%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT313+3 : TPTP v9.2.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n014.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 04:38:04 PM UTC 2026
% Result : Theorem 54.74s 34.50s
% Output : CNFRefutation 54.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of formulae : 89 ( 17 unt; 0 def)
% Number of atoms : 422 ( 31 equ)
% Maximal formula atoms : 70 ( 4 avg)
% Number of connectives : 521 ( 188 ~; 203 |; 76 &)
% ( 11 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-3 aty)
% Number of variables : 141 ( 3 sgn 88 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_m2_lattice4,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(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_m2_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_filter_2) ).
fof(t43_filter_2,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( ( v14_lattices(X1)
& r2_hidden(k6_lattices(X1),X2) )
=> ( r1_filter_2(u1_struct_0(X1),X2,k17_filter_2(X1))
& X2 = u1_struct_0(X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_filter_2) ).
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/sandbox/benchmark/Axioms/SET007/SET007+9.ax',t4_subset) ).
fof(t2_tarski,axiom,
! [X1,X2] :
( ! [X3] :
( r2_hidden(X3,X1)
<=> r2_hidden(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+1.ax',t2_tarski) ).
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/sandbox/benchmark/Axioms/SET007/SET007+7.ax',d2_subset_1) ).
fof(d3_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) )
=> ( m2_filter_2(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(k3_lattices(X1,X3,X4),X2) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_filter_2) ).
fof(t44_lattices,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v14_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> k3_lattices(X1,k6_lattices(X1),X2) = k6_lattices(X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+205.ax',t44_lattices) ).
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(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/sandbox/benchmark/Axioms/SET007/SET007+9.ax',t5_subset) ).
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] :
~ ( r2_hidden(X1,X2)
& v1_xboole_0(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+3.ax',t7_boole) ).
fof(d8_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> k17_filter_2(X1) = u1_struct_0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_filter_2) ).
fof(redefinition_r1_filter_2,axiom,
! [X1,X2,X3] :
( ( ~ v1_xboole_0(X1)
& m1_subset_1(X2,k1_zfmisc_1(X1))
& m1_subset_1(X3,k1_zfmisc_1(X1)) )
=> ( r1_filter_2(X1,X2,X3)
<=> X2 = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_filter_2) ).
fof(dt_m1_filter_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_0(X2,X1)
=> ( ~ v1_xboole_0(X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+242.ax',dt_m1_filter_0) ).
fof(t15_filter_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> m1_filter_0(u1_struct_0(X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+242.ax',t15_filter_0) ).
fof(c_0_16,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(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_17,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[dt_m2_filter_2]) ).
fof(c_0_18,plain,
! [X811,X812] :
( v3_struct_0(X811)
| ~ v10_lattices(X811)
| ~ l3_lattices(X811)
| ~ m2_lattice4(X812,X811)
| m1_subset_1(X812,k1_zfmisc_1(u1_struct_0(X811))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
fof(c_0_19,plain,
! [X528,X529] :
( ( ~ v1_xboole_0(X529)
| ~ m2_filter_2(X529,X528)
| v3_struct_0(X528)
| ~ v10_lattices(X528)
| ~ l3_lattices(X528) )
& ( m2_lattice4(X529,X528)
| ~ m2_filter_2(X529,X528)
| v3_struct_0(X528)
| ~ v10_lattices(X528)
| ~ l3_lattices(X528) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])]) ).
fof(c_0_20,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( ( v14_lattices(X1)
& r2_hidden(k6_lattices(X1),X2) )
=> ( r1_filter_2(u1_struct_0(X1),X2,k17_filter_2(X1))
& X2 = u1_struct_0(X1) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t43_filter_2])]) ).
cnf(c_0_21,plain,
( v3_struct_0(X1)
| m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m2_lattice4(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
( m2_lattice4(X1,X2)
| v3_struct_0(X2)
| ~ m2_filter_2(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_23,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v10_lattices(esk1_0)
& l3_lattices(esk1_0)
& m2_filter_2(esk2_0,esk1_0)
& v14_lattices(esk1_0)
& r2_hidden(k6_lattices(esk1_0),esk2_0)
& ( ~ r1_filter_2(u1_struct_0(esk1_0),esk2_0,k17_filter_2(esk1_0))
| esk2_0 != u1_struct_0(esk1_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).
