%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT339+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 : n008.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 04:38:11 PM UTC 2026
% Result : Theorem 3.79s 3.16s
% Output : CNFRefutation 3.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 24
% Syntax : Number of formulae : 142 ( 34 unt; 0 def)
% Number of atoms : 682 ( 70 equ)
% Maximal formula atoms : 40 ( 4 avg)
% Number of connectives : 820 ( 280 ~; 299 |; 173 &)
% ( 6 <=>; 62 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 38 ( 36 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 2 con; 0-3 aty)
% Number of variables : 183 ( 7 sgn 114 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k5_conlat_1,axiom,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ( v6_conlat_1(k5_conlat_1(X1),X1)
& ~ v7_conlat_1(k5_conlat_1(X1),X1)
& v9_conlat_1(k5_conlat_1(X1),X1)
& v10_conlat_1(k5_conlat_1(X1),X1)
& l3_conlat_1(k5_conlat_1(X1),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_conlat_1) ).
fof(t5_conlat_2,conjecture,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ( k3_conlat_2(X1,k1_pre_topc(k11_conlat_1(X1))) = k6_conlat_1(X1)
& k2_conlat_2(X1,k1_pre_topc(k11_conlat_1(X1))) = k5_conlat_1(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_conlat_2) ).
fof(d1_conlat_2,axiom,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ! [X2] :
( ( v6_conlat_1(X2,X1)
& ~ v7_conlat_1(X2,X1)
& v9_conlat_1(X2,X1)
& l3_conlat_1(X2,X1) )
=> k1_conlat_2(X1,X2) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_conlat_2) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( v1_xboole_0(X1)
& X1 != X2
& v1_xboole_0(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(fc1_pre_topc,axiom,
! [X1] :
( l1_struct_0(X1)
=> ( v1_xboole_0(k1_pre_topc(X1))
& v1_membered(k1_pre_topc(X1))
& v2_membered(k1_pre_topc(X1))
& v3_membered(k1_pre_topc(X1))
& v4_membered(k1_pre_topc(X1))
& v5_membered(k1_pre_topc(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_pre_topc) ).
fof(dt_k1_conlat_2,axiom,
! [X1,X2] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1)
& v6_conlat_1(X2,X1)
& ~ v7_conlat_1(X2,X1)
& v9_conlat_1(X2,X1)
& l3_conlat_1(X2,X1) )
=> m1_subset_1(k1_conlat_2(X1,X2),u1_struct_0(k11_conlat_1(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_conlat_2) ).
fof(dt_l1_lattices,axiom,
! [X1] :
( l1_lattices(X1)
=> l1_struct_0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).
fof(t6_boole,axiom,
! [X1] :
( v1_xboole_0(X1)
=> X1 = k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( m1_subset_1(X2,k1_zfmisc_1(X1))
& v1_xboole_0(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(dt_k11_conlat_1,axiom,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ( ~ v3_struct_0(k11_conlat_1(X1))
& v3_lattices(k11_conlat_1(X1))
& l3_lattices(k11_conlat_1(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_conlat_1) ).
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(d2_conlat_2,axiom,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k11_conlat_1(X1))))
=> k2_conlat_2(X1,X2) = k16_lattice3(k11_conlat_1(X1),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_conlat_2) ).
fof(fc1_conlat_2,axiom,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ( ~ v3_struct_0(k11_conlat_1(X1))
& v3_lattices(k11_conlat_1(X1))
& v4_lattices(k11_conlat_1(X1))
& v5_lattices(k11_conlat_1(X1))
& v6_lattices(k11_conlat_1(X1))
& v7_lattices(k11_conlat_1(X1))
& v8_lattices(k11_conlat_1(X1))
& v9_lattices(k11_conlat_1(X1))
& v10_lattices(k11_conlat_1(X1))
& v13_lattices(k11_conlat_1(X1))
& v14_lattices(k11_conlat_1(X1))
& v15_lattices(k11_conlat_1(X1))
& v4_lattice3(k11_conlat_1(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_conlat_2) ).
fof(t1_conlat_2,axiom,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ( k5_lattices(k11_conlat_1(X1)) = k6_conlat_1(X1)
& k6_lattices(k11_conlat_1(X1)) = k5_conlat_1(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_conlat_2) ).
fof(d16_lattice3,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( r3_lattice3(X1,X2,X3)
<=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( r2_hidden(X4,X3)
=> r1_lattices(X1,X2,X4) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_lattice3) ).
fof(d3_conlat_2,axiom,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k11_conlat_1(X1))))
=> k3_conlat_2(X1,X2) = k15_lattice3(k11_conlat_1(X1),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_conlat_2) ).
fof(t50_lattice3,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v4_lattice3(X1)
& l3_lattices(X1) )
=> ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v13_lattices(X1)
& l3_lattices(X1)
& k5_lattices(X1) = k15_lattice3(X1,k1_xboole_0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_lattice3) ).
