TSTP Solution File: SEU354+2 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU354+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:42:03 EDT 2024
% Result : Theorem 0.21s 0.56s
% Output : CNFRefutation 0.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 85
% Syntax : Number of formulae : 333 ( 70 unt; 0 def)
% Number of atoms : 848 ( 53 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 763 ( 248 ~; 268 |; 166 &)
% ( 59 <=>; 21 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 84 ( 82 usr; 54 prp; 0-2 aty)
% Number of functors : 27 ( 27 usr; 18 con; 0-3 aty)
% Number of variables : 101 ( 81 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A] :
( rel_str(A)
=> ( strict_rel_str(A)
=> A = rel_str_of(the_carrier(A),the_InternalRel(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A] :
( latt_str(A)
=> ( strict_latt_str(A)
=> A = latt_str_of(the_carrier(A),the_L_join(A),the_L_meet(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A] :
( ordinal(A)
=> ! [B] :
( element(B,A)
=> ( epsilon_transitive(B)
& epsilon_connected(B)
& ordinal(B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A] :
( latt_str(A)
=> ( ( ~ empty_carrier(A)
& lattice(A) )
=> ( ~ empty_carrier(A)
& join_commutative(A)
& join_associative(A)
& meet_commutative(A)
& meet_associative(A)
& meet_absorbing(A)
& join_absorbing(A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [A] :
( ( relation(A)
& empty(A)
& function(A) )
=> ( relation(A)
& function(A)
& one_to_one(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [A] :
( latt_str(A)
=> ( ( ~ empty_carrier(A)
& join_commutative(A)
& join_associative(A)
& meet_commutative(A)
& meet_associative(A)
& meet_absorbing(A)
& join_absorbing(A) )
=> ( ~ empty_carrier(A)
& lattice(A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [A] :
( ( epsilon_transitive(A)
& epsilon_connected(A) )
=> ordinal(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [A] :
( empty(A)
=> ( epsilon_transitive(A)
& epsilon_connected(A)
& ordinal(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f102,axiom,
! [A,B] :
( element(B,A)
=> ( proper_element(B,A)
<=> B != union(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f128,axiom,
! [A] :
( A = omega
<=> ( in(empty_set,A)
& being_limit_ordinal(A)
& ordinal(A)
& ! [B] :
( ordinal(B)
=> ( ( in(empty_set,B)
& being_limit_ordinal(B) )
=> subset(A,B) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f255,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f264,axiom,
( epsilon_transitive(omega)
& epsilon_connected(omega)
& ordinal(omega)
& ~ empty(omega) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f279,axiom,
( relation(empty_set)
& relation_empty_yielding(empty_set)
& function(empty_set)
& one_to_one(empty_set)
& empty(empty_set)
& epsilon_transitive(empty_set)
& epsilon_connected(empty_set)
& ordinal(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f358,axiom,
? [A] :
( ~ empty(A)
& epsilon_transitive(A)
& epsilon_connected(A)
& ordinal(A)
& natural(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f363,axiom,
? [A] :
( rel_str(A)
& strict_rel_str(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f364,axiom,
? [A] :
( epsilon_transitive(A)
& epsilon_connected(A)
& ordinal(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f365,axiom,
? [A] :
( epsilon_transitive(A)
& epsilon_connected(A)
& ordinal(A)
& being_limit_ordinal(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f366,axiom,
? [A] :
( relation(A)
& function(A)
& one_to_one(A)
& empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f367,axiom,
? [A] :
( empty(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f370,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f372,axiom,
? [A] :
( relation(A)
& empty(A)
& function(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f374,axiom,
? [A] :
( rel_str(A)
& ~ empty_carrier(A)
& strict_rel_str(A)
& reflexive_relstr(A)
& transitive_relstr(A)
& antisymmetric_relstr(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f375,axiom,
? [A] :
( relation(A)
& function(A)
& one_to_one(A)
& empty(A)
& epsilon_transitive(A)
& epsilon_connected(A)
& ordinal(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f384,axiom,
? [A] :
( latt_str(A)
& strict_latt_str(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f385,axiom,
? [A] :
( ~ empty(A)
& epsilon_transitive(A)
& epsilon_connected(A)
& ordinal(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f392,axiom,
? [A] :
( latt_str(A)
& ~ empty_carrier(A)
& strict_latt_str(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f395,axiom,
? [A] :
( latt_str(A)
& ~ empty_carrier(A)
& strict_latt_str(A)
& join_commutative(A)
& join_associative(A)
& meet_commutative(A)
& meet_associative(A)
& meet_absorbing(A)
& join_absorbing(A)
& lattice(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f517,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f627,conjecture,
! [A,B] :
( element(B,powerset(A))
=> ( proper_element(B,powerset(A))
<=> B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f628,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(A))
=> ( proper_element(B,powerset(A))
<=> B != A ) ),
inference(negated_conjecture,[status(cth)],[f627]) ).
fof(f668,lemma,
! [A] : union(powerset(A)) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f672,plain,
! [A] :
( ~ rel_str(A)
| ~ strict_rel_str(A)
| A = rel_str_of(the_carrier(A),the_InternalRel(A)) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f673,plain,
! [X0] :
( ~ rel_str(X0)
| ~ strict_rel_str(X0)
| X0 = rel_str_of(the_carrier(X0),the_InternalRel(X0)) ),
inference(cnf_transformation,[status(esa)],[f672]) ).
fof(f674,plain,
! [A] :
( ~ latt_str(A)
| ~ strict_latt_str(A)
| A = latt_str_of(the_carrier(A),the_L_join(A),the_L_meet(A)) ),
inference(pre_NNF_transformation,[status(esa)],[f2]) ).
fof(f675,plain,
! [X0] :
( ~ latt_str(X0)
| ~ strict_latt_str(X0)
| X0 = latt_str_of(the_carrier(X0),the_L_join(X0),the_L_meet(X0)) ),
inference(cnf_transformation,[status(esa)],[f674]) ).
fof(f720,plain,
! [A] :
( ~ ordinal(A)
| ! [B] :
( ~ element(B,A)
| ( epsilon_transitive(B)
& epsilon_connected(B)
& ordinal(B) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f721,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ element(X1,X0)
| epsilon_transitive(X1) ),
inference(cnf_transformation,[status(esa)],[f720]) ).
fof(f722,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ element(X1,X0)
| epsilon_connected(X1) ),
inference(cnf_transformation,[status(esa)],[f720]) ).
fof(f723,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ element(X1,X0)
| ordinal(X1) ),
inference(cnf_transformation,[status(esa)],[f720]) ).
fof(f729,plain,
! [A] :
( ~ empty(A)
| function(A) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f730,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(cnf_transformation,[status(esa)],[f729]) ).
fof(f734,plain,
! [A] :
( ~ latt_str(A)
| empty_carrier(A)
| ~ lattice(A)
| ( ~ empty_carrier(A)
& join_commutative(A)
& join_associative(A)
& meet_commutative(A)
& meet_associative(A)
& meet_absorbing(A)
& join_absorbing(A) ) ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f736,plain,
! [X0] :
( ~ latt_str(X0)
| empty_carrier(X0)
| ~ lattice(X0)
| join_commutative(X0) ),
inference(cnf_transformation,[status(esa)],[f734]) ).