fof(c_0_24,plain,
! [X473,X474,X475] :
( ~ r2_hidden(X473,X474)
| ~ m1_subset_1(X474,k1_zfmisc_1(X475))
| m1_subset_1(X473,X475) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
cnf(c_0_25,plain,
( v3_struct_0(X1)
| m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ m2_filter_2(X2,X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,negated_conjecture,
m2_filter_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_27,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,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_24]) ).
cnf(c_0_31,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_25,c_0_26]),c_0_27]),c_0_28])]),c_0_29]) ).
fof(c_0_32,plain,
! [X447,X448] :
( ( ~ r2_hidden(esk4_2(X447,X448),X447)
| ~ r2_hidden(esk4_2(X447,X448),X448)
| X447 = X448 )
& ( r2_hidden(esk4_2(X447,X448),X447)
| r2_hidden(esk4_2(X447,X448),X448)
| X447 = X448 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])]) ).
fof(c_0_33,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_34,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) )
=> ( m2_filter_2(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(k3_lattices(X1,X3,X4),X2) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d3_filter_2]) ).
fof(c_0_35,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v14_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> k3_lattices(X1,k6_lattices(X1),X2) = k6_lattices(X1) ) ),
inference(fof_simplification,[status(thm)],[t44_lattices]) ).
fof(c_0_36,plain,
! [X469,X470] :
( ~ r2_hidden(X469,X470)
| m1_subset_1(X469,X470) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
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_30,c_0_31]) ).
cnf(c_0_38,plain,
( r2_hidden(esk4_2(X1,X2),X1)
| r2_hidden(esk4_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_39,plain,
! [X476,X477,X478] :
( ~ r2_hidden(X476,X477)
| ~ m1_subset_1(X477,k1_zfmisc_1(X478))
| ~ v1_xboole_0(X478) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
fof(c_0_40,plain,
! [X456,X457] :
( ( ~ m1_subset_1(X457,X456)
| r2_hidden(X457,X456)
| v1_xboole_0(X456) )
& ( ~ r2_hidden(X457,X456)
| m1_subset_1(X457,X456)
| v1_xboole_0(X456) )
& ( ~ m1_subset_1(X457,X456)
| v1_xboole_0(X457)
| ~ v1_xboole_0(X456) )
& ( ~ v1_xboole_0(X457)
| m1_subset_1(X457,X456)
| ~ v1_xboole_0(X456) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])]) ).
fof(c_0_41,plain,
! [X561] : m1_subset_1(esk18_1(X561),X561),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(c_0_42,plain,
! [X454,X455] :
( ~ r2_hidden(X454,X455)
| ~ v1_xboole_0(X455) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(c_0_43,plain,
! [X532,X533,X534,X535] :
( ( ~ r2_hidden(X534,X533)
| ~ r2_hidden(X535,X533)
| r2_hidden(k3_lattices(X532,X534,X535),X533)
| ~ m1_subset_1(X535,u1_struct_0(X532))
| ~ m1_subset_1(X534,u1_struct_0(X532))
| ~ m2_filter_2(X533,X532)
| v1_xboole_0(X533)
| ~ m2_lattice4(X533,X532)
| v3_struct_0(X532)
| ~ v10_lattices(X532)
| ~ l3_lattices(X532) )
& ( r2_hidden(X534,X533)
| ~ r2_hidden(k3_lattices(X532,X534,X535),X533)
| ~ m1_subset_1(X535,u1_struct_0(X532))
| ~ m1_subset_1(X534,u1_struct_0(X532))
| ~ m2_filter_2(X533,X532)
| v1_xboole_0(X533)
| ~ m2_lattice4(X533,X532)
| v3_struct_0(X532)
| ~ v10_lattices(X532)
| ~ l3_lattices(X532) )
& ( r2_hidden(X535,X533)
| ~ r2_hidden(k3_lattices(X532,X534,X535),X533)
| ~ m1_subset_1(X535,u1_struct_0(X532))
| ~ m1_subset_1(X534,u1_struct_0(X532))
