%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LAT310+4 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 01:04:50 PM UTC 2026
% Result : Theorem 111.39s 20.78s
% Output : CNFRefutation 111.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 90 ( 33 unt; 0 def)
% Number of atoms : 388 ( 15 equ)
% Maximal formula atoms : 45 ( 4 avg)
% Number of connectives : 470 ( 172 ~; 163 |; 78 &)
% ( 10 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 140 ( 3 sgn 90 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t39_filter_2,conjecture,
! [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) )
=> ! [X3] :
( ( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
& ~ v1_xboole_0(X3) )
=> ! [X4] :
( ( m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X1)))
& ~ v1_xboole_0(X4) )
=> ( r1_tarski(k19_filter_2(X1,k19_filter_2(X1,X2)),k19_filter_2(X1,X2))
& ( r1_tarski(X3,X4)
=> r1_tarski(k19_filter_2(X1,X3),k19_filter_2(X1,X4)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_filter_2) ).
fof(dt_k19_filter_2,axiom,
! [X1,X2] :
( ( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
& ~ v1_xboole_0(X2)
& l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> m2_filter_2(k19_filter_2(X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k19_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/sandbox/benchmark/theBenchmark.p',dt_m2_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/sandbox/benchmark/Axioms/SET007/SET007+375.ax',dt_m2_lattice4) ).
fof(t3_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,k1_zfmisc_1(X2))
<=> r1_tarski(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+9.ax',t3_subset) ).
fof(d2_subset_1,axiom,
! [X1,X2] :
( ( v1_xboole_0(X1)
=> ( m1_subset_1(X2,X1)
<=> v1_xboole_0(X2) ) )
& ( ~ v1_xboole_0(X1)
=> ( m1_subset_1(X2,X1)
<=> r2_hidden(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+7.ax',d2_subset_1) ).
fof(d11_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) )
=> ! [X3] :
( m2_filter_2(X3,X1)
=> ( X3 = k19_filter_2(X1,X2)
<=> ( ! [X4] :
( m2_filter_2(X4,X1)
=> ( r1_tarski(X2,X4)
=> r1_tarski(X3,X4) ) )
& r1_tarski(X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_filter_2) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( r1_tarski(X1,X2)
<=> ! [X3] :
( r2_hidden(X3,X1)
=> r2_hidden(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+1.ax',d3_tarski) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : m1_subset_1(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+7.ax',existence_m1_subset_1) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( v1_xboole_0(X2)
& r2_hidden(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+3.ax',t7_boole) ).
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/sandbox/benchmark/theBenchmark.p',t38_filter_2) ).
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/sandbox/benchmark/theBenchmark.p',redefinition_r1_filter_2) ).
fof(t1_xboole_1,axiom,
! [X1,X2,X3] :
( ( r1_tarski(X2,X3)
& r1_tarski(X1,X2) )
=> r1_tarski(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t1_xboole_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : r1_tarski(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+1.ax',reflexivity_r1_tarski) ).
fof(c_0_14,negated_conjecture,
~ ! [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) )
=> ! [X3] :
( ( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
& ~ v1_xboole_0(X3) )
=> ! [X4] :
( ( m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X1)))
& ~ v1_xboole_0(X4) )
=> ( r1_tarski(k19_filter_2(X1,k19_filter_2(X1,X2)),k19_filter_2(X1,X2))
& ( r1_tarski(X3,X4)
=> r1_tarski(k19_filter_2(X1,X3),k19_filter_2(X1,X4)) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[t39_filter_2]) ).
fof(c_0_15,plain,
! [X1,X2] :
( ( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
& ~ v1_xboole_0(X2)
& l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> m2_filter_2(k19_filter_2(X1,X2),X1) ),
inference(fof_simplification,[status(thm)],[dt_k19_filter_2]) ).
