TSTP Solution File: LAT332+1 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : LAT332+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n032.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 : 600s
% DateTime : Sun Jul 17 04:47:16 EDT 2022
% Result : Theorem 0.17s 2.35s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 21
% Syntax : Number of formulae : 100 ( 6 unt; 0 def)
% Number of atoms : 427 ( 72 equ)
% Maximal formula atoms : 88 ( 4 avg)
% Number of connectives : 544 ( 217 ~; 242 |; 58 &)
% ( 3 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 1 con; 0-3 aty)
% Number of variables : 168 ( 12 sgn 83 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc1_relset_1,axiom,
! [X1,X2,X3] :
( m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
=> v1_relat_1(X3) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',cc1_relset_1) ).
fof(dt_m2_relset_1,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
=> m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',dt_m2_relset_1) ).
fof(t97_relat_1,axiom,
! [X1,X2] :
( v1_relat_1(X2)
=> ( r1_tarski(k1_relat_1(X2),X1)
=> k7_relat_1(X2,X1) = X2 ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',t97_relat_1) ).
fof(t3_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,k1_zfmisc_1(X2))
<=> r1_tarski(X1,X2) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',t3_subset) ).
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/solver/bin/../tmp/theBenchmark.p',redefinition_m2_relset_1) ).
fof(redefinition_k4_relset_1,axiom,
! [X1,X2,X3] :
( m1_relset_1(X3,X1,X2)
=> k4_relset_1(X1,X2,X3) = k1_relat_1(X3) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',redefinition_k4_relset_1) ).
fof(dt_k4_relset_1,axiom,
! [X1,X2,X3] :
( m1_relset_1(X3,X1,X2)
=> m1_subset_1(k4_relset_1(X1,X2,X3),k1_zfmisc_1(X1)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',dt_k4_relset_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/sandbox/solver/bin/../tmp/theBenchmark.p',dt_u1_lattices) ).
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/sandbox/solver/bin/../tmp/theBenchmark.p',dt_m2_filter_2) ).
fof(dt_k17_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> m2_filter_2(k17_filter_2(X1),X1) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',dt_k17_filter_2) ).
fof(fc1_struct_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fc1_struct_0) ).
fof(dt_l1_lattices,axiom,
! [X1] :
( l1_lattices(X1)
=> l1_struct_0(X1) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',dt_l1_lattices) ).
fof(d3_realset1,axiom,
! [X1] :
( v1_relat_1(X1)
=> ! [X2] : k1_realset1(X1,X2) = k7_relat_1(X1,k2_zfmisc_1(X2,X2)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',d3_realset1) ).
fof(d8_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> k17_filter_2(X1) = u1_struct_0(X1) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',d8_filter_2) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( l1_lattices(X1)
& l2_lattices(X1) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',dt_l3_lattices) ).
fof(d16_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) )
=> ! [X3] :
( m2_nat_lat(X3,X1)
=> ( X3 = k23_filter_2(X1,X2)
<=> ? [X4] :
( v1_funct_1(X4)
& v1_funct_2(X4,k2_zfmisc_1(X2,X2),X2)
& m2_relset_1(X4,k2_zfmisc_1(X2,X2),X2)
& ? [X5] :
( v1_funct_1(X5)
& v1_funct_2(X5,k2_zfmisc_1(X2,X2),X2)
& m2_relset_1(X5,k2_zfmisc_1(X2,X2),X2)
& X4 = k1_realset1(u2_lattices(X1),X2)
& X5 = k1_realset1(u1_lattices(X1),X2)
& X3 = g3_lattices(X2,X4,X5) ) ) ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',d16_filter_2) ).
