%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU348+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n010.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 08:59:03 AM UTC 2026
% Result : Theorem 259.57s 259.88s
% Output : Proof 260.67s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(abstractness_v1_orders_2,axiom,
! [A] :
( rel_str(A)
=> ( strict_rel_str(A)
=> A = rel_str_of(the_carrier(A),the_InternalRel(A)) ) ),
file('theBenchmark.p',abstractness_v1_orders_2) ).
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(cc1_lattices,axiom,
! [A] :
( latt_str(A)
=> ( ( lattice(A)
& ~ empty_carrier(A) )
=> ( join_absorbing(A)
& meet_absorbing(A)
& meet_associative(A)
& meet_commutative(A)
& join_associative(A)
& join_commutative(A)
& ~ empty_carrier(A) ) ) ),
file('theBenchmark.p',cc1_lattices) ).
fof(cc1_relset_1,axiom,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
=> relation(C) ),
file('theBenchmark.p',cc1_relset_1) ).
fof(cc2_lattices,axiom,
! [A] :
( latt_str(A)
=> ( ( join_absorbing(A)
& meet_absorbing(A)
& meet_associative(A)
& meet_commutative(A)
& join_associative(A)
& join_commutative(A)
& ~ empty_carrier(A) )
=> ( lattice(A)
& ~ empty_carrier(A) ) ) ),
file('theBenchmark.p',cc2_lattices) ).
fof(d2_lattice3,axiom,
! [A] :
( ( latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> poset_of_lattice(A) = rel_str_of(the_carrier(A),k2_lattice3(A)) ),
file('theBenchmark.p',d2_lattice3) ).
fof(d3_lattice3,axiom,
! [A] :
( ( latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> cast_to_el_of_LattPOSet(A,B) = B ) ),
file('theBenchmark.p',d3_lattice3) ).
fof(d4_lattice3,axiom,
! [A] :
( ( latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(poset_of_lattice(A)))
=> cast_to_el_of_lattice(A,B) = B ) ),
file('theBenchmark.p',d4_lattice3) ).
fof(dt_g1_orders_2,axiom,
! [A,B] :
( relation_of2(B,A,A)
=> ( rel_str(rel_str_of(A,B))
& strict_rel_str(rel_str_of(A,B)) ) ),
file('theBenchmark.p',dt_g1_orders_2) ).
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(dt_k2_lattice3,axiom,
! [A] :
( ( latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> ( relation_of2_as_subset(k2_lattice3(A),the_carrier(A),the_carrier(A))
& v1_partfun1(k2_lattice3(A),the_carrier(A),the_carrier(A))
& transitive(k2_lattice3(A))
& antisymmetric(k2_lattice3(A))
& reflexive(k2_lattice3(A)) ) ),
file('theBenchmark.p',dt_k2_lattice3) ).
fof(dt_k2_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k2_zfmisc_1) ).
fof(dt_k3_lattice3,axiom,
! [A] :
( ( latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> ( rel_str(poset_of_lattice(A))
& antisymmetric_relstr(poset_of_lattice(A))
& transitive_relstr(poset_of_lattice(A))
& reflexive_relstr(poset_of_lattice(A))
& strict_rel_str(poset_of_lattice(A)) ) ),
file('theBenchmark.p',dt_k3_lattice3) ).
fof(dt_k4_lattice3,axiom,
! [A,B] :
( ( element(B,the_carrier(A))
& latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> element(cast_to_el_of_LattPOSet(A,B),the_carrier(poset_of_lattice(A))) ),
file('theBenchmark.p',dt_k4_lattice3) ).
fof(dt_k5_lattice3,axiom,
! [A,B] :
( ( element(B,the_carrier(poset_of_lattice(A)))
& latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> element(cast_to_el_of_lattice(A,B),the_carrier(A)) ),
file('theBenchmark.p',dt_k5_lattice3) ).
fof(dt_k9_filter_1,axiom,
! [A] :
( ( latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> relation(relation_of_lattice(A)) ),
file('theBenchmark.p',dt_k9_filter_1) ).
fof(dt_l1_lattices,axiom,
! [A] :
( meet_semilatt_str(A)
=> one_sorted_str(A) ),
file('theBenchmark.p',dt_l1_lattices) ).
fof(dt_l1_orders_2,axiom,
! [A] :
( rel_str(A)
=> one_sorted_str(A) ),
file('theBenchmark.p',dt_l1_orders_2) ).
fof(dt_l1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_l1_struct_0) ).
fof(dt_l2_lattices,axiom,
! [A] :
( join_semilatt_str(A)
=> one_sorted_str(A) ),
file('theBenchmark.p',dt_l2_lattices) ).
fof(dt_l3_lattices,axiom,
! [A] :
( latt_str(A)
=> ( join_semilatt_str(A)
& meet_semilatt_str(A) ) ),
file('theBenchmark.p',dt_l3_lattices) ).
fof(dt_m1_relset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_relset_1) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(dt_m2_relset_1,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> element(C,powerset(cartesian_product2(A,B))) ),
file('theBenchmark.p',dt_m2_relset_1) ).
fof(dt_u1_orders_2,axiom,
! [A] :
( rel_str(A)
=> relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)) ),
file('theBenchmark.p',dt_u1_orders_2) ).
fof(dt_u1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_u1_struct_0) ).
fof(existence_l1_lattices,axiom,
? [A] : meet_semilatt_str(A),
file('theBenchmark.p',existence_l1_lattices) ).
fof(existence_l1_orders_2,axiom,
? [A] : rel_str(A),
file('theBenchmark.p',existence_l1_orders_2) ).
fof(existence_l1_struct_0,axiom,
? [A] : one_sorted_str(A),
file('theBenchmark.p',existence_l1_struct_0) ).
fof(existence_l2_lattices,axiom,
? [A] : join_semilatt_str(A),
file('theBenchmark.p',existence_l2_lattices) ).
fof(existence_l3_lattices,axiom,
? [A] : latt_str(A),
file('theBenchmark.p',existence_l3_lattices) ).
fof(existence_m1_relset_1,axiom,
! [A,B] :
? [C] : relation_of2(C,A,B),
file('theBenchmark.p',existence_m1_relset_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(existence_m2_relset_1,axiom,
! [A,B] :
? [C] : relation_of2_as_subset(C,A,B),
file('theBenchmark.p',existence_m2_relset_1) ).
fof(fc1_orders_2,axiom,
! [A,B] :
( ( relation_of2(B,A,A)
& ~ empty(A) )
=> ( strict_rel_str(rel_str_of(A,B))
& ~ empty_carrier(rel_str_of(A,B)) ) ),
file('theBenchmark.p',fc1_orders_2) ).
fof(fc1_struct_0,axiom,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ~ empty(the_carrier(A)) ),
file('theBenchmark.p',fc1_struct_0) ).
fof(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(fc2_orders_2,axiom,
! [A] :
( ( rel_str(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A) )
=> ( v1_partfun1(the_InternalRel(A),the_carrier(A),the_carrier(A))
& transitive(the_InternalRel(A))
& antisymmetric(the_InternalRel(A))
& reflexive(the_InternalRel(A))
& relation(the_InternalRel(A)) ) ),
file('theBenchmark.p',fc2_orders_2) ).
fof(fc3_orders_2,axiom,
! [A,B] :
( ( relation_of2(B,A,A)
& v1_partfun1(B,A,A)
& transitive(B)
& antisymmetric(B)
& reflexive(B) )
=> ( antisymmetric_relstr(rel_str_of(A,B))
& transitive_relstr(rel_str_of(A,B))
& reflexive_relstr(rel_str_of(A,B))
& strict_rel_str(rel_str_of(A,B)) ) ),
file('theBenchmark.p',fc3_orders_2) ).
fof(fc4_lattice3,axiom,
! [A] :
( ( latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> ( antisymmetric_relstr(poset_of_lattice(A))
& transitive_relstr(poset_of_lattice(A))
& reflexive_relstr(poset_of_lattice(A))
& strict_rel_str(poset_of_lattice(A))
& ~ empty_carrier(poset_of_lattice(A)) ) ),
file('theBenchmark.p',fc4_lattice3) ).