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/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(fc1_xboole_0,axiom,
v1_xboole_0(k1_xboole_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(t34_lattice3,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v4_lattice3(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( X2 = k16_lattice3(X1,X3)
<=> ( r3_lattice3(X1,X2,X3)
& ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( r3_lattice3(X1,X4,X3)
=> r3_lattices(X1,X4,X2) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_lattice3) ).
fof(d24_conlat_1,axiom,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(k11_conlat_1(X1)))
=> k12_conlat_1(X1,X2) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d24_conlat_1) ).
fof(dt_k12_conlat_1,axiom,
! [X1,X2] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1)
& m1_subset_1(X2,u1_struct_0(k11_conlat_1(X1))) )
=> ( v6_conlat_1(k12_conlat_1(X1,X2),X1)
& ~ v7_conlat_1(k12_conlat_1(X1,X2),X1)
& v9_conlat_1(k12_conlat_1(X1,X2),X1)
& l3_conlat_1(k12_conlat_1(X1,X2),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k12_conlat_1) ).
fof(t47_conlat_1,axiom,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(k11_conlat_1(X1)))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(k11_conlat_1(X1)))
=> ( r3_lattices(k11_conlat_1(X1),X2,X3)
<=> r2_conlat_1(X1,k12_conlat_1(X1,X2),k12_conlat_1(X1,X3)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_conlat_1) ).
fof(t34_conlat_1,axiom,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ! [X2] :
( ( ~ v7_conlat_1(X2,X1)
& v9_conlat_1(X2,X1)
& l3_conlat_1(X2,X1) )
=> ( r2_conlat_1(X1,X2,k5_conlat_1(X1))
& r2_conlat_1(X1,k6_conlat_1(X1),X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_conlat_1) ).
fof(c_0_24,plain,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ( v6_conlat_1(k5_conlat_1(X1),X1)
& ~ v7_conlat_1(k5_conlat_1(X1),X1)
& v9_conlat_1(k5_conlat_1(X1),X1)
& v10_conlat_1(k5_conlat_1(X1),X1)
& l3_conlat_1(k5_conlat_1(X1),X1) ) ),
inference(fof_simplification,[status(thm)],[dt_k5_conlat_1]) ).
fof(c_0_25,negated_conjecture,
~ ! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ( k3_conlat_2(X1,k1_pre_topc(k11_conlat_1(X1))) = k6_conlat_1(X1)
& k2_conlat_2(X1,k1_pre_topc(k11_conlat_1(X1))) = k5_conlat_1(X1) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t5_conlat_2])]) ).
fof(c_0_26,plain,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ! [X2] :
( ( v6_conlat_1(X2,X1)
& ~ v7_conlat_1(X2,X1)
& v9_conlat_1(X2,X1)
& l3_conlat_1(X2,X1) )
=> k1_conlat_2(X1,X2) = X2 ) ),
inference(fof_simplification,[status(thm)],[d1_conlat_2]) ).
fof(c_0_27,plain,
! [X270] :
( ( v6_conlat_1(k5_conlat_1(X270),X270)
| v3_conlat_1(X270)
| ~ l2_conlat_1(X270) )
& ( ~ v7_conlat_1(k5_conlat_1(X270),X270)
| v3_conlat_1(X270)
| ~ l2_conlat_1(X270) )
& ( v9_conlat_1(k5_conlat_1(X270),X270)
| v3_conlat_1(X270)
| ~ l2_conlat_1(X270) )
& ( v10_conlat_1(k5_conlat_1(X270),X270)
| v3_conlat_1(X270)
| ~ l2_conlat_1(X270) )
& ( l3_conlat_1(k5_conlat_1(X270),X270)
| v3_conlat_1(X270)
| ~ l2_conlat_1(X270) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])]) ).
fof(c_0_28,negated_conjecture,
( ~ v3_conlat_1(esk1_0)
& l2_conlat_1(esk1_0)
& ( k3_conlat_2(esk1_0,k1_pre_topc(k11_conlat_1(esk1_0))) != k6_conlat_1(esk1_0)
| k2_conlat_2(esk1_0,k1_pre_topc(k11_conlat_1(esk1_0))) != k5_conlat_1(esk1_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])]) ).
fof(c_0_29,plain,
! [X416,X417] :
( ~ v1_xboole_0(X416)
| X416 = X417
| ~ v1_xboole_0(X417) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(c_0_30,plain,
! [X305] :
( ( v1_xboole_0(k1_pre_topc(X305))
| ~ l1_struct_0(X305) )
& ( v1_membered(k1_pre_topc(X305))
| ~ l1_struct_0(X305) )
& ( v2_membered(k1_pre_topc(X305))
| ~ l1_struct_0(X305) )
& ( v3_membered(k1_pre_topc(X305))
| ~ l1_struct_0(X305) )
& ( v4_membered(k1_pre_topc(X305))
| ~ l1_struct_0(X305) )
& ( v5_membered(k1_pre_topc(X305))
| ~ l1_struct_0(X305) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc1_pre_topc])])]) ).
fof(c_0_31,plain,
! [X1,X2] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1)
& v6_conlat_1(X2,X1)
& ~ v7_conlat_1(X2,X1)
& v9_conlat_1(X2,X1)
& l3_conlat_1(X2,X1) )
=> m1_subset_1(k1_conlat_2(X1,X2),u1_struct_0(k11_conlat_1(X1))) ),
inference(fof_simplification,[status(thm)],[dt_k1_conlat_2]) ).
fof(c_0_32,plain,
! [X240,X241] :
( v3_conlat_1(X240)
| ~ l2_conlat_1(X240)
| ~ v6_conlat_1(X241,X240)
| v7_conlat_1(X241,X240)
| ~ v9_conlat_1(X241,X240)
| ~ l3_conlat_1(X241,X240)
| k1_conlat_2(X240,X241) = X241 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])]) ).
