%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT331+1 : 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 : n009.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 04:38:09 PM UTC 2026
% Result : Theorem 8.59s 5.79s
% Output : CNFRefutation 8.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 9
% Syntax : Number of formulae : 83 ( 19 unt; 0 def)
% Number of atoms : 496 ( 94 equ)
% Maximal formula atoms : 98 ( 5 avg)
% Number of connectives : 681 ( 268 ~; 293 |; 90 &)
% ( 5 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 145 ( 14 sgn 55 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
<=> m1_relset_1(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(dt_u2_lattices,axiom,
! [X1] :
( l2_lattices(X1)
=> ( v1_funct_1(u2_lattices(X1))
& v1_funct_2(u2_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
& m2_relset_1(u2_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u2_lattices) ).
fof(free_g3_lattices,axiom,
! [X1,X2,X3] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)
& m1_relset_1(X2,k2_zfmisc_1(X1,X1),X1)
& v1_funct_1(X3)
& v1_funct_2(X3,k2_zfmisc_1(X1,X1),X1)
& m1_relset_1(X3,k2_zfmisc_1(X1,X1),X1) )
=> ! [X4,X5,X6] :
( g3_lattices(X1,X2,X3) = g3_lattices(X4,X5,X6)
=> ( X1 = X4
& X2 = X5
& X3 = X6 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g3_lattices) ).
fof(dt_u1_lattices,axiom,
! [X1] :
( l1_lattices(X1)
=> ( v1_funct_1(u1_lattices(X1))
& v1_funct_2(u1_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
& m2_relset_1(u1_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_lattices) ).
fof(t68_filter_2,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v10_lattices(X2)
& l3_lattices(X2) )
=> ! [X3] :
( m1_filter_2(X3,X1)
=> ! [X4] :
( m1_filter_2(X4,X2)
=> ( ( g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1)) = g3_lattices(u1_struct_0(X2),u2_lattices(X2),u1_lattices(X2))
& X3 = X4 )
=> k8_filter_0(X1,X3) = k8_filter_0(X2,X4) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_filter_2) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( l1_lattices(X1)
& l2_lattices(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(d10_filter_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_0(X2,X1)
=> ! [X3] :
( ( ~ v3_struct_0(X3)
& v10_lattices(X3)
& l3_lattices(X3) )
=> ( X3 = k8_filter_0(X1,X2)
<=> ? [X4] :
( v1_funct_1(X4)
& v1_funct_2(X4,k2_zfmisc_1(X2,X2),X2)
& m2_relset_1(X4,k2_zfmisc_1(X2,X2),X2)
& ? [X5] :
( v1_funct_1(X5)
& v1_funct_2(X5,k2_zfmisc_1(X2,X2),X2)
& m2_relset_1(X5,k2_zfmisc_1(X2,X2),X2)
& X4 = k1_realset1(u2_lattices(X1),X2)
& X5 = k1_realset1(u1_lattices(X1),X2)
& X3 = g3_lattices(X2,X4,X5) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_filter_0) ).
fof(dt_k8_filter_0,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_filter_0(X2,X1) )
=> ( ~ v3_struct_0(k8_filter_0(X1,X2))
& v10_lattices(k8_filter_0(X1,X2))
& l3_lattices(k8_filter_0(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_filter_0) ).
fof(redefinition_m1_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_2(X2,X1)
<=> m1_filter_0(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m1_filter_2) ).
fof(c_0_9,plain,
! [X239,X240,X241] :
( ( ~ m2_relset_1(X241,X239,X240)
| m1_relset_1(X241,X239,X240) )
& ( ~ m1_relset_1(X241,X239,X240)
| m2_relset_1(X241,X239,X240) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
fof(c_0_10,plain,
! [X176] :
( ( v1_funct_1(u2_lattices(X176))
| ~ l2_lattices(X176) )
& ( v1_funct_2(u2_lattices(X176),k2_zfmisc_1(u1_struct_0(X176),u1_struct_0(X176)),u1_struct_0(X176))
| ~ l2_lattices(X176) )
& ( m2_relset_1(u2_lattices(X176),k2_zfmisc_1(u1_struct_0(X176),u1_struct_0(X176)),u1_struct_0(X176))
| ~ l2_lattices(X176) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u2_lattices])])]) ).