| ~ m2_filter_2(X533,X532)
| v1_xboole_0(X533)
| ~ m2_lattice4(X533,X532)
| v3_struct_0(X532)
| ~ v10_lattices(X532)
| ~ l3_lattices(X532) )
& ( m1_subset_1(esk12_2(X532,X533),u1_struct_0(X532))
| m2_filter_2(X533,X532)
| v1_xboole_0(X533)
| ~ m2_lattice4(X533,X532)
| v3_struct_0(X532)
| ~ v10_lattices(X532)
| ~ l3_lattices(X532) )
& ( m1_subset_1(esk13_2(X532,X533),u1_struct_0(X532))
| m2_filter_2(X533,X532)
| v1_xboole_0(X533)
| ~ m2_lattice4(X533,X532)
| v3_struct_0(X532)
| ~ v10_lattices(X532)
| ~ l3_lattices(X532) )
& ( ~ r2_hidden(esk12_2(X532,X533),X533)
| ~ r2_hidden(esk13_2(X532,X533),X533)
| ~ r2_hidden(k3_lattices(X532,esk12_2(X532,X533),esk13_2(X532,X533)),X533)
| m2_filter_2(X533,X532)
| v1_xboole_0(X533)
| ~ m2_lattice4(X533,X532)
| v3_struct_0(X532)
| ~ v10_lattices(X532)
| ~ l3_lattices(X532) )
& ( r2_hidden(esk12_2(X532,X533),X533)
| r2_hidden(k3_lattices(X532,esk12_2(X532,X533),esk13_2(X532,X533)),X533)
| m2_filter_2(X533,X532)
| v1_xboole_0(X533)
| ~ m2_lattice4(X533,X532)
| v3_struct_0(X532)
| ~ v10_lattices(X532)
| ~ l3_lattices(X532) )
& ( r2_hidden(esk13_2(X532,X533),X533)
| r2_hidden(k3_lattices(X532,esk12_2(X532,X533),esk13_2(X532,X533)),X533)
| m2_filter_2(X533,X532)
| v1_xboole_0(X533)
| ~ m2_lattice4(X533,X532)
| v3_struct_0(X532)
| ~ v10_lattices(X532)
| ~ l3_lattices(X532) ) ),
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_34])])])])]) ).
fof(c_0_44,plain,
! [X499,X500] :
( v3_struct_0(X499)
| ~ v10_lattices(X499)
| ~ v14_lattices(X499)
| ~ l3_lattices(X499)
| ~ m1_subset_1(X500,u1_struct_0(X499))
| k3_lattices(X499,k6_lattices(X499),X500) = k6_lattices(X499) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])]) ).
cnf(c_0_45,plain,
( m1_subset_1(X1,X2)
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_46,negated_conjecture,
( esk2_0 = X1
| m1_subset_1(esk4_2(esk2_0,X1),u1_struct_0(esk1_0))
| r2_hidden(esk4_2(esk2_0,X1),X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_47,plain,
( ~ r2_hidden(X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X3))
| ~ v1_xboole_0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_48,plain,
( r2_hidden(X1,X2)
| v1_xboole_0(X2)
| ~ m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_49,plain,
m1_subset_1(esk18_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_50,plain,
( ~ r2_hidden(X1,X2)
| ~ v1_xboole_0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_51,negated_conjecture,
r2_hidden(k6_lattices(esk1_0),esk2_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_52,plain,
( r2_hidden(X1,X2)
| v1_xboole_0(X2)
| v3_struct_0(X3)
| ~ r2_hidden(k3_lattices(X3,X4,X1),X2)
| ~ m1_subset_1(X1,u1_struct_0(X3))
| ~ m1_subset_1(X4,u1_struct_0(X3))
| ~ m2_filter_2(X2,X3)
| ~ m2_lattice4(X2,X3)
| ~ v10_lattices(X3)
| ~ l3_lattices(X3) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_53,plain,
( v3_struct_0(X1)
| k3_lattices(X1,k6_lattices(X1),X2) = k6_lattices(X1)
| ~ v10_lattices(X1)
| ~ v14_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_54,negated_conjecture,
v14_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_55,negated_conjecture,
( esk2_0 = X1
| m1_subset_1(esk4_2(esk2_0,X1),u1_struct_0(esk1_0))
| m1_subset_1(esk4_2(esk2_0,X1),X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_56,negated_conjecture,
( ~ v1_xboole_0(u1_struct_0(esk1_0))
| ~ r2_hidden(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_47,c_0_31]) ).