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/sandbox/solver/bin/../tmp/theBenchmark.p',dt_u2_lattices) ).
fof(t72_filter_2,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( k23_filter_2(X1,k17_filter_2(X1)) = g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1))
& k23_filter_2(X1,k1_filter_2(X1)) = g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1)) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',t72_filter_2) ).
fof(redefinition_k1_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> k1_filter_2(X1) = k1_filter_0(X1) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',redefinition_k1_filter_2) ).
fof(d2_filter_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> k1_filter_0(X1) = u1_struct_0(X1) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',d2_filter_0) ).
fof(dt_k23_filter_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) )
=> m2_nat_lat(k23_filter_2(X1,X2),X1) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',dt_k23_filter_2) ).
fof(c_0_21,plain,
! [X4,X5,X6] :
( ~ m1_subset_1(X6,k1_zfmisc_1(k2_zfmisc_1(X4,X5)))
| v1_relat_1(X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])]) ).
fof(c_0_22,plain,
! [X4,X5,X6] :
( ~ m2_relset_1(X6,X4,X5)
| m1_subset_1(X6,k1_zfmisc_1(k2_zfmisc_1(X4,X5))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_relset_1])]) ).
fof(c_0_23,plain,
! [X3,X4] :
( ~ v1_relat_1(X4)
| ~ r1_tarski(k1_relat_1(X4),X3)
| k7_relat_1(X4,X3) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t97_relat_1])]) ).
fof(c_0_24,plain,
! [X3,X4,X3,X4] :
( ( ~ m1_subset_1(X3,k1_zfmisc_1(X4))
| r1_tarski(X3,X4) )
& ( ~ r1_tarski(X3,X4)
| m1_subset_1(X3,k1_zfmisc_1(X4)) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])])]) ).
cnf(c_0_25,plain,
( v1_relat_1(X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,plain,
( m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))
| ~ m2_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_27,plain,
! [X4,X5,X6,X4,X5,X6] :
( ( ~ m2_relset_1(X6,X4,X5)
| m1_relset_1(X6,X4,X5) )
& ( ~ m1_relset_1(X6,X4,X5)
| m2_relset_1(X6,X4,X5) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])])])]) ).
cnf(c_0_28,plain,
( k7_relat_1(X1,X2) = X1
| ~ r1_tarski(k1_relat_1(X1),X2)
| ~ v1_relat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
( r1_tarski(X1,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_30,plain,
! [X4,X5,X6] :
( ~ m1_relset_1(X6,X4,X5)
| k4_relset_1(X4,X5,X6) = k1_relat_1(X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_relset_1])]) ).
cnf(c_0_31,plain,
( v1_relat_1(X1)
| ~ m2_relset_1(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
( m2_relset_1(X1,X2,X3)
| ~ m1_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
( k7_relat_1(X1,X2) = X1
| ~ v1_relat_1(X1)
| ~ m1_subset_1(k1_relat_1(X1),k1_zfmisc_1(X2)) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
( k4_relset_1(X1,X2,X3) = k1_relat_1(X3)
| ~ m1_relset_1(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,plain,
( v1_relat_1(X1)
| ~ m1_relset_1(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
fof(c_0_36,plain,
! [X4,X5,X6] :
( ~ m1_relset_1(X6,X4,X5)
| m1_subset_1(k4_relset_1(X4,X5,X6),k1_zfmisc_1(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k4_relset_1])]) ).
fof(c_0_37,plain,
! [X2] :
( ( v1_funct_1(u1_lattices(X2))
| ~ l1_lattices(X2) )
& ( v1_funct_2(u1_lattices(X2),k2_zfmisc_1(u1_struct_0(X2),u1_struct_0(X2)),u1_struct_0(X2))
| ~ l1_lattices(X2) )
& ( m2_relset_1(u1_lattices(X2),k2_zfmisc_1(u1_struct_0(X2),u1_struct_0(X2)),u1_struct_0(X2))
| ~ l1_lattices(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_lattices])])]) ).
cnf(c_0_38,plain,
( k7_relat_1(X1,X2) = X1
| ~ m1_relset_1(X1,X3,X4)
| ~ m1_subset_1(k4_relset_1(X3,X4,X1),k1_zfmisc_1(X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_39,plain,
( m1_subset_1(k4_relset_1(X1,X2,X3),k1_zfmisc_1(X1))
| ~ m1_relset_1(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_40,plain,
( m1_relset_1(X1,X2,X3)
| ~ m2_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_41,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_37]) ).