fof(f737,plain,
! [X0] :
( ~ latt_str(X0)
| empty_carrier(X0)
| ~ lattice(X0)
| join_associative(X0) ),
inference(cnf_transformation,[status(esa)],[f734]) ).
fof(f738,plain,
! [X0] :
( ~ latt_str(X0)
| empty_carrier(X0)
| ~ lattice(X0)
| meet_commutative(X0) ),
inference(cnf_transformation,[status(esa)],[f734]) ).
fof(f739,plain,
! [X0] :
( ~ latt_str(X0)
| empty_carrier(X0)
| ~ lattice(X0)
| meet_associative(X0) ),
inference(cnf_transformation,[status(esa)],[f734]) ).
fof(f740,plain,
! [X0] :
( ~ latt_str(X0)
| empty_carrier(X0)
| ~ lattice(X0)
| meet_absorbing(X0) ),
inference(cnf_transformation,[status(esa)],[f734]) ).
fof(f741,plain,
! [X0] :
( ~ latt_str(X0)
| empty_carrier(X0)
| ~ lattice(X0)
| join_absorbing(X0) ),
inference(cnf_transformation,[status(esa)],[f734]) ).
fof(f750,plain,
! [A] :
( ~ empty(A)
| relation(A) ),
inference(pre_NNF_transformation,[status(esa)],[f24]) ).
fof(f751,plain,
! [X0] :
( ~ empty(X0)
| relation(X0) ),
inference(cnf_transformation,[status(esa)],[f750]) ).
fof(f770,plain,
! [A] :
( ~ relation(A)
| ~ empty(A)
| ~ function(A)
| ( relation(A)
& function(A)
& one_to_one(A) ) ),
inference(pre_NNF_transformation,[status(esa)],[f30]) ).
fof(f773,plain,
! [X0] :
( ~ relation(X0)
| ~ empty(X0)
| ~ function(X0)
| one_to_one(X0) ),
inference(cnf_transformation,[status(esa)],[f770]) ).
fof(f779,plain,
! [A] :
( ~ latt_str(A)
| empty_carrier(A)
| ~ join_commutative(A)
| ~ join_associative(A)
| ~ meet_commutative(A)
| ~ meet_associative(A)
| ~ meet_absorbing(A)
| ~ join_absorbing(A)
| ( ~ empty_carrier(A)
& lattice(A) ) ),
inference(pre_NNF_transformation,[status(esa)],[f32]) ).
fof(f781,plain,
! [X0] :
( ~ latt_str(X0)
| empty_carrier(X0)
| ~ join_commutative(X0)
| ~ join_associative(X0)
| ~ meet_commutative(X0)
| ~ meet_associative(X0)
| ~ meet_absorbing(X0)
| ~ join_absorbing(X0)
| lattice(X0) ),
inference(cnf_transformation,[status(esa)],[f779]) ).
fof(f784,plain,
! [A] :
( ~ epsilon_transitive(A)
| ~ epsilon_connected(A)
| ordinal(A) ),
inference(pre_NNF_transformation,[status(esa)],[f34]) ).
fof(f785,plain,
! [X0] :
( ~ epsilon_transitive(X0)
| ~ epsilon_connected(X0)
| ordinal(X0) ),
inference(cnf_transformation,[status(esa)],[f784]) ).
fof(f797,plain,
! [A] :
( ~ empty(A)
| ( epsilon_transitive(A)
& epsilon_connected(A)
& ordinal(A) ) ),
inference(pre_NNF_transformation,[status(esa)],[f38]) ).
fof(f798,plain,
! [X0] :
( ~ empty(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[status(esa)],[f797]) ).
fof(f799,plain,
! [X0] :
( ~ empty(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[status(esa)],[f797]) ).
fof(f1193,plain,
! [A,B] :
( ~ element(B,A)
| ( proper_element(B,A)
<=> B != union(A) ) ),
inference(pre_NNF_transformation,[status(esa)],[f102]) ).
fof(f1194,plain,
! [A,B] :
( ~ element(B,A)
| ( ( ~ proper_element(B,A)
| B != union(A) )
& ( proper_element(B,A)
| B = union(A) ) ) ),
inference(NNF_transformation,[status(esa)],[f1193]) ).
fof(f1195,plain,
! [X0,X1] :
( ~ element(X0,X1)
| ~ proper_element(X0,X1)
| X0 != union(X1) ),
inference(cnf_transformation,[status(esa)],[f1194]) ).
fof(f1196,plain,
! [X0,X1] :
( ~ element(X0,X1)
| proper_element(X0,X1)
| X0 = union(X1) ),
inference(cnf_transformation,[status(esa)],[f1194]) ).
fof(f1372,plain,
! [A] :
( A = omega
<=> ( in(empty_set,A)
& being_limit_ordinal(A)
& ordinal(A)
& ! [B] :
( ~ ordinal(B)
| ~ in(empty_set,B)
| ~ being_limit_ordinal(B)
| subset(A,B) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f128]) ).
fof(f1373,plain,
! [A] :
( ( A != omega
| ( in(empty_set,A)
& being_limit_ordinal(A)
& ordinal(A)
& ! [B] :
( ~ ordinal(B)
| ~ in(empty_set,B)
| ~ being_limit_ordinal(B)
| subset(A,B) ) ) )
& ( A = omega
| ~ in(empty_set,A)
| ~ being_limit_ordinal(A)
| ~ ordinal(A)
| ? [B] :
( ordinal(B)
& in(empty_set,B)
& being_limit_ordinal(B)
& ~ subset(A,B) ) ) ),
inference(NNF_transformation,[status(esa)],[f1372]) ).
fof(f1374,plain,
( ! [A] :
( A != omega
| ( in(empty_set,A)
& being_limit_ordinal(A)
& ordinal(A)
& ! [B] :
( ~ ordinal(B)
| ~ in(empty_set,B)
| ~ being_limit_ordinal(B)
| subset(A,B) ) ) )
& ! [A] :
( A = omega
| ~ in(empty_set,A)
| ~ being_limit_ordinal(A)
| ~ ordinal(A)
| ? [B] :
( ordinal(B)
& in(empty_set,B)
& being_limit_ordinal(B)
& ~ subset(A,B) ) ) ),
inference(miniscoping,[status(esa)],[f1373]) ).
fof(f1375,plain,
( ! [A] :
( A != omega
| ( in(empty_set,A)
& being_limit_ordinal(A)
& ordinal(A)
& ! [B] :
( ~ ordinal(B)
| ~ in(empty_set,B)
| ~ being_limit_ordinal(B)
| subset(A,B) ) ) )
& ! [A] :
( A = omega
| ~ in(empty_set,A)
| ~ being_limit_ordinal(A)
| ~ ordinal(A)
| ( ordinal(sk0_90(A))
& in(empty_set,sk0_90(A))
& being_limit_ordinal(sk0_90(A))
& ~ subset(A,sk0_90(A)) ) ) ),
inference(skolemization,[status(esa)],[f1374]) ).