fof(fc4_subset_1,axiom,
! [A,B] :
( ( ~ empty(B)
& ~ empty(A) )
=> ~ empty(cartesian_product2(A,B)) ),
file('theBenchmark.p',fc4_subset_1) ).
fof(free_g1_orders_2,axiom,
! [A,B] :
( relation_of2(B,A,A)
=> ! [C,D] :
( rel_str_of(A,B) = rel_str_of(C,D)
=> ( B = D
& A = C ) ) ),
file('theBenchmark.p',free_g1_orders_2) ).
fof(rc1_orders_2,axiom,
? [A] :
( strict_rel_str(A)
& rel_str(A) ),
file('theBenchmark.p',rc1_orders_2) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc1_subset_1) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_orders_2,axiom,
? [A] :
( antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& strict_rel_str(A)
& ~ empty_carrier(A)
& rel_str(A) ),
file('theBenchmark.p',rc2_orders_2) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(rc3_struct_0,axiom,
? [A] :
( ~ empty_carrier(A)
& one_sorted_str(A) ),
file('theBenchmark.p',rc3_struct_0) ).
fof(rc5_struct_0,axiom,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ? [B] :
( ~ empty(B)
& element(B,powerset(the_carrier(A))) ) ),
file('theBenchmark.p',rc5_struct_0) ).
fof(redefinition_k2_lattice3,axiom,
! [A] :
( ( latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> k2_lattice3(A) = relation_of_lattice(A) ),
file('theBenchmark.p',redefinition_k2_lattice3) ).
fof(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
<=> relation_of2(C,A,B) ),
file('theBenchmark.p',redefinition_m2_relset_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t28_lattice3,axiom,
! [A,B] :
( ( latt_str(B)
& lattice(B)
& ~ empty_carrier(B) )
=> ! [C] :
( element(C,the_carrier(B))
=> ( latt_set_smaller(B,C,A)
<=> relstr_element_smaller(poset_of_lattice(B),A,cast_to_el_of_LattPOSet(B,C)) ) ) ),
file('theBenchmark.p',t28_lattice3) ).
fof(t29_lattice3,conjecture,
! [A,B] :
( ( latt_str(B)
& lattice(B)
& ~ empty_carrier(B) )
=> ! [C] :
( element(C,the_carrier(poset_of_lattice(B)))
=> ( relstr_element_smaller(poset_of_lattice(B),A,C)
<=> latt_set_smaller(B,cast_to_el_of_lattice(B,C),A) ) ) ),
file('theBenchmark.p',t29_lattice3) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(f_1_1,plain,
! [A] :
( A = rel_str_of(the_carrier(A),the_InternalRel(A))
| ~ strict_rel_str(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[abstractness_v1_orders_2]) ).
fof(f_1_2,plain,
! [U_0] :
( U_0 = rel_str_of(the_carrier(U_0),the_InternalRel(U_0))
| ~ strict_rel_str(U_0)
| ~ rel_str(U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( U_0 = rel_str_of(the_carrier(U_0),the_InternalRel(U_0))
| ~ strict_rel_str(U_0)
| ~ rel_str(U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_2_2,plain,
! [U_2,U_1] :
( ~ in(U_1,U_2)
| ~ in(U_2,U_1) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( ~ in(U_1,U_2)
| ~ in(U_2,U_1) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A] :
( ( join_absorbing(A)
& meet_absorbing(A)
& meet_associative(A)
& meet_commutative(A)
& join_associative(A)
& join_commutative(A)
& ~ empty_carrier(A) )
| ~ lattice(A)
| empty_carrier(A)
| ~ latt_str(A) ),
inference(fof_nnf,[status(thm)],[cc1_lattices]) ).
fof(f_3_2,plain,
! [U_3] :
( ( join_absorbing(U_3)
& meet_absorbing(U_3)
& meet_associative(U_3)
& meet_commutative(U_3)
& join_associative(U_3)
& join_commutative(U_3)
& ~ empty_carrier(U_3) )
| ~ lattice(U_3)
| empty_carrier(U_3)
| ~ latt_str(U_3) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( ~ empty_carrier(U_3)
| ~ lattice(U_3)
| empty_carrier(U_3)
| ~ latt_str(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( join_commutative(U_3)
| ~ lattice(U_3)
| empty_carrier(U_3)
| ~ latt_str(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
cnf(f_3_5,plain,
( join_associative(U_3)
| ~ lattice(U_3)
| empty_carrier(U_3)
| ~ latt_str(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
cnf(f_3_6,plain,
( meet_commutative(U_3)
| ~ lattice(U_3)
| empty_carrier(U_3)
| ~ latt_str(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
cnf(f_3_7,plain,
( meet_associative(U_3)
| ~ lattice(U_3)
| empty_carrier(U_3)
| ~ latt_str(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
cnf(f_3_8,plain,
( meet_absorbing(U_3)
| ~ lattice(U_3)
| empty_carrier(U_3)
| ~ latt_str(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
cnf(f_3_9,plain,
( join_absorbing(U_3)
| ~ lattice(U_3)
| empty_carrier(U_3)
| ~ latt_str(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A,B,C] :
( relation(C)
| ~ element(C,powerset(cartesian_product2(A,B))) ),
inference(fof_nnf,[status(thm)],[cc1_relset_1]) ).
fof(f_4_2,plain,
! [U_6,U_5,U_4] :
( relation(U_4)
| ~ element(U_4,powerset(cartesian_product2(U_6,U_5))) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( relation(U_4)
| ~ element(U_4,powerset(cartesian_product2(U_6,U_5))) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A] :
( ( lattice(A)
& ~ empty_carrier(A) )
| ~ join_absorbing(A)
| ~ meet_absorbing(A)
| ~ meet_associative(A)
| ~ meet_commutative(A)
| ~ join_associative(A)
| ~ join_commutative(A)
| empty_carrier(A)
| ~ latt_str(A) ),
inference(fof_nnf,[status(thm)],[cc2_lattices]) ).
fof(f_5_2,plain,
! [U_7] :
( ( lattice(U_7)
& ~ empty_carrier(U_7) )
| ~ join_absorbing(U_7)
| ~ meet_absorbing(U_7)
| ~ meet_associative(U_7)
| ~ meet_commutative(U_7)
| ~ join_associative(U_7)
| ~ join_commutative(U_7)
| empty_carrier(U_7)
| ~ latt_str(U_7) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( ~ empty_carrier(U_7)
| ~ join_absorbing(U_7)
| ~ meet_absorbing(U_7)
| ~ meet_associative(U_7)
| ~ meet_commutative(U_7)
| ~ join_associative(U_7)
| ~ join_commutative(U_7)
| empty_carrier(U_7)
| ~ latt_str(U_7) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( lattice(U_7)
| ~ join_absorbing(U_7)
| ~ meet_absorbing(U_7)
| ~ meet_associative(U_7)
| ~ meet_commutative(U_7)
| ~ join_associative(U_7)
| ~ join_commutative(U_7)
| empty_carrier(U_7)
| ~ latt_str(U_7) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A] :
( poset_of_lattice(A) = rel_str_of(the_carrier(A),k2_lattice3(A))
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[d2_lattice3]) ).
fof(f_6_2,plain,
! [U_8] :
( poset_of_lattice(U_8) = rel_str_of(the_carrier(U_8),k2_lattice3(U_8))
| ~ latt_str(U_8)
| ~ lattice(U_8)
| empty_carrier(U_8) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( poset_of_lattice(U_8) = rel_str_of(the_carrier(U_8),k2_lattice3(U_8))
| ~ latt_str(U_8)
| ~ lattice(U_8)
| empty_carrier(U_8) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A] :
( ! [B] :
( cast_to_el_of_LattPOSet(A,B) = B
| ~ element(B,the_carrier(A)) )
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[d3_lattice3]) ).
