%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LAT310+2 : 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 : n016.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 120.60s 24.04s
% Output : CNFRefutation 120.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 87 ( 30 unt; 0 def)
% Number of atoms : 365 ( 19 equ)
% Maximal formula atoms : 45 ( 4 avg)
% Number of connectives : 446 ( 168 ~; 153 |; 73 &)
% ( 6 <=>; 46 =>; 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 : 137 ( 4 sgn 92 !; 0 ?)
% 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(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(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(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(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(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(fc2_xboole_0,axiom,
! [X1,X2] :
( ~ v1_xboole_0(X1)
=> ~ v1_xboole_0(k2_xboole_0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+2.ax',fc2_xboole_0) ).
fof(t12_xboole_1,axiom,
! [X1,X2] :
( r1_tarski(X1,X2)
=> k2_xboole_0(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t12_xboole_1) ).
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,
! [X93,X94] :
( m2_filter_2(k19_filter_2(X93,X94),X93)
| ~ m1_subset_1(X94,k1_zfmisc_1(u1_struct_0(X93)))
| v1_xboole_0(X94)
| ~ l3_lattices(X93)
| ~ v10_lattices(X93)
| v3_struct_0(X93) ),
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,
! [X242,X243] :
( ( ~ l3_lattices(X242)
| ~ v10_lattices(X242)
| v3_struct_0(X242)
| ~ m2_filter_2(X243,X242)
| m2_lattice4(X243,X242) )
& ( ~ l3_lattices(X242)
| ~ v10_lattices(X242)
| v3_struct_0(X242)
| ~ m2_filter_2(X243,X242)
| ~ v1_xboole_0(X243) ) ),
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,
! [X485,X486] :
( m1_subset_1(X486,k1_zfmisc_1(u1_struct_0(X485)))
| ~ m2_lattice4(X486,X485)
| ~ l3_lattices(X485)
| ~ v10_lattices(X485)
| v3_struct_0(X485) ),
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,
! [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_32,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_33,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_34,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_35,plain,
! [X49,X50] :
( ( m1_subset_1(X49,k1_zfmisc_1(X50))
| ~ r1_tarski(X49,X50) )
& ( r1_tarski(X49,X50)
| ~ m1_subset_1(X49,k1_zfmisc_1(X50)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])]) ).
fof(c_0_36,plain,
! [X95,X96,X97,X98] :
( ( ~ l3_lattices(X95)
| ~ v10_lattices(X95)
| v3_struct_0(X95)
| ~ m1_subset_1(X96,k1_zfmisc_1(u1_struct_0(X95)))
| v1_xboole_0(X96)
| ~ m2_filter_2(X97,X95)
| X97 = k19_filter_2(X95,X96)
| ~ r1_tarski(X96,X97)
| ~ r1_tarski(X97,esk9_3(X95,X96,X97)) )
& ( ~ l3_lattices(X95)
| ~ v10_lattices(X95)
| v3_struct_0(X95)
| ~ m1_subset_1(X96,k1_zfmisc_1(u1_struct_0(X95)))
| v1_xboole_0(X96)
| ~ m2_filter_2(X97,X95)
| X97 = k19_filter_2(X95,X96)
| ~ r1_tarski(X96,X97)
| r1_tarski(X96,esk9_3(X95,X96,X97)) )
& ( ~ l3_lattices(X95)
| ~ v10_lattices(X95)
| v3_struct_0(X95)
| ~ m1_subset_1(X96,k1_zfmisc_1(u1_struct_0(X95)))
| v1_xboole_0(X96)
| ~ m2_filter_2(X97,X95)
| X97 = k19_filter_2(X95,X96)
| ~ r1_tarski(X96,X97)
| m2_filter_2(esk9_3(X95,X96,X97),X95) )
& ( ~ l3_lattices(X95)
| ~ v10_lattices(X95)
| v3_struct_0(X95)
| ~ m1_subset_1(X96,k1_zfmisc_1(u1_struct_0(X95)))
| v1_xboole_0(X96)
| ~ m2_filter_2(X97,X95)
| X97 != k19_filter_2(X95,X96)
| r1_tarski(X97,X98)
| ~ r1_tarski(X96,X98)
| ~ m2_filter_2(X98,X95) )
& ( ~ l3_lattices(X95)
| ~ v10_lattices(X95)
| v3_struct_0(X95)
| ~ m1_subset_1(X96,k1_zfmisc_1(u1_struct_0(X95)))
| v1_xboole_0(X96)
| ~ m2_filter_2(X97,X95)
| X97 != k19_filter_2(X95,X96)
| r1_tarski(X96,X97) ) ),
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_31])])])])])]) ).