cnf(c_0_57,plain,
( v1_xboole_0(X1)
| r2_hidden(esk18_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_58,negated_conjecture,
~ v1_xboole_0(esk2_0),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
fof(c_0_59,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> k17_filter_2(X1) = u1_struct_0(X1) ),
inference(fof_simplification,[status(thm)],[d8_filter_2]) ).
cnf(c_0_60,plain,
( v3_struct_0(X1)
| r2_hidden(X2,X3)
| ~ m2_filter_2(X3,X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X4,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ r2_hidden(k3_lattices(X1,X4,X2),X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_52,c_0_22]),c_0_50]) ).
cnf(c_0_61,negated_conjecture,
( k3_lattices(esk1_0,k6_lattices(esk1_0),X1) = k6_lattices(esk1_0)
| ~ m1_subset_1(X1,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_53,c_0_54]),c_0_27]),c_0_28])]),c_0_29]) ).
cnf(c_0_62,negated_conjecture,
m1_subset_1(k6_lattices(esk1_0),u1_struct_0(esk1_0)),
inference(spm,[status(thm)],[c_0_37,c_0_51]) ).
cnf(c_0_63,negated_conjecture,
( esk2_0 = u1_struct_0(esk1_0)
| m1_subset_1(esk4_2(esk2_0,u1_struct_0(esk1_0)),u1_struct_0(esk1_0)) ),
inference(ef,[status(thm)],[c_0_55]) ).
cnf(c_0_64,negated_conjecture,
~ v1_xboole_0(u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]) ).
fof(c_0_65,plain,
! [X441] :
( v3_struct_0(X441)
| ~ v10_lattices(X441)
| ~ l3_lattices(X441)
| k17_filter_2(X441) = u1_struct_0(X441) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_59])]) ).
cnf(c_0_66,negated_conjecture,
( r2_hidden(X1,X2)
| ~ m2_filter_2(X2,esk1_0)
| ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ r2_hidden(k6_lattices(esk1_0),X2) ),
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_60,c_0_61]),c_0_27]),c_0_28]),c_0_62])]),c_0_29]) ).
cnf(c_0_67,plain,
( X1 = X2
| ~ r2_hidden(esk4_2(X1,X2),X1)
| ~ r2_hidden(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_68,negated_conjecture,
( esk2_0 = u1_struct_0(esk1_0)
| r2_hidden(esk4_2(esk2_0,u1_struct_0(esk1_0)),u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_63]),c_0_64]) ).
fof(c_0_69,plain,
! [X1,X2,X3] :
( ( ~ v1_xboole_0(X1)
& m1_subset_1(X2,k1_zfmisc_1(X1))
& m1_subset_1(X3,k1_zfmisc_1(X1)) )
=> ( r1_filter_2(X1,X2,X3)
<=> X2 = X3 ) ),
inference(fof_simplification,[status(thm)],[redefinition_r1_filter_2]) ).
cnf(c_0_70,negated_conjecture,
( ~ r1_filter_2(u1_struct_0(esk1_0),esk2_0,k17_filter_2(esk1_0))
| esk2_0 != u1_struct_0(esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_71,plain,
( v3_struct_0(X1)
| k17_filter_2(X1) = u1_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_72,negated_conjecture,
( esk2_0 = u1_struct_0(esk1_0)
| r2_hidden(esk4_2(esk2_0,u1_struct_0(esk1_0)),X1)
| ~ m2_filter_2(X1,esk1_0)
| ~ r2_hidden(k6_lattices(esk1_0),X1) ),
inference(spm,[status(thm)],[c_0_66,c_0_63]) ).
