%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT304+1 : TPTP v9.2.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n010.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 04:38:00 PM UTC 2026
% Result : Theorem 6.01s 4.49s
% Output : CNFRefutation 6.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of formulae : 98 ( 9 unt; 0 def)
% Number of atoms : 480 ( 40 equ)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 639 ( 257 ~; 251 |; 100 &)
% ( 5 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-3 aty)
% Number of variables : 156 ( 16 sgn 71 !; 0 ?)
% 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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',dt_u1_lattices) ).
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/sandbox2/benchmark/theBenchmark.p',t15_filter_0) ).
fof(fc6_lattice2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( ~ v3_struct_0(k1_lattice2(X1))
& v3_lattices(k1_lattice2(X1))
& v4_lattices(k1_lattice2(X1))
& v5_lattices(k1_lattice2(X1))
& v6_lattices(k1_lattice2(X1))
& v7_lattices(k1_lattice2(X1))
& v8_lattices(k1_lattice2(X1))
& v9_lattices(k1_lattice2(X1))
& v10_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_lattice2) ).
fof(t28_filter_2,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> m2_filter_2(u1_struct_0(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_filter_2) ).
fof(d2_lattice2,axiom,
! [X1] :
( l3_lattices(X1)
=> k1_lattice2(X1) = g3_lattices(u1_struct_0(X1),u1_lattices(X1),u2_lattices(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_lattice2) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( l1_lattices(X1)
& l2_lattices(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(dt_k1_lattice2,axiom,
! [X1] :
( l3_lattices(X1)
=> ( v3_lattices(k1_lattice2(X1))
& l3_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattice2) ).
fof(fc3_lattices,axiom,
! [X1,X2,X3] :
( ( ~ v1_xboole_0(X1)
& 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) )
=> ( ~ v3_struct_0(g3_lattices(X1,X2,X3))
& v3_lattices(g3_lattices(X1,X2,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_lattices) ).
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/sandbox2/benchmark/theBenchmark.p',redefinition_m1_filter_2) ).
fof(dt_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) )
=> ( v3_lattices(g3_lattices(X1,X2,X3))
& l3_lattices(g3_lattices(X1,X2,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g3_lattices) ).
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/sandbox2/benchmark/theBenchmark.p',dt_m1_filter_0) ).
fof(t21_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
<=> m1_filter_2(X2,k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_filter_2) ).
fof(abstractness_v3_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( v3_lattices(X1)
=> X1 = g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v3_lattices) ).
fof(c_0_16,plain,
! [X212,X213,X214] :
( ( ~ m2_relset_1(X214,X212,X213)
| m1_relset_1(X214,X212,X213) )
& ( ~ m1_relset_1(X214,X212,X213)
| m2_relset_1(X214,X212,X213) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
fof(c_0_17,plain,
! [X153] :
( ( v1_funct_1(u2_lattices(X153))
| ~ l2_lattices(X153) )
& ( v1_funct_2(u2_lattices(X153),k2_zfmisc_1(u1_struct_0(X153),u1_struct_0(X153)),u1_struct_0(X153))
| ~ l2_lattices(X153) )
& ( m2_relset_1(u2_lattices(X153),k2_zfmisc_1(u1_struct_0(X153),u1_struct_0(X153)),u1_struct_0(X153))
| ~ l2_lattices(X153) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u2_lattices])])]) ).