fof(f_7_2,plain,
! [U_10] :
( ! [U_9] :
( cast_to_el_of_LattPOSet(U_10,U_9) = U_9
| ~ element(U_9,the_carrier(U_10)) )
| ~ latt_str(U_10)
| ~ lattice(U_10)
| empty_carrier(U_10) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( cast_to_el_of_LattPOSet(U_10,U_9) = U_9
| ~ element(U_9,the_carrier(U_10))
| ~ latt_str(U_10)
| ~ lattice(U_10)
| empty_carrier(U_10) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [A] :
( ! [B] :
( cast_to_el_of_lattice(A,B) = B
| ~ element(B,the_carrier(poset_of_lattice(A))) )
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[d4_lattice3]) ).
fof(f_8_2,plain,
! [U_12] :
( ! [U_11] :
( cast_to_el_of_lattice(U_12,U_11) = U_11
| ~ element(U_11,the_carrier(poset_of_lattice(U_12))) )
| ~ latt_str(U_12)
| ~ lattice(U_12)
| empty_carrier(U_12) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( cast_to_el_of_lattice(U_12,U_11) = U_11
| ~ element(U_11,the_carrier(poset_of_lattice(U_12)))
| ~ latt_str(U_12)
| ~ lattice(U_12)
| empty_carrier(U_12) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [A,B] :
( ( rel_str(rel_str_of(A,B))
& strict_rel_str(rel_str_of(A,B)) )
| ~ relation_of2(B,A,A) ),
inference(fof_nnf,[status(thm)],[dt_g1_orders_2]) ).
fof(f_9_2,plain,
! [U_14,U_13] :
( ( rel_str(rel_str_of(U_14,U_13))
& strict_rel_str(rel_str_of(U_14,U_13)) )
| ~ relation_of2(U_13,U_14,U_14) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( strict_rel_str(rel_str_of(U_14,U_13))
| ~ relation_of2(U_13,U_14,U_14) ),
inference(clausify,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( rel_str(rel_str_of(U_14,U_13))
| ~ relation_of2(U_13,U_14,U_14) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_10_2,plain,
$true,
inference(clausify,[status(thm)],[f_10_1]) ).
fof(f_11_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_11_2,plain,
$true,
inference(clausify,[status(thm)],[f_11_1]) ).
fof(f_12_1,plain,
! [A] :
( ( relation_of2_as_subset(k2_lattice3(A),the_carrier(A),the_carrier(A))
& v1_partfun1(k2_lattice3(A),the_carrier(A),the_carrier(A))
& transitive(k2_lattice3(A))
& antisymmetric(k2_lattice3(A))
& reflexive(k2_lattice3(A)) )
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_lattice3]) ).
fof(f_12_2,plain,
! [U_15] :
( ( relation_of2_as_subset(k2_lattice3(U_15),the_carrier(U_15),the_carrier(U_15))
& v1_partfun1(k2_lattice3(U_15),the_carrier(U_15),the_carrier(U_15))
& transitive(k2_lattice3(U_15))
& antisymmetric(k2_lattice3(U_15))
& reflexive(k2_lattice3(U_15)) )
| ~ latt_str(U_15)
| ~ lattice(U_15)
| empty_carrier(U_15) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( reflexive(k2_lattice3(U_15))
| ~ latt_str(U_15)
| ~ lattice(U_15)
| empty_carrier(U_15) ),
inference(clausify,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
( antisymmetric(k2_lattice3(U_15))
| ~ latt_str(U_15)
| ~ lattice(U_15)
| empty_carrier(U_15) ),
inference(clausify,[status(thm)],[f_12_2]) ).
cnf(f_12_5,plain,
( transitive(k2_lattice3(U_15))
| ~ latt_str(U_15)
| ~ lattice(U_15)
| empty_carrier(U_15) ),
inference(clausify,[status(thm)],[f_12_2]) ).
cnf(f_12_6,plain,
( v1_partfun1(k2_lattice3(U_15),the_carrier(U_15),the_carrier(U_15))
| ~ latt_str(U_15)
| ~ lattice(U_15)
| empty_carrier(U_15) ),
inference(clausify,[status(thm)],[f_12_2]) ).
cnf(f_12_7,plain,
( relation_of2_as_subset(k2_lattice3(U_15),the_carrier(U_15),the_carrier(U_15))
| ~ latt_str(U_15)
| ~ lattice(U_15)
| empty_carrier(U_15) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
cnf(f_13_2,plain,
$true,
inference(clausify,[status(thm)],[f_13_1]) ).
fof(f_14_1,plain,
! [A] :
( ( rel_str(poset_of_lattice(A))
& antisymmetric_relstr(poset_of_lattice(A))
& transitive_relstr(poset_of_lattice(A))
& reflexive_relstr(poset_of_lattice(A))
& strict_rel_str(poset_of_lattice(A)) )
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[dt_k3_lattice3]) ).
fof(f_14_2,plain,
! [U_16] :
( ( rel_str(poset_of_lattice(U_16))
& antisymmetric_relstr(poset_of_lattice(U_16))
& transitive_relstr(poset_of_lattice(U_16))
& reflexive_relstr(poset_of_lattice(U_16))
& strict_rel_str(poset_of_lattice(U_16)) )
| ~ latt_str(U_16)
| ~ lattice(U_16)
| empty_carrier(U_16) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( strict_rel_str(poset_of_lattice(U_16))
| ~ latt_str(U_16)
| ~ lattice(U_16)
| empty_carrier(U_16) ),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
( reflexive_relstr(poset_of_lattice(U_16))
| ~ latt_str(U_16)
| ~ lattice(U_16)
| empty_carrier(U_16) ),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_5,plain,
( transitive_relstr(poset_of_lattice(U_16))
| ~ latt_str(U_16)
| ~ lattice(U_16)
| empty_carrier(U_16) ),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_6,plain,
( antisymmetric_relstr(poset_of_lattice(U_16))
| ~ latt_str(U_16)
| ~ lattice(U_16)
| empty_carrier(U_16) ),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_7,plain,
( rel_str(poset_of_lattice(U_16))
| ~ latt_str(U_16)
| ~ lattice(U_16)
| empty_carrier(U_16) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [A,B] :
( element(cast_to_el_of_LattPOSet(A,B),the_carrier(poset_of_lattice(A)))
| ~ element(B,the_carrier(A))
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[dt_k4_lattice3]) ).
fof(f_15_2,plain,
! [U_18,U_17] :
( element(cast_to_el_of_LattPOSet(U_18,U_17),the_carrier(poset_of_lattice(U_18)))
| ~ element(U_17,the_carrier(U_18))
| ~ latt_str(U_18)
| ~ lattice(U_18)
| empty_carrier(U_18) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( element(cast_to_el_of_LattPOSet(U_18,U_17),the_carrier(poset_of_lattice(U_18)))
| ~ element(U_17,the_carrier(U_18))
| ~ latt_str(U_18)
| ~ lattice(U_18)
| empty_carrier(U_18) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [A,B] :
( element(cast_to_el_of_lattice(A,B),the_carrier(A))
| ~ element(B,the_carrier(poset_of_lattice(A)))
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[dt_k5_lattice3]) ).
fof(f_16_2,plain,
! [U_20,U_19] :
( element(cast_to_el_of_lattice(U_20,U_19),the_carrier(U_20))
| ~ element(U_19,the_carrier(poset_of_lattice(U_20)))
| ~ latt_str(U_20)
| ~ lattice(U_20)
| empty_carrier(U_20) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( element(cast_to_el_of_lattice(U_20,U_19),the_carrier(U_20))
| ~ element(U_19,the_carrier(poset_of_lattice(U_20)))
| ~ latt_str(U_20)
| ~ lattice(U_20)
| empty_carrier(U_20) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [A] :
( relation(relation_of_lattice(A))
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[dt_k9_filter_1]) ).
fof(f_17_2,plain,
! [U_21] :
( relation(relation_of_lattice(U_21))
| ~ latt_str(U_21)
| ~ lattice(U_21)
| empty_carrier(U_21) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( relation(relation_of_lattice(U_21))
| ~ latt_str(U_21)
| ~ lattice(U_21)
| empty_carrier(U_21) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [A] :
( one_sorted_str(A)
| ~ meet_semilatt_str(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_lattices]) ).