fof(c_0_16,negated_conjecture,
~ ! [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) )
=> ! [X3] :
( ( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
& ~ v1_xboole_0(X3) )
=> ! [X4] :
( ( m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X1)))
& ~ v1_xboole_0(X4) )
=> ( r1_tarski(k19_filter_2(X1,k19_filter_2(X1,X2)),k19_filter_2(X1,X2))
& ( r1_tarski(X3,X4)
=> r1_tarski(k19_filter_2(X1,X3),k19_filter_2(X1,X4)) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_17,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_18,plain,
! [X154,X155] :
( m2_filter_2(k19_filter_2(X154,X155),X154)
| ~ m1_subset_1(X155,k1_zfmisc_1(u1_struct_0(X154)))
| v1_xboole_0(X155)
| ~ l3_lattices(X154)
| ~ v10_lattices(X154)
| v3_struct_0(X154) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
fof(c_0_19,negated_conjecture,
( ( ~ r1_tarski(k19_filter_2(esk1_0,k19_filter_2(esk1_0,esk2_0)),k19_filter_2(esk1_0,esk2_0))
| ~ r1_tarski(k19_filter_2(esk1_0,esk3_0),k19_filter_2(esk1_0,esk4_0)) )
& ( ~ r1_tarski(k19_filter_2(esk1_0,k19_filter_2(esk1_0,esk2_0)),k19_filter_2(esk1_0,esk2_0))
| r1_tarski(esk3_0,esk4_0) )
& m1_subset_1(esk4_0,k1_zfmisc_1(u1_struct_0(esk1_0)))
& ~ v1_xboole_0(esk4_0)
& m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk1_0)))
& ~ v1_xboole_0(esk3_0)
& m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0)))
& ~ v1_xboole_0(esk2_0)
& l3_lattices(esk1_0)
& v10_lattices(esk1_0)
& ~ v3_struct_0(esk1_0) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])])]) ).
fof(c_0_20,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_21,plain,
! [X347,X348] :
( ( ~ l3_lattices(X347)
| ~ v10_lattices(X347)
| v3_struct_0(X347)
| ~ m2_filter_2(X348,X347)
| m2_lattice4(X348,X347) )
& ( ~ l3_lattices(X347)
| ~ v10_lattices(X347)
| v3_struct_0(X347)
| ~ m2_filter_2(X348,X347)
| ~ v1_xboole_0(X348) ) ),
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_17])])])])]) ).
cnf(c_0_22,plain,
( ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| m2_filter_2(k19_filter_2(X1,X2),X1)
| v1_xboole_0(X2)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,negated_conjecture,
~ v1_xboole_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_28,plain,
! [X667,X668] :
( m1_subset_1(X668,k1_zfmisc_1(u1_struct_0(X667)))
| ~ m2_lattice4(X668,X667)
| ~ l3_lattices(X667)
| ~ v10_lattices(X667)
| v3_struct_0(X667) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).
cnf(c_0_29,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_21]) ).
cnf(c_0_30,negated_conjecture,
m2_filter_2(k19_filter_2(esk1_0,esk2_0),esk1_0),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25])]),c_0_26]),c_0_27]) ).
fof(c_0_31,plain,
! [X108,X109] :
( ( m1_subset_1(X108,k1_zfmisc_1(X109))
| ~ r1_tarski(X108,X109) )
& ( r1_tarski(X108,X109)
| ~ m1_subset_1(X108,k1_zfmisc_1(X109)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])]) ).
fof(c_0_32,plain,
! [X1,X2] :
( ( v1_xboole_0(X1)
=> ( m1_subset_1(X2,X1)
<=> v1_xboole_0(X2) ) )
& ( ~ v1_xboole_0(X1)
=> ( m1_subset_1(X2,X1)
<=> r2_hidden(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[d2_subset_1]) ).
fof(c_0_33,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) )
=> ! [X3] :
( m2_filter_2(X3,X1)
=> ( X3 = k19_filter_2(X1,X2)
<=> ( ! [X4] :
( m2_filter_2(X4,X1)
=> ( r1_tarski(X2,X4)
=> r1_tarski(X3,X4) ) )
& r1_tarski(X2,X3) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d11_filter_2]) ).
cnf(c_0_34,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_28]) ).
cnf(c_0_35,negated_conjecture,
m2_lattice4(k19_filter_2(esk1_0,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_29,c_0_30]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_36,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_21]) ).
fof(c_0_37,plain,
! [X56,X57,X58,X59,X60] :
( ( r1_tarski(X59,X60)
| ~ r2_hidden(esk5_2(X59,X60),X60) )
& ( r1_tarski(X59,X60)
| r2_hidden(esk5_2(X59,X60),X59) )
& ( r2_hidden(X58,X57)
| ~ r2_hidden(X58,X56)
| ~ r1_tarski(X56,X57) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])])]) ).