cnf(c_0_33,plain,
( v9_conlat_1(k5_conlat_1(X1),X1)
| v3_conlat_1(X1)
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,negated_conjecture,
l2_conlat_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,negated_conjecture,
~ v3_conlat_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,plain,
( v6_conlat_1(k5_conlat_1(X1),X1)
| v3_conlat_1(X1)
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,plain,
( l3_conlat_1(k5_conlat_1(X1),X1)
| v3_conlat_1(X1)
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_38,plain,
( X1 = X2
| ~ v1_xboole_0(X1)
| ~ v1_xboole_0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,plain,
( v1_xboole_0(k1_pre_topc(X1))
| ~ l1_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_40,plain,
! [X274] :
( ~ l1_lattices(X274)
| l1_struct_0(X274) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_lattices])]) ).
fof(c_0_41,plain,
! [X413] :
( ~ v1_xboole_0(X413)
| X413 = k1_xboole_0 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_42,plain,
! [X362] :
( m1_subset_1(esk26_1(X362),k1_zfmisc_1(X362))
& v1_xboole_0(esk26_1(X362)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(c_0_43,plain,
! [X263,X264] :
( v3_conlat_1(X263)
| ~ l2_conlat_1(X263)
| ~ v6_conlat_1(X264,X263)
| v7_conlat_1(X264,X263)
| ~ v9_conlat_1(X264,X263)
| ~ l3_conlat_1(X264,X263)
| m1_subset_1(k1_conlat_2(X263,X264),u1_struct_0(k11_conlat_1(X263))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])]) ).
cnf(c_0_44,plain,
( v3_conlat_1(X1)
| v7_conlat_1(X2,X1)
| k1_conlat_2(X1,X2) = X2
| ~ l2_conlat_1(X1)
| ~ v6_conlat_1(X2,X1)
| ~ v9_conlat_1(X2,X1)
| ~ l3_conlat_1(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_45,negated_conjecture,
v9_conlat_1(k5_conlat_1(esk1_0),esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_46,negated_conjecture,
v6_conlat_1(k5_conlat_1(esk1_0),esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_34]),c_0_35]) ).
cnf(c_0_47,negated_conjecture,
l3_conlat_1(k5_conlat_1(esk1_0),esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_34]),c_0_35]) ).
fof(c_0_48,plain,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ( ~ v3_struct_0(k11_conlat_1(X1))
& v3_lattices(k11_conlat_1(X1))
& l3_lattices(k11_conlat_1(X1)) ) ),
inference(fof_simplification,[status(thm)],[dt_k11_conlat_1]) ).
cnf(c_0_49,plain,
( X1 = k1_pre_topc(X2)
| ~ l1_struct_0(X2)
| ~ v1_xboole_0(X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_50,plain,
( l1_struct_0(X1)
| ~ l1_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_51,plain,
! [X277] :
( ( l1_lattices(X277)
| ~ l3_lattices(X277) )
& ( l2_lattices(X277)
| ~ l3_lattices(X277) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
fof(c_0_52,plain,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k11_conlat_1(X1))))
=> k2_conlat_2(X1,X2) = k16_lattice3(k11_conlat_1(X1),X2) ) ),
inference(fof_simplification,[status(thm)],[d2_conlat_2]) ).
cnf(c_0_53,plain,
( X1 = k1_xboole_0
| ~ v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_54,plain,
v1_xboole_0(esk26_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
fof(c_0_55,plain,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ( ~ v3_struct_0(k11_conlat_1(X1))
& v3_lattices(k11_conlat_1(X1))
& v4_lattices(k11_conlat_1(X1))
& v5_lattices(k11_conlat_1(X1))
& v6_lattices(k11_conlat_1(X1))
& v7_lattices(k11_conlat_1(X1))
& v8_lattices(k11_conlat_1(X1))
& v9_lattices(k11_conlat_1(X1))
& v10_lattices(k11_conlat_1(X1))
& v13_lattices(k11_conlat_1(X1))
& v14_lattices(k11_conlat_1(X1))
& v15_lattices(k11_conlat_1(X1))
& v4_lattice3(k11_conlat_1(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc1_conlat_2]) ).
fof(c_0_56,plain,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ( k5_lattices(k11_conlat_1(X1)) = k6_conlat_1(X1)
& k6_lattices(k11_conlat_1(X1)) = k5_conlat_1(X1) ) ),
inference(fof_simplification,[status(thm)],[t1_conlat_2]) ).
fof(c_0_57,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( r3_lattice3(X1,X2,X3)
<=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( r2_hidden(X4,X3)
=> r1_lattices(X1,X2,X4) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d16_lattice3]) ).
cnf(c_0_58,plain,
( v3_conlat_1(X1)
| v7_conlat_1(X2,X1)
| m1_subset_1(k1_conlat_2(X1,X2),u1_struct_0(k11_conlat_1(X1)))
| ~ l2_conlat_1(X1)
| ~ v6_conlat_1(X2,X1)
| ~ v9_conlat_1(X2,X1)
| ~ l3_conlat_1(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_59,negated_conjecture,
( k1_conlat_2(esk1_0,k5_conlat_1(esk1_0)) = k5_conlat_1(esk1_0)
| v7_conlat_1(k5_conlat_1(esk1_0),esk1_0) ),
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_44,c_0_45]),c_0_46]),c_0_47]),c_0_34])]),c_0_35]) ).
fof(c_0_60,plain,
! [X256] :
( ( ~ v3_struct_0(k11_conlat_1(X256))
| v3_conlat_1(X256)
| ~ l2_conlat_1(X256) )
& ( v3_lattices(k11_conlat_1(X256))
| v3_conlat_1(X256)
| ~ l2_conlat_1(X256) )
& ( l3_lattices(k11_conlat_1(X256))
| v3_conlat_1(X256)
| ~ l2_conlat_1(X256) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_48])])]) ).