fof(c_0_42,plain,
! [X3,X4] :
( ( ~ v1_xboole_0(X4)
| ~ m2_filter_2(X4,X3)
| v3_struct_0(X3)
| ~ v10_lattices(X3)
| ~ l3_lattices(X3) )
& ( m2_lattice4(X4,X3)
| ~ m2_filter_2(X4,X3)
| v3_struct_0(X3)
| ~ v10_lattices(X3)
| ~ l3_lattices(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_m2_filter_2])])])])])])]) ).
fof(c_0_43,plain,
! [X2] :
( v3_struct_0(X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2)
| m2_filter_2(k17_filter_2(X2),X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k17_filter_2])])]) ).
fof(c_0_44,plain,
! [X2] :
( v3_struct_0(X2)
| ~ l1_struct_0(X2)
| ~ v1_xboole_0(u1_struct_0(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc1_struct_0])])]) ).
fof(c_0_45,plain,
! [X2] :
( ~ l1_lattices(X2)
| l1_struct_0(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_lattices])]) ).
fof(c_0_46,plain,
! [X3,X4] :
( ~ v1_relat_1(X3)
| k1_realset1(X3,X4) = k7_relat_1(X3,k2_zfmisc_1(X4,X4)) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_realset1])])])])]) ).
cnf(c_0_47,plain,
( k7_relat_1(X1,X2) = X1
| ~ m1_relset_1(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_48,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_40,c_0_41]) ).
cnf(c_0_49,plain,
( v3_struct_0(X1)
| m2_lattice4(X2,X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m2_filter_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_50,plain,
( m2_filter_2(k17_filter_2(X1),X1)
| v3_struct_0(X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
fof(c_0_51,plain,
! [X2] :
( v3_struct_0(X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2)
| k17_filter_2(X2) = u1_struct_0(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d8_filter_2])])]) ).
cnf(c_0_52,plain,
( v3_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1))
| ~ l1_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_53,plain,
( l1_struct_0(X1)
| ~ l1_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
fof(c_0_54,plain,
! [X2] :
( ( l1_lattices(X2)
| ~ l3_lattices(X2) )
& ( l2_lattices(X2)
| ~ l3_lattices(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
fof(c_0_55,plain,
! [X6,X7,X8,X11,X12] :
( ( v1_funct_1(esk2_3(X6,X7,X8))
| X8 != k23_filter_2(X6,X7)
| ~ m2_nat_lat(X8,X6)
| v1_xboole_0(X7)
| ~ m2_lattice4(X7,X6)
| v3_struct_0(X6)
| ~ v10_lattices(X6)
| ~ l3_lattices(X6) )
& ( v1_funct_2(esk2_3(X6,X7,X8),k2_zfmisc_1(X7,X7),X7)
| X8 != k23_filter_2(X6,X7)
| ~ m2_nat_lat(X8,X6)
| v1_xboole_0(X7)
| ~ m2_lattice4(X7,X6)
| v3_struct_0(X6)
| ~ v10_lattices(X6)
| ~ l3_lattices(X6) )
& ( m2_relset_1(esk2_3(X6,X7,X8),k2_zfmisc_1(X7,X7),X7)
| X8 != k23_filter_2(X6,X7)
| ~ m2_nat_lat(X8,X6)
| v1_xboole_0(X7)
| ~ m2_lattice4(X7,X6)
| v3_struct_0(X6)
| ~ v10_lattices(X6)
| ~ l3_lattices(X6) )
& ( v1_funct_1(esk3_3(X6,X7,X8))
| X8 != k23_filter_2(X6,X7)
| ~ m2_nat_lat(X8,X6)
| v1_xboole_0(X7)
| ~ m2_lattice4(X7,X6)
| v3_struct_0(X6)
