%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU387+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 : n013.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 08:59:10 AM UTC 2026
% Result : Theorem 261.15s 261.41s
% Output : Proof 261.46s
% 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(cc10_waybel_0,axiom,
! [A] :
( rel_str(A)
=> ( ( complete_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
=> ( join_complete_relstr(A)
& up_complete_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) ) ) ),
file('theBenchmark.p',cc10_waybel_0) ).
fof(cc11_waybel_0,axiom,
! [A] :
( rel_str(A)
=> ( ( join_complete_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
=> ( lower_bounded_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) ) ) ),
file('theBenchmark.p',cc11_waybel_0) ).
fof(cc12_waybel_0,axiom,
! [A] :
( rel_str(A)
=> ( ( up_complete_relstr(A)
& lower_bounded_relstr(A)
& with_suprema_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
=> ( bounded_relstr(A)
& upper_bounded_relstr(A)
& lower_bounded_relstr(A)
& complete_relstr(A)
& with_infima_relstr(A)
& with_suprema_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) ) ) ),
file('theBenchmark.p',cc12_waybel_0) ).
fof(cc13_waybel_0,axiom,
! [A] :
( rel_str(A)
=> ( ( join_complete_relstr(A)
& antisymmetric_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
=> ( with_infima_relstr(A)
& antisymmetric_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) ) ) ),
file('theBenchmark.p',cc13_waybel_0) ).
fof(cc14_waybel_0,axiom,
! [A] :
( rel_str(A)
=> ( ( join_complete_relstr(A)
& upper_bounded_relstr(A)
& antisymmetric_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
=> ( upper_bounded_relstr(A)
& with_suprema_relstr(A)
& antisymmetric_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) ) ) ),
file('theBenchmark.p',cc14_waybel_0) ).
fof(cc1_finset_1,axiom,
! [A] :
( empty(A)
=> finite(A) ),
file('theBenchmark.p',cc1_finset_1) ).
fof(cc1_lattice3,axiom,
! [A] :
( rel_str(A)
=> ( with_suprema_relstr(A)
=> ~ empty_carrier(A) ) ),
file('theBenchmark.p',cc1_lattice3) ).
fof(cc1_relat_1,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('theBenchmark.p',cc1_relat_1) ).
fof(cc1_relset_1,axiom,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
=> relation(C) ),
file('theBenchmark.p',cc1_relset_1) ).
fof(cc1_yellow_0,axiom,
! [A] :
( rel_str(A)
=> ( ( complete_relstr(A)
& ~ empty_carrier(A) )
=> ( with_infima_relstr(A)
& with_suprema_relstr(A)
& ~ empty_carrier(A) ) ) ),
file('theBenchmark.p',cc1_yellow_0) ).
fof(cc2_finset_1,axiom,
! [A] :
( finite(A)
=> ! [B] :
( element(B,powerset(A))
=> finite(B) ) ),
file('theBenchmark.p',cc2_finset_1) ).
fof(cc2_lattice3,axiom,
! [A] :
( rel_str(A)
=> ( with_infima_relstr(A)
=> ~ empty_carrier(A) ) ),
file('theBenchmark.p',cc2_lattice3) ).
fof(cc2_yellow_0,axiom,
! [A] :
( rel_str(A)
=> ( ( trivial_carrier(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
=> ( complete_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) ) ) ),
file('theBenchmark.p',cc2_yellow_0) ).
fof(cc3_yellow_0,axiom,
! [A] :
( rel_str(A)
=> ( ( complete_relstr(A)
& ~ empty_carrier(A) )
=> ( bounded_relstr(A)
& ~ empty_carrier(A) ) ) ),
file('theBenchmark.p',cc3_yellow_0) ).
fof(cc4_yellow_0,axiom,
! [A] :
( rel_str(A)
=> ( bounded_relstr(A)
=> ( upper_bounded_relstr(A)
& lower_bounded_relstr(A) ) ) ),
file('theBenchmark.p',cc4_yellow_0) ).
fof(cc5_waybel_0,axiom,
! [A] :
( rel_str(A)
=> ( ( trivial_carrier(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
=> ( connected_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) ) ) ),
file('theBenchmark.p',cc5_waybel_0) ).
fof(cc5_yellow_0,axiom,
! [A] :
( rel_str(A)
=> ( ( upper_bounded_relstr(A)
& lower_bounded_relstr(A) )
=> bounded_relstr(A) ) ),
file('theBenchmark.p',cc5_yellow_0) ).
fof(cc9_waybel_0,axiom,
! [A] :
( rel_str(A)
=> ( ( up_complete_relstr(A)
& with_suprema_relstr(A)
& reflexive_relstr(A) )
=> ( upper_bounded_relstr(A)
& with_suprema_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) ) ) ),
file('theBenchmark.p',cc9_waybel_0) ).
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_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k2_zfmisc_1) ).
fof(dt_k3_yellow_0,axiom,
! [A] :
( rel_str(A)
=> element(bottom_of_relstr(A),the_carrier(A)) ),
file('theBenchmark.p',dt_k3_yellow_0) ).
fof(dt_k3_yellow_1,axiom,
! [A] :
( rel_str(boole_POSet(A))
& strict_rel_str(boole_POSet(A)) ),
file('theBenchmark.p',dt_k3_yellow_1) ).
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_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_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_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(fc12_relat_1,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc12_relat_1) ).
fof(fc14_finset_1,axiom,
! [A,B] :
( ( finite(B)
& finite(A) )
=> finite(cartesian_product2(A,B)) ),
file('theBenchmark.p',fc14_finset_1) ).
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_waybel_7,axiom,
! [A] :
( complete_relstr(boole_POSet(A))
& with_infima_relstr(boole_POSet(A))
& with_suprema_relstr(boole_POSet(A))
& boolean_relstr(boole_POSet(A))
& complemented_relstr(boole_POSet(A))
& heyting_relstr(boole_POSet(A))
& distributive_relstr(boole_POSet(A))
& ~ v1_yellow_3(boole_POSet(A))
& join_complete_relstr(boole_POSet(A))
& up_complete_relstr(boole_POSet(A))
& bounded_relstr(boole_POSet(A))
& upper_bounded_relstr(boole_POSet(A))
& lower_bounded_relstr(boole_POSet(A))
& antisymmetric_relstr(boole_POSet(A))
& transitive_relstr(boole_POSet(A))
& reflexive_relstr(boole_POSet(A))
& strict_rel_str(boole_POSet(A))
& ~ empty_carrier(boole_POSet(A)) ),
file('theBenchmark.p',fc1_waybel_7) ).
fof(fc2_waybel_7,axiom,
! [A] :
( ~ empty(A)
=> ( complete_relstr(boole_POSet(A))
& with_infima_relstr(boole_POSet(A))
& with_suprema_relstr(boole_POSet(A))
& boolean_relstr(boole_POSet(A))
& complemented_relstr(boole_POSet(A))
& heyting_relstr(boole_POSet(A))
& distributive_relstr(boole_POSet(A))
& ~ v1_yellow_3(boole_POSet(A))
& join_complete_relstr(boole_POSet(A))
& up_complete_relstr(boole_POSet(A))
& bounded_relstr(boole_POSet(A))
& upper_bounded_relstr(boole_POSet(A))
& lower_bounded_relstr(boole_POSet(A))
& antisymmetric_relstr(boole_POSet(A))
& transitive_relstr(boole_POSet(A))
& reflexive_relstr(boole_POSet(A))
& strict_rel_str(boole_POSet(A))
& ~ trivial_carrier(boole_POSet(A))
& ~ empty_carrier(boole_POSet(A)) ) ),
file('theBenchmark.p',fc2_waybel_7) ).
fof(fc4_relat_1,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc4_relat_1) ).
fof(fc4_subset_1,axiom,
! [A,B] :
( ( ~ empty(B)
& ~ empty(A) )
=> ~ empty(cartesian_product2(A,B)) ),
file('theBenchmark.p',fc4_subset_1) ).
fof(fc7_yellow_1,axiom,
! [A] :
( antisymmetric_relstr(boole_POSet(A))
& transitive_relstr(boole_POSet(A))
& reflexive_relstr(boole_POSet(A))
& strict_rel_str(boole_POSet(A))
& ~ empty_carrier(boole_POSet(A)) ),
file('theBenchmark.p',fc7_yellow_1) ).
fof(fc8_yellow_1,axiom,
! [A] :
( complete_relstr(boole_POSet(A))
& with_infima_relstr(boole_POSet(A))
& with_suprema_relstr(boole_POSet(A))
& bounded_relstr(boole_POSet(A))
& upper_bounded_relstr(boole_POSet(A))
& lower_bounded_relstr(boole_POSet(A))
& antisymmetric_relstr(boole_POSet(A))
& transitive_relstr(boole_POSet(A))
& reflexive_relstr(boole_POSet(A))
& strict_rel_str(boole_POSet(A))
& ~ empty_carrier(boole_POSet(A)) ),
file('theBenchmark.p',fc8_yellow_1) ).
fof(fc8_yellow_6,axiom,
! [A] :
( complete_relstr(boole_POSet(A))
& with_infima_relstr(boole_POSet(A))
& with_suprema_relstr(boole_POSet(A))
& ~ v1_yellow_3(boole_POSet(A))
& join_complete_relstr(boole_POSet(A))
& up_complete_relstr(boole_POSet(A))
& directed_relstr(boole_POSet(A))
& bounded_relstr(boole_POSet(A))
& upper_bounded_relstr(boole_POSet(A))
& lower_bounded_relstr(boole_POSet(A))
& antisymmetric_relstr(boole_POSet(A))
& transitive_relstr(boole_POSet(A))
& reflexive_relstr(boole_POSet(A))
& strict_rel_str(boole_POSet(A))
& ~ empty_carrier(boole_POSet(A)) ),
file('theBenchmark.p',fc8_yellow_6) ).
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(rc10_waybel_0,axiom,
! [A] :
( ( rel_str(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
=> ? [B] :
( upper_relstr_subset(B,A)
& filtered_subset(B,A)
& ~ empty(B)
& element(B,powerset(the_carrier(A))) ) ),
file('theBenchmark.p',rc10_waybel_0) ).
fof(rc12_waybel_0,axiom,
? [A] :
( connected_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A)
& rel_str(A) ),
file('theBenchmark.p',rc12_waybel_0) ).
fof(rc13_waybel_0,axiom,
? [A] :
( join_complete_relstr(A)
& up_complete_relstr(A)
& bounded_relstr(A)
& upper_bounded_relstr(A)
& lower_bounded_relstr(A)
& complete_relstr(A)
& with_infima_relstr(A)
& with_suprema_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& strict_rel_str(A)
& ~ empty_carrier(A)
& rel_str(A) ),
file('theBenchmark.p',rc13_waybel_0) ).
fof(rc1_finset_1,axiom,
? [A] :
( finite(A)
& ~ empty(A) ),
file('theBenchmark.p',rc1_finset_1) ).
fof(rc1_lattice3,axiom,
? [A] :
( complete_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& strict_rel_str(A)
& ~ empty_carrier(A)
& rel_str(A) ),
file('theBenchmark.p',rc1_lattice3) ).
fof(rc1_relat_1,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('theBenchmark.p',rc1_relat_1) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc1_subset_1) ).
fof(rc1_waybel_7,axiom,
? [A] :
( with_infima_relstr(A)
& with_suprema_relstr(A)
& boolean_relstr(A)
& complemented_relstr(A)
& heyting_relstr(A)
& distributive_relstr(A)
& ~ v1_yellow_3(A)
& bounded_relstr(A)
& upper_bounded_relstr(A)
& lower_bounded_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& strict_rel_str(A)
& ~ trivial_carrier(A)
& ~ empty_carrier(A)
& rel_str(A) ),
file('theBenchmark.p',rc1_waybel_7) ).
fof(rc1_yellow_0,axiom,
? [A] :
( trivial_carrier(A)
& complete_relstr(A)
& with_infima_relstr(A)
& with_suprema_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& strict_rel_str(A)
& ~ empty_carrier(A)
& rel_str(A) ),
file('theBenchmark.p',rc1_yellow_0) ).
fof(rc2_lattice3,axiom,
? [A] :
( complete_relstr(A)
& with_infima_relstr(A)
& with_suprema_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& strict_rel_str(A)
& ~ empty_carrier(A)
& rel_str(A) ),
file('theBenchmark.p',rc2_lattice3) ).
fof(rc2_relat_1,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('theBenchmark.p',rc2_relat_1) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
fof(rc2_waybel_7,axiom,
! [A] :
? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(powerset(A))) ),
file('theBenchmark.p',rc2_waybel_7) ).
fof(rc2_yellow_0,axiom,
? [A] :
( bounded_relstr(A)
& upper_bounded_relstr(A)
& lower_bounded_relstr(A)
& complete_relstr(A)
& with_infima_relstr(A)
& with_suprema_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A)
& rel_str(A) ),
file('theBenchmark.p',rc2_yellow_0) ).
fof(rc3_finset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc3_finset_1) ).
fof(rc3_relat_1,axiom,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
file('theBenchmark.p',rc3_relat_1) ).
fof(rc3_struct_0,axiom,
? [A] :
( ~ empty_carrier(A)
& one_sorted_str(A) ),
file('theBenchmark.p',rc3_struct_0) ).
fof(rc3_waybel_7,axiom,
! [A] :
( one_sorted_str(A)
=> ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(powerset(the_carrier(A)))) ) ),
file('theBenchmark.p',rc3_waybel_7) ).
fof(rc4_finset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc4_finset_1) ).
fof(rc4_waybel_7,axiom,
! [A] :
( ( rel_str(A)
& upper_bounded_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& ~ trivial_carrier(A)
& ~ empty_carrier(A) )
=> ? [B] :
( upper_relstr_subset(B,A)
& filtered_subset(B,A)
& proper_element(B,powerset(the_carrier(A)))
& ~ empty(B)
& element(B,powerset(the_carrier(A))) ) ),
file('theBenchmark.p',rc4_waybel_7) ).
fof(rc4_yellow_6,axiom,
? [A] :
( directed_relstr(A)
& transitive_relstr(A)
& strict_rel_str(A)
& ~ empty_carrier(A)
& rel_str(A) ),
file('theBenchmark.p',rc4_yellow_6) ).
