%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LAT327+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:48:13 AM UTC 2026
% Result : Theorem 0.21s 0.49s
% Output : Proof 0.21s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(t64_filter_2,conjecture,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r3_lattices(A,B,C)
=> ( r2_hidden(C,k22_filter_2(A,B,C))
& r2_hidden(B,k22_filter_2(A,B,C)) ) ) ) ) ),
file('theBenchmark.p',t64_filter_2) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : r1_tarski(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_k1_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k1_zfmisc_1) ).
fof(fc1_subset_1,axiom,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(fc1_xboole_0,axiom,
v1_xboole_0(k1_xboole_0),
file('theBenchmark.p',fc1_xboole_0) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) ) ),
file('theBenchmark.p',rc1_subset_1) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
fof(rc5_struct_0,axiom,
! [A] :
( ( l1_struct_0(A)
& ~ v3_struct_0(A) )
=> ? [B] :
( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ),
file('theBenchmark.p',rc5_struct_0) ).
fof(t3_subset,axiom,
! [A,B] :
( m1_subset_1(A,k1_zfmisc_1(B))
<=> r1_tarski(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( m1_subset_1(B,k1_zfmisc_1(C))
& r2_hidden(A,B) )
=> m1_subset_1(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( v1_xboole_0(C)
& m1_subset_1(B,k1_zfmisc_1(C))
& r2_hidden(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( v1_xboole_0(B)
& A != B
& v1_xboole_0(A) ),
file('theBenchmark.p',t8_boole) ).
fof(existence_l1_lattices,axiom,
? [A] : l1_lattices(A),
file('theBenchmark.p',existence_l1_lattices) ).
fof(existence_l1_struct_0,axiom,
? [A] : l1_struct_0(A),
file('theBenchmark.p',existence_l1_struct_0) ).
fof(existence_l2_lattices,axiom,
? [A] : l2_lattices(A),
file('theBenchmark.p',existence_l2_lattices) ).
fof(existence_m2_lattice4,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ? [B] : m2_lattice4(B,A) ),
file('theBenchmark.p',existence_m2_lattice4) ).
fof(dt_l1_lattices,axiom,
! [A] :
( l1_lattices(A)
=> l1_struct_0(A) ),
file('theBenchmark.p',dt_l1_lattices) ).
fof(dt_l1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_l1_struct_0) ).
fof(dt_l2_lattices,axiom,
! [A] :
( l2_lattices(A)
=> l1_struct_0(A) ),
file('theBenchmark.p',dt_l2_lattices) ).
fof(dt_m2_lattice4,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_lattice4(B,A)
=> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ),
file('theBenchmark.p',dt_m2_lattice4) ).
fof(cc1_funct_1,axiom,
! [A] :
( v1_xboole_0(A)
=> v1_funct_1(A) ),
file('theBenchmark.p',cc1_funct_1) ).
fof(cc2_lattices,axiom,
! [A] :
( l3_lattices(A)
=> ( ( v9_lattices(A)
& v8_lattices(A)
& v7_lattices(A)
& v6_lattices(A)
& v5_lattices(A)
& v4_lattices(A)
& ~ v3_struct_0(A) )
=> ( v10_lattices(A)
& ~ v3_struct_0(A) ) ) ),
file('theBenchmark.p',cc2_lattices) ).
fof(fc1_struct_0,axiom,
! [A] :
( ( l1_struct_0(A)
& ~ v3_struct_0(A) )
=> ~ v1_xboole_0(u1_struct_0(A)) ),
file('theBenchmark.p',fc1_struct_0) ).
fof(rc1_lattice4,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ? [B] :
( ~ v1_xboole_0(B)
& m2_lattice4(B,A) ) ),
file('theBenchmark.p',rc1_lattice4) ).
fof(rc1_xboole_0,axiom,
? [A] : v1_xboole_0(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ v1_xboole_0(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(rc3_struct_0,axiom,
? [A] :
( ~ v3_struct_0(A)
& l1_struct_0(A) ),
file('theBenchmark.p',rc3_struct_0) ).
fof(t2_subset,axiom,
! [A,B] :
( m1_subset_1(A,B)
=> ( r2_hidden(A,B)
| v1_xboole_0(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t6_boole,axiom,
! [A] :
( v1_xboole_0(A)
=> A = k1_xboole_0 ),
file('theBenchmark.p',t6_boole) ).
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( r2_hidden(A,B)
=> ~ r2_hidden(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(reflexivity_r3_lattices,axiom,
! [A,B,C] :
( ( m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(B,u1_struct_0(A))
& l3_lattices(A)
& v9_lattices(A)
& v8_lattices(A)
& v6_lattices(A)
& ~ v3_struct_0(A) )
=> r3_lattices(A,B,B) ),
file('theBenchmark.p',reflexivity_r3_lattices) ).
fof(existence_l3_lattices,axiom,
? [A] : l3_lattices(A),
file('theBenchmark.p',existence_l3_lattices) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : m1_subset_1(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(redefinition_r3_lattices,axiom,
! [A,B,C] :
( ( m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(B,u1_struct_0(A))
& l3_lattices(A)
& v9_lattices(A)
& v8_lattices(A)
& v6_lattices(A)
& ~ v3_struct_0(A) )
=> ( r3_lattices(A,B,C)
<=> r1_lattices(A,B,C) ) ),
file('theBenchmark.p',redefinition_r3_lattices) ).