cnf(c_0_38,plain,
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| r1_tarski(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_39,negated_conjecture,
m1_subset_1(esk4_0,k1_zfmisc_1(u1_struct_0(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_40,plain,
! [X212,X213] :
( ( ~ v1_xboole_0(X212)
| m1_subset_1(X213,X212)
| ~ v1_xboole_0(X213) )
& ( ~ v1_xboole_0(X212)
| v1_xboole_0(X213)
| ~ m1_subset_1(X213,X212) )
& ( v1_xboole_0(X212)
| m1_subset_1(X213,X212)
| ~ r2_hidden(X213,X212) )
& ( v1_xboole_0(X212)
| r2_hidden(X213,X212)
| ~ m1_subset_1(X213,X212) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])])]) ).
fof(c_0_41,plain,
! [X170] : m1_subset_1(esk10_1(X170),X170),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(c_0_42,plain,
! [X156,X157,X158,X159] :
( ( ~ l3_lattices(X156)
| ~ v10_lattices(X156)
| v3_struct_0(X156)
| ~ m1_subset_1(X157,k1_zfmisc_1(u1_struct_0(X156)))
| v1_xboole_0(X157)
| ~ m2_filter_2(X158,X156)
| X158 = k19_filter_2(X156,X157)
| ~ r1_tarski(X157,X158)
| ~ r1_tarski(X158,esk9_3(X156,X157,X158)) )
& ( ~ l3_lattices(X156)
| ~ v10_lattices(X156)
| v3_struct_0(X156)
| ~ m1_subset_1(X157,k1_zfmisc_1(u1_struct_0(X156)))
| v1_xboole_0(X157)
| ~ m2_filter_2(X158,X156)
| X158 = k19_filter_2(X156,X157)
| ~ r1_tarski(X157,X158)
| r1_tarski(X157,esk9_3(X156,X157,X158)) )
& ( ~ l3_lattices(X156)
| ~ v10_lattices(X156)
| v3_struct_0(X156)
| ~ m1_subset_1(X157,k1_zfmisc_1(u1_struct_0(X156)))
| v1_xboole_0(X157)
| ~ m2_filter_2(X158,X156)
| X158 = k19_filter_2(X156,X157)
| ~ r1_tarski(X157,X158)
| m2_filter_2(esk9_3(X156,X157,X158),X156) )
& ( ~ l3_lattices(X156)
| ~ v10_lattices(X156)
| v3_struct_0(X156)
| ~ m1_subset_1(X157,k1_zfmisc_1(u1_struct_0(X156)))
| v1_xboole_0(X157)
| ~ m2_filter_2(X158,X156)
| X158 != k19_filter_2(X156,X157)
| r1_tarski(X158,X159)
| ~ r1_tarski(X157,X159)
| ~ m2_filter_2(X159,X156) )
& ( ~ l3_lattices(X156)
| ~ v10_lattices(X156)
| v3_struct_0(X156)
| ~ m1_subset_1(X157,k1_zfmisc_1(u1_struct_0(X156)))
| v1_xboole_0(X157)
| ~ m2_filter_2(X158,X156)
| X158 != k19_filter_2(X156,X157)
| r1_tarski(X157,X158) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])])])])]) ).
fof(c_0_43,plain,
! [X208,X209] :
( ~ v1_xboole_0(X209)
| ~ r2_hidden(X208,X209) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])])]) ).
fof(c_0_44,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_45,negated_conjecture,
m1_subset_1(k19_filter_2(esk1_0,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_34,c_0_35]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_46,negated_conjecture,
~ v1_xboole_0(k19_filter_2(esk1_0,esk2_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_30]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_47,plain,
( ~ r2_hidden(X3,X1)
| ~ r1_tarski(X1,X2)
| r2_hidden(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_48,negated_conjecture,
r1_tarski(esk4_0,u1_struct_0(esk1_0)),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_49,plain,
( ~ m1_subset_1(X1,X2)
| v1_xboole_0(X2)
| r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_50,plain,
m1_subset_1(esk10_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_51,plain,
( ~ l3_lattices(X3)
| ~ v10_lattices(X3)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X3)))
| ~ m2_filter_2(X2,X3)
| X2 != k19_filter_2(X3,X1)
| v3_struct_0(X3)
| v1_xboole_0(X1)
| r1_tarski(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_52,plain,
( ~ v1_xboole_0(X2)
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_53,plain,
( r1_tarski(X1,X2)
| r2_hidden(esk5_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_54,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_55,plain,
! [X168,X169] :
( r1_filter_2(u1_struct_0(X168),k19_filter_2(X168,X169),X169)
| ~ m2_filter_2(X169,X168)
| ~ l3_lattices(X168)
| ~ v10_lattices(X168)
| v3_struct_0(X168) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])])]) ).