fof(c_0_18,plain,
! [X187,X188,X189,X190,X191,X192] :
( ( X187 = X190
| g3_lattices(X187,X188,X189) != g3_lattices(X190,X191,X192)
| ~ v1_funct_1(X188)
| ~ v1_funct_2(X188,k2_zfmisc_1(X187,X187),X187)
| ~ m1_relset_1(X188,k2_zfmisc_1(X187,X187),X187)
| ~ v1_funct_1(X189)
| ~ v1_funct_2(X189,k2_zfmisc_1(X187,X187),X187)
| ~ m1_relset_1(X189,k2_zfmisc_1(X187,X187),X187) )
& ( X188 = X191
| g3_lattices(X187,X188,X189) != g3_lattices(X190,X191,X192)
| ~ v1_funct_1(X188)
| ~ v1_funct_2(X188,k2_zfmisc_1(X187,X187),X187)
| ~ m1_relset_1(X188,k2_zfmisc_1(X187,X187),X187)
| ~ v1_funct_1(X189)
| ~ v1_funct_2(X189,k2_zfmisc_1(X187,X187),X187)
| ~ m1_relset_1(X189,k2_zfmisc_1(X187,X187),X187) )
& ( X189 = X192
| g3_lattices(X187,X188,X189) != g3_lattices(X190,X191,X192)
| ~ v1_funct_1(X188)
| ~ v1_funct_2(X188,k2_zfmisc_1(X187,X187),X187)
| ~ m1_relset_1(X188,k2_zfmisc_1(X187,X187),X187)
| ~ v1_funct_1(X189)
| ~ v1_funct_2(X189,k2_zfmisc_1(X187,X187),X187)
| ~ m1_relset_1(X189,k2_zfmisc_1(X187,X187),X187) ) ),
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_19,plain,
( m1_relset_1(X1,X2,X3)
| ~ m2_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,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_17]) ).
fof(c_0_21,plain,
! [X152] :
( ( v1_funct_1(u1_lattices(X152))
| ~ l1_lattices(X152) )
& ( v1_funct_2(u1_lattices(X152),k2_zfmisc_1(u1_struct_0(X152),u1_struct_0(X152)),u1_struct_0(X152))
| ~ l1_lattices(X152) )
& ( m2_relset_1(u1_lattices(X152),k2_zfmisc_1(u1_struct_0(X152),u1_struct_0(X152)),u1_struct_0(X152))
| ~ l1_lattices(X152) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_lattices])])]) ).
cnf(c_0_22,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_18]) ).
cnf(c_0_23,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_19,c_0_20]) ).
cnf(c_0_24,plain,
( v1_funct_1(u2_lattices(X1))
| ~ l2_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,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_17]) ).
cnf(c_0_26,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_21]) ).
fof(c_0_27,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]) ).
fof(c_0_28,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( ~ v3_struct_0(k1_lattice2(X1))
& v3_lattices(k1_lattice2(X1))
& v4_lattices(k1_lattice2(X1))
& v5_lattices(k1_lattice2(X1))
& v6_lattices(k1_lattice2(X1))
& v7_lattices(k1_lattice2(X1))
& v8_lattices(k1_lattice2(X1))
& v9_lattices(k1_lattice2(X1))
& v10_lattices(k1_lattice2(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc6_lattice2]) ).
fof(c_0_29,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> m2_filter_2(u1_struct_0(X1),X1) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t28_filter_2])]) ).
cnf(c_0_30,plain,
( X1 = X2
| g3_lattices(u1_struct_0(X3),X1,u2_lattices(X3)) != g3_lattices(X4,X2,X5)
| ~ 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_22,c_0_23]),c_0_24]),c_0_25]) ).
cnf(c_0_31,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_19,c_0_26]) ).
cnf(c_0_32,plain,
( v1_funct_1(u1_lattices(X1))
| ~ l1_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_33,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_21]) ).
fof(c_0_34,plain,
! [X133] :
( ~ l3_lattices(X133)
| k1_lattice2(X133) = g3_lattices(u1_struct_0(X133),u1_lattices(X133),u2_lattices(X133)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_lattice2])]) ).
fof(c_0_35,plain,
! [X140] :
( ( l1_lattices(X140)
| ~ l3_lattices(X140) )
& ( l2_lattices(X140)
| ~ l3_lattices(X140) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
fof(c_0_36,plain,
! [X216] :
( v3_struct_0(X216)
| ~ v10_lattices(X216)
| ~ l3_lattices(X216)
| m1_filter_0(u1_struct_0(X216),X216) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])]) ).
fof(c_0_37,plain,
! [X137] :
( ( v3_lattices(k1_lattice2(X137))
| ~ l3_lattices(X137) )
& ( l3_lattices(k1_lattice2(X137))
| ~ l3_lattices(X137) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_lattice2])])]) ).