fof(dt_k22_filter_2,axiom,
! [A,B,C] :
( ( m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(B,u1_struct_0(A))
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ( m2_lattice4(k22_filter_2(A,B,C),A)
& ~ v1_xboole_0(k22_filter_2(A,B,C)) ) ),
file('theBenchmark.p',dt_k22_filter_2) ).
fof(dt_l3_lattices,axiom,
! [A] :
( l3_lattices(A)
=> ( l2_lattices(A)
& l1_lattices(A) ) ),
file('theBenchmark.p',dt_l3_lattices) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(dt_u1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_u1_struct_0) ).
fof(cc1_lattices,axiom,
! [A] :
( l3_lattices(A)
=> ( ( v10_lattices(A)
& ~ v3_struct_0(A) )
=> ( v9_lattices(A)
& v8_lattices(A)
& v7_lattices(A)
& v6_lattices(A)
& v5_lattices(A)
& v4_lattices(A)
& ~ v3_struct_0(A) ) ) ),
file('theBenchmark.p',cc1_lattices) ).
fof(t1_subset,axiom,
! [A,B] :
( r2_hidden(A,B)
=> m1_subset_1(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( v1_xboole_0(B)
& r2_hidden(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t63_filter_2,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r3_lattices(A,B,C)
=> ( r2_hidden(D,k22_filter_2(A,B,C))
<=> ( r3_lattices(A,D,C)
& r3_lattices(A,B,D) ) ) ) ) ) ) ),
file('theBenchmark.p',t63_filter_2) ).
fof(f_1_1,negated_conjecture,
~ ! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r3_lattices(A,B,C)
=> ( r2_hidden(C,k22_filter_2(A,B,C))
& r2_hidden(B,k22_filter_2(A,B,C)) ) ) ) ) ),
inference(negate,[status(cth)],[t64_filter_2]) ).
fof(f_1_2,negated_conjecture,
? [A] :
( ? [B] :
( ? [C] :
( ( ~ r2_hidden(C,k22_filter_2(A,B,C))
| ~ r2_hidden(B,k22_filter_2(A,B,C)) )
& r3_lattices(A,B,C)
& m1_subset_1(C,u1_struct_0(A)) )
& m1_subset_1(B,u1_struct_0(A)) )
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[f_1_1]) ).
fof(f_1_3,negated_conjecture,
? [U_2] :
( ? [U_1] :
( ? [U_0] :
( ( ~ r2_hidden(U_0,k22_filter_2(U_2,U_1,U_0))
| ~ r2_hidden(U_1,k22_filter_2(U_2,U_1,U_0)) )
& r3_lattices(U_2,U_1,U_0)
& m1_subset_1(U_0,u1_struct_0(U_2)) )
& m1_subset_1(U_1,u1_struct_0(U_2)) )
& l3_lattices(U_2)
& v10_lattices(U_2)
& ~ v3_struct_0(U_2) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
( ? [U_1] :
( ? [U_0] :
( ( ~ r2_hidden(U_0,k22_filter_2(sK1,U_1,U_0))
| ~ r2_hidden(U_1,k22_filter_2(sK1,U_1,U_0)) )
& r3_lattices(sK1,U_1,U_0)
& m1_subset_1(U_0,u1_struct_0(sK1)) )
& m1_subset_1(U_1,u1_struct_0(sK1)) )
& l3_lattices(sK1)
& v10_lattices(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_2,sK1)],[f_1_3]) ).
fof(f_1_5,negated_conjecture,
( ? [U_0] :
( ( ~ r2_hidden(U_0,k22_filter_2(sK1,sK2,U_0))
| ~ r2_hidden(sK2,k22_filter_2(sK1,sK2,U_0)) )
& r3_lattices(sK1,sK2,U_0)
& m1_subset_1(U_0,u1_struct_0(sK1)) )
& m1_subset_1(sK2,u1_struct_0(sK1))
& l3_lattices(sK1)
& v10_lattices(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_1,sK2)],[f_1_4]) ).
fof(f_1_6,negated_conjecture,
( ( ~ r2_hidden(sK3,k22_filter_2(sK1,sK2,sK3))
| ~ r2_hidden(sK2,k22_filter_2(sK1,sK2,sK3)) )
& r3_lattices(sK1,sK2,sK3)
& m1_subset_1(sK3,u1_struct_0(sK1))
& m1_subset_1(sK2,u1_struct_0(sK1))
& l3_lattices(sK1)
& v10_lattices(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_0,sK3)],[f_1_5]) ).
fof(f_1_7,negated_conjecture,
( ( ~ r2_hidden(sK3,k22_filter_2(sK1,sK2,sK3))
| ~ r2_hidden(sK2,k22_filter_2(sK1,sK2,sK3)) )
& r3_lattices(sK1,sK2,sK3)
& m1_subset_1(sK3,u1_struct_0(sK1))
& m1_subset_1(sK2,u1_struct_0(sK1))
& l3_lattices(sK1)
& v10_lattices(sK1)
& ~ v3_struct_0(sK1) ),
inference(definitional_conversion,[status(esa)],[f_1_6]) ).