cnf(c_0_56,negated_conjecture,
m2_filter_2(k19_filter_2(esk1_0,k19_filter_2(esk1_0,esk2_0)),esk1_0),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_45]),c_0_24]),c_0_25])]),c_0_26]),c_0_46]) ).
cnf(c_0_57,negated_conjecture,
( ~ r2_hidden(X1,esk4_0)
| r2_hidden(X1,u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_58,plain,
( r2_hidden(esk10_1(X1),X1)
| v1_xboole_0(X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_59,negated_conjecture,
~ v1_xboole_0(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_60,plain,
( ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| r1_tarski(X2,k19_filter_2(X1,X2))
| v1_xboole_0(X2)
| v3_struct_0(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_51]),c_0_22]) ).
cnf(c_0_61,plain,
( ~ v1_xboole_0(X1)
| r1_tarski(X1,X2) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
fof(c_0_62,plain,
! [X473,X474,X475] :
( ( ~ m1_subset_1(X475,k1_zfmisc_1(X473))
| ~ m1_subset_1(X474,k1_zfmisc_1(X473))
| v1_xboole_0(X473)
| r1_filter_2(X473,X474,X475)
| X474 != X475 )
& ( ~ m1_subset_1(X475,k1_zfmisc_1(X473))
| ~ m1_subset_1(X474,k1_zfmisc_1(X473))
| v1_xboole_0(X473)
| X474 = X475
| ~ r1_filter_2(X473,X474,X475) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_54])])])]) ).
cnf(c_0_63,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_55]) ).
cnf(c_0_64,negated_conjecture,
m2_lattice4(k19_filter_2(esk1_0,k19_filter_2(esk1_0,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_29,c_0_56]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_65,negated_conjecture,
r2_hidden(esk10_1(esk4_0),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]) ).
fof(c_0_66,plain,
! [X65,X66,X67] :
( r1_tarski(X65,X67)
| ~ r1_tarski(X66,X67)
| ~ r1_tarski(X65,X66) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])])]) ).
cnf(c_0_67,plain,
( ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| r1_tarski(X2,k19_filter_2(X1,X2))
| v3_struct_0(X1) ),
inference(csr,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_68,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_62]) ).
cnf(c_0_69,negated_conjecture,
r1_filter_2(u1_struct_0(esk1_0),k19_filter_2(esk1_0,k19_filter_2(esk1_0,esk2_0)),k19_filter_2(esk1_0,esk2_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_30]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_70,negated_conjecture,
m1_subset_1(k19_filter_2(esk1_0,k19_filter_2(esk1_0,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_34,c_0_64]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_71,negated_conjecture,
~ v1_xboole_0(u1_struct_0(esk1_0)),
inference(spm,[status(thm)],[c_0_52,c_0_65]) ).
fof(c_0_72,plain,
! [X62] : r1_tarski(X62,X62),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_73,plain,
( ~ l3_lattices(X2)
| ~ v10_lattices(X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
| ~ m2_filter_2(X4,X2)
| X4 != k19_filter_2(X2,X3)
| ~ r1_tarski(X3,X1)
| ~ m2_filter_2(X1,X2)
| v3_struct_0(X2)
| v1_xboole_0(X3)
| r1_tarski(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_74,plain,
( ~ r1_tarski(X2,X3)
| ~ r1_tarski(X1,X2)
| r1_tarski(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_75,negated_conjecture,
r1_tarski(esk4_0,k19_filter_2(esk1_0,esk4_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_39]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_76,negated_conjecture,
( ~ r1_tarski(k19_filter_2(esk1_0,k19_filter_2(esk1_0,esk2_0)),k19_filter_2(esk1_0,esk2_0))
| r1_tarski(esk3_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_77,negated_conjecture,
k19_filter_2(esk1_0,k19_filter_2(esk1_0,esk2_0)) = k19_filter_2(esk1_0,esk2_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_45]),c_0_70])]),c_0_71]) ).
cnf(c_0_78,plain,
r1_tarski(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_79,plain,
( ~ r1_tarski(X2,X3)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m2_filter_2(X3,X1)
| r1_tarski(k19_filter_2(X1,X2),X3)
| v1_xboole_0(X2)
| v3_struct_0(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_73]),c_0_22]) ).
cnf(c_0_80,negated_conjecture,
m2_filter_2(k19_filter_2(esk1_0,esk4_0),esk1_0),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_39]),c_0_24]),c_0_25])]),c_0_26]),c_0_59]) ).
