%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LAT313+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:04:51 PM UTC 2026
% Result : Theorem 0.24s 5.62s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 90 ( 26 unt; 0 def)
% Number of atoms : 334 ( 27 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 386 ( 142 ~; 139 |; 64 &)
% ( 3 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 113 ( 2 sgn 71 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t43_filter_2,conjecture,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( ( r2_hidden(k6_lattices(X1),X2)
& v14_lattices(X1) )
=> ( X2 = u1_struct_0(X1)
& r1_filter_2(u1_struct_0(X1),X2,k17_filter_2(X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_filter_2) ).
fof(dt_m2_filter_2,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( m2_lattice4(X2,X1)
& ~ v1_xboole_0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_filter_2) ).
fof(d8_filter_2,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> k17_filter_2(X1) = u1_struct_0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_filter_2) ).
fof(dt_m2_lattice4,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_lattice4(X2,X1)
=> m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_lattice4) ).
fof(dt_k17_filter_2,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> m2_filter_2(k17_filter_2(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k17_filter_2) ).
fof(dt_k6_lattices,axiom,
! [X1] :
( ( l2_lattices(X1)
& ~ v3_struct_0(X1) )
=> m1_subset_1(k6_lattices(X1),u1_struct_0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_lattices) ).
fof(t42_filter_2,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
& ~ v1_xboole_0(X2) )
=> ( ( r2_hidden(k6_lattices(X1),X2)
& v14_lattices(X1) )
=> ( k19_filter_2(X1,X2) = u1_struct_0(X1)
& r1_filter_2(u1_struct_0(X1),k19_filter_2(X1,X2),k17_filter_2(X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_filter_2) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( l2_lattices(X1)
& l1_lattices(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( v1_xboole_0(X2)
& r2_hidden(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(t3_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,k1_zfmisc_1(X2))
<=> r1_tarski(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : r1_tarski(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( m1_subset_1(X2,k1_zfmisc_1(X3))
& r2_hidden(X1,X2) )
=> m1_subset_1(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(t38_filter_2,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> r1_filter_2(u1_struct_0(X1),k19_filter_2(X1,X2),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_filter_2) ).
fof(t2_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,X2)
=> ( r2_hidden(X1,X2)
| v1_xboole_0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(redefinition_r1_filter_2,axiom,
! [X1,X2,X3] :
( ( m1_subset_1(X3,k1_zfmisc_1(X1))
& m1_subset_1(X2,k1_zfmisc_1(X1))
& ~ v1_xboole_0(X1) )
=> ( r1_filter_2(X1,X2,X3)
<=> X2 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_filter_2) ).
fof(c_0_15,negated_conjecture,
~ ! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( ( r2_hidden(k6_lattices(X1),X2)
& v14_lattices(X1) )
=> ( X2 = u1_struct_0(X1)
& r1_filter_2(u1_struct_0(X1),X2,k17_filter_2(X1)) ) ) ) ),
inference(assume_negation,[status(cth)],[t43_filter_2]) ).
fof(c_0_16,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( m2_lattice4(X2,X1)
& ~ v1_xboole_0(X2) ) ) ),
inference(fof_simplification,[status(thm)],[dt_m2_filter_2]) ).
fof(c_0_17,negated_conjecture,
~ ! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( ( r2_hidden(k6_lattices(X1),X2)
& v14_lattices(X1) )
=> ( X2 = u1_struct_0(X1)
& r1_filter_2(u1_struct_0(X1),X2,k17_filter_2(X1)) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_18,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> k17_filter_2(X1) = u1_struct_0(X1) ),
inference(fof_simplification,[status(thm)],[d8_filter_2]) ).
fof(c_0_19,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_lattice4(X2,X1)
=> m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ) ),
inference(fof_simplification,[status(thm)],[dt_m2_lattice4]) ).
fof(c_0_20,plain,
! [X19,X20] :
( ( ~ l3_lattices(X19)
| ~ v10_lattices(X19)
| v3_struct_0(X19)
| ~ m2_filter_2(X20,X19)
| m2_lattice4(X20,X19) )
& ( ~ l3_lattices(X19)
| ~ v10_lattices(X19)
| v3_struct_0(X19)
| ~ m2_filter_2(X20,X19)
| ~ v1_xboole_0(X20) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])])]) ).