cnf(f_1_8,negated_conjecture,
~ v3_struct_0(sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_9,negated_conjecture,
v10_lattices(sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_10,negated_conjecture,
l3_lattices(sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_11,negated_conjecture,
m1_subset_1(sK2,u1_struct_0(sK1)),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_12,negated_conjecture,
m1_subset_1(sK3,u1_struct_0(sK1)),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_13,negated_conjecture,
r3_lattices(sK1,sK2,sK3),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_14,negated_conjecture,
( ~ r2_hidden(sK3,k22_filter_2(sK1,sK2,sK3))
| ~ r2_hidden(sK2,k22_filter_2(sK1,sK2,sK3)) ),
inference(clausify,[status(thm)],[f_1_7]) ).
fof(f_2_1,plain,
! [A,B] : r1_tarski(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_2_2,plain,
! [U_4,U_3] : r1_tarski(U_4,U_4),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_4] : r1_tarski(U_4,U_4),
inference(miniscope,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
r1_tarski(U_4,U_4),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_3_2,plain,
$true,
inference(clausify,[status(thm)],[f_3_1]) ).
fof(f_4_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_4_2,plain,
$true,
inference(clausify,[status(thm)],[f_4_1]) ).
fof(f_5_1,plain,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_5_2,plain,
! [U_5] : ~ v1_xboole_0(k1_zfmisc_1(U_5)),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
~ v1_xboole_0(k1_zfmisc_1(U_5)),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
v1_xboole_0(k1_xboole_0),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_6_2,plain,
v1_xboole_0(k1_xboole_0),
inference(clausify,[status(thm)],[f_6_1]) ).
fof(f_7_1,plain,
! [A] :
( ? [B] :
( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) )
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_7_2,plain,
! [U_7] :
( ? [U_6] :
( ~ v1_xboole_0(U_6)
& m1_subset_1(U_6,k1_zfmisc_1(U_7)) )
| v1_xboole_0(U_7) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_7] :
( ( ~ v1_xboole_0(sK4(U_7))
& m1_subset_1(sK4(U_7),k1_zfmisc_1(U_7)) )
| v1_xboole_0(U_7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_6,sK4(U_7))],[f_7_2]) ).
cnf(f_7_4,plain,
( m1_subset_1(sK4(U_7),k1_zfmisc_1(U_7))
| v1_xboole_0(U_7) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( ~ v1_xboole_0(sK4(U_7))
| v1_xboole_0(U_7) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [A] :
? [B] :
( v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_8_2,plain,
! [U_9] :
? [U_8] :
( v1_xboole_0(U_8)
& m1_subset_1(U_8,k1_zfmisc_1(U_9)) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_9] :
( v1_xboole_0(sK5(U_9))
& m1_subset_1(sK5(U_9),k1_zfmisc_1(U_9)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_8,sK5(U_9))],[f_8_2]) ).
cnf(f_8_4,plain,
m1_subset_1(sK5(U_9),k1_zfmisc_1(U_9)),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_5,plain,
v1_xboole_0(sK5(U_9)),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [A] :
( ? [B] :
( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
| ~ l1_struct_0(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc5_struct_0]) ).
fof(f_9_2,plain,
! [U_11] :
( ? [U_10] :
( ~ v1_xboole_0(U_10)
& m1_subset_1(U_10,k1_zfmisc_1(u1_struct_0(U_11))) )
| ~ l1_struct_0(U_11)
| v3_struct_0(U_11) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_11] :
( ( ~ v1_xboole_0(sK6(U_11))
& m1_subset_1(sK6(U_11),k1_zfmisc_1(u1_struct_0(U_11))) )
| ~ l1_struct_0(U_11)
| v3_struct_0(U_11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_10,sK6(U_11))],[f_9_2]) ).
cnf(f_9_4,plain,
( m1_subset_1(sK6(U_11),k1_zfmisc_1(u1_struct_0(U_11)))
| ~ l1_struct_0(U_11)
| v3_struct_0(U_11) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_5,plain,
( ~ v1_xboole_0(sK6(U_11))
| ~ l1_struct_0(U_11)
| v3_struct_0(U_11) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [A,B] :
( ( m1_subset_1(A,k1_zfmisc_1(B))
| ~ r1_tarski(A,B) )
& ( r1_tarski(A,B)
| ~ m1_subset_1(A,k1_zfmisc_1(B)) ) ),
inference(fof_nnf,[status(thm)],[t3_subset]) ).
