%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT313+4 : 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 : n004.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 75.79s 66.30s
% Output : CNFRefutation 75.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 19
% Syntax : Number of formulae : 107 ( 16 unt; 0 def)
% Number of atoms : 548 ( 27 equ)
% Maximal formula atoms : 87 ( 5 avg)
% Number of connectives : 658 ( 217 ~; 259 |; 113 &)
% ( 10 <=>; 59 =>; 0 <=; 0 <~>)
% Maximal formula depth : 38 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 2 con; 0-3 aty)
% Number of variables : 179 ( 3 sgn 109 !; 3 ?)
% 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(rc1_subset_1,axiom,
! [X1] :
( ~ v1_xboole_0(X1)
=> ? [X2] :
( m1_subset_1(X2,k1_zfmisc_1(X1))
& ~ v1_xboole_0(X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+7.ax',rc1_subset_1) ).
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(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(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(t12_filter_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_0(X2,X1)
=> ( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v14_lattices(X1)
& l3_lattices(X1) )
=> r2_hidden(k6_lattices(X1),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+242.ax',t12_filter_0) ).
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(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(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(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(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(t45_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))
=> r3_lattices(X1,X2,k6_lattices(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+205.ax',t45_lattices) ).
fof(t22_filter_2,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))) )
=> ( 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) ) ) )
& ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( ( r2_hidden(X3,X2)
& r3_lattices(X1,X4,X3) )
=> r2_hidden(X4,X2) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_filter_2) ).
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(c_0_18,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_19,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_20,plain,
! [X1] :
( ~ v1_xboole_0(X1)
=> ? [X2] :
( m1_subset_1(X2,k1_zfmisc_1(X1))
& ~ v1_xboole_0(X2) ) ),
inference(fof_simplification,[status(thm)],[rc1_subset_1]) ).
fof(c_0_21,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_22,plain,
! [X1058,X1059] :
( v3_struct_0(X1058)
| ~ v10_lattices(X1058)
| ~ l3_lattices(X1058)
| ~ m2_lattice4(X1059,X1058)
| m1_subset_1(X1059,k1_zfmisc_1(u1_struct_0(X1058))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
fof(c_0_23,plain,
! [X652,X653] :
( ( ~ v1_xboole_0(X653)
| ~ m2_filter_2(X653,X652)
| v3_struct_0(X652)
| ~ v10_lattices(X652)
| ~ l3_lattices(X652) )
& ( m2_lattice4(X653,X652)
| ~ m2_filter_2(X653,X652)
| v3_struct_0(X652)
| ~ v10_lattices(X652)
| ~ l3_lattices(X652) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])]) ).
fof(c_0_24,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])]) ).
fof(c_0_25,plain,
! [X712,X713,X714] :
( ~ r2_hidden(X712,X713)
| ~ m1_subset_1(X713,k1_zfmisc_1(X714))
| m1_subset_1(X712,X714) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(c_0_26,plain,
! [X688] :
( ( m1_subset_1(esk17_1(X688),k1_zfmisc_1(X688))
| v1_xboole_0(X688) )
& ( ~ v1_xboole_0(esk17_1(X688))
| v1_xboole_0(X688) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).
fof(c_0_27,plain,
! [X592,X593] :
( ( ~ m1_subset_1(X593,X592)
| r2_hidden(X593,X592)
| v1_xboole_0(X592) )
& ( ~ r2_hidden(X593,X592)
| m1_subset_1(X593,X592)
| v1_xboole_0(X592) )
& ( ~ m1_subset_1(X593,X592)
| v1_xboole_0(X593)
| ~ v1_xboole_0(X592) )
& ( ~ v1_xboole_0(X593)
| m1_subset_1(X593,X592)
| ~ v1_xboole_0(X592) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
fof(c_0_28,plain,
! [X685] : m1_subset_1(esk16_1(X685),X685),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
cnf(c_0_29,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_22]) ).
cnf(c_0_30,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_23]) ).
fof(c_0_31,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_24])])]) ).
cnf(c_0_32,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_25]) ).
cnf(c_0_33,plain,
( m1_subset_1(esk17_1(X1),k1_zfmisc_1(X1))
| v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_34,plain,
( r2_hidden(X1,X2)
| v1_xboole_0(X2)
| ~ m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,plain,
m1_subset_1(esk16_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_36,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_0(X2,X1)
=> ( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v14_lattices(X1)
& l3_lattices(X1) )
=> r2_hidden(k6_lattices(X1),X2) ) ) ),
inference(fof_simplification,[status(thm)],[t12_filter_0]) ).
