%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LAT313+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 : n018.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 1.01s 0.96s
% Output : CNFRefutation 1.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 17
% Syntax : Number of formulae : 92 ( 30 unt; 0 def)
% Number of atoms : 325 ( 38 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 372 ( 139 ~; 119 |; 70 &)
% ( 5 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 138 ( 4 sgn 94 !; 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/sandbox/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/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(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(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(d1_xboole_0,axiom,
! [X1] :
( X1 = k1_xboole_0
<=> ! [X2] : ~ r2_hidden(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+2.ax',d1_xboole_0) ).
fof(t49_zfmisc_1,axiom,
! [X1,X2] : k2_xboole_0(k1_tarski(X1),X2) != k1_xboole_0,
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+6.ax',t49_zfmisc_1) ).
fof(t46_zfmisc_1,axiom,
! [X1,X2] :
( r2_hidden(X1,X2)
=> k2_xboole_0(k1_tarski(X1),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+6.ax',t46_zfmisc_1) ).
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(t5_subset,axiom,
! [X1,X2,X3] :
~ ( v1_xboole_0(X3)
& m1_subset_1(X2,k1_zfmisc_1(X3))
& r2_hidden(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+9.ax',t5_subset) ).
fof(symmetry_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)
=> r1_filter_2(X1,X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_filter_2) ).
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/sandbox/benchmark/theBenchmark.p',t42_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(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/sandbox/benchmark/theBenchmark.p',d8_filter_2) ).
fof(t37_zfmisc_1,axiom,
! [X1,X2] :
( r1_tarski(k1_tarski(X1),X2)
<=> r2_hidden(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+6.ax',t37_zfmisc_1) ).
fof(t80_zfmisc_1,axiom,
! [X1] : r1_tarski(k1_tarski(X1),k1_zfmisc_1(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+6.ax',t80_zfmisc_1) ).
fof(t1_subset,axiom,
! [X1,X2] :
( r2_hidden(X1,X2)
=> m1_subset_1(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+9.ax',t1_subset) ).
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(assume_negation,[status(cth)],[t43_filter_2]) ).
fof(c_0_18,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_19,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_17]) ).
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,
! [X109,X110] :
( ( ~ l3_lattices(X109)
| ~ v10_lattices(X109)
| v3_struct_0(X109)
| ~ m2_filter_2(X110,X109)
| m2_lattice4(X110,X109) )
& ( ~ l3_lattices(X109)
| ~ v10_lattices(X109)
| v3_struct_0(X109)
| ~ m2_filter_2(X110,X109)
| ~ v1_xboole_0(X110) ) ),
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_18])])])])]) ).
fof(c_0_22,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_19])])])]) ).
fof(c_0_23,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_24,plain,
! [X533,X534] :
( m1_subset_1(X534,k1_zfmisc_1(u1_struct_0(X533)))
| ~ m2_lattice4(X534,X533)
| ~ l3_lattices(X533)
| ~ v10_lattices(X533)
| v3_struct_0(X533) ),
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_25,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_26,negated_conjecture,
m2_filter_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_30,plain,
! [X55,X56] :
( ~ v1_xboole_0(X56)
| ~ r2_hidden(X55,X56) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])])]) ).
fof(c_0_31,plain,
! [X199,X200] :
( m2_filter_2(k19_filter_2(X199,X200),X199)
| ~ m1_subset_1(X200,k1_zfmisc_1(u1_struct_0(X199)))
| v1_xboole_0(X200)
| ~ l3_lattices(X199)
| ~ v10_lattices(X199)
| v3_struct_0(X199) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])]) ).
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_24]) ).
cnf(c_0_33,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_25,c_0_26]),c_0_27]),c_0_28])]),c_0_29]) ).
cnf(c_0_34,plain,
( ~ v1_xboole_0(X2)
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,negated_conjecture,
r2_hidden(k6_lattices(esk1_0),esk2_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_36,plain,
! [X1] :
( X1 = k1_xboole_0
<=> ! [X2] : ~ r2_hidden(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(c_0_37,plain,
! [X1,X2] : k2_xboole_0(k1_tarski(X1),X2) != k1_xboole_0,
inference(fof_simplification,[status(thm)],[t49_zfmisc_1]) ).
fof(c_0_38,plain,
! [X684,X685] :
( k2_xboole_0(k1_tarski(X684),X685) = X685
| ~ r2_hidden(X684,X685) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t46_zfmisc_1])])]) ).