fof(c_0_37,plain,
! [X145,X146] :
( ~ v1_xboole_0(X146)
| ~ r2_hidden(X145,X146) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])])]) ).
fof(c_0_38,plain,
! [X18,X19,X20,X21,X22] :
( ( r1_tarski(X21,X22)
| ~ r2_hidden(esk5_2(X21,X22),X22) )
& ( r1_tarski(X21,X22)
| r2_hidden(esk5_2(X21,X22),X21) )
& ( r2_hidden(X20,X19)
| ~ r2_hidden(X20,X18)
| ~ r1_tarski(X18,X19) ) ),
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])])])])])])]) ).
fof(c_0_39,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_40,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_32,c_0_33]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_41,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_34,c_0_30]),c_0_24]),c_0_25])]),c_0_26]) ).
fof(c_0_42,plain,
! [X1,X2] :
( ~ v1_xboole_0(X1)
=> ~ v1_xboole_0(k2_xboole_0(X1,X2)) ),
inference(fof_simplification,[status(thm)],[fc2_xboole_0]) ).
fof(c_0_43,plain,
! [X736,X737] :
( k2_xboole_0(X736,X737) = X737
| ~ r1_tarski(X736,X737) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])])]) ).
cnf(c_0_44,plain,
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| r1_tarski(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_45,negated_conjecture,
m1_subset_1(esk4_0,k1_zfmisc_1(u1_struct_0(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_46,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_36]) ).
cnf(c_0_47,plain,
( ~ v1_xboole_0(X2)
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_48,plain,
( r1_tarski(X1,X2)
| r2_hidden(esk5_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_49,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_50,plain,
! [X107,X108] :
( r1_filter_2(u1_struct_0(X107),k19_filter_2(X107,X108),X108)
| ~ m2_filter_2(X108,X107)
| ~ l3_lattices(X107)
| ~ v10_lattices(X107)
| v3_struct_0(X107) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])])]) ).
cnf(c_0_51,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_40]),c_0_24]),c_0_25])]),c_0_26]),c_0_41]) ).
fof(c_0_52,plain,
! [X697,X698] :
( ~ v1_xboole_0(k2_xboole_0(X697,X698))
| v1_xboole_0(X697) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])]) ).
cnf(c_0_53,plain,
( ~ r1_tarski(X1,X2)
| k2_xboole_0(X1,X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_54,negated_conjecture,
r1_tarski(esk4_0,u1_struct_0(esk1_0)),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_55,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_46]),c_0_22]) ).
cnf(c_0_56,plain,
( ~ v1_xboole_0(X1)
| r1_tarski(X1,X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
fof(c_0_57,plain,
! [X337,X338,X339] :
( ( ~ m1_subset_1(X339,k1_zfmisc_1(X337))
| ~ m1_subset_1(X338,k1_zfmisc_1(X337))
| v1_xboole_0(X337)
| r1_filter_2(X337,X338,X339)
| X338 != X339 )
& ( ~ m1_subset_1(X339,k1_zfmisc_1(X337))
| ~ m1_subset_1(X338,k1_zfmisc_1(X337))
| v1_xboole_0(X337)
| X338 = X339
| ~ r1_filter_2(X337,X338,X339) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])])]) ).
cnf(c_0_58,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_50]) ).
cnf(c_0_59,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_51]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_60,plain,
( ~ v1_xboole_0(k2_xboole_0(X1,X2))
| v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_61,negated_conjecture,
k2_xboole_0(esk4_0,u1_struct_0(esk1_0)) = u1_struct_0(esk1_0),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_62,negated_conjecture,
~ v1_xboole_0(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_63,plain,
! [X27,X28,X29] :
( r1_tarski(X27,X29)
| ~ r1_tarski(X28,X29)
| ~ r1_tarski(X27,X28) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])])]) ).
cnf(c_0_64,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_55,c_0_56]) ).
cnf(c_0_65,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_57]) ).