fof(f1376,plain,
! [X0] :
( X0 != omega
| in(empty_set,X0) ),
inference(cnf_transformation,[status(esa)],[f1375]) ).
fof(f1378,plain,
! [X0] :
( X0 != omega
| ordinal(X0) ),
inference(cnf_transformation,[status(esa)],[f1375]) ).
fof(f1710,plain,
empty(empty_set),
inference(cnf_transformation,[status(esa)],[f255]) ).
fof(f1737,plain,
epsilon_transitive(omega),
inference(cnf_transformation,[status(esa)],[f264]) ).
fof(f1798,plain,
function(empty_set),
inference(cnf_transformation,[status(esa)],[f279]) ).
fof(f2111,plain,
( ~ empty(sk0_138)
& epsilon_transitive(sk0_138)
& epsilon_connected(sk0_138)
& ordinal(sk0_138)
& natural(sk0_138) ),
inference(skolemization,[status(esa)],[f358]) ).
fof(f2113,plain,
epsilon_transitive(sk0_138),
inference(cnf_transformation,[status(esa)],[f2111]) ).
fof(f2114,plain,
epsilon_connected(sk0_138),
inference(cnf_transformation,[status(esa)],[f2111]) ).
fof(f2135,plain,
( rel_str(sk0_143)
& strict_rel_str(sk0_143) ),
inference(skolemization,[status(esa)],[f363]) ).
fof(f2136,plain,
rel_str(sk0_143),
inference(cnf_transformation,[status(esa)],[f2135]) ).
fof(f2137,plain,
strict_rel_str(sk0_143),
inference(cnf_transformation,[status(esa)],[f2135]) ).
fof(f2138,plain,
( epsilon_transitive(sk0_144)
& epsilon_connected(sk0_144)
& ordinal(sk0_144) ),
inference(skolemization,[status(esa)],[f364]) ).
fof(f2139,plain,
epsilon_transitive(sk0_144),
inference(cnf_transformation,[status(esa)],[f2138]) ).
fof(f2140,plain,
epsilon_connected(sk0_144),
inference(cnf_transformation,[status(esa)],[f2138]) ).
fof(f2142,plain,
( epsilon_transitive(sk0_145)
& epsilon_connected(sk0_145)
& ordinal(sk0_145)
& being_limit_ordinal(sk0_145) ),
inference(skolemization,[status(esa)],[f365]) ).
fof(f2143,plain,
epsilon_transitive(sk0_145),
inference(cnf_transformation,[status(esa)],[f2142]) ).
fof(f2144,plain,
epsilon_connected(sk0_145),
inference(cnf_transformation,[status(esa)],[f2142]) ).
fof(f2147,plain,
( relation(sk0_146)
& function(sk0_146)
& one_to_one(sk0_146)
& empty(sk0_146) ),
inference(skolemization,[status(esa)],[f366]) ).
fof(f2149,plain,
function(sk0_146),
inference(cnf_transformation,[status(esa)],[f2147]) ).
fof(f2151,plain,
empty(sk0_146),
inference(cnf_transformation,[status(esa)],[f2147]) ).
fof(f2152,plain,
( empty(sk0_147)
& relation(sk0_147) ),
inference(skolemization,[status(esa)],[f367]) ).
fof(f2153,plain,
empty(sk0_147),
inference(cnf_transformation,[status(esa)],[f2152]) ).
fof(f2163,plain,
empty(sk0_150),
inference(skolemization,[status(esa)],[f370]) ).
fof(f2164,plain,
empty(sk0_150),
inference(cnf_transformation,[status(esa)],[f2163]) ).
fof(f2176,plain,
( relation(sk0_152)
& empty(sk0_152)
& function(sk0_152) ),
inference(skolemization,[status(esa)],[f372]) ).
fof(f2178,plain,
empty(sk0_152),
inference(cnf_transformation,[status(esa)],[f2176]) ).
fof(f2179,plain,
function(sk0_152),
inference(cnf_transformation,[status(esa)],[f2176]) ).
fof(f2188,plain,
( rel_str(sk0_154)
& ~ empty_carrier(sk0_154)
& strict_rel_str(sk0_154)
& reflexive_relstr(sk0_154)
& transitive_relstr(sk0_154)
& antisymmetric_relstr(sk0_154) ),
inference(skolemization,[status(esa)],[f374]) ).
fof(f2189,plain,
rel_str(sk0_154),
inference(cnf_transformation,[status(esa)],[f2188]) ).
fof(f2191,plain,
strict_rel_str(sk0_154),
inference(cnf_transformation,[status(esa)],[f2188]) ).
fof(f2195,plain,
( relation(sk0_155)
& function(sk0_155)
& one_to_one(sk0_155)
& empty(sk0_155)
& epsilon_transitive(sk0_155)
& epsilon_connected(sk0_155)
& ordinal(sk0_155) ),
inference(skolemization,[status(esa)],[f375]) ).
fof(f2197,plain,
function(sk0_155),
inference(cnf_transformation,[status(esa)],[f2195]) ).
fof(f2199,plain,
empty(sk0_155),
inference(cnf_transformation,[status(esa)],[f2195]) ).
fof(f2232,plain,
( latt_str(sk0_164)
& strict_latt_str(sk0_164) ),
inference(skolemization,[status(esa)],[f384]) ).
fof(f2233,plain,
latt_str(sk0_164),
inference(cnf_transformation,[status(esa)],[f2232]) ).
fof(f2234,plain,
strict_latt_str(sk0_164),
inference(cnf_transformation,[status(esa)],[f2232]) ).
fof(f2235,plain,
( ~ empty(sk0_165)
& epsilon_transitive(sk0_165)
& epsilon_connected(sk0_165)
& ordinal(sk0_165) ),
inference(skolemization,[status(esa)],[f385]) ).
fof(f2237,plain,
epsilon_transitive(sk0_165),
inference(cnf_transformation,[status(esa)],[f2235]) ).
fof(f2238,plain,
epsilon_connected(sk0_165),
inference(cnf_transformation,[status(esa)],[f2235]) ).
fof(f2267,plain,
( latt_str(sk0_172)
& ~ empty_carrier(sk0_172)
& strict_latt_str(sk0_172) ),
inference(skolemization,[status(esa)],[f392]) ).
fof(f2268,plain,
latt_str(sk0_172),
inference(cnf_transformation,[status(esa)],[f2267]) ).
fof(f2270,plain,
strict_latt_str(sk0_172),
inference(cnf_transformation,[status(esa)],[f2267]) ).
fof(f2280,plain,
( latt_str(sk0_175)
& ~ empty_carrier(sk0_175)
& strict_latt_str(sk0_175)
& join_commutative(sk0_175)
& join_associative(sk0_175)
& meet_commutative(sk0_175)
& meet_associative(sk0_175)
& meet_absorbing(sk0_175)
& join_absorbing(sk0_175)
& lattice(sk0_175) ),
inference(skolemization,[status(esa)],[f395]) ).
fof(f2281,plain,
latt_str(sk0_175),
inference(cnf_transformation,[status(esa)],[f2280]) ).