fof(f_10_2,plain,
! [U_13,U_12] :
( ( m1_subset_1(U_13,k1_zfmisc_1(U_12))
| ~ r1_tarski(U_13,U_12) )
& ( r1_tarski(U_13,U_12)
| ~ m1_subset_1(U_13,k1_zfmisc_1(U_12)) ) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ! [U_17,U_15] :
( m1_subset_1(U_17,k1_zfmisc_1(U_15))
| ~ r1_tarski(U_17,U_15) )
& ! [U_16,U_14] :
( r1_tarski(U_16,U_14)
| ~ m1_subset_1(U_16,k1_zfmisc_1(U_14)) ) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
( r1_tarski(U_16,U_14)
| ~ m1_subset_1(U_16,k1_zfmisc_1(U_14)) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_5,plain,
( m1_subset_1(U_17,k1_zfmisc_1(U_15))
| ~ r1_tarski(U_17,U_15) ),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
! [A,B,C] :
( m1_subset_1(A,C)
| ~ m1_subset_1(B,k1_zfmisc_1(C))
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_11_2,plain,
! [U_20,U_19,U_18] :
( m1_subset_1(U_20,U_18)
| ~ m1_subset_1(U_19,k1_zfmisc_1(U_18))
| ~ r2_hidden(U_20,U_19) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( m1_subset_1(U_20,U_18)
| ~ m1_subset_1(U_19,k1_zfmisc_1(U_18))
| ~ r2_hidden(U_20,U_19) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [A,B,C] :
( ~ v1_xboole_0(C)
| ~ m1_subset_1(B,k1_zfmisc_1(C))
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_12_2,plain,
! [U_23,U_22,U_21] :
( ~ v1_xboole_0(U_21)
| ~ m1_subset_1(U_22,k1_zfmisc_1(U_21))
| ~ r2_hidden(U_23,U_22) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_23,U_22] :
( ! [U_21] :
( ~ v1_xboole_0(U_21)
| ~ m1_subset_1(U_22,k1_zfmisc_1(U_21)) )
| ~ r2_hidden(U_23,U_22) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
( ~ v1_xboole_0(U_21)
| ~ m1_subset_1(U_22,k1_zfmisc_1(U_21))
| ~ r2_hidden(U_23,U_22) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| A = B
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_13_2,plain,
! [U_25,U_24] :
( ~ v1_xboole_0(U_24)
| U_25 = U_24
| ~ v1_xboole_0(U_25) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_25] :
( ! [U_24] :
( ~ v1_xboole_0(U_24)
| U_25 = U_24 )
| ~ v1_xboole_0(U_25) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
( ~ v1_xboole_0(U_24)
| U_25 = U_24
| ~ v1_xboole_0(U_25) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
? [A] : l1_lattices(A),
inference(fof_nnf,[status(thm)],[existence_l1_lattices]) ).
fof(f_14_2,plain,
? [U_26] : l1_lattices(U_26),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
l1_lattices(sK7),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_26,sK7)],[f_14_2]) ).
cnf(f_14_4,plain,
l1_lattices(sK7),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
? [A] : l1_struct_0(A),
inference(fof_nnf,[status(thm)],[existence_l1_struct_0]) ).
fof(f_15_2,plain,
? [U_27] : l1_struct_0(U_27),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
l1_struct_0(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_27,sK8)],[f_15_2]) ).
cnf(f_15_4,plain,
l1_struct_0(sK8),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
? [A] : l2_lattices(A),
inference(fof_nnf,[status(thm)],[existence_l2_lattices]) ).
fof(f_16_2,plain,
? [U_28] : l2_lattices(U_28),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
l2_lattices(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_28,sK9)],[f_16_2]) ).
cnf(f_16_4,plain,
l2_lattices(sK9),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
! [A] :
( ? [B] : m2_lattice4(B,A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[existence_m2_lattice4]) ).
fof(f_17_2,plain,
! [U_30] :
( ? [U_29] : m2_lattice4(U_29,U_30)
| ~ l3_lattices(U_30)
| ~ v10_lattices(U_30)
| v3_struct_0(U_30) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_30] :
( m2_lattice4(sK10(U_30),U_30)
| ~ l3_lattices(U_30)
| ~ v10_lattices(U_30)
| v3_struct_0(U_30) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_29,sK10(U_30))],[f_17_2]) ).
cnf(f_17_4,plain,
( m2_lattice4(sK10(U_30),U_30)
| ~ l3_lattices(U_30)
| ~ v10_lattices(U_30)
| v3_struct_0(U_30) ),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
! [A] :
( l1_struct_0(A)
| ~ l1_lattices(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_lattices]) ).
fof(f_18_2,plain,
! [U_31] :
( l1_struct_0(U_31)
| ~ l1_lattices(U_31) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( l1_struct_0(U_31)
| ~ l1_lattices(U_31) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
cnf(f_19_2,plain,
$true,
inference(clausify,[status(thm)],[f_19_1]) ).
fof(f_20_1,plain,
! [A] :
( l1_struct_0(A)
| ~ l2_lattices(A) ),
inference(fof_nnf,[status(thm)],[dt_l2_lattices]) ).
fof(f_20_2,plain,
! [U_32] :
( l1_struct_0(U_32)
| ~ l2_lattices(U_32) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
( l1_struct_0(U_32)
| ~ l2_lattices(U_32) ),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
! [A] :
( ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
| ~ m2_lattice4(B,A) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_m2_lattice4]) ).
fof(f_21_2,plain,
! [U_34] :
( ! [U_33] :
( m1_subset_1(U_33,k1_zfmisc_1(u1_struct_0(U_34)))
| ~ m2_lattice4(U_33,U_34) )
| ~ l3_lattices(U_34)
| ~ v10_lattices(U_34)
| v3_struct_0(U_34) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
( m1_subset_1(U_33,k1_zfmisc_1(u1_struct_0(U_34)))
| ~ m2_lattice4(U_33,U_34)
| ~ l3_lattices(U_34)
| ~ v10_lattices(U_34)
| v3_struct_0(U_34) ),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
! [A] :
( v1_funct_1(A)
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_22_2,plain,
! [U_35] :
( v1_funct_1(U_35)
| ~ v1_xboole_0(U_35) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( v1_funct_1(U_35)
| ~ v1_xboole_0(U_35) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
! [A] :
( ( v10_lattices(A)
& ~ v3_struct_0(A) )
| ~ v9_lattices(A)
| ~ v8_lattices(A)
| ~ v7_lattices(A)
| ~ v6_lattices(A)
| ~ v5_lattices(A)
| ~ v4_lattices(A)
| v3_struct_0(A)
| ~ l3_lattices(A) ),
inference(fof_nnf,[status(thm)],[cc2_lattices]) ).