cnf(c_0_66,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_58,c_0_30]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_67,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_32,c_0_59]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_68,negated_conjecture,
~ v1_xboole_0(u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]) ).
fof(c_0_69,plain,
! [X24] : r1_tarski(X24,X24),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_70,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_36]) ).
cnf(c_0_71,plain,
( ~ r1_tarski(X2,X3)
| ~ r1_tarski(X1,X2)
| r1_tarski(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_72,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_64,c_0_45]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_73,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_74,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_65,c_0_66]),c_0_40]),c_0_67])]),c_0_68]) ).
cnf(c_0_75,plain,
r1_tarski(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_76,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_70]),c_0_22]) ).
cnf(c_0_77,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_45]),c_0_24]),c_0_25])]),c_0_26]),c_0_62]) ).
cnf(c_0_78,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_79,negated_conjecture,
( ~ r1_tarski(X1,esk4_0)
| r1_tarski(X1,k19_filter_2(esk1_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_80,negated_conjecture,
r1_tarski(esk3_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_74]),c_0_75])]) ).
cnf(c_0_81,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_76,c_0_77]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_82,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_78,c_0_74]),c_0_75])]) ).
cnf(c_0_83,negated_conjecture,
~ v1_xboole_0(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_84,negated_conjecture,
r1_tarski(esk3_0,k19_filter_2(esk1_0,esk4_0)),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_85,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_86,plain,
$false,
inference(cdclpropres,[status(thm)],[c_0_81,c_0_82,c_0_83,c_0_84,c_0_85]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LAT310+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/5.46 % Computer : n016.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
% 0.19/5.47 % CPULimit : 300
% 0.19/5.47 % WCLimit : 300
% 0.19/5.47 % DateTime : Sun Sep 20 23:38:00 UTC 2026
% 0.19/5.47 % CPUTime :
% 0.19/5.47 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/5.54 Running first-order theorem proving
% 0.24/5.54 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
% 120.60/24.04 % Version: 3.5.1
% 120.60/24.04 % Preprocessing class: FMLMSMSLSSSNFFN.
% 120.60/24.04 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 120.60/24.04 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 120.60/24.04 % Starting new_bool_3 with 600s (2) cores
% 120.60/24.04 % Starting new_bool_1 with 600s (2) cores
% 120.60/24.04 % Starting sh5l with 300s (1) cores
% 120.60/24.04 % new_bool_1 with pid 1047743 completed with status 0
% 120.60/24.04 % Result found by new_bool_1
% 120.60/24.04 % Preprocessing class: FMLMSMSLSSSNFFN.
% 120.60/24.04 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 120.60/24.04 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 120.60/24.04 % Starting new_bool_3 with 600s (2) cores
% 120.60/24.04 % Starting new_bool_1 with 600s (2) cores
% 120.60/24.04 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 120.60/24.04 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 120.60/24.04 % Search class: FGHSM-FSLM32-MFFFFFNN
% 120.60/24.04 % Scheduled 12 strats onto 2 cores with 600 seconds (600 total)
% 120.60/24.04 % Starting SubtermCWHack with 55s (1) cores
% 120.60/24.04 % Starting new_bool_1 with 61s (1) cores
% 120.60/24.04 % new_bool_1 with pid 1047748 completed with status 0
% 120.60/24.04 % Result found by new_bool_1
% 120.60/24.04 % Preprocessing class: FMLMSMSLSSSNFFN.
% 120.60/24.04 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 120.60/24.04 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 120.60/24.04 % Starting new_bool_3 with 600s (2) cores
% 120.60/24.04 % Starting new_bool_1 with 600s (2) cores
% 120.60/24.04 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 120.60/24.04 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 120.60/24.04 % Search class: FGHSM-FSLM32-MFFFFFNN
% 120.60/24.04 % Scheduled 12 strats onto 2 cores with 600 seconds (600 total)
% 120.60/24.04 % Starting SubtermCWHack with 55s (1) cores
% 120.60/24.04 % Starting new_bool_1 with 61s (1) cores
% 120.60/24.04 % Preprocessing time : 0.019 s
% 120.60/24.04 % Presaturation interreduction done
% 120.60/24.04 % SatCheck found unsatisfiable ground set
% 120.60/24.04
% 120.60/24.04 % Proof found!