fof(f_18_2,plain,
! [U_22] :
( one_sorted_str(U_22)
| ~ meet_semilatt_str(U_22) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( one_sorted_str(U_22)
| ~ meet_semilatt_str(U_22) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [A] :
( one_sorted_str(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_orders_2]) ).
fof(f_19_2,plain,
! [U_23] :
( one_sorted_str(U_23)
| ~ rel_str(U_23) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
( one_sorted_str(U_23)
| ~ rel_str(U_23) ),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
cnf(f_20_2,plain,
$true,
inference(clausify,[status(thm)],[f_20_1]) ).
fof(f_21_1,plain,
! [A] :
( one_sorted_str(A)
| ~ join_semilatt_str(A) ),
inference(fof_nnf,[status(thm)],[dt_l2_lattices]) ).
fof(f_21_2,plain,
! [U_24] :
( one_sorted_str(U_24)
| ~ join_semilatt_str(U_24) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
( one_sorted_str(U_24)
| ~ join_semilatt_str(U_24) ),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
! [A] :
( ( join_semilatt_str(A)
& meet_semilatt_str(A) )
| ~ latt_str(A) ),
inference(fof_nnf,[status(thm)],[dt_l3_lattices]) ).
fof(f_22_2,plain,
! [U_25] :
( ( join_semilatt_str(U_25)
& meet_semilatt_str(U_25) )
| ~ latt_str(U_25) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( meet_semilatt_str(U_25)
| ~ latt_str(U_25) ),
inference(clausify,[status(thm)],[f_22_2]) ).
cnf(f_22_4,plain,
( join_semilatt_str(U_25)
| ~ latt_str(U_25) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_relset_1]) ).
cnf(f_23_2,plain,
$true,
inference(clausify,[status(thm)],[f_23_1]) ).
fof(f_24_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_24_2,plain,
$true,
inference(clausify,[status(thm)],[f_24_1]) ).
fof(f_25_1,plain,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
| ~ relation_of2_as_subset(C,A,B) ),
inference(fof_nnf,[status(thm)],[dt_m2_relset_1]) ).
fof(f_25_2,plain,
! [U_28,U_27,U_26] :
( element(U_26,powerset(cartesian_product2(U_28,U_27)))
| ~ relation_of2_as_subset(U_26,U_28,U_27) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
( element(U_26,powerset(cartesian_product2(U_28,U_27)))
| ~ relation_of2_as_subset(U_26,U_28,U_27) ),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
! [A] :
( relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A))
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[dt_u1_orders_2]) ).
fof(f_26_2,plain,
! [U_29] :
( relation_of2_as_subset(the_InternalRel(U_29),the_carrier(U_29),the_carrier(U_29))
| ~ rel_str(U_29) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
( relation_of2_as_subset(the_InternalRel(U_29),the_carrier(U_29),the_carrier(U_29))
| ~ rel_str(U_29) ),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_struct_0]) ).
cnf(f_27_2,plain,
$true,
inference(clausify,[status(thm)],[f_27_1]) ).
fof(f_28_1,plain,
? [A] : meet_semilatt_str(A),
inference(fof_nnf,[status(thm)],[existence_l1_lattices]) ).
fof(f_28_2,plain,
? [U_30] : meet_semilatt_str(U_30),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
meet_semilatt_str(sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_30,sK1)],[f_28_2]) ).
cnf(f_28_4,plain,
meet_semilatt_str(sK1),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
? [A] : rel_str(A),
inference(fof_nnf,[status(thm)],[existence_l1_orders_2]) ).
fof(f_29_2,plain,
? [U_31] : rel_str(U_31),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
rel_str(sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_31,sK2)],[f_29_2]) ).
cnf(f_29_4,plain,
rel_str(sK2),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_1,plain,
? [A] : one_sorted_str(A),
inference(fof_nnf,[status(thm)],[existence_l1_struct_0]) ).
fof(f_30_2,plain,
? [U_32] : one_sorted_str(U_32),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
one_sorted_str(sK3),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_32,sK3)],[f_30_2]) ).
cnf(f_30_4,plain,
one_sorted_str(sK3),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
? [A] : join_semilatt_str(A),
inference(fof_nnf,[status(thm)],[existence_l2_lattices]) ).
fof(f_31_2,plain,
? [U_33] : join_semilatt_str(U_33),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
join_semilatt_str(sK4),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_33,sK4)],[f_31_2]) ).
cnf(f_31_4,plain,
join_semilatt_str(sK4),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
? [A] : latt_str(A),
inference(fof_nnf,[status(thm)],[existence_l3_lattices]) ).
fof(f_32_2,plain,
? [U_34] : latt_str(U_34),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
latt_str(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_34,sK5)],[f_32_2]) ).
cnf(f_32_4,plain,
latt_str(sK5),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
! [A,B] :
? [C] : relation_of2(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m1_relset_1]) ).
fof(f_33_2,plain,
! [U_37,U_36] :
? [U_35] : relation_of2(U_35,U_37,U_36),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_37,U_36] : relation_of2(sK6(U_37,U_36),U_37,U_36),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_35,sK6(U_37,U_36))],[f_33_2]) ).
cnf(f_33_4,plain,
relation_of2(sK6(U_37,U_36),U_37,U_36),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_34_2,plain,
! [U_39] :
? [U_38] : element(U_38,U_39),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_39] : element(sK7(U_39),U_39),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_38,sK7(U_39))],[f_34_2]) ).
cnf(f_34_4,plain,
element(sK7(U_39),U_39),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
! [A,B] :
? [C] : relation_of2_as_subset(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m2_relset_1]) ).
fof(f_35_2,plain,
! [U_42,U_41] :
? [U_40] : relation_of2_as_subset(U_40,U_42,U_41),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_42,U_41] : relation_of2_as_subset(sK8(U_42,U_41),U_42,U_41),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_40,sK8(U_42,U_41))],[f_35_2]) ).
cnf(f_35_4,plain,
relation_of2_as_subset(sK8(U_42,U_41),U_42,U_41),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
! [A,B] :
( ( strict_rel_str(rel_str_of(A,B))
& ~ empty_carrier(rel_str_of(A,B)) )
| ~ relation_of2(B,A,A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc1_orders_2]) ).
fof(f_36_2,plain,
! [U_44,U_43] :
( ( strict_rel_str(rel_str_of(U_44,U_43))
& ~ empty_carrier(rel_str_of(U_44,U_43)) )
| ~ relation_of2(U_43,U_44,U_44)
| empty(U_44) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
cnf(f_36_3,plain,
( ~ empty_carrier(rel_str_of(U_44,U_43))
| ~ relation_of2(U_43,U_44,U_44)
| empty(U_44) ),
inference(clausify,[status(thm)],[f_36_2]) ).
cnf(f_36_4,plain,
( strict_rel_str(rel_str_of(U_44,U_43))
| ~ relation_of2(U_43,U_44,U_44)
| empty(U_44) ),
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_1,plain,
! [A] :
( ~ empty(the_carrier(A))
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[fc1_struct_0]) ).
fof(f_37_2,plain,
! [U_45] :
( ~ empty(the_carrier(U_45))
| ~ one_sorted_str(U_45)
| empty_carrier(U_45) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
cnf(f_37_3,plain,
( ~ empty(the_carrier(U_45))
| ~ one_sorted_str(U_45)
| empty_carrier(U_45) ),
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_38_2,plain,
! [U_46] : ~ empty(powerset(U_46)),
inference(variable_rename,[status(thm)],[f_38_1]) ).
cnf(f_38_3,plain,
~ empty(powerset(U_46)),
inference(clausify,[status(thm)],[f_38_2]) ).
fof(f_39_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_39_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_39_1]) ).
fof(f_40_1,plain,
! [A] :
( ( v1_partfun1(the_InternalRel(A),the_carrier(A),the_carrier(A))
& transitive(the_InternalRel(A))
& antisymmetric(the_InternalRel(A))
& reflexive(the_InternalRel(A))
& relation(the_InternalRel(A)) )
| ~ rel_str(A)
| ~ antisymmetric_relstr(A)
| ~ transitive_relstr(A)
| ~ reflexive_relstr(A) ),
inference(fof_nnf,[status(thm)],[fc2_orders_2]) ).