fof(c_0_21,negated_conjecture,
( ( esk2_0 != u1_struct_0(esk1_0)
| ~ r1_filter_2(u1_struct_0(esk1_0),esk2_0,k17_filter_2(esk1_0)) )
& r2_hidden(k6_lattices(esk1_0),esk2_0)
& v14_lattices(esk1_0)
& m2_filter_2(esk2_0,esk1_0)
& l3_lattices(esk1_0)
& v10_lattices(esk1_0)
& ~ v3_struct_0(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])]) ).
fof(c_0_22,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> m2_filter_2(k17_filter_2(X1),X1) ),
inference(fof_simplification,[status(thm)],[dt_k17_filter_2]) ).
fof(c_0_23,plain,
! [X11] :
( k17_filter_2(X11) = u1_struct_0(X11)
| ~ l3_lattices(X11)
| ~ v10_lattices(X11)
| v3_struct_0(X11) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
fof(c_0_24,plain,
! [X1] :
( ( l2_lattices(X1)
& ~ v3_struct_0(X1) )
=> m1_subset_1(k6_lattices(X1),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k6_lattices]) ).
fof(c_0_25,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
& ~ v1_xboole_0(X2) )
=> ( ( r2_hidden(k6_lattices(X1),X2)
& v14_lattices(X1) )
=> ( k19_filter_2(X1,X2) = u1_struct_0(X1)
& r1_filter_2(u1_struct_0(X1),k19_filter_2(X1,X2),k17_filter_2(X1)) ) ) ) ),
inference(fof_simplification,[status(thm)],[t42_filter_2]) ).
fof(c_0_26,plain,
! [X21,X22] :
( m1_subset_1(X22,k1_zfmisc_1(u1_struct_0(X21)))
| ~ m2_lattice4(X22,X21)
| ~ l3_lattices(X21)
| ~ v10_lattices(X21)
| v3_struct_0(X21) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])]) ).
cnf(c_0_27,plain,
( ~ l3_lattices(X2)
| ~ v10_lattices(X2)
| ~ m2_filter_2(X1,X2)
| v3_struct_0(X2)
| m2_lattice4(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,negated_conjecture,
m2_filter_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_31,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_32,plain,
! [X12] :
( m2_filter_2(k17_filter_2(X12),X12)
| ~ l3_lattices(X12)
| ~ v10_lattices(X12)
| v3_struct_0(X12) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])]) ).
cnf(c_0_33,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| k17_filter_2(X1) = u1_struct_0(X1)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_34,plain,
! [X15] :
( m1_subset_1(k6_lattices(X15),u1_struct_0(X15))
| ~ l2_lattices(X15)
| v3_struct_0(X15) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])]) ).
fof(c_0_35,plain,
! [X18] :
( ( ~ l3_lattices(X18)
| l2_lattices(X18) )
& ( ~ l3_lattices(X18)
| l1_lattices(X18) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])])]) ).
fof(c_0_36,plain,
! [X64,X65] :
( ( ~ l3_lattices(X64)
| ~ v10_lattices(X64)
| v3_struct_0(X64)
| ~ m1_subset_1(X65,k1_zfmisc_1(u1_struct_0(X64)))
| v1_xboole_0(X65)
| ~ r2_hidden(k6_lattices(X64),X65)
| ~ v14_lattices(X64)
| k19_filter_2(X64,X65) = u1_struct_0(X64) )
& ( ~ l3_lattices(X64)
| ~ v10_lattices(X64)
| v3_struct_0(X64)
| ~ m1_subset_1(X65,k1_zfmisc_1(u1_struct_0(X64)))
| v1_xboole_0(X65)
| ~ r2_hidden(k6_lattices(X64),X65)
| ~ v14_lattices(X64)
| r1_filter_2(u1_struct_0(X64),k19_filter_2(X64,X65),k17_filter_2(X64)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])])])]) ).