% 120.60/24.04 % SZS status Theorem
% 120.60/24.04 % SZS output start CNFRefutation
% See solution above
% 120.60/24.05 % Parsed axioms : 2968
% 120.60/24.05 % Removed by relevancy pruning/SinE : 2610
% 120.60/24.05 % Initial clauses : 743
% 120.60/24.05 % Removed in clause preprocessing : 22
% 120.60/24.05 % Initial clauses in saturation : 721
% 120.60/24.05 % Processed clauses : 66171
% 120.60/24.05 % ...of these trivial : 1363
% 120.60/24.05 % ...subsumed : 54808
% 120.60/24.05 % ...remaining for further processing : 10000
% 120.60/24.05 % Other redundant clauses eliminated : 2024
% 120.60/24.05 % Clauses deleted for lack of memory : 0
% 120.60/24.05 % Backward-subsumed : 268
% 120.60/24.05 % Backward-rewritten : 398
% 120.60/24.05 % Generated clauses : 739507
% 120.60/24.05 % ...of the previous two non-redundant : 649999
% 120.60/24.05 % ...aggressively subsumed : 0
% 120.60/24.05 % Contextual simplify-reflections : 154
% 120.60/24.05 % Paramodulations : 737440
% 120.60/24.05 % Factorizations : 16
% 120.60/24.05 % NegExts : 0
% 120.60/24.05 % Equation resolutions : 2046
% 120.60/24.05 % Disequality decompositions : 0
% 120.60/24.05 % Total rewrite steps : 351862
% 120.60/24.05 % ...of those cached : 290090
% 120.60/24.05 % Propositional unsat checks : 2
% 120.60/24.05 % Propositional check models : 0
% 120.60/24.05 % Propositional check unsatisfiable : 1
% 120.60/24.05 % Propositional clauses : 592508
% 120.60/24.05 % Propositional clauses after purity: 31604
% 120.60/24.05 % Propositional unsat core size : 5
% 120.60/24.05 % Propositional preprocessing time : 0.000
% 120.60/24.05 % Propositional encoding time : 2.430
% 120.60/24.05 % Propositional solver time : 0.617
% 120.60/24.05 % Success case prop preproc time : 0.000
% 120.60/24.05 % Success case prop encoding time : 1.716
% 120.60/24.05 % Success case prop solver time : 0.099
% 120.60/24.05 % Current number of processed clauses : 8601
% 120.60/24.05 % Positive orientable unit clauses : 3438
% 120.60/24.05 % Positive unorientable unit clauses: 6
% 120.60/24.05 % Negative unit clauses : 2183
% 120.60/24.05 % Non-unit-clauses : 2974
% 120.60/24.05 % Current number of unprocessed clauses: 583907
% 120.60/24.05 % ...number of literals in the above : 1175699
% 120.60/24.05 % Current number of archived formulas : 0
% 120.60/24.05 % Current number of archived clauses : 1346
% 120.60/24.05 % Clause-clause subsumption calls (NU) : 968003
% 120.60/24.05 % Rec. Clause-clause subsumption calls : 503688
% 120.60/24.05 % Non-unit clause-clause subsumptions : 6467
% 120.60/24.05 % Unit Clause-clause subsumption calls : 841245
% 120.60/24.05 % Rewrite failures with RHS unbound : 0
% 120.60/24.05 % BW rewrite match attempts : 41257
% 120.60/24.05 % BW rewrite match successes : 749
% 120.60/24.05 % Condensation attempts : 0
% 120.60/24.05 % Condensation successes : 0
% 120.60/24.05 % Termbank termtop insertions : 17511689
% 120.60/24.05 % Search garbage collected termcells : 30982
% 120.60/24.05
% 120.60/24.05 % -------------------------------------------------
% 120.60/24.05 % User time : 17.262 s
% 120.60/24.05 % System time : 0.706 s
% 120.60/24.05 % Total time : 17.968 s
% 120.60/24.05 % Maximum resident set size: 9452 pages
% 120.60/24.05
% 120.60/24.05 % -------------------------------------------------
% 120.60/24.05 % User time : 34.734 s
% 120.60/24.05 % System time : 1.364 s
% 120.60/24.05 % Total time : 36.098 s
% 120.60/24.05 % Maximum resident set size: 8192 pages
% 120.60/24.05 % E exiting
%------------------------------------------------------------------------------