%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT297+3 : TPTP v9.2.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:37:58 PM UTC 2026
% Result : Theorem 9.30s 9.25s
% Output : CNFRefutation 9.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 76 ( 14 unt; 0 def)
% Number of atoms : 429 ( 6 equ)
% Maximal formula atoms : 70 ( 5 avg)
% Number of connectives : 556 ( 203 ~; 240 |; 63 &)
% ( 12 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 126 ( 8 sgn 72 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t13_filter_2,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> ( ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( ( r2_hidden(X3,X2)
& r2_hidden(X4,X2) )
<=> r2_hidden(k4_lattices(X1,X3,X4),X2) ) ) )
=> m2_lattice4(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_filter_2) ).
fof(t11_lattice4,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_0(X2,X1)
=> m2_lattice4(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+375.ax',t11_lattice4) ).
fof(d1_filter_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( ( ~ v1_xboole_0(X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
=> ( m1_filter_0(X2,X1)
<=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( ( r2_hidden(X3,X2)
& r2_hidden(X4,X2) )
<=> r2_hidden(k4_lattices(X1,X3,X4),X2) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+242.ax',d1_filter_0) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( r2_hidden(X1,X2)
& m1_subset_1(X2,k1_zfmisc_1(X3)) )
=> m1_subset_1(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+9.ax',t4_subset) ).
fof(d2_subset_1,axiom,
! [X1,X2] :
( ( ~ v1_xboole_0(X1)
=> ( m1_subset_1(X2,X1)
<=> r2_hidden(X2,X1) ) )
& ( v1_xboole_0(X1)
=> ( m1_subset_1(X2,X1)
<=> v1_xboole_0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+7.ax',d2_subset_1) ).
fof(t1_subset,axiom,
! [X1,X2] :
( r2_hidden(X1,X2)
=> m1_subset_1(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+9.ax',t1_subset) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( v1_xboole_0(X1)
& X1 != X2
& v1_xboole_0(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+3.ax',t8_boole) ).
fof(rc2_funct_1,axiom,
? [X1] :
( v1_relat_1(X1)
& v1_xboole_0(X1)
& v1_funct_1(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+11.ax',rc2_funct_1) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( r2_hidden(X1,X2)
& v1_xboole_0(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+3.ax',t7_boole) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( m1_subset_1(X2,k1_zfmisc_1(X1))
& v1_xboole_0(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+7.ax',rc2_subset_1) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( r2_hidden(X1,X2)
& m1_subset_1(X2,k1_zfmisc_1(X3))
& v1_xboole_0(X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+9.ax',t5_subset) ).
fof(d10_lattice4,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> ( m2_lattice4(X2,X1)
<=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( ( r2_hidden(X3,X2)
& r2_hidden(X4,X2) )
=> ( r2_hidden(k4_lattices(X1,X3,X4),X2)
& r2_hidden(k3_lattices(X1,X3,X4),X2) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+375.ax',d10_lattice4) ).
fof(c_0_12,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> ( ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( ( r2_hidden(X3,X2)
& r2_hidden(X4,X2) )
<=> r2_hidden(k4_lattices(X1,X3,X4),X2) ) ) )
=> m2_lattice4(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t13_filter_2])]) ).
fof(c_0_13,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_0(X2,X1)
=> m2_lattice4(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[t11_lattice4]) ).
fof(c_0_14,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( ( ~ v1_xboole_0(X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
=> ( m1_filter_0(X2,X1)
<=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( ( r2_hidden(X3,X2)
& r2_hidden(X4,X2) )
<=> r2_hidden(k4_lattices(X1,X3,X4),X2) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d1_filter_0]) ).