fof(c_0_11,plain,
! [X214,X215,X216,X217,X218,X219] :
( ( X214 = X217
| g3_lattices(X214,X215,X216) != g3_lattices(X217,X218,X219)
| ~ v1_funct_1(X215)
| ~ v1_funct_2(X215,k2_zfmisc_1(X214,X214),X214)
| ~ m1_relset_1(X215,k2_zfmisc_1(X214,X214),X214)
| ~ v1_funct_1(X216)
| ~ v1_funct_2(X216,k2_zfmisc_1(X214,X214),X214)
| ~ m1_relset_1(X216,k2_zfmisc_1(X214,X214),X214) )
& ( X215 = X218
| g3_lattices(X214,X215,X216) != g3_lattices(X217,X218,X219)
| ~ v1_funct_1(X215)
| ~ v1_funct_2(X215,k2_zfmisc_1(X214,X214),X214)
| ~ m1_relset_1(X215,k2_zfmisc_1(X214,X214),X214)
| ~ v1_funct_1(X216)
| ~ v1_funct_2(X216,k2_zfmisc_1(X214,X214),X214)
| ~ m1_relset_1(X216,k2_zfmisc_1(X214,X214),X214) )
& ( X216 = X219
| g3_lattices(X214,X215,X216) != g3_lattices(X217,X218,X219)
| ~ v1_funct_1(X215)
| ~ v1_funct_2(X215,k2_zfmisc_1(X214,X214),X214)
| ~ m1_relset_1(X215,k2_zfmisc_1(X214,X214),X214)
| ~ v1_funct_1(X216)
| ~ v1_funct_2(X216,k2_zfmisc_1(X214,X214),X214)
| ~ m1_relset_1(X216,k2_zfmisc_1(X214,X214),X214) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[free_g3_lattices])])])]) ).
cnf(c_0_12,plain,
( m1_relset_1(X1,X2,X3)
| ~ m2_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( m2_relset_1(u2_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ l2_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X175] :
( ( v1_funct_1(u1_lattices(X175))
| ~ l1_lattices(X175) )
& ( v1_funct_2(u1_lattices(X175),k2_zfmisc_1(u1_struct_0(X175),u1_struct_0(X175)),u1_struct_0(X175))
| ~ l1_lattices(X175) )
& ( m2_relset_1(u1_lattices(X175),k2_zfmisc_1(u1_struct_0(X175),u1_struct_0(X175)),u1_struct_0(X175))
| ~ l1_lattices(X175) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_lattices])])]) ).
cnf(c_0_15,plain,
( X1 = X2
| g3_lattices(X3,X4,X1) != g3_lattices(X5,X6,X2)
| ~ v1_funct_1(X4)
| ~ v1_funct_2(X4,k2_zfmisc_1(X3,X3),X3)
| ~ m1_relset_1(X4,k2_zfmisc_1(X3,X3),X3)
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k2_zfmisc_1(X3,X3),X3)
| ~ m1_relset_1(X1,k2_zfmisc_1(X3,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( m1_relset_1(u2_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ l2_lattices(X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( v1_funct_1(u2_lattices(X1))
| ~ l2_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
( v1_funct_2(u2_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ l2_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,plain,
( m2_relset_1(u1_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ l1_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_20,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v10_lattices(X2)
& l3_lattices(X2) )
=> ! [X3] :
( m1_filter_2(X3,X1)
=> ! [X4] :
( m1_filter_2(X4,X2)
=> ( ( g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1)) = g3_lattices(u1_struct_0(X2),u2_lattices(X2),u1_lattices(X2))
& X3 = X4 )
=> k8_filter_0(X1,X3) = k8_filter_0(X2,X4) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t68_filter_2])]) ).
cnf(c_0_21,plain,
( X1 = X2
| g3_lattices(u1_struct_0(X3),u2_lattices(X3),X1) != g3_lattices(X4,X5,X2)
| ~ l2_lattices(X3)
| ~ m1_relset_1(X1,k2_zfmisc_1(u1_struct_0(X3),u1_struct_0(X3)),u1_struct_0(X3))
| ~ v1_funct_2(X1,k2_zfmisc_1(u1_struct_0(X3),u1_struct_0(X3)),u1_struct_0(X3))
| ~ v1_funct_1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18]) ).
