%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU369+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n005.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 : Fri Sep 25 02:57:14 PM UTC 2026
% Result : Theorem 4.62s 2.06s
% Output : CNFRefutation 4.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 19
% Syntax : Number of formulae : 169 ( 57 unt; 3 def)
% Number of atoms : 729 ( 66 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 766 ( 308 ~; 327 |; 101 &)
% ( 11 <=>; 18 =>; 0 <=; 1 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 41 ( 39 usr; 4 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 263 ( 0 sgn 254 !; 9 ?; 133 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( rel_str(X0)
=> ( strict_rel_str(X0)
=> X0 = rel_str_of(the_carrier(X0),the_InternalRel(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
fof(f21,axiom,
! [X0] :
( ( latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> poset_of_lattice(X0) = rel_str_of(the_carrier(X0),k2_lattice3(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_lattice3) ).
fof(f22,axiom,
! [X0] : boole_POSet(X0) = poset_of_lattice(boole_lattice(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_yellow_1) ).
fof(f23,axiom,
! [X0] :
( ( latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> cast_to_el_of_LattPOSet(X0,X1) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_lattice3) ).
fof(f28,axiom,
! [X0] :
( latt_str(boole_lattice(X0))
& strict_latt_str(boole_lattice(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattice3) ).
fof(f36,axiom,
! [X0] :
( rel_str(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_yellow_1) ).
fof(f49,axiom,
! [X0] :
( rel_str(X0)
=> relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_orders_2) ).
fof(f60,axiom,
! [X0] :
( complete_latt_str(boole_lattice(X0))
& boolean_lattstr(boole_lattice(X0))
& complemented_lattstr(boole_lattice(X0))
& bounded_lattstr(boole_lattice(X0))
& upper_bounded_semilattstr(boole_lattice(X0))
& lower_bounded_semilattstr(boole_lattice(X0))
& modular_lattstr(boole_lattice(X0))
& distributive_lattstr(boole_lattice(X0))
& lattice(boole_lattice(X0))
& join_absorbing(boole_lattice(X0))
& meet_absorbing(boole_lattice(X0))
& meet_associative(boole_lattice(X0))
& meet_commutative(boole_lattice(X0))
& join_associative(boole_lattice(X0))
& join_commutative(boole_lattice(X0))
& strict_latt_str(boole_lattice(X0))
& ~ empty_carrier(boole_lattice(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_knaster) ).
fof(f72,axiom,
! [X0] :
( boolean_lattstr(boole_lattice(X0))
& complemented_lattstr(boole_lattice(X0))
& bounded_lattstr(boole_lattice(X0))
& upper_bounded_semilattstr(boole_lattice(X0))
& lower_bounded_semilattstr(boole_lattice(X0))
& modular_lattstr(boole_lattice(X0))
& distributive_lattstr(boole_lattice(X0))
& lattice(boole_lattice(X0))
& join_absorbing(boole_lattice(X0))
& meet_absorbing(boole_lattice(X0))
& meet_associative(boole_lattice(X0))
& meet_commutative(boole_lattice(X0))
& join_associative(boole_lattice(X0))
& join_commutative(boole_lattice(X0))
& strict_latt_str(boole_lattice(X0))
& ~ empty_carrier(boole_lattice(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_lattice3) ).
fof(f81,axiom,
! [X0] :
( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_yellow_1) ).
fof(f82,axiom,
! [X0,X1] :
( relation_of2(X1,X0,X0)
=> ! [X2,X3] :
( rel_str_of(X0,X1) = rel_str_of(X2,X3)
=> ( X1 = X3
& X0 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_orders_2) ).
fof(f105,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f106,axiom,
! [X0,X1,X2] :
( ( element(X2,the_carrier(X0))
& element(X1,the_carrier(X0))
& latt_str(X0)
& join_absorbing(X0)
& meet_absorbing(X0)
& meet_commutative(X0)
& ~ empty_carrier(X0) )
=> ( below_refl(X0,X1,X2)
<=> below(X0,X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r3_lattices) ).
fof(f112,axiom,
! [X0,X1] :
( element(X1,the_carrier(boole_lattice(X0)))
=> ! [X2] :
( element(X2,the_carrier(boole_lattice(X0)))
=> ( below(boole_lattice(X0),X1,X2)
<=> subset(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_lattice3) ).
fof(f114,conjecture,
! [X0,X1] :
( element(X1,the_carrier(boole_POSet(X0)))
=> ! [X2] :
( element(X2,the_carrier(boole_POSet(X0)))
=> ( related_reflexive(boole_POSet(X0),X1,X2)
<=> subset(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_yellow_1) ).
fof(f115,negated_conjecture,
~ ! [X0,X1] :
( element(X1,the_carrier(boole_POSet(X0)))
=> ! [X2] :
( element(X2,the_carrier(boole_POSet(X0)))
=> ( related_reflexive(boole_POSet(X0),X1,X2)
<=> subset(X1,X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f114]) ).
fof(f121,axiom,
! [X0] :
( ( latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( below_refl(X0,X1,X2)
<=> related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_lattice3) ).
fof(f125,plain,
! [X0] :
( complete_latt_str(boole_lattice(X0))
& boolean_lattstr(boole_lattice(X0))
& complemented_lattstr(boole_lattice(X0))
& bounded_lattstr(boole_lattice(X0))
& upper_bounded_semilattstr(boole_lattice(X0))
& lower_bounded_semilattstr(boole_lattice(X0))
& distributive_lattstr(boole_lattice(X0))
& lattice(boole_lattice(X0))
& join_absorbing(boole_lattice(X0))
& meet_absorbing(boole_lattice(X0))
& meet_associative(boole_lattice(X0))
& meet_commutative(boole_lattice(X0))
& join_associative(boole_lattice(X0))
& join_commutative(boole_lattice(X0))
& strict_latt_str(boole_lattice(X0))
& ~ empty_carrier(boole_lattice(X0)) ),
inference(pure_predicate_removal,[],[f60]) ).