cnf(c_0_37,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_29,c_0_30]) ).
cnf(c_0_38,negated_conjecture,
m2_filter_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_39,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_40,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_41,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_42,plain,
! [X715,X716,X717] :
( ~ r2_hidden(X715,X716)
| ~ m1_subset_1(X716,k1_zfmisc_1(X717))
| ~ v1_xboole_0(X717) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
cnf(c_0_43,plain,
( m1_subset_1(X1,X2)
| v1_xboole_0(X2)
| ~ r2_hidden(X1,esk17_1(X2)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_44,plain,
( v1_xboole_0(X1)
| r2_hidden(esk16_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_45,plain,
( v1_xboole_0(X1)
| ~ v1_xboole_0(esk17_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_46,plain,
! [X590,X591] :
( ~ r2_hidden(X590,X591)
| ~ v1_xboole_0(X591) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(c_0_47,plain,
! [X627,X628] :
( v3_struct_0(X627)
| ~ v10_lattices(X627)
| ~ l3_lattices(X627)
| ~ m1_filter_0(X628,X627)
| v3_struct_0(X627)
| ~ v10_lattices(X627)
| ~ v14_lattices(X627)
| ~ l3_lattices(X627)
| r2_hidden(k6_lattices(X627),X628) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])]) ).
cnf(c_0_48,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_37,c_0_38]),c_0_39]),c_0_40])]),c_0_41]) ).
fof(c_0_49,plain,
! [X583,X584] :
( ( ~ r2_hidden(esk4_2(X583,X584),X583)
| ~ r2_hidden(esk4_2(X583,X584),X584)
| X583 = X584 )
& ( r2_hidden(esk4_2(X583,X584),X583)
| r2_hidden(esk4_2(X583,X584),X584)
| X583 = X584 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])]) ).
cnf(c_0_50,plain,
( ~ r2_hidden(X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X3))
| ~ v1_xboole_0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_51,plain,
( m1_subset_1(esk16_1(esk17_1(X1)),X1)
| v1_xboole_0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).
cnf(c_0_52,plain,
( ~ r2_hidden(X1,X2)
| ~ v1_xboole_0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_53,negated_conjecture,
r2_hidden(k6_lattices(esk1_0),esk2_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_54,plain,
! [X594,X595] :
( ~ r2_hidden(X594,X595)
| m1_subset_1(X594,X595) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
cnf(c_0_55,plain,
( v3_struct_0(X1)
| v3_struct_0(X1)
| r2_hidden(k6_lattices(X1),X2)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_filter_0(X2,X1)
| ~ v10_lattices(X1)
| ~ v14_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
fof(c_0_56,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_57,negated_conjecture,
( m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ r2_hidden(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_32,c_0_48]) ).
cnf(c_0_58,plain,
( r2_hidden(esk4_2(X1,X2),X1)
| r2_hidden(esk4_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_59,negated_conjecture,
( ~ v1_xboole_0(u1_struct_0(esk1_0))
| ~ r2_hidden(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_50,c_0_48]) ).
cnf(c_0_60,plain,
( v1_xboole_0(X1)
| r2_hidden(esk16_1(esk17_1(X1)),X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_51]) ).
cnf(c_0_61,negated_conjecture,
~ v1_xboole_0(esk2_0),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
fof(c_0_62,plain,
! [X1,X2] :
( epred1_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) ) ) )
& ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( ( r2_hidden(X3,X2)
& r3_lattices(X1,X4,X3) )
=> r2_hidden(X4,X2) ) ) ) ) ),
introduced(definition) ).
fof(c_0_63,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v14_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> r3_lattices(X1,X2,k6_lattices(X1)) ) ),
inference(fof_simplification,[status(thm)],[t45_lattices]) ).
cnf(c_0_64,plain,
( m1_subset_1(X1,X2)
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_65,plain,
( v3_struct_0(X1)
| r2_hidden(k6_lattices(X1),X2)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ v14_lattices(X1)
| ~ m1_filter_0(X2,X1) ),
inference(cn,[status(thm)],[c_0_55]) ).
fof(c_0_66,plain,
! [X879] :
( v3_struct_0(X879)
| ~ v10_lattices(X879)
| ~ l3_lattices(X879)
| m1_filter_0(u1_struct_0(X879),X879) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_56])]) ).
cnf(c_0_67,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_57,c_0_58]) ).
cnf(c_0_68,negated_conjecture,
~ v1_xboole_0(u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]) ).