fof(c_0_15,negated_conjecture,
! [X165,X166] :
( ~ v3_struct_0(esk1_0)
& v10_lattices(esk1_0)
& l3_lattices(esk1_0)
& m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0)))
& ( ~ r2_hidden(X165,esk2_0)
| ~ r2_hidden(X166,esk2_0)
| r2_hidden(k4_lattices(esk1_0,X165,X166),esk2_0)
| ~ m1_subset_1(X166,u1_struct_0(esk1_0))
| ~ m1_subset_1(X165,u1_struct_0(esk1_0)) )
& ( r2_hidden(X165,esk2_0)
| ~ r2_hidden(k4_lattices(esk1_0,X165,X166),esk2_0)
| ~ m1_subset_1(X166,u1_struct_0(esk1_0))
| ~ m1_subset_1(X165,u1_struct_0(esk1_0)) )
& ( r2_hidden(X166,esk2_0)
| ~ r2_hidden(k4_lattices(esk1_0,X165,X166),esk2_0)
| ~ m1_subset_1(X166,u1_struct_0(esk1_0))
| ~ m1_subset_1(X165,u1_struct_0(esk1_0)) )
& ~ m2_lattice4(esk2_0,esk1_0) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])])]) ).
fof(c_0_16,plain,
! [X176,X177] :
( v3_struct_0(X176)
| ~ v10_lattices(X176)
| ~ l3_lattices(X176)
| ~ m1_filter_0(X177,X176)
| m2_lattice4(X177,X176) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_17,plain,
! [X210,X211,X212] :
( ~ r2_hidden(X210,X211)
| ~ m1_subset_1(X211,k1_zfmisc_1(X212))
| m1_subset_1(X210,X212) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(c_0_18,plain,
! [X247,X248,X249,X250] :
( ( ~ r2_hidden(X249,X248)
| ~ r2_hidden(X250,X248)
| r2_hidden(k4_lattices(X247,X249,X250),X248)
| ~ m1_subset_1(X250,u1_struct_0(X247))
| ~ m1_subset_1(X249,u1_struct_0(X247))
| ~ m1_filter_0(X248,X247)
| v1_xboole_0(X248)
| ~ m1_subset_1(X248,k1_zfmisc_1(u1_struct_0(X247)))
| v3_struct_0(X247)
| ~ v10_lattices(X247)
| ~ l3_lattices(X247) )
& ( r2_hidden(X249,X248)
| ~ r2_hidden(k4_lattices(X247,X249,X250),X248)
| ~ m1_subset_1(X250,u1_struct_0(X247))
| ~ m1_subset_1(X249,u1_struct_0(X247))
| ~ m1_filter_0(X248,X247)
| v1_xboole_0(X248)
| ~ m1_subset_1(X248,k1_zfmisc_1(u1_struct_0(X247)))
| v3_struct_0(X247)
| ~ v10_lattices(X247)
| ~ l3_lattices(X247) )
& ( r2_hidden(X250,X248)
| ~ r2_hidden(k4_lattices(X247,X249,X250),X248)
| ~ m1_subset_1(X250,u1_struct_0(X247))
| ~ m1_subset_1(X249,u1_struct_0(X247))
| ~ m1_filter_0(X248,X247)
| v1_xboole_0(X248)
| ~ m1_subset_1(X248,k1_zfmisc_1(u1_struct_0(X247)))
| v3_struct_0(X247)
| ~ v10_lattices(X247)
| ~ l3_lattices(X247) )
& ( m1_subset_1(esk12_2(X247,X248),u1_struct_0(X247))
| m1_filter_0(X248,X247)
| v1_xboole_0(X248)
| ~ m1_subset_1(X248,k1_zfmisc_1(u1_struct_0(X247)))
| v3_struct_0(X247)
| ~ v10_lattices(X247)
| ~ l3_lattices(X247) )
& ( m1_subset_1(esk13_2(X247,X248),u1_struct_0(X247))
| m1_filter_0(X248,X247)
| v1_xboole_0(X248)
| ~ m1_subset_1(X248,k1_zfmisc_1(u1_struct_0(X247)))
| v3_struct_0(X247)
| ~ v10_lattices(X247)
| ~ l3_lattices(X247) )
& ( ~ r2_hidden(esk12_2(X247,X248),X248)
| ~ r2_hidden(esk13_2(X247,X248),X248)
| ~ r2_hidden(k4_lattices(X247,esk12_2(X247,X248),esk13_2(X247,X248)),X248)
| m1_filter_0(X248,X247)
| v1_xboole_0(X248)