| ~ v10_lattices(X6)
| ~ l3_lattices(X6) )
& ( v1_funct_2(esk3_3(X6,X7,X8),k2_zfmisc_1(X7,X7),X7)
| X8 != k23_filter_2(X6,X7)
| ~ m2_nat_lat(X8,X6)
| v1_xboole_0(X7)
| ~ m2_lattice4(X7,X6)
| v3_struct_0(X6)
| ~ v10_lattices(X6)
| ~ l3_lattices(X6) )
& ( m2_relset_1(esk3_3(X6,X7,X8),k2_zfmisc_1(X7,X7),X7)
| X8 != k23_filter_2(X6,X7)
| ~ m2_nat_lat(X8,X6)
| v1_xboole_0(X7)
| ~ m2_lattice4(X7,X6)
| v3_struct_0(X6)
| ~ v10_lattices(X6)
| ~ l3_lattices(X6) )
& ( esk2_3(X6,X7,X8) = k1_realset1(u2_lattices(X6),X7)
| X8 != k23_filter_2(X6,X7)
| ~ m2_nat_lat(X8,X6)
| v1_xboole_0(X7)
| ~ m2_lattice4(X7,X6)
| v3_struct_0(X6)
| ~ v10_lattices(X6)
| ~ l3_lattices(X6) )
& ( esk3_3(X6,X7,X8) = k1_realset1(u1_lattices(X6),X7)
| X8 != k23_filter_2(X6,X7)
| ~ m2_nat_lat(X8,X6)
| v1_xboole_0(X7)
| ~ m2_lattice4(X7,X6)
| v3_struct_0(X6)
| ~ v10_lattices(X6)
| ~ l3_lattices(X6) )
& ( X8 = g3_lattices(X7,esk2_3(X6,X7,X8),esk3_3(X6,X7,X8))
| X8 != k23_filter_2(X6,X7)
| ~ m2_nat_lat(X8,X6)
| v1_xboole_0(X7)
| ~ m2_lattice4(X7,X6)
| v3_struct_0(X6)
| ~ v10_lattices(X6)
| ~ l3_lattices(X6) )
& ( ~ v1_funct_1(X11)
| ~ v1_funct_2(X11,k2_zfmisc_1(X7,X7),X7)
| ~ m2_relset_1(X11,k2_zfmisc_1(X7,X7),X7)
| ~ v1_funct_1(X12)
| ~ v1_funct_2(X12,k2_zfmisc_1(X7,X7),X7)
| ~ m2_relset_1(X12,k2_zfmisc_1(X7,X7),X7)
| X11 != k1_realset1(u2_lattices(X6),X7)
| X12 != k1_realset1(u1_lattices(X6),X7)
| X8 != g3_lattices(X7,X11,X12)
| X8 = k23_filter_2(X6,X7)
| ~ m2_nat_lat(X8,X6)
| v1_xboole_0(X7)
| ~ m2_lattice4(X7,X6)
| v3_struct_0(X6)
| ~ v10_lattices(X6)
| ~ l3_lattices(X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d16_filter_2])])])])])])])]) ).
cnf(c_0_56,plain,
( k1_realset1(X1,X2) = k7_relat_1(X1,k2_zfmisc_1(X2,X2))
| ~ v1_relat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_57,plain,
( k7_relat_1(u1_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1))) = u1_lattices(X1)
| ~ l1_lattices(X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_58,plain,
( v1_relat_1(u1_lattices(X1))
| ~ l1_lattices(X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_41]) ).
cnf(c_0_59,plain,
( m2_lattice4(k17_filter_2(X1),X1)
| v3_struct_0(X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_60,plain,
( k17_filter_2(X1) = u1_struct_0(X1)
| v3_struct_0(X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_61,plain,
( v3_struct_0(X1)
| ~ l1_lattices(X1)
| ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_62,plain,
( l1_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
fof(c_0_63,plain,
! [X2] :
( ( v1_funct_1(u2_lattices(X2))
| ~ l2_lattices(X2) )
& ( v1_funct_2(u2_lattices(X2),k2_zfmisc_1(u1_struct_0(X2),u1_struct_0(X2)),u1_struct_0(X2))
| ~ l2_lattices(X2) )
& ( m2_relset_1(u2_lattices(X2),k2_zfmisc_1(u1_struct_0(X2),u1_struct_0(X2)),u1_struct_0(X2))
| ~ l2_lattices(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u2_lattices])])]) ).