cnf(c_0_81,negated_conjecture,
( ~ r1_tarski(k19_filter_2(esk1_0,k19_filter_2(esk1_0,esk2_0)),k19_filter_2(esk1_0,esk2_0))
| ~ r1_tarski(k19_filter_2(esk1_0,esk3_0),k19_filter_2(esk1_0,esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_82,negated_conjecture,
( ~ r1_tarski(X1,esk4_0)
| r1_tarski(X1,k19_filter_2(esk1_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_83,negated_conjecture,
r1_tarski(esk3_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_77]),c_0_78])]) ).
cnf(c_0_84,negated_conjecture,
( ~ r1_tarski(X1,k19_filter_2(esk1_0,esk4_0))
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(esk1_0)))
| r1_tarski(k19_filter_2(esk1_0,X1),k19_filter_2(esk1_0,esk4_0))
| v1_xboole_0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_85,negated_conjecture,
~ r1_tarski(k19_filter_2(esk1_0,esk3_0),k19_filter_2(esk1_0,esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_77]),c_0_78])]) ).
cnf(c_0_86,negated_conjecture,
~ v1_xboole_0(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_87,negated_conjecture,
r1_tarski(esk3_0,k19_filter_2(esk1_0,esk4_0)),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_88,negated_conjecture,
m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_89,plain,
$false,
inference(cdclpropres,[status(thm)],[c_0_84,c_0_85,c_0_86,c_0_87,c_0_88]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LAT310+4 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.41 % Computer : n013.cluster.edu
% 0.18/0.41 % Model : x86_64 x86_64
% 0.18/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.41 % Memory : 8046.5625MB
% 0.18/0.41 % OS : Linux 6.8.0-71-generic
% 0.18/0.41 % CPULimit : 300
% 0.18/0.41 % WCLimit : 300
% 0.18/0.41 % DateTime : Sun Sep 20 23:33:18 UTC 2026
% 0.18/0.41 % CPUTime :
% 0.18/0.41 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.47 Running first-order theorem proving
% 0.18/0.47 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 111.39/20.78 % Version: 3.5.1
% 111.39/20.78 % Preprocessing class: FMLLMLLLSSSNFFN.
% 111.39/20.78 % Scheduled 4 strats onto 8 cores with 297 seconds (2376 total)
% 111.39/20.78 % Starting new_bool_3 with 891s (3) cores
% 111.39/20.78 % Starting new_bool_1 with 891s (3) cores
% 111.39/20.78 % Starting sh5l with 297s (1) cores
% 111.39/20.78 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 297s (1) cores
% 111.39/20.78 % new_bool_1 with pid 3648376 completed with status 0
% 111.39/20.78 % Result found by new_bool_1
% 111.39/20.78 % Preprocessing class: FMLLMLLLSSSNFFN.
% 111.39/20.78 % Scheduled 4 strats onto 8 cores with 297 seconds (2376 total)
% 111.39/20.78 % Starting new_bool_3 with 891s (3) cores
% 111.39/20.78 % Starting new_bool_1 with 891s (3) cores
% 111.39/20.78 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 111.39/20.78 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 111.39/20.78 % Search class: FGHSM-SMLM32-MFFFFFNN
% 111.39/20.78 % Scheduled 13 strats onto 3 cores with 891 seconds (891 total)
% 111.39/20.78 % Starting SubtermCWHack with 81s (1) cores
% 111.39/20.78 % Starting new_bool_1 with 90s (1) cores
% 111.39/20.78 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 67s (1) cores
% 111.39/20.78 % new_bool_1 with pid 3648380 completed with status 0
% 111.39/20.78 % Result found by new_bool_1
% 111.39/20.78 % Preprocessing class: FMLLMLLLSSSNFFN.
% 111.39/20.78 % Scheduled 4 strats onto 8 cores with 297 seconds (2376 total)
% 111.39/20.78 % Starting new_bool_3 with 891s (3) cores
% 111.39/20.78 % Starting new_bool_1 with 891s (3) cores
% 111.39/20.78 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 111.39/20.78 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 111.39/20.78 % Search class: FGHSM-SMLM32-MFFFFFNN
% 111.39/20.78 % Scheduled 13 strats onto 3 cores with 891 seconds (891 total)
% 111.39/20.78 % Starting SubtermCWHack with 81s (1) cores
% 111.39/20.78 % Starting new_bool_1 with 90s (1) cores
% 111.39/20.78 % Preprocessing time : 0.096 s
% 111.39/20.78 % Presaturation interreduction done
% 111.39/20.78 % SatCheck found unsatisfiable ground set
% 111.39/20.78
% 111.39/20.78 % Proof found!