cnf(c_0_61,plain,
( X1 = k1_pre_topc(X2)
| ~ l1_lattices(X2)
| ~ v1_xboole_0(X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_62,plain,
( l1_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
fof(c_0_63,plain,
! [X246,X247] :
( v3_conlat_1(X246)
| ~ l2_conlat_1(X246)
| ~ m1_subset_1(X247,k1_zfmisc_1(u1_struct_0(k11_conlat_1(X246))))
| k2_conlat_2(X246,X247) = k16_lattice3(k11_conlat_1(X246),X247) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])]) ).
cnf(c_0_64,plain,
m1_subset_1(esk26_1(X1),k1_zfmisc_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_65,plain,
esk26_1(X1) = k1_xboole_0,
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
fof(c_0_66,plain,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k11_conlat_1(X1))))
=> k3_conlat_2(X1,X2) = k15_lattice3(k11_conlat_1(X1),X2) ) ),
inference(fof_simplification,[status(thm)],[d3_conlat_2]) ).
fof(c_0_67,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v4_lattice3(X1)
& l3_lattices(X1) )
=> ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v13_lattices(X1)
& l3_lattices(X1)
& k5_lattices(X1) = k15_lattice3(X1,k1_xboole_0) ) ),
inference(fof_simplification,[status(thm)],[t50_lattice3]) ).
fof(c_0_68,plain,
! [X304] :
( ( ~ v3_struct_0(k11_conlat_1(X304))
| v3_conlat_1(X304)
| ~ l2_conlat_1(X304) )
& ( v3_lattices(k11_conlat_1(X304))
| v3_conlat_1(X304)
| ~ l2_conlat_1(X304) )
& ( v4_lattices(k11_conlat_1(X304))
| v3_conlat_1(X304)
| ~ l2_conlat_1(X304) )
& ( v5_lattices(k11_conlat_1(X304))
| v3_conlat_1(X304)
| ~ l2_conlat_1(X304) )
& ( v6_lattices(k11_conlat_1(X304))
| v3_conlat_1(X304)
| ~ l2_conlat_1(X304) )
& ( v7_lattices(k11_conlat_1(X304))
| v3_conlat_1(X304)
| ~ l2_conlat_1(X304) )
& ( v8_lattices(k11_conlat_1(X304))
| v3_conlat_1(X304)
| ~ l2_conlat_1(X304) )
& ( v9_lattices(k11_conlat_1(X304))
| v3_conlat_1(X304)
| ~ l2_conlat_1(X304) )
& ( v10_lattices(k11_conlat_1(X304))
| v3_conlat_1(X304)
| ~ l2_conlat_1(X304) )
& ( v13_lattices(k11_conlat_1(X304))
| v3_conlat_1(X304)
| ~ l2_conlat_1(X304) )
& ( v14_lattices(k11_conlat_1(X304))
| v3_conlat_1(X304)
| ~ l2_conlat_1(X304) )
& ( v15_lattices(k11_conlat_1(X304))
| v3_conlat_1(X304)
| ~ l2_conlat_1(X304) )
& ( v4_lattice3(k11_conlat_1(X304))
| v3_conlat_1(X304)
| ~ l2_conlat_1(X304) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])]) ).
fof(c_0_69,plain,
! [X385] :
( ( k5_lattices(k11_conlat_1(X385)) = k6_conlat_1(X385)
| v3_conlat_1(X385)
| ~ l2_conlat_1(X385) )
& ( k6_lattices(k11_conlat_1(X385)) = k5_conlat_1(X385)
| v3_conlat_1(X385)
| ~ l2_conlat_1(X385) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_56])])]) ).
fof(c_0_70,plain,
! [X410,X411,X412] :
( ~ r2_hidden(X410,X411)
| ~ m1_subset_1(X411,k1_zfmisc_1(X412))
| ~ v1_xboole_0(X412) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
fof(c_0_71,plain,
! [X234,X235,X236,X237,X238] :
( ( ~ r3_lattice3(X234,X235,X236)
| ~ m1_subset_1(X237,u1_struct_0(X234))
| ~ r2_hidden(X237,X236)
| r1_lattices(X234,X235,X237)
| ~ m1_subset_1(X235,u1_struct_0(X234))
| v3_struct_0(X234)
| ~ l3_lattices(X234) )
& ( m1_subset_1(esk2_3(X234,X235,X238),u1_struct_0(X234))
| r3_lattice3(X234,X235,X238)
| ~ m1_subset_1(X235,u1_struct_0(X234))
| v3_struct_0(X234)
| ~ l3_lattices(X234) )
& ( r2_hidden(esk2_3(X234,X235,X238),X238)
| r3_lattice3(X234,X235,X238)
| ~ m1_subset_1(X235,u1_struct_0(X234))
| v3_struct_0(X234)
| ~ l3_lattices(X234) )
& ( ~ r1_lattices(X234,X235,esk2_3(X234,X235,X238))
| r3_lattice3(X234,X235,X238)
| ~ m1_subset_1(X235,u1_struct_0(X234))
| v3_struct_0(X234)
| ~ l3_lattices(X234) ) ),
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_57])])])])])]) ).