fof(f_23_2,plain,
! [U_36] :
( ( v10_lattices(U_36)
& ~ v3_struct_0(U_36) )
| ~ v9_lattices(U_36)
| ~ v8_lattices(U_36)
| ~ v7_lattices(U_36)
| ~ v6_lattices(U_36)
| ~ v5_lattices(U_36)
| ~ v4_lattices(U_36)
| v3_struct_0(U_36)
| ~ l3_lattices(U_36) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
( ~ v3_struct_0(U_36)
| ~ v9_lattices(U_36)
| ~ v8_lattices(U_36)
| ~ v7_lattices(U_36)
| ~ v6_lattices(U_36)
| ~ v5_lattices(U_36)
| ~ v4_lattices(U_36)
| v3_struct_0(U_36)
| ~ l3_lattices(U_36) ),
inference(clausify,[status(thm)],[f_23_2]) ).
cnf(f_23_4,plain,
( v10_lattices(U_36)
| ~ v9_lattices(U_36)
| ~ v8_lattices(U_36)
| ~ v7_lattices(U_36)
| ~ v6_lattices(U_36)
| ~ v5_lattices(U_36)
| ~ v4_lattices(U_36)
| v3_struct_0(U_36)
| ~ l3_lattices(U_36) ),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
! [A] :
( ~ v1_xboole_0(u1_struct_0(A))
| ~ l1_struct_0(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[fc1_struct_0]) ).
fof(f_24_2,plain,
! [U_37] :
( ~ v1_xboole_0(u1_struct_0(U_37))
| ~ l1_struct_0(U_37)
| v3_struct_0(U_37) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
( ~ v1_xboole_0(u1_struct_0(U_37))
| ~ l1_struct_0(U_37)
| v3_struct_0(U_37) ),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,plain,
! [A] :
( ? [B] :
( ~ v1_xboole_0(B)
& m2_lattice4(B,A) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc1_lattice4]) ).
fof(f_25_2,plain,
! [U_39] :
( ? [U_38] :
( ~ v1_xboole_0(U_38)
& m2_lattice4(U_38,U_39) )
| ~ l3_lattices(U_39)
| ~ v10_lattices(U_39)
| v3_struct_0(U_39) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_39] :
( ( ~ v1_xboole_0(sK11(U_39))
& m2_lattice4(sK11(U_39),U_39) )
| ~ l3_lattices(U_39)
| ~ v10_lattices(U_39)
| v3_struct_0(U_39) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_38,sK11(U_39))],[f_25_2]) ).
cnf(f_25_4,plain,
( m2_lattice4(sK11(U_39),U_39)
| ~ l3_lattices(U_39)
| ~ v10_lattices(U_39)
| v3_struct_0(U_39) ),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_5,plain,
( ~ v1_xboole_0(sK11(U_39))
| ~ l3_lattices(U_39)
| ~ v10_lattices(U_39)
| v3_struct_0(U_39) ),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
? [A] : v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_26_2,plain,
? [U_40] : v1_xboole_0(U_40),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
v1_xboole_0(sK12),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_40,sK12)],[f_26_2]) ).
cnf(f_26_4,plain,
v1_xboole_0(sK12),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
? [A] : ~ v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_27_2,plain,
? [U_41] : ~ v1_xboole_0(U_41),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
~ v1_xboole_0(sK13),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_41,sK13)],[f_27_2]) ).
cnf(f_27_4,plain,
~ v1_xboole_0(sK13),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
? [A] :
( ~ v3_struct_0(A)
& l1_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc3_struct_0]) ).
fof(f_28_2,plain,
? [U_42] :
( ~ v3_struct_0(U_42)
& l1_struct_0(U_42) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( ~ v3_struct_0(sK14)
& l1_struct_0(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_42,sK14)],[f_28_2]) ).
cnf(f_28_4,plain,
l1_struct_0(sK14),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(f_28_5,plain,
~ v3_struct_0(sK14),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
! [A,B] :
( r2_hidden(A,B)
| v1_xboole_0(B)
| ~ m1_subset_1(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_29_2,plain,
! [U_44,U_43] :
( r2_hidden(U_44,U_43)
| v1_xboole_0(U_43)
| ~ m1_subset_1(U_44,U_43) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( r2_hidden(U_44,U_43)
| v1_xboole_0(U_43)
| ~ m1_subset_1(U_44,U_43) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
! [A] :
( A = k1_xboole_0
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_30_2,plain,
! [U_45] :
( U_45 = k1_xboole_0
| ~ v1_xboole_0(U_45) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( U_45 = k1_xboole_0
| ~ v1_xboole_0(U_45) ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
! [A,B] :
( ~ r2_hidden(B,A)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_31_2,plain,
! [U_47,U_46] :
( ~ r2_hidden(U_46,U_47)
| ~ r2_hidden(U_47,U_46) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( ~ r2_hidden(U_46,U_47)
| ~ r2_hidden(U_47,U_46) ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
! [A,B,C] :
( r3_lattices(A,B,B)
| ~ m1_subset_1(C,u1_struct_0(A))
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l3_lattices(A)
| ~ v9_lattices(A)
| ~ v8_lattices(A)
| ~ v6_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[reflexivity_r3_lattices]) ).