% 111.39/20.78 % SZS status Theorem
% 111.39/20.78 % SZS output start CNFRefutation
% See solution above
% 111.39/20.78 % Parsed axioms : 34702
% 111.39/20.78 % Removed by relevancy pruning/SinE : 34301
% 111.39/20.78 % Initial clauses : 1100
% 111.39/20.78 % Removed in clause preprocessing : 39
% 111.39/20.78 % Initial clauses in saturation : 1061
% 111.39/20.78 % Processed clauses : 34896
% 111.39/20.78 % ...of these trivial : 281
% 111.39/20.78 % ...subsumed : 24615
% 111.39/20.78 % ...remaining for further processing : 10000
% 111.39/20.78 % Other redundant clauses eliminated : 756
% 111.39/20.78 % Clauses deleted for lack of memory : 0
% 111.39/20.78 % Backward-subsumed : 636
% 111.39/20.78 % Backward-rewritten : 312
% 111.39/20.78 % Generated clauses : 251837
% 111.39/20.78 % ...of the previous two non-redundant : 240009
% 111.39/20.78 % ...aggressively subsumed : 0
% 111.39/20.78 % Contextual simplify-reflections : 156
% 111.39/20.78 % Paramodulations : 251060
% 111.39/20.78 % Factorizations : 4
% 111.39/20.78 % NegExts : 0
% 111.39/20.78 % Equation resolutions : 776
% 111.39/20.78 % Disequality decompositions : 0
% 111.39/20.78 % Total rewrite steps : 42705
% 111.39/20.78 % ...of those cached : 40226
% 111.39/20.78 % Propositional unsat checks : 2
% 111.39/20.78 % Propositional check models : 0
% 111.39/20.78 % Propositional check unsatisfiable : 1
% 111.39/20.78 % Propositional clauses : 213668
% 111.39/20.78 % Propositional clauses after purity: 11562
% 111.39/20.78 % Propositional unsat core size : 5
% 111.39/20.78 % Propositional preprocessing time : 0.000
% 111.39/20.78 % Propositional encoding time : 0.666
% 111.39/20.78 % Propositional solver time : 0.228
% 111.39/20.78 % Success case prop preproc time : 0.000
% 111.39/20.78 % Success case prop encoding time : 0.480
% 111.39/20.78 % Success case prop solver time : 0.066
% 111.39/20.78 % Current number of processed clauses : 7983
% 111.39/20.78 % Positive orientable unit clauses : 1917
% 111.39/20.78 % Positive unorientable unit clauses: 5
% 111.39/20.78 % Negative unit clauses : 1825
% 111.39/20.78 % Non-unit-clauses : 4236
% 111.39/20.78 % Current number of unprocessed clauses: 205685
% 111.39/20.78 % ...number of literals in the above : 710754
% 111.39/20.78 % Current number of archived formulas : 0
% 111.39/20.78 % Current number of archived clauses : 1937
% 111.39/20.78 % Clause-clause subsumption calls (NU) : 2486690
% 111.39/20.78 % Rec. Clause-clause subsumption calls : 981252
% 111.39/20.78 % Non-unit clause-clause subsumptions : 6842
% 111.39/20.78 % Unit Clause-clause subsumption calls : 355332
% 111.39/20.78 % Rewrite failures with RHS unbound : 24
% 111.39/20.78 % BW rewrite match attempts : 44883
% 111.39/20.78 % BW rewrite match successes : 119
% 111.39/20.78 % Condensation attempts : 0
% 111.39/20.78 % Condensation successes : 0
% 111.39/20.78 % Termbank termtop insertions : 6515302
% 111.39/20.78 % Search garbage collected termcells : 358022
% 111.39/20.78
% 111.39/20.78 % -------------------------------------------------
% 111.39/20.78 % User time : 15.644 s
% 111.39/20.78 % System time : 0.638 s
% 111.39/20.78 % Total time : 16.282 s
% 111.39/20.78 % Maximum resident set size: 69600 pages
% 111.39/20.78
% 111.39/20.78 % -------------------------------------------------
% 111.39/20.78 % User time : 47.672 s
% 111.39/20.78 % System time : 1.585 s
% 111.39/20.78 % Total time : 49.257 s
% 111.39/20.78 % Maximum resident set size: 57088 pages
% 111.39/20.78 % E exiting
%------------------------------------------------------------------------------