TSTP Solution File: SEU369+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SEU369+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n029.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 : Fri May 3 03:05:59 EDT 2024
% Result : Theorem 7.81s 1.70s
% Output : CNFRefutation 7.81s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( rel_str(X0)
=> ( strict_rel_str(X0)
=> rel_str_of(the_carrier(X0),the_InternalRel(X0)) = 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(f61,axiom,
! [X0] :
( strict_latt_str(boole_lattice(X0))
& ~ empty_carrier(boole_lattice(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_lattice3) ).
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,[],[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(f124,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(f127,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(f132,plain,
! [X0] :
( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f133,plain,
! [X0] :
( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f132]) ).
fof(f167,plain,
! [X0] :
( poset_of_lattice(X0) = rel_str_of(the_carrier(X0),k2_lattice3(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f168,plain,
! [X0] :
( poset_of_lattice(X0) = rel_str_of(the_carrier(X0),k2_lattice3(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f167]) ).
fof(f169,plain,
! [X0] :
( ! [X1] :
( cast_to_el_of_LattPOSet(X0,X1) = X1
| ~ element(X1,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f170,plain,
! [X0] :
( ! [X1] :
( cast_to_el_of_LattPOSet(X0,X1) = X1
| ~ element(X1,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f169]) ).
fof(f187,plain,
! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f212,plain,
! [X0,X1] :
( ! [X2,X3] :
( ( X1 = X3
& X0 = X2 )
| rel_str_of(X0,X1) != rel_str_of(X2,X3) )
| ~ relation_of2(X1,X0,X0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f220,plain,
! [X0,X1,X2] :
( ( below_refl(X0,X1,X2)
<=> below(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) ),
inference(ennf_transformation,[],[f106]) ).
fof(f221,plain,
! [X0,X1,X2] :
( ( below_refl(X0,X1,X2)
<=> below(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) ),
inference(flattening,[],[f220]) ).
fof(f229,plain,
! [X0,X1] :
( ! [X2] :
( ( below(boole_lattice(X0),X1,X2)
<=> subset(X1,X2) )
| ~ element(X2,the_carrier(boole_lattice(X0))) )
| ~ element(X1,the_carrier(boole_lattice(X0))) ),
inference(ennf_transformation,[],[f112]) ).
fof(f232,plain,
? [X0,X1] :
( ? [X2] :
( ( related_reflexive(boole_POSet(X0),X1,X2)
<~> subset(X1,X2) )
& element(X2,the_carrier(boole_POSet(X0))) )
& element(X1,the_carrier(boole_POSet(X0))) ),
inference(ennf_transformation,[],[f115]) ).
fof(f238,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( 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)) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f121]) ).
fof(f239,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( 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)) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f238]) ).
fof(f304,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(f305,plain,
! [X0,X1,X2] :
( ( ( below_refl(X0,X1,X2)
| ~ below(X0,X1,X2) )
& ( below(X0,X1,X2)
| ~ below_refl(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) ),
inference(nnf_transformation,[],[f221]) ).
fof(f307,plain,
! [X0,X1] :
( ! [X2] :
( ( ( below(boole_lattice(X0),X1,X2)
| ~ subset(X1,X2) )
& ( subset(X1,X2)
| ~ below(boole_lattice(X0),X1,X2) ) )
| ~ element(X2,the_carrier(boole_lattice(X0))) )
| ~ element(X1,the_carrier(boole_lattice(X0))) ),
inference(nnf_transformation,[],[f229]) ).
fof(f308,plain,
? [X0,X1] :
( ? [X2] :
( ( ~ subset(X1,X2)
| ~ related_reflexive(boole_POSet(X0),X1,X2) )
& ( subset(X1,X2)
| related_reflexive(boole_POSet(X0),X1,X2) )
& element(X2,the_carrier(boole_POSet(X0))) )
& element(X1,the_carrier(boole_POSet(X0))) ),
inference(nnf_transformation,[],[f232]) ).