fof(f_32_2,plain,
! [U_50,U_49,U_48] :
( r3_lattices(U_50,U_49,U_49)
| ~ m1_subset_1(U_48,u1_struct_0(U_50))
| ~ m1_subset_1(U_49,u1_struct_0(U_50))
| ~ l3_lattices(U_50)
| ~ v9_lattices(U_50)
| ~ v8_lattices(U_50)
| ~ v6_lattices(U_50)
| v3_struct_0(U_50) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_50,U_49] :
( ! [U_48] : ~ m1_subset_1(U_48,u1_struct_0(U_50))
| ~ m1_subset_1(U_49,u1_struct_0(U_50))
| ~ l3_lattices(U_50)
| ~ v9_lattices(U_50)
| ~ v8_lattices(U_50)
| ~ v6_lattices(U_50)
| v3_struct_0(U_50)
| r3_lattices(U_50,U_49,U_49) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
cnf(f_32_4,plain,
( ~ m1_subset_1(U_48,u1_struct_0(U_50))
| ~ m1_subset_1(U_49,u1_struct_0(U_50))
| ~ l3_lattices(U_50)
| ~ v9_lattices(U_50)
| ~ v8_lattices(U_50)
| ~ v6_lattices(U_50)
| v3_struct_0(U_50)
| r3_lattices(U_50,U_49,U_49) ),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
? [A] : l3_lattices(A),
inference(fof_nnf,[status(thm)],[existence_l3_lattices]) ).
fof(f_33_2,plain,
? [U_51] : l3_lattices(U_51),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
l3_lattices(sK15),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_51,sK15)],[f_33_2]) ).
cnf(f_33_4,plain,
l3_lattices(sK15),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,plain,
! [A] :
? [B] : m1_subset_1(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_34_2,plain,
! [U_53] :
? [U_52] : m1_subset_1(U_52,U_53),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_53] : m1_subset_1(sK16(U_53),U_53),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_52,sK16(U_53))],[f_34_2]) ).
cnf(f_34_4,plain,
m1_subset_1(sK16(U_53),U_53),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
! [A,B,C] :
( ( ( r3_lattices(A,B,C)
| ~ r1_lattices(A,B,C) )
& ( r1_lattices(A,B,C)
| ~ r3_lattices(A,B,C) ) )
| ~ m1_subset_1(C,u1_struct_0(A))
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l3_lattices(A)
| ~ v9_lattices(A)
| ~ v8_lattices(A)
| ~ v6_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[redefinition_r3_lattices]) ).
fof(f_35_2,plain,
! [U_56,U_55,U_54] :
( ( ( r3_lattices(U_56,U_55,U_54)
| ~ r1_lattices(U_56,U_55,U_54) )
& ( r1_lattices(U_56,U_55,U_54)
| ~ r3_lattices(U_56,U_55,U_54) ) )
| ~ m1_subset_1(U_54,u1_struct_0(U_56))
| ~ m1_subset_1(U_55,u1_struct_0(U_56))
| ~ l3_lattices(U_56)
| ~ v9_lattices(U_56)
| ~ v8_lattices(U_56)
| ~ v6_lattices(U_56)
| v3_struct_0(U_56) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
( r1_lattices(U_56,U_55,U_54)
| ~ r3_lattices(U_56,U_55,U_54)
| ~ m1_subset_1(U_54,u1_struct_0(U_56))
| ~ m1_subset_1(U_55,u1_struct_0(U_56))
| ~ l3_lattices(U_56)
| ~ v9_lattices(U_56)
| ~ v8_lattices(U_56)
| ~ v6_lattices(U_56)
| v3_struct_0(U_56) ),
inference(clausify,[status(thm)],[f_35_2]) ).
cnf(f_35_4,plain,
( r3_lattices(U_56,U_55,U_54)
| ~ r1_lattices(U_56,U_55,U_54)
| ~ m1_subset_1(U_54,u1_struct_0(U_56))
| ~ m1_subset_1(U_55,u1_struct_0(U_56))
| ~ l3_lattices(U_56)
| ~ v9_lattices(U_56)
| ~ v8_lattices(U_56)
| ~ v6_lattices(U_56)
| v3_struct_0(U_56) ),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_1,plain,
! [A,B,C] :
( ( m2_lattice4(k22_filter_2(A,B,C),A)
& ~ v1_xboole_0(k22_filter_2(A,B,C)) )
| ~ m1_subset_1(C,u1_struct_0(A))
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_k22_filter_2]) ).
fof(f_36_2,plain,
! [U_59,U_58,U_57] :
( ( m2_lattice4(k22_filter_2(U_59,U_58,U_57),U_59)
& ~ v1_xboole_0(k22_filter_2(U_59,U_58,U_57)) )
| ~ m1_subset_1(U_57,u1_struct_0(U_59))
| ~ m1_subset_1(U_58,u1_struct_0(U_59))
| ~ l3_lattices(U_59)
| ~ v10_lattices(U_59)
| v3_struct_0(U_59) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
cnf(f_36_3,plain,
( ~ v1_xboole_0(k22_filter_2(U_59,U_58,U_57))
| ~ m1_subset_1(U_57,u1_struct_0(U_59))
| ~ m1_subset_1(U_58,u1_struct_0(U_59))
| ~ l3_lattices(U_59)
| ~ v10_lattices(U_59)
| v3_struct_0(U_59) ),
inference(clausify,[status(thm)],[f_36_2]) ).