fof(c_0_38,plain,
! [X186] :
( ( ~ v3_struct_0(k1_lattice2(X186))
| v3_struct_0(X186)
| ~ v10_lattices(X186)
| ~ l3_lattices(X186) )
& ( v3_lattices(k1_lattice2(X186))
| v3_struct_0(X186)
| ~ v10_lattices(X186)
| ~ l3_lattices(X186) )
& ( v4_lattices(k1_lattice2(X186))
| v3_struct_0(X186)
| ~ v10_lattices(X186)
| ~ l3_lattices(X186) )
& ( v5_lattices(k1_lattice2(X186))
| v3_struct_0(X186)
| ~ v10_lattices(X186)
| ~ l3_lattices(X186) )
& ( v6_lattices(k1_lattice2(X186))
| v3_struct_0(X186)
| ~ v10_lattices(X186)
| ~ l3_lattices(X186) )
& ( v7_lattices(k1_lattice2(X186))
| v3_struct_0(X186)
| ~ v10_lattices(X186)
| ~ l3_lattices(X186) )
& ( v8_lattices(k1_lattice2(X186))
| v3_struct_0(X186)
| ~ v10_lattices(X186)
| ~ l3_lattices(X186) )
& ( v9_lattices(k1_lattice2(X186))
| v3_struct_0(X186)
| ~ v10_lattices(X186)
| ~ l3_lattices(X186) )
& ( v10_lattices(k1_lattice2(X186))
| v3_struct_0(X186)
| ~ v10_lattices(X186)
| ~ l3_lattices(X186) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])]) ).
fof(c_0_39,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v10_lattices(esk1_0)
& l3_lattices(esk1_0)
& ~ m2_filter_2(u1_struct_0(esk1_0),esk1_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])]) ).
cnf(c_0_40,plain,
( u1_lattices(X1) = X2
| g3_lattices(u1_struct_0(X1),u1_lattices(X1),u2_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_30,c_0_31]),c_0_32]),c_0_33]) ).
cnf(c_0_41,plain,
( k1_lattice2(X1) = g3_lattices(u1_struct_0(X1),u1_lattices(X1),u2_lattices(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,plain,
( l1_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,plain,
( l2_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_44,plain,
! [X1,X2,X3] :
( ( ~ v1_xboole_0(X1)
& 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) )
=> ( ~ v3_struct_0(g3_lattices(X1,X2,X3))
& v3_lattices(g3_lattices(X1,X2,X3)) ) ),
inference(fof_simplification,[status(thm)],[fc3_lattices]) ).
fof(c_0_45,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_46,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_36]) ).
cnf(c_0_47,plain,
( l3_lattices(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_48,plain,
( v10_lattices(k1_lattice2(X1))
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_49,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_50,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_51,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_52,plain,
( u1_lattices(X1) = X2
| k1_lattice2(X1) != g3_lattices(X3,X2,X4)
| ~ l3_lattices(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_43]) ).
fof(c_0_53,plain,
! [X134,X135,X136] :
( ( v3_lattices(g3_lattices(X134,X135,X136))
| ~ v1_funct_1(X135)
| ~ v1_funct_2(X135,k2_zfmisc_1(X134,X134),X134)
| ~ m1_relset_1(X135,k2_zfmisc_1(X134,X134),X134)
| ~ v1_funct_1(X136)
| ~ v1_funct_2(X136,k2_zfmisc_1(X134,X134),X134)
| ~ m1_relset_1(X136,k2_zfmisc_1(X134,X134),X134) )
& ( l3_lattices(g3_lattices(X134,X135,X136))
| ~ v1_funct_1(X135)
| ~ v1_funct_2(X135,k2_zfmisc_1(X134,X134),X134)
| ~ m1_relset_1(X135,k2_zfmisc_1(X134,X134),X134)
| ~ v1_funct_1(X136)
| ~ v1_funct_2(X136,k2_zfmisc_1(X134,X134),X134)
| ~ m1_relset_1(X136,k2_zfmisc_1(X134,X134),X134) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_g3_lattices])])]) ).