fof(f309,plain,
? [X0,X1] :
( ? [X2] :
( ( ~ subset(X1,X2)
| ~ related_reflexive(boole_POSet(X0),X1,X2) )
& ( subset(X1,X2)
| related_reflexive(boole_POSet(X0),X1,X2) )
& element(X2,the_carrier(boole_POSet(X0))) )
& element(X1,the_carrier(boole_POSet(X0))) ),
inference(flattening,[],[f308]) ).
fof(f310,plain,
( ? [X0,X1] :
( ? [X2] :
( ( ~ subset(X1,X2)
| ~ related_reflexive(boole_POSet(X0),X1,X2) )
& ( subset(X1,X2)
| related_reflexive(boole_POSet(X0),X1,X2) )
& element(X2,the_carrier(boole_POSet(X0))) )
& element(X1,the_carrier(boole_POSet(X0))) )
=> ( ? [X2] :
( ( ~ subset(sK31,X2)
| ~ related_reflexive(boole_POSet(sK30),sK31,X2) )
& ( subset(sK31,X2)
| related_reflexive(boole_POSet(sK30),sK31,X2) )
& element(X2,the_carrier(boole_POSet(sK30))) )
& element(sK31,the_carrier(boole_POSet(sK30))) ) ),
introduced(choice_axiom,[]) ).
fof(f311,plain,
( ? [X2] :
( ( ~ subset(sK31,X2)
| ~ related_reflexive(boole_POSet(sK30),sK31,X2) )
& ( subset(sK31,X2)
| related_reflexive(boole_POSet(sK30),sK31,X2) )
& element(X2,the_carrier(boole_POSet(sK30))) )
=> ( ( ~ subset(sK31,sK32)
| ~ related_reflexive(boole_POSet(sK30),sK31,sK32) )
& ( subset(sK31,sK32)
| related_reflexive(boole_POSet(sK30),sK31,sK32) )
& element(sK32,the_carrier(boole_POSet(sK30))) ) ),
introduced(choice_axiom,[]) ).
fof(f312,plain,
( ( ~ subset(sK31,sK32)
| ~ related_reflexive(boole_POSet(sK30),sK31,sK32) )
& ( subset(sK31,sK32)
| related_reflexive(boole_POSet(sK30),sK31,sK32) )
& element(sK32,the_carrier(boole_POSet(sK30)))
& element(sK31,the_carrier(boole_POSet(sK30))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30,sK31,sK32])],[f309,f311,f310]) ).
fof(f314,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( 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) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(nnf_transformation,[],[f239]) ).
fof(f315,plain,
! [X0] :
( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f376,plain,
! [X0] :
( poset_of_lattice(X0) = rel_str_of(the_carrier(X0),k2_lattice3(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f168]) ).
fof(f377,plain,
! [X0] : boole_POSet(X0) = poset_of_lattice(boole_lattice(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f378,plain,
! [X0,X1] :
( cast_to_el_of_LattPOSet(X0,X1) = X1
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f170]) ).
fof(f387,plain,
! [X0] : latt_str(boole_lattice(X0)),
inference(cnf_transformation,[],[f28]) ).
fof(f399,plain,
! [X0] : rel_str(boole_POSet(X0)),
inference(cnf_transformation,[],[f36]) ).
fof(f410,plain,
! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f187]) ).
fof(f426,plain,
! [X0] : meet_commutative(boole_lattice(X0)),
inference(cnf_transformation,[],[f127]) ).
fof(f428,plain,
! [X0] : meet_absorbing(boole_lattice(X0)),
inference(cnf_transformation,[],[f127]) ).
fof(f429,plain,
! [X0] : join_absorbing(boole_lattice(X0)),
inference(cnf_transformation,[],[f127]) ).
fof(f430,plain,
! [X0] : lattice(boole_lattice(X0)),
inference(cnf_transformation,[],[f127]) ).
fof(f438,plain,
! [X0] : ~ empty_carrier(boole_lattice(X0)),
inference(cnf_transformation,[],[f61]) ).