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,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_31]) ).
cnf(c_0_41,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_32,c_0_33]),c_0_27]),c_0_28])]),c_0_29]) ).
cnf(c_0_42,negated_conjecture,
~ v1_xboole_0(esk2_0),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
fof(c_0_43,plain,
! [X179,X180,X181] :
( ~ v1_xboole_0(X181)
| ~ m1_subset_1(X180,k1_zfmisc_1(X181))
| ~ r2_hidden(X179,X180) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])])]) ).
fof(c_0_44,plain,
! [X545,X546,X547] :
( ( X547 = k1_xboole_0
| r2_hidden(esk68_1(X547),X547) )
& ( ~ r2_hidden(X546,X545)
| X545 != k1_xboole_0 ) ),
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)],[c_0_36])])])])])]) ).
fof(c_0_45,plain,
! [X686,X687] : k2_xboole_0(k1_tarski(X686),X687) != k1_xboole_0,
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_37])]) ).
cnf(c_0_46,plain,
( ~ r2_hidden(X1,X2)
| k2_xboole_0(k1_tarski(X1),X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_47,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)
=> r1_filter_2(X1,X3,X2) ) ),
inference(fof_simplification,[status(thm)],[symmetry_r1_filter_2]) ).
fof(c_0_48,plain,
! [X30,X31] :
( r1_filter_2(u1_struct_0(X30),k19_filter_2(X30,X31),X31)
| ~ m2_filter_2(X31,X30)
| ~ l3_lattices(X30)
| ~ v10_lattices(X30)
| v3_struct_0(X30) ),
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_49,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_40,c_0_41]),c_0_27]),c_0_28])]),c_0_29]),c_0_42]) ).
cnf(c_0_50,plain,
( ~ v1_xboole_0(X3)
| ~ m1_subset_1(X2,k1_zfmisc_1(X3))
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_51,plain,
( X1 = k1_xboole_0
| r2_hidden(esk68_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_52,plain,
k2_xboole_0(k1_tarski(X1),X2) != k1_xboole_0,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_53,negated_conjecture,
k2_xboole_0(k1_tarski(k6_lattices(esk1_0)),esk2_0) = esk2_0,
inference(spm,[status(thm)],[c_0_46,c_0_35]) ).
fof(c_0_54,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_55,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_56,plain,
! [X16,X17,X18] :
( r1_filter_2(X16,X18,X17)
| ~ r1_filter_2(X16,X17,X18)
| ~ m1_subset_1(X18,k1_zfmisc_1(X16))
| ~ m1_subset_1(X17,k1_zfmisc_1(X16))
| v1_xboole_0(X16) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])])]) ).
cnf(c_0_57,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_48]) ).
cnf(c_0_58,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_25,c_0_49]),c_0_27]),c_0_28])]),c_0_29]) ).
cnf(c_0_59,plain,
( ~ v1_xboole_0(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| X1 = k1_xboole_0 ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_60,negated_conjecture,
esk2_0 != k1_xboole_0,
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
fof(c_0_61,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_62,plain,
! [X38,X39] :
( ( ~ l3_lattices(X38)
| ~ v10_lattices(X38)
| v3_struct_0(X38)
| ~ m1_subset_1(X39,k1_zfmisc_1(u1_struct_0(X38)))
| v1_xboole_0(X39)
| ~ r2_hidden(k6_lattices(X38),X39)
| ~ v14_lattices(X38)
| k19_filter_2(X38,X39) = u1_struct_0(X38) )
& ( ~ l3_lattices(X38)
| ~ v10_lattices(X38)
| v3_struct_0(X38)
| ~ m1_subset_1(X39,k1_zfmisc_1(u1_struct_0(X38)))
| v1_xboole_0(X39)
| ~ r2_hidden(k6_lattices(X38),X39)
| ~ v14_lattices(X38)
| r1_filter_2(u1_struct_0(X38),k19_filter_2(X38,X39),k17_filter_2(X38)) ) ),
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_54])])])])]) ).
fof(c_0_63,plain,
! [X22,X23,X24] :
( ( ~ m1_subset_1(X24,k1_zfmisc_1(X22))
| ~ m1_subset_1(X23,k1_zfmisc_1(X22))
| v1_xboole_0(X22)
| r1_filter_2(X22,X23,X24)
| X23 != X24 )
& ( ~ m1_subset_1(X24,k1_zfmisc_1(X22))
| ~ m1_subset_1(X23,k1_zfmisc_1(X22))
| v1_xboole_0(X22)
| X23 = X24
| ~ r1_filter_2(X22,X23,X24) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])])]) ).
cnf(c_0_64,plain,
( ~ r1_filter_2(X1,X2,X3)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ m1_subset_1(X2,k1_zfmisc_1(X1))
| r1_filter_2(X1,X3,X2)
| v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_65,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_57,c_0_26]),c_0_27]),c_0_28])]),c_0_29]) ).
cnf(c_0_66,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_58]),c_0_27]),c_0_28])]),c_0_29]) ).
cnf(c_0_67,negated_conjecture,
~ v1_xboole_0(u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_41]),c_0_60]) ).