cnf(c_0_22,plain,
( m1_relset_1(u1_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ l1_lattices(X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_19]) ).
cnf(c_0_23,plain,
( v1_funct_1(u1_lattices(X1))
| ~ l1_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,plain,
( v1_funct_2(u1_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ l1_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_25,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v10_lattices(esk1_0)
& l3_lattices(esk1_0)
& ~ v3_struct_0(esk2_0)
& v10_lattices(esk2_0)
& l3_lattices(esk2_0)
& m1_filter_2(esk3_0,esk1_0)
& m1_filter_2(esk4_0,esk2_0)
& g3_lattices(u1_struct_0(esk1_0),u2_lattices(esk1_0),u1_lattices(esk1_0)) = g3_lattices(u1_struct_0(esk2_0),u2_lattices(esk2_0),u1_lattices(esk2_0))
& esk3_0 = esk4_0
& k8_filter_0(esk1_0,esk3_0) != k8_filter_0(esk2_0,esk4_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).
cnf(c_0_26,plain,
( u1_lattices(X1) = X2
| g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1)) != g3_lattices(X3,X4,X2)
| ~ l2_lattices(X1)
| ~ l1_lattices(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_24]) ).
cnf(c_0_27,negated_conjecture,
g3_lattices(u1_struct_0(esk1_0),u2_lattices(esk1_0),u1_lattices(esk1_0)) = g3_lattices(u1_struct_0(esk2_0),u2_lattices(esk2_0),u1_lattices(esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_28,negated_conjecture,
( u1_lattices(esk2_0) = X1
| g3_lattices(u1_struct_0(esk1_0),u2_lattices(esk1_0),u1_lattices(esk1_0)) != g3_lattices(X2,X3,X1)
| ~ l2_lattices(esk2_0)
| ~ l1_lattices(esk2_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_29,plain,
! [X165] :
( ( l1_lattices(X165)
| ~ l3_lattices(X165) )
& ( l2_lattices(X165)
| ~ l3_lattices(X165) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
cnf(c_0_30,negated_conjecture,
( u1_lattices(esk2_0) = u1_lattices(esk1_0)
| ~ l2_lattices(esk2_0)
| ~ l1_lattices(esk2_0) ),
inference(er,[status(thm)],[c_0_28]) ).
cnf(c_0_31,plain,
( l2_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_32,negated_conjecture,
l3_lattices(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_33,plain,
( X1 = X2
| g3_lattices(X3,X1,X4) != g3_lattices(X5,X2,X6)
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k2_zfmisc_1(X3,X3),X3)
| ~ m1_relset_1(X1,k2_zfmisc_1(X3,X3),X3)
| ~ v1_funct_1(X4)
| ~ v1_funct_2(X4,k2_zfmisc_1(X3,X3),X3)
| ~ m1_relset_1(X4,k2_zfmisc_1(X3,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_34,negated_conjecture,
( u1_lattices(esk2_0) = u1_lattices(esk1_0)
| ~ l1_lattices(esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
cnf(c_0_35,plain,
( l1_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,plain,
( X1 = X2
| g3_lattices(u1_struct_0(X3),X1,u1_lattices(X3)) != g3_lattices(X4,X2,X5)
| ~ l1_lattices(X3)
| ~ m1_relset_1(X1,k2_zfmisc_1(u1_struct_0(X3),u1_struct_0(X3)),u1_struct_0(X3))
| ~ v1_funct_2(X1,k2_zfmisc_1(u1_struct_0(X3),u1_struct_0(X3)),u1_struct_0(X3))
| ~ v1_funct_1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_22]),c_0_23]),c_0_24]) ).
cnf(c_0_37,negated_conjecture,
u1_lattices(esk2_0) = u1_lattices(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_32])]) ).
fof(c_0_38,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_0(X2,X1)
=> ! [X3] :
( ( ~ v3_struct_0(X3)
& v10_lattices(X3)
& l3_lattices(X3) )
=> ( X3 = k8_filter_0(X1,X2)
<=> ? [X4] :
( v1_funct_1(X4)
& v1_funct_2(X4,k2_zfmisc_1(X2,X2),X2)
& m2_relset_1(X4,k2_zfmisc_1(X2,X2),X2)
& ? [X5] :
( v1_funct_1(X5)
& v1_funct_2(X5,k2_zfmisc_1(X2,X2),X2)
& m2_relset_1(X5,k2_zfmisc_1(X2,X2),X2)
& X4 = k1_realset1(u2_lattices(X1),X2)
& X5 = k1_realset1(u1_lattices(X1),X2)
& X3 = g3_lattices(X2,X4,X5) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d10_filter_0]) ).