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_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(t18_yellow_1,axiom,
! [A] : bottom_of_relstr(boole_POSet(A)) = empty_set,
file('theBenchmark.p',t18_yellow_1) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t2_yellow19,conjecture,
! [A] :
( ~ empty(A)
=> ! [B] :
( ( element(B,powerset(the_carrier(boole_POSet(A))))
& proper_element(B,powerset(the_carrier(boole_POSet(A))))
& upper_relstr_subset(B,boole_POSet(A))
& filtered_subset(B,boole_POSet(A))
& ~ empty(B) )
=> ! [C] :
~ ( empty(C)
& in(C,B) ) ) ),
file('theBenchmark.p',t2_yellow19) ).
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(t8_waybel_7,axiom,
! [A] :
( ( rel_str(A)
& lower_bounded_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
=> ! [B] :
( ( element(B,powerset(the_carrier(A)))
& upper_relstr_subset(B,A)
& filtered_subset(B,A)
& ~ empty(B) )
=> ( proper_element(B,powerset(the_carrier(A)))
<=> ~ in(bottom_of_relstr(A),B) ) ) ),
file('theBenchmark.p',t8_waybel_7) ).
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_complete_relstr(A)
& up_complete_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
| ~ complete_relstr(A)
| ~ reflexive_relstr(A)
| empty_carrier(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[cc10_waybel_0]) ).
fof(f_3_2,plain,
! [U_3] :
( ( join_complete_relstr(U_3)
& up_complete_relstr(U_3)
& reflexive_relstr(U_3)
& ~ empty_carrier(U_3) )
| ~ complete_relstr(U_3)
| ~ reflexive_relstr(U_3)
| empty_carrier(U_3)
| ~ rel_str(U_3) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( ~ empty_carrier(U_3)
| ~ complete_relstr(U_3)
| ~ reflexive_relstr(U_3)
| empty_carrier(U_3)
| ~ rel_str(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( reflexive_relstr(U_3)
| ~ complete_relstr(U_3)
| ~ reflexive_relstr(U_3)
| empty_carrier(U_3)
| ~ rel_str(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
cnf(f_3_5,plain,
( up_complete_relstr(U_3)
| ~ complete_relstr(U_3)
| ~ reflexive_relstr(U_3)
| empty_carrier(U_3)
| ~ rel_str(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
cnf(f_3_6,plain,
( join_complete_relstr(U_3)
| ~ complete_relstr(U_3)
| ~ reflexive_relstr(U_3)
| empty_carrier(U_3)
| ~ rel_str(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A] :
( ( lower_bounded_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
| ~ join_complete_relstr(A)
| ~ reflexive_relstr(A)
| empty_carrier(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[cc11_waybel_0]) ).
fof(f_4_2,plain,
! [U_4] :
( ( lower_bounded_relstr(U_4)
& reflexive_relstr(U_4)
& ~ empty_carrier(U_4) )
| ~ join_complete_relstr(U_4)
| ~ reflexive_relstr(U_4)
| empty_carrier(U_4)
| ~ rel_str(U_4) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( ~ empty_carrier(U_4)
| ~ join_complete_relstr(U_4)
| ~ reflexive_relstr(U_4)
| empty_carrier(U_4)
| ~ rel_str(U_4) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( reflexive_relstr(U_4)
| ~ join_complete_relstr(U_4)
| ~ reflexive_relstr(U_4)
| empty_carrier(U_4)
| ~ rel_str(U_4) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_5,plain,
( lower_bounded_relstr(U_4)
| ~ join_complete_relstr(U_4)
| ~ reflexive_relstr(U_4)
| empty_carrier(U_4)
| ~ rel_str(U_4) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A] :
( ( bounded_relstr(A)
& upper_bounded_relstr(A)
& lower_bounded_relstr(A)
& complete_relstr(A)
& with_infima_relstr(A)
& with_suprema_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
| ~ up_complete_relstr(A)
| ~ lower_bounded_relstr(A)
| ~ with_suprema_relstr(A)
| ~ antisymmetric_relstr(A)
| ~ transitive_relstr(A)
| ~ reflexive_relstr(A)
| empty_carrier(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[cc12_waybel_0]) ).
fof(f_5_2,plain,
! [U_5] :
( ( bounded_relstr(U_5)
& upper_bounded_relstr(U_5)
& lower_bounded_relstr(U_5)
& complete_relstr(U_5)
& with_infima_relstr(U_5)
& with_suprema_relstr(U_5)
& antisymmetric_relstr(U_5)
& transitive_relstr(U_5)
& reflexive_relstr(U_5)
& ~ empty_carrier(U_5) )
| ~ up_complete_relstr(U_5)
| ~ lower_bounded_relstr(U_5)
| ~ with_suprema_relstr(U_5)
| ~ antisymmetric_relstr(U_5)
| ~ transitive_relstr(U_5)
| ~ reflexive_relstr(U_5)
| empty_carrier(U_5)
| ~ rel_str(U_5) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( ~ empty_carrier(U_5)
| ~ up_complete_relstr(U_5)
| ~ lower_bounded_relstr(U_5)
| ~ with_suprema_relstr(U_5)
| ~ antisymmetric_relstr(U_5)
| ~ transitive_relstr(U_5)
| ~ reflexive_relstr(U_5)
| empty_carrier(U_5)
| ~ rel_str(U_5) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( reflexive_relstr(U_5)
| ~ up_complete_relstr(U_5)
| ~ lower_bounded_relstr(U_5)
| ~ with_suprema_relstr(U_5)
| ~ antisymmetric_relstr(U_5)
| ~ transitive_relstr(U_5)
| ~ reflexive_relstr(U_5)
| empty_carrier(U_5)
| ~ rel_str(U_5) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_5,plain,
( transitive_relstr(U_5)
| ~ up_complete_relstr(U_5)
| ~ lower_bounded_relstr(U_5)
| ~ with_suprema_relstr(U_5)
| ~ antisymmetric_relstr(U_5)
| ~ transitive_relstr(U_5)
| ~ reflexive_relstr(U_5)
| empty_carrier(U_5)
| ~ rel_str(U_5) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_6,plain,
( antisymmetric_relstr(U_5)
| ~ up_complete_relstr(U_5)
| ~ lower_bounded_relstr(U_5)
| ~ with_suprema_relstr(U_5)
| ~ antisymmetric_relstr(U_5)
| ~ transitive_relstr(U_5)
| ~ reflexive_relstr(U_5)
| empty_carrier(U_5)
| ~ rel_str(U_5) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_7,plain,
( with_suprema_relstr(U_5)
| ~ up_complete_relstr(U_5)
| ~ lower_bounded_relstr(U_5)
| ~ with_suprema_relstr(U_5)
| ~ antisymmetric_relstr(U_5)
| ~ transitive_relstr(U_5)
| ~ reflexive_relstr(U_5)
| empty_carrier(U_5)
| ~ rel_str(U_5) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_8,plain,
( with_infima_relstr(U_5)
| ~ up_complete_relstr(U_5)
| ~ lower_bounded_relstr(U_5)
| ~ with_suprema_relstr(U_5)
| ~ antisymmetric_relstr(U_5)
| ~ transitive_relstr(U_5)
| ~ reflexive_relstr(U_5)
| empty_carrier(U_5)
| ~ rel_str(U_5) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_9,plain,
( complete_relstr(U_5)
| ~ up_complete_relstr(U_5)
| ~ lower_bounded_relstr(U_5)
| ~ with_suprema_relstr(U_5)
| ~ antisymmetric_relstr(U_5)
| ~ transitive_relstr(U_5)
| ~ reflexive_relstr(U_5)
| empty_carrier(U_5)
| ~ rel_str(U_5) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_10,plain,
( lower_bounded_relstr(U_5)
| ~ up_complete_relstr(U_5)
| ~ lower_bounded_relstr(U_5)
| ~ with_suprema_relstr(U_5)
| ~ antisymmetric_relstr(U_5)
| ~ transitive_relstr(U_5)
| ~ reflexive_relstr(U_5)
| empty_carrier(U_5)
| ~ rel_str(U_5) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_11,plain,
( upper_bounded_relstr(U_5)
| ~ up_complete_relstr(U_5)
| ~ lower_bounded_relstr(U_5)
| ~ with_suprema_relstr(U_5)
| ~ antisymmetric_relstr(U_5)
| ~ transitive_relstr(U_5)
| ~ reflexive_relstr(U_5)
| empty_carrier(U_5)
| ~ rel_str(U_5) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_12,plain,
( bounded_relstr(U_5)
| ~ up_complete_relstr(U_5)
| ~ lower_bounded_relstr(U_5)
| ~ with_suprema_relstr(U_5)
| ~ antisymmetric_relstr(U_5)
| ~ transitive_relstr(U_5)
| ~ reflexive_relstr(U_5)
| empty_carrier(U_5)
| ~ rel_str(U_5) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A] :
( ( with_infima_relstr(A)
& antisymmetric_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
| ~ join_complete_relstr(A)
| ~ antisymmetric_relstr(A)
| ~ reflexive_relstr(A)
| empty_carrier(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[cc13_waybel_0]) ).
fof(f_6_2,plain,
! [U_6] :
( ( with_infima_relstr(U_6)
& antisymmetric_relstr(U_6)
& reflexive_relstr(U_6)
& ~ empty_carrier(U_6) )
| ~ join_complete_relstr(U_6)
| ~ antisymmetric_relstr(U_6)
| ~ reflexive_relstr(U_6)
| empty_carrier(U_6)
| ~ rel_str(U_6) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( ~ empty_carrier(U_6)
| ~ join_complete_relstr(U_6)
| ~ antisymmetric_relstr(U_6)
| ~ reflexive_relstr(U_6)
| empty_carrier(U_6)
| ~ rel_str(U_6) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( reflexive_relstr(U_6)
| ~ join_complete_relstr(U_6)
| ~ antisymmetric_relstr(U_6)
| ~ reflexive_relstr(U_6)
| empty_carrier(U_6)
| ~ rel_str(U_6) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_5,plain,
( antisymmetric_relstr(U_6)
| ~ join_complete_relstr(U_6)
| ~ antisymmetric_relstr(U_6)
| ~ reflexive_relstr(U_6)
| empty_carrier(U_6)
| ~ rel_str(U_6) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_6,plain,
( with_infima_relstr(U_6)
| ~ join_complete_relstr(U_6)
| ~ antisymmetric_relstr(U_6)
| ~ reflexive_relstr(U_6)
| empty_carrier(U_6)
| ~ rel_str(U_6) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A] :
( ( upper_bounded_relstr(A)
& with_suprema_relstr(A)
& antisymmetric_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
| ~ join_complete_relstr(A)
| ~ upper_bounded_relstr(A)
| ~ antisymmetric_relstr(A)
| ~ reflexive_relstr(A)
| empty_carrier(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[cc14_waybel_0]) ).
fof(f_7_2,plain,
! [U_7] :
( ( upper_bounded_relstr(U_7)
& with_suprema_relstr(U_7)
& antisymmetric_relstr(U_7)
& reflexive_relstr(U_7)
& ~ empty_carrier(U_7) )
| ~ join_complete_relstr(U_7)
| ~ upper_bounded_relstr(U_7)
| ~ antisymmetric_relstr(U_7)
| ~ reflexive_relstr(U_7)
| empty_carrier(U_7)
| ~ rel_str(U_7) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( ~ empty_carrier(U_7)
| ~ join_complete_relstr(U_7)
| ~ upper_bounded_relstr(U_7)
| ~ antisymmetric_relstr(U_7)
| ~ reflexive_relstr(U_7)
| empty_carrier(U_7)
| ~ rel_str(U_7) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( reflexive_relstr(U_7)
| ~ join_complete_relstr(U_7)
| ~ upper_bounded_relstr(U_7)
| ~ antisymmetric_relstr(U_7)
| ~ reflexive_relstr(U_7)
| empty_carrier(U_7)
| ~ rel_str(U_7) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_5,plain,
( antisymmetric_relstr(U_7)
| ~ join_complete_relstr(U_7)
| ~ upper_bounded_relstr(U_7)
| ~ antisymmetric_relstr(U_7)
| ~ reflexive_relstr(U_7)
| empty_carrier(U_7)
| ~ rel_str(U_7) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_6,plain,
( with_suprema_relstr(U_7)
| ~ join_complete_relstr(U_7)
| ~ upper_bounded_relstr(U_7)
| ~ antisymmetric_relstr(U_7)
| ~ reflexive_relstr(U_7)
| empty_carrier(U_7)
| ~ rel_str(U_7) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_7,plain,
( upper_bounded_relstr(U_7)
| ~ join_complete_relstr(U_7)
| ~ upper_bounded_relstr(U_7)
| ~ antisymmetric_relstr(U_7)
| ~ reflexive_relstr(U_7)
| empty_carrier(U_7)
| ~ rel_str(U_7) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [A] :
( finite(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_finset_1]) ).
fof(f_8_2,plain,
! [U_8] :
( finite(U_8)
| ~ empty(U_8) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( finite(U_8)
| ~ empty(U_8) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [A] :
( ~ empty_carrier(A)
| ~ with_suprema_relstr(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[cc1_lattice3]) ).
fof(f_9_2,plain,
! [U_9] :
( ~ empty_carrier(U_9)
| ~ with_suprema_relstr(U_9)
| ~ rel_str(U_9) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( ~ empty_carrier(U_9)
| ~ with_suprema_relstr(U_9)
| ~ rel_str(U_9) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_10_2,plain,
! [U_10] :
( relation(U_10)
| ~ empty(U_10) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( relation(U_10)
| ~ empty(U_10) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [A,B,C] :
( relation(C)
| ~ element(C,powerset(cartesian_product2(A,B))) ),
inference(fof_nnf,[status(thm)],[cc1_relset_1]) ).
fof(f_11_2,plain,
! [U_13,U_12,U_11] :
( relation(U_11)
| ~ element(U_11,powerset(cartesian_product2(U_13,U_12))) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( relation(U_11)
| ~ element(U_11,powerset(cartesian_product2(U_13,U_12))) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [A] :
( ( with_infima_relstr(A)
& with_suprema_relstr(A)
& ~ empty_carrier(A) )
| ~ complete_relstr(A)
| empty_carrier(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[cc1_yellow_0]) ).