fof(c_0_37,plain,
! [X73,X74] :
( ~ v1_xboole_0(X74)
| ~ r2_hidden(X73,X74) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])])]) ).
fof(c_0_38,plain,
! [X62,X63] :
( ( m1_subset_1(X62,k1_zfmisc_1(X63))
| ~ r1_tarski(X62,X63) )
& ( r1_tarski(X62,X63)
| ~ m1_subset_1(X62,k1_zfmisc_1(X63)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])]) ).
fof(c_0_39,plain,
! [X52] : r1_tarski(X52,X52),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(c_0_40,plain,
! [X66,X67,X68] :
( m1_subset_1(X66,X68)
| ~ m1_subset_1(X67,k1_zfmisc_1(X68))
| ~ r2_hidden(X66,X67) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])])]) ).
cnf(c_0_41,plain,
( ~ m2_lattice4(X2,X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_42,negated_conjecture,
m2_lattice4(esk2_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_27,c_0_28]),c_0_29]),c_0_30])]),c_0_31]) ).
cnf(c_0_43,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| m2_filter_2(k17_filter_2(X1),X1)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_44,negated_conjecture,
k17_filter_2(esk1_0) = u1_struct_0(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_29]),c_0_30])]),c_0_31]) ).
fof(c_0_45,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> r1_filter_2(u1_struct_0(X1),k19_filter_2(X1,X2),X2) ) ),
inference(fof_simplification,[status(thm)],[t38_filter_2]) ).
cnf(c_0_46,plain,
( ~ l2_lattices(X1)
| m1_subset_1(k6_lattices(X1),u1_struct_0(X1))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_47,plain,
( ~ l3_lattices(X1)
| l2_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_48,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ r2_hidden(k6_lattices(X1),X2)
| ~ v14_lattices(X1)
| v3_struct_0(X1)
| v1_xboole_0(X2)
| k19_filter_2(X1,X2) = u1_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_49,plain,
( ~ v1_xboole_0(X2)
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_50,plain,
( ~ r1_tarski(X1,X2)
| m1_subset_1(X1,k1_zfmisc_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_51,plain,
r1_tarski(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_52,plain,
! [X58,X59] :
( r2_hidden(X58,X59)
| v1_xboole_0(X59)
| ~ m1_subset_1(X58,X59) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])])]) ).
cnf(c_0_53,plain,
( ~ m1_subset_1(X2,k1_zfmisc_1(X3))
| ~ r2_hidden(X1,X2)
| m1_subset_1(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_54,negated_conjecture,
m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_29]),c_0_30])]),c_0_31]) ).
cnf(c_0_55,plain,
( ~ l3_lattices(X2)
| ~ v10_lattices(X2)
| ~ m2_filter_2(X1,X2)
| ~ v1_xboole_0(X1)
| v3_struct_0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_56,negated_conjecture,
m2_filter_2(u1_struct_0(esk1_0),esk1_0),
inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_29]),c_0_30])]),c_0_31]),c_0_44]) ).
fof(c_0_57,plain,
! [X1,X2,X3] :
( ( m1_subset_1(X3,k1_zfmisc_1(X1))
& m1_subset_1(X2,k1_zfmisc_1(X1))
& ~ v1_xboole_0(X1) )
=> ( r1_filter_2(X1,X2,X3)
<=> X2 = X3 ) ),
inference(fof_simplification,[status(thm)],[redefinition_r1_filter_2]) ).
fof(c_0_58,plain,
! [X60,X61] :
( r1_filter_2(u1_struct_0(X60),k19_filter_2(X60,X61),X61)
| ~ m2_filter_2(X61,X60)
| ~ l3_lattices(X60)
| ~ v10_lattices(X60)
| v3_struct_0(X60) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])])]) ).