cnf(c_0_39,plain,
( u2_lattices(X1) = X2
| g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1)) != g3_lattices(X3,X2,X4)
| ~ l2_lattices(X1)
| ~ l1_lattices(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_16]),c_0_17]),c_0_18]) ).
cnf(c_0_40,negated_conjecture,
g3_lattices(u1_struct_0(esk2_0),u2_lattices(esk2_0),u1_lattices(esk1_0)) = g3_lattices(u1_struct_0(esk1_0),u2_lattices(esk1_0),u1_lattices(esk1_0)),
inference(rw,[status(thm)],[c_0_27,c_0_37]) ).
fof(c_0_41,plain,
! [X147,X148,X149,X152,X153] :
( ( v1_funct_1(esk5_3(X147,X148,X149))
| X149 != k8_filter_0(X147,X148)
| v3_struct_0(X149)
| ~ v10_lattices(X149)
| ~ l3_lattices(X149)
| ~ m1_filter_0(X148,X147)
| v3_struct_0(X147)
| ~ v10_lattices(X147)
| ~ l3_lattices(X147) )
& ( v1_funct_2(esk5_3(X147,X148,X149),k2_zfmisc_1(X148,X148),X148)
| X149 != k8_filter_0(X147,X148)
| v3_struct_0(X149)
| ~ v10_lattices(X149)
| ~ l3_lattices(X149)
| ~ m1_filter_0(X148,X147)
| v3_struct_0(X147)
| ~ v10_lattices(X147)
| ~ l3_lattices(X147) )
& ( m2_relset_1(esk5_3(X147,X148,X149),k2_zfmisc_1(X148,X148),X148)
| X149 != k8_filter_0(X147,X148)
| v3_struct_0(X149)
| ~ v10_lattices(X149)
| ~ l3_lattices(X149)
| ~ m1_filter_0(X148,X147)
| v3_struct_0(X147)
| ~ v10_lattices(X147)
| ~ l3_lattices(X147) )
& ( v1_funct_1(esk6_3(X147,X148,X149))
| X149 != k8_filter_0(X147,X148)
| v3_struct_0(X149)
| ~ v10_lattices(X149)
| ~ l3_lattices(X149)
| ~ m1_filter_0(X148,X147)
| v3_struct_0(X147)
| ~ v10_lattices(X147)
| ~ l3_lattices(X147) )
& ( v1_funct_2(esk6_3(X147,X148,X149),k2_zfmisc_1(X148,X148),X148)
| X149 != k8_filter_0(X147,X148)
| v3_struct_0(X149)
| ~ v10_lattices(X149)
| ~ l3_lattices(X149)
| ~ m1_filter_0(X148,X147)
| v3_struct_0(X147)
| ~ v10_lattices(X147)
| ~ l3_lattices(X147) )
& ( m2_relset_1(esk6_3(X147,X148,X149),k2_zfmisc_1(X148,X148),X148)
| X149 != k8_filter_0(X147,X148)
| v3_struct_0(X149)
| ~ v10_lattices(X149)
| ~ l3_lattices(X149)
| ~ m1_filter_0(X148,X147)
| v3_struct_0(X147)
| ~ v10_lattices(X147)
| ~ l3_lattices(X147) )
& ( esk5_3(X147,X148,X149) = k1_realset1(u2_lattices(X147),X148)
| X149 != k8_filter_0(X147,X148)
| v3_struct_0(X149)
| ~ v10_lattices(X149)
| ~ l3_lattices(X149)
| ~ m1_filter_0(X148,X147)
| v3_struct_0(X147)
| ~ v10_lattices(X147)
| ~ l3_lattices(X147) )
& ( esk6_3(X147,X148,X149) = k1_realset1(u1_lattices(X147),X148)
| X149 != k8_filter_0(X147,X148)
| v3_struct_0(X149)
| ~ v10_lattices(X149)
| ~ l3_lattices(X149)
| ~ m1_filter_0(X148,X147)
| v3_struct_0(X147)
| ~ v10_lattices(X147)
| ~ l3_lattices(X147) )
& ( X149 = g3_lattices(X148,esk5_3(X147,X148,X149),esk6_3(X147,X148,X149))
| X149 != k8_filter_0(X147,X148)
| v3_struct_0(X149)
| ~ v10_lattices(X149)
| ~ l3_lattices(X149)
| ~ m1_filter_0(X148,X147)
| v3_struct_0(X147)
| ~ v10_lattices(X147)
| ~ l3_lattices(X147) )
& ( ~ v1_funct_1(X152)
| ~ v1_funct_2(X152,k2_zfmisc_1(X148,X148),X148)