fof(f127,plain,
! [X0] :
( boolean_lattstr(boole_lattice(X0))
& complemented_lattstr(boole_lattice(X0))
& bounded_lattstr(boole_lattice(X0))
& upper_bounded_semilattstr(boole_lattice(X0))
& lower_bounded_semilattstr(boole_lattice(X0))
& distributive_lattstr(boole_lattice(X0))
& lattice(boole_lattice(X0))
& join_absorbing(boole_lattice(X0))
& meet_absorbing(boole_lattice(X0))
& meet_associative(boole_lattice(X0))
& meet_commutative(boole_lattice(X0))
& join_associative(boole_lattice(X0))
& join_commutative(boole_lattice(X0))
& strict_latt_str(boole_lattice(X0))
& ~ empty_carrier(boole_lattice(X0)) ),
inference(pure_predicate_removal,[],[f72]) ).
fof(f132,plain,
! [X0] :
( ~ rel_str(X0)
| ~ strict_rel_str(X0)
| X0 = rel_str_of(the_carrier(X0),the_InternalRel(X0)) ),
inference(ennf_transformation,[],[f1]) ).
fof(f133,plain,
! [X0] :
( ~ rel_str(X0)
| ~ strict_rel_str(X0)
| X0 = rel_str_of(the_carrier(X0),the_InternalRel(X0)) ),
inference(flattening,[],[f132]) ).
fof(f167,plain,
! [X0] :
( ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| poset_of_lattice(X0) = rel_str_of(the_carrier(X0),k2_lattice3(X0)) ),
inference(ennf_transformation,[],[f21]) ).
fof(f168,plain,
! [X0] :
( ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| poset_of_lattice(X0) = rel_str_of(the_carrier(X0),k2_lattice3(X0)) ),
inference(flattening,[],[f167]) ).
fof(f169,plain,
! [X0] :
( ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| cast_to_el_of_LattPOSet(X0,X1) = X1 ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f170,plain,
! [X0] :
( ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| cast_to_el_of_LattPOSet(X0,X1) = X1 ) ),
inference(flattening,[],[f169]) ).
fof(f187,plain,
! [X0] :
( ~ rel_str(X0)
| relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ),
inference(ennf_transformation,[],[f49]) ).
fof(f212,plain,
! [X0,X1] :
( ~ relation_of2(X1,X0,X0)
| ! [X2,X3] :
( rel_str_of(X0,X1) != rel_str_of(X2,X3)
| ( X1 = X3
& X0 = X2 ) ) ),
inference(ennf_transformation,[],[f82]) ).
fof(f220,plain,
! [X0,X1,X2] :
( ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0)
| ( below_refl(X0,X1,X2)
<=> below(X0,X1,X2) ) ),
inference(ennf_transformation,[],[f106]) ).
fof(f221,plain,
! [X0,X1,X2] :
( ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0)
| ( below_refl(X0,X1,X2)
<=> below(X0,X1,X2) ) ),
inference(flattening,[],[f220]) ).
fof(f229,plain,
! [X0,X1] :
( ~ element(X1,the_carrier(boole_lattice(X0)))
| ! [X2] :
( ~ element(X2,the_carrier(boole_lattice(X0)))
| ( below(boole_lattice(X0),X1,X2)
<=> subset(X1,X2) ) ) ),
inference(ennf_transformation,[],[f112]) ).
fof(f232,plain,
? [X0,X1] :
( element(X1,the_carrier(boole_POSet(X0)))
& ? [X2] :
( element(X2,the_carrier(boole_POSet(X0)))
& ( related_reflexive(boole_POSet(X0),X1,X2)
<~> subset(X1,X2) ) ) ),
inference(ennf_transformation,[],[f115]) ).
fof(f238,plain,
! [X0] :
( ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ( below_refl(X0,X1,X2)
<=> related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2)) ) ) ) ),
inference(ennf_transformation,[],[f121]) ).
fof(f239,plain,
! [X0] :
( ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ( below_refl(X0,X1,X2)
<=> related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2)) ) ) ) ),
inference(flattening,[],[f238]) ).
fof(f276,plain,
! [X0,X1,X2] :
( ( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) )
& ( ~ relation_of2(X2,X0,X1)
| relation_of2_as_subset(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f105]) ).
fof(f277,plain,
! [X0,X1,X2] :
( ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0)
| ( ( ~ below_refl(X0,X1,X2)
| below(X0,X1,X2) )
& ( ~ below(X0,X1,X2)
| below_refl(X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f221]) ).
fof(f279,plain,
! [X0,X1] :
( ~ element(X1,the_carrier(boole_lattice(X0)))
| ! [X2] :
( ~ element(X2,the_carrier(boole_lattice(X0)))
| ( ( ~ below(boole_lattice(X0),X1,X2)
| subset(X1,X2) )
& ( ~ subset(X1,X2)
| below(boole_lattice(X0),X1,X2) ) ) ) ),
inference(nnf_transformation,[],[f229]) ).
fof(f280,plain,
? [X0,X1] :
( element(X1,the_carrier(boole_POSet(X0)))
& ? [X2] :
( element(X2,the_carrier(boole_POSet(X0)))
& ( related_reflexive(boole_POSet(X0),X1,X2)
| subset(X1,X2) )
& ( ~ related_reflexive(boole_POSet(X0),X1,X2)
| ~ subset(X1,X2) ) ) ),
inference(nnf_transformation,[],[f232]) ).