fof(f2282,plain,
~ empty_carrier(sk0_175),
inference(cnf_transformation,[status(esa)],[f2280]) ).
fof(f2283,plain,
strict_latt_str(sk0_175),
inference(cnf_transformation,[status(esa)],[f2280]) ).
fof(f2289,plain,
join_absorbing(sk0_175),
inference(cnf_transformation,[status(esa)],[f2280]) ).
fof(f2290,plain,
lattice(sk0_175),
inference(cnf_transformation,[status(esa)],[f2280]) ).
fof(f2998,plain,
! [A,B] :
( ~ in(A,B)
| element(A,B) ),
inference(pre_NNF_transformation,[status(esa)],[f517]) ).
fof(f2999,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2998]) ).
fof(f3374,plain,
? [A,B] :
( element(B,powerset(A))
& ( proper_element(B,powerset(A))
<~> B != A ) ),
inference(pre_NNF_transformation,[status(esa)],[f628]) ).
fof(f3375,plain,
? [A,B] :
( element(B,powerset(A))
& ( proper_element(B,powerset(A))
| B != A )
& ( ~ proper_element(B,powerset(A))
| B = A ) ),
inference(NNF_transformation,[status(esa)],[f3374]) ).
fof(f3376,plain,
( element(sk0_386,powerset(sk0_385))
& ( proper_element(sk0_386,powerset(sk0_385))
| sk0_386 != sk0_385 )
& ( ~ proper_element(sk0_386,powerset(sk0_385))
| sk0_386 = sk0_385 ) ),
inference(skolemization,[status(esa)],[f3375]) ).
fof(f3377,plain,
element(sk0_386,powerset(sk0_385)),
inference(cnf_transformation,[status(esa)],[f3376]) ).
fof(f3378,plain,
( proper_element(sk0_386,powerset(sk0_385))
| sk0_386 != sk0_385 ),
inference(cnf_transformation,[status(esa)],[f3376]) ).
fof(f3379,plain,
( ~ proper_element(sk0_386,powerset(sk0_385))
| sk0_386 = sk0_385 ),
inference(cnf_transformation,[status(esa)],[f3376]) ).
fof(f3502,plain,
! [X0] : union(powerset(X0)) = X0,
inference(cnf_transformation,[status(esa)],[f668]) ).
fof(f3968,plain,
( spl0_35
<=> proper_element(sk0_386,powerset(sk0_385)) ),
introduced(split_symbol_definition) ).
fof(f3971,plain,
( spl0_36
<=> sk0_386 = sk0_385 ),
introduced(split_symbol_definition) ).
fof(f3972,plain,
( sk0_386 = sk0_385
| ~ spl0_36 ),
inference(component_clause,[status(thm)],[f3971]) ).
fof(f3973,plain,
( sk0_386 != sk0_385
| spl0_36 ),
inference(component_clause,[status(thm)],[f3971]) ).
fof(f3974,plain,
( spl0_35
| ~ spl0_36 ),
inference(split_clause,[status(thm)],[f3378,f3968,f3971]) ).
fof(f3975,plain,
( ~ spl0_35
| spl0_36 ),
inference(split_clause,[status(thm)],[f3379,f3968,f3971]) ).
fof(f4114,plain,
! [X0] :
( ~ element(union(X0),X0)
| ~ proper_element(union(X0),X0) ),
inference(destructive_equality_resolution,[status(esa)],[f1195]) ).
fof(f4138,plain,
in(empty_set,omega),
inference(destructive_equality_resolution,[status(esa)],[f1376]) ).
fof(f4140,plain,
ordinal(omega),
inference(destructive_equality_resolution,[status(esa)],[f1378]) ).
fof(f4304,plain,
( spl0_54
<=> sk0_386 = union(powerset(sk0_385)) ),
introduced(split_symbol_definition) ).
fof(f4305,plain,
( sk0_386 = union(powerset(sk0_385))
| ~ spl0_54 ),
inference(component_clause,[status(thm)],[f4304]) ).
fof(f4306,plain,
( sk0_386 != union(powerset(sk0_385))
| spl0_54 ),
inference(component_clause,[status(thm)],[f4304]) ).
fof(f4307,plain,
( proper_element(sk0_386,powerset(sk0_385))
| sk0_386 = union(powerset(sk0_385)) ),
inference(resolution,[status(thm)],[f1196,f3377]) ).
fof(f4308,plain,
( spl0_35
| spl0_54 ),
inference(split_clause,[status(thm)],[f4307,f3968,f4304]) ).
fof(f4333,plain,
( spl0_60
<=> element(union(powerset(sk0_385)),powerset(sk0_385)) ),
introduced(split_symbol_definition) ).
fof(f4335,plain,
( ~ element(union(powerset(sk0_385)),powerset(sk0_385))
| spl0_60 ),
inference(component_clause,[status(thm)],[f4333]) ).
fof(f4336,plain,
( ~ element(union(powerset(sk0_385)),powerset(sk0_385))
| ~ proper_element(sk0_386,powerset(sk0_385))
| ~ spl0_54 ),
inference(paramodulation,[status(thm)],[f4305,f4114]) ).
fof(f4337,plain,
( ~ spl0_60
| ~ spl0_35
| ~ spl0_54 ),
inference(split_clause,[status(thm)],[f4336,f4333,f3968,f4304]) ).
fof(f4368,plain,
( spl0_65
<=> rel_str(sk0_143) ),
introduced(split_symbol_definition) ).
fof(f4370,plain,
( ~ rel_str(sk0_143)
| spl0_65 ),
inference(component_clause,[status(thm)],[f4368]) ).
fof(f4371,plain,
( spl0_66
<=> sk0_143 = rel_str_of(the_carrier(sk0_143),the_InternalRel(sk0_143)) ),
introduced(split_symbol_definition) ).
fof(f4374,plain,
( ~ rel_str(sk0_143)
| sk0_143 = rel_str_of(the_carrier(sk0_143),the_InternalRel(sk0_143)) ),
inference(resolution,[status(thm)],[f2137,f673]) ).
fof(f4375,plain,
( ~ spl0_65
| spl0_66 ),
inference(split_clause,[status(thm)],[f4374,f4368,f4371]) ).
fof(f4376,plain,
( $false
| spl0_65 ),
inference(forward_subsumption_resolution,[status(thm)],[f4370,f2136]) ).
fof(f4377,plain,
spl0_65,
inference(contradiction_clause,[status(thm)],[f4376]) ).
fof(f4392,plain,
( spl0_69
<=> rel_str(sk0_154) ),
introduced(split_symbol_definition) ).
fof(f4394,plain,
( ~ rel_str(sk0_154)
| spl0_69 ),
inference(component_clause,[status(thm)],[f4392]) ).
fof(f4395,plain,
( spl0_70
<=> sk0_154 = rel_str_of(the_carrier(sk0_154),the_InternalRel(sk0_154)) ),
introduced(split_symbol_definition) ).