fof(c_0_68,plain,
! [X666,X667] :
( ( r1_tarski(k1_tarski(X666),X667)
| ~ r2_hidden(X666,X667) )
& ( r2_hidden(X666,X667)
| ~ r1_tarski(k1_tarski(X666),X667) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_zfmisc_1])])]) ).
fof(c_0_69,plain,
! [X705] : r1_tarski(k1_tarski(X705),k1_zfmisc_1(X705)),
inference(variable_rename,[status(thm)],[t80_zfmisc_1]) ).
fof(c_0_70,plain,
! [X36] :
( k17_filter_2(X36) = u1_struct_0(X36)
| ~ l3_lattices(X36)
| ~ v10_lattices(X36)
| v3_struct_0(X36) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_61])])]) ).
cnf(c_0_71,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_62]) ).
cnf(c_0_72,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_63]) ).
cnf(c_0_73,negated_conjecture,
r1_filter_2(u1_struct_0(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_64,c_0_65]),c_0_41]),c_0_66])]),c_0_67]) ).
fof(c_0_74,plain,
! [X59,X60] :
( m1_subset_1(X59,X60)
| ~ r2_hidden(X59,X60) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])])]) ).
cnf(c_0_75,plain,
( ~ r1_tarski(k1_tarski(X1),X2)
| r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_76,plain,
r1_tarski(k1_tarski(X1),k1_zfmisc_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
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_22]) ).
cnf(c_0_78,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_70]) ).
cnf(c_0_79,plain,
( ~ r2_hidden(k6_lattices(X1),X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ v14_lattices(X1)
| v3_struct_0(X1)
| k19_filter_2(X1,X2) = u1_struct_0(X1) ),
inference(csr,[status(thm)],[c_0_71,c_0_34]) ).
cnf(c_0_80,negated_conjecture,
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_72,c_0_73]),c_0_66]),c_0_41])]),c_0_67]) ).
cnf(c_0_81,negated_conjecture,
v14_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_82,plain,
( ~ m1_subset_1(X2,k1_zfmisc_1(X3))
| ~ m1_subset_1(X1,k1_zfmisc_1(X3))
| X1 != X2
| v1_xboole_0(X3)
| r1_filter_2(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_83,plain,
( ~ r2_hidden(X1,X2)
| m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_84,plain,
r2_hidden(X1,k1_zfmisc_1(X1)),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_85,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(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_27]),c_0_28])]),c_0_29]) ).
cnf(c_0_86,negated_conjecture,
u1_struct_0(esk1_0) = esk2_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_79,c_0_35]),c_0_80]),c_0_81]),c_0_27]),c_0_28]),c_0_41])]),c_0_29]) ).
cnf(c_0_87,plain,
( ~ m1_subset_1(X2,k1_zfmisc_1(X1))
| v1_xboole_0(X1)
| r1_filter_2(X1,X2,X2) ),
inference(er,[status(thm)],[c_0_82]) ).
cnf(c_0_88,plain,
m1_subset_1(X1,k1_zfmisc_1(X1)),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_89,negated_conjecture,
~ r1_filter_2(esk2_0,esk2_0,esk2_0),
inference(cn,[status(thm)],[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_90,plain,
( v1_xboole_0(X1)
| r1_filter_2(X1,X1,X1) ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_91,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT313+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 23:35:44 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.41 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
% 1.01/0.96 % Version: 3.5.1
% 1.01/0.96 % Preprocessing class: FMLMSMSLSSSNFFN.
% 1.01/0.96 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.01/0.96 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 1.01/0.96 % Starting new_bool_3 with 600s (2) cores
% 1.01/0.96 % Starting new_bool_1 with 600s (2) cores
% 1.01/0.96 % Starting sh5l with 300s (1) cores
% 1.01/0.96 % new_bool_3 with pid 448826 completed with status 0
% 1.01/0.96 % Result found by new_bool_3
% 1.01/0.96 % Preprocessing class: FMLMSMSLSSSNFFN.
% 1.01/0.96 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.01/0.96 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 1.01/0.96 % Starting new_bool_3 with 600s (2) cores
% 1.01/0.96 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.01/0.96 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.01/0.96 % Search class: FGHSM-FSLM32-MFFFFFNN
% 1.01/0.96 % Scheduled 12 strats onto 2 cores with 600 seconds (600 total)
% 1.01/0.96 % Starting SubtermCWHack with 55s (1) cores
% 1.01/0.96 % Starting new_bool_3 with 61s (1) cores
% 1.01/0.96 % new_bool_3 with pid 448832 completed with status 0
% 1.01/0.96 % Result found by new_bool_3
% 1.01/0.96 % Preprocessing class: FMLMSMSLSSSNFFN.