| ~ m2_relset_1(X152,k2_zfmisc_1(X148,X148),X148)
| ~ v1_funct_1(X153)
| ~ v1_funct_2(X153,k2_zfmisc_1(X148,X148),X148)
| ~ m2_relset_1(X153,k2_zfmisc_1(X148,X148),X148)
| X152 != k1_realset1(u2_lattices(X147),X148)
| X153 != k1_realset1(u1_lattices(X147),X148)
| X149 != g3_lattices(X148,X152,X153)
| X149 = k8_filter_0(X147,X148)
| v3_struct_0(X149)
| ~ v10_lattices(X149)
| ~ l3_lattices(X149)
| ~ m1_filter_0(X148,X147)
| v3_struct_0(X147)
| ~ v10_lattices(X147)
| ~ l3_lattices(X147) ) ),
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_38])])])])]) ).
cnf(c_0_42,negated_conjecture,
( u2_lattices(X1) = u2_lattices(esk2_0)
| g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1)) != g3_lattices(u1_struct_0(esk1_0),u2_lattices(esk1_0),u1_lattices(esk1_0))
| ~ l2_lattices(X1)
| ~ l1_lattices(X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_43,plain,
( X1 = g3_lattices(X2,esk5_3(X3,X2,X1),esk6_3(X3,X2,X1))
| v3_struct_0(X1)
| v3_struct_0(X3)
| X1 != k8_filter_0(X3,X2)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_filter_0(X2,X3)
| ~ v10_lattices(X3)
| ~ l3_lattices(X3) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_44,plain,
( esk5_3(X1,X2,X3) = k1_realset1(u2_lattices(X1),X2)
| v3_struct_0(X3)
| v3_struct_0(X1)
| X3 != k8_filter_0(X1,X2)
| ~ v10_lattices(X3)
| ~ l3_lattices(X3)
| ~ m1_filter_0(X2,X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_45,plain,
( esk6_3(X1,X2,X3) = k1_realset1(u1_lattices(X1),X2)
| v3_struct_0(X3)
| v3_struct_0(X1)
| X3 != k8_filter_0(X1,X2)
| ~ v10_lattices(X3)
| ~ l3_lattices(X3)
| ~ m1_filter_0(X2,X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_46,negated_conjecture,
v10_lattices(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_47,negated_conjecture,
~ v3_struct_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_48,negated_conjecture,
( u2_lattices(esk2_0) = u2_lattices(esk1_0)
| ~ l2_lattices(esk1_0)
| ~ l1_lattices(esk1_0) ),
inference(er,[status(thm)],[c_0_42]) ).
cnf(c_0_49,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_50,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_filter_0(X2,X1) )
=> ( ~ v3_struct_0(k8_filter_0(X1,X2))
& v10_lattices(k8_filter_0(X1,X2))
& l3_lattices(k8_filter_0(X1,X2)) ) ),
inference(fof_simplification,[status(thm)],[dt_k8_filter_0]) ).
cnf(c_0_51,plain,
( g3_lattices(X1,k1_realset1(u2_lattices(X2),X1),esk6_3(X2,X1,X3)) = X3
| v3_struct_0(X2)
| v3_struct_0(X3)
| X3 != k8_filter_0(X2,X1)
| ~ m1_filter_0(X1,X2)
| ~ l3_lattices(X2)
| ~ l3_lattices(X3)
| ~ v10_lattices(X2)
| ~ v10_lattices(X3) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_52,negated_conjecture,
( esk6_3(esk2_0,X1,X2) = k1_realset1(u1_lattices(esk1_0),X1)
| v3_struct_0(X2)
| X2 != k8_filter_0(esk2_0,X1)
| ~ m1_filter_0(X1,esk2_0)
| ~ l3_lattices(X2)
| ~ v10_lattices(X2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_37]),c_0_32]),c_0_46])]),c_0_47]) ).