fof(f477,plain,
! [X0] : ~ empty_carrier(boole_lattice(X0)),
inference(cnf_transformation,[],[f124]) ).
fof(f481,plain,
! [X0] : meet_commutative(boole_lattice(X0)),
inference(cnf_transformation,[],[f124]) ).
fof(f483,plain,
! [X0] : meet_absorbing(boole_lattice(X0)),
inference(cnf_transformation,[],[f124]) ).
fof(f484,plain,
! [X0] : join_absorbing(boole_lattice(X0)),
inference(cnf_transformation,[],[f124]) ).
fof(f485,plain,
! [X0] : lattice(boole_lattice(X0)),
inference(cnf_transformation,[],[f124]) ).
fof(f531,plain,
! [X0] : strict_rel_str(boole_POSet(X0)),
inference(cnf_transformation,[],[f81]) ).
fof(f541,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| rel_str_of(X0,X1) != rel_str_of(X2,X3)
| ~ relation_of2(X1,X0,X0) ),
inference(cnf_transformation,[],[f212]) ).
fof(f675,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f304]) ).
fof(f677,plain,
! [X2,X0,X1] :
( below(X0,X1,X2)
| ~ below_refl(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) ),
inference(cnf_transformation,[],[f305]) ).
fof(f678,plain,
! [X2,X0,X1] :
( below_refl(X0,X1,X2)
| ~ below(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) ),
inference(cnf_transformation,[],[f305]) ).
fof(f685,plain,
! [X2,X0,X1] :
( subset(X1,X2)
| ~ below(boole_lattice(X0),X1,X2)
| ~ element(X2,the_carrier(boole_lattice(X0)))
| ~ element(X1,the_carrier(boole_lattice(X0))) ),
inference(cnf_transformation,[],[f307]) ).
fof(f686,plain,
! [X2,X0,X1] :
( below(boole_lattice(X0),X1,X2)
| ~ subset(X1,X2)
| ~ element(X2,the_carrier(boole_lattice(X0)))
| ~ element(X1,the_carrier(boole_lattice(X0))) ),
inference(cnf_transformation,[],[f307]) ).
fof(f688,plain,
element(sK31,the_carrier(boole_POSet(sK30))),
inference(cnf_transformation,[],[f312]) ).
fof(f689,plain,
element(sK32,the_carrier(boole_POSet(sK30))),
inference(cnf_transformation,[],[f312]) ).
fof(f690,plain,
( subset(sK31,sK32)
| related_reflexive(boole_POSet(sK30),sK31,sK32) ),
inference(cnf_transformation,[],[f312]) ).
fof(f691,plain,
( ~ subset(sK31,sK32)
| ~ related_reflexive(boole_POSet(sK30),sK31,sK32) ),
inference(cnf_transformation,[],[f312]) ).
fof(f698,plain,
! [X2,X0,X1] :
( 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)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f314]) ).
fof(f699,plain,
! [X2,X0,X1] :
( 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))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f314]) ).
fof(f703,plain,
! [X0] : rel_str(poset_of_lattice(boole_lattice(X0))),
inference(definition_unfolding,[],[f399,f377]) ).
fof(f719,plain,
! [X0] : strict_rel_str(poset_of_lattice(boole_lattice(X0))),
inference(definition_unfolding,[],[f531,f377]) ).
fof(f721,plain,
( ~ subset(sK31,sK32)
| ~ related_reflexive(poset_of_lattice(boole_lattice(sK30)),sK31,sK32) ),
inference(definition_unfolding,[],[f691,f377]) ).
fof(f722,plain,
( subset(sK31,sK32)
| related_reflexive(poset_of_lattice(boole_lattice(sK30)),sK31,sK32) ),
inference(definition_unfolding,[],[f690,f377]) ).
fof(f723,plain,
element(sK32,the_carrier(poset_of_lattice(boole_lattice(sK30)))),
inference(definition_unfolding,[],[f689,f377]) ).
fof(f724,plain,
element(sK31,the_carrier(poset_of_lattice(boole_lattice(sK30)))),
inference(definition_unfolding,[],[f688,f377]) ).