| ~ m1_subset_1(X248,k1_zfmisc_1(u1_struct_0(X247)))
| v3_struct_0(X247)
| ~ v10_lattices(X247)
| ~ l3_lattices(X247) )
& ( r2_hidden(esk12_2(X247,X248),X248)
| r2_hidden(k4_lattices(X247,esk12_2(X247,X248),esk13_2(X247,X248)),X248)
| m1_filter_0(X248,X247)
| v1_xboole_0(X248)
| ~ m1_subset_1(X248,k1_zfmisc_1(u1_struct_0(X247)))
| v3_struct_0(X247)
| ~ v10_lattices(X247)
| ~ l3_lattices(X247) )
& ( r2_hidden(esk13_2(X247,X248),X248)
| r2_hidden(k4_lattices(X247,esk12_2(X247,X248),esk13_2(X247,X248)),X248)
| m1_filter_0(X248,X247)
| v1_xboole_0(X248)
| ~ m1_subset_1(X248,k1_zfmisc_1(u1_struct_0(X247)))
| v3_struct_0(X247)
| ~ v10_lattices(X247)
| ~ l3_lattices(X247) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])])]) ).
cnf(c_0_19,negated_conjecture,
~ m2_lattice4(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
( v3_struct_0(X1)
| m2_lattice4(X2,X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_filter_0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_24,plain,
! [X1,X2] :
( ( ~ v1_xboole_0(X1)
=> ( m1_subset_1(X2,X1)
<=> r2_hidden(X2,X1) ) )
& ( v1_xboole_0(X1)
=> ( m1_subset_1(X2,X1)
<=> v1_xboole_0(X2) ) ) ),
inference(fof_simplification,[status(thm)],[d2_subset_1]) ).
fof(c_0_25,plain,
! [X206,X207] :
( ~ r2_hidden(X206,X207)
| m1_subset_1(X206,X207) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
cnf(c_0_26,plain,
( m1_subset_1(X1,X3)
| ~ r2_hidden(X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,negated_conjecture,
m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_28,negated_conjecture,
( r2_hidden(X1,esk2_0)
| ~ r2_hidden(k4_lattices(esk1_0,X1,X2),esk2_0)
| ~ m1_subset_1(X2,u1_struct_0(esk1_0))
| ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_29,plain,
( r2_hidden(esk12_2(X1,X2),X2)
| r2_hidden(k4_lattices(X1,esk12_2(X1,X2),esk13_2(X1,X2)),X2)
| m1_filter_0(X2,X1)
| v1_xboole_0(X2)
| v3_struct_0(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_30,negated_conjecture,
~ m1_filter_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_19,c_0_20]),c_0_21]),c_0_22])]),c_0_23]) ).
fof(c_0_31,plain,
! [X265,X266] :
( ~ v1_xboole_0(X265)
| X265 = X266
| ~ v1_xboole_0(X266) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(c_0_32,plain,
( v1_relat_1(esk22_0)
& v1_xboole_0(esk22_0)
& v1_funct_1(esk22_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_funct_1])]) ).
fof(c_0_33,plain,
! [X191,X192] :
( ~ r2_hidden(X191,X192)
| ~ v1_xboole_0(X192) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(c_0_34,plain,
! [X193,X194] :
( ( ~ m1_subset_1(X194,X193)
| r2_hidden(X194,X193)
| v1_xboole_0(X193) )
& ( ~ r2_hidden(X194,X193)
| m1_subset_1(X194,X193)
| v1_xboole_0(X193) )
& ( ~ m1_subset_1(X194,X193)
| v1_xboole_0(X194)
| ~ v1_xboole_0(X193) )
& ( ~ v1_xboole_0(X194)
| m1_subset_1(X194,X193)
| ~ v1_xboole_0(X193) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])]) ).