cnf(c_0_72,plain,
( v3_conlat_1(X1)
| ~ v7_conlat_1(k5_conlat_1(X1),X1)
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_73,negated_conjecture,
( v7_conlat_1(k5_conlat_1(esk1_0),esk1_0)
| m1_subset_1(k5_conlat_1(esk1_0),u1_struct_0(k11_conlat_1(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_58,c_0_59]),c_0_45]),c_0_46]),c_0_47]),c_0_34])]),c_0_35]) ).
cnf(c_0_74,plain,
( l3_lattices(k11_conlat_1(X1))
| v3_conlat_1(X1)
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_75,plain,
( v3_conlat_1(X1)
| ~ v3_struct_0(k11_conlat_1(X1))
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_76,plain,
( X1 = k1_pre_topc(X2)
| ~ v1_xboole_0(X1)
| ~ l3_lattices(X2) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_77,plain,
v1_xboole_0(k1_xboole_0),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]) ).
cnf(c_0_78,plain,
( v3_conlat_1(X1)
| k2_conlat_2(X1,X2) = k16_lattice3(k11_conlat_1(X1),X2)
| ~ l2_conlat_1(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k11_conlat_1(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_79,plain,
m1_subset_1(k1_xboole_0,k1_zfmisc_1(X1)),
inference(rw,[status(thm)],[c_0_64,c_0_65]) ).
fof(c_0_80,plain,
! [X248,X249] :
( v3_conlat_1(X248)
| ~ l2_conlat_1(X248)
| ~ m1_subset_1(X249,k1_zfmisc_1(u1_struct_0(k11_conlat_1(X248))))
| k3_conlat_2(X248,X249) = k15_lattice3(k11_conlat_1(X248),X249) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_66])])]) ).
fof(c_0_81,plain,
! [X409] :
( ( ~ v3_struct_0(X409)
| v3_struct_0(X409)
| ~ v10_lattices(X409)
| ~ v4_lattice3(X409)
| ~ l3_lattices(X409) )
& ( v10_lattices(X409)
| v3_struct_0(X409)
| ~ v10_lattices(X409)
| ~ v4_lattice3(X409)
| ~ l3_lattices(X409) )
& ( v13_lattices(X409)
| v3_struct_0(X409)
| ~ v10_lattices(X409)
| ~ v4_lattice3(X409)
| ~ l3_lattices(X409) )
& ( l3_lattices(X409)
| v3_struct_0(X409)
| ~ v10_lattices(X409)
| ~ v4_lattice3(X409)
| ~ l3_lattices(X409) )
& ( k5_lattices(X409) = k15_lattice3(X409,k1_xboole_0)
| v3_struct_0(X409)
| ~ v10_lattices(X409)
| ~ v4_lattice3(X409)
| ~ l3_lattices(X409) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_67])])]) ).
cnf(c_0_82,plain,
( v4_lattice3(k11_conlat_1(X1))
| v3_conlat_1(X1)
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_83,plain,
( k5_lattices(k11_conlat_1(X1)) = k6_conlat_1(X1)
| v3_conlat_1(X1)
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_84,plain,
( v10_lattices(k11_conlat_1(X1))
| v3_conlat_1(X1)
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
fof(c_0_85,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v4_lattice3(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( X2 = k16_lattice3(X1,X3)
<=> ( r3_lattice3(X1,X2,X3)
& ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( r3_lattice3(X1,X4,X3)
=> r3_lattices(X1,X4,X2) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[t34_lattice3]) ).
cnf(c_0_86,plain,
( ~ r2_hidden(X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X3))
| ~ v1_xboole_0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_87,plain,
( r2_hidden(esk2_3(X1,X2,X3),X3)
| r3_lattice3(X1,X2,X3)
| v3_struct_0(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_88,negated_conjecture,
m1_subset_1(k5_conlat_1(esk1_0),u1_struct_0(k11_conlat_1(esk1_0))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_34])]),c_0_35]) ).
cnf(c_0_89,negated_conjecture,
l3_lattices(k11_conlat_1(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_34]),c_0_35]) ).
cnf(c_0_90,negated_conjecture,
~ v3_struct_0(k11_conlat_1(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_75]),c_0_34])]) ).
cnf(c_0_91,negated_conjecture,
( k3_conlat_2(esk1_0,k1_pre_topc(k11_conlat_1(esk1_0))) != k6_conlat_1(esk1_0)
| k2_conlat_2(esk1_0,k1_pre_topc(k11_conlat_1(esk1_0))) != k5_conlat_1(esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_92,plain,
( k1_pre_topc(X1) = k1_xboole_0
| ~ l3_lattices(X1) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_93,plain,
( k2_conlat_2(X1,k1_xboole_0) = k16_lattice3(k11_conlat_1(X1),k1_xboole_0)
| v3_conlat_1(X1)
| ~ l2_conlat_1(X1) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_94,plain,
( v3_conlat_1(X1)
| k3_conlat_2(X1,X2) = k15_lattice3(k11_conlat_1(X1),X2)
| ~ l2_conlat_1(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k11_conlat_1(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_95,plain,
( k5_lattices(X1) = k15_lattice3(X1,k1_xboole_0)
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ v4_lattice3(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_96,negated_conjecture,
v4_lattice3(k11_conlat_1(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_34]),c_0_35]) ).
cnf(c_0_97,negated_conjecture,
k5_lattices(k11_conlat_1(esk1_0)) = k6_conlat_1(esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_34]),c_0_35]) ).
cnf(c_0_98,negated_conjecture,
v10_lattices(k11_conlat_1(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_34]),c_0_35]) ).