cnf(c_0_64,plain,
( v3_struct_0(X1)
| v1_xboole_0(X2)
| X3 = g3_lattices(X2,esk2_3(X1,X2,X3),esk3_3(X1,X2,X3))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m2_lattice4(X2,X1)
| ~ m2_nat_lat(X3,X1)
| X3 != k23_filter_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_65,plain,
( v3_struct_0(X1)
| v1_xboole_0(X2)
| esk2_3(X1,X2,X3) = k1_realset1(u2_lattices(X1),X2)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m2_lattice4(X2,X1)
| ~ m2_nat_lat(X3,X1)
| X3 != k23_filter_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_66,plain,
( v3_struct_0(X1)
| v1_xboole_0(X2)
| esk3_3(X1,X2,X3) = k1_realset1(u1_lattices(X1),X2)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m2_lattice4(X2,X1)
| ~ m2_nat_lat(X3,X1)
| X3 != k23_filter_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_67,plain,
( k1_realset1(u1_lattices(X1),u1_struct_0(X1)) = u1_lattices(X1)
| ~ l1_lattices(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]) ).
cnf(c_0_68,plain,
( m2_lattice4(u1_struct_0(X1),X1)
| v3_struct_0(X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_69,plain,
( v3_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1))
| ~ l3_lattices(X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_70,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_63]) ).
cnf(c_0_71,plain,
( g3_lattices(X1,k1_realset1(u2_lattices(X2),X1),esk3_3(X2,X1,X3)) = X3
| v1_xboole_0(X1)
| v3_struct_0(X2)
| X3 != k23_filter_2(X2,X1)
| ~ m2_nat_lat(X3,X2)
| ~ m2_lattice4(X1,X2)
| ~ l3_lattices(X2)
| ~ v10_lattices(X2) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_72,plain,
( esk3_3(X1,u1_struct_0(X1),X2) = u1_lattices(X1)
| v3_struct_0(X1)
| X2 != k23_filter_2(X1,u1_struct_0(X1))
| ~ m2_nat_lat(X2,X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_62]),c_0_68]),c_0_69]) ).
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_40,c_0_70]) ).
fof(c_0_74,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( k23_filter_2(X1,k17_filter_2(X1)) = g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1))
& k23_filter_2(X1,k1_filter_2(X1)) = g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1)) ) ),
inference(assume_negation,[status(cth)],[t72_filter_2]) ).
cnf(c_0_75,plain,
( g3_lattices(u1_struct_0(X1),k1_realset1(u2_lattices(X1),u1_struct_0(X1)),u1_lattices(X1)) = X2
| v3_struct_0(X1)
| X2 != k23_filter_2(X1,u1_struct_0(X1))
| ~ m2_nat_lat(X2,X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_68]),c_0_69]) ).
cnf(c_0_76,plain,
( k7_relat_1(u2_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1))) = u2_lattices(X1)
| ~ l2_lattices(X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_73]) ).
cnf(c_0_77,plain,
( v1_relat_1(u2_lattices(X1))
| ~ l2_lattices(X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_70]) ).
fof(c_0_78,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v10_lattices(esk1_0)
& l3_lattices(esk1_0)
& ( k23_filter_2(esk1_0,k17_filter_2(esk1_0)) != g3_lattices(u1_struct_0(esk1_0),u2_lattices(esk1_0),u1_lattices(esk1_0))
| k23_filter_2(esk1_0,k1_filter_2(esk1_0)) != g3_lattices(u1_struct_0(esk1_0),u2_lattices(esk1_0),u1_lattices(esk1_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_74])])])]) ).
cnf(c_0_79,plain,
( g3_lattices(u1_struct_0(X1),k1_realset1(u2_lattices(X1),u1_struct_0(X1)),u1_lattices(X1)) = k23_filter_2(X1,u1_struct_0(X1))
| v3_struct_0(X1)
| ~ m2_nat_lat(k23_filter_2(X1,u1_struct_0(X1)),X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(er,[status(thm)],[c_0_75]) ).