fof(f_12_2,plain,
! [U_14] :
( ( with_infima_relstr(U_14)
& with_suprema_relstr(U_14)
& ~ empty_carrier(U_14) )
| ~ complete_relstr(U_14)
| empty_carrier(U_14)
| ~ rel_str(U_14) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( ~ empty_carrier(U_14)
| ~ complete_relstr(U_14)
| empty_carrier(U_14)
| ~ rel_str(U_14) ),
inference(clausify,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
( with_suprema_relstr(U_14)
| ~ complete_relstr(U_14)
| empty_carrier(U_14)
| ~ rel_str(U_14) ),
inference(clausify,[status(thm)],[f_12_2]) ).
cnf(f_12_5,plain,
( with_infima_relstr(U_14)
| ~ complete_relstr(U_14)
| empty_carrier(U_14)
| ~ rel_str(U_14) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [A] :
( ! [B] :
( finite(B)
| ~ element(B,powerset(A)) )
| ~ finite(A) ),
inference(fof_nnf,[status(thm)],[cc2_finset_1]) ).
fof(f_13_2,plain,
! [U_16] :
( ! [U_15] :
( finite(U_15)
| ~ element(U_15,powerset(U_16)) )
| ~ finite(U_16) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
( finite(U_15)
| ~ element(U_15,powerset(U_16))
| ~ finite(U_16) ),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
! [A] :
( ~ empty_carrier(A)
| ~ with_infima_relstr(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[cc2_lattice3]) ).
fof(f_14_2,plain,
! [U_17] :
( ~ empty_carrier(U_17)
| ~ with_infima_relstr(U_17)
| ~ rel_str(U_17) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( ~ empty_carrier(U_17)
| ~ with_infima_relstr(U_17)
| ~ rel_str(U_17) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [A] :
( ( complete_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
| ~ trivial_carrier(A)
| ~ reflexive_relstr(A)
| empty_carrier(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[cc2_yellow_0]) ).
fof(f_15_2,plain,
! [U_18] :
( ( complete_relstr(U_18)
& antisymmetric_relstr(U_18)
& transitive_relstr(U_18)
& reflexive_relstr(U_18)
& ~ empty_carrier(U_18) )
| ~ trivial_carrier(U_18)
| ~ reflexive_relstr(U_18)
| empty_carrier(U_18)
| ~ rel_str(U_18) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( ~ empty_carrier(U_18)
| ~ trivial_carrier(U_18)
| ~ reflexive_relstr(U_18)
| empty_carrier(U_18)
| ~ rel_str(U_18) ),
inference(clausify,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
( reflexive_relstr(U_18)
| ~ trivial_carrier(U_18)
| ~ reflexive_relstr(U_18)
| empty_carrier(U_18)
| ~ rel_str(U_18) ),
inference(clausify,[status(thm)],[f_15_2]) ).
cnf(f_15_5,plain,
( transitive_relstr(U_18)
| ~ trivial_carrier(U_18)
| ~ reflexive_relstr(U_18)
| empty_carrier(U_18)
| ~ rel_str(U_18) ),
inference(clausify,[status(thm)],[f_15_2]) ).
cnf(f_15_6,plain,
( antisymmetric_relstr(U_18)
| ~ trivial_carrier(U_18)
| ~ reflexive_relstr(U_18)
| empty_carrier(U_18)
| ~ rel_str(U_18) ),
inference(clausify,[status(thm)],[f_15_2]) ).
cnf(f_15_7,plain,
( complete_relstr(U_18)
| ~ trivial_carrier(U_18)
| ~ reflexive_relstr(U_18)
| empty_carrier(U_18)
| ~ rel_str(U_18) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [A] :
( ( bounded_relstr(A)
& ~ empty_carrier(A) )
| ~ complete_relstr(A)
| empty_carrier(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[cc3_yellow_0]) ).
fof(f_16_2,plain,
! [U_19] :
( ( bounded_relstr(U_19)
& ~ empty_carrier(U_19) )
| ~ complete_relstr(U_19)
| empty_carrier(U_19)
| ~ rel_str(U_19) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( ~ empty_carrier(U_19)
| ~ complete_relstr(U_19)
| empty_carrier(U_19)
| ~ rel_str(U_19) ),
inference(clausify,[status(thm)],[f_16_2]) ).
cnf(f_16_4,plain,
( bounded_relstr(U_19)
| ~ complete_relstr(U_19)
| empty_carrier(U_19)
| ~ rel_str(U_19) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [A] :
( ( upper_bounded_relstr(A)
& lower_bounded_relstr(A) )
| ~ bounded_relstr(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[cc4_yellow_0]) ).
fof(f_17_2,plain,
! [U_20] :
( ( upper_bounded_relstr(U_20)
& lower_bounded_relstr(U_20) )
| ~ bounded_relstr(U_20)
| ~ rel_str(U_20) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( lower_bounded_relstr(U_20)
| ~ bounded_relstr(U_20)
| ~ rel_str(U_20) ),
inference(clausify,[status(thm)],[f_17_2]) ).
cnf(f_17_4,plain,
( upper_bounded_relstr(U_20)
| ~ bounded_relstr(U_20)
| ~ rel_str(U_20) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [A] :
( ( connected_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
| ~ trivial_carrier(A)
| ~ reflexive_relstr(A)
| empty_carrier(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[cc5_waybel_0]) ).
fof(f_18_2,plain,
! [U_21] :
( ( connected_relstr(U_21)
& reflexive_relstr(U_21)
& ~ empty_carrier(U_21) )
| ~ trivial_carrier(U_21)
| ~ reflexive_relstr(U_21)
| empty_carrier(U_21)
| ~ rel_str(U_21) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( ~ empty_carrier(U_21)
| ~ trivial_carrier(U_21)
| ~ reflexive_relstr(U_21)
| empty_carrier(U_21)
| ~ rel_str(U_21) ),
inference(clausify,[status(thm)],[f_18_2]) ).
cnf(f_18_4,plain,
( reflexive_relstr(U_21)
| ~ trivial_carrier(U_21)
| ~ reflexive_relstr(U_21)
| empty_carrier(U_21)
| ~ rel_str(U_21) ),
inference(clausify,[status(thm)],[f_18_2]) ).
cnf(f_18_5,plain,
( connected_relstr(U_21)
| ~ trivial_carrier(U_21)
| ~ reflexive_relstr(U_21)
| empty_carrier(U_21)
| ~ rel_str(U_21) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [A] :
( bounded_relstr(A)
| ~ upper_bounded_relstr(A)
| ~ lower_bounded_relstr(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[cc5_yellow_0]) ).
fof(f_19_2,plain,
! [U_22] :
( bounded_relstr(U_22)
| ~ upper_bounded_relstr(U_22)
| ~ lower_bounded_relstr(U_22)
| ~ rel_str(U_22) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
( bounded_relstr(U_22)
| ~ upper_bounded_relstr(U_22)
| ~ lower_bounded_relstr(U_22)
| ~ rel_str(U_22) ),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
! [A] :
( ( upper_bounded_relstr(A)
& with_suprema_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
| ~ up_complete_relstr(A)
| ~ with_suprema_relstr(A)
| ~ reflexive_relstr(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[cc9_waybel_0]) ).
fof(f_20_2,plain,
! [U_23] :
( ( upper_bounded_relstr(U_23)
& with_suprema_relstr(U_23)
& reflexive_relstr(U_23)
& ~ empty_carrier(U_23) )
| ~ up_complete_relstr(U_23)
| ~ with_suprema_relstr(U_23)
| ~ reflexive_relstr(U_23)
| ~ rel_str(U_23) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
( ~ empty_carrier(U_23)
| ~ up_complete_relstr(U_23)
| ~ with_suprema_relstr(U_23)
| ~ reflexive_relstr(U_23)
| ~ rel_str(U_23) ),
inference(clausify,[status(thm)],[f_20_2]) ).
cnf(f_20_4,plain,
( reflexive_relstr(U_23)
| ~ up_complete_relstr(U_23)
| ~ with_suprema_relstr(U_23)
| ~ reflexive_relstr(U_23)
| ~ rel_str(U_23) ),
inference(clausify,[status(thm)],[f_20_2]) ).
cnf(f_20_5,plain,
( with_suprema_relstr(U_23)
| ~ up_complete_relstr(U_23)
| ~ with_suprema_relstr(U_23)
| ~ reflexive_relstr(U_23)
| ~ rel_str(U_23) ),
inference(clausify,[status(thm)],[f_20_2]) ).
cnf(f_20_6,plain,
( upper_bounded_relstr(U_23)
| ~ up_complete_relstr(U_23)
| ~ with_suprema_relstr(U_23)
| ~ reflexive_relstr(U_23)
| ~ rel_str(U_23) ),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_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_21_2,plain,
! [U_25,U_24] :
( ( rel_str(rel_str_of(U_25,U_24))
& strict_rel_str(rel_str_of(U_25,U_24)) )
| ~ relation_of2(U_24,U_25,U_25) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
( strict_rel_str(rel_str_of(U_25,U_24))
| ~ relation_of2(U_24,U_25,U_25) ),
inference(clausify,[status(thm)],[f_21_2]) ).
cnf(f_21_4,plain,
( rel_str(rel_str_of(U_25,U_24))
| ~ relation_of2(U_24,U_25,U_25) ),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_22_2,plain,
$true,
inference(clausify,[status(thm)],[f_22_1]) ).
fof(f_23_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_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_k2_zfmisc_1]) ).
cnf(f_24_2,plain,
$true,
inference(clausify,[status(thm)],[f_24_1]) ).
fof(f_25_1,plain,
! [A] :
( element(bottom_of_relstr(A),the_carrier(A))
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[dt_k3_yellow_0]) ).
fof(f_25_2,plain,
! [U_26] :
( element(bottom_of_relstr(U_26),the_carrier(U_26))
| ~ rel_str(U_26) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
( element(bottom_of_relstr(U_26),the_carrier(U_26))
| ~ rel_str(U_26) ),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
! [A] :
( rel_str(boole_POSet(A))
& strict_rel_str(boole_POSet(A)) ),
inference(fof_nnf,[status(thm)],[dt_k3_yellow_1]) ).
fof(f_26_2,plain,
! [U_27] :
( rel_str(boole_POSet(U_27))
& strict_rel_str(boole_POSet(U_27)) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( ! [U_29] : rel_str(boole_POSet(U_29))
& ! [U_28] : strict_rel_str(boole_POSet(U_28)) ),
inference(miniscope,[status(thm)],[f_26_2]) ).
cnf(f_26_4,plain,
strict_rel_str(boole_POSet(U_28)),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_5,plain,
rel_str(boole_POSet(U_29)),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [A] :
( one_sorted_str(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_orders_2]) ).
fof(f_27_2,plain,
! [U_30] :
( one_sorted_str(U_30)
| ~ rel_str(U_30) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( one_sorted_str(U_30)
| ~ rel_str(U_30) ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
cnf(f_28_2,plain,
$true,
inference(clausify,[status(thm)],[f_28_1]) ).
fof(f_29_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_relset_1]) ).
cnf(f_29_2,plain,
$true,
inference(clausify,[status(thm)],[f_29_1]) ).
fof(f_30_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_30_2,plain,
$true,
inference(clausify,[status(thm)],[f_30_1]) ).
fof(f_31_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_31_2,plain,
! [U_33,U_32,U_31] :
( element(U_31,powerset(cartesian_product2(U_33,U_32)))
| ~ relation_of2_as_subset(U_31,U_33,U_32) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( element(U_31,powerset(cartesian_product2(U_33,U_32)))
| ~ relation_of2_as_subset(U_31,U_33,U_32) ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_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_32_2,plain,
! [U_34] :
( relation_of2_as_subset(the_InternalRel(U_34),the_carrier(U_34),the_carrier(U_34))
| ~ rel_str(U_34) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
( relation_of2_as_subset(the_InternalRel(U_34),the_carrier(U_34),the_carrier(U_34))
| ~ rel_str(U_34) ),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_struct_0]) ).
cnf(f_33_2,plain,
$true,
inference(clausify,[status(thm)],[f_33_1]) ).
fof(f_34_1,plain,
? [A] : rel_str(A),
inference(fof_nnf,[status(thm)],[existence_l1_orders_2]) ).
fof(f_34_2,plain,
? [U_35] : rel_str(U_35),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
rel_str(sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_35,sK1)],[f_34_2]) ).
cnf(f_34_4,plain,
rel_str(sK1),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
? [A] : one_sorted_str(A),
inference(fof_nnf,[status(thm)],[existence_l1_struct_0]) ).
fof(f_35_2,plain,
? [U_36] : one_sorted_str(U_36),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
one_sorted_str(sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_36,sK2)],[f_35_2]) ).
cnf(f_35_4,plain,
one_sorted_str(sK2),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
! [A,B] :
? [C] : relation_of2(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m1_relset_1]) ).
fof(f_36_2,plain,
! [U_39,U_38] :
? [U_37] : relation_of2(U_37,U_39,U_38),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_39,U_38] : relation_of2(sK3(U_39,U_38),U_39,U_38),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_37,sK3(U_39,U_38))],[f_36_2]) ).
cnf(f_36_4,plain,
relation_of2(sK3(U_39,U_38),U_39,U_38),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_37_2,plain,
! [U_41] :
? [U_40] : element(U_40,U_41),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_41] : element(sK4(U_41),U_41),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_40,sK4(U_41))],[f_37_2]) ).
cnf(f_37_4,plain,
element(sK4(U_41),U_41),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_1,plain,
! [A,B] :
? [C] : relation_of2_as_subset(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m2_relset_1]) ).
fof(f_38_2,plain,
! [U_44,U_43] :
? [U_42] : relation_of2_as_subset(U_42,U_44,U_43),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_44,U_43] : relation_of2_as_subset(sK5(U_44,U_43),U_44,U_43),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_42,sK5(U_44,U_43))],[f_38_2]) ).
cnf(f_38_4,plain,
relation_of2_as_subset(sK5(U_44,U_43),U_44,U_43),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
cnf(f_39_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_39_1]) ).
cnf(f_39_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_39_1]) ).
cnf(f_39_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_39_1]) ).
fof(f_40_1,plain,
! [A,B] :
( finite(cartesian_product2(A,B))
| ~ finite(B)
| ~ finite(A) ),
inference(fof_nnf,[status(thm)],[fc14_finset_1]) ).