fof(f_40_2,plain,
! [U_47] :
( ( v1_partfun1(the_InternalRel(U_47),the_carrier(U_47),the_carrier(U_47))
& transitive(the_InternalRel(U_47))
& antisymmetric(the_InternalRel(U_47))
& reflexive(the_InternalRel(U_47))
& relation(the_InternalRel(U_47)) )
| ~ rel_str(U_47)
| ~ antisymmetric_relstr(U_47)
| ~ transitive_relstr(U_47)
| ~ reflexive_relstr(U_47) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
cnf(f_40_3,plain,
( relation(the_InternalRel(U_47))
| ~ rel_str(U_47)
| ~ antisymmetric_relstr(U_47)
| ~ transitive_relstr(U_47)
| ~ reflexive_relstr(U_47) ),
inference(clausify,[status(thm)],[f_40_2]) ).
cnf(f_40_4,plain,
( reflexive(the_InternalRel(U_47))
| ~ rel_str(U_47)
| ~ antisymmetric_relstr(U_47)
| ~ transitive_relstr(U_47)
| ~ reflexive_relstr(U_47) ),
inference(clausify,[status(thm)],[f_40_2]) ).
cnf(f_40_5,plain,
( antisymmetric(the_InternalRel(U_47))
| ~ rel_str(U_47)
| ~ antisymmetric_relstr(U_47)
| ~ transitive_relstr(U_47)
| ~ reflexive_relstr(U_47) ),
inference(clausify,[status(thm)],[f_40_2]) ).
cnf(f_40_6,plain,
( transitive(the_InternalRel(U_47))
| ~ rel_str(U_47)
| ~ antisymmetric_relstr(U_47)
| ~ transitive_relstr(U_47)
| ~ reflexive_relstr(U_47) ),
inference(clausify,[status(thm)],[f_40_2]) ).
cnf(f_40_7,plain,
( v1_partfun1(the_InternalRel(U_47),the_carrier(U_47),the_carrier(U_47))
| ~ rel_str(U_47)
| ~ antisymmetric_relstr(U_47)
| ~ transitive_relstr(U_47)
| ~ reflexive_relstr(U_47) ),
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_1,plain,
! [A,B] :
( ( antisymmetric_relstr(rel_str_of(A,B))
& transitive_relstr(rel_str_of(A,B))
& reflexive_relstr(rel_str_of(A,B))
& strict_rel_str(rel_str_of(A,B)) )
| ~ relation_of2(B,A,A)
| ~ v1_partfun1(B,A,A)
| ~ transitive(B)
| ~ antisymmetric(B)
| ~ reflexive(B) ),
inference(fof_nnf,[status(thm)],[fc3_orders_2]) ).
fof(f_41_2,plain,
! [U_49,U_48] :
( ( antisymmetric_relstr(rel_str_of(U_49,U_48))
& transitive_relstr(rel_str_of(U_49,U_48))
& reflexive_relstr(rel_str_of(U_49,U_48))
& strict_rel_str(rel_str_of(U_49,U_48)) )
| ~ relation_of2(U_48,U_49,U_49)
| ~ v1_partfun1(U_48,U_49,U_49)
| ~ transitive(U_48)
| ~ antisymmetric(U_48)
| ~ reflexive(U_48) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
cnf(f_41_3,plain,
( strict_rel_str(rel_str_of(U_49,U_48))
| ~ relation_of2(U_48,U_49,U_49)
| ~ v1_partfun1(U_48,U_49,U_49)
| ~ transitive(U_48)
| ~ antisymmetric(U_48)
| ~ reflexive(U_48) ),
inference(clausify,[status(thm)],[f_41_2]) ).
cnf(f_41_4,plain,
( reflexive_relstr(rel_str_of(U_49,U_48))
| ~ relation_of2(U_48,U_49,U_49)
| ~ v1_partfun1(U_48,U_49,U_49)
| ~ transitive(U_48)
| ~ antisymmetric(U_48)
| ~ reflexive(U_48) ),
inference(clausify,[status(thm)],[f_41_2]) ).
cnf(f_41_5,plain,
( transitive_relstr(rel_str_of(U_49,U_48))
| ~ relation_of2(U_48,U_49,U_49)
| ~ v1_partfun1(U_48,U_49,U_49)
| ~ transitive(U_48)
| ~ antisymmetric(U_48)
| ~ reflexive(U_48) ),
inference(clausify,[status(thm)],[f_41_2]) ).
cnf(f_41_6,plain,
( antisymmetric_relstr(rel_str_of(U_49,U_48))
| ~ relation_of2(U_48,U_49,U_49)
| ~ v1_partfun1(U_48,U_49,U_49)
| ~ transitive(U_48)
| ~ antisymmetric(U_48)
| ~ reflexive(U_48) ),
inference(clausify,[status(thm)],[f_41_2]) ).
fof(f_42_1,plain,
! [A] :
( ( antisymmetric_relstr(poset_of_lattice(A))
& transitive_relstr(poset_of_lattice(A))
& reflexive_relstr(poset_of_lattice(A))
& strict_rel_str(poset_of_lattice(A))
& ~ empty_carrier(poset_of_lattice(A)) )
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[fc4_lattice3]) ).
fof(f_42_2,plain,
! [U_50] :
( ( antisymmetric_relstr(poset_of_lattice(U_50))
& transitive_relstr(poset_of_lattice(U_50))
& reflexive_relstr(poset_of_lattice(U_50))
& strict_rel_str(poset_of_lattice(U_50))
& ~ empty_carrier(poset_of_lattice(U_50)) )
| ~ latt_str(U_50)
| ~ lattice(U_50)
| empty_carrier(U_50) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
cnf(f_42_3,plain,
( ~ empty_carrier(poset_of_lattice(U_50))
| ~ latt_str(U_50)
| ~ lattice(U_50)
| empty_carrier(U_50) ),
inference(clausify,[status(thm)],[f_42_2]) ).
cnf(f_42_4,plain,
( strict_rel_str(poset_of_lattice(U_50))
| ~ latt_str(U_50)
| ~ lattice(U_50)
| empty_carrier(U_50) ),
inference(clausify,[status(thm)],[f_42_2]) ).
cnf(f_42_5,plain,
( reflexive_relstr(poset_of_lattice(U_50))
| ~ latt_str(U_50)
| ~ lattice(U_50)
| empty_carrier(U_50) ),
inference(clausify,[status(thm)],[f_42_2]) ).
cnf(f_42_6,plain,
( transitive_relstr(poset_of_lattice(U_50))
| ~ latt_str(U_50)
| ~ lattice(U_50)
| empty_carrier(U_50) ),
inference(clausify,[status(thm)],[f_42_2]) ).
cnf(f_42_7,plain,
( antisymmetric_relstr(poset_of_lattice(U_50))
| ~ latt_str(U_50)
| ~ lattice(U_50)
| empty_carrier(U_50) ),
inference(clausify,[status(thm)],[f_42_2]) ).
fof(f_43_1,plain,
! [A,B] :
( ~ empty(cartesian_product2(A,B))
| empty(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc4_subset_1]) ).
fof(f_43_2,plain,
! [U_52,U_51] :
( ~ empty(cartesian_product2(U_52,U_51))
| empty(U_51)
| empty(U_52) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
cnf(f_43_3,plain,
( ~ empty(cartesian_product2(U_52,U_51))
| empty(U_51)
| empty(U_52) ),
inference(clausify,[status(thm)],[f_43_2]) ).
fof(f_44_1,plain,
! [A,B] :
( ! [C,D] :
( ( B = D
& A = C )
| rel_str_of(A,B) != rel_str_of(C,D) )
| ~ relation_of2(B,A,A) ),
inference(fof_nnf,[status(thm)],[free_g1_orders_2]) ).
fof(f_44_2,plain,
! [U_56,U_55] :
( ! [U_54,U_53] :
( ( U_55 = U_53
& U_56 = U_54 )
| rel_str_of(U_56,U_55) != rel_str_of(U_54,U_53) )
| ~ relation_of2(U_55,U_56,U_56) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
cnf(f_44_3,plain,
( U_56 = U_54
| rel_str_of(U_56,U_55) != rel_str_of(U_54,U_53)
| ~ relation_of2(U_55,U_56,U_56) ),
inference(clausify,[status(thm)],[f_44_2]) ).