fof(f281,plain,
? [X0,X1] :
( element(X1,the_carrier(boole_POSet(X0)))
& ? [X2] :
( element(X2,the_carrier(boole_POSet(X0)))
& ( related_reflexive(boole_POSet(X0),X1,X2)
| subset(X1,X2) )
& ( ~ related_reflexive(boole_POSet(X0),X1,X2)
| ~ subset(X1,X2) ) ) ),
inference(flattening,[],[f280]) ).
fof(f282,plain,
( element(sK31,the_carrier(boole_POSet(sK30)))
& element(sK32,the_carrier(boole_POSet(sK30)))
& ( related_reflexive(boole_POSet(sK30),sK31,sK32)
| subset(sK31,sK32) )
& ( ~ related_reflexive(boole_POSet(sK30),sK31,sK32)
| ~ subset(sK31,sK32) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30,sK31,sK32]),skolemize(X0,sK30),skolemize(X1,sK31),skolemize(X2,sK32)],[f281]) ).
fof(f284,plain,
! [X0] :
( ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ( ( ~ below_refl(X0,X1,X2)
| related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2)) )
& ( ~ related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2))
| below_refl(X0,X1,X2) ) ) ) ) ),
inference(nnf_transformation,[],[f239]) ).
fof(f285,plain,
! [X0] :
( ~ rel_str(X0)
| ~ strict_rel_str(X0)
| rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0 ),
inference(cnf_transformation,[],[f133]) ).
fof(f346,plain,
! [X0] :
( ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| poset_of_lattice(X0) = rel_str_of(the_carrier(X0),k2_lattice3(X0)) ),
inference(cnf_transformation,[],[f168]) ).
fof(f347,plain,
! [X0] : boole_POSet(X0) = poset_of_lattice(boole_lattice(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f348,plain,
! [X0,X1] :
( ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ element(X1,the_carrier(X0))
| cast_to_el_of_LattPOSet(X0,X1) = X1 ),
inference(cnf_transformation,[],[f170]) ).
fof(f356,plain,
! [X0] : latt_str(boole_lattice(X0)),
inference(cnf_transformation,[],[f28]) ).
fof(f368,plain,
! [X0] : rel_str(boole_POSet(X0)),
inference(cnf_transformation,[],[f36]) ).
fof(f380,plain,
! [X0] :
( ~ rel_str(X0)
| relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ),
inference(cnf_transformation,[],[f187]) ).
fof(f399,plain,
! [X0] : lattice(boole_lattice(X0)),
inference(cnf_transformation,[],[f125]) ).
fof(f400,plain,
! [X0] : join_absorbing(boole_lattice(X0)),
inference(cnf_transformation,[],[f125]) ).
fof(f401,plain,
! [X0] : meet_absorbing(boole_lattice(X0)),
inference(cnf_transformation,[],[f125]) ).
fof(f403,plain,
! [X0] : meet_commutative(boole_lattice(X0)),
inference(cnf_transformation,[],[f125]) ).
fof(f407,plain,
! [X0] : ~ empty_carrier(boole_lattice(X0)),
inference(cnf_transformation,[],[f125]) ).
fof(f453,plain,
! [X0] : lattice(boole_lattice(X0)),
inference(cnf_transformation,[],[f127]) ).
fof(f454,plain,
! [X0] : join_absorbing(boole_lattice(X0)),
inference(cnf_transformation,[],[f127]) ).
fof(f455,plain,
! [X0] : meet_absorbing(boole_lattice(X0)),
inference(cnf_transformation,[],[f127]) ).
fof(f457,plain,
! [X0] : meet_commutative(boole_lattice(X0)),
inference(cnf_transformation,[],[f127]) ).
fof(f461,plain,
! [X0] : ~ empty_carrier(boole_lattice(X0)),
inference(cnf_transformation,[],[f127]) ).
fof(f509,plain,
! [X0] : strict_rel_str(boole_POSet(X0)),
inference(cnf_transformation,[],[f81]) ).
fof(f512,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2(X1,X0,X0)
| rel_str_of(X0,X1) != rel_str_of(X2,X3)
| X0 = X2 ),
inference(cnf_transformation,[],[f212]) ).
fof(f645,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f276]) ).
fof(f647,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0)
| ~ below_refl(X0,X1,X2)
| below(X0,X1,X2) ),
inference(cnf_transformation,[],[f277]) ).
fof(f648,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0)
| ~ below(X0,X1,X2)
| below_refl(X0,X1,X2) ),
inference(cnf_transformation,[],[f277]) ).
fof(f655,plain,
! [X2,X0,X1] :
( ~ element(X1,the_carrier(boole_lattice(X0)))
| ~ element(X2,the_carrier(boole_lattice(X0)))
| ~ below(boole_lattice(X0),X1,X2)
| subset(X1,X2) ),
inference(cnf_transformation,[],[f279]) ).
fof(f656,plain,
! [X2,X0,X1] :
( ~ element(X1,the_carrier(boole_lattice(X0)))
| ~ element(X2,the_carrier(boole_lattice(X0)))
| ~ subset(X1,X2)
| below(boole_lattice(X0),X1,X2) ),
inference(cnf_transformation,[],[f279]) ).
fof(f658,plain,
element(sK31,the_carrier(boole_POSet(sK30))),
inference(cnf_transformation,[],[f282]) ).
fof(f659,plain,
element(sK32,the_carrier(boole_POSet(sK30))),
inference(cnf_transformation,[],[f282]) ).
fof(f660,plain,
( related_reflexive(boole_POSet(sK30),sK31,sK32)
| subset(sK31,sK32) ),
inference(cnf_transformation,[],[f282]) ).