cnf(f_36_4,plain,
( m2_lattice4(k22_filter_2(U_59,U_58,U_57),U_59)
| ~ m1_subset_1(U_57,u1_struct_0(U_59))
| ~ m1_subset_1(U_58,u1_struct_0(U_59))
| ~ l3_lattices(U_59)
| ~ v10_lattices(U_59)
| v3_struct_0(U_59) ),
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_1,plain,
! [A] :
( ( l2_lattices(A)
& l1_lattices(A) )
| ~ l3_lattices(A) ),
inference(fof_nnf,[status(thm)],[dt_l3_lattices]) ).
fof(f_37_2,plain,
! [U_60] :
( ( l2_lattices(U_60)
& l1_lattices(U_60) )
| ~ l3_lattices(U_60) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
cnf(f_37_3,plain,
( l1_lattices(U_60)
| ~ l3_lattices(U_60) ),
inference(clausify,[status(thm)],[f_37_2]) ).
cnf(f_37_4,plain,
( l2_lattices(U_60)
| ~ l3_lattices(U_60) ),
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_38_2,plain,
$true,
inference(clausify,[status(thm)],[f_38_1]) ).
fof(f_39_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_struct_0]) ).
cnf(f_39_2,plain,
$true,
inference(clausify,[status(thm)],[f_39_1]) ).
fof(f_40_1,plain,
! [A] :
( ( v9_lattices(A)
& v8_lattices(A)
& v7_lattices(A)
& v6_lattices(A)
& v5_lattices(A)
& v4_lattices(A)
& ~ v3_struct_0(A) )
| ~ v10_lattices(A)
| v3_struct_0(A)
| ~ l3_lattices(A) ),
inference(fof_nnf,[status(thm)],[cc1_lattices]) ).
fof(f_40_2,plain,
! [U_61] :
( ( v9_lattices(U_61)
& v8_lattices(U_61)
& v7_lattices(U_61)
& v6_lattices(U_61)
& v5_lattices(U_61)
& v4_lattices(U_61)
& ~ v3_struct_0(U_61) )
| ~ v10_lattices(U_61)
| v3_struct_0(U_61)
| ~ l3_lattices(U_61) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
cnf(f_40_3,plain,
( ~ v3_struct_0(U_61)
| ~ v10_lattices(U_61)
| v3_struct_0(U_61)
| ~ l3_lattices(U_61) ),
inference(clausify,[status(thm)],[f_40_2]) ).
cnf(f_40_4,plain,
( v4_lattices(U_61)
| ~ v10_lattices(U_61)
| v3_struct_0(U_61)
| ~ l3_lattices(U_61) ),
inference(clausify,[status(thm)],[f_40_2]) ).
cnf(f_40_5,plain,
( v5_lattices(U_61)
| ~ v10_lattices(U_61)
| v3_struct_0(U_61)
| ~ l3_lattices(U_61) ),
inference(clausify,[status(thm)],[f_40_2]) ).
cnf(f_40_6,plain,
( v6_lattices(U_61)
| ~ v10_lattices(U_61)
| v3_struct_0(U_61)
| ~ l3_lattices(U_61) ),
inference(clausify,[status(thm)],[f_40_2]) ).
cnf(f_40_7,plain,
( v7_lattices(U_61)
| ~ v10_lattices(U_61)
| v3_struct_0(U_61)
| ~ l3_lattices(U_61) ),
inference(clausify,[status(thm)],[f_40_2]) ).
cnf(f_40_8,plain,
( v8_lattices(U_61)
| ~ v10_lattices(U_61)
| v3_struct_0(U_61)
| ~ l3_lattices(U_61) ),
inference(clausify,[status(thm)],[f_40_2]) ).
cnf(f_40_9,plain,
( v9_lattices(U_61)
| ~ v10_lattices(U_61)
| v3_struct_0(U_61)
| ~ l3_lattices(U_61) ),
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_1,plain,
! [A,B] :
( m1_subset_1(A,B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_41_2,plain,
! [U_63,U_62] :
( m1_subset_1(U_63,U_62)
| ~ r2_hidden(U_63,U_62) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
cnf(f_41_3,plain,
( m1_subset_1(U_63,U_62)
| ~ r2_hidden(U_63,U_62) ),
inference(clausify,[status(thm)],[f_41_2]) ).
fof(f_42_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_42_2,plain,
! [U_65,U_64] :
( ~ v1_xboole_0(U_64)
| ~ r2_hidden(U_65,U_64) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
cnf(f_42_3,plain,
( ~ v1_xboole_0(U_64)
| ~ r2_hidden(U_65,U_64) ),
inference(clausify,[status(thm)],[f_42_2]) ).
fof(f_43_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ! [D] :
( ( ( r2_hidden(D,k22_filter_2(A,B,C))
| ~ r3_lattices(A,D,C)
| ~ r3_lattices(A,B,D) )
& ( ( r3_lattices(A,D,C)
& r3_lattices(A,B,D) )
| ~ r2_hidden(D,k22_filter_2(A,B,C)) ) )
| ~ r3_lattices(A,B,C)
| ~ m1_subset_1(D,u1_struct_0(A)) )
| ~ m1_subset_1(C,u1_struct_0(A)) )
| ~ m1_subset_1(B,u1_struct_0(A)) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t63_filter_2]) ).