cnf(f_44_4,plain,
( U_55 = U_53
| rel_str_of(U_56,U_55) != rel_str_of(U_54,U_53)
| ~ relation_of2(U_55,U_56,U_56) ),
inference(clausify,[status(thm)],[f_44_2]) ).
fof(f_45_1,plain,
? [A] :
( strict_rel_str(A)
& rel_str(A) ),
inference(fof_nnf,[status(thm)],[rc1_orders_2]) ).
fof(f_45_2,plain,
? [U_57] :
( strict_rel_str(U_57)
& rel_str(U_57) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
( strict_rel_str(sK9)
& rel_str(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_57,sK9)],[f_45_2]) ).
cnf(f_45_4,plain,
rel_str(sK9),
inference(clausify,[status(thm)],[f_45_3]) ).
cnf(f_45_5,plain,
strict_rel_str(sK9),
inference(clausify,[status(thm)],[f_45_3]) ).
fof(f_46_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_46_2,plain,
! [U_59] :
( ? [U_58] :
( ~ empty(U_58)
& element(U_58,powerset(U_59)) )
| empty(U_59) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_59] :
( ( ~ empty(sK10(U_59))
& element(sK10(U_59),powerset(U_59)) )
| empty(U_59) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_58,sK10(U_59))],[f_46_2]) ).
cnf(f_46_4,plain,
( element(sK10(U_59),powerset(U_59))
| empty(U_59) ),
inference(clausify,[status(thm)],[f_46_3]) ).
cnf(f_46_5,plain,
( ~ empty(sK10(U_59))
| empty(U_59) ),
inference(clausify,[status(thm)],[f_46_3]) ).
fof(f_47_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_47_2,plain,
? [U_60] : empty(U_60),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
empty(sK11),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_60,sK11)],[f_47_2]) ).
cnf(f_47_4,plain,
empty(sK11),
inference(clausify,[status(thm)],[f_47_3]) ).
fof(f_48_1,plain,
? [A] :
( antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& strict_rel_str(A)
& ~ empty_carrier(A)
& rel_str(A) ),
inference(fof_nnf,[status(thm)],[rc2_orders_2]) ).
fof(f_48_2,plain,
? [U_61] :
( antisymmetric_relstr(U_61)
& transitive_relstr(U_61)
& reflexive_relstr(U_61)
& strict_rel_str(U_61)
& ~ empty_carrier(U_61)
& rel_str(U_61) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
( antisymmetric_relstr(sK12)
& transitive_relstr(sK12)
& reflexive_relstr(sK12)
& strict_rel_str(sK12)
& ~ empty_carrier(sK12)
& rel_str(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_61,sK12)],[f_48_2]) ).
cnf(f_48_4,plain,
rel_str(sK12),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_5,plain,
~ empty_carrier(sK12),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_6,plain,
strict_rel_str(sK12),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_7,plain,
reflexive_relstr(sK12),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_8,plain,
transitive_relstr(sK12),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_9,plain,
antisymmetric_relstr(sK12),
inference(clausify,[status(thm)],[f_48_3]) ).
fof(f_49_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_49_2,plain,
! [U_63] :
? [U_62] :
( empty(U_62)
& element(U_62,powerset(U_63)) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
! [U_63] :
( empty(sK13(U_63))
& element(sK13(U_63),powerset(U_63)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_62,sK13(U_63))],[f_49_2]) ).
cnf(f_49_4,plain,
element(sK13(U_63),powerset(U_63)),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_5,plain,
empty(sK13(U_63)),
inference(clausify,[status(thm)],[f_49_3]) ).
fof(f_50_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_50_2,plain,
? [U_64] : ~ empty(U_64),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
~ empty(sK14),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_64,sK14)],[f_50_2]) ).
cnf(f_50_4,plain,
~ empty(sK14),
inference(clausify,[status(thm)],[f_50_3]) ).
fof(f_51_1,plain,
? [A] :
( ~ empty_carrier(A)
& one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[rc3_struct_0]) ).
fof(f_51_2,plain,
? [U_65] :
( ~ empty_carrier(U_65)
& one_sorted_str(U_65) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
( ~ empty_carrier(sK15)
& one_sorted_str(sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_65,sK15)],[f_51_2]) ).
cnf(f_51_4,plain,
one_sorted_str(sK15),
inference(clausify,[status(thm)],[f_51_3]) ).
cnf(f_51_5,plain,
~ empty_carrier(sK15),
inference(clausify,[status(thm)],[f_51_3]) ).
fof(f_52_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(the_carrier(A))) )
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[rc5_struct_0]) ).
fof(f_52_2,plain,
! [U_67] :
( ? [U_66] :
( ~ empty(U_66)
& element(U_66,powerset(the_carrier(U_67))) )
| ~ one_sorted_str(U_67)
| empty_carrier(U_67) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
! [U_67] :
( ( ~ empty(sK16(U_67))
& element(sK16(U_67),powerset(the_carrier(U_67))) )
| ~ one_sorted_str(U_67)
| empty_carrier(U_67) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_66,sK16(U_67))],[f_52_2]) ).
cnf(f_52_4,plain,
( element(sK16(U_67),powerset(the_carrier(U_67)))
| ~ one_sorted_str(U_67)
| empty_carrier(U_67) ),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_5,plain,
( ~ empty(sK16(U_67))
| ~ one_sorted_str(U_67)
| empty_carrier(U_67) ),
inference(clausify,[status(thm)],[f_52_3]) ).
fof(f_53_1,plain,
! [A] :
( k2_lattice3(A) = relation_of_lattice(A)
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[redefinition_k2_lattice3]) ).
fof(f_53_2,plain,
! [U_68] :
( k2_lattice3(U_68) = relation_of_lattice(U_68)
| ~ latt_str(U_68)
| ~ lattice(U_68)
| empty_carrier(U_68) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
cnf(f_53_3,plain,
( k2_lattice3(U_68) = relation_of_lattice(U_68)
| ~ latt_str(U_68)
| ~ lattice(U_68)
| empty_carrier(U_68) ),
inference(clausify,[status(thm)],[f_53_2]) ).
fof(f_54_1,plain,
! [A,B,C] :
( ( relation_of2_as_subset(C,A,B)
| ~ relation_of2(C,A,B) )
& ( relation_of2(C,A,B)
| ~ relation_of2_as_subset(C,A,B) ) ),
inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1]) ).
fof(f_54_2,plain,
! [U_71,U_70,U_69] :
( ( relation_of2_as_subset(U_69,U_71,U_70)
| ~ relation_of2(U_69,U_71,U_70) )
& ( relation_of2(U_69,U_71,U_70)
| ~ relation_of2_as_subset(U_69,U_71,U_70) ) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
( ! [U_77,U_75,U_73] :
( relation_of2_as_subset(U_73,U_77,U_75)
| ~ relation_of2(U_73,U_77,U_75) )
& ! [U_76,U_74,U_72] :
( relation_of2(U_72,U_76,U_74)
| ~ relation_of2_as_subset(U_72,U_76,U_74) ) ),
inference(miniscope,[status(thm)],[f_54_2]) ).
cnf(f_54_4,plain,
( relation_of2(U_72,U_76,U_74)
| ~ relation_of2_as_subset(U_72,U_76,U_74) ),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_5,plain,
( relation_of2_as_subset(U_73,U_77,U_75)
| ~ relation_of2(U_73,U_77,U_75) ),
inference(clausify,[status(thm)],[f_54_3]) ).
fof(f_55_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_55_2,plain,
! [U_79,U_78] : subset(U_79,U_79),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
! [U_79] : subset(U_79,U_79),
inference(miniscope,[status(thm)],[f_55_2]) ).
cnf(f_55_4,plain,
subset(U_79,U_79),
inference(clausify,[status(thm)],[f_55_3]) ).