fof(f4398,plain,
( ~ rel_str(sk0_154)
| sk0_154 = rel_str_of(the_carrier(sk0_154),the_InternalRel(sk0_154)) ),
inference(resolution,[status(thm)],[f2191,f673]) ).
fof(f4399,plain,
( ~ spl0_69
| spl0_70 ),
inference(split_clause,[status(thm)],[f4398,f4392,f4395]) ).
fof(f4400,plain,
( $false
| spl0_69 ),
inference(forward_subsumption_resolution,[status(thm)],[f4394,f2189]) ).
fof(f4401,plain,
spl0_69,
inference(contradiction_clause,[status(thm)],[f4400]) ).
fof(f4419,plain,
( spl0_73
<=> latt_str(sk0_164) ),
introduced(split_symbol_definition) ).
fof(f4421,plain,
( ~ latt_str(sk0_164)
| spl0_73 ),
inference(component_clause,[status(thm)],[f4419]) ).
fof(f4422,plain,
( spl0_74
<=> sk0_164 = latt_str_of(the_carrier(sk0_164),the_L_join(sk0_164),the_L_meet(sk0_164)) ),
introduced(split_symbol_definition) ).
fof(f4425,plain,
( ~ latt_str(sk0_164)
| sk0_164 = latt_str_of(the_carrier(sk0_164),the_L_join(sk0_164),the_L_meet(sk0_164)) ),
inference(resolution,[status(thm)],[f2234,f675]) ).
fof(f4426,plain,
( ~ spl0_73
| spl0_74 ),
inference(split_clause,[status(thm)],[f4425,f4419,f4422]) ).
fof(f4427,plain,
( $false
| spl0_73 ),
inference(forward_subsumption_resolution,[status(thm)],[f4421,f2233]) ).
fof(f4428,plain,
spl0_73,
inference(contradiction_clause,[status(thm)],[f4427]) ).
fof(f4444,plain,
( spl0_75
<=> latt_str(sk0_172) ),
introduced(split_symbol_definition) ).
fof(f4446,plain,
( ~ latt_str(sk0_172)
| spl0_75 ),
inference(component_clause,[status(thm)],[f4444]) ).
fof(f4447,plain,
( spl0_76
<=> sk0_172 = latt_str_of(the_carrier(sk0_172),the_L_join(sk0_172),the_L_meet(sk0_172)) ),
introduced(split_symbol_definition) ).
fof(f4450,plain,
( ~ latt_str(sk0_172)
| sk0_172 = latt_str_of(the_carrier(sk0_172),the_L_join(sk0_172),the_L_meet(sk0_172)) ),
inference(resolution,[status(thm)],[f2270,f675]) ).
fof(f4451,plain,
( ~ spl0_75
| spl0_76 ),
inference(split_clause,[status(thm)],[f4450,f4444,f4447]) ).
fof(f4452,plain,
( $false
| spl0_75 ),
inference(forward_subsumption_resolution,[status(thm)],[f4446,f2268]) ).
fof(f4453,plain,
spl0_75,
inference(contradiction_clause,[status(thm)],[f4452]) ).
fof(f4454,plain,
( spl0_77
<=> latt_str(sk0_175) ),
introduced(split_symbol_definition) ).
fof(f4456,plain,
( ~ latt_str(sk0_175)
| spl0_77 ),
inference(component_clause,[status(thm)],[f4454]) ).
fof(f4457,plain,
( spl0_78
<=> sk0_175 = latt_str_of(the_carrier(sk0_175),the_L_join(sk0_175),the_L_meet(sk0_175)) ),
introduced(split_symbol_definition) ).
fof(f4460,plain,
( ~ latt_str(sk0_175)
| sk0_175 = latt_str_of(the_carrier(sk0_175),the_L_join(sk0_175),the_L_meet(sk0_175)) ),
inference(resolution,[status(thm)],[f2283,f675]) ).
fof(f4461,plain,
( ~ spl0_77
| spl0_78 ),
inference(split_clause,[status(thm)],[f4460,f4454,f4457]) ).
fof(f4462,plain,
( $false
| spl0_77 ),
inference(forward_subsumption_resolution,[status(thm)],[f4456,f2281]) ).
fof(f4463,plain,
spl0_77,
inference(contradiction_clause,[status(thm)],[f4462]) ).
fof(f4570,plain,
function(sk0_150),
inference(resolution,[status(thm)],[f730,f2164]) ).
fof(f4571,plain,
function(sk0_147),
inference(resolution,[status(thm)],[f730,f2153]) ).
fof(f4575,plain,
( spl0_91
<=> empty_carrier(sk0_175) ),
introduced(split_symbol_definition) ).
fof(f4576,plain,
( empty_carrier(sk0_175)
| ~ spl0_91 ),
inference(component_clause,[status(thm)],[f4575]) ).
fof(f4578,plain,
( spl0_92
<=> join_commutative(sk0_175) ),
introduced(split_symbol_definition) ).
fof(f4581,plain,
( ~ latt_str(sk0_175)
| empty_carrier(sk0_175)
| join_commutative(sk0_175) ),
inference(resolution,[status(thm)],[f736,f2290]) ).
fof(f4582,plain,
( ~ spl0_77
| spl0_91
| spl0_92 ),
inference(split_clause,[status(thm)],[f4581,f4454,f4575,f4578]) ).
fof(f4583,plain,
( $false
| ~ spl0_91 ),
inference(forward_subsumption_resolution,[status(thm)],[f4576,f2282]) ).
fof(f4584,plain,
~ spl0_91,
inference(contradiction_clause,[status(thm)],[f4583]) ).
fof(f4586,plain,
( spl0_93
<=> join_associative(sk0_175) ),
introduced(split_symbol_definition) ).
fof(f4589,plain,
( ~ latt_str(sk0_175)
| empty_carrier(sk0_175)
| join_associative(sk0_175) ),
inference(resolution,[status(thm)],[f737,f2290]) ).
fof(f4590,plain,
( ~ spl0_77
| spl0_91
| spl0_93 ),
inference(split_clause,[status(thm)],[f4589,f4454,f4575,f4586]) ).
fof(f4592,plain,
( spl0_94
<=> meet_commutative(sk0_175) ),
introduced(split_symbol_definition) ).
fof(f4595,plain,
( ~ latt_str(sk0_175)
| empty_carrier(sk0_175)
| meet_commutative(sk0_175) ),
inference(resolution,[status(thm)],[f738,f2290]) ).
fof(f4596,plain,
( ~ spl0_77
| spl0_91
| spl0_94 ),
inference(split_clause,[status(thm)],[f4595,f4454,f4575,f4592]) ).
fof(f4598,plain,
( spl0_95
<=> meet_associative(sk0_175) ),
introduced(split_symbol_definition) ).
fof(f4601,plain,
( ~ latt_str(sk0_175)
| empty_carrier(sk0_175)
| meet_associative(sk0_175) ),
inference(resolution,[status(thm)],[f739,f2290]) ).
fof(f4602,plain,
( ~ spl0_77
| spl0_91
| spl0_95 ),
inference(split_clause,[status(thm)],[f4601,f4454,f4575,f4598]) ).