cnf(c_0_35,plain,
( m1_subset_1(X1,X2)
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_36,negated_conjecture,
( r2_hidden(k4_lattices(esk1_0,X1,X2),esk2_0)
| ~ r2_hidden(X1,esk2_0)
| ~ r2_hidden(X2,esk2_0)
| ~ m1_subset_1(X2,u1_struct_0(esk1_0))
| ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_37,negated_conjecture,
( m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ r2_hidden(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_38,negated_conjecture,
( v1_xboole_0(esk2_0)
| r2_hidden(esk12_2(esk1_0,esk2_0),esk2_0)
| ~ m1_subset_1(esk13_2(esk1_0,esk2_0),u1_struct_0(esk1_0))
| ~ m1_subset_1(esk12_2(esk1_0,esk2_0),u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_21]),c_0_22]),c_0_27])]),c_0_30]),c_0_23]) ).
cnf(c_0_39,plain,
( X1 = X2
| ~ v1_xboole_0(X1)
| ~ v1_xboole_0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_40,plain,
v1_xboole_0(esk22_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_41,plain,
! [X260] :
( m1_subset_1(esk16_1(X260),k1_zfmisc_1(X260))
& v1_xboole_0(esk16_1(X260)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
cnf(c_0_42,plain,
( m1_filter_0(X2,X1)
| v1_xboole_0(X2)
| v3_struct_0(X1)
| ~ r2_hidden(esk12_2(X1,X2),X2)
| ~ r2_hidden(esk13_2(X1,X2),X2)
| ~ r2_hidden(k4_lattices(X1,esk12_2(X1,X2),esk13_2(X1,X2)),X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_43,plain,
( ~ r2_hidden(X1,X2)
| ~ v1_xboole_0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_44,plain,
( r2_hidden(X1,X2)
| v1_xboole_0(X2)
| ~ m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_45,negated_conjecture,
( m1_subset_1(k4_lattices(esk1_0,X1,X2),esk2_0)
| ~ r2_hidden(X2,esk2_0)
| ~ r2_hidden(X1,esk2_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_37]) ).
cnf(c_0_46,negated_conjecture,
( m1_subset_1(esk12_2(esk1_0,esk2_0),esk2_0)
| v1_xboole_0(esk2_0)
| ~ m1_subset_1(esk13_2(esk1_0,esk2_0),u1_struct_0(esk1_0))
| ~ m1_subset_1(esk12_2(esk1_0,esk2_0),u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_35,c_0_38]) ).
cnf(c_0_47,plain,
( m1_subset_1(esk13_2(X1,X2),u1_struct_0(X1))
| m1_filter_0(X2,X1)
| v1_xboole_0(X2)
| v3_struct_0(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_48,plain,
( X1 = esk22_0
| ~ v1_xboole_0(X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_49,plain,
v1_xboole_0(esk16_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_50,plain,
( m1_filter_0(X1,X2)
| v3_struct_0(X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))
| ~ r2_hidden(k4_lattices(X2,esk12_2(X2,X1),esk13_2(X2,X1)),X1)
| ~ r2_hidden(esk12_2(X2,X1),X1)
| ~ r2_hidden(esk13_2(X2,X1),X1) ),
inference(csr,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_51,negated_conjecture,
( r2_hidden(k4_lattices(esk1_0,X1,X2),esk2_0)
| ~ r2_hidden(X2,esk2_0)
| ~ r2_hidden(X1,esk2_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_43]) ).
cnf(c_0_52,negated_conjecture,
( r2_hidden(X1,esk2_0)
| ~ r2_hidden(k4_lattices(esk1_0,X2,X1),esk2_0)
| ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ m1_subset_1(X2,u1_struct_0(esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_53,plain,
( r2_hidden(esk13_2(X1,X2),X2)
| r2_hidden(k4_lattices(X1,esk12_2(X1,X2),esk13_2(X1,X2)),X2)
| m1_filter_0(X2,X1)
| v1_xboole_0(X2)
| v3_struct_0(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_54,negated_conjecture,
( m1_subset_1(esk12_2(esk1_0,esk2_0),esk2_0)
| v1_xboole_0(esk2_0)
| ~ m1_subset_1(esk12_2(esk1_0,esk2_0),u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_21]),c_0_22]),c_0_27])]),c_0_30]),c_0_23]) ).