fof(c_0_99,plain,
! [X395,X396,X397,X398,X399] :
( ( r3_lattice3(X395,X396,X397)
| X396 != k16_lattice3(X395,X397)
| ~ m1_subset_1(X396,u1_struct_0(X395))
| v3_struct_0(X395)
| ~ v10_lattices(X395)
| ~ v4_lattice3(X395)
| ~ l3_lattices(X395) )
& ( ~ m1_subset_1(X398,u1_struct_0(X395))
| ~ r3_lattice3(X395,X398,X397)
| r3_lattices(X395,X398,X396)
| X396 != k16_lattice3(X395,X397)
| ~ m1_subset_1(X396,u1_struct_0(X395))
| v3_struct_0(X395)
| ~ v10_lattices(X395)
| ~ v4_lattice3(X395)
| ~ l3_lattices(X395) )
& ( m1_subset_1(esk36_3(X395,X396,X399),u1_struct_0(X395))
| ~ r3_lattice3(X395,X396,X399)
| X396 = k16_lattice3(X395,X399)
| ~ m1_subset_1(X396,u1_struct_0(X395))
| v3_struct_0(X395)
| ~ v10_lattices(X395)
| ~ v4_lattice3(X395)
| ~ l3_lattices(X395) )
& ( r3_lattice3(X395,esk36_3(X395,X396,X399),X399)
| ~ r3_lattice3(X395,X396,X399)
| X396 = k16_lattice3(X395,X399)
| ~ m1_subset_1(X396,u1_struct_0(X395))
| v3_struct_0(X395)
| ~ v10_lattices(X395)
| ~ v4_lattice3(X395)
| ~ l3_lattices(X395) )
& ( ~ r3_lattices(X395,esk36_3(X395,X396,X399),X396)
| ~ r3_lattice3(X395,X396,X399)
| X396 = k16_lattice3(X395,X399)
| ~ m1_subset_1(X396,u1_struct_0(X395))
| v3_struct_0(X395)
| ~ v10_lattices(X395)
| ~ v4_lattice3(X395)
| ~ l3_lattices(X395) ) ),
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_85])])])])])]) ).
cnf(c_0_100,plain,
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X2,k1_xboole_0) ),
inference(spm,[status(thm)],[c_0_86,c_0_79]) ).
cnf(c_0_101,negated_conjecture,
( r3_lattice3(k11_conlat_1(esk1_0),k5_conlat_1(esk1_0),X1)
| r2_hidden(esk2_3(k11_conlat_1(esk1_0),k5_conlat_1(esk1_0),X1),X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89])]),c_0_90]) ).
cnf(c_0_102,negated_conjecture,
( k3_conlat_2(esk1_0,k1_xboole_0) != k6_conlat_1(esk1_0)
| k2_conlat_2(esk1_0,k1_xboole_0) != k5_conlat_1(esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_89])]) ).
cnf(c_0_103,negated_conjecture,
k2_conlat_2(esk1_0,k1_xboole_0) = k16_lattice3(k11_conlat_1(esk1_0),k1_xboole_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_34]),c_0_35]) ).
cnf(c_0_104,plain,
( k15_lattice3(k11_conlat_1(X1),k1_xboole_0) = k3_conlat_2(X1,k1_xboole_0)
| v3_conlat_1(X1)
| ~ l2_conlat_1(X1) ),
inference(spm,[status(thm)],[c_0_94,c_0_79]) ).
cnf(c_0_105,negated_conjecture,
k15_lattice3(k11_conlat_1(esk1_0),k1_xboole_0) = k6_conlat_1(esk1_0),
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_95,c_0_96]),c_0_97]),c_0_98]),c_0_89])]),c_0_90]) ).
fof(c_0_106,plain,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(k11_conlat_1(X1)))
=> k12_conlat_1(X1,X2) = X2 ) ),
inference(fof_simplification,[status(thm)],[d24_conlat_1]) ).
fof(c_0_107,plain,
! [X1,X2] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1)
& m1_subset_1(X2,u1_struct_0(k11_conlat_1(X1))) )
=> ( v6_conlat_1(k12_conlat_1(X1,X2),X1)
& ~ v7_conlat_1(k12_conlat_1(X1,X2),X1)
& v9_conlat_1(k12_conlat_1(X1,X2),X1)
& l3_conlat_1(k12_conlat_1(X1,X2),X1) ) ),
inference(fof_simplification,[status(thm)],[dt_k12_conlat_1]) ).
cnf(c_0_108,plain,
( m1_subset_1(esk36_3(X1,X2,X3),u1_struct_0(X1))
| X2 = k16_lattice3(X1,X3)
| v3_struct_0(X1)
| ~ r3_lattice3(X1,X2,X3)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ v10_lattices(X1)
| ~ v4_lattice3(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_109,negated_conjecture,
( r3_lattice3(k11_conlat_1(esk1_0),k5_conlat_1(esk1_0),k1_xboole_0)
| ~ v1_xboole_0(X1) ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_110,negated_conjecture,
( k16_lattice3(k11_conlat_1(esk1_0),k1_xboole_0) != k5_conlat_1(esk1_0)
| k3_conlat_2(esk1_0,k1_xboole_0) != k6_conlat_1(esk1_0) ),
inference(rw,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_111,negated_conjecture,
k3_conlat_2(esk1_0,k1_xboole_0) = k6_conlat_1(esk1_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_34]),c_0_105]),c_0_35]) ).