cnf(c_0_59,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ r2_hidden(k6_lattices(X1),X2)
| ~ v14_lattices(X1)
| v3_struct_0(X1)
| v1_xboole_0(X2)
| r1_filter_2(u1_struct_0(X1),k19_filter_2(X1,X2),k17_filter_2(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_60,plain,
( ~ l3_lattices(X1)
| v3_struct_0(X1)
| m1_subset_1(k6_lattices(X1),u1_struct_0(X1)) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_61,plain,
( ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ v14_lattices(X1)
| ~ r2_hidden(k6_lattices(X1),X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| v3_struct_0(X1)
| k19_filter_2(X1,X2) = u1_struct_0(X1) ),
inference(csr,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_62,plain,
m1_subset_1(X1,k1_zfmisc_1(X1)),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_63,plain,
( ~ m1_subset_1(X1,X2)
| r2_hidden(X1,X2)
| v1_xboole_0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_64,negated_conjecture,
( ~ r2_hidden(X1,esk2_0)
| m1_subset_1(X1,u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_65,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_55,c_0_56]),c_0_29]),c_0_30])]),c_0_31]) ).
fof(c_0_66,plain,
! [X46,X47,X48] :
( ( ~ m1_subset_1(X48,k1_zfmisc_1(X46))
| ~ m1_subset_1(X47,k1_zfmisc_1(X46))
| v1_xboole_0(X46)
| r1_filter_2(X46,X47,X48)
| X47 != X48 )
& ( ~ m1_subset_1(X48,k1_zfmisc_1(X46))
| ~ m1_subset_1(X47,k1_zfmisc_1(X46))
| v1_xboole_0(X46)
| X47 = X48
| ~ r1_filter_2(X46,X47,X48) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])])]) ).
cnf(c_0_67,plain,
( ~ m2_filter_2(X2,X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| r1_filter_2(u1_struct_0(X1),k19_filter_2(X1,X2),X2)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_68,negated_conjecture,
r2_hidden(k6_lattices(esk1_0),esk2_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_69,negated_conjecture,
v14_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_70,plain,
( ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ v14_lattices(X1)
| ~ r2_hidden(k6_lattices(X1),X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| v3_struct_0(X1)
| r1_filter_2(u1_struct_0(X1),k19_filter_2(X1,X2),k17_filter_2(X1)) ),
inference(csr,[status(thm)],[c_0_59,c_0_49]) ).
cnf(c_0_71,negated_conjecture,
m1_subset_1(k6_lattices(esk1_0),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_29]),c_0_31]) ).
cnf(c_0_72,plain,
( ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ v14_lattices(X1)
| ~ r2_hidden(k6_lattices(X1),u1_struct_0(X1))
| v3_struct_0(X1)
| k19_filter_2(X1,u1_struct_0(X1)) = u1_struct_0(X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_73,negated_conjecture,
( ~ r2_hidden(X1,esk2_0)
| r2_hidden(X1,u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]) ).
cnf(c_0_74,plain,
( ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ m1_subset_1(X2,k1_zfmisc_1(X1))
| ~ r1_filter_2(X1,X2,X3)
| v1_xboole_0(X1)
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_75,negated_conjecture,
r1_filter_2(u1_struct_0(esk1_0),k19_filter_2(esk1_0,esk2_0),esk2_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_28]),c_0_29]),c_0_30])]),c_0_31]) ).
cnf(c_0_76,negated_conjecture,
k19_filter_2(esk1_0,esk2_0) = u1_struct_0(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_54]),c_0_68]),c_0_69]),c_0_29]),c_0_30])]),c_0_31]) ).
cnf(c_0_77,negated_conjecture,
( esk2_0 != u1_struct_0(esk1_0)
| ~ r1_filter_2(u1_struct_0(esk1_0),esk2_0,k17_filter_2(esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_78,plain,
( ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ v14_lattices(X1)
| ~ r2_hidden(k6_lattices(X1),u1_struct_0(X1))
| v3_struct_0(X1)
| r1_filter_2(u1_struct_0(X1),k19_filter_2(X1,u1_struct_0(X1)),k17_filter_2(X1)) ),
inference(spm,[status(thm)],[c_0_70,c_0_62]) ).
cnf(c_0_79,negated_conjecture,
r2_hidden(k6_lattices(esk1_0),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_71]),c_0_65]) ).