fof(c_0_69,plain,
! [X1070,X1071,X1072,X1073,X1074,X1075,X1076,X1077] :
( ( ~ m1_subset_1(X1072,u1_struct_0(X1070))
| ~ m1_subset_1(X1073,u1_struct_0(X1070))
| ~ r2_hidden(X1072,X1071)
| ~ r2_hidden(X1073,X1071)
| r2_hidden(k3_lattices(X1070,X1072,X1073),X1071)
| ~ epred1_2(X1071,X1070) )
& ( ~ m1_subset_1(X1074,u1_struct_0(X1070))
| ~ m1_subset_1(X1075,u1_struct_0(X1070))
| ~ r2_hidden(X1074,X1071)
| ~ r3_lattices(X1070,X1075,X1074)
| r2_hidden(X1075,X1071)
| ~ epred1_2(X1071,X1070) )
& ( m1_subset_1(esk67_2(X1076,X1077),u1_struct_0(X1076))
| m1_subset_1(esk65_2(X1076,X1077),u1_struct_0(X1076))
| epred1_2(X1077,X1076) )
& ( m1_subset_1(esk68_2(X1076,X1077),u1_struct_0(X1076))
| m1_subset_1(esk65_2(X1076,X1077),u1_struct_0(X1076))
| epred1_2(X1077,X1076) )
& ( r2_hidden(esk67_2(X1076,X1077),X1077)
| m1_subset_1(esk65_2(X1076,X1077),u1_struct_0(X1076))
| epred1_2(X1077,X1076) )
& ( r3_lattices(X1076,esk68_2(X1076,X1077),esk67_2(X1076,X1077))
| m1_subset_1(esk65_2(X1076,X1077),u1_struct_0(X1076))
| epred1_2(X1077,X1076) )
& ( ~ r2_hidden(esk68_2(X1076,X1077),X1077)
| m1_subset_1(esk65_2(X1076,X1077),u1_struct_0(X1076))
| epred1_2(X1077,X1076) )
& ( m1_subset_1(esk67_2(X1076,X1077),u1_struct_0(X1076))
| m1_subset_1(esk66_2(X1076,X1077),u1_struct_0(X1076))
| epred1_2(X1077,X1076) )
& ( m1_subset_1(esk68_2(X1076,X1077),u1_struct_0(X1076))
| m1_subset_1(esk66_2(X1076,X1077),u1_struct_0(X1076))
| epred1_2(X1077,X1076) )
& ( r2_hidden(esk67_2(X1076,X1077),X1077)
| m1_subset_1(esk66_2(X1076,X1077),u1_struct_0(X1076))
| epred1_2(X1077,X1076) )
& ( r3_lattices(X1076,esk68_2(X1076,X1077),esk67_2(X1076,X1077))
| m1_subset_1(esk66_2(X1076,X1077),u1_struct_0(X1076))
| epred1_2(X1077,X1076) )
& ( ~ r2_hidden(esk68_2(X1076,X1077),X1077)
| m1_subset_1(esk66_2(X1076,X1077),u1_struct_0(X1076))
| epred1_2(X1077,X1076) )
& ( m1_subset_1(esk67_2(X1076,X1077),u1_struct_0(X1076))
| r2_hidden(esk65_2(X1076,X1077),X1077)
| epred1_2(X1077,X1076) )
& ( m1_subset_1(esk68_2(X1076,X1077),u1_struct_0(X1076))
| r2_hidden(esk65_2(X1076,X1077),X1077)
| epred1_2(X1077,X1076) )
& ( r2_hidden(esk67_2(X1076,X1077),X1077)
| r2_hidden(esk65_2(X1076,X1077),X1077)
| epred1_2(X1077,X1076) )
& ( r3_lattices(X1076,esk68_2(X1076,X1077),esk67_2(X1076,X1077))
| r2_hidden(esk65_2(X1076,X1077),X1077)
| epred1_2(X1077,X1076) )
& ( ~ r2_hidden(esk68_2(X1076,X1077),X1077)
| r2_hidden(esk65_2(X1076,X1077),X1077)
| epred1_2(X1077,X1076) )
& ( m1_subset_1(esk67_2(X1076,X1077),u1_struct_0(X1076))
| r2_hidden(esk66_2(X1076,X1077),X1077)
| epred1_2(X1077,X1076) )
& ( m1_subset_1(esk68_2(X1076,X1077),u1_struct_0(X1076))
| r2_hidden(esk66_2(X1076,X1077),X1077)
| epred1_2(X1077,X1076) )
& ( r2_hidden(esk67_2(X1076,X1077),X1077)
| r2_hidden(esk66_2(X1076,X1077),X1077)
| epred1_2(X1077,X1076) )
& ( r3_lattices(X1076,esk68_2(X1076,X1077),esk67_2(X1076,X1077))
| r2_hidden(esk66_2(X1076,X1077),X1077)
| epred1_2(X1077,X1076) )
& ( ~ r2_hidden(esk68_2(X1076,X1077),X1077)