fof(f4637,plain,
( spl0_96
<=> meet_absorbing(sk0_175) ),
introduced(split_symbol_definition) ).
fof(f4640,plain,
( ~ latt_str(sk0_175)
| empty_carrier(sk0_175)
| meet_absorbing(sk0_175) ),
inference(resolution,[status(thm)],[f740,f2290]) ).
fof(f4641,plain,
( ~ spl0_77
| spl0_91
| spl0_96 ),
inference(split_clause,[status(thm)],[f4640,f4454,f4575,f4637]) ).
fof(f4664,plain,
epsilon_transitive(sk0_150),
inference(resolution,[status(thm)],[f798,f2164]) ).
fof(f4665,plain,
epsilon_transitive(sk0_147),
inference(resolution,[status(thm)],[f798,f2153]) ).
fof(f4666,plain,
epsilon_transitive(sk0_146),
inference(resolution,[status(thm)],[f798,f2151]) ).
fof(f4672,plain,
epsilon_connected(sk0_150),
inference(resolution,[status(thm)],[f799,f2164]) ).
fof(f4673,plain,
epsilon_connected(sk0_147),
inference(resolution,[status(thm)],[f799,f2153]) ).
fof(f4674,plain,
epsilon_connected(sk0_146),
inference(resolution,[status(thm)],[f799,f2151]) ).
fof(f4677,plain,
( spl0_97
<=> join_absorbing(sk0_175) ),
introduced(split_symbol_definition) ).
fof(f4680,plain,
( ~ latt_str(sk0_175)
| empty_carrier(sk0_175)
| join_absorbing(sk0_175) ),
inference(resolution,[status(thm)],[f741,f2290]) ).
fof(f4681,plain,
( ~ spl0_77
| spl0_91
| spl0_97 ),
inference(split_clause,[status(thm)],[f4680,f4454,f4575,f4677]) ).
fof(f4746,plain,
element(empty_set,omega),
inference(resolution,[status(thm)],[f4138,f2999]) ).
fof(f4765,plain,
( spl0_99
<=> ordinal(omega) ),
introduced(split_symbol_definition) ).
fof(f4767,plain,
( ~ ordinal(omega)
| spl0_99 ),
inference(component_clause,[status(thm)],[f4765]) ).
fof(f4768,plain,
( spl0_100
<=> ordinal(empty_set) ),
introduced(split_symbol_definition) ).
fof(f4771,plain,
( ~ ordinal(omega)
| ordinal(empty_set) ),
inference(resolution,[status(thm)],[f4746,f723]) ).
fof(f4772,plain,
( ~ spl0_99
| spl0_100 ),
inference(split_clause,[status(thm)],[f4771,f4765,f4768]) ).
fof(f4773,plain,
( spl0_101
<=> epsilon_connected(empty_set) ),
introduced(split_symbol_definition) ).
fof(f4776,plain,
( ~ ordinal(omega)
| epsilon_connected(empty_set) ),
inference(resolution,[status(thm)],[f4746,f722]) ).
fof(f4777,plain,
( ~ spl0_99
| spl0_101 ),
inference(split_clause,[status(thm)],[f4776,f4765,f4773]) ).
fof(f4778,plain,
( spl0_102
<=> epsilon_transitive(empty_set) ),
introduced(split_symbol_definition) ).
fof(f4781,plain,
( ~ ordinal(omega)
| epsilon_transitive(empty_set) ),
inference(resolution,[status(thm)],[f4746,f721]) ).
fof(f4782,plain,
( ~ spl0_99
| spl0_102 ),
inference(split_clause,[status(thm)],[f4781,f4765,f4778]) ).
fof(f4851,plain,
( $false
| spl0_99 ),
inference(forward_subsumption_resolution,[status(thm)],[f4767,f4140]) ).
fof(f4852,plain,
spl0_99,
inference(contradiction_clause,[status(thm)],[f4851]) ).
fof(f4930,plain,
! [X0] :
( ~ empty(X0)
| ~ function(X0)
| one_to_one(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f773,f751]) ).
fof(f4934,plain,
( spl0_118
<=> empty(sk0_147) ),
introduced(split_symbol_definition) ).
fof(f4936,plain,
( ~ empty(sk0_147)
| spl0_118 ),
inference(component_clause,[status(thm)],[f4934]) ).
fof(f4937,plain,
( spl0_119
<=> one_to_one(sk0_147) ),
introduced(split_symbol_definition) ).
fof(f4940,plain,
( ~ empty(sk0_147)
| one_to_one(sk0_147) ),
inference(resolution,[status(thm)],[f4930,f4571]) ).
fof(f4941,plain,
( ~ spl0_118
| spl0_119 ),
inference(split_clause,[status(thm)],[f4940,f4934,f4937]) ).
fof(f4942,plain,
( spl0_120
<=> empty(sk0_150) ),
introduced(split_symbol_definition) ).
fof(f4944,plain,
( ~ empty(sk0_150)
| spl0_120 ),
inference(component_clause,[status(thm)],[f4942]) ).
fof(f4945,plain,
( spl0_121
<=> one_to_one(sk0_150) ),
introduced(split_symbol_definition) ).
fof(f4948,plain,
( ~ empty(sk0_150)
| one_to_one(sk0_150) ),
inference(resolution,[status(thm)],[f4930,f4570]) ).
fof(f4949,plain,
( ~ spl0_120
| spl0_121 ),
inference(split_clause,[status(thm)],[f4948,f4942,f4945]) ).
fof(f4970,plain,
( spl0_126
<=> empty(sk0_155) ),
introduced(split_symbol_definition) ).
fof(f4972,plain,
( ~ empty(sk0_155)
| spl0_126 ),
inference(component_clause,[status(thm)],[f4970]) ).
fof(f4973,plain,
( spl0_127
<=> one_to_one(sk0_155) ),
introduced(split_symbol_definition) ).
fof(f4976,plain,
( ~ empty(sk0_155)
| one_to_one(sk0_155) ),
inference(resolution,[status(thm)],[f4930,f2197]) ).
fof(f4977,plain,
( ~ spl0_126
| spl0_127 ),
inference(split_clause,[status(thm)],[f4976,f4970,f4973]) ).
fof(f4978,plain,
( spl0_128
<=> empty(sk0_152) ),
introduced(split_symbol_definition) ).
fof(f4980,plain,
( ~ empty(sk0_152)
| spl0_128 ),
inference(component_clause,[status(thm)],[f4978]) ).
fof(f4981,plain,
( spl0_129
<=> one_to_one(sk0_152) ),
introduced(split_symbol_definition) ).
fof(f4984,plain,
( ~ empty(sk0_152)
| one_to_one(sk0_152) ),
inference(resolution,[status(thm)],[f4930,f2179]) ).
fof(f4985,plain,
( ~ spl0_128
| spl0_129 ),
inference(split_clause,[status(thm)],[f4984,f4978,f4981]) ).
fof(f4986,plain,
( spl0_130
<=> empty(sk0_146) ),
introduced(split_symbol_definition) ).
fof(f4988,plain,
( ~ empty(sk0_146)
| spl0_130 ),
inference(component_clause,[status(thm)],[f4986]) ).
