%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT332+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 : n020.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 3.93s 3.13s
% Output : CNFRefutation 3.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 21
% Syntax : Number of formulae : 107 ( 6 unt; 0 def)
% Number of atoms : 472 ( 78 equ)
% Maximal formula atoms : 88 ( 4 avg)
% Number of connectives : 593 ( 228 ~; 241 |; 85 &)
% ( 4 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 1 con; 0-3 aty)
% Number of variables : 170 ( 5 sgn 90 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k4_relset_1,axiom,
! [X1,X2,X3] :
( m1_relset_1(X3,X1,X2)
=> m1_subset_1(k4_relset_1(X1,X2,X3),k1_zfmisc_1(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relset_1) ).
fof(redefinition_k4_relset_1,axiom,
! [X1,X2,X3] :
( m1_relset_1(X3,X1,X2)
=> k4_relset_1(X1,X2,X3) = k1_relat_1(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
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(cc1_relset_1,axiom,
! [X1,X2,X3] :
( m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
=> v1_relat_1(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(dt_m2_relset_1,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
=> m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
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(t97_relat_1,axiom,
! [X1,X2] :
( v1_relat_1(X2)
=> ( r1_tarski(k1_relat_1(X2),X1)
=> k7_relat_1(X2,X1) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t97_relat_1) ).
fof(t3_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,k1_zfmisc_1(X2))
<=> r1_tarski(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(dt_k17_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> m2_filter_2(k17_filter_2(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k17_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(fc1_struct_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(d16_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) )
=> ! [X3] :
( m2_nat_lat(X3,X1)
=> ( X3 = k23_filter_2(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',d16_filter_2) ).
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(dt_l1_lattices,axiom,
! [X1] :
( l1_lattices(X1)
=> l1_struct_0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
fof(d3_realset1,axiom,
! [X1] :
( v1_relat_1(X1)
=> ! [X2] : k1_realset1(X1,X2) = k7_relat_1(X1,k2_zfmisc_1(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_realset1) ).
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(t72_filter_2,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( k23_filter_2(X1,k17_filter_2(X1)) = g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1))
& k23_filter_2(X1,k1_filter_2(X1)) = g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_filter_2) ).
fof(redefinition_k1_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> k1_filter_2(X1) = k1_filter_0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_filter_2) ).
fof(d2_filter_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> k1_filter_0(X1) = u1_struct_0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_filter_0) ).
fof(dt_k23_filter_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) )
=> m2_nat_lat(k23_filter_2(X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k23_filter_2) ).
fof(c_0_21,plain,
! [X207,X208,X209] :
( ~ m1_relset_1(X209,X207,X208)
| m1_subset_1(k4_relset_1(X207,X208,X209),k1_zfmisc_1(X207)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k4_relset_1])]) ).
fof(c_0_22,plain,
! [X301,X302,X303] :
( ~ m1_relset_1(X303,X301,X302)
| k4_relset_1(X301,X302,X303) = k1_relat_1(X303) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_relset_1])]) ).
fof(c_0_23,plain,
! [X310,X311,X312] :
( ( ~ m2_relset_1(X312,X310,X311)
| m1_relset_1(X312,X310,X311) )
& ( ~ m1_relset_1(X312,X310,X311)
| m2_relset_1(X312,X310,X311) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
fof(c_0_24,plain,
! [X233] :
( ( v1_funct_1(u2_lattices(X233))
| ~ l2_lattices(X233) )
& ( v1_funct_2(u2_lattices(X233),k2_zfmisc_1(u1_struct_0(X233),u1_struct_0(X233)),u1_struct_0(X233))
| ~ l2_lattices(X233) )
& ( m2_relset_1(u2_lattices(X233),k2_zfmisc_1(u1_struct_0(X233),u1_struct_0(X233)),u1_struct_0(X233))
| ~ l2_lattices(X233) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u2_lattices])])]) ).
fof(c_0_25,plain,
! [X180,X181,X182] :
( ~ m1_subset_1(X182,k1_zfmisc_1(k2_zfmisc_1(X180,X181)))
| v1_relat_1(X182) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])]) ).
fof(c_0_26,plain,
! [X229,X230,X231] :
( ~ m2_relset_1(X231,X229,X230)
| m1_subset_1(X231,k1_zfmisc_1(k2_zfmisc_1(X229,X230))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_relset_1])]) ).
fof(c_0_27,plain,
! [X232] :
( ( v1_funct_1(u1_lattices(X232))
| ~ l1_lattices(X232) )
& ( v1_funct_2(u1_lattices(X232),k2_zfmisc_1(u1_struct_0(X232),u1_struct_0(X232)),u1_struct_0(X232))
| ~ l1_lattices(X232) )
& ( m2_relset_1(u1_lattices(X232),k2_zfmisc_1(u1_struct_0(X232),u1_struct_0(X232)),u1_struct_0(X232))
| ~ l1_lattices(X232) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_lattices])])]) ).
fof(c_0_28,plain,
! [X340,X341] :
( ~ v1_relat_1(X341)
| ~ r1_tarski(k1_relat_1(X341),X340)
| k7_relat_1(X341,X340) = X341 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t97_relat_1])]) ).
fof(c_0_29,plain,
! [X327,X328] :
( ( ~ m1_subset_1(X327,k1_zfmisc_1(X328))
| r1_tarski(X327,X328) )
& ( ~ r1_tarski(X327,X328)
| m1_subset_1(X327,k1_zfmisc_1(X328)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
cnf(c_0_30,plain,
( m1_subset_1(k4_relset_1(X2,X3,X1),k1_zfmisc_1(X2))
| ~ m1_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_31,plain,
( k4_relset_1(X2,X3,X1) = k1_relat_1(X1)
| ~ m1_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_32,plain,
( m1_relset_1(X1,X2,X3)
| ~ m2_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,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_24]) ).
cnf(c_0_34,plain,
( v1_relat_1(X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_35,plain,
( m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))
| ~ m2_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_36,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> m2_filter_2(k17_filter_2(X1),X1) ),
inference(fof_simplification,[status(thm)],[dt_k17_filter_2]) ).
fof(c_0_37,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]) ).
fof(c_0_38,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).
cnf(c_0_39,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_27]) ).
fof(c_0_40,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) )
=> ! [X3] :
( m2_nat_lat(X3,X1)
=> ( X3 = k23_filter_2(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)],[d16_filter_2]) ).
cnf(c_0_41,plain,
( k7_relat_1(X1,X2) = X1
| ~ v1_relat_1(X1)
| ~ r1_tarski(k1_relat_1(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_42,plain,
( r1_tarski(X1,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_43,plain,
( m1_subset_1(k1_relat_1(X1),k1_zfmisc_1(X2))
| ~ m1_relset_1(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_44,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_32,c_0_33]) ).
cnf(c_0_45,plain,
( v1_relat_1(X1)
| ~ m2_relset_1(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
fof(c_0_46,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_47,plain,
! [X202] :
( v3_struct_0(X202)
| ~ v10_lattices(X202)
| ~ l3_lattices(X202)
| m2_filter_2(k17_filter_2(X202),X202) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])]) ).
fof(c_0_48,plain,
! [X198] :
( v3_struct_0(X198)
| ~ v10_lattices(X198)
| ~ l3_lattices(X198)
| k17_filter_2(X198) = u1_struct_0(X198) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])]) ).
fof(c_0_49,plain,
! [X258] :
( v3_struct_0(X258)
| ~ l1_struct_0(X258)
| ~ v1_xboole_0(u1_struct_0(X258)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])]) ).
fof(c_0_50,plain,
! [X216] :
( ~ l1_lattices(X216)
| l1_struct_0(X216) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_lattices])]) ).
cnf(c_0_51,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_32,c_0_39]) ).
fof(c_0_52,plain,
! [X185,X186,X187,X190,X191] :
( ( v1_funct_1(esk2_3(X185,X186,X187))
| X187 != k23_filter_2(X185,X186)
| ~ m2_nat_lat(X187,X185)
| v1_xboole_0(X186)
| ~ m2_lattice4(X186,X185)
| v3_struct_0(X185)
| ~ v10_lattices(X185)
| ~ l3_lattices(X185) )
& ( v1_funct_2(esk2_3(X185,X186,X187),k2_zfmisc_1(X186,X186),X186)
| X187 != k23_filter_2(X185,X186)
| ~ m2_nat_lat(X187,X185)
| v1_xboole_0(X186)
| ~ m2_lattice4(X186,X185)
| v3_struct_0(X185)
| ~ v10_lattices(X185)
| ~ l3_lattices(X185) )
& ( m2_relset_1(esk2_3(X185,X186,X187),k2_zfmisc_1(X186,X186),X186)
| X187 != k23_filter_2(X185,X186)
| ~ m2_nat_lat(X187,X185)
| v1_xboole_0(X186)
| ~ m2_lattice4(X186,X185)
| v3_struct_0(X185)
| ~ v10_lattices(X185)
| ~ l3_lattices(X185) )
& ( v1_funct_1(esk3_3(X185,X186,X187))
| X187 != k23_filter_2(X185,X186)
| ~ m2_nat_lat(X187,X185)
| v1_xboole_0(X186)
| ~ m2_lattice4(X186,X185)
| v3_struct_0(X185)
| ~ v10_lattices(X185)
| ~ l3_lattices(X185) )
& ( v1_funct_2(esk3_3(X185,X186,X187),k2_zfmisc_1(X186,X186),X186)
| X187 != k23_filter_2(X185,X186)
| ~ m2_nat_lat(X187,X185)
| v1_xboole_0(X186)
| ~ m2_lattice4(X186,X185)
| v3_struct_0(X185)
| ~ v10_lattices(X185)
| ~ l3_lattices(X185) )
& ( m2_relset_1(esk3_3(X185,X186,X187),k2_zfmisc_1(X186,X186),X186)
| X187 != k23_filter_2(X185,X186)
| ~ m2_nat_lat(X187,X185)
| v1_xboole_0(X186)
| ~ m2_lattice4(X186,X185)
| v3_struct_0(X185)
| ~ v10_lattices(X185)
| ~ l3_lattices(X185) )
& ( esk2_3(X185,X186,X187) = k1_realset1(u2_lattices(X185),X186)
| X187 != k23_filter_2(X185,X186)
| ~ m2_nat_lat(X187,X185)
| v1_xboole_0(X186)
| ~ m2_lattice4(X186,X185)
| v3_struct_0(X185)
| ~ v10_lattices(X185)
| ~ l3_lattices(X185) )
& ( esk3_3(X185,X186,X187) = k1_realset1(u1_lattices(X185),X186)
| X187 != k23_filter_2(X185,X186)
| ~ m2_nat_lat(X187,X185)
| v1_xboole_0(X186)
| ~ m2_lattice4(X186,X185)
| v3_struct_0(X185)
| ~ v10_lattices(X185)
| ~ l3_lattices(X185) )
& ( X187 = g3_lattices(X186,esk2_3(X185,X186,X187),esk3_3(X185,X186,X187))
| X187 != k23_filter_2(X185,X186)
| ~ m2_nat_lat(X187,X185)
| v1_xboole_0(X186)
| ~ m2_lattice4(X186,X185)
| v3_struct_0(X185)
| ~ v10_lattices(X185)
| ~ l3_lattices(X185) )
& ( ~ v1_funct_1(X190)
| ~ v1_funct_2(X190,k2_zfmisc_1(X186,X186),X186)
| ~ m2_relset_1(X190,k2_zfmisc_1(X186,X186),X186)
| ~ v1_funct_1(X191)
| ~ v1_funct_2(X191,k2_zfmisc_1(X186,X186),X186)
| ~ m2_relset_1(X191,k2_zfmisc_1(X186,X186),X186)
| X190 != k1_realset1(u2_lattices(X185),X186)
| X191 != k1_realset1(u1_lattices(X185),X186)
| X187 != g3_lattices(X186,X190,X191)
| X187 = k23_filter_2(X185,X186)
| ~ m2_nat_lat(X187,X185)
| v1_xboole_0(X186)
| ~ m2_lattice4(X186,X185)
| v3_struct_0(X185)
| ~ v10_lattices(X185)
| ~ l3_lattices(X185) ) ),
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_40])])])])]) ).
fof(c_0_53,plain,
! [X196,X197] :
( ~ v1_relat_1(X196)
| k1_realset1(X196,X197) = k7_relat_1(X196,k2_zfmisc_1(X197,X197)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_realset1])])]) ).
cnf(c_0_54,plain,
( k7_relat_1(X1,X2) = X1
| ~ v1_relat_1(X1)
| ~ m1_subset_1(k1_relat_1(X1),k1_zfmisc_1(X2)) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_55,plain,
( m1_subset_1(k1_relat_1(u2_lattices(X1)),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1))))
| ~ l2_lattices(X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_56,plain,
( v1_relat_1(u2_lattices(X1))
| ~ l2_lattices(X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_33]) ).
fof(c_0_57,plain,
! [X223,X224] :
( ( ~ v1_xboole_0(X224)
| ~ m2_filter_2(X224,X223)
| v3_struct_0(X223)
| ~ v10_lattices(X223)
| ~ l3_lattices(X223) )
& ( m2_lattice4(X224,X223)
| ~ m2_filter_2(X224,X223)
| v3_struct_0(X223)
| ~ v10_lattices(X223)
| ~ l3_lattices(X223) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_46])])])]) ).
cnf(c_0_58,plain,
( v3_struct_0(X1)
| m2_filter_2(k17_filter_2(X1),X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_59,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_48]) ).
cnf(c_0_60,plain,
( v3_struct_0(X1)
| ~ l1_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_61,plain,
( l1_struct_0(X1)
| ~ l1_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
fof(c_0_62,plain,
! [X218] :
( ( l1_lattices(X218)
| ~ l3_lattices(X218) )
& ( l2_lattices(X218)
| ~ l3_lattices(X218) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
cnf(c_0_63,plain,
( m1_subset_1(k1_relat_1(u1_lattices(X1)),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1))))
| ~ l1_lattices(X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_51]) ).
cnf(c_0_64,plain,
( v1_relat_1(u1_lattices(X1))
| ~ l1_lattices(X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_39]) ).
cnf(c_0_65,plain,
( X1 = g3_lattices(X2,esk2_3(X3,X2,X1),esk3_3(X3,X2,X1))
| v1_xboole_0(X2)
| v3_struct_0(X3)
| X1 != k23_filter_2(X3,X2)
| ~ m2_nat_lat(X1,X3)
| ~ m2_lattice4(X2,X3)
| ~ v10_lattices(X3)
| ~ l3_lattices(X3) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_66,plain,
( esk2_3(X1,X2,X3) = k1_realset1(u2_lattices(X1),X2)
| v1_xboole_0(X2)
| v3_struct_0(X1)
| X3 != k23_filter_2(X1,X2)
| ~ m2_nat_lat(X3,X1)
| ~ m2_lattice4(X2,X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_67,plain,
( k1_realset1(X1,X2) = k7_relat_1(X1,k2_zfmisc_1(X2,X2))
| ~ v1_relat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_68,plain,
( k7_relat_1(u2_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1))) = u2_lattices(X1)
| ~ l2_lattices(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]) ).
cnf(c_0_69,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_57]) ).
cnf(c_0_70,plain,
( m2_filter_2(u1_struct_0(X1),X1)
| v3_struct_0(X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_71,plain,
( v3_struct_0(X1)
| ~ l1_lattices(X1)
| ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_72,plain,
( l1_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_73,plain,
( k7_relat_1(u1_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1))) = u1_lattices(X1)
| ~ l1_lattices(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_63]),c_0_64]) ).
cnf(c_0_74,plain,
( g3_lattices(X1,k1_realset1(u2_lattices(X2),X1),esk3_3(X2,X1,X3)) = X3
| v1_xboole_0(X1)
| v3_struct_0(X2)
| X3 != k23_filter_2(X2,X1)
| ~ m2_nat_lat(X3,X2)
| ~ m2_lattice4(X1,X2)
| ~ l3_lattices(X2)
| ~ v10_lattices(X2) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_75,plain,
( k1_realset1(u2_lattices(X1),u1_struct_0(X1)) = u2_lattices(X1)
| ~ l2_lattices(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_56]) ).
cnf(c_0_76,plain,
( m2_lattice4(u1_struct_0(X1),X1)
| v3_struct_0(X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_77,plain,
( l2_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_78,plain,
( v3_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1))
| ~ l3_lattices(X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_79,plain,
( esk3_3(X1,X2,X3) = k1_realset1(u1_lattices(X1),X2)
| v1_xboole_0(X2)
| v3_struct_0(X1)
| X3 != k23_filter_2(X1,X2)
| ~ m2_nat_lat(X3,X1)
| ~ m2_lattice4(X2,X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_80,plain,
( k1_realset1(u1_lattices(X1),u1_struct_0(X1)) = u1_lattices(X1)
| ~ l1_lattices(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_73]),c_0_64]) ).
fof(c_0_81,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( k23_filter_2(X1,k17_filter_2(X1)) = g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1))
& k23_filter_2(X1,k1_filter_2(X1)) = g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1)) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t72_filter_2])]) ).
cnf(c_0_82,plain,
( g3_lattices(u1_struct_0(X1),u2_lattices(X1),esk3_3(X1,u1_struct_0(X1),X2)) = X2
| v3_struct_0(X1)
| X2 != k23_filter_2(X1,u1_struct_0(X1))
| ~ m2_nat_lat(X2,X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]),c_0_77]),c_0_78]) ).
cnf(c_0_83,plain,
( esk3_3(X1,u1_struct_0(X1),X2) = u1_lattices(X1)
| v3_struct_0(X1)
| X2 != k23_filter_2(X1,u1_struct_0(X1))
| ~ m2_nat_lat(X2,X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_76]),c_0_72]),c_0_78]) ).
fof(c_0_84,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v10_lattices(esk1_0)
& l3_lattices(esk1_0)
& ( k23_filter_2(esk1_0,k17_filter_2(esk1_0)) != g3_lattices(u1_struct_0(esk1_0),u2_lattices(esk1_0),u1_lattices(esk1_0))
| k23_filter_2(esk1_0,k1_filter_2(esk1_0)) != g3_lattices(u1_struct_0(esk1_0),u2_lattices(esk1_0),u1_lattices(esk1_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_81])])]) ).
cnf(c_0_85,plain,
( g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1)) = X2
| v3_struct_0(X1)
| X2 != k23_filter_2(X1,u1_struct_0(X1))
| ~ m2_nat_lat(X2,X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
fof(c_0_86,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> k1_filter_2(X1) = k1_filter_0(X1) ),
inference(fof_simplification,[status(thm)],[redefinition_k1_filter_2]) ).
cnf(c_0_87,negated_conjecture,
( k23_filter_2(esk1_0,k17_filter_2(esk1_0)) != g3_lattices(u1_struct_0(esk1_0),u2_lattices(esk1_0),u1_lattices(esk1_0))
| k23_filter_2(esk1_0,k1_filter_2(esk1_0)) != g3_lattices(u1_struct_0(esk1_0),u2_lattices(esk1_0),u1_lattices(esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_88,plain,
( g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1)) = k23_filter_2(X1,u1_struct_0(X1))
| v3_struct_0(X1)
| ~ m2_nat_lat(k23_filter_2(X1,u1_struct_0(X1)),X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(er,[status(thm)],[c_0_85]) ).
cnf(c_0_89,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_90,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_91,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
fof(c_0_92,plain,
! [X300] :
( v3_struct_0(X300)
| ~ v10_lattices(X300)
| ~ l3_lattices(X300)
| k1_filter_2(X300) = k1_filter_0(X300) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_86])]) ).
fof(c_0_93,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> k1_filter_0(X1) = u1_struct_0(X1) ),
inference(fof_simplification,[status(thm)],[d2_filter_0]) ).
cnf(c_0_94,negated_conjecture,
( k23_filter_2(esk1_0,k17_filter_2(esk1_0)) != k23_filter_2(esk1_0,u1_struct_0(esk1_0))
| k23_filter_2(esk1_0,k1_filter_2(esk1_0)) != k23_filter_2(esk1_0,u1_struct_0(esk1_0))
| ~ m2_nat_lat(k23_filter_2(esk1_0,u1_struct_0(esk1_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_87,c_0_88]),c_0_89]),c_0_90])]),c_0_91]) ).
cnf(c_0_95,plain,
( v3_struct_0(X1)
| k1_filter_2(X1) = k1_filter_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
fof(c_0_96,plain,
! [X195] :
( v3_struct_0(X195)
| ~ v10_lattices(X195)
| ~ l3_lattices(X195)
| k1_filter_0(X195) = u1_struct_0(X195) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_93])]) ).
cnf(c_0_97,negated_conjecture,
( k23_filter_2(esk1_0,k17_filter_2(esk1_0)) != k23_filter_2(esk1_0,u1_struct_0(esk1_0))
| k23_filter_2(esk1_0,k1_filter_0(esk1_0)) != k23_filter_2(esk1_0,u1_struct_0(esk1_0))
| ~ m2_nat_lat(k23_filter_2(esk1_0,u1_struct_0(esk1_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_94,c_0_95]),c_0_89]),c_0_90])]),c_0_91]) ).
cnf(c_0_98,plain,
( v3_struct_0(X1)
| k1_filter_0(X1) = u1_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
fof(c_0_99,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) )
=> m2_nat_lat(k23_filter_2(X1,X2),X1) ),
inference(fof_simplification,[status(thm)],[dt_k23_filter_2]) ).
cnf(c_0_100,negated_conjecture,
( k23_filter_2(esk1_0,k17_filter_2(esk1_0)) != k23_filter_2(esk1_0,u1_struct_0(esk1_0))
| ~ m2_nat_lat(k23_filter_2(esk1_0,u1_struct_0(esk1_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_97,c_0_98]),c_0_89]),c_0_90])]),c_0_91]) ).
fof(c_0_101,plain,
! [X205,X206] :
( v3_struct_0(X205)
| ~ v10_lattices(X205)
| ~ l3_lattices(X205)
| v1_xboole_0(X206)
| ~ m2_lattice4(X206,X205)
| m2_nat_lat(k23_filter_2(X205,X206),X205) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_99])]) ).
cnf(c_0_102,negated_conjecture,
~ m2_nat_lat(k23_filter_2(esk1_0,u1_struct_0(esk1_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_100,c_0_59]),c_0_89]),c_0_90])]),c_0_91]) ).
cnf(c_0_103,plain,
( v3_struct_0(X1)
| v1_xboole_0(X2)
| m2_nat_lat(k23_filter_2(X1,X2),X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m2_lattice4(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_104,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk1_0))
| ~ m2_lattice4(u1_struct_0(esk1_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_102,c_0_103]),c_0_89]),c_0_90])]),c_0_91]) ).
cnf(c_0_105,negated_conjecture,
v1_xboole_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_104,c_0_76]),c_0_89]),c_0_90])]),c_0_91]) ).
cnf(c_0_106,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_105]),c_0_89])]),c_0_91]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT332+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
% 0.14/0.33 % Computer : n020.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 21:23:05 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 3.93/3.13 % Version : CSE_E---1.7
% 3.93/3.13 % Problem : theBenchmark.p
% 3.93/3.13 % SZS status Theorem for theBenchmark.p
% 3.93/3.13 % SZS output start CNFRefutation
% See solution above
% 3.93/3.14 % Total time : 2.373s
%------------------------------------------------------------------------------