cnf(c_0_73,negated_conjecture,
( esk2_0 = u1_struct_0(esk1_0)
| ~ r2_hidden(esk4_2(esk2_0,u1_struct_0(esk1_0)),esk2_0) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
fof(c_0_74,plain,
! [X427,X428,X429] :
( ( ~ r1_filter_2(X427,X428,X429)
| X428 = X429
| v1_xboole_0(X427)
| ~ m1_subset_1(X428,k1_zfmisc_1(X427))
| ~ m1_subset_1(X429,k1_zfmisc_1(X427)) )
& ( X428 != X429
| r1_filter_2(X427,X428,X429)
| v1_xboole_0(X427)
| ~ m1_subset_1(X428,k1_zfmisc_1(X427))
| ~ m1_subset_1(X429,k1_zfmisc_1(X427)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_69])])]) ).
fof(c_0_75,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_0(X2,X1)
=> ( ~ v1_xboole_0(X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ) ) ),
inference(fof_simplification,[status(thm)],[dt_m1_filter_0]) ).
fof(c_0_76,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> m1_filter_0(u1_struct_0(X1),X1) ),
inference(fof_simplification,[status(thm)],[t15_filter_0]) ).
cnf(c_0_77,negated_conjecture,
( esk2_0 != u1_struct_0(esk1_0)
| ~ r1_filter_2(u1_struct_0(esk1_0),esk2_0,u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_27]),c_0_28])]),c_0_29]) ).
cnf(c_0_78,negated_conjecture,
esk2_0 = u1_struct_0(esk1_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_26]),c_0_51])]),c_0_73]) ).
cnf(c_0_79,plain,
( r1_filter_2(X3,X1,X2)
| v1_xboole_0(X3)
| X1 != X2
| ~ m1_subset_1(X1,k1_zfmisc_1(X3))
| ~ m1_subset_1(X2,k1_zfmisc_1(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
fof(c_0_80,plain,
! [X700,X701] :
( ( ~ v1_xboole_0(X701)
| ~ m1_filter_0(X701,X700)
| v3_struct_0(X700)
| ~ v10_lattices(X700)
| ~ l3_lattices(X700) )
& ( m1_subset_1(X701,k1_zfmisc_1(u1_struct_0(X700)))
| ~ m1_filter_0(X701,X700)
| v3_struct_0(X700)
| ~ v10_lattices(X700)
| ~ l3_lattices(X700) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_75])])])]) ).
fof(c_0_81,plain,
! [X699] :
( v3_struct_0(X699)
| ~ v10_lattices(X699)
| ~ l3_lattices(X699)
| m1_filter_0(u1_struct_0(X699),X699) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_76])]) ).
cnf(c_0_82,negated_conjecture,
~ r1_filter_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_78]),c_0_78])]) ).
cnf(c_0_83,plain,
( r1_filter_2(X1,X2,X2)
| v1_xboole_0(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(X1)) ),
inference(er,[status(thm)],[c_0_79]) ).
cnf(c_0_84,plain,
( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))
| v3_struct_0(X2)
| ~ m1_filter_0(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_85,plain,
( v3_struct_0(X1)
| m1_filter_0(u1_struct_0(X1),X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_86,negated_conjecture,
~ m1_subset_1(u1_struct_0(esk1_0),k1_zfmisc_1(u1_struct_0(esk1_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_64]) ).
cnf(c_0_87,plain,
( v3_struct_0(X1)
| m1_subset_1(u1_struct_0(X1),k1_zfmisc_1(u1_struct_0(X1)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_88,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_86,c_0_87]),c_0_27]),c_0_28])]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT313+3 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n014.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 21:12:53 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 54.74/34.50 % Version : CSE_E---1.7
% 54.74/34.50 % Problem : theBenchmark.p
% 54.74/34.50 % SZS status Theorem for theBenchmark.p
% 54.74/34.50 % SZS output start CNFRefutation
% See solution above
% 54.83/34.66 % Total time : 27.957s
%------------------------------------------------------------------------------