fof(f_56_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_56_2,plain,
! [U_81,U_80] :
( element(U_81,U_80)
| ~ in(U_81,U_80) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
cnf(f_56_3,plain,
( element(U_81,U_80)
| ~ in(U_81,U_80) ),
inference(clausify,[status(thm)],[f_56_2]) ).
fof(f_57_1,plain,
! [A,B] :
( ! [C] :
( ( ( latt_set_smaller(B,C,A)
| ~ relstr_element_smaller(poset_of_lattice(B),A,cast_to_el_of_LattPOSet(B,C)) )
& ( relstr_element_smaller(poset_of_lattice(B),A,cast_to_el_of_LattPOSet(B,C))
| ~ latt_set_smaller(B,C,A) ) )
| ~ element(C,the_carrier(B)) )
| ~ latt_str(B)
| ~ lattice(B)
| empty_carrier(B) ),
inference(fof_nnf,[status(thm)],[t28_lattice3]) ).
fof(f_57_2,plain,
! [U_84,U_83] :
( ! [U_82] :
( ( ( latt_set_smaller(U_83,U_82,U_84)
| ~ relstr_element_smaller(poset_of_lattice(U_83),U_84,cast_to_el_of_LattPOSet(U_83,U_82)) )
& ( relstr_element_smaller(poset_of_lattice(U_83),U_84,cast_to_el_of_LattPOSet(U_83,U_82))
| ~ latt_set_smaller(U_83,U_82,U_84) ) )
| ~ element(U_82,the_carrier(U_83)) )
| ~ latt_str(U_83)
| ~ lattice(U_83)
| empty_carrier(U_83) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
cnf(f_57_3,plain,
( relstr_element_smaller(poset_of_lattice(U_83),U_84,cast_to_el_of_LattPOSet(U_83,U_82))
| ~ latt_set_smaller(U_83,U_82,U_84)
| ~ element(U_82,the_carrier(U_83))
| ~ latt_str(U_83)
| ~ lattice(U_83)
| empty_carrier(U_83) ),
inference(clausify,[status(thm)],[f_57_2]) ).
cnf(f_57_4,plain,
( latt_set_smaller(U_83,U_82,U_84)
| ~ relstr_element_smaller(poset_of_lattice(U_83),U_84,cast_to_el_of_LattPOSet(U_83,U_82))
| ~ element(U_82,the_carrier(U_83))
| ~ latt_str(U_83)
| ~ lattice(U_83)
| empty_carrier(U_83) ),
inference(clausify,[status(thm)],[f_57_2]) ).
fof(f_58_1,negated_conjecture,
~ ! [A,B] :
( ( latt_str(B)
& lattice(B)
& ~ empty_carrier(B) )
=> ! [C] :
( element(C,the_carrier(poset_of_lattice(B)))
=> ( relstr_element_smaller(poset_of_lattice(B),A,C)
<=> latt_set_smaller(B,cast_to_el_of_lattice(B,C),A) ) ) ),
inference(negate,[status(cth)],[t29_lattice3]) ).
fof(f_58_2,negated_conjecture,
? [A,B] :
( ? [C] :
( ( ( ~ relstr_element_smaller(poset_of_lattice(B),A,C)
& latt_set_smaller(B,cast_to_el_of_lattice(B,C),A) )
| ( ~ latt_set_smaller(B,cast_to_el_of_lattice(B,C),A)
& relstr_element_smaller(poset_of_lattice(B),A,C) ) )
& element(C,the_carrier(poset_of_lattice(B))) )
& latt_str(B)
& lattice(B)
& ~ empty_carrier(B) ),
inference(fof_nnf,[status(thm)],[f_58_1]) ).
fof(f_58_3,negated_conjecture,
? [U_87,U_86] :
( ? [U_85] :
( ( ( ~ relstr_element_smaller(poset_of_lattice(U_86),U_87,U_85)
& latt_set_smaller(U_86,cast_to_el_of_lattice(U_86,U_85),U_87) )
| ( ~ latt_set_smaller(U_86,cast_to_el_of_lattice(U_86,U_85),U_87)
& relstr_element_smaller(poset_of_lattice(U_86),U_87,U_85) ) )
& element(U_85,the_carrier(poset_of_lattice(U_86))) )
& latt_str(U_86)
& lattice(U_86)
& ~ empty_carrier(U_86) ),
inference(variable_rename,[status(thm)],[f_58_2]) ).
fof(f_58_4,negated_conjecture,
? [U_86] :
( ? [U_85] :
( ( ( ~ relstr_element_smaller(poset_of_lattice(U_86),sK17,U_85)
& latt_set_smaller(U_86,cast_to_el_of_lattice(U_86,U_85),sK17) )
| ( ~ latt_set_smaller(U_86,cast_to_el_of_lattice(U_86,U_85),sK17)
& relstr_element_smaller(poset_of_lattice(U_86),sK17,U_85) ) )
& element(U_85,the_carrier(poset_of_lattice(U_86))) )
& latt_str(U_86)
& lattice(U_86)
& ~ empty_carrier(U_86) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_87,sK17)],[f_58_3]) ).
fof(f_58_5,negated_conjecture,
( ? [U_85] :
( ( ( ~ relstr_element_smaller(poset_of_lattice(sK18),sK17,U_85)
& latt_set_smaller(sK18,cast_to_el_of_lattice(sK18,U_85),sK17) )
| ( ~ latt_set_smaller(sK18,cast_to_el_of_lattice(sK18,U_85),sK17)
& relstr_element_smaller(poset_of_lattice(sK18),sK17,U_85) ) )
& element(U_85,the_carrier(poset_of_lattice(sK18))) )
& latt_str(sK18)
& lattice(sK18)
& ~ empty_carrier(sK18) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_86,sK18)],[f_58_4]) ).
fof(f_58_6,negated_conjecture,
( ( ( ~ relstr_element_smaller(poset_of_lattice(sK18),sK17,sK19)
& latt_set_smaller(sK18,cast_to_el_of_lattice(sK18,sK19),sK17) )
| ( ~ latt_set_smaller(sK18,cast_to_el_of_lattice(sK18,sK19),sK17)
& relstr_element_smaller(poset_of_lattice(sK18),sK17,sK19) ) )
& element(sK19,the_carrier(poset_of_lattice(sK18)))
& latt_str(sK18)
& lattice(sK18)
& ~ empty_carrier(sK18) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_85,sK19)],[f_58_5]) ).
cnf(f_58_7,negated_conjecture,
~ empty_carrier(sK18),
inference(clausify,[status(thm)],[f_58_6]) ).
cnf(f_58_8,negated_conjecture,
lattice(sK18),
inference(clausify,[status(thm)],[f_58_6]) ).
cnf(f_58_9,negated_conjecture,
latt_str(sK18),
inference(clausify,[status(thm)],[f_58_6]) ).
cnf(f_58_10,negated_conjecture,
element(sK19,the_carrier(poset_of_lattice(sK18))),
inference(clausify,[status(thm)],[f_58_6]) ).
cnf(f_58_11,negated_conjecture,
( latt_set_smaller(sK18,cast_to_el_of_lattice(sK18,sK19),sK17)
| relstr_element_smaller(poset_of_lattice(sK18),sK17,sK19) ),
inference(clausify,[status(thm)],[f_58_6]) ).
cnf(f_58_12,negated_conjecture,
( ~ relstr_element_smaller(poset_of_lattice(sK18),sK17,sK19)
| relstr_element_smaller(poset_of_lattice(sK18),sK17,sK19) ),
inference(clausify,[status(thm)],[f_58_6]) ).
cnf(f_58_13,negated_conjecture,
( latt_set_smaller(sK18,cast_to_el_of_lattice(sK18,sK19),sK17)
| ~ latt_set_smaller(sK18,cast_to_el_of_lattice(sK18,sK19),sK17) ),
inference(clausify,[status(thm)],[f_58_6]) ).
cnf(f_58_14,negated_conjecture,
( ~ relstr_element_smaller(poset_of_lattice(sK18),sK17,sK19)
| ~ latt_set_smaller(sK18,cast_to_el_of_lattice(sK18,sK19),sK17) ),
inference(clausify,[status(thm)],[f_58_6]) ).