| r2_hidden(esk66_2(X1076,X1077),X1077)
| epred1_2(X1077,X1076) )
& ( m1_subset_1(esk67_2(X1076,X1077),u1_struct_0(X1076))
| ~ r2_hidden(k3_lattices(X1076,esk65_2(X1076,X1077),esk66_2(X1076,X1077)),X1077)
| epred1_2(X1077,X1076) )
& ( m1_subset_1(esk68_2(X1076,X1077),u1_struct_0(X1076))
| ~ r2_hidden(k3_lattices(X1076,esk65_2(X1076,X1077),esk66_2(X1076,X1077)),X1077)
| epred1_2(X1077,X1076) )
& ( r2_hidden(esk67_2(X1076,X1077),X1077)
| ~ r2_hidden(k3_lattices(X1076,esk65_2(X1076,X1077),esk66_2(X1076,X1077)),X1077)
| epred1_2(X1077,X1076) )
& ( r3_lattices(X1076,esk68_2(X1076,X1077),esk67_2(X1076,X1077))
| ~ r2_hidden(k3_lattices(X1076,esk65_2(X1076,X1077),esk66_2(X1076,X1077)),X1077)
| epred1_2(X1077,X1076) )
& ( ~ r2_hidden(esk68_2(X1076,X1077),X1077)
| ~ r2_hidden(k3_lattices(X1076,esk65_2(X1076,X1077),esk66_2(X1076,X1077)),X1077)
| epred1_2(X1077,X1076) ) ),
inference(distribute,[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_62])])])])])]) ).
fof(c_0_70,plain,
! [X620,X621] :
( v3_struct_0(X620)
| ~ v10_lattices(X620)
| ~ v14_lattices(X620)
| ~ l3_lattices(X620)
| ~ m1_subset_1(X621,u1_struct_0(X620))
| r3_lattices(X620,X621,k6_lattices(X620)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_63])])]) ).
cnf(c_0_71,plain,
( v3_struct_0(X1)
| m1_subset_1(k6_lattices(X1),X2)
| ~ m1_filter_0(X2,X1)
| ~ v14_lattices(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_72,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_66]) ).
cnf(c_0_73,negated_conjecture,
( esk2_0 = X1
| r2_hidden(esk4_2(esk2_0,X1),u1_struct_0(esk1_0))
| r2_hidden(esk4_2(esk2_0,X1),X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_67]),c_0_68]) ).
cnf(c_0_74,plain,
( r2_hidden(X3,X4)
| ~ m1_subset_1(X1,u1_struct_0(X2))
| ~ m1_subset_1(X3,u1_struct_0(X2))
| ~ r2_hidden(X1,X4)
| ~ r3_lattices(X2,X3,X1)
| ~ epred1_2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_75,plain,
( v3_struct_0(X1)
| r3_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_70]) ).
cnf(c_0_76,plain,
( v3_struct_0(X1)
| m1_subset_1(k6_lattices(X1),u1_struct_0(X1))
| ~ v14_lattices(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_77,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(ef,[status(thm)],[c_0_73]) ).
fof(c_0_78,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))) )
=> ( m2_filter_2(X2,X1)
<=> epred1_2(X2,X1) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[t22_filter_2]),c_0_62]) ).
fof(c_0_79,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_80,plain,
( X1 = X2
| ~ r2_hidden(esk4_2(X1,X2),X1)
| ~ r2_hidden(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_81,plain,
( v3_struct_0(X1)
| r2_hidden(X2,X3)
| ~ epred1_2(X3,X1)
| ~ v14_lattices(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ r2_hidden(k6_lattices(X1),X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]) ).
cnf(c_0_82,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(spm,[status(thm)],[c_0_64,c_0_77]) ).