fof(c_0_54,plain,
! [X179,X180,X181] :
( ( ~ v3_struct_0(g3_lattices(X179,X180,X181))
| v1_xboole_0(X179)
| ~ v1_funct_1(X180)
| ~ v1_funct_2(X180,k2_zfmisc_1(X179,X179),X179)
| ~ m1_relset_1(X180,k2_zfmisc_1(X179,X179),X179)
| ~ v1_funct_1(X181)
| ~ v1_funct_2(X181,k2_zfmisc_1(X179,X179),X179)
| ~ m1_relset_1(X181,k2_zfmisc_1(X179,X179),X179) )
& ( v3_lattices(g3_lattices(X179,X180,X181))
| v1_xboole_0(X179)
| ~ v1_funct_1(X180)
| ~ v1_funct_2(X180,k2_zfmisc_1(X179,X179),X179)
| ~ m1_relset_1(X180,k2_zfmisc_1(X179,X179),X179)
| ~ v1_funct_1(X181)
| ~ v1_funct_2(X181,k2_zfmisc_1(X179,X179),X179)
| ~ m1_relset_1(X181,k2_zfmisc_1(X179,X179),X179) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])]) ).
fof(c_0_55,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_56,plain,
! [X210,X211] :
( ( ~ m1_filter_2(X211,X210)
| m1_filter_0(X211,X210)
| v3_struct_0(X210)
| ~ v10_lattices(X210)
| ~ l3_lattices(X210) )
& ( ~ m1_filter_0(X211,X210)
| m1_filter_2(X211,X210)
| v3_struct_0(X210)
| ~ v10_lattices(X210)
| ~ l3_lattices(X210) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])])]) ).
cnf(c_0_57,plain,
( m1_filter_0(u1_struct_0(k1_lattice2(X1)),k1_lattice2(X1))
| v3_struct_0(k1_lattice2(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(k1_lattice2(X1)) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_58,negated_conjecture,
v10_lattices(k1_lattice2(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50])]),c_0_51]) ).
cnf(c_0_59,plain,
( X1 = X2
| g3_lattices(X1,X3,X4) != g3_lattices(X2,X5,X6)
| ~ v1_funct_1(X3)
| ~ v1_funct_2(X3,k2_zfmisc_1(X1,X1),X1)
| ~ m1_relset_1(X3,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_1(X4)
| ~ v1_funct_2(X4,k2_zfmisc_1(X1,X1),X1)
| ~ m1_relset_1(X4,k2_zfmisc_1(X1,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_60,plain,
( u1_lattices(X1) = u1_lattices(X2)
| k1_lattice2(X1) != k1_lattice2(X2)
| ~ l3_lattices(X1)
| ~ l3_lattices(X2) ),
inference(spm,[status(thm)],[c_0_52,c_0_41]) ).
cnf(c_0_61,plain,
( l3_lattices(g3_lattices(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) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_62,plain,
( v3_lattices(g3_lattices(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) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_63,plain,
( v1_xboole_0(X1)
| ~ v3_struct_0(g3_lattices(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) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
fof(c_0_64,plain,
! [X141,X142] :
( ( ~ v1_xboole_0(X142)
| ~ m1_filter_0(X142,X141)
| v3_struct_0(X141)
| ~ v10_lattices(X141)
| ~ l3_lattices(X141) )
& ( m1_subset_1(X142,k1_zfmisc_1(u1_struct_0(X141)))
| ~ m1_filter_0(X142,X141)
| v3_struct_0(X141)
| ~ v10_lattices(X141)
| ~ l3_lattices(X141) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])])]) ).
fof(c_0_65,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
<=> m1_filter_2(X2,k1_lattice2(X1)) ) ),
inference(fof_simplification,[status(thm)],[t21_filter_2]) ).