fof(f_43_2,plain,
! [U_69] :
( ! [U_68] :
( ! [U_67] :
( ! [U_66] :
( ( ( r2_hidden(U_66,k22_filter_2(U_69,U_68,U_67))
| ~ r3_lattices(U_69,U_66,U_67)
| ~ r3_lattices(U_69,U_68,U_66) )
& ( ( r3_lattices(U_69,U_66,U_67)
& r3_lattices(U_69,U_68,U_66) )
| ~ r2_hidden(U_66,k22_filter_2(U_69,U_68,U_67)) ) )
| ~ r3_lattices(U_69,U_68,U_67)
| ~ m1_subset_1(U_66,u1_struct_0(U_69)) )
| ~ m1_subset_1(U_67,u1_struct_0(U_69)) )
| ~ m1_subset_1(U_68,u1_struct_0(U_69)) )
| ~ l3_lattices(U_69)
| ~ v10_lattices(U_69)
| v3_struct_0(U_69) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
cnf(f_43_3,plain,
( r3_lattices(U_69,U_68,U_66)
| ~ r2_hidden(U_66,k22_filter_2(U_69,U_68,U_67))
| ~ r3_lattices(U_69,U_68,U_67)
| ~ m1_subset_1(U_66,u1_struct_0(U_69))
| ~ m1_subset_1(U_67,u1_struct_0(U_69))
| ~ m1_subset_1(U_68,u1_struct_0(U_69))
| ~ l3_lattices(U_69)
| ~ v10_lattices(U_69)
| v3_struct_0(U_69) ),
inference(clausify,[status(thm)],[f_43_2]) ).
cnf(f_43_4,plain,
( r3_lattices(U_69,U_66,U_67)
| ~ r2_hidden(U_66,k22_filter_2(U_69,U_68,U_67))
| ~ r3_lattices(U_69,U_68,U_67)
| ~ m1_subset_1(U_66,u1_struct_0(U_69))
| ~ m1_subset_1(U_67,u1_struct_0(U_69))
| ~ m1_subset_1(U_68,u1_struct_0(U_69))
| ~ l3_lattices(U_69)
| ~ v10_lattices(U_69)
| v3_struct_0(U_69) ),
inference(clausify,[status(thm)],[f_43_2]) ).
cnf(f_43_5,plain,
( r2_hidden(U_66,k22_filter_2(U_69,U_68,U_67))
| ~ r3_lattices(U_69,U_66,U_67)
| ~ r3_lattices(U_69,U_68,U_66)
| ~ r3_lattices(U_69,U_68,U_67)
| ~ m1_subset_1(U_66,u1_struct_0(U_69))
| ~ m1_subset_1(U_67,u1_struct_0(U_69))
| ~ m1_subset_1(U_68,u1_struct_0(U_69))
| ~ l3_lattices(U_69)
| ~ v10_lattices(U_69)
| v3_struct_0(U_69) ),
inference(clausify,[status(thm)],[f_43_2]) ).
cnf(f_3_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_3_2]) ).
cnf(f_4_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_2]) ).
cnf(f_19_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_19_2]) ).
cnf(f_23_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_23_3]) ).
cnf(f_38_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_38_2]) ).
cnf(f_39_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_39_2]) ).
cnf(f_40_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_40_3]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( u1_struct_0(Eq_x_0) = u1_struct_0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( k22_filter_2(Eq_x_0,Eq_x_1,Eq_x_2) = k22_filter_2(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( k1_zfmisc_1(Eq_x_0) = k1_zfmisc_1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( sK4(Eq_x_0) = sK4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( sK5(Eq_x_0) = sK5(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK6(Eq_x_0) = sK6(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK10(Eq_x_0) = sK10(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK11(Eq_x_0) = sK11(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK16(Eq_x_0) = sK16(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( v3_struct_0(Eq_y_0)
| ~ v3_struct_0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_14,axiom,
( v10_lattices(Eq_y_0)
| ~ v10_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_15,axiom,
( l3_lattices(Eq_y_0)
| ~ l3_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_16,axiom,
( m1_subset_1(Eq_y_0,Eq_y_1)
| ~ m1_subset_1(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,axiom,
( r3_lattices(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ r3_lattices(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,axiom,
( r2_hidden(Eq_y_0,Eq_y_1)
| ~ r2_hidden(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,axiom,
( r1_tarski(Eq_y_0,Eq_y_1)
| ~ r1_tarski(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_20,axiom,
( v1_xboole_0(Eq_y_0)
| ~ v1_xboole_0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,axiom,
( l1_struct_0(Eq_y_0)
| ~ l1_struct_0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,axiom,
( l1_lattices(Eq_y_0)
| ~ l1_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,axiom,
( l2_lattices(Eq_y_0)
| ~ l2_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( m2_lattice4(Eq_y_0,Eq_y_1)
| ~ m2_lattice4(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,axiom,
( v1_funct_1(Eq_y_0)
| ~ v1_funct_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,axiom,
( v4_lattices(Eq_y_0)
| ~ v4_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,axiom,
( v5_lattices(Eq_y_0)
| ~ v5_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,axiom,
( v6_lattices(Eq_y_0)
| ~ v6_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_29,axiom,
( v7_lattices(Eq_y_0)
| ~ v7_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_30,axiom,
( v8_lattices(Eq_y_0)
| ~ v8_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_31,axiom,
( v9_lattices(Eq_y_0)
| ~ v9_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_32,axiom,
( r1_lattices(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ r1_lattices(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT327+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n014.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 19 13:22:50 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.21/0.49 % SZS status Theorem for theBenchmark
% 0.21/0.49 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------