fof(c_0_55,plain,
! [X213,X214,X215] :
( ~ r2_hidden(X213,X214)
| ~ m1_subset_1(X214,k1_zfmisc_1(X215))
| ~ v1_xboole_0(X215) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
cnf(c_0_56,plain,
m1_subset_1(esk16_1(X1),k1_zfmisc_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_57,plain,
esk16_1(X1) = esk22_0,
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
fof(c_0_58,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> ( m2_lattice4(X2,X1)
<=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( ( r2_hidden(X3,X2)
& r2_hidden(X4,X2) )
=> ( r2_hidden(k4_lattices(X1,X3,X4),X2)
& r2_hidden(k3_lattices(X1,X3,X4),X2) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d10_lattice4]) ).
cnf(c_0_59,negated_conjecture,
( ~ r2_hidden(esk12_2(esk1_0,esk2_0),esk2_0)
| ~ r2_hidden(esk13_2(esk1_0,esk2_0),esk2_0) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_21]),c_0_22]),c_0_27])]),c_0_30]),c_0_23]) ).
cnf(c_0_60,negated_conjecture,
( v1_xboole_0(esk2_0)
| r2_hidden(esk13_2(esk1_0,esk2_0),esk2_0)
| ~ m1_subset_1(esk12_2(esk1_0,esk2_0),u1_struct_0(esk1_0))
| ~ m1_subset_1(esk13_2(esk1_0,esk2_0),u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_21]),c_0_22]),c_0_27])]),c_0_30]),c_0_23]) ).
cnf(c_0_61,negated_conjecture,
( v1_xboole_0(esk2_0)
| r2_hidden(esk12_2(esk1_0,esk2_0),esk2_0)
| ~ m1_subset_1(esk12_2(esk1_0,esk2_0),u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_44,c_0_54]) ).
cnf(c_0_62,plain,
( ~ r2_hidden(X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X3))
| ~ v1_xboole_0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_63,plain,
m1_subset_1(esk22_0,k1_zfmisc_1(X1)),
inference(rw,[status(thm)],[c_0_56,c_0_57]) ).
fof(c_0_64,plain,
! [X169,X170,X171,X172] :
( ( r2_hidden(k4_lattices(X169,X171,X172),X170)
| ~ r2_hidden(X171,X170)
| ~ r2_hidden(X172,X170)
| ~ m1_subset_1(X172,u1_struct_0(X169))
| ~ m1_subset_1(X171,u1_struct_0(X169))
| ~ m2_lattice4(X170,X169)
| ~ m1_subset_1(X170,k1_zfmisc_1(u1_struct_0(X169)))
| v3_struct_0(X169)
| ~ v10_lattices(X169)
| ~ l3_lattices(X169) )
& ( r2_hidden(k3_lattices(X169,X171,X172),X170)
| ~ r2_hidden(X171,X170)
| ~ r2_hidden(X172,X170)
| ~ m1_subset_1(X172,u1_struct_0(X169))
| ~ m1_subset_1(X171,u1_struct_0(X169))
| ~ m2_lattice4(X170,X169)
| ~ m1_subset_1(X170,k1_zfmisc_1(u1_struct_0(X169)))
| v3_struct_0(X169)
| ~ v10_lattices(X169)
| ~ l3_lattices(X169) )
& ( m1_subset_1(esk4_2(X169,X170),u1_struct_0(X169))
| m2_lattice4(X170,X169)
| ~ m1_subset_1(X170,k1_zfmisc_1(u1_struct_0(X169)))
| v3_struct_0(X169)
| ~ v10_lattices(X169)
| ~ l3_lattices(X169) )
& ( m1_subset_1(esk5_2(X169,X170),u1_struct_0(X169))
| m2_lattice4(X170,X169)
| ~ m1_subset_1(X170,k1_zfmisc_1(u1_struct_0(X169)))
| v3_struct_0(X169)
| ~ v10_lattices(X169)
| ~ l3_lattices(X169) )
& ( r2_hidden(esk4_2(X169,X170),X170)
| m2_lattice4(X170,X169)
| ~ m1_subset_1(X170,k1_zfmisc_1(u1_struct_0(X169)))