fof(f_40_2,plain,
! [U_46,U_45] :
( finite(cartesian_product2(U_46,U_45))
| ~ finite(U_45)
| ~ finite(U_46) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
cnf(f_40_3,plain,
( finite(cartesian_product2(U_46,U_45))
| ~ finite(U_45)
| ~ finite(U_46) ),
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_1,plain,
! [A] :
( ~ empty(the_carrier(A))
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[fc1_struct_0]) ).
fof(f_41_2,plain,
! [U_47] :
( ~ empty(the_carrier(U_47))
| ~ one_sorted_str(U_47)
| empty_carrier(U_47) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
cnf(f_41_3,plain,
( ~ empty(the_carrier(U_47))
| ~ one_sorted_str(U_47)
| empty_carrier(U_47) ),
inference(clausify,[status(thm)],[f_41_2]) ).
fof(f_42_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_42_2,plain,
! [U_48] : ~ empty(powerset(U_48)),
inference(variable_rename,[status(thm)],[f_42_1]) ).
cnf(f_42_3,plain,
~ empty(powerset(U_48)),
inference(clausify,[status(thm)],[f_42_2]) ).
fof(f_43_1,plain,
! [A] :
( complete_relstr(boole_POSet(A))
& with_infima_relstr(boole_POSet(A))
& with_suprema_relstr(boole_POSet(A))
& boolean_relstr(boole_POSet(A))
& complemented_relstr(boole_POSet(A))
& heyting_relstr(boole_POSet(A))
& distributive_relstr(boole_POSet(A))
& ~ v1_yellow_3(boole_POSet(A))
& join_complete_relstr(boole_POSet(A))
& up_complete_relstr(boole_POSet(A))
& bounded_relstr(boole_POSet(A))
& upper_bounded_relstr(boole_POSet(A))
& lower_bounded_relstr(boole_POSet(A))
& antisymmetric_relstr(boole_POSet(A))
& transitive_relstr(boole_POSet(A))
& reflexive_relstr(boole_POSet(A))
& strict_rel_str(boole_POSet(A))
& ~ empty_carrier(boole_POSet(A)) ),
inference(fof_nnf,[status(thm)],[fc1_waybel_7]) ).
fof(f_43_2,plain,
! [U_49] :
( complete_relstr(boole_POSet(U_49))
& with_infima_relstr(boole_POSet(U_49))
& with_suprema_relstr(boole_POSet(U_49))
& boolean_relstr(boole_POSet(U_49))
& complemented_relstr(boole_POSet(U_49))
& heyting_relstr(boole_POSet(U_49))
& distributive_relstr(boole_POSet(U_49))
& ~ v1_yellow_3(boole_POSet(U_49))
& join_complete_relstr(boole_POSet(U_49))
& up_complete_relstr(boole_POSet(U_49))
& bounded_relstr(boole_POSet(U_49))
& upper_bounded_relstr(boole_POSet(U_49))
& lower_bounded_relstr(boole_POSet(U_49))
& antisymmetric_relstr(boole_POSet(U_49))
& transitive_relstr(boole_POSet(U_49))
& reflexive_relstr(boole_POSet(U_49))
& strict_rel_str(boole_POSet(U_49))
& ~ empty_carrier(boole_POSet(U_49)) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
( ! [U_67] : complete_relstr(boole_POSet(U_67))
& ! [U_66] : with_infima_relstr(boole_POSet(U_66))
& ! [U_65] : with_suprema_relstr(boole_POSet(U_65))
& ! [U_64] : boolean_relstr(boole_POSet(U_64))
& ! [U_63] : complemented_relstr(boole_POSet(U_63))
& ! [U_62] : heyting_relstr(boole_POSet(U_62))
& ! [U_61] : distributive_relstr(boole_POSet(U_61))
& ! [U_60] : ~ v1_yellow_3(boole_POSet(U_60))
& ! [U_59] : join_complete_relstr(boole_POSet(U_59))
& ! [U_58] : up_complete_relstr(boole_POSet(U_58))
& ! [U_57] : bounded_relstr(boole_POSet(U_57))
& ! [U_56] : upper_bounded_relstr(boole_POSet(U_56))
& ! [U_55] : lower_bounded_relstr(boole_POSet(U_55))
& ! [U_54] : antisymmetric_relstr(boole_POSet(U_54))
& ! [U_53] : transitive_relstr(boole_POSet(U_53))
& ! [U_52] : reflexive_relstr(boole_POSet(U_52))
& ! [U_51] : strict_rel_str(boole_POSet(U_51))
& ! [U_50] : ~ empty_carrier(boole_POSet(U_50)) ),
inference(miniscope,[status(thm)],[f_43_2]) ).
cnf(f_43_4,plain,
~ empty_carrier(boole_POSet(U_50)),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_5,plain,
strict_rel_str(boole_POSet(U_51)),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_6,plain,
reflexive_relstr(boole_POSet(U_52)),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_7,plain,
transitive_relstr(boole_POSet(U_53)),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_8,plain,
antisymmetric_relstr(boole_POSet(U_54)),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_9,plain,
lower_bounded_relstr(boole_POSet(U_55)),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_10,plain,
upper_bounded_relstr(boole_POSet(U_56)),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_11,plain,
bounded_relstr(boole_POSet(U_57)),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_12,plain,
up_complete_relstr(boole_POSet(U_58)),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_13,plain,
join_complete_relstr(boole_POSet(U_59)),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_14,plain,
~ v1_yellow_3(boole_POSet(U_60)),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_15,plain,
distributive_relstr(boole_POSet(U_61)),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_16,plain,
heyting_relstr(boole_POSet(U_62)),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_17,plain,
complemented_relstr(boole_POSet(U_63)),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_18,plain,
boolean_relstr(boole_POSet(U_64)),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_19,plain,
with_suprema_relstr(boole_POSet(U_65)),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_20,plain,
with_infima_relstr(boole_POSet(U_66)),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_21,plain,
complete_relstr(boole_POSet(U_67)),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_1,plain,
! [A] :
( ( complete_relstr(boole_POSet(A))
& with_infima_relstr(boole_POSet(A))
& with_suprema_relstr(boole_POSet(A))
& boolean_relstr(boole_POSet(A))
& complemented_relstr(boole_POSet(A))
& heyting_relstr(boole_POSet(A))
& distributive_relstr(boole_POSet(A))
& ~ v1_yellow_3(boole_POSet(A))
& join_complete_relstr(boole_POSet(A))
& up_complete_relstr(boole_POSet(A))
& bounded_relstr(boole_POSet(A))
& upper_bounded_relstr(boole_POSet(A))
& lower_bounded_relstr(boole_POSet(A))
& antisymmetric_relstr(boole_POSet(A))
& transitive_relstr(boole_POSet(A))
& reflexive_relstr(boole_POSet(A))
& strict_rel_str(boole_POSet(A))
& ~ trivial_carrier(boole_POSet(A))
& ~ empty_carrier(boole_POSet(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_waybel_7]) ).
fof(f_44_2,plain,
! [U_68] :
( ( complete_relstr(boole_POSet(U_68))
& with_infima_relstr(boole_POSet(U_68))
& with_suprema_relstr(boole_POSet(U_68))
& boolean_relstr(boole_POSet(U_68))
& complemented_relstr(boole_POSet(U_68))
& heyting_relstr(boole_POSet(U_68))
& distributive_relstr(boole_POSet(U_68))
& ~ v1_yellow_3(boole_POSet(U_68))
& join_complete_relstr(boole_POSet(U_68))
& up_complete_relstr(boole_POSet(U_68))
& bounded_relstr(boole_POSet(U_68))
& upper_bounded_relstr(boole_POSet(U_68))
& lower_bounded_relstr(boole_POSet(U_68))
& antisymmetric_relstr(boole_POSet(U_68))
& transitive_relstr(boole_POSet(U_68))
& reflexive_relstr(boole_POSet(U_68))
& strict_rel_str(boole_POSet(U_68))
& ~ trivial_carrier(boole_POSet(U_68))
& ~ empty_carrier(boole_POSet(U_68)) )
| empty(U_68) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
cnf(f_44_3,plain,
( ~ empty_carrier(boole_POSet(U_68))
| empty(U_68) ),
inference(clausify,[status(thm)],[f_44_2]) ).
cnf(f_44_4,plain,
( ~ trivial_carrier(boole_POSet(U_68))
| empty(U_68) ),
inference(clausify,[status(thm)],[f_44_2]) ).
cnf(f_44_5,plain,
( strict_rel_str(boole_POSet(U_68))
| empty(U_68) ),
inference(clausify,[status(thm)],[f_44_2]) ).
cnf(f_44_6,plain,
( reflexive_relstr(boole_POSet(U_68))
| empty(U_68) ),
inference(clausify,[status(thm)],[f_44_2]) ).
cnf(f_44_7,plain,
( transitive_relstr(boole_POSet(U_68))
| empty(U_68) ),
inference(clausify,[status(thm)],[f_44_2]) ).
cnf(f_44_8,plain,
( antisymmetric_relstr(boole_POSet(U_68))
| empty(U_68) ),
inference(clausify,[status(thm)],[f_44_2]) ).
cnf(f_44_9,plain,
( lower_bounded_relstr(boole_POSet(U_68))
| empty(U_68) ),
inference(clausify,[status(thm)],[f_44_2]) ).
cnf(f_44_10,plain,
( upper_bounded_relstr(boole_POSet(U_68))
| empty(U_68) ),
inference(clausify,[status(thm)],[f_44_2]) ).
cnf(f_44_11,plain,
( bounded_relstr(boole_POSet(U_68))
| empty(U_68) ),
inference(clausify,[status(thm)],[f_44_2]) ).
cnf(f_44_12,plain,
( up_complete_relstr(boole_POSet(U_68))
| empty(U_68) ),
inference(clausify,[status(thm)],[f_44_2]) ).
cnf(f_44_13,plain,
( join_complete_relstr(boole_POSet(U_68))
| empty(U_68) ),
inference(clausify,[status(thm)],[f_44_2]) ).
cnf(f_44_14,plain,
( ~ v1_yellow_3(boole_POSet(U_68))
| empty(U_68) ),
inference(clausify,[status(thm)],[f_44_2]) ).
cnf(f_44_15,plain,
( distributive_relstr(boole_POSet(U_68))
| empty(U_68) ),
inference(clausify,[status(thm)],[f_44_2]) ).
cnf(f_44_16,plain,
( heyting_relstr(boole_POSet(U_68))
| empty(U_68) ),
inference(clausify,[status(thm)],[f_44_2]) ).
cnf(f_44_17,plain,
( complemented_relstr(boole_POSet(U_68))
| empty(U_68) ),
inference(clausify,[status(thm)],[f_44_2]) ).
cnf(f_44_18,plain,
( boolean_relstr(boole_POSet(U_68))
| empty(U_68) ),
inference(clausify,[status(thm)],[f_44_2]) ).
cnf(f_44_19,plain,
( with_suprema_relstr(boole_POSet(U_68))
| empty(U_68) ),
inference(clausify,[status(thm)],[f_44_2]) ).
cnf(f_44_20,plain,
( with_infima_relstr(boole_POSet(U_68))
| empty(U_68) ),
inference(clausify,[status(thm)],[f_44_2]) ).
cnf(f_44_21,plain,
( complete_relstr(boole_POSet(U_68))
| empty(U_68) ),
inference(clausify,[status(thm)],[f_44_2]) ).
fof(f_45_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_45_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_45_1]) ).
cnf(f_45_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_45_1]) ).
fof(f_46_1,plain,
! [A,B] :
( ~ empty(cartesian_product2(A,B))
| empty(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc4_subset_1]) ).
fof(f_46_2,plain,
! [U_70,U_69] :
( ~ empty(cartesian_product2(U_70,U_69))
| empty(U_69)
| empty(U_70) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
cnf(f_46_3,plain,
( ~ empty(cartesian_product2(U_70,U_69))
| empty(U_69)
| empty(U_70) ),
inference(clausify,[status(thm)],[f_46_2]) ).
fof(f_47_1,plain,
! [A] :
( antisymmetric_relstr(boole_POSet(A))
& transitive_relstr(boole_POSet(A))
& reflexive_relstr(boole_POSet(A))
& strict_rel_str(boole_POSet(A))
& ~ empty_carrier(boole_POSet(A)) ),
inference(fof_nnf,[status(thm)],[fc7_yellow_1]) ).
fof(f_47_2,plain,
! [U_71] :
( antisymmetric_relstr(boole_POSet(U_71))
& transitive_relstr(boole_POSet(U_71))
& reflexive_relstr(boole_POSet(U_71))
& strict_rel_str(boole_POSet(U_71))
& ~ empty_carrier(boole_POSet(U_71)) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
( ! [U_76] : antisymmetric_relstr(boole_POSet(U_76))
& ! [U_75] : transitive_relstr(boole_POSet(U_75))
& ! [U_74] : reflexive_relstr(boole_POSet(U_74))
& ! [U_73] : strict_rel_str(boole_POSet(U_73))
& ! [U_72] : ~ empty_carrier(boole_POSet(U_72)) ),
inference(miniscope,[status(thm)],[f_47_2]) ).
cnf(f_47_4,plain,
~ empty_carrier(boole_POSet(U_72)),
inference(clausify,[status(thm)],[f_47_3]) ).
cnf(f_47_5,plain,
strict_rel_str(boole_POSet(U_73)),
inference(clausify,[status(thm)],[f_47_3]) ).
cnf(f_47_6,plain,
reflexive_relstr(boole_POSet(U_74)),
inference(clausify,[status(thm)],[f_47_3]) ).
cnf(f_47_7,plain,
transitive_relstr(boole_POSet(U_75)),
inference(clausify,[status(thm)],[f_47_3]) ).
cnf(f_47_8,plain,
antisymmetric_relstr(boole_POSet(U_76)),
inference(clausify,[status(thm)],[f_47_3]) ).
fof(f_48_1,plain,
! [A] :
( complete_relstr(boole_POSet(A))
& with_infima_relstr(boole_POSet(A))
& with_suprema_relstr(boole_POSet(A))
& bounded_relstr(boole_POSet(A))
& upper_bounded_relstr(boole_POSet(A))
& lower_bounded_relstr(boole_POSet(A))
& antisymmetric_relstr(boole_POSet(A))
& transitive_relstr(boole_POSet(A))
& reflexive_relstr(boole_POSet(A))
& strict_rel_str(boole_POSet(A))
& ~ empty_carrier(boole_POSet(A)) ),
inference(fof_nnf,[status(thm)],[fc8_yellow_1]) ).