cnf(c_0_80,negated_conjecture,
k19_filter_2(esk1_0,u1_struct_0(esk1_0)) = u1_struct_0(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_69]),c_0_29]),c_0_30]),c_0_68])]),c_0_31]) ).
cnf(c_0_81,negated_conjecture,
( ~ r1_filter_2(u1_struct_0(esk1_0),X1,esk2_0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(esk1_0)))
| X1 = esk2_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_54]),c_0_65]) ).
cnf(c_0_82,negated_conjecture,
r1_filter_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),esk2_0),
inference(rw,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_83,plain,
( ~ r1_filter_2(X2,X1,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| v1_xboole_0(X2)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_74,c_0_62]) ).
cnf(c_0_84,negated_conjecture,
( ~ r1_filter_2(u1_struct_0(esk1_0),esk2_0,u1_struct_0(esk1_0))
| u1_struct_0(esk1_0) != esk2_0 ),
inference(rw,[status(thm)],[c_0_77,c_0_44]) ).
cnf(c_0_85,negated_conjecture,
r1_filter_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80]),c_0_44]),c_0_69]),c_0_29]),c_0_30])]),c_0_31]) ).
cnf(c_0_86,negated_conjecture,
u1_struct_0(esk1_0) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_62])]) ).
cnf(c_0_87,negated_conjecture,
~ r1_filter_2(u1_struct_0(esk1_0),esk2_0,u1_struct_0(esk1_0)),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_54]),c_0_65]),c_0_84]) ).
cnf(c_0_88,negated_conjecture,
r1_filter_2(esk2_0,esk2_0,esk2_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_86]),c_0_86]),c_0_86]) ).
cnf(c_0_89,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_86]),c_0_86]),c_0_88])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LAT313+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/5.46 % Computer : n020.cluster.edu
% 0.19/5.46 % Model : x86_64 x86_64
% 0.19/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.46 % Memory : 8046.5625MB
% 0.19/5.46 % OS : Linux 6.8.0-71-generic
% 0.19/5.46 % CPULimit : 300
% 0.19/5.46 % WCLimit : 300
% 0.19/5.46 % DateTime : Sun Sep 20 23:34:38 UTC 2026
% 0.19/5.47 % CPUTime :
% 0.19/5.47 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/5.54 Running first-order theorem proving
% 0.24/5.54 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.24/5.62 % Version: 3.5.1
% 0.24/5.62 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.24/5.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/5.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.24/5.62 % Starting new_bool_3 with 300s (1) cores
% 0.24/5.62 % Starting new_bool_1 with 300s (1) cores
% 0.24/5.62 % Starting sh5l with 300s (1) cores
% 0.24/5.62 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1468567 completed with status 0
% 0.24/5.62 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.24/5.62 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.24/5.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/5.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.24/5.62 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/5.62 % No SInE strategy applied
% 0.24/5.62 % Search class: FGHSM-FFMM21-SFFFFFNN
% 0.24/5.62 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/5.62 % Starting SubtermCWHack with 136s (1) cores
% 0.24/5.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.24/5.62 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 136s (1) cores
% 0.24/5.62 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.24/5.62 % Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S5PRR_S04AN with 136s (1) cores
% 0.24/5.62 % G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with pid 1468575 completed with status 0
% 0.24/5.62 % Result found by G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN
% 0.24/5.62 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.24/5.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/5.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.24/5.62 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/5.62 % No SInE strategy applied
% 0.24/5.62 % Search class: FGHSM-FFMM21-SFFFFFNN
% 0.24/5.62 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/5.62 % Starting SubtermCWHack with 136s (1) cores
% 0.24/5.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.24/5.62 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 136s (1) cores
% 0.24/5.62 % Preprocessing time : 0.002 s
% 0.24/5.62
% 0.24/5.62 % Proof found!