fof(c_0_112,plain,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(k11_conlat_1(X1)))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(k11_conlat_1(X1)))
=> ( r3_lattices(k11_conlat_1(X1),X2,X3)
<=> r2_conlat_1(X1,k12_conlat_1(X1,X2),k12_conlat_1(X1,X3)) ) ) ) ),
inference(fof_simplification,[status(thm)],[t47_conlat_1]) ).
fof(c_0_113,plain,
! [X244,X245] :
( v3_conlat_1(X244)
| ~ l2_conlat_1(X244)
| ~ m1_subset_1(X245,u1_struct_0(k11_conlat_1(X244)))
| k12_conlat_1(X244,X245) = X245 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_106])])]) ).
fof(c_0_114,plain,
! [X257,X258] :
( ( v6_conlat_1(k12_conlat_1(X257,X258),X257)
| v3_conlat_1(X257)
| ~ l2_conlat_1(X257)
| ~ m1_subset_1(X258,u1_struct_0(k11_conlat_1(X257))) )
& ( ~ v7_conlat_1(k12_conlat_1(X257,X258),X257)
| v3_conlat_1(X257)
| ~ l2_conlat_1(X257)
| ~ m1_subset_1(X258,u1_struct_0(k11_conlat_1(X257))) )
& ( v9_conlat_1(k12_conlat_1(X257,X258),X257)
| v3_conlat_1(X257)
| ~ l2_conlat_1(X257)
| ~ m1_subset_1(X258,u1_struct_0(k11_conlat_1(X257))) )
& ( l3_conlat_1(k12_conlat_1(X257,X258),X257)
| v3_conlat_1(X257)
| ~ l2_conlat_1(X257)
| ~ m1_subset_1(X258,u1_struct_0(k11_conlat_1(X257))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_107])])]) ).
cnf(c_0_115,negated_conjecture,
( k16_lattice3(k11_conlat_1(esk1_0),X1) = k5_conlat_1(esk1_0)
| m1_subset_1(esk36_3(k11_conlat_1(esk1_0),k5_conlat_1(esk1_0),X1),u1_struct_0(k11_conlat_1(esk1_0)))
| ~ r3_lattice3(k11_conlat_1(esk1_0),k5_conlat_1(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_108,c_0_88]),c_0_96]),c_0_98]),c_0_89])]),c_0_90]) ).
cnf(c_0_116,negated_conjecture,
r3_lattice3(k11_conlat_1(esk1_0),k5_conlat_1(esk1_0),k1_xboole_0),
inference(spm,[status(thm)],[c_0_109,c_0_77]) ).
cnf(c_0_117,negated_conjecture,
k16_lattice3(k11_conlat_1(esk1_0),k1_xboole_0) != k5_conlat_1(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_111])]) ).
fof(c_0_118,plain,
! [X403,X404,X405] :
( ( ~ r3_lattices(k11_conlat_1(X403),X404,X405)
| r2_conlat_1(X403,k12_conlat_1(X403,X404),k12_conlat_1(X403,X405))
| ~ m1_subset_1(X405,u1_struct_0(k11_conlat_1(X403)))
| ~ m1_subset_1(X404,u1_struct_0(k11_conlat_1(X403)))
| v3_conlat_1(X403)
| ~ l2_conlat_1(X403) )
& ( ~ r2_conlat_1(X403,k12_conlat_1(X403,X404),k12_conlat_1(X403,X405))
| r3_lattices(k11_conlat_1(X403),X404,X405)
| ~ m1_subset_1(X405,u1_struct_0(k11_conlat_1(X403)))
| ~ m1_subset_1(X404,u1_struct_0(k11_conlat_1(X403)))
| v3_conlat_1(X403)
| ~ l2_conlat_1(X403) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_112])])])]) ).
cnf(c_0_119,plain,
( v3_conlat_1(X1)
| k12_conlat_1(X1,X2) = X2
| ~ l2_conlat_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(k11_conlat_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
fof(c_0_120,plain,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ! [X2] :
( ( ~ v7_conlat_1(X2,X1)
& v9_conlat_1(X2,X1)
& l3_conlat_1(X2,X1) )
=> ( r2_conlat_1(X1,X2,k5_conlat_1(X1))
& r2_conlat_1(X1,k6_conlat_1(X1),X2) ) ) ),
inference(fof_simplification,[status(thm)],[t34_conlat_1]) ).
cnf(c_0_121,plain,
( v9_conlat_1(k12_conlat_1(X1,X2),X1)
| v3_conlat_1(X1)
| ~ l2_conlat_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(k11_conlat_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_122,negated_conjecture,
m1_subset_1(esk36_3(k11_conlat_1(esk1_0),k5_conlat_1(esk1_0),k1_xboole_0),u1_struct_0(k11_conlat_1(esk1_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_117]) ).
cnf(c_0_123,plain,
( v3_conlat_1(X1)
| ~ v7_conlat_1(k12_conlat_1(X1,X2),X1)
| ~ l2_conlat_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(k11_conlat_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_124,plain,
( l3_conlat_1(k12_conlat_1(X1,X2),X1)
| v3_conlat_1(X1)
| ~ l2_conlat_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(k11_conlat_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_125,plain,
( r3_lattices(k11_conlat_1(X1),X2,X3)
| v3_conlat_1(X1)
| ~ r2_conlat_1(X1,k12_conlat_1(X1,X2),k12_conlat_1(X1,X3))
| ~ m1_subset_1(X3,u1_struct_0(k11_conlat_1(X1)))
| ~ m1_subset_1(X2,u1_struct_0(k11_conlat_1(X1)))
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_126,negated_conjecture,
k12_conlat_1(esk1_0,k5_conlat_1(esk1_0)) = k5_conlat_1(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_88]),c_0_34])]),c_0_35]) ).