cnf(c_0_53,negated_conjecture,
( u2_lattices(esk2_0) = u2_lattices(esk1_0)
| ~ l1_lattices(esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_31]),c_0_49])]) ).
cnf(c_0_54,plain,
( g3_lattices(X1,esk5_3(X2,X1,X3),k1_realset1(u1_lattices(X2),X1)) = X3
| v3_struct_0(X2)
| v3_struct_0(X3)
| X3 != k8_filter_0(X2,X1)
| ~ m1_filter_0(X1,X2)
| ~ l3_lattices(X2)
| ~ l3_lattices(X3)
| ~ v10_lattices(X2)
| ~ v10_lattices(X3) ),
inference(spm,[status(thm)],[c_0_43,c_0_45]) ).
fof(c_0_55,plain,
! [X161,X162] :
( ( ~ v3_struct_0(k8_filter_0(X161,X162))
| v3_struct_0(X161)
| ~ v10_lattices(X161)
| ~ l3_lattices(X161)
| ~ m1_filter_0(X162,X161) )
& ( v10_lattices(k8_filter_0(X161,X162))
| v3_struct_0(X161)
| ~ v10_lattices(X161)
| ~ l3_lattices(X161)
| ~ m1_filter_0(X162,X161) )
& ( l3_lattices(k8_filter_0(X161,X162))
| v3_struct_0(X161)
| ~ v10_lattices(X161)
| ~ l3_lattices(X161)
| ~ m1_filter_0(X162,X161) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_50])])]) ).
cnf(c_0_56,negated_conjecture,
( g3_lattices(X1,k1_realset1(u2_lattices(esk2_0),X1),k1_realset1(u1_lattices(esk1_0),X1)) = X2
| v3_struct_0(X2)
| X2 != k8_filter_0(esk2_0,X1)
| ~ m1_filter_0(X1,esk2_0)
| ~ l3_lattices(X2)
| ~ v10_lattices(X2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_32]),c_0_46])]),c_0_47]) ).
cnf(c_0_57,negated_conjecture,
u2_lattices(esk2_0) = u2_lattices(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_35]),c_0_49])]) ).
cnf(c_0_58,plain,
( g3_lattices(X1,k1_realset1(u2_lattices(X2),X1),k1_realset1(u1_lattices(X2),X1)) = X3
| v3_struct_0(X3)
| v3_struct_0(X2)
| X3 != k8_filter_0(X2,X1)
| ~ m1_filter_0(X1,X2)
| ~ l3_lattices(X2)
| ~ l3_lattices(X3)
| ~ v10_lattices(X2)
| ~ v10_lattices(X3) ),
inference(spm,[status(thm)],[c_0_54,c_0_44]) ).
cnf(c_0_59,plain,
( v10_lattices(k8_filter_0(X1,X2))
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_filter_0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_60,plain,
( l3_lattices(k8_filter_0(X1,X2))
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_filter_0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_61,plain,
( v3_struct_0(X1)
| ~ v3_struct_0(k8_filter_0(X1,X2))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_filter_0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_62,negated_conjecture,
( g3_lattices(X1,k1_realset1(u2_lattices(esk1_0),X1),k1_realset1(u1_lattices(esk1_0),X1)) = X2
| v3_struct_0(X2)
| X2 != k8_filter_0(esk2_0,X1)
| ~ m1_filter_0(X1,esk2_0)
| ~ l3_lattices(X2)
| ~ v10_lattices(X2) ),
inference(rw,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_63,plain,
( g3_lattices(X1,k1_realset1(u2_lattices(X2),X1),k1_realset1(u1_lattices(X2),X1)) = k8_filter_0(X2,X1)
| v3_struct_0(X2)
| ~ m1_filter_0(X1,X2)
| ~ l3_lattices(X2)
| ~ v10_lattices(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_58]),c_0_59]),c_0_60]),c_0_61]) ).