| v3_struct_0(X169)
| ~ v10_lattices(X169)
| ~ l3_lattices(X169) )
& ( r2_hidden(esk5_2(X169,X170),X170)
| m2_lattice4(X170,X169)
| ~ m1_subset_1(X170,k1_zfmisc_1(u1_struct_0(X169)))
| v3_struct_0(X169)
| ~ v10_lattices(X169)
| ~ l3_lattices(X169) )
& ( ~ r2_hidden(k4_lattices(X169,esk4_2(X169,X170),esk5_2(X169,X170)),X170)
| ~ r2_hidden(k3_lattices(X169,esk4_2(X169,X170),esk5_2(X169,X170)),X170)
| m2_lattice4(X170,X169)
| ~ m1_subset_1(X170,k1_zfmisc_1(u1_struct_0(X169)))
| v3_struct_0(X169)
| ~ v10_lattices(X169)
| ~ l3_lattices(X169) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_58])])])])]) ).
cnf(c_0_65,negated_conjecture,
( v1_xboole_0(esk2_0)
| ~ m1_subset_1(esk12_2(esk1_0,esk2_0),u1_struct_0(esk1_0))
| ~ m1_subset_1(esk13_2(esk1_0,esk2_0),u1_struct_0(esk1_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]) ).
cnf(c_0_66,plain,
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X2,esk22_0) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_67,plain,
( r2_hidden(esk4_2(X1,X2),X2)
| m2_lattice4(X2,X1)
| v3_struct_0(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_68,negated_conjecture,
( v1_xboole_0(esk2_0)
| ~ m1_subset_1(esk12_2(esk1_0,esk2_0),u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_47]),c_0_21]),c_0_22]),c_0_27])]),c_0_30]),c_0_23]) ).
cnf(c_0_69,plain,
( m1_subset_1(esk12_2(X1,X2),u1_struct_0(X1))
| m1_filter_0(X2,X1)
| v1_xboole_0(X2)
| v3_struct_0(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_70,plain,
( m2_lattice4(esk22_0,X1)
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ v1_xboole_0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_63])]) ).
cnf(c_0_71,negated_conjecture,
v1_xboole_0(esk2_0),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_21]),c_0_22]),c_0_27])]),c_0_30]),c_0_23]) ).
cnf(c_0_72,plain,
( m2_lattice4(esk22_0,X1)
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(spm,[status(thm)],[c_0_70,c_0_40]) ).
cnf(c_0_73,negated_conjecture,
esk22_0 = esk2_0,
inference(spm,[status(thm)],[c_0_48,c_0_71]) ).
cnf(c_0_74,plain,
( m2_lattice4(esk2_0,X1)
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(rw,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_75,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_74]),c_0_21]),c_0_22])]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : LAT297+3 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.06/0.25 % Computer : n024.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 300
% 0.06/0.25 % DateTime : Mon May 4 16:06:28 EDT 2026
% 0.06/0.25 % CPUTime :
% 0.06/0.26 % start to proof: theBenchmark
% 9.30/9.25 % Version : CSE_E---1.7
% 9.30/9.25 % Problem : theBenchmark.p
% 9.30/9.25 % SZS status Theorem for theBenchmark.p
% 9.30/9.25 % SZS output start CNFRefutation
% See solution above
% 9.30/9.25 % Total time : 8.912s
%------------------------------------------------------------------------------