fof(f661,plain,
( ~ related_reflexive(boole_POSet(sK30),sK31,sK32)
| ~ subset(sK31,sK32) ),
inference(cnf_transformation,[],[f282]) ).
fof(f668,plain,
! [X2,X0,X1] :
( ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ below_refl(X0,X1,X2)
| related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2)) ),
inference(cnf_transformation,[],[f284]) ).
fof(f669,plain,
! [X2,X0,X1] :
( ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2))
| below_refl(X0,X1,X2) ),
inference(cnf_transformation,[],[f284]) ).
fof(f674,plain,
! [X0] : rel_str(poset_of_lattice(boole_lattice(X0))),
inference(definition_unfolding,[],[f368,f347]) ).
fof(f681,plain,
! [X0] : strict_rel_str(poset_of_lattice(boole_lattice(X0))),
inference(definition_unfolding,[],[f509,f347]) ).
fof(f691,plain,
( ~ related_reflexive(poset_of_lattice(boole_lattice(sK30)),sK31,sK32)
| ~ subset(sK31,sK32) ),
inference(definition_unfolding,[],[f661,f347]) ).
fof(f692,plain,
( related_reflexive(poset_of_lattice(boole_lattice(sK30)),sK31,sK32)
| subset(sK31,sK32) ),
inference(definition_unfolding,[],[f660,f347]) ).
fof(f693,plain,
element(sK32,the_carrier(poset_of_lattice(boole_lattice(sK30)))),
inference(definition_unfolding,[],[f659,f347]) ).
fof(f694,plain,
element(sK31,the_carrier(poset_of_lattice(boole_lattice(sK30)))),
inference(definition_unfolding,[],[f658,f347]) ).
tcf(c_49,plain,
! [X0: $i] :
( ( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0 )
| ~ rel_str(X0)
| ~ strict_rel_str(X0) ),
inference(cnf_transformation,[],[f285]) ).
tcf(c_98,plain,
! [X0: $i] :
( empty_carrier(X0)
| ( rel_str_of(the_carrier(X0),k2_lattice3(X0)) = poset_of_lattice(X0) )
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f346]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X1)
| ( cast_to_el_of_LattPOSet(X1,X0) = X0 )
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X0,the_carrier(X1)) ),
inference(cnf_transformation,[],[f348]) ).
tcf(c_107,plain,
! [X0: $i] : latt_str(boole_lattice(X0)),
inference(cnf_transformation,[],[f356]) ).
tcf(c_119,plain,
! [X0: $i] : rel_str(poset_of_lattice(boole_lattice(X0))),
inference(cnf_transformation,[],[f674]) ).
tcf(c_130,plain,
! [X0: $i] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f380]) ).
tcf(c_142,plain,
! [X0: $i] : ~ empty_carrier(boole_lattice(X0)),
inference(cnf_transformation,[],[f407]) ).
tcf(c_146,plain,
! [X0: $i] : meet_commutative(boole_lattice(X0)),
inference(cnf_transformation,[],[f403]) ).
tcf(c_148,plain,
! [X0: $i] : meet_absorbing(boole_lattice(X0)),
inference(cnf_transformation,[],[f401]) ).
tcf(c_149,plain,
! [X0: $i] : join_absorbing(boole_lattice(X0)),
inference(cnf_transformation,[],[f400]) ).
tcf(c_150,plain,
! [X0: $i] : lattice(boole_lattice(X0)),
inference(cnf_transformation,[],[f399]) ).
tcf(c_197,plain,
! [X0: $i] : ~ empty_carrier(boole_lattice(X0)),
inference(cnf_transformation,[],[f461]) ).
tcf(c_201,plain,
! [X0: $i] : meet_commutative(boole_lattice(X0)),
inference(cnf_transformation,[],[f457]) ).
tcf(c_203,plain,
! [X0: $i] : meet_absorbing(boole_lattice(X0)),
inference(cnf_transformation,[],[f455]) ).
tcf(c_204,plain,
! [X0: $i] : join_absorbing(boole_lattice(X0)),
inference(cnf_transformation,[],[f454]) ).
tcf(c_205,plain,
! [X0: $i] : lattice(boole_lattice(X0)),
inference(cnf_transformation,[],[f453]) ).
tcf(c_251,plain,
! [X0: $i] : strict_rel_str(poset_of_lattice(boole_lattice(X0))),
inference(cnf_transformation,[],[f681]) ).
tcf(c_261,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X2 )
| ~ relation_of2(X1,X0,X0)
| ( rel_str_of(X0,X1) != rel_str_of(X2,X3) ) ),
inference(cnf_transformation,[],[f512]) ).
tcf(c_396,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f645]) ).
tcf(c_397,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X0)
| below_refl(X0,X1,X2)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| ~ latt_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ below(X0,X1,X2) ),
inference(cnf_transformation,[],[f648]) ).
tcf(c_398,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X0)
| below(X0,X1,X2)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| ~ latt_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ below_refl(X0,X1,X2) ),
inference(cnf_transformation,[],[f647]) ).
tcf(c_405,plain,
! [X0: $i,X1: $i,X2: $i] :
( below(boole_lattice(X1),X0,X2)
| ~ subset(X0,X2)
| ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ element(X0,the_carrier(boole_lattice(X1))) ),
inference(cnf_transformation,[],[f656]) ).
tcf(c_406,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X1,X2)
| ~ element(X2,the_carrier(boole_lattice(X0)))
| ~ element(X1,the_carrier(boole_lattice(X0)))
| ~ below(boole_lattice(X0),X1,X2) ),
inference(cnf_transformation,[],[f655]) ).
tcf(c_408,negated_conjecture,
( ~ subset(sK31,sK32)
| ~ related_reflexive(poset_of_lattice(boole_lattice(sK30)),sK31,sK32) ),
inference(cnf_transformation,[],[f691]) ).