fof(f_59_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_59_2,plain,
! [U_89,U_88] :
( in(U_89,U_88)
| empty(U_88)
| ~ element(U_89,U_88) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
cnf(f_59_3,plain,
( in(U_89,U_88)
| empty(U_88)
| ~ element(U_89,U_88) ),
inference(clausify,[status(thm)],[f_59_2]) ).
fof(f_60_1,plain,
! [A,B] :
( ( element(A,powerset(B))
| ~ subset(A,B) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(fof_nnf,[status(thm)],[t3_subset]) ).
fof(f_60_2,plain,
! [U_91,U_90] :
( ( element(U_91,powerset(U_90))
| ~ subset(U_91,U_90) )
& ( subset(U_91,U_90)
| ~ element(U_91,powerset(U_90)) ) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
( ! [U_95,U_93] :
( element(U_95,powerset(U_93))
| ~ subset(U_95,U_93) )
& ! [U_94,U_92] :
( subset(U_94,U_92)
| ~ element(U_94,powerset(U_92)) ) ),
inference(miniscope,[status(thm)],[f_60_2]) ).
cnf(f_60_4,plain,
( subset(U_94,U_92)
| ~ element(U_94,powerset(U_92)) ),
inference(clausify,[status(thm)],[f_60_3]) ).
cnf(f_60_5,plain,
( element(U_95,powerset(U_93))
| ~ subset(U_95,U_93) ),
inference(clausify,[status(thm)],[f_60_3]) ).
fof(f_61_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_61_2,plain,
! [U_98,U_97,U_96] :
( element(U_98,U_96)
| ~ element(U_97,powerset(U_96))
| ~ in(U_98,U_97) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
cnf(f_61_3,plain,
( element(U_98,U_96)
| ~ element(U_97,powerset(U_96))
| ~ in(U_98,U_97) ),
inference(clausify,[status(thm)],[f_61_2]) ).
fof(f_62_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_62_2,plain,
! [U_101,U_100,U_99] :
( ~ empty(U_99)
| ~ element(U_100,powerset(U_99))
| ~ in(U_101,U_100) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
! [U_101,U_100] :
( ! [U_99] :
( ~ empty(U_99)
| ~ element(U_100,powerset(U_99)) )
| ~ in(U_101,U_100) ),
inference(miniscope,[status(thm)],[f_62_2]) ).
cnf(f_62_4,plain,
( ~ empty(U_99)
| ~ element(U_100,powerset(U_99))
| ~ in(U_101,U_100) ),
inference(clausify,[status(thm)],[f_62_3]) ).
fof(f_63_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_63_2,plain,
! [U_102] :
( U_102 = empty_set
| ~ empty(U_102) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
cnf(f_63_3,plain,
( U_102 = empty_set
| ~ empty(U_102) ),
inference(clausify,[status(thm)],[f_63_2]) ).
fof(f_64_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_64_2,plain,
! [U_104,U_103] :
( ~ empty(U_103)
| ~ in(U_104,U_103) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
cnf(f_64_3,plain,
( ~ empty(U_103)
| ~ in(U_104,U_103) ),
inference(clausify,[status(thm)],[f_64_2]) ).
fof(f_65_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_65_2,plain,
! [U_106,U_105] :
( ~ empty(U_105)
| U_106 = U_105
| ~ empty(U_106) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
fof(f_65_3,plain,
! [U_106] :
( ! [U_105] :
( ~ empty(U_105)
| U_106 = U_105 )
| ~ empty(U_106) ),
inference(miniscope,[status(thm)],[f_65_2]) ).
cnf(f_65_4,plain,
( ~ empty(U_105)
| U_106 = U_105
| ~ empty(U_106) ),
inference(clausify,[status(thm)],[f_65_3]) ).
cnf(f_3_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_3_3]) ).
cnf(f_5_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_3]) ).
cnf(f_10_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_10_2]) ).
cnf(f_11_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_11_2]) ).
cnf(f_13_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_13_2]) ).
cnf(f_20_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_20_2]) ).
cnf(f_23_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_23_2]) ).
cnf(f_24_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_24_2]) ).
cnf(f_27_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_27_2]) ).
cnf(f_58_12_true,negated_conjecture,
$true,
inference(clause_is_true,[status(thm)],[f_58_12]) ).
cnf(f_58_13_true,negated_conjecture,
$true,
inference(clause_is_true,[status(thm)],[f_58_13]) ).
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,
( the_carrier(Eq_x_0) = the_carrier(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( the_InternalRel(Eq_x_0) = the_InternalRel(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( rel_str_of(Eq_x_0,Eq_x_1) = rel_str_of(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( cartesian_product2(Eq_x_0,Eq_x_1) = cartesian_product2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( poset_of_lattice(Eq_x_0) = poset_of_lattice(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( k2_lattice3(Eq_x_0) = k2_lattice3(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( cast_to_el_of_LattPOSet(Eq_x_0,Eq_x_1) = cast_to_el_of_LattPOSet(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( cast_to_el_of_lattice(Eq_x_0,Eq_x_1) = cast_to_el_of_lattice(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( relation_of_lattice(Eq_x_0) = relation_of_lattice(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK6(Eq_x_0,Eq_x_1) = sK6(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK7(Eq_x_0) = sK7(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK8(Eq_x_0,Eq_x_1) = sK8(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( sK10(Eq_x_0) = sK10(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( sK13(Eq_x_0) = sK13(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( sK16(Eq_x_0) = sK16(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( rel_str(Eq_y_0)
| ~ rel_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,axiom,
( strict_rel_str(Eq_y_0)
| ~ strict_rel_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,axiom,
( in(Eq_y_0,Eq_y_1)
| ~ in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,axiom,
( latt_str(Eq_y_0)
| ~ latt_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( empty_carrier(Eq_y_0)
| ~ empty_carrier(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,axiom,
( lattice(Eq_y_0)
| ~ lattice(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,axiom,
( join_commutative(Eq_y_0)
| ~ join_commutative(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,axiom,
( join_associative(Eq_y_0)
| ~ join_associative(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,axiom,
( meet_commutative(Eq_y_0)
| ~ meet_commutative(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_29,axiom,
( meet_associative(Eq_y_0)
| ~ meet_associative(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_30,axiom,
( meet_absorbing(Eq_y_0)
| ~ meet_absorbing(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_31,axiom,
( join_absorbing(Eq_y_0)
| ~ join_absorbing(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_32,axiom,
( element(Eq_y_0,Eq_y_1)
| ~ element(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_33,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_34,axiom,
( relation_of2(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ relation_of2(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_35,axiom,
( reflexive(Eq_y_0)
| ~ reflexive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_36,axiom,
( antisymmetric(Eq_y_0)
| ~ antisymmetric(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_37,axiom,
( transitive(Eq_y_0)
| ~ transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_38,axiom,
( v1_partfun1(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ v1_partfun1(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_39,axiom,
( relation_of2_as_subset(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ relation_of2_as_subset(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_40,axiom,
( reflexive_relstr(Eq_y_0)
| ~ reflexive_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_41,axiom,
( transitive_relstr(Eq_y_0)
| ~ transitive_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_42,axiom,
( antisymmetric_relstr(Eq_y_0)
| ~ antisymmetric_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_43,axiom,
( meet_semilatt_str(Eq_y_0)
| ~ meet_semilatt_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_44,axiom,
( one_sorted_str(Eq_y_0)
| ~ one_sorted_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_45,axiom,
( join_semilatt_str(Eq_y_0)
| ~ join_semilatt_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_46,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_47,axiom,
( subset(Eq_y_0,Eq_y_1)
| ~ subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_48,axiom,
( latt_set_smaller(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ latt_set_smaller(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_49,axiom,
( relstr_element_smaller(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ relstr_element_smaller(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
% 0.00/0.03 % Problem : SEU348+1 : TPTP v9.3.1. Released v3.3.0.
% 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
% 0.11/0.37 % Computer : n010.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 00:00:53 UTC 2026
% 0.03/0.37 % CPUTime :
% 259.57/259.88 % SZS status Theorem for theBenchmark
% 259.57/259.88 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------