cnf(c_0_83,negated_conjecture,
v14_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_84,plain,
! [X669,X670] :
( ( ~ m2_filter_2(X670,X669)
| epred1_2(X670,X669)
| v1_xboole_0(X670)
| ~ m1_subset_1(X670,k1_zfmisc_1(u1_struct_0(X669)))
| v3_struct_0(X669)
| ~ v10_lattices(X669)
| ~ l3_lattices(X669) )
& ( ~ epred1_2(X670,X669)
| m2_filter_2(X670,X669)
| v1_xboole_0(X670)
| ~ m1_subset_1(X670,k1_zfmisc_1(u1_struct_0(X669)))
| v3_struct_0(X669)
| ~ v10_lattices(X669)
| ~ l3_lattices(X669) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_78])])])]) ).
fof(c_0_85,plain,
! [X577] :
( v3_struct_0(X577)
| ~ v10_lattices(X577)
| ~ l3_lattices(X577)
| k17_filter_2(X577) = u1_struct_0(X577) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_79])]) ).
cnf(c_0_86,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_80,c_0_77]) ).
cnf(c_0_87,negated_conjecture,
( esk2_0 = u1_struct_0(esk1_0)
| r2_hidden(esk4_2(esk2_0,u1_struct_0(esk1_0)),X1)
| ~ epred1_2(X1,esk1_0)
| ~ r2_hidden(k6_lattices(esk1_0),X1) ),
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_81,c_0_82]),c_0_83]),c_0_39]),c_0_40])]),c_0_41]) ).
cnf(c_0_88,plain,
( epred1_2(X1,X2)
| v1_xboole_0(X1)
| v3_struct_0(X2)
| ~ m2_filter_2(X1,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_89,plain,
( v3_struct_0(X2)
| ~ v1_xboole_0(X1)
| ~ m2_filter_2(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_90,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_91,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_31]) ).
cnf(c_0_92,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_85]) ).
cnf(c_0_93,negated_conjecture,
( esk2_0 = u1_struct_0(esk1_0)
| ~ epred1_2(esk2_0,esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_53])]) ).
cnf(c_0_94,plain,
( epred1_2(X1,X2)
| v3_struct_0(X2)
| ~ m2_filter_2(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2))) ),
inference(csr,[status(thm)],[c_0_88,c_0_89]) ).
fof(c_0_95,plain,
! [X563,X564,X565] :
( ( ~ r1_filter_2(X563,X564,X565)
| X564 = X565
| v1_xboole_0(X563)
| ~ m1_subset_1(X564,k1_zfmisc_1(X563))
| ~ m1_subset_1(X565,k1_zfmisc_1(X563)) )
& ( X564 != X565
| r1_filter_2(X563,X564,X565)
| v1_xboole_0(X563)
| ~ m1_subset_1(X564,k1_zfmisc_1(X563))
| ~ m1_subset_1(X565,k1_zfmisc_1(X563)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_90])])]) ).
fof(c_0_96,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]) ).
cnf(c_0_97,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_91,c_0_92]),c_0_39]),c_0_40])]),c_0_41]) ).
cnf(c_0_98,negated_conjecture,
esk2_0 = u1_struct_0(esk1_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(spm,[status(thm)],[c_0_93,c_0_94]),c_0_38]),c_0_39]),c_0_40]),c_0_48])]),c_0_41]) ).
cnf(c_0_99,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_95]) ).
fof(c_0_100,plain,
! [X880,X881] :
( ( ~ v1_xboole_0(X881)
| ~ m1_filter_0(X881,X880)
| v3_struct_0(X880)
| ~ v10_lattices(X880)
| ~ l3_lattices(X880) )
& ( m1_subset_1(X881,k1_zfmisc_1(u1_struct_0(X880)))
| ~ m1_filter_0(X881,X880)
| v3_struct_0(X880)
| ~ v10_lattices(X880)
| ~ l3_lattices(X880) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_96])])])]) ).
cnf(c_0_101,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_97,c_0_98]),c_0_98])]) ).
cnf(c_0_102,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_99]) ).
cnf(c_0_103,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_100]) ).
cnf(c_0_104,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_101,c_0_102]),c_0_68]) ).
cnf(c_0_105,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_103,c_0_72]) ).
cnf(c_0_106,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_104,c_0_105]),c_0_39]),c_0_40])]),c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT313+4 : 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
% 0.15/0.33 % Computer : n004.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 21:13:07 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 75.79/66.30 % Version : CSE_E---1.7
% 75.79/66.30 % Problem : theBenchmark.p
% 75.79/66.30 % SZS status Theorem for theBenchmark.p
% 75.79/66.30 % SZS output start CNFRefutation
% See solution above
% 75.79/66.36 % Total time : 63.338s
%------------------------------------------------------------------------------