tcf(c_409,negated_conjecture,
( subset(sK31,sK32)
| related_reflexive(poset_of_lattice(boole_lattice(sK30)),sK31,sK32) ),
inference(cnf_transformation,[],[f692]) ).
tcf(c_410,negated_conjecture,
element(sK32,the_carrier(poset_of_lattice(boole_lattice(sK30)))),
inference(cnf_transformation,[],[f693]) ).
tcf(c_411,negated_conjecture,
element(sK31,the_carrier(poset_of_lattice(boole_lattice(sK30)))),
inference(cnf_transformation,[],[f694]) ).
tcf(c_418,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X0)
| below_refl(X0,X1,X2)
| ~ lattice(X0)
| ~ latt_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2)) ),
inference(cnf_transformation,[],[f669]) ).
tcf(c_419,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X0)
| related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2))
| ~ lattice(X0)
| ~ latt_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ below_refl(X0,X1,X2) ),
inference(cnf_transformation,[],[f668]) ).
tcf(c_4497,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( empty_carrier(X1)
| subset(X3,X5)
| ~ join_absorbing(X1)
| ~ meet_absorbing(X1)
| ~ meet_commutative(X1)
| ~ latt_str(X1)
| ~ element(X4,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ below_refl(X1,X2,X4)
| ~ element(X5,the_carrier(boole_lattice(X0)))
| ~ element(X3,the_carrier(boole_lattice(X0)))
| ( X4 != X5 )
| ( X2 != X3 )
| ( boole_lattice(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_398,c_406]) ).
tcf(c_4498,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(boole_lattice(X0))
| subset(X1,X2)
| ~ join_absorbing(boole_lattice(X0))
| ~ meet_absorbing(boole_lattice(X0))
| ~ meet_commutative(boole_lattice(X0))
| ~ latt_str(boole_lattice(X0))
| ~ element(X2,the_carrier(boole_lattice(X0)))
| ~ element(X1,the_carrier(boole_lattice(X0)))
| ~ below_refl(boole_lattice(X0),X1,X2) ),
inference(unflattening,[status(thm)],[c_4497]) ).
tcf(c_4499,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ below_refl(boole_lattice(X0),X1,X2)
| ~ element(X1,the_carrier(boole_lattice(X0)))
| ~ element(X2,the_carrier(boole_lattice(X0)))
| subset(X1,X2) ),
inference(global_subsumption_just,[status(thm)],[c_4498,c_204,c_203,c_201,c_107,c_197,c_4498]) ).
tcf(c_4500,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X1,X2)
| ~ element(X2,the_carrier(boole_lattice(X0)))
| ~ element(X1,the_carrier(boole_lattice(X0)))
| ~ below_refl(boole_lattice(X0),X1,X2) ),
inference(renaming,[status(thm)],[c_4499]) ).
tcf(c_4513,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( empty_carrier(X1)
| below_refl(X1,X2,X4)
| ~ join_absorbing(X1)
| ~ meet_absorbing(X1)
| ~ meet_commutative(X1)
| ~ latt_str(X1)
| ~ subset(X3,X5)
| ~ element(X4,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ element(X5,the_carrier(boole_lattice(X0)))
| ~ element(X3,the_carrier(boole_lattice(X0)))
| ( X4 != X5 )
| ( X2 != X3 )
| ( boole_lattice(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_397,c_405]) ).
tcf(c_4514,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(boole_lattice(X1))
| below_refl(boole_lattice(X1),X0,X2)
| ~ join_absorbing(boole_lattice(X1))
| ~ meet_absorbing(boole_lattice(X1))
| ~ meet_commutative(boole_lattice(X1))
| ~ latt_str(boole_lattice(X1))
| ~ subset(X0,X2)
| ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ element(X0,the_carrier(boole_lattice(X1))) ),
inference(unflattening,[status(thm)],[c_4513]) ).
tcf(c_4534,plain,
! [X0: $i,X1: $i,X2: $i] :
( below_refl(boole_lattice(X1),X0,X2)
| ~ subset(X0,X2)
| ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ element(X0,the_carrier(boole_lattice(X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4514,c_142,c_149,c_148,c_146,c_107]) ).
tcf(c_5699,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( empty_carrier(X1)
| subset(X3,X5)
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X4,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ element(X5,the_carrier(boole_lattice(X0)))
| ~ element(X3,the_carrier(boole_lattice(X0)))
| ~ related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X4))
| ( X4 != X5 )
| ( X2 != X3 )
| ( boole_lattice(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_418,c_4500]) ).
tcf(c_5700,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(boole_lattice(X0))
| subset(X1,X2)
| ~ lattice(boole_lattice(X0))
| ~ latt_str(boole_lattice(X0))
| ~ element(X2,the_carrier(boole_lattice(X0)))
| ~ element(X1,the_carrier(boole_lattice(X0)))
| ~ related_reflexive(poset_of_lattice(boole_lattice(X0)),cast_to_el_of_LattPOSet(boole_lattice(X0),X1),cast_to_el_of_LattPOSet(boole_lattice(X0),X2)) ),
inference(unflattening,[status(thm)],[c_5699]) ).
tcf(c_5701,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ related_reflexive(poset_of_lattice(boole_lattice(X0)),cast_to_el_of_LattPOSet(boole_lattice(X0),X1),cast_to_el_of_LattPOSet(boole_lattice(X0),X2))
| ~ element(X1,the_carrier(boole_lattice(X0)))
| ~ element(X2,the_carrier(boole_lattice(X0)))
| subset(X1,X2) ),
inference(global_subsumption_just,[status(thm)],[c_5700,c_205,c_107,c_197,c_5700]) ).