cnf(c_49,plain,
( ~ strict_rel_str(X0)
| ~ rel_str(X0)
| rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0 ),
inference(cnf_transformation,[],[f315]) ).
cnf(c_98,plain,
( ~ latt_str(X0)
| ~ lattice(X0)
| rel_str_of(the_carrier(X0),k2_lattice3(X0)) = poset_of_lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f376]) ).
cnf(c_99,plain,
( ~ element(X0,the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1)
| cast_to_el_of_LattPOSet(X1,X0) = X0
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f378]) ).
cnf(c_106,plain,
latt_str(boole_lattice(X0)),
inference(cnf_transformation,[],[f387]) ).
cnf(c_118,plain,
rel_str(poset_of_lattice(boole_lattice(X0))),
inference(cnf_transformation,[],[f703]) ).
cnf(c_130,plain,
( ~ rel_str(X0)
| relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ),
inference(cnf_transformation,[],[f410]) ).
cnf(c_149,plain,
lattice(boole_lattice(X0)),
inference(cnf_transformation,[],[f430]) ).
cnf(c_150,plain,
join_absorbing(boole_lattice(X0)),
inference(cnf_transformation,[],[f429]) ).
cnf(c_151,plain,
meet_absorbing(boole_lattice(X0)),
inference(cnf_transformation,[],[f428]) ).
cnf(c_153,plain,
meet_commutative(boole_lattice(X0)),
inference(cnf_transformation,[],[f426]) ).
cnf(c_159,plain,
~ empty_carrier(boole_lattice(X0)),
inference(cnf_transformation,[],[f438]) ).
cnf(c_203,plain,
lattice(boole_lattice(X0)),
inference(cnf_transformation,[],[f485]) ).
cnf(c_204,plain,
join_absorbing(boole_lattice(X0)),
inference(cnf_transformation,[],[f484]) ).
cnf(c_205,plain,
meet_absorbing(boole_lattice(X0)),
inference(cnf_transformation,[],[f483]) ).
cnf(c_207,plain,
meet_commutative(boole_lattice(X0)),
inference(cnf_transformation,[],[f481]) ).
cnf(c_211,plain,
~ empty_carrier(boole_lattice(X0)),
inference(cnf_transformation,[],[f477]) ).
cnf(c_259,plain,
strict_rel_str(poset_of_lattice(boole_lattice(X0))),
inference(cnf_transformation,[],[f719]) ).
cnf(c_262,plain,
( rel_str_of(X0,X1) != rel_str_of(X2,X3)
| ~ relation_of2(X1,X0,X0)
| X0 = X2 ),
inference(cnf_transformation,[],[f541]) ).
cnf(c_396,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[],[f675]) ).
cnf(c_397,plain,
( ~ below(X0,X1,X2)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| below_refl(X0,X1,X2)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f678]) ).
cnf(c_398,plain,
( ~ below_refl(X0,X1,X2)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| below(X0,X1,X2)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f677]) ).
cnf(c_405,plain,
( ~ element(X0,the_carrier(boole_lattice(X1)))
| ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ subset(X0,X2)
| below(boole_lattice(X1),X0,X2) ),
inference(cnf_transformation,[],[f686]) ).
cnf(c_406,plain,
( ~ below(boole_lattice(X0),X1,X2)
| ~ element(X1,the_carrier(boole_lattice(X0)))
| ~ element(X2,the_carrier(boole_lattice(X0)))
| subset(X1,X2) ),
inference(cnf_transformation,[],[f685]) ).
cnf(c_408,negated_conjecture,
( ~ related_reflexive(poset_of_lattice(boole_lattice(sK30)),sK31,sK32)
| ~ subset(sK31,sK32) ),
inference(cnf_transformation,[],[f721]) ).
cnf(c_409,negated_conjecture,
( related_reflexive(poset_of_lattice(boole_lattice(sK30)),sK31,sK32)
| subset(sK31,sK32) ),
inference(cnf_transformation,[],[f722]) ).