cnf(c_0_80,plain,
( k1_realset1(u2_lattices(X1),u1_struct_0(X1)) = u2_lattices(X1)
| ~ l2_lattices(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_76]),c_0_77]) ).
cnf(c_0_81,plain,
( l2_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_82,negated_conjecture,
( k23_filter_2(esk1_0,k1_filter_2(esk1_0)) != g3_lattices(u1_struct_0(esk1_0),u2_lattices(esk1_0),u1_lattices(esk1_0))
| k23_filter_2(esk1_0,k17_filter_2(esk1_0)) != g3_lattices(u1_struct_0(esk1_0),u2_lattices(esk1_0),u1_lattices(esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_83,plain,
( g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1)) = k23_filter_2(X1,u1_struct_0(X1))
| v3_struct_0(X1)
| ~ m2_nat_lat(k23_filter_2(X1,u1_struct_0(X1)),X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]) ).
cnf(c_0_84,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_85,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_86,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
fof(c_0_87,plain,
! [X2] :
( v3_struct_0(X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2)
| k1_filter_2(X2) = k1_filter_0(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_k1_filter_2])])]) ).
cnf(c_0_88,negated_conjecture,
( k23_filter_2(esk1_0,k17_filter_2(esk1_0)) != k23_filter_2(esk1_0,u1_struct_0(esk1_0))
| k23_filter_2(esk1_0,k1_filter_2(esk1_0)) != k23_filter_2(esk1_0,u1_struct_0(esk1_0))
| ~ m2_nat_lat(k23_filter_2(esk1_0,u1_struct_0(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_82,c_0_83]),c_0_84]),c_0_85])]),c_0_86]) ).
cnf(c_0_89,plain,
( k1_filter_2(X1) = k1_filter_0(X1)
| v3_struct_0(X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
fof(c_0_90,plain,
! [X2] :
( v3_struct_0(X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2)
| k1_filter_0(X2) = u1_struct_0(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d2_filter_0])])]) ).
cnf(c_0_91,negated_conjecture,
( k23_filter_2(esk1_0,k17_filter_2(esk1_0)) != k23_filter_2(esk1_0,u1_struct_0(esk1_0))
| k23_filter_2(esk1_0,k1_filter_0(esk1_0)) != k23_filter_2(esk1_0,u1_struct_0(esk1_0))
| ~ m2_nat_lat(k23_filter_2(esk1_0,u1_struct_0(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_88,c_0_89]),c_0_84]),c_0_85])]),c_0_86]) ).
cnf(c_0_92,plain,
( k1_filter_0(X1) = u1_struct_0(X1)
| v3_struct_0(X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_93,negated_conjecture,
( k23_filter_2(esk1_0,k17_filter_2(esk1_0)) != k23_filter_2(esk1_0,u1_struct_0(esk1_0))
| ~ m2_nat_lat(k23_filter_2(esk1_0,u1_struct_0(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_91,c_0_92]),c_0_84]),c_0_85])]),c_0_86]) ).
fof(c_0_94,plain,
! [X3,X4] :
( v3_struct_0(X3)
| ~ v10_lattices(X3)
| ~ l3_lattices(X3)
| v1_xboole_0(X4)
| ~ m2_lattice4(X4,X3)
| m2_nat_lat(k23_filter_2(X3,X4),X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k23_filter_2])])]) ).
cnf(c_0_95,negated_conjecture,
~ m2_nat_lat(k23_filter_2(esk1_0,u1_struct_0(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_93,c_0_60]),c_0_84]),c_0_85])]),c_0_86]) ).
cnf(c_0_96,plain,
( m2_nat_lat(k23_filter_2(X1,X2),X1)
| v1_xboole_0(X2)
| v3_struct_0(X1)
| ~ m2_lattice4(X2,X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_97,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk1_0))
| ~ m2_lattice4(u1_struct_0(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_95,c_0_96]),c_0_84]),c_0_85])]),c_0_86]) ).
cnf(c_0_98,negated_conjecture,
v1_xboole_0(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_97,c_0_68]),c_0_84]),c_0_85])]),c_0_86]) ).
cnf(c_0_99,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_98]),c_0_84])]),c_0_86]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : LAT332+1 : TPTP v8.1.0. Released v3.4.0.