tcf(c_5702,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X1,X2)
| ~ element(X2,the_carrier(boole_lattice(X0)))
| ~ element(X1,the_carrier(boole_lattice(X0)))
| ~ related_reflexive(poset_of_lattice(boole_lattice(X0)),cast_to_el_of_LattPOSet(boole_lattice(X0),X1),cast_to_el_of_LattPOSet(boole_lattice(X0),X2)) ),
inference(renaming,[status(thm)],[c_5701]) ).
tcf(c_5715,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( empty_carrier(X1)
| related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X4))
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ subset(X3,X5)
| ~ element(X4,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ element(X5,the_carrier(boole_lattice(X0)))
| ~ element(X3,the_carrier(boole_lattice(X0)))
| ( X4 != X5 )
| ( X2 != X3 )
| ( boole_lattice(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_419,c_4534]) ).
tcf(c_5716,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(boole_lattice(X1))
| related_reflexive(poset_of_lattice(boole_lattice(X1)),cast_to_el_of_LattPOSet(boole_lattice(X1),X0),cast_to_el_of_LattPOSet(boole_lattice(X1),X2))
| ~ lattice(boole_lattice(X1))
| ~ latt_str(boole_lattice(X1))
| ~ subset(X0,X2)
| ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ element(X0,the_carrier(boole_lattice(X1))) ),
inference(unflattening,[status(thm)],[c_5715]) ).
tcf(c_5732,plain,
! [X0: $i,X1: $i,X2: $i] :
( related_reflexive(poset_of_lattice(boole_lattice(X1)),cast_to_el_of_LattPOSet(boole_lattice(X1),X0),cast_to_el_of_LattPOSet(boole_lattice(X1),X2))
| ~ subset(X0,X2)
| ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ element(X0,the_carrier(boole_lattice(X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5716,c_142,c_150,c_107]) ).
tcf(c_6448,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X1)
| ( rel_str_of(the_carrier(X1),k2_lattice3(X1)) = poset_of_lattice(X1) )
| ~ latt_str(X1)
| ( boole_lattice(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_98,c_150]) ).
tcf(c_6449,plain,
! [X0: $i] :
( empty_carrier(boole_lattice(X0))
| ( rel_str_of(the_carrier(boole_lattice(X0)),k2_lattice3(boole_lattice(X0))) = poset_of_lattice(boole_lattice(X0)) )
| ~ latt_str(boole_lattice(X0)) ),
inference(unflattening,[status(thm)],[c_6448]) ).
tcf(c_6451,plain,
! [X0: $i] : rel_str_of(the_carrier(boole_lattice(X0)),k2_lattice3(boole_lattice(X0))) = poset_of_lattice(boole_lattice(X0)),
inference(global_subsumption_just,[status(thm)],[c_6449,c_107,c_197,c_6449]) ).
tcf(c_6902,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| ( cast_to_el_of_LattPOSet(X1,X2) = X2 )
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ( boole_lattice(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_99,c_150]) ).
tcf(c_6903,plain,
! [X0: $i,X1: $i] :
( empty_carrier(boole_lattice(X1))
| ( cast_to_el_of_LattPOSet(boole_lattice(X1),X0) = X0 )
| ~ latt_str(boole_lattice(X1))
| ~ element(X0,the_carrier(boole_lattice(X1))) ),
inference(unflattening,[status(thm)],[c_6902]) ).
tcf(c_6913,plain,
! [X0: $i,X1: $i] :
( ( cast_to_el_of_LattPOSet(boole_lattice(X1),X0) = X0 )
| ~ element(X0,the_carrier(boole_lattice(X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6903,c_142,c_107]) ).
tcf(c_21845,plain,
! [X0: $i,X1: $i] :
( ( cast_to_el_of_LattPOSet(boole_lattice(X1),X0) = X0 )
| ~ element(X0,the_carrier(boole_lattice(X1))) ),
inference(prop_impl_just,[status(thm)],[c_6913]) ).
tcf(c_30055,definition,
iPr_def_20 = boole_lattice(sK30),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_30056,definition,
iPr_def_21 = poset_of_lattice(iPr_def_20),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_30057,definition,
iPr_def_22 = the_carrier(iPr_def_21),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_30058,negated_conjecture,
element(sK31,iPr_def_22),
inference(demodulation,[status(thm)],[c_411,c_30055,c_30056,c_30057]) ).
tcf(c_30059,negated_conjecture,
element(sK32,iPr_def_22),
inference(demodulation,[status(thm)],[c_410]) ).
tcf(c_30060,negated_conjecture,
( subset(sK31,sK32)
| related_reflexive(iPr_def_21,sK31,sK32) ),
inference(demodulation,[status(thm)],[c_409]) ).
tcf(c_30061,negated_conjecture,
( ~ subset(sK31,sK32)
| ~ related_reflexive(iPr_def_21,sK31,sK32) ),
inference(demodulation,[status(thm)],[c_408]) ).
tcf(c_33275,plain,
strict_rel_str(poset_of_lattice(iPr_def_20)),
inference(superposition,[status(thm)],[c_30055,c_251]) ).
tcf(c_33277,plain,
rel_str(poset_of_lattice(iPr_def_20)),
inference(superposition,[status(thm)],[c_30055,c_119]) ).
tcf(c_33280,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ element(X1,the_carrier(boole_lattice(sK30)))
| ~ element(X0,the_carrier(boole_lattice(sK30)))
| ~ related_reflexive(poset_of_lattice(iPr_def_20),cast_to_el_of_LattPOSet(iPr_def_20,X0),cast_to_el_of_LattPOSet(iPr_def_20,X1)) ),
inference(superposition,[status(thm)],[c_30055,c_5702]) ).
tcf(c_33283,plain,
! [X0: $i,X1: $i] :
( related_reflexive(poset_of_lattice(iPr_def_20),cast_to_el_of_LattPOSet(iPr_def_20,X0),cast_to_el_of_LattPOSet(iPr_def_20,X1))
| ~ subset(X0,X1)
| ~ element(X1,the_carrier(boole_lattice(sK30)))
| ~ element(X0,the_carrier(boole_lattice(sK30))) ),
inference(superposition,[status(thm)],[c_30055,c_5732]) ).
tcf(c_33284,plain,
rel_str(iPr_def_21),
inference(light_normalisation,[status(thm)],[c_33277,c_30056]) ).
tcf(c_33285,plain,
strict_rel_str(iPr_def_21),
inference(light_normalisation,[status(thm)],[c_33275,c_30056]) ).
tcf(c_33296,plain,
! [X0: $i,X1: $i] :
( related_reflexive(iPr_def_21,cast_to_el_of_LattPOSet(iPr_def_20,X0),cast_to_el_of_LattPOSet(iPr_def_20,X1))
| ~ subset(X0,X1)
| ~ element(X1,the_carrier(iPr_def_20))
| ~ element(X0,the_carrier(iPr_def_20)) ),
inference(light_normalisation,[status(thm)],[c_33283,c_30055,c_30056]) ).
tcf(c_33301,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ element(X1,the_carrier(iPr_def_20))
| ~ element(X0,the_carrier(iPr_def_20))
| ~ related_reflexive(iPr_def_21,cast_to_el_of_LattPOSet(iPr_def_20,X0),cast_to_el_of_LattPOSet(iPr_def_20,X1)) ),
inference(light_normalisation,[status(thm)],[c_33280,c_30055,c_30056]) ).
tcf(c_33467,plain,
rel_str_of(the_carrier(iPr_def_20),k2_lattice3(iPr_def_20)) = poset_of_lattice(iPr_def_20),
inference(superposition,[status(thm)],[c_30055,c_6451]) ).
tcf(c_33469,plain,
rel_str_of(the_carrier(iPr_def_20),k2_lattice3(iPr_def_20)) = iPr_def_21,
inference(light_normalisation,[status(thm)],[c_33467,c_30056]) ).
tcf(c_33589,plain,
( relation_of2_as_subset(the_InternalRel(iPr_def_21),iPr_def_22,iPr_def_22)
| ~ rel_str(iPr_def_21) ),
inference(superposition,[status(thm)],[c_30057,c_130]) ).
tcf(c_33592,plain,
relation_of2_as_subset(the_InternalRel(iPr_def_21),iPr_def_22,iPr_def_22),
inference(forward_subsumption_resolution,[status(thm)],[c_33589,c_33284]) ).
tcf(c_33634,plain,
relation_of2(the_InternalRel(iPr_def_21),iPr_def_22,iPr_def_22),
inference(superposition,[status(thm)],[c_33592,c_396]) ).
tcf(c_34057,plain,
! [X0: $i] :
( ( cast_to_el_of_LattPOSet(boole_lattice(sK30),X0) = X0 )
| ~ element(X0,the_carrier(iPr_def_20)) ),
inference(superposition,[status(thm)],[c_30055,c_21845]) ).
tcf(c_34058,plain,
! [X0: $i] :
( ( cast_to_el_of_LattPOSet(iPr_def_20,X0) = X0 )
| ~ element(X0,the_carrier(iPr_def_20)) ),
inference(light_normalisation,[status(thm)],[c_34057,c_30055]) ).
tcf(c_34080,plain,
( ( rel_str_of(the_carrier(iPr_def_21),the_InternalRel(iPr_def_21)) = iPr_def_21 )
| ~ rel_str(iPr_def_21) ),
inference(superposition,[status(thm)],[c_33285,c_49]) ).
tcf(c_34086,plain,
( ( rel_str_of(iPr_def_22,the_InternalRel(iPr_def_21)) = iPr_def_21 )
| ~ rel_str(iPr_def_21) ),
inference(light_normalisation,[status(thm)],[c_34080,c_30057]) ).
tcf(c_34087,plain,
rel_str_of(iPr_def_22,the_InternalRel(iPr_def_21)) = iPr_def_21,
inference(forward_subsumption_resolution,[status(thm)],[c_34086,c_33284]) ).
tcf(c_34189,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_22 )
| ~ relation_of2(the_InternalRel(iPr_def_21),iPr_def_22,iPr_def_22)
| ( rel_str_of(X0,X1) != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_34087,c_261]) ).
tcf(c_34225,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_22 )
| ( rel_str_of(X0,X1) != iPr_def_21 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34189,c_33634]) ).
tcf(c_36448,plain,
the_carrier(iPr_def_20) = iPr_def_22,
inference(superposition,[status(thm)],[c_33469,c_34225]) ).
tcf(c_36489,plain,
! [X0: $i] :
( ( cast_to_el_of_LattPOSet(iPr_def_20,X0) = X0 )
| ~ element(X0,iPr_def_22) ),
inference(demodulation,[status(thm)],[c_34058,c_36448]) ).
tcf(c_36496,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ element(X1,iPr_def_22)
| ~ element(X0,iPr_def_22)
| ~ related_reflexive(iPr_def_21,cast_to_el_of_LattPOSet(iPr_def_20,X0),cast_to_el_of_LattPOSet(iPr_def_20,X1)) ),
inference(demodulation,[status(thm)],[c_33301,c_36448]) ).