fof(f_48_2,plain,
! [U_77] :
( complete_relstr(boole_POSet(U_77))
& with_infima_relstr(boole_POSet(U_77))
& with_suprema_relstr(boole_POSet(U_77))
& bounded_relstr(boole_POSet(U_77))
& upper_bounded_relstr(boole_POSet(U_77))
& lower_bounded_relstr(boole_POSet(U_77))
& antisymmetric_relstr(boole_POSet(U_77))
& transitive_relstr(boole_POSet(U_77))
& reflexive_relstr(boole_POSet(U_77))
& strict_rel_str(boole_POSet(U_77))
& ~ empty_carrier(boole_POSet(U_77)) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
( ! [U_88] : complete_relstr(boole_POSet(U_88))
& ! [U_87] : with_infima_relstr(boole_POSet(U_87))
& ! [U_86] : with_suprema_relstr(boole_POSet(U_86))
& ! [U_85] : bounded_relstr(boole_POSet(U_85))
& ! [U_84] : upper_bounded_relstr(boole_POSet(U_84))
& ! [U_83] : lower_bounded_relstr(boole_POSet(U_83))
& ! [U_82] : antisymmetric_relstr(boole_POSet(U_82))
& ! [U_81] : transitive_relstr(boole_POSet(U_81))
& ! [U_80] : reflexive_relstr(boole_POSet(U_80))
& ! [U_79] : strict_rel_str(boole_POSet(U_79))
& ! [U_78] : ~ empty_carrier(boole_POSet(U_78)) ),
inference(miniscope,[status(thm)],[f_48_2]) ).
cnf(f_48_4,plain,
~ empty_carrier(boole_POSet(U_78)),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_5,plain,
strict_rel_str(boole_POSet(U_79)),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_6,plain,
reflexive_relstr(boole_POSet(U_80)),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_7,plain,
transitive_relstr(boole_POSet(U_81)),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_8,plain,
antisymmetric_relstr(boole_POSet(U_82)),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_9,plain,
lower_bounded_relstr(boole_POSet(U_83)),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_10,plain,
upper_bounded_relstr(boole_POSet(U_84)),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_11,plain,
bounded_relstr(boole_POSet(U_85)),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_12,plain,
with_suprema_relstr(boole_POSet(U_86)),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_13,plain,
with_infima_relstr(boole_POSet(U_87)),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_14,plain,
complete_relstr(boole_POSet(U_88)),
inference(clausify,[status(thm)],[f_48_3]) ).
fof(f_49_1,plain,
! [A] :
( complete_relstr(boole_POSet(A))
& with_infima_relstr(boole_POSet(A))
& with_suprema_relstr(boole_POSet(A))
& ~ v1_yellow_3(boole_POSet(A))
& join_complete_relstr(boole_POSet(A))
& up_complete_relstr(boole_POSet(A))
& directed_relstr(boole_POSet(A))
& bounded_relstr(boole_POSet(A))
& upper_bounded_relstr(boole_POSet(A))
& lower_bounded_relstr(boole_POSet(A))
& antisymmetric_relstr(boole_POSet(A))
& transitive_relstr(boole_POSet(A))
& reflexive_relstr(boole_POSet(A))
& strict_rel_str(boole_POSet(A))
& ~ empty_carrier(boole_POSet(A)) ),
inference(fof_nnf,[status(thm)],[fc8_yellow_6]) ).
fof(f_49_2,plain,
! [U_89] :
( complete_relstr(boole_POSet(U_89))
& with_infima_relstr(boole_POSet(U_89))
& with_suprema_relstr(boole_POSet(U_89))
& ~ v1_yellow_3(boole_POSet(U_89))
& join_complete_relstr(boole_POSet(U_89))
& up_complete_relstr(boole_POSet(U_89))
& directed_relstr(boole_POSet(U_89))
& bounded_relstr(boole_POSet(U_89))
& upper_bounded_relstr(boole_POSet(U_89))
& lower_bounded_relstr(boole_POSet(U_89))
& antisymmetric_relstr(boole_POSet(U_89))
& transitive_relstr(boole_POSet(U_89))
& reflexive_relstr(boole_POSet(U_89))
& strict_rel_str(boole_POSet(U_89))
& ~ empty_carrier(boole_POSet(U_89)) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
( ! [U_104] : complete_relstr(boole_POSet(U_104))
& ! [U_103] : with_infima_relstr(boole_POSet(U_103))
& ! [U_102] : with_suprema_relstr(boole_POSet(U_102))
& ! [U_101] : ~ v1_yellow_3(boole_POSet(U_101))
& ! [U_100] : join_complete_relstr(boole_POSet(U_100))
& ! [U_99] : up_complete_relstr(boole_POSet(U_99))
& ! [U_98] : directed_relstr(boole_POSet(U_98))
& ! [U_97] : bounded_relstr(boole_POSet(U_97))
& ! [U_96] : upper_bounded_relstr(boole_POSet(U_96))
& ! [U_95] : lower_bounded_relstr(boole_POSet(U_95))
& ! [U_94] : antisymmetric_relstr(boole_POSet(U_94))
& ! [U_93] : transitive_relstr(boole_POSet(U_93))
& ! [U_92] : reflexive_relstr(boole_POSet(U_92))
& ! [U_91] : strict_rel_str(boole_POSet(U_91))
& ! [U_90] : ~ empty_carrier(boole_POSet(U_90)) ),
inference(miniscope,[status(thm)],[f_49_2]) ).
cnf(f_49_4,plain,
~ empty_carrier(boole_POSet(U_90)),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_5,plain,
strict_rel_str(boole_POSet(U_91)),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_6,plain,
reflexive_relstr(boole_POSet(U_92)),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_7,plain,
transitive_relstr(boole_POSet(U_93)),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_8,plain,
antisymmetric_relstr(boole_POSet(U_94)),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_9,plain,
lower_bounded_relstr(boole_POSet(U_95)),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_10,plain,
upper_bounded_relstr(boole_POSet(U_96)),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_11,plain,
bounded_relstr(boole_POSet(U_97)),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_12,plain,
directed_relstr(boole_POSet(U_98)),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_13,plain,
up_complete_relstr(boole_POSet(U_99)),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_14,plain,
join_complete_relstr(boole_POSet(U_100)),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_15,plain,
~ v1_yellow_3(boole_POSet(U_101)),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_16,plain,
with_suprema_relstr(boole_POSet(U_102)),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_17,plain,
with_infima_relstr(boole_POSet(U_103)),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_18,plain,
complete_relstr(boole_POSet(U_104)),
inference(clausify,[status(thm)],[f_49_3]) ).
fof(f_50_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_50_2,plain,
! [U_108,U_107] :
( ! [U_106,U_105] :
( ( U_107 = U_105
& U_108 = U_106 )
| rel_str_of(U_108,U_107) != rel_str_of(U_106,U_105) )
| ~ relation_of2(U_107,U_108,U_108) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
cnf(f_50_3,plain,
( U_108 = U_106
| rel_str_of(U_108,U_107) != rel_str_of(U_106,U_105)
| ~ relation_of2(U_107,U_108,U_108) ),
inference(clausify,[status(thm)],[f_50_2]) ).
cnf(f_50_4,plain,
( U_107 = U_105
| rel_str_of(U_108,U_107) != rel_str_of(U_106,U_105)
| ~ relation_of2(U_107,U_108,U_108) ),
inference(clausify,[status(thm)],[f_50_2]) ).
fof(f_51_1,plain,
! [A] :
( ? [B] :
( upper_relstr_subset(B,A)
& filtered_subset(B,A)
& ~ empty(B)
& element(B,powerset(the_carrier(A))) )
| ~ rel_str(A)
| ~ transitive_relstr(A)
| ~ reflexive_relstr(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[rc10_waybel_0]) ).
fof(f_51_2,plain,
! [U_110] :
( ? [U_109] :
( upper_relstr_subset(U_109,U_110)
& filtered_subset(U_109,U_110)
& ~ empty(U_109)
& element(U_109,powerset(the_carrier(U_110))) )
| ~ rel_str(U_110)
| ~ transitive_relstr(U_110)
| ~ reflexive_relstr(U_110)
| empty_carrier(U_110) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
! [U_110] :
( ( upper_relstr_subset(sK6(U_110),U_110)
& filtered_subset(sK6(U_110),U_110)
& ~ empty(sK6(U_110))
& element(sK6(U_110),powerset(the_carrier(U_110))) )
| ~ rel_str(U_110)
| ~ transitive_relstr(U_110)
| ~ reflexive_relstr(U_110)
| empty_carrier(U_110) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_109,sK6(U_110))],[f_51_2]) ).
cnf(f_51_4,plain,
( element(sK6(U_110),powerset(the_carrier(U_110)))
| ~ rel_str(U_110)
| ~ transitive_relstr(U_110)
| ~ reflexive_relstr(U_110)
| empty_carrier(U_110) ),
inference(clausify,[status(thm)],[f_51_3]) ).
cnf(f_51_5,plain,
( ~ empty(sK6(U_110))
| ~ rel_str(U_110)
| ~ transitive_relstr(U_110)
| ~ reflexive_relstr(U_110)
| empty_carrier(U_110) ),
inference(clausify,[status(thm)],[f_51_3]) ).
cnf(f_51_6,plain,
( filtered_subset(sK6(U_110),U_110)
| ~ rel_str(U_110)
| ~ transitive_relstr(U_110)
| ~ reflexive_relstr(U_110)
| empty_carrier(U_110) ),
inference(clausify,[status(thm)],[f_51_3]) ).
cnf(f_51_7,plain,
( upper_relstr_subset(sK6(U_110),U_110)
| ~ rel_str(U_110)
| ~ transitive_relstr(U_110)
| ~ reflexive_relstr(U_110)
| empty_carrier(U_110) ),
inference(clausify,[status(thm)],[f_51_3]) ).
fof(f_52_1,plain,
? [A] :
( connected_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A)
& rel_str(A) ),
inference(fof_nnf,[status(thm)],[rc12_waybel_0]) ).
fof(f_52_2,plain,
? [U_111] :
( connected_relstr(U_111)
& antisymmetric_relstr(U_111)
& transitive_relstr(U_111)
& reflexive_relstr(U_111)
& ~ empty_carrier(U_111)
& rel_str(U_111) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
( connected_relstr(sK7)
& antisymmetric_relstr(sK7)
& transitive_relstr(sK7)
& reflexive_relstr(sK7)
& ~ empty_carrier(sK7)
& rel_str(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_111,sK7)],[f_52_2]) ).
cnf(f_52_4,plain,
rel_str(sK7),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_5,plain,
~ empty_carrier(sK7),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_6,plain,
reflexive_relstr(sK7),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_7,plain,
transitive_relstr(sK7),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_8,plain,
antisymmetric_relstr(sK7),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_9,plain,
connected_relstr(sK7),
inference(clausify,[status(thm)],[f_52_3]) ).
fof(f_53_1,plain,
? [A] :
( join_complete_relstr(A)
& up_complete_relstr(A)
& bounded_relstr(A)
& upper_bounded_relstr(A)
& lower_bounded_relstr(A)
& complete_relstr(A)
& with_infima_relstr(A)
& with_suprema_relstr(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)],[rc13_waybel_0]) ).
fof(f_53_2,plain,
? [U_112] :
( join_complete_relstr(U_112)
& up_complete_relstr(U_112)
& bounded_relstr(U_112)
& upper_bounded_relstr(U_112)
& lower_bounded_relstr(U_112)
& complete_relstr(U_112)
& with_infima_relstr(U_112)
& with_suprema_relstr(U_112)
& antisymmetric_relstr(U_112)
& transitive_relstr(U_112)
& reflexive_relstr(U_112)
& strict_rel_str(U_112)
& ~ empty_carrier(U_112)
& rel_str(U_112) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
( join_complete_relstr(sK8)
& up_complete_relstr(sK8)
& bounded_relstr(sK8)
& upper_bounded_relstr(sK8)
& lower_bounded_relstr(sK8)
& complete_relstr(sK8)
& with_infima_relstr(sK8)
& with_suprema_relstr(sK8)
& antisymmetric_relstr(sK8)
& transitive_relstr(sK8)
& reflexive_relstr(sK8)
& strict_rel_str(sK8)
& ~ empty_carrier(sK8)
& rel_str(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_112,sK8)],[f_53_2]) ).
cnf(f_53_4,plain,
rel_str(sK8),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_5,plain,
~ empty_carrier(sK8),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_6,plain,
strict_rel_str(sK8),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_7,plain,
reflexive_relstr(sK8),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_8,plain,
transitive_relstr(sK8),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_9,plain,
antisymmetric_relstr(sK8),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_10,plain,
with_suprema_relstr(sK8),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_11,plain,
with_infima_relstr(sK8),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_12,plain,
complete_relstr(sK8),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_13,plain,
lower_bounded_relstr(sK8),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_14,plain,
upper_bounded_relstr(sK8),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_15,plain,
bounded_relstr(sK8),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_16,plain,
up_complete_relstr(sK8),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_17,plain,
join_complete_relstr(sK8),
inference(clausify,[status(thm)],[f_53_3]) ).
fof(f_54_1,plain,
? [A] :
( finite(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_finset_1]) ).
fof(f_54_2,plain,
? [U_113] :
( finite(U_113)
& ~ empty(U_113) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
( finite(sK9)
& ~ empty(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_113,sK9)],[f_54_2]) ).
cnf(f_54_4,plain,
~ empty(sK9),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_5,plain,
finite(sK9),
inference(clausify,[status(thm)],[f_54_3]) ).
fof(f_55_1,plain,
? [A] :
( complete_relstr(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)],[rc1_lattice3]) ).
fof(f_55_2,plain,
? [U_114] :
( complete_relstr(U_114)
& antisymmetric_relstr(U_114)
& transitive_relstr(U_114)
& reflexive_relstr(U_114)
& strict_rel_str(U_114)
& ~ empty_carrier(U_114)
& rel_str(U_114) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
( complete_relstr(sK10)
& antisymmetric_relstr(sK10)
& transitive_relstr(sK10)
& reflexive_relstr(sK10)
& strict_rel_str(sK10)
& ~ empty_carrier(sK10)
& rel_str(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_114,sK10)],[f_55_2]) ).
cnf(f_55_4,plain,
rel_str(sK10),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_5,plain,
~ empty_carrier(sK10),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_6,plain,
strict_rel_str(sK10),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_7,plain,
reflexive_relstr(sK10),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_8,plain,
transitive_relstr(sK10),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_9,plain,
antisymmetric_relstr(sK10),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_10,plain,
complete_relstr(sK10),
inference(clausify,[status(thm)],[f_55_3]) ).
fof(f_56_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_56_2,plain,
? [U_115] :
( relation(U_115)
& empty(U_115) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
( relation(sK11)
& empty(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_115,sK11)],[f_56_2]) ).
cnf(f_56_4,plain,
empty(sK11),
inference(clausify,[status(thm)],[f_56_3]) ).
cnf(f_56_5,plain,
relation(sK11),
inference(clausify,[status(thm)],[f_56_3]) ).
fof(f_57_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_57_2,plain,
! [U_117] :
( ? [U_116] :
( ~ empty(U_116)
& element(U_116,powerset(U_117)) )
| empty(U_117) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
! [U_117] :
( ( ~ empty(sK12(U_117))
& element(sK12(U_117),powerset(U_117)) )
| empty(U_117) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_116,sK12(U_117))],[f_57_2]) ).
cnf(f_57_4,plain,
( element(sK12(U_117),powerset(U_117))
| empty(U_117) ),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_5,plain,
( ~ empty(sK12(U_117))
| empty(U_117) ),
inference(clausify,[status(thm)],[f_57_3]) ).
fof(f_58_1,plain,
? [A] :
( with_infima_relstr(A)
& with_suprema_relstr(A)
& boolean_relstr(A)
& complemented_relstr(A)
& heyting_relstr(A)
& distributive_relstr(A)
& ~ v1_yellow_3(A)
& bounded_relstr(A)
& upper_bounded_relstr(A)
& lower_bounded_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& strict_rel_str(A)
& ~ trivial_carrier(A)
& ~ empty_carrier(A)
& rel_str(A) ),
inference(fof_nnf,[status(thm)],[rc1_waybel_7]) ).
fof(f_58_2,plain,
? [U_118] :
( with_infima_relstr(U_118)
& with_suprema_relstr(U_118)
& boolean_relstr(U_118)
& complemented_relstr(U_118)
& heyting_relstr(U_118)
& distributive_relstr(U_118)
& ~ v1_yellow_3(U_118)
& bounded_relstr(U_118)
& upper_bounded_relstr(U_118)
& lower_bounded_relstr(U_118)
& antisymmetric_relstr(U_118)
& transitive_relstr(U_118)
& reflexive_relstr(U_118)
& strict_rel_str(U_118)
& ~ trivial_carrier(U_118)
& ~ empty_carrier(U_118)
& rel_str(U_118) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
( with_infima_relstr(sK13)
& with_suprema_relstr(sK13)
& boolean_relstr(sK13)
& complemented_relstr(sK13)
& heyting_relstr(sK13)
& distributive_relstr(sK13)
& ~ v1_yellow_3(sK13)
& bounded_relstr(sK13)
& upper_bounded_relstr(sK13)
& lower_bounded_relstr(sK13)
& antisymmetric_relstr(sK13)
& transitive_relstr(sK13)
& reflexive_relstr(sK13)
& strict_rel_str(sK13)
& ~ trivial_carrier(sK13)
& ~ empty_carrier(sK13)
& rel_str(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_118,sK13)],[f_58_2]) ).
cnf(f_58_4,plain,
rel_str(sK13),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_5,plain,
~ empty_carrier(sK13),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_6,plain,
~ trivial_carrier(sK13),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_7,plain,
strict_rel_str(sK13),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_8,plain,
reflexive_relstr(sK13),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_9,plain,
transitive_relstr(sK13),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_10,plain,
antisymmetric_relstr(sK13),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_11,plain,
lower_bounded_relstr(sK13),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_12,plain,
upper_bounded_relstr(sK13),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_13,plain,
bounded_relstr(sK13),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_14,plain,
~ v1_yellow_3(sK13),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_15,plain,
distributive_relstr(sK13),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_16,plain,
heyting_relstr(sK13),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_17,plain,
complemented_relstr(sK13),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_18,plain,
boolean_relstr(sK13),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_19,plain,
with_suprema_relstr(sK13),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_20,plain,
with_infima_relstr(sK13),
inference(clausify,[status(thm)],[f_58_3]) ).
fof(f_59_1,plain,
? [A] :
( trivial_carrier(A)
& complete_relstr(A)
& with_infima_relstr(A)
& with_suprema_relstr(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)],[rc1_yellow_0]) ).
fof(f_59_2,plain,
? [U_119] :
( trivial_carrier(U_119)
& complete_relstr(U_119)
& with_infima_relstr(U_119)
& with_suprema_relstr(U_119)
& antisymmetric_relstr(U_119)
& transitive_relstr(U_119)
& reflexive_relstr(U_119)
& strict_rel_str(U_119)
& ~ empty_carrier(U_119)
& rel_str(U_119) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
( trivial_carrier(sK14)
& complete_relstr(sK14)
& with_infima_relstr(sK14)
& with_suprema_relstr(sK14)
& antisymmetric_relstr(sK14)
& transitive_relstr(sK14)
& reflexive_relstr(sK14)
& strict_rel_str(sK14)
& ~ empty_carrier(sK14)
& rel_str(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_119,sK14)],[f_59_2]) ).
cnf(f_59_4,plain,
rel_str(sK14),
inference(clausify,[status(thm)],[f_59_3]) ).
cnf(f_59_5,plain,
~ empty_carrier(sK14),
inference(clausify,[status(thm)],[f_59_3]) ).
cnf(f_59_6,plain,
strict_rel_str(sK14),
inference(clausify,[status(thm)],[f_59_3]) ).
cnf(f_59_7,plain,
reflexive_relstr(sK14),
inference(clausify,[status(thm)],[f_59_3]) ).
cnf(f_59_8,plain,
transitive_relstr(sK14),
inference(clausify,[status(thm)],[f_59_3]) ).
cnf(f_59_9,plain,
antisymmetric_relstr(sK14),
inference(clausify,[status(thm)],[f_59_3]) ).
cnf(f_59_10,plain,
with_suprema_relstr(sK14),
inference(clausify,[status(thm)],[f_59_3]) ).
cnf(f_59_11,plain,
with_infima_relstr(sK14),
inference(clausify,[status(thm)],[f_59_3]) ).
cnf(f_59_12,plain,
complete_relstr(sK14),
inference(clausify,[status(thm)],[f_59_3]) ).
cnf(f_59_13,plain,
trivial_carrier(sK14),
inference(clausify,[status(thm)],[f_59_3]) ).
fof(f_60_1,plain,
? [A] :
( complete_relstr(A)
& with_infima_relstr(A)
& with_suprema_relstr(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_lattice3]) ).
fof(f_60_2,plain,
? [U_120] :
( complete_relstr(U_120)
& with_infima_relstr(U_120)
& with_suprema_relstr(U_120)
& antisymmetric_relstr(U_120)
& transitive_relstr(U_120)
& reflexive_relstr(U_120)
& strict_rel_str(U_120)
& ~ empty_carrier(U_120)
& rel_str(U_120) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
( complete_relstr(sK15)
& with_infima_relstr(sK15)
& with_suprema_relstr(sK15)
& antisymmetric_relstr(sK15)
& transitive_relstr(sK15)
& reflexive_relstr(sK15)
& strict_rel_str(sK15)
& ~ empty_carrier(sK15)
& rel_str(sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_120,sK15)],[f_60_2]) ).
cnf(f_60_4,plain,
rel_str(sK15),
inference(clausify,[status(thm)],[f_60_3]) ).
cnf(f_60_5,plain,
~ empty_carrier(sK15),
inference(clausify,[status(thm)],[f_60_3]) ).
cnf(f_60_6,plain,
strict_rel_str(sK15),
inference(clausify,[status(thm)],[f_60_3]) ).
cnf(f_60_7,plain,
reflexive_relstr(sK15),
inference(clausify,[status(thm)],[f_60_3]) ).
cnf(f_60_8,plain,
transitive_relstr(sK15),
inference(clausify,[status(thm)],[f_60_3]) ).
cnf(f_60_9,plain,
antisymmetric_relstr(sK15),
inference(clausify,[status(thm)],[f_60_3]) ).
cnf(f_60_10,plain,
with_suprema_relstr(sK15),
inference(clausify,[status(thm)],[f_60_3]) ).
cnf(f_60_11,plain,
with_infima_relstr(sK15),
inference(clausify,[status(thm)],[f_60_3]) ).
cnf(f_60_12,plain,
complete_relstr(sK15),
inference(clausify,[status(thm)],[f_60_3]) ).
fof(f_61_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_61_2,plain,
? [U_121] :
( relation(U_121)
& ~ empty(U_121) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
fof(f_61_3,plain,
( relation(sK16)
& ~ empty(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_121,sK16)],[f_61_2]) ).
cnf(f_61_4,plain,
~ empty(sK16),
inference(clausify,[status(thm)],[f_61_3]) ).
cnf(f_61_5,plain,
relation(sK16),
inference(clausify,[status(thm)],[f_61_3]) ).
fof(f_62_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_62_2,plain,
! [U_123] :
? [U_122] :
( empty(U_122)
& element(U_122,powerset(U_123)) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
! [U_123] :
( empty(sK17(U_123))
& element(sK17(U_123),powerset(U_123)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_122,sK17(U_123))],[f_62_2]) ).
cnf(f_62_4,plain,
element(sK17(U_123),powerset(U_123)),
inference(clausify,[status(thm)],[f_62_3]) ).
cnf(f_62_5,plain,
empty(sK17(U_123)),
inference(clausify,[status(thm)],[f_62_3]) ).
fof(f_63_1,plain,
! [A] :
? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[rc2_waybel_7]) ).
fof(f_63_2,plain,
! [U_125] :
? [U_124] :
( finite(U_124)
& ~ empty(U_124)
& element(U_124,powerset(powerset(U_125))) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
fof(f_63_3,plain,
! [U_125] :
( finite(sK18(U_125))
& ~ empty(sK18(U_125))
& element(sK18(U_125),powerset(powerset(U_125))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_124,sK18(U_125))],[f_63_2]) ).
cnf(f_63_4,plain,
element(sK18(U_125),powerset(powerset(U_125))),
inference(clausify,[status(thm)],[f_63_3]) ).
cnf(f_63_5,plain,
~ empty(sK18(U_125)),
inference(clausify,[status(thm)],[f_63_3]) ).
cnf(f_63_6,plain,
finite(sK18(U_125)),
inference(clausify,[status(thm)],[f_63_3]) ).
fof(f_64_1,plain,
? [A] :
( bounded_relstr(A)
& upper_bounded_relstr(A)
& lower_bounded_relstr(A)
& complete_relstr(A)
& with_infima_relstr(A)
& with_suprema_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A)
& rel_str(A) ),
inference(fof_nnf,[status(thm)],[rc2_yellow_0]) ).
fof(f_64_2,plain,
? [U_126] :
( bounded_relstr(U_126)
& upper_bounded_relstr(U_126)
& lower_bounded_relstr(U_126)
& complete_relstr(U_126)
& with_infima_relstr(U_126)
& with_suprema_relstr(U_126)
& antisymmetric_relstr(U_126)
& transitive_relstr(U_126)
& reflexive_relstr(U_126)
& ~ empty_carrier(U_126)
& rel_str(U_126) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
fof(f_64_3,plain,
( bounded_relstr(sK19)
& upper_bounded_relstr(sK19)
& lower_bounded_relstr(sK19)
& complete_relstr(sK19)
& with_infima_relstr(sK19)
& with_suprema_relstr(sK19)
& antisymmetric_relstr(sK19)
& transitive_relstr(sK19)
& reflexive_relstr(sK19)
& ~ empty_carrier(sK19)
& rel_str(sK19) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_126,sK19)],[f_64_2]) ).
cnf(f_64_4,plain,
rel_str(sK19),
inference(clausify,[status(thm)],[f_64_3]) ).
cnf(f_64_5,plain,
~ empty_carrier(sK19),
inference(clausify,[status(thm)],[f_64_3]) ).
cnf(f_64_6,plain,
reflexive_relstr(sK19),
inference(clausify,[status(thm)],[f_64_3]) ).
cnf(f_64_7,plain,
transitive_relstr(sK19),
inference(clausify,[status(thm)],[f_64_3]) ).
cnf(f_64_8,plain,
antisymmetric_relstr(sK19),
inference(clausify,[status(thm)],[f_64_3]) ).
cnf(f_64_9,plain,
with_suprema_relstr(sK19),
inference(clausify,[status(thm)],[f_64_3]) ).
cnf(f_64_10,plain,
with_infima_relstr(sK19),
inference(clausify,[status(thm)],[f_64_3]) ).
cnf(f_64_11,plain,
complete_relstr(sK19),
inference(clausify,[status(thm)],[f_64_3]) ).
cnf(f_64_12,plain,
lower_bounded_relstr(sK19),
inference(clausify,[status(thm)],[f_64_3]) ).
cnf(f_64_13,plain,
upper_bounded_relstr(sK19),
inference(clausify,[status(thm)],[f_64_3]) ).
cnf(f_64_14,plain,
bounded_relstr(sK19),
inference(clausify,[status(thm)],[f_64_3]) ).
fof(f_65_1,plain,
! [A] :
( ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc3_finset_1]) ).
fof(f_65_2,plain,
! [U_128] :
( ? [U_127] :
( finite(U_127)
& ~ empty(U_127)
& element(U_127,powerset(U_128)) )
| empty(U_128) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
fof(f_65_3,plain,
! [U_128] :
( ( finite(sK20(U_128))
& ~ empty(sK20(U_128))
& element(sK20(U_128),powerset(U_128)) )
| empty(U_128) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_127,sK20(U_128))],[f_65_2]) ).
cnf(f_65_4,plain,
( element(sK20(U_128),powerset(U_128))
| empty(U_128) ),
inference(clausify,[status(thm)],[f_65_3]) ).
cnf(f_65_5,plain,
( ~ empty(sK20(U_128))
| empty(U_128) ),
inference(clausify,[status(thm)],[f_65_3]) ).
cnf(f_65_6,plain,
( finite(sK20(U_128))
| empty(U_128) ),
inference(clausify,[status(thm)],[f_65_3]) ).
fof(f_66_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_66_2,plain,
? [U_129] :
( relation_empty_yielding(U_129)
& relation(U_129) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
fof(f_66_3,plain,
( relation_empty_yielding(sK21)
& relation(sK21) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_129,sK21)],[f_66_2]) ).
cnf(f_66_4,plain,
relation(sK21),
inference(clausify,[status(thm)],[f_66_3]) ).
cnf(f_66_5,plain,
relation_empty_yielding(sK21),
inference(clausify,[status(thm)],[f_66_3]) ).
fof(f_67_1,plain,
? [A] :
( ~ empty_carrier(A)
& one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[rc3_struct_0]) ).
fof(f_67_2,plain,
? [U_130] :
( ~ empty_carrier(U_130)
& one_sorted_str(U_130) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
fof(f_67_3,plain,
( ~ empty_carrier(sK22)
& one_sorted_str(sK22) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_130,sK22)],[f_67_2]) ).
cnf(f_67_4,plain,
one_sorted_str(sK22),
inference(clausify,[status(thm)],[f_67_3]) ).
cnf(f_67_5,plain,
~ empty_carrier(sK22),
inference(clausify,[status(thm)],[f_67_3]) ).
fof(f_68_1,plain,
! [A] :
( ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(powerset(the_carrier(A)))) )
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[rc3_waybel_7]) ).
fof(f_68_2,plain,
! [U_132] :
( ? [U_131] :
( finite(U_131)
& ~ empty(U_131)
& element(U_131,powerset(powerset(the_carrier(U_132)))) )
| ~ one_sorted_str(U_132) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
fof(f_68_3,plain,
! [U_132] :
( ( finite(sK23(U_132))
& ~ empty(sK23(U_132))
& element(sK23(U_132),powerset(powerset(the_carrier(U_132)))) )
| ~ one_sorted_str(U_132) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_131,sK23(U_132))],[f_68_2]) ).
cnf(f_68_4,plain,
( element(sK23(U_132),powerset(powerset(the_carrier(U_132))))
| ~ one_sorted_str(U_132) ),
inference(clausify,[status(thm)],[f_68_3]) ).
cnf(f_68_5,plain,
( ~ empty(sK23(U_132))
| ~ one_sorted_str(U_132) ),
inference(clausify,[status(thm)],[f_68_3]) ).
cnf(f_68_6,plain,
( finite(sK23(U_132))
| ~ one_sorted_str(U_132) ),
inference(clausify,[status(thm)],[f_68_3]) ).
fof(f_69_1,plain,
! [A] :
( ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc4_finset_1]) ).
fof(f_69_2,plain,
! [U_134] :
( ? [U_133] :
( finite(U_133)
& ~ empty(U_133)
& element(U_133,powerset(U_134)) )
| empty(U_134) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
fof(f_69_3,plain,
! [U_134] :
( ( finite(sK24(U_134))
& ~ empty(sK24(U_134))
& element(sK24(U_134),powerset(U_134)) )
| empty(U_134) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_133,sK24(U_134))],[f_69_2]) ).
cnf(f_69_4,plain,
( element(sK24(U_134),powerset(U_134))
| empty(U_134) ),
inference(clausify,[status(thm)],[f_69_3]) ).
cnf(f_69_5,plain,
( ~ empty(sK24(U_134))
| empty(U_134) ),
inference(clausify,[status(thm)],[f_69_3]) ).
cnf(f_69_6,plain,
( finite(sK24(U_134))
| empty(U_134) ),
inference(clausify,[status(thm)],[f_69_3]) ).
fof(f_70_1,plain,
! [A] :
( ? [B] :
( upper_relstr_subset(B,A)
& filtered_subset(B,A)
& proper_element(B,powerset(the_carrier(A)))
& ~ empty(B)
& element(B,powerset(the_carrier(A))) )
| ~ rel_str(A)
| ~ upper_bounded_relstr(A)
| ~ antisymmetric_relstr(A)
| ~ transitive_relstr(A)
| ~ reflexive_relstr(A)
| trivial_carrier(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[rc4_waybel_7]) ).
fof(f_70_2,plain,
! [U_136] :
( ? [U_135] :
( upper_relstr_subset(U_135,U_136)
& filtered_subset(U_135,U_136)
& proper_element(U_135,powerset(the_carrier(U_136)))
& ~ empty(U_135)
& element(U_135,powerset(the_carrier(U_136))) )
| ~ rel_str(U_136)
| ~ upper_bounded_relstr(U_136)
| ~ antisymmetric_relstr(U_136)
| ~ transitive_relstr(U_136)
| ~ reflexive_relstr(U_136)
| trivial_carrier(U_136)
| empty_carrier(U_136) ),
inference(variable_rename,[status(thm)],[f_70_1]) ).
fof(f_70_3,plain,
! [U_136] :
( ( upper_relstr_subset(sK25(U_136),U_136)
& filtered_subset(sK25(U_136),U_136)
& proper_element(sK25(U_136),powerset(the_carrier(U_136)))
& ~ empty(sK25(U_136))
& element(sK25(U_136),powerset(the_carrier(U_136))) )
| ~ rel_str(U_136)
| ~ upper_bounded_relstr(U_136)
| ~ antisymmetric_relstr(U_136)
| ~ transitive_relstr(U_136)
| ~ reflexive_relstr(U_136)
| trivial_carrier(U_136)
| empty_carrier(U_136) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_135,sK25(U_136))],[f_70_2]) ).
cnf(f_70_4,plain,
( element(sK25(U_136),powerset(the_carrier(U_136)))
| ~ rel_str(U_136)
| ~ upper_bounded_relstr(U_136)
| ~ antisymmetric_relstr(U_136)
| ~ transitive_relstr(U_136)
| ~ reflexive_relstr(U_136)
| trivial_carrier(U_136)
| empty_carrier(U_136) ),
inference(clausify,[status(thm)],[f_70_3]) ).
cnf(f_70_5,plain,
( ~ empty(sK25(U_136))
| ~ rel_str(U_136)
| ~ upper_bounded_relstr(U_136)
| ~ antisymmetric_relstr(U_136)
| ~ transitive_relstr(U_136)
| ~ reflexive_relstr(U_136)
| trivial_carrier(U_136)
| empty_carrier(U_136) ),
inference(clausify,[status(thm)],[f_70_3]) ).
cnf(f_70_6,plain,
( proper_element(sK25(U_136),powerset(the_carrier(U_136)))
| ~ rel_str(U_136)
| ~ upper_bounded_relstr(U_136)
| ~ antisymmetric_relstr(U_136)
| ~ transitive_relstr(U_136)
| ~ reflexive_relstr(U_136)
| trivial_carrier(U_136)
| empty_carrier(U_136) ),
inference(clausify,[status(thm)],[f_70_3]) ).
cnf(f_70_7,plain,
( filtered_subset(sK25(U_136),U_136)
| ~ rel_str(U_136)
| ~ upper_bounded_relstr(U_136)
| ~ antisymmetric_relstr(U_136)
| ~ transitive_relstr(U_136)
| ~ reflexive_relstr(U_136)
| trivial_carrier(U_136)
| empty_carrier(U_136) ),
inference(clausify,[status(thm)],[f_70_3]) ).
cnf(f_70_8,plain,
( upper_relstr_subset(sK25(U_136),U_136)
| ~ rel_str(U_136)
| ~ upper_bounded_relstr(U_136)
| ~ antisymmetric_relstr(U_136)
| ~ transitive_relstr(U_136)
| ~ reflexive_relstr(U_136)
| trivial_carrier(U_136)
| empty_carrier(U_136) ),
inference(clausify,[status(thm)],[f_70_3]) ).
fof(f_71_1,plain,
? [A] :
( directed_relstr(A)
& transitive_relstr(A)
& strict_rel_str(A)
& ~ empty_carrier(A)
& rel_str(A) ),
inference(fof_nnf,[status(thm)],[rc4_yellow_6]) ).
fof(f_71_2,plain,
? [U_137] :
( directed_relstr(U_137)
& transitive_relstr(U_137)
& strict_rel_str(U_137)
& ~ empty_carrier(U_137)
& rel_str(U_137) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
fof(f_71_3,plain,
( directed_relstr(sK26)
& transitive_relstr(sK26)
& strict_rel_str(sK26)
& ~ empty_carrier(sK26)
& rel_str(sK26) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_137,sK26)],[f_71_2]) ).
cnf(f_71_4,plain,
rel_str(sK26),
inference(clausify,[status(thm)],[f_71_3]) ).
cnf(f_71_5,plain,
~ empty_carrier(sK26),
inference(clausify,[status(thm)],[f_71_3]) ).
cnf(f_71_6,plain,
strict_rel_str(sK26),
inference(clausify,[status(thm)],[f_71_3]) ).
cnf(f_71_7,plain,
transitive_relstr(sK26),
inference(clausify,[status(thm)],[f_71_3]) ).
cnf(f_71_8,plain,
directed_relstr(sK26),
inference(clausify,[status(thm)],[f_71_3]) ).
fof(f_72_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_72_2,plain,
! [U_139] :
( ? [U_138] :
( ~ empty(U_138)
& element(U_138,powerset(the_carrier(U_139))) )
| ~ one_sorted_str(U_139)
| empty_carrier(U_139) ),
inference(variable_rename,[status(thm)],[f_72_1]) ).
fof(f_72_3,plain,
! [U_139] :
( ( ~ empty(sK27(U_139))
& element(sK27(U_139),powerset(the_carrier(U_139))) )
| ~ one_sorted_str(U_139)
| empty_carrier(U_139) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_138,sK27(U_139))],[f_72_2]) ).
cnf(f_72_4,plain,
( element(sK27(U_139),powerset(the_carrier(U_139)))
| ~ one_sorted_str(U_139)
| empty_carrier(U_139) ),
inference(clausify,[status(thm)],[f_72_3]) ).
cnf(f_72_5,plain,
( ~ empty(sK27(U_139))
| ~ one_sorted_str(U_139)
| empty_carrier(U_139) ),
inference(clausify,[status(thm)],[f_72_3]) ).
fof(f_73_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_73_2,plain,
! [U_142,U_141,U_140] :
( ( relation_of2_as_subset(U_140,U_142,U_141)
| ~ relation_of2(U_140,U_142,U_141) )
& ( relation_of2(U_140,U_142,U_141)
| ~ relation_of2_as_subset(U_140,U_142,U_141) ) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
fof(f_73_3,plain,
( ! [U_148,U_146,U_144] :
( relation_of2_as_subset(U_144,U_148,U_146)
| ~ relation_of2(U_144,U_148,U_146) )
& ! [U_147,U_145,U_143] :
( relation_of2(U_143,U_147,U_145)
| ~ relation_of2_as_subset(U_143,U_147,U_145) ) ),
inference(miniscope,[status(thm)],[f_73_2]) ).
cnf(f_73_4,plain,
( relation_of2(U_143,U_147,U_145)
| ~ relation_of2_as_subset(U_143,U_147,U_145) ),
inference(clausify,[status(thm)],[f_73_3]) ).
cnf(f_73_5,plain,
( relation_of2_as_subset(U_144,U_148,U_146)
| ~ relation_of2(U_144,U_148,U_146) ),
inference(clausify,[status(thm)],[f_73_3]) ).
fof(f_74_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_74_2,plain,
! [U_150,U_149] : subset(U_150,U_150),
inference(variable_rename,[status(thm)],[f_74_1]) ).
fof(f_74_3,plain,
! [U_150] : subset(U_150,U_150),
inference(miniscope,[status(thm)],[f_74_2]) ).
cnf(f_74_4,plain,
subset(U_150,U_150),
inference(clausify,[status(thm)],[f_74_3]) ).
fof(f_75_1,plain,
! [A] : bottom_of_relstr(boole_POSet(A)) = empty_set,
inference(fof_nnf,[status(thm)],[t18_yellow_1]) ).
fof(f_75_2,plain,
! [U_151] : bottom_of_relstr(boole_POSet(U_151)) = empty_set,
inference(variable_rename,[status(thm)],[f_75_1]) ).
cnf(f_75_3,plain,
bottom_of_relstr(boole_POSet(U_151)) = empty_set,
inference(clausify,[status(thm)],[f_75_2]) ).
fof(f_76_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_76_2,plain,
! [U_153,U_152] :
( element(U_153,U_152)
| ~ in(U_153,U_152) ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
cnf(f_76_3,plain,
( element(U_153,U_152)
| ~ in(U_153,U_152) ),
inference(clausify,[status(thm)],[f_76_2]) ).
fof(f_77_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_77_2,plain,
! [U_155,U_154] :
( in(U_155,U_154)
| empty(U_154)
| ~ element(U_155,U_154) ),
inference(variable_rename,[status(thm)],[f_77_1]) ).
cnf(f_77_3,plain,
( in(U_155,U_154)
| empty(U_154)
| ~ element(U_155,U_154) ),
inference(clausify,[status(thm)],[f_77_2]) ).
fof(f_78_1,negated_conjecture,
~ ! [A] :
( ~ empty(A)
=> ! [B] :
( ( element(B,powerset(the_carrier(boole_POSet(A))))
& proper_element(B,powerset(the_carrier(boole_POSet(A))))
& upper_relstr_subset(B,boole_POSet(A))
& filtered_subset(B,boole_POSet(A))
& ~ empty(B) )
=> ! [C] :
~ ( empty(C)
& in(C,B) ) ) ),
inference(negate,[status(cth)],[t2_yellow19]) ).
fof(f_78_2,negated_conjecture,
? [A] :
( ? [B] :
( ? [C] :
( empty(C)
& in(C,B) )
& element(B,powerset(the_carrier(boole_POSet(A))))
& proper_element(B,powerset(the_carrier(boole_POSet(A))))
& upper_relstr_subset(B,boole_POSet(A))
& filtered_subset(B,boole_POSet(A))
& ~ empty(B) )
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[f_78_1]) ).
fof(f_78_3,negated_conjecture,
? [U_158] :
( ? [U_157] :
( ? [U_156] :
( empty(U_156)
& in(U_156,U_157) )
& element(U_157,powerset(the_carrier(boole_POSet(U_158))))
& proper_element(U_157,powerset(the_carrier(boole_POSet(U_158))))
& upper_relstr_subset(U_157,boole_POSet(U_158))
& filtered_subset(U_157,boole_POSet(U_158))
& ~ empty(U_157) )
& ~ empty(U_158) ),
inference(variable_rename,[status(thm)],[f_78_2]) ).
fof(f_78_4,negated_conjecture,
( ? [U_157] :
( ? [U_156] :
( empty(U_156)
& in(U_156,U_157) )
& element(U_157,powerset(the_carrier(boole_POSet(sK28))))
& proper_element(U_157,powerset(the_carrier(boole_POSet(sK28))))
& upper_relstr_subset(U_157,boole_POSet(sK28))
& filtered_subset(U_157,boole_POSet(sK28))
& ~ empty(U_157) )
& ~ empty(sK28) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_158,sK28)],[f_78_3]) ).
fof(f_78_5,negated_conjecture,
( ? [U_156] :
( empty(U_156)
& in(U_156,sK29) )
& element(sK29,powerset(the_carrier(boole_POSet(sK28))))
& proper_element(sK29,powerset(the_carrier(boole_POSet(sK28))))
& upper_relstr_subset(sK29,boole_POSet(sK28))
& filtered_subset(sK29,boole_POSet(sK28))
& ~ empty(sK29)
& ~ empty(sK28) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_157,sK29)],[f_78_4]) ).
fof(f_78_6,negated_conjecture,
( empty(sK30)
& in(sK30,sK29)
& element(sK29,powerset(the_carrier(boole_POSet(sK28))))
& proper_element(sK29,powerset(the_carrier(boole_POSet(sK28))))
& upper_relstr_subset(sK29,boole_POSet(sK28))
& filtered_subset(sK29,boole_POSet(sK28))
& ~ empty(sK29)
& ~ empty(sK28) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_156,sK30)],[f_78_5]) ).
cnf(f_78_7,negated_conjecture,
~ empty(sK28),
inference(clausify,[status(thm)],[f_78_6]) ).
cnf(f_78_8,negated_conjecture,
~ empty(sK29),
inference(clausify,[status(thm)],[f_78_6]) ).
cnf(f_78_9,negated_conjecture,
filtered_subset(sK29,boole_POSet(sK28)),
inference(clausify,[status(thm)],[f_78_6]) ).
cnf(f_78_10,negated_conjecture,
upper_relstr_subset(sK29,boole_POSet(sK28)),
inference(clausify,[status(thm)],[f_78_6]) ).
cnf(f_78_11,negated_conjecture,
proper_element(sK29,powerset(the_carrier(boole_POSet(sK28)))),
inference(clausify,[status(thm)],[f_78_6]) ).
cnf(f_78_12,negated_conjecture,
element(sK29,powerset(the_carrier(boole_POSet(sK28)))),
inference(clausify,[status(thm)],[f_78_6]) ).
cnf(f_78_13,negated_conjecture,
in(sK30,sK29),
inference(clausify,[status(thm)],[f_78_6]) ).
cnf(f_78_14,negated_conjecture,
empty(sK30),
inference(clausify,[status(thm)],[f_78_6]) ).
fof(f_79_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_79_2,plain,
! [U_160,U_159] :
( ( element(U_160,powerset(U_159))
| ~ subset(U_160,U_159) )
& ( subset(U_160,U_159)
| ~ element(U_160,powerset(U_159)) ) ),
inference(variable_rename,[status(thm)],[f_79_1]) ).
fof(f_79_3,plain,
( ! [U_164,U_162] :
( element(U_164,powerset(U_162))
| ~ subset(U_164,U_162) )
& ! [U_163,U_161] :
( subset(U_163,U_161)
| ~ element(U_163,powerset(U_161)) ) ),
inference(miniscope,[status(thm)],[f_79_2]) ).
cnf(f_79_4,plain,
( subset(U_163,U_161)
| ~ element(U_163,powerset(U_161)) ),
inference(clausify,[status(thm)],[f_79_3]) ).
cnf(f_79_5,plain,
( element(U_164,powerset(U_162))
| ~ subset(U_164,U_162) ),
inference(clausify,[status(thm)],[f_79_3]) ).
fof(f_80_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_80_2,plain,
! [U_167,U_166,U_165] :
( element(U_167,U_165)
| ~ element(U_166,powerset(U_165))
| ~ in(U_167,U_166) ),
inference(variable_rename,[status(thm)],[f_80_1]) ).
cnf(f_80_3,plain,
( element(U_167,U_165)
| ~ element(U_166,powerset(U_165))
| ~ in(U_167,U_166) ),
inference(clausify,[status(thm)],[f_80_2]) ).
fof(f_81_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_81_2,plain,
! [U_170,U_169,U_168] :
( ~ empty(U_168)
| ~ element(U_169,powerset(U_168))
| ~ in(U_170,U_169) ),
inference(variable_rename,[status(thm)],[f_81_1]) ).
fof(f_81_3,plain,
! [U_170,U_169] :
( ! [U_168] :
( ~ empty(U_168)
| ~ element(U_169,powerset(U_168)) )
| ~ in(U_170,U_169) ),
inference(miniscope,[status(thm)],[f_81_2]) ).
cnf(f_81_4,plain,
( ~ empty(U_168)
| ~ element(U_169,powerset(U_168))
| ~ in(U_170,U_169) ),
inference(clausify,[status(thm)],[f_81_3]) ).
fof(f_82_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_82_2,plain,
! [U_171] :
( U_171 = empty_set
| ~ empty(U_171) ),
inference(variable_rename,[status(thm)],[f_82_1]) ).
cnf(f_82_3,plain,
( U_171 = empty_set
| ~ empty(U_171) ),
inference(clausify,[status(thm)],[f_82_2]) ).
fof(f_83_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_83_2,plain,
! [U_173,U_172] :
( ~ empty(U_172)
| ~ in(U_173,U_172) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
cnf(f_83_3,plain,
( ~ empty(U_172)
| ~ in(U_173,U_172) ),
inference(clausify,[status(thm)],[f_83_2]) ).
fof(f_84_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_84_2,plain,
! [U_175,U_174] :
( ~ empty(U_174)
| U_175 = U_174
| ~ empty(U_175) ),
inference(variable_rename,[status(thm)],[f_84_1]) ).
fof(f_84_3,plain,
! [U_175] :
( ! [U_174] :
( ~ empty(U_174)
| U_175 = U_174 )
| ~ empty(U_175) ),
inference(miniscope,[status(thm)],[f_84_2]) ).
cnf(f_84_4,plain,
( ~ empty(U_174)
| U_175 = U_174
| ~ empty(U_175) ),
inference(clausify,[status(thm)],[f_84_3]) ).
fof(f_85_1,plain,
! [A] :
( ! [B] :
( ( ( proper_element(B,powerset(the_carrier(A)))
| in(bottom_of_relstr(A),B) )
& ( ~ in(bottom_of_relstr(A),B)
| ~ proper_element(B,powerset(the_carrier(A))) ) )
| ~ element(B,powerset(the_carrier(A)))
| ~ upper_relstr_subset(B,A)
| ~ filtered_subset(B,A)
| empty(B) )
| ~ rel_str(A)
| ~ lower_bounded_relstr(A)
| ~ antisymmetric_relstr(A)
| ~ transitive_relstr(A)
| ~ reflexive_relstr(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[t8_waybel_7]) ).
fof(f_85_2,plain,
! [U_177] :
( ! [U_176] :
( ( ( proper_element(U_176,powerset(the_carrier(U_177)))
| in(bottom_of_relstr(U_177),U_176) )
& ( ~ in(bottom_of_relstr(U_177),U_176)
| ~ proper_element(U_176,powerset(the_carrier(U_177))) ) )
| ~ element(U_176,powerset(the_carrier(U_177)))
| ~ upper_relstr_subset(U_176,U_177)
| ~ filtered_subset(U_176,U_177)
| empty(U_176) )
| ~ rel_str(U_177)
| ~ lower_bounded_relstr(U_177)
| ~ antisymmetric_relstr(U_177)
| ~ transitive_relstr(U_177)
| ~ reflexive_relstr(U_177)
| empty_carrier(U_177) ),
inference(variable_rename,[status(thm)],[f_85_1]) ).
cnf(f_85_3,plain,
( ~ in(bottom_of_relstr(U_177),U_176)
| ~ proper_element(U_176,powerset(the_carrier(U_177)))
| ~ element(U_176,powerset(the_carrier(U_177)))
| ~ upper_relstr_subset(U_176,U_177)
| ~ filtered_subset(U_176,U_177)
| empty(U_176)
| ~ rel_str(U_177)
| ~ lower_bounded_relstr(U_177)
| ~ antisymmetric_relstr(U_177)
| ~ transitive_relstr(U_177)
| ~ reflexive_relstr(U_177)
| empty_carrier(U_177) ),
inference(clausify,[status(thm)],[f_85_2]) ).
cnf(f_85_4,plain,
( proper_element(U_176,powerset(the_carrier(U_177)))
| in(bottom_of_relstr(U_177),U_176)
| ~ element(U_176,powerset(the_carrier(U_177)))
| ~ upper_relstr_subset(U_176,U_177)
| ~ filtered_subset(U_176,U_177)
| empty(U_176)
| ~ rel_str(U_177)
| ~ lower_bounded_relstr(U_177)
| ~ antisymmetric_relstr(U_177)
| ~ transitive_relstr(U_177)
| ~ reflexive_relstr(U_177)
| empty_carrier(U_177) ),
inference(clausify,[status(thm)],[f_85_2]) ).
cnf(f_3_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_3_3]) ).
cnf(f_3_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_3_4]) ).
cnf(f_4_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_3]) ).
cnf(f_4_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_4]) ).
cnf(f_5_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_3]) ).
cnf(f_5_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_4]) ).
cnf(f_5_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_5]) ).
cnf(f_5_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_6]) ).
cnf(f_5_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_7]) ).
cnf(f_5_10_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_10]) ).
cnf(f_6_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_3]) ).
cnf(f_6_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_4]) ).
cnf(f_6_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_5]) ).
cnf(f_7_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_3]) ).
cnf(f_7_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_4]) ).
cnf(f_7_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_5]) ).
cnf(f_7_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_7]) ).
cnf(f_12_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_12_3]) ).
cnf(f_15_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_15_3]) ).
cnf(f_15_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_15_4]) ).
cnf(f_16_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_16_3]) ).
cnf(f_18_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_18_3]) ).
cnf(f_18_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_18_4]) ).
cnf(f_20_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_20_4]) ).
cnf(f_20_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_20_5]) ).
cnf(f_22_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_22_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_28_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_28_2]) ).
cnf(f_29_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_29_2]) ).
cnf(f_30_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_30_2]) ).
cnf(f_33_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_33_2]) ).
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,
( bottom_of_relstr(Eq_x_0) = bottom_of_relstr(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( boole_POSet(Eq_x_0) = boole_POSet(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK3(Eq_x_0,Eq_x_1) = sK3(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,
( sK4(Eq_x_0) = sK4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK5(Eq_x_0,Eq_x_1) = sK5(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK6(Eq_x_0) = sK6(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK12(Eq_x_0) = sK12(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK17(Eq_x_0) = sK17(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( sK18(Eq_x_0) = sK18(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( sK20(Eq_x_0) = sK20(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( sK23(Eq_x_0) = sK23(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( sK24(Eq_x_0) = sK24(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( sK25(Eq_x_0) = sK25(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( sK27(Eq_x_0) = sK27(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( rel_str(Eq_y_0)
| ~ rel_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,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_25,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_26,axiom,
( empty_carrier(Eq_y_0)
| ~ empty_carrier(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,axiom,
( reflexive_relstr(Eq_y_0)
| ~ reflexive_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,axiom,
( complete_relstr(Eq_y_0)
| ~ complete_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_29,axiom,
( up_complete_relstr(Eq_y_0)
| ~ up_complete_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_30,axiom,
( join_complete_relstr(Eq_y_0)
| ~ join_complete_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_31,axiom,
( lower_bounded_relstr(Eq_y_0)
| ~ lower_bounded_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_32,axiom,
( transitive_relstr(Eq_y_0)
| ~ transitive_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_33,axiom,
( antisymmetric_relstr(Eq_y_0)
| ~ antisymmetric_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_34,axiom,
( with_suprema_relstr(Eq_y_0)
| ~ with_suprema_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_35,axiom,
( with_infima_relstr(Eq_y_0)
| ~ with_infima_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_36,axiom,
( upper_bounded_relstr(Eq_y_0)
| ~ upper_bounded_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_37,axiom,
( bounded_relstr(Eq_y_0)
| ~ bounded_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_38,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_39,axiom,
( finite(Eq_y_0)
| ~ finite(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_40,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_41,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_42,axiom,
( trivial_carrier(Eq_y_0)
| ~ trivial_carrier(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_43,axiom,
( connected_relstr(Eq_y_0)
| ~ connected_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_44,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_45,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_46,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_47,axiom,
( relation_empty_yielding(Eq_y_0)
| ~ relation_empty_yielding(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_48,axiom,
( v1_yellow_3(Eq_y_0)
| ~ v1_yellow_3(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_49,axiom,
( distributive_relstr(Eq_y_0)
| ~ distributive_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_50,axiom,
( heyting_relstr(Eq_y_0)
| ~ heyting_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_51,axiom,
( complemented_relstr(Eq_y_0)
| ~ complemented_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_52,axiom,
( boolean_relstr(Eq_y_0)
| ~ boolean_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_53,axiom,
( directed_relstr(Eq_y_0)
| ~ directed_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_54,axiom,
( filtered_subset(Eq_y_0,Eq_y_1)
| ~ filtered_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_55,axiom,
( upper_relstr_subset(Eq_y_0,Eq_y_1)
| ~ upper_relstr_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_56,axiom,
( proper_element(Eq_y_0,Eq_y_1)
| ~ proper_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_57,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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU387+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
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 00:08:35 UTC 2026
% 0.10/0.37 % CPUTime :
% 261.15/261.41 % SZS status Theorem for theBenchmark
% 261.15/261.41 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------