% 0.00/0.10 % Command : run_ET %s %d
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Tue Jun 28 23:24:57 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.17/2.35 # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.17/2.35 # Preprocessing time : 0.017 s
% 0.17/2.35
% 0.17/2.35 # Proof found!
% 0.17/2.35 # SZS status Theorem
% 0.17/2.35 # SZS output start CNFRefutation
% See solution above
% 0.17/2.35 # Proof object total steps : 100
% 0.17/2.35 # Proof object clause steps : 57
% 0.17/2.35 # Proof object formula steps : 43
% 0.17/2.35 # Proof object conjectures : 14
% 0.17/2.35 # Proof object clause conjectures : 11
% 0.17/2.35 # Proof object formula conjectures : 3
% 0.17/2.35 # Proof object initial clauses used : 28
% 0.17/2.35 # Proof object initial formulas used : 21
% 0.17/2.35 # Proof object generating inferences : 29
% 0.17/2.35 # Proof object simplifying inferences : 36
% 0.17/2.35 # Training examples: 0 positive, 0 negative
% 0.17/2.35 # Parsed axioms : 99
% 0.17/2.35 # Removed by relevancy pruning/SinE : 0
% 0.17/2.35 # Initial clauses : 200
% 0.17/2.35 # Removed in clause preprocessing : 13
% 0.17/2.35 # Initial clauses in saturation : 187
% 0.17/2.35 # Processed clauses : 5355
% 0.17/2.35 # ...of these trivial : 30
% 0.17/2.35 # ...subsumed : 3275
% 0.17/2.35 # ...remaining for further processing : 2050
% 0.17/2.35 # Other redundant clauses eliminated : 13
% 0.17/2.35 # Clauses deleted for lack of memory : 0
% 0.17/2.35 # Backward-subsumed : 167
% 0.17/2.35 # Backward-rewritten : 15
% 0.17/2.35 # Generated clauses : 33602
% 0.17/2.35 # ...of the previous two non-trivial : 27040
% 0.17/2.35 # Contextual simplify-reflections : 7753
% 0.17/2.35 # Paramodulations : 33516
% 0.17/2.35 # Factorizations : 0
% 0.17/2.35 # Equation resolutions : 86
% 0.17/2.35 # Current number of processed clauses : 1867
% 0.17/2.35 # Positive orientable unit clauses : 58
% 0.17/2.35 # Positive unorientable unit clauses: 0
% 0.17/2.35 # Negative unit clauses : 10
% 0.17/2.35 # Non-unit-clauses : 1799
% 0.17/2.35 # Current number of unprocessed clauses: 20629
% 0.17/2.35 # ...number of literals in the above : 168451
% 0.17/2.35 # Current number of archived formulas : 0
% 0.17/2.35 # Current number of archived clauses : 182
% 0.17/2.35 # Clause-clause subsumption calls (NU) : 2617864
% 0.17/2.35 # Rec. Clause-clause subsumption calls : 244455
% 0.17/2.35 # Non-unit clause-clause subsumptions : 11192
% 0.17/2.35 # Unit Clause-clause subsumption calls : 2266
% 0.17/2.35 # Rewrite failures with RHS unbound : 0
% 0.17/2.35 # BW rewrite match attempts : 17
% 0.17/2.35 # BW rewrite match successes : 4
% 0.17/2.35 # Condensation attempts : 0
% 0.17/2.35 # Condensation successes : 0
% 0.17/2.35 # Termbank termtop insertions : 875008
% 0.17/2.35
% 0.17/2.35 # -------------------------------------------------
% 0.17/2.35 # User time : 1.723 s
% 0.17/2.35 # System time : 0.017 s
% 0.17/2.35 # Total time : 1.740 s
% 0.17/2.35 # Maximum resident set size: 27036 pages
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