% 0.24/5.62 % SZS status Theorem
% 0.24/5.62 % SZS output start CNFRefutation
% See solution above
% 0.24/5.62 % Parsed axioms : 50
% 0.24/5.62 % Removed by relevancy pruning/SinE : 0
% 0.24/5.62 % Initial clauses : 73
% 0.24/5.62 % Removed in clause preprocessing : 7
% 0.24/5.62 % Initial clauses in saturation : 66
% 0.24/5.62 % Processed clauses : 208
% 0.24/5.62 % ...of these trivial : 2
% 0.24/5.62 % ...subsumed : 15
% 0.24/5.62 % ...remaining for further processing : 190
% 0.24/5.62 % Other redundant clauses eliminated : 1
% 0.24/5.62 % Clauses deleted for lack of memory : 0
% 0.24/5.62 % Backward-subsumed : 2
% 0.24/5.62 % Backward-rewritten : 26
% 0.24/5.62 % Generated clauses : 286
% 0.24/5.62 % ...of the previous two non-redundant : 282
% 0.24/5.62 % ...aggressively subsumed : 0
% 0.24/5.62 % Contextual simplify-reflections : 9
% 0.24/5.62 % Paramodulations : 285
% 0.24/5.62 % Factorizations : 0
% 0.24/5.62 % NegExts : 0
% 0.24/5.62 % Equation resolutions : 1
% 0.24/5.62 % Disequality decompositions : 0
% 0.24/5.62 % Total rewrite steps : 209
% 0.24/5.62 % ...of those cached : 178
% 0.24/5.62 % Propositional unsat checks : 0
% 0.24/5.62 % Propositional check models : 0
% 0.24/5.62 % Propositional check unsatisfiable : 0
% 0.24/5.62 % Propositional clauses : 0
% 0.24/5.62 % Propositional clauses after purity: 0
% 0.24/5.62 % Propositional unsat core size : 0
% 0.24/5.62 % Propositional preprocessing time : 0.000
% 0.24/5.62 % Propositional encoding time : 0.000
% 0.24/5.62 % Propositional solver time : 0.000
% 0.24/5.62 % Success case prop preproc time : 0.000
% 0.24/5.62 % Success case prop encoding time : 0.000
% 0.24/5.62 % Success case prop solver time : 0.000
% 0.24/5.62 % Current number of processed clauses : 161
% 0.24/5.62 % Positive orientable unit clauses : 41
% 0.24/5.62 % Positive unorientable unit clauses: 0
% 0.24/5.62 % Negative unit clauses : 11
% 0.24/5.62 % Non-unit-clauses : 109
% 0.24/5.62 % Current number of unprocessed clauses: 128
% 0.24/5.62 % ...number of literals in the above : 381
% 0.24/5.62 % Current number of archived formulas : 0
% 0.24/5.62 % Current number of archived clauses : 28
% 0.24/5.62 % Clause-clause subsumption calls (NU) : 3568
% 0.24/5.62 % Rec. Clause-clause subsumption calls : 1164
% 0.24/5.62 % Non-unit clause-clause subsumptions : 17
% 0.24/5.62 % Unit Clause-clause subsumption calls : 273
% 0.24/5.62 % Rewrite failures with RHS unbound : 0
% 0.24/5.62 % BW rewrite match attempts : 18
% 0.24/5.62 % BW rewrite match successes : 5
% 0.24/5.62 % Condensation attempts : 0
% 0.24/5.62 % Condensation successes : 0
% 0.24/5.62 % Termbank termtop insertions : 10192
% 0.24/5.62 % Search garbage collected termcells : 871
% 0.24/5.62
% 0.24/5.62 % -------------------------------------------------
% 0.24/5.62 % User time : 0.023 s
% 0.24/5.62 % System time : 0.007 s
% 0.24/5.62 % Total time : 0.031 s
% 0.24/5.62 % Maximum resident set size: 3880 pages
% 0.24/5.62
% 0.24/5.62 % -------------------------------------------------
% 0.24/5.62 % User time : 0.078 s
% 0.24/5.62 % System time : 0.023 s
% 0.24/5.62 % Total time : 0.101 s
% 0.24/5.62 % Maximum resident set size: 4864 pages
% 0.24/5.62 % E exiting
%------------------------------------------------------------------------------