cnf(c_0_64,negated_conjecture,
( g3_lattices(X1,k1_realset1(u2_lattices(esk1_0),X1),k1_realset1(u1_lattices(esk1_0),X1)) = k8_filter_0(esk2_0,X1)
| v3_struct_0(k8_filter_0(esk2_0,X1))
| ~ m1_filter_0(X1,esk2_0)
| ~ l3_lattices(k8_filter_0(esk2_0,X1))
| ~ v10_lattices(k8_filter_0(esk2_0,X1)) ),
inference(er,[status(thm)],[c_0_62]) ).
cnf(c_0_65,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_66,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_67,negated_conjecture,
( k8_filter_0(esk2_0,X1) = k8_filter_0(esk1_0,X1)
| v3_struct_0(k8_filter_0(esk2_0,X1))
| ~ m1_filter_0(X1,esk1_0)
| ~ m1_filter_0(X1,esk2_0)
| ~ l3_lattices(k8_filter_0(esk2_0,X1))
| ~ v10_lattices(k8_filter_0(esk2_0,X1)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_49]),c_0_65])]),c_0_66]) ).
fof(c_0_68,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_2(X2,X1)
<=> m1_filter_0(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[redefinition_m1_filter_2]) ).
cnf(c_0_69,negated_conjecture,
( k8_filter_0(esk2_0,X1) = k8_filter_0(esk1_0,X1)
| v3_struct_0(k8_filter_0(esk2_0,X1))
| ~ m1_filter_0(X1,esk1_0)
| ~ m1_filter_0(X1,esk2_0)
| ~ l3_lattices(k8_filter_0(esk2_0,X1)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_59]),c_0_32]),c_0_46])]),c_0_47]) ).
fof(c_0_70,plain,
! [X237,X238] :
( ( ~ m1_filter_2(X238,X237)
| m1_filter_0(X238,X237)
| v3_struct_0(X237)
| ~ v10_lattices(X237)
| ~ l3_lattices(X237) )
& ( ~ m1_filter_0(X238,X237)
| m1_filter_2(X238,X237)
| v3_struct_0(X237)
| ~ v10_lattices(X237)
| ~ l3_lattices(X237) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_68])])])]) ).
cnf(c_0_71,negated_conjecture,
m1_filter_2(esk4_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_72,negated_conjecture,
esk3_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_73,negated_conjecture,
k8_filter_0(esk1_0,esk3_0) != k8_filter_0(esk2_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_74,negated_conjecture,
( k8_filter_0(esk2_0,X1) = k8_filter_0(esk1_0,X1)
| v3_struct_0(k8_filter_0(esk2_0,X1))
| ~ m1_filter_0(X1,esk1_0)
| ~ m1_filter_0(X1,esk2_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_60]),c_0_32]),c_0_46])]),c_0_47]) ).
cnf(c_0_75,plain,
( m1_filter_0(X1,X2)
| v3_struct_0(X2)
| ~ m1_filter_2(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_76,negated_conjecture,
m1_filter_2(esk3_0,esk2_0),
inference(rw,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_77,negated_conjecture,
m1_filter_2(esk3_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_78,negated_conjecture,
k8_filter_0(esk2_0,esk3_0) != k8_filter_0(esk1_0,esk3_0),
inference(rw,[status(thm)],[c_0_73,c_0_72]) ).
cnf(c_0_79,negated_conjecture,
( k8_filter_0(esk2_0,X1) = k8_filter_0(esk1_0,X1)
| ~ m1_filter_0(X1,esk2_0)
| ~ m1_filter_0(X1,esk1_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_74]),c_0_32]),c_0_46])]),c_0_47]) ).
cnf(c_0_80,negated_conjecture,
m1_filter_0(esk3_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_75,c_0_76]),c_0_32]),c_0_46])]),c_0_47]) ).
cnf(c_0_81,negated_conjecture,
m1_filter_0(esk3_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_75,c_0_77]),c_0_49]),c_0_65])]),c_0_66]) ).
cnf(c_0_82,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80]),c_0_81])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT331+1 : 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 : n009.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 21:21:11 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 8.59/5.79 % Version : CSE_E---1.7
% 8.59/5.79 % Problem : theBenchmark.p
% 8.59/5.79 % SZS status Theorem for theBenchmark.p
% 8.59/5.79 % SZS output start CNFRefutation
% See solution above
% 8.69/5.81 % Total time : 4.373s
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