fof(c_0_127,plain,
! [X393,X394] :
( ( r2_conlat_1(X393,X394,k5_conlat_1(X393))
| v7_conlat_1(X394,X393)
| ~ v9_conlat_1(X394,X393)
| ~ l3_conlat_1(X394,X393)
| v3_conlat_1(X393)
| ~ l2_conlat_1(X393) )
& ( r2_conlat_1(X393,k6_conlat_1(X393),X394)
| v7_conlat_1(X394,X393)
| ~ v9_conlat_1(X394,X393)
| ~ l3_conlat_1(X394,X393)
| v3_conlat_1(X393)
| ~ l2_conlat_1(X393) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_120])])])]) ).
cnf(c_0_128,negated_conjecture,
v9_conlat_1(k12_conlat_1(esk1_0,esk36_3(k11_conlat_1(esk1_0),k5_conlat_1(esk1_0),k1_xboole_0)),esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_34])]),c_0_35]) ).
cnf(c_0_129,negated_conjecture,
k12_conlat_1(esk1_0,esk36_3(k11_conlat_1(esk1_0),k5_conlat_1(esk1_0),k1_xboole_0)) = esk36_3(k11_conlat_1(esk1_0),k5_conlat_1(esk1_0),k1_xboole_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_122]),c_0_34])]),c_0_35]) ).
cnf(c_0_130,negated_conjecture,
~ v7_conlat_1(k12_conlat_1(esk1_0,esk36_3(k11_conlat_1(esk1_0),k5_conlat_1(esk1_0),k1_xboole_0)),esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_122]),c_0_34])]),c_0_35]) ).
cnf(c_0_131,negated_conjecture,
l3_conlat_1(k12_conlat_1(esk1_0,esk36_3(k11_conlat_1(esk1_0),k5_conlat_1(esk1_0),k1_xboole_0)),esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_122]),c_0_34])]),c_0_35]) ).
cnf(c_0_132,negated_conjecture,
( r3_lattices(k11_conlat_1(esk1_0),X1,k5_conlat_1(esk1_0))
| ~ r2_conlat_1(esk1_0,k12_conlat_1(esk1_0,X1),k5_conlat_1(esk1_0))
| ~ m1_subset_1(X1,u1_struct_0(k11_conlat_1(esk1_0))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_88]),c_0_34])]),c_0_35]) ).
cnf(c_0_133,plain,
( r2_conlat_1(X1,X2,k5_conlat_1(X1))
| v7_conlat_1(X2,X1)
| v3_conlat_1(X1)
| ~ v9_conlat_1(X2,X1)
| ~ l3_conlat_1(X2,X1)
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_134,negated_conjecture,
v9_conlat_1(esk36_3(k11_conlat_1(esk1_0),k5_conlat_1(esk1_0),k1_xboole_0),esk1_0),
inference(rw,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_135,negated_conjecture,
~ v7_conlat_1(esk36_3(k11_conlat_1(esk1_0),k5_conlat_1(esk1_0),k1_xboole_0),esk1_0),
inference(rw,[status(thm)],[c_0_130,c_0_129]) ).
cnf(c_0_136,negated_conjecture,
l3_conlat_1(esk36_3(k11_conlat_1(esk1_0),k5_conlat_1(esk1_0),k1_xboole_0),esk1_0),
inference(rw,[status(thm)],[c_0_131,c_0_129]) ).
cnf(c_0_137,negated_conjecture,
( r3_lattices(k11_conlat_1(esk1_0),esk36_3(k11_conlat_1(esk1_0),k5_conlat_1(esk1_0),k1_xboole_0),k5_conlat_1(esk1_0))
| ~ r2_conlat_1(esk1_0,esk36_3(k11_conlat_1(esk1_0),k5_conlat_1(esk1_0),k1_xboole_0),k5_conlat_1(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_129]),c_0_122])]) ).
cnf(c_0_138,negated_conjecture,
r2_conlat_1(esk1_0,esk36_3(k11_conlat_1(esk1_0),k5_conlat_1(esk1_0),k1_xboole_0),k5_conlat_1(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_34])]),c_0_135]),c_0_35]),c_0_136])]) ).
cnf(c_0_139,plain,
( X2 = k16_lattice3(X1,X3)
| v3_struct_0(X1)
| ~ r3_lattices(X1,esk36_3(X1,X2,X3),X2)
| ~ r3_lattice3(X1,X2,X3)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ v10_lattices(X1)
| ~ v4_lattice3(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_140,negated_conjecture,
r3_lattices(k11_conlat_1(esk1_0),esk36_3(k11_conlat_1(esk1_0),k5_conlat_1(esk1_0),k1_xboole_0),k5_conlat_1(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_137,c_0_138])]) ).
cnf(c_0_141,negated_conjecture,
$false,
inference(sr,[status(thm)],[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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_96]),c_0_116]),c_0_88]),c_0_98]),c_0_89])]),c_0_117]),c_0_90]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT339+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
% 0.16/0.33 % Computer : n008.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 21:25:28 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 3.79/3.16 % Version : CSE_E---1.7
% 3.79/3.16 % Problem : theBenchmark.p
% 3.79/3.16 % SZS status Theorem for theBenchmark.p
% 3.79/3.16 % SZS output start CNFRefutation
% See solution above
% 3.79/3.17 % Total time : 2.421s
%------------------------------------------------------------------------------