cnf(c_410,negated_conjecture,
element(sK32,the_carrier(poset_of_lattice(boole_lattice(sK30)))),
inference(cnf_transformation,[],[f723]) ).
cnf(c_411,negated_conjecture,
element(sK31,the_carrier(poset_of_lattice(boole_lattice(sK30)))),
inference(cnf_transformation,[],[f724]) ).
cnf(c_418,plain,
( ~ related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2))
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| below_refl(X0,X1,X2)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f699]) ).
cnf(c_419,plain,
( ~ below_refl(X0,X1,X2)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2))
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f698]) ).
cnf(c_4473,plain,
( boole_lattice(X0) != X1
| X2 != X3
| X4 != X5
| ~ element(X3,the_carrier(boole_lattice(X0)))
| ~ element(X5,the_carrier(boole_lattice(X0)))
| ~ below_refl(X1,X2,X4)
| ~ element(X2,the_carrier(X1))
| ~ element(X4,the_carrier(X1))
| ~ latt_str(X1)
| ~ join_absorbing(X1)
| ~ meet_absorbing(X1)
| ~ meet_commutative(X1)
| subset(X3,X5)
| empty_carrier(X1) ),
inference(resolution_lifted,[status(thm)],[c_398,c_406]) ).
cnf(c_4474,plain,
( ~ below_refl(boole_lattice(X0),X1,X2)
| ~ element(X1,the_carrier(boole_lattice(X0)))
| ~ element(X2,the_carrier(boole_lattice(X0)))
| ~ latt_str(boole_lattice(X0))
| ~ join_absorbing(boole_lattice(X0))
| ~ meet_absorbing(boole_lattice(X0))
| ~ meet_commutative(boole_lattice(X0))
| subset(X1,X2)
| empty_carrier(boole_lattice(X0)) ),
inference(unflattening,[status(thm)],[c_4473]) ).
cnf(c_4475,plain,
( 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(global_subsumption_just,[status(thm)],[c_4474,c_207,c_205,c_204,c_106,c_211,c_4474]) ).
cnf(c_4476,plain,
( ~ 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(renaming,[status(thm)],[c_4475]) ).
cnf(c_4489,plain,
( boole_lattice(X0) != X1
| X2 != X3
| X4 != X5
| ~ element(X3,the_carrier(boole_lattice(X0)))
| ~ element(X5,the_carrier(boole_lattice(X0)))
| ~ element(X2,the_carrier(X1))
| ~ element(X4,the_carrier(X1))
| ~ subset(X3,X5)
| ~ latt_str(X1)
| ~ join_absorbing(X1)
| ~ meet_absorbing(X1)
| ~ meet_commutative(X1)
| below_refl(X1,X2,X4)
| empty_carrier(X1) ),
inference(resolution_lifted,[status(thm)],[c_397,c_405]) ).
cnf(c_4490,plain,
( ~ element(X0,the_carrier(boole_lattice(X1)))
| ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ subset(X0,X2)
| ~ latt_str(boole_lattice(X1))
| ~ join_absorbing(boole_lattice(X1))
| ~ meet_absorbing(boole_lattice(X1))
| ~ meet_commutative(boole_lattice(X1))
| below_refl(boole_lattice(X1),X0,X2)
| empty_carrier(boole_lattice(X1)) ),
inference(unflattening,[status(thm)],[c_4489]) ).
cnf(c_4510,plain,
( ~ element(X0,the_carrier(boole_lattice(X1)))
| ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ subset(X0,X2)
| below_refl(boole_lattice(X1),X0,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4490,c_159,c_153,c_151,c_150,c_106]) ).
cnf(c_5111,plain,
( boole_lattice(X0) != X1
| X2 != X3
| X4 != X5
| ~ related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X4))
| ~ element(X3,the_carrier(boole_lattice(X0)))
| ~ element(X5,the_carrier(boole_lattice(X0)))
| ~ element(X2,the_carrier(X1))
| ~ element(X4,the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1)
| subset(X3,X5)
| empty_carrier(X1) ),
inference(resolution_lifted,[status(thm)],[c_418,c_4476]) ).