cnf(c_0_66,plain,
( m1_filter_2(X1,X2)
| v3_struct_0(X2)
| ~ m1_filter_0(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_67,negated_conjecture,
( m1_filter_0(u1_struct_0(k1_lattice2(esk1_0)),k1_lattice2(esk1_0))
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_49])]) ).
cnf(c_0_68,plain,
( u1_struct_0(X1) = X2
| g3_lattices(u1_struct_0(X1),X3,u2_lattices(X1)) != g3_lattices(X2,X4,X5)
| ~ l2_lattices(X1)
| ~ m1_relset_1(X3,k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ v1_funct_2(X3,k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ v1_funct_1(X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_23]),c_0_24]),c_0_25]) ).
cnf(c_0_69,negated_conjecture,
( u1_lattices(esk1_0) = u1_lattices(X1)
| k1_lattice2(esk1_0) != k1_lattice2(X1)
| ~ l3_lattices(X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_49]) ).
cnf(c_0_70,plain,
( l3_lattices(g3_lattices(u1_struct_0(X1),X2,u2_lattices(X1)))
| ~ l2_lattices(X1)
| ~ m1_relset_1(X2,k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ v1_funct_2(X2,k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ v1_funct_1(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_23]),c_0_24]),c_0_25]) ).
cnf(c_0_71,plain,
( v3_lattices(g3_lattices(u1_struct_0(X1),X2,u2_lattices(X1)))
| ~ l2_lattices(X1)
| ~ m1_relset_1(X2,k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ v1_funct_2(X2,k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ v1_funct_1(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_23]),c_0_24]),c_0_25]) ).
cnf(c_0_72,plain,
( v1_xboole_0(u1_struct_0(X1))
| ~ l2_lattices(X1)
| ~ m1_relset_1(X2,k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ v1_funct_2(X2,k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ v1_funct_1(X2)
| ~ v3_struct_0(g3_lattices(u1_struct_0(X1),X2,u2_lattices(X1))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_23]),c_0_24]),c_0_25]) ).
cnf(c_0_73,plain,
( v3_struct_0(X2)
| ~ v1_xboole_0(X1)
| ~ m1_filter_0(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_74,negated_conjecture,
m1_filter_0(u1_struct_0(esk1_0),esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_49]),c_0_50])]),c_0_51]) ).
fof(c_0_75,plain,
! [X219,X220] :
( ( ~ m2_filter_2(X220,X219)
| m1_filter_2(X220,k1_lattice2(X219))
| v3_struct_0(X219)
| ~ v10_lattices(X219)
| ~ l3_lattices(X219) )
& ( ~ m1_filter_2(X220,k1_lattice2(X219))
| m2_filter_2(X220,X219)
| v3_struct_0(X219)
| ~ v10_lattices(X219)
| ~ l3_lattices(X219) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_65])])])]) ).
cnf(c_0_76,negated_conjecture,
( m1_filter_2(u1_struct_0(k1_lattice2(esk1_0)),k1_lattice2(esk1_0))
| v3_struct_0(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_58])]) ).
cnf(c_0_77,plain,
( u1_struct_0(X1) = X2
| g3_lattices(u1_struct_0(X1),u1_lattices(X1),u2_lattices(X1)) != g3_lattices(X2,X3,X4)
| ~ l2_lattices(X1)
| ~ l1_lattices(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_31]),c_0_32]),c_0_33]) ).
cnf(c_0_78,negated_conjecture,
( g3_lattices(u1_struct_0(esk1_0),u1_lattices(X1),u2_lattices(esk1_0)) = k1_lattice2(esk1_0)
| k1_lattice2(esk1_0) != k1_lattice2(X1)
| ~ l3_lattices(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_69]),c_0_49])]) ).
fof(c_0_79,plain,
! [X123] :
( ~ l3_lattices(X123)
| ~ v3_lattices(X123)
| X123 = g3_lattices(u1_struct_0(X123),u2_lattices(X123),u1_lattices(X123)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[abstractness_v3_lattices])]) ).
cnf(c_0_80,plain,
( l3_lattices(g3_lattices(u1_struct_0(X1),u1_lattices(X1),u2_lattices(X1)))
| ~ l2_lattices(X1)
| ~ l1_lattices(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_31]),c_0_32]),c_0_33]) ).
cnf(c_0_81,plain,
( v3_lattices(g3_lattices(u1_struct_0(X1),u1_lattices(X1),u2_lattices(X1)))
| ~ l2_lattices(X1)
| ~ l1_lattices(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_31]),c_0_32]),c_0_33]) ).
cnf(c_0_82,plain,
( v1_xboole_0(u1_struct_0(X1))
| ~ l2_lattices(X1)
| ~ l1_lattices(X1)
| ~ v3_struct_0(g3_lattices(u1_struct_0(X1),u1_lattices(X1),u2_lattices(X1))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_31]),c_0_32]),c_0_33]) ).
cnf(c_0_83,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_73,c_0_74]),c_0_49]),c_0_50])]),c_0_51]) ).
cnf(c_0_84,plain,
( m2_filter_2(X1,X2)
| v3_struct_0(X2)
| ~ m1_filter_2(X1,k1_lattice2(X2))
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_85,negated_conjecture,
( m1_filter_2(u1_struct_0(k1_lattice2(esk1_0)),k1_lattice2(esk1_0))
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_47]),c_0_49])]) ).
cnf(c_0_86,negated_conjecture,
( u1_struct_0(esk1_0) = X1
| g3_lattices(X1,X2,X3) != k1_lattice2(esk1_0)
| ~ l2_lattices(esk1_0)
| ~ l1_lattices(esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_49])]) ).
cnf(c_0_87,plain,
( X1 = g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1))
| ~ l3_lattices(X1)
| ~ v3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_88,negated_conjecture,
( l3_lattices(k1_lattice2(esk1_0))
| ~ l2_lattices(esk1_0)
| ~ l1_lattices(esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_78]),c_0_49])]) ).
cnf(c_0_89,negated_conjecture,
( v3_lattices(k1_lattice2(esk1_0))
| ~ l2_lattices(esk1_0)
| ~ l1_lattices(esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_78]),c_0_49])]) ).
cnf(c_0_90,negated_conjecture,
( k1_lattice2(esk1_0) != k1_lattice2(X1)
| ~ l2_lattices(esk1_0)
| ~ l1_lattices(esk1_0)
| ~ l3_lattices(X1)
| ~ v3_struct_0(g3_lattices(u1_struct_0(esk1_0),u1_lattices(X1),u2_lattices(esk1_0))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_69]),c_0_83]) ).
cnf(c_0_91,negated_conjecture,
( m2_filter_2(u1_struct_0(k1_lattice2(esk1_0)),esk1_0)
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_49]),c_0_50])]),c_0_51]) ).
cnf(c_0_92,negated_conjecture,
( u1_struct_0(k1_lattice2(esk1_0)) = u1_struct_0(esk1_0)
| ~ l2_lattices(esk1_0)
| ~ l1_lattices(esk1_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87])]),c_0_88]),c_0_89]) ).
cnf(c_0_93,negated_conjecture,
~ m2_filter_2(u1_struct_0(esk1_0),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_94,negated_conjecture,
( ~ l2_lattices(esk1_0)
| ~ l1_lattices(esk1_0)
| ~ v3_struct_0(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_41]),c_0_49])]) ).
cnf(c_0_95,negated_conjecture,
( ~ l2_lattices(esk1_0)
| ~ l1_lattices(esk1_0) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93]),c_0_94]) ).
cnf(c_0_96,negated_conjecture,
~ l1_lattices(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_43]),c_0_49])]) ).
cnf(c_0_97,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_42]),c_0_49])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT304+1 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n010.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 21:08:51 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 6.01/4.49 % Version : CSE_E---1.7
% 6.01/4.49 % Problem : theBenchmark.p
% 6.01/4.49 % SZS status Theorem for theBenchmark.p
% 6.01/4.49 % SZS output start CNFRefutation
% See solution above
% 6.11/4.51 % Total time : 3.373s
%------------------------------------------------------------------------------