% 1.01/0.96 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.01/0.96 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 1.01/0.96 % Starting new_bool_3 with 600s (2) cores
% 1.01/0.96 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.01/0.96 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.01/0.96 % Search class: FGHSM-FSLM32-MFFFFFNN
% 1.01/0.96 % Scheduled 12 strats onto 2 cores with 600 seconds (600 total)
% 1.01/0.96 % Starting SubtermCWHack with 55s (1) cores
% 1.01/0.96 % Starting new_bool_3 with 61s (1) cores
% 1.01/0.96 % Preprocessing time : 0.011 s
% 1.01/0.96 % Presaturation interreduction done
% 1.01/0.96
% 1.01/0.96 % Proof found!
% 1.01/0.96 % SZS status Theorem
% 1.01/0.96 % SZS output start CNFRefutation
% See solution above
% 1.01/0.96 % Parsed axioms : 2972
% 1.01/0.96 % Removed by relevancy pruning/SinE : 2603
% 1.01/0.96 % Initial clauses : 813
% 1.01/0.96 % Removed in clause preprocessing : 21
% 1.01/0.96 % Initial clauses in saturation : 792
% 1.01/0.96 % Processed clauses : 4480
% 1.01/0.96 % ...of these trivial : 27
% 1.01/0.96 % ...subsumed : 1981
% 1.01/0.96 % ...remaining for further processing : 2472
% 1.01/0.96 % Other redundant clauses eliminated : 203
% 1.01/0.96 % Clauses deleted for lack of memory : 0
% 1.01/0.96 % Backward-subsumed : 10
% 1.01/0.96 % Backward-rewritten : 205
% 1.01/0.96 % Generated clauses : 17279
% 1.01/0.96 % ...of the previous two non-redundant : 16716
% 1.01/0.96 % ...aggressively subsumed : 0
% 1.01/0.96 % Contextual simplify-reflections : 51
% 1.01/0.96 % Paramodulations : 17078
% 1.01/0.96 % Factorizations : 3
% 1.01/0.96 % NegExts : 0
% 1.01/0.96 % Equation resolutions : 206
% 1.01/0.96 % Disequality decompositions : 0
% 1.01/0.96 % Total rewrite steps : 2485
% 1.01/0.96 % ...of those cached : 2196
% 1.01/0.96 % Propositional unsat checks : 0
% 1.01/0.96 % Propositional check models : 0
% 1.01/0.96 % Propositional check unsatisfiable : 0
% 1.01/0.96 % Propositional clauses : 0
% 1.01/0.96 % Propositional clauses after purity: 0
% 1.01/0.96 % Propositional unsat core size : 0
% 1.01/0.96 % Propositional preprocessing time : 0.000
% 1.01/0.96 % Propositional encoding time : 0.000
% 1.01/0.96 % Propositional solver time : 0.000
% 1.01/0.96 % Success case prop preproc time : 0.000
% 1.01/0.96 % Success case prop encoding time : 0.000
% 1.01/0.96 % Success case prop solver time : 0.000
% 1.01/0.96 % Current number of processed clauses : 1463
% 1.01/0.96 % Positive orientable unit clauses : 297
% 1.01/0.96 % Positive unorientable unit clauses: 0
% 1.01/0.96 % Negative unit clauses : 410
% 1.01/0.96 % Non-unit-clauses : 756
% 1.01/0.96 % Current number of unprocessed clauses: 13742
% 1.01/0.96 % ...number of literals in the above : 46436
% 1.01/0.96 % Current number of archived formulas : 0
% 1.01/0.96 % Current number of archived clauses : 958
% 1.01/0.96 % Clause-clause subsumption calls (NU) : 265484
% 1.01/0.96 % Rec. Clause-clause subsumption calls : 53724
% 1.01/0.96 % Non-unit clause-clause subsumptions : 439
% 1.01/0.96 % Unit Clause-clause subsumption calls : 25937
% 1.01/0.96 % Rewrite failures with RHS unbound : 0
% 1.01/0.96 % BW rewrite match attempts : 72
% 1.01/0.96 % BW rewrite match successes : 17
% 1.01/0.96 % Condensation attempts : 0
% 1.01/0.96 % Condensation successes : 0
% 1.01/0.96 % Termbank termtop insertions : 351618
% 1.01/0.96 % Search garbage collected termcells : 33613
% 1.01/0.96
% 1.01/0.96 % -------------------------------------------------
% 1.01/0.96 % User time : 0.395 s
% 1.01/0.96 % System time : 0.043 s
% 1.01/0.96 % Total time : 0.438 s
% 1.01/0.96 % Maximum resident set size: 10228 pages
% 1.01/0.96
% 1.01/0.96 % -------------------------------------------------
% 1.01/0.96 % User time : 0.835 s
% 1.01/0.96 % System time : 0.075 s
% 1.01/0.96 % Total time : 0.911 s
% 1.01/0.96 % Maximum resident set size: 8192 pages
% 1.01/0.96 % E exiting
%------------------------------------------------------------------------------