tcf(c_36497,plain,
! [X0: $i,X1: $i] :
( related_reflexive(iPr_def_21,cast_to_el_of_LattPOSet(iPr_def_20,X0),cast_to_el_of_LattPOSet(iPr_def_20,X1))
| ~ element(X1,iPr_def_22)
| ~ element(X0,iPr_def_22)
| ~ subset(X0,X1) ),
inference(demodulation,[status(thm)],[c_33296,c_36448]) ).
tcf(c_37093,plain,
cast_to_el_of_LattPOSet(iPr_def_20,sK31) = sK31,
inference(superposition,[status(thm)],[c_30058,c_36489]) ).
tcf(c_37094,plain,
cast_to_el_of_LattPOSet(iPr_def_20,sK32) = sK32,
inference(superposition,[status(thm)],[c_30059,c_36489]) ).
tcf(c_39879,plain,
! [X0: $i] :
( subset(X0,sK32)
| ~ element(sK32,iPr_def_22)
| ~ element(X0,iPr_def_22)
| ~ related_reflexive(iPr_def_21,cast_to_el_of_LattPOSet(iPr_def_20,X0),sK32) ),
inference(superposition,[status(thm)],[c_37094,c_36496]) ).
tcf(c_39880,plain,
! [X0: $i] :
( subset(X0,sK32)
| ~ element(X0,iPr_def_22)
| ~ related_reflexive(iPr_def_21,cast_to_el_of_LattPOSet(iPr_def_20,X0),sK32) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39879,c_30059]) ).
tcf(c_40023,plain,
( subset(sK31,sK32)
| ~ element(sK31,iPr_def_22)
| ~ related_reflexive(iPr_def_21,sK31,sK32) ),
inference(superposition,[status(thm)],[c_37093,c_39880]) ).
tcf(c_40025,plain,
( subset(sK31,sK32)
| ~ related_reflexive(iPr_def_21,sK31,sK32) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40023,c_30058]) ).
tcf(c_40029,plain,
subset(sK31,sK32),
inference(global_subsumption_just,[status(thm)],[c_40025,c_30060,c_40025]) ).
tcf(c_40031,plain,
~ related_reflexive(iPr_def_21,sK31,sK32),
inference(backward_subsumption_resolution,[status(thm)],[c_30061,c_40029]) ).
tcf(c_40093,plain,
! [X0: $i] :
( related_reflexive(iPr_def_21,cast_to_el_of_LattPOSet(iPr_def_20,X0),sK32)
| ~ element(sK32,iPr_def_22)
| ~ subset(X0,sK32)
| ~ element(X0,iPr_def_22) ),
inference(superposition,[status(thm)],[c_37094,c_36497]) ).
tcf(c_40095,plain,
! [X0: $i] :
( related_reflexive(iPr_def_21,cast_to_el_of_LattPOSet(iPr_def_20,X0),sK32)
| ~ subset(X0,sK32)
| ~ element(X0,iPr_def_22) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40093,c_30059]) ).
tcf(c_40348,plain,
( related_reflexive(iPr_def_21,sK31,sK32)
| ~ subset(sK31,sK32)
| ~ element(sK31,iPr_def_22) ),
inference(superposition,[status(thm)],[c_37093,c_40095]) ).
tcf(c_40352,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_40348,c_40031,c_40029,c_30058]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU369+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n005.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 13:52:04 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.41 % Proving...
% 4.62/2.06 % SZS status Started for theBenchmark.p
% 4.62/2.06 % SZS status Theorem for theBenchmark.p
% 4.62/2.06
% 4.62/2.06 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.62/2.06
% 4.62/2.06 % ------ iProver source info
% 4.62/2.06
% 4.62/2.06 % git: date: 2026-07-19 20:42:38 +0200
% 4.62/2.06 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.62/2.06 % git: non_committed_changes: false
% 4.62/2.06
% 4.62/2.06 % ------ Parsing...
% 4.62/2.06 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.62/2.06
% 4.62/2.06 % ------ Preprocessing... sup_sim: 2 sf_s rm: 59 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe_e sup_sim: 36 sf_s rm: 28 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 28 0s sf_e pe_s pe_e %
% 4.62/2.06
% 4.62/2.06 % ------ Preprocessing... gs_s sp: 10 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.62/2.06
% 4.62/2.06 % ------ Preprocessing... sf_s rm: 11 0s sf_e sf_s rm: 0 0s sf_e
% 4.62/2.06 % ------ Proving...
% 4.62/2.06 % ------ Problem Properties
% 4.62/2.06
% 4.62/2.06 %
% 4.62/2.06 % clauses 225
% 4.62/2.06 % conjectures 4
% 4.62/2.06 % EPR 86
% 4.62/2.06 % Horn 210
% 4.62/2.06 % unary 142
% 4.62/2.07 % binary 49
% 4.62/2.07 % lits 393
% 4.62/2.07 % lits eq 36
% 4.62/2.07 % fd_pure 0
% 4.62/2.07 % fd_pseudo 0
% 4.62/2.07 % fd_cond 1
% 4.62/2.07 % fd_pseudo_cond 6
% 4.62/2.07 % AC symbols 0
% 4.62/2.07
% 4.62/2.07 % ------ Schedule dynamic 5 is on
% 4.62/2.07
% 4.62/2.07 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.62/2.07
% 4.62/2.07
% 4.62/2.07 % ------
% 4.62/2.07 % Current options:
% 4.62/2.07 % ------
% 4.62/2.07
% 4.62/2.07
% 4.62/2.07 %
% 4.62/2.07
% 4.62/2.07 % ------ Proving...
% 4.62/2.07 %
% 4.62/2.07
% 4.62/2.07 % SZS status Theorem for theBenchmark.p
% 4.62/2.07
% 4.62/2.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.62/2.07
% 4.62/2.07
%------------------------------------------------------------------------------