset(esk1_0),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
fof(c_0_86,plain,
! [X312] :
( v3_struct_0(X312)
| ~ v2_pre_topc(X312)
| ~ l1_pre_topc(X312)
| ~ v1_xboole_0(k1_lopclset(X312)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_81])]) ).
cnf(c_0_87,negated_conjecture,
( v1_xboole_0(k1_lopclset(esk1_0))
| m1_subset_1(k2_pre_topc(esk1_0),k1_lopclset(esk1_0)) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_88,negated_conjecture,
~ m1_subset_1(k2_pre_topc(esk1_0),k1_lopclset(esk1_0)),
inference(rw,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_89,plain,
( v3_struct_0(X1)
| ~ v2_pre_topc(X1)
| ~ l1_pre_topc(X1)
| ~ v1_xboole_0(k1_lopclset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_90,negated_conjecture,
v1_xboole_0(k1_lopclset(esk1_0)),
inference(sr,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_91,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_21]),c_0_22])]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : LAT286+1 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.06 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Mon May 4 20:59:46 EDT 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 % start to proof: theBenchmark
% 90.46/51.54 % Version : CSE_E---1.7
% 90.46/51.54 % Problem : theBenchmark.p
% 90.46/51.54 % SZS status Theorem for theBenchmark.p
% 90.46/51.54 % SZS output start CNFRefutation
% See solution above
% 90.75/51.82 % Total time : 40.260s
%------------------------------------------------------------------------------