fof(f4989,plain,
( spl0_131
<=> one_to_one(sk0_146) ),
introduced(split_symbol_definition) ).
fof(f4992,plain,
( ~ empty(sk0_146)
| one_to_one(sk0_146) ),
inference(resolution,[status(thm)],[f4930,f2149]) ).
fof(f4993,plain,
( ~ spl0_130
| spl0_131 ),
inference(split_clause,[status(thm)],[f4992,f4986,f4989]) ).
fof(f5002,plain,
( spl0_134
<=> empty(empty_set) ),
introduced(split_symbol_definition) ).
fof(f5004,plain,
( ~ empty(empty_set)
| spl0_134 ),
inference(component_clause,[status(thm)],[f5002]) ).
fof(f5005,plain,
( spl0_135
<=> one_to_one(empty_set) ),
introduced(split_symbol_definition) ).
fof(f5008,plain,
( ~ empty(empty_set)
| one_to_one(empty_set) ),
inference(resolution,[status(thm)],[f4930,f1798]) ).
fof(f5009,plain,
( ~ spl0_134
| spl0_135 ),
inference(split_clause,[status(thm)],[f5008,f5002,f5005]) ).
fof(f5010,plain,
( $false
| spl0_134 ),
inference(forward_subsumption_resolution,[status(thm)],[f5004,f1710]) ).
fof(f5011,plain,
spl0_134,
inference(contradiction_clause,[status(thm)],[f5010]) ).
fof(f5012,plain,
( $false
| spl0_130 ),
inference(forward_subsumption_resolution,[status(thm)],[f4988,f2151]) ).
fof(f5013,plain,
spl0_130,
inference(contradiction_clause,[status(thm)],[f5012]) ).
fof(f5014,plain,
( $false
| spl0_128 ),
inference(forward_subsumption_resolution,[status(thm)],[f4980,f2178]) ).
fof(f5015,plain,
spl0_128,
inference(contradiction_clause,[status(thm)],[f5014]) ).
fof(f5016,plain,
( $false
| spl0_126 ),
inference(forward_subsumption_resolution,[status(thm)],[f4972,f2199]) ).
fof(f5017,plain,
spl0_126,
inference(contradiction_clause,[status(thm)],[f5016]) ).
fof(f5018,plain,
( $false
| spl0_120 ),
inference(forward_subsumption_resolution,[status(thm)],[f4944,f2164]) ).
fof(f5019,plain,
spl0_120,
inference(contradiction_clause,[status(thm)],[f5018]) ).
fof(f5020,plain,
( $false
| spl0_118 ),
inference(forward_subsumption_resolution,[status(thm)],[f4936,f2153]) ).
fof(f5021,plain,
spl0_118,
inference(contradiction_clause,[status(thm)],[f5020]) ).
fof(f5068,plain,
( spl0_136
<=> lattice(sk0_175) ),
introduced(split_symbol_definition) ).
fof(f5071,plain,
( ~ latt_str(sk0_175)
| empty_carrier(sk0_175)
| ~ join_commutative(sk0_175)
| ~ join_associative(sk0_175)
| ~ meet_commutative(sk0_175)
| ~ meet_associative(sk0_175)
| ~ meet_absorbing(sk0_175)
| lattice(sk0_175) ),
inference(resolution,[status(thm)],[f781,f2289]) ).
fof(f5072,plain,
( ~ spl0_77
| spl0_91
| ~ spl0_92
| ~ spl0_93
| ~ spl0_94
| ~ spl0_95
| ~ spl0_96
| spl0_136 ),
inference(split_clause,[status(thm)],[f5071,f4454,f4575,f4578,f4586,f4592,f4598,f4637,f5068]) ).
fof(f5074,plain,
( spl0_137
<=> epsilon_transitive(sk0_146) ),
introduced(split_symbol_definition) ).
fof(f5076,plain,
( ~ epsilon_transitive(sk0_146)
| spl0_137 ),
inference(component_clause,[status(thm)],[f5074]) ).
fof(f5077,plain,
( spl0_138
<=> ordinal(sk0_146) ),
introduced(split_symbol_definition) ).
fof(f5080,plain,
( ~ epsilon_transitive(sk0_146)
| ordinal(sk0_146) ),
inference(resolution,[status(thm)],[f785,f4674]) ).
fof(f5081,plain,
( ~ spl0_137
| spl0_138 ),
inference(split_clause,[status(thm)],[f5080,f5074,f5077]) ).
fof(f5082,plain,
( spl0_139
<=> epsilon_transitive(sk0_147) ),
introduced(split_symbol_definition) ).
fof(f5084,plain,
( ~ epsilon_transitive(sk0_147)
| spl0_139 ),
inference(component_clause,[status(thm)],[f5082]) ).
fof(f5085,plain,
( spl0_140
<=> ordinal(sk0_147) ),
introduced(split_symbol_definition) ).
fof(f5088,plain,
( ~ epsilon_transitive(sk0_147)
| ordinal(sk0_147) ),
inference(resolution,[status(thm)],[f785,f4673]) ).
fof(f5089,plain,
( ~ spl0_139
| spl0_140 ),
inference(split_clause,[status(thm)],[f5088,f5082,f5085]) ).
fof(f5090,plain,
( spl0_141
<=> epsilon_transitive(sk0_150) ),
introduced(split_symbol_definition) ).
fof(f5092,plain,
( ~ epsilon_transitive(sk0_150)
| spl0_141 ),
inference(component_clause,[status(thm)],[f5090]) ).
fof(f5093,plain,
( spl0_142
<=> ordinal(sk0_150) ),
introduced(split_symbol_definition) ).
fof(f5096,plain,
( ~ epsilon_transitive(sk0_150)
| ordinal(sk0_150) ),
inference(resolution,[status(thm)],[f785,f4672]) ).
fof(f5097,plain,
( ~ spl0_141
| spl0_142 ),
inference(split_clause,[status(thm)],[f5096,f5090,f5093]) ).
fof(f5099,plain,
( spl0_143
<=> epsilon_transitive(sk0_165) ),
introduced(split_symbol_definition) ).
fof(f5101,plain,
( ~ epsilon_transitive(sk0_165)
| spl0_143 ),
inference(component_clause,[status(thm)],[f5099]) ).
fof(f5102,plain,
( spl0_144
<=> ordinal(sk0_165) ),
introduced(split_symbol_definition) ).
fof(f5105,plain,
( ~ epsilon_transitive(sk0_165)
| ordinal(sk0_165) ),
inference(resolution,[status(thm)],[f785,f2238]) ).
fof(f5106,plain,
( ~ spl0_143
| spl0_144 ),
inference(split_clause,[status(thm)],[f5105,f5099,f5102]) ).
fof(f5107,plain,
( spl0_145
<=> epsilon_transitive(sk0_145) ),
introduced(split_symbol_definition) ).
fof(f5109,plain,
( ~ epsilon_transitive(sk0_145)
| spl0_145 ),
inference(component_clause,[status(thm)],[f5107]) ).
fof(f5110,plain,
( spl0_146
<=> ordinal(sk0_145) ),
introduced(split_symbol_definition) ).
fof(f5113,plain,
( ~ epsilon_transitive(sk0_145)
| ordinal(sk0_145) ),
inference(resolution,[status(thm)],[f785,f2144]) ).
fof(f5114,plain,
( ~ spl0_145
| spl0_146 ),
inference(split_clause,[status(thm)],[f5113,f5107,f5110]) ).
fof(f5115,plain,
( spl0_147
<=> epsilon_transitive(sk0_144) ),
introduced(split_symbol_definition) ).
fof(f5117,plain,
( ~ epsilon_transitive(sk0_144)
| spl0_147 ),
inference(component_clause,[status(thm)],[f5115]) ).
fof(f5118,plain,
( spl0_148
<=> ordinal(sk0_144) ),
introduced(split_symbol_definition) ).
fof(f5121,plain,
( ~ epsilon_transitive(sk0_144)
| ordinal(sk0_144) ),
inference(resolution,[status(thm)],[f785,f2140]) ).
fof(f5122,plain,
( ~ spl0_147
| spl0_148 ),
inference(split_clause,[status(thm)],[f5121,f5115,f5118]) ).
fof(f5123,plain,
( spl0_149
<=> epsilon_transitive(sk0_138) ),
introduced(split_symbol_definition) ).
fof(f5125,plain,
( ~ epsilon_transitive(sk0_138)
| spl0_149 ),
inference(component_clause,[status(thm)],[f5123]) ).
fof(f5126,plain,
( spl0_150
<=> ordinal(sk0_138) ),
introduced(split_symbol_definition) ).
fof(f5129,plain,
( ~ epsilon_transitive(sk0_138)
| ordinal(sk0_138) ),
inference(resolution,[status(thm)],[f785,f2114]) ).
fof(f5130,plain,
( ~ spl0_149
| spl0_150 ),
inference(split_clause,[status(thm)],[f5129,f5123,f5126]) ).
fof(f5133,plain,
( spl0_151
<=> epsilon_transitive(omega) ),
introduced(split_symbol_definition) ).
fof(f5135,plain,
( ~ epsilon_transitive(omega)
| spl0_151 ),
inference(component_clause,[status(thm)],[f5133]) ).
fof(f5138,plain,
( $false
| spl0_149 ),
inference(forward_subsumption_resolution,[status(thm)],[f5125,f2113]) ).
fof(f5139,plain,
spl0_149,
inference(contradiction_clause,[status(thm)],[f5138]) ).
fof(f5140,plain,
( $false
| spl0_147 ),
inference(forward_subsumption_resolution,[status(thm)],[f5117,f2139]) ).
fof(f5141,plain,
spl0_147,
inference(contradiction_clause,[status(thm)],[f5140]) ).
fof(f5142,plain,
( $false
| spl0_145 ),
inference(forward_subsumption_resolution,[status(thm)],[f5109,f2143]) ).
fof(f5143,plain,
spl0_145,
inference(contradiction_clause,[status(thm)],[f5142]) ).
fof(f5144,plain,
( $false
| spl0_143 ),
inference(forward_subsumption_resolution,[status(thm)],[f5101,f2237]) ).
fof(f5145,plain,
spl0_143,
inference(contradiction_clause,[status(thm)],[f5144]) ).
fof(f5146,plain,
( $false
| spl0_141 ),
inference(forward_subsumption_resolution,[status(thm)],[f5092,f4664]) ).
fof(f5147,plain,
spl0_141,
inference(contradiction_clause,[status(thm)],[f5146]) ).
fof(f5148,plain,
( $false
| spl0_139 ),
inference(forward_subsumption_resolution,[status(thm)],[f5084,f4665]) ).
fof(f5149,plain,
spl0_139,
inference(contradiction_clause,[status(thm)],[f5148]) ).
fof(f5150,plain,
( $false
| spl0_137 ),
inference(forward_subsumption_resolution,[status(thm)],[f5076,f4666]) ).
fof(f5151,plain,
spl0_137,
inference(contradiction_clause,[status(thm)],[f5150]) ).
fof(f5171,plain,
( $false
| spl0_151 ),
inference(forward_subsumption_resolution,[status(thm)],[f5135,f1737]) ).
fof(f5172,plain,
spl0_151,
inference(contradiction_clause,[status(thm)],[f5171]) ).
fof(f5173,plain,
( ~ element(sk0_386,powerset(sk0_385))
| ~ spl0_54
| spl0_60 ),
inference(forward_demodulation,[status(thm)],[f4305,f4335]) ).
fof(f5174,plain,
( $false
| ~ spl0_54
| spl0_60 ),
inference(forward_subsumption_resolution,[status(thm)],[f5173,f3377]) ).
fof(f5175,plain,
( ~ spl0_54
| spl0_60 ),
inference(contradiction_clause,[status(thm)],[f5174]) ).
fof(f5384,plain,
( sk0_386 = sk0_385
| ~ spl0_54 ),
inference(forward_demodulation,[status(thm)],[f3502,f4305]) ).
fof(f5385,plain,
( $false
| spl0_36
| ~ spl0_54 ),
inference(forward_subsumption_resolution,[status(thm)],[f5384,f3973]) ).
fof(f5386,plain,
( spl0_36
| ~ spl0_54 ),
inference(contradiction_clause,[status(thm)],[f5385]) ).
fof(f5392,plain,
( sk0_386 != sk0_385
| spl0_54 ),
inference(forward_demodulation,[status(thm)],[f3502,f4306]) ).
fof(f5496,plain,
( sk0_385 != sk0_385
| ~ spl0_36
| spl0_54 ),
inference(forward_demodulation,[status(thm)],[f3972,f5392]) ).
fof(f5497,plain,
( $false
| ~ spl0_36
| spl0_54 ),
inference(trivial_equality_resolution,[status(esa)],[f5496]) ).
fof(f5498,plain,
( ~ spl0_36
| spl0_54 ),
inference(contradiction_clause,[status(thm)],[f5497]) ).
fof(f5499,plain,
$false,
inference(sat_refutation,[status(thm)],[f3974,f3975,f4308,f4337,f4375,f4377,f4399,f4401,f4426,f4428,f4451,f4453,f4461,f4463,f4582,f4584,f4590,f4596,f4602,f4641,f4681,f4772,f4777,f4782,f4852,f4941,f4949,f4977,f4985,f4993,f5009,f5011,f5013,f5015,f5017,f5019,f5021,f5072,f5081,f5089,f5097,f5106,f5114,f5122,f5130,f5139,f5141,f5143,f5145,f5147,f5149,f5151,f5172,f5175,f5386,f5498]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU354+2 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n002.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Apr 29 20:03:24 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.43 % Drodi V3.6.0
% 0.21/0.56 % Refutation found
% 0.21/0.56 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.19/0.61 % Elapsed time: 0.242647 seconds
% 1.19/0.61 % CPU time: 1.169324 seconds
% 1.19/0.61 % Total memory used: 151.231 MB
% 1.19/0.61 % Net memory used: 150.312 MB
%------------------------------------------------------------------------------