cnf(c_5112,plain,
( ~ 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)))
| ~ latt_str(boole_lattice(X0))
| ~ lattice(boole_lattice(X0))
| subset(X1,X2)
| empty_carrier(boole_lattice(X0)) ),
inference(unflattening,[status(thm)],[c_5111]) ).
cnf(c_5113,plain,
( 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(global_subsumption_just,[status(thm)],[c_5112,c_203,c_106,c_211,c_5112]) ).
cnf(c_5114,plain,
( ~ 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(renaming,[status(thm)],[c_5113]) ).
cnf(c_5127,plain,
( boole_lattice(X0) != X1
| X2 != X3
| X4 != X5
| ~ element(X3,the_carrier(boole_lattice(X0)))
| ~ element(X5,the_carrier(boole_lattice(X0)))
| ~ element(X2,the_carrier(X1))
| ~ element(X4,the_carrier(X1))
| ~ subset(X3,X5)
| ~ latt_str(X1)
| ~ lattice(X1)
| related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X4))
| empty_carrier(X1) ),
inference(resolution_lifted,[status(thm)],[c_419,c_4510]) ).
cnf(c_5128,plain,
( ~ element(X0,the_carrier(boole_lattice(X1)))
| ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ subset(X0,X2)
| ~ latt_str(boole_lattice(X1))
| ~ lattice(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))
| empty_carrier(boole_lattice(X1)) ),
inference(unflattening,[status(thm)],[c_5127]) ).
cnf(c_5144,plain,
( ~ element(X0,the_carrier(boole_lattice(X1)))
| ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ subset(X0,X2)
| 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)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5128,c_159,c_149,c_106]) ).
cnf(c_5860,plain,
( boole_lattice(X0) != X1
| ~ latt_str(X1)
| rel_str_of(the_carrier(X1),k2_lattice3(X1)) = poset_of_lattice(X1)
| empty_carrier(X1) ),
inference(resolution_lifted,[status(thm)],[c_98,c_149]) ).
cnf(c_5861,plain,
( ~ latt_str(boole_lattice(X0))
| rel_str_of(the_carrier(boole_lattice(X0)),k2_lattice3(boole_lattice(X0))) = poset_of_lattice(boole_lattice(X0))
| empty_carrier(boole_lattice(X0)) ),
inference(unflattening,[status(thm)],[c_5860]) ).
cnf(c_5863,plain,
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_5861,c_106,c_211,c_5861]) ).
cnf(c_6314,plain,
( boole_lattice(X0) != X1
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1)
| cast_to_el_of_LattPOSet(X1,X2) = X2
| empty_carrier(X1) ),
inference(resolution_lifted,[status(thm)],[c_99,c_149]) ).
cnf(c_6315,plain,
( ~ element(X0,the_carrier(boole_lattice(X1)))
| ~ latt_str(boole_lattice(X1))
| cast_to_el_of_LattPOSet(boole_lattice(X1),X0) = X0
| empty_carrier(boole_lattice(X1)) ),
inference(unflattening,[status(thm)],[c_6314]) ).
cnf(c_6325,plain,
( ~ element(X0,the_carrier(boole_lattice(X1)))
| cast_to_el_of_LattPOSet(boole_lattice(X1),X0) = X0 ),
inference(forward_subsumption_resolution,[status(thm)],[c_6315,c_159,c_106]) ).
cnf(c_21257,plain,
( ~ element(X0,the_carrier(boole_lattice(X1)))
| cast_to_el_of_LattPOSet(boole_lattice(X1),X0) = X0 ),
inference(prop_impl_just,[status(thm)],[c_6325]) ).
cnf(c_29467,plain,
boole_lattice(sK30) = sP10_iProver_def,
definition ).
cnf(c_29468,plain,
poset_of_lattice(sP10_iProver_def) = sP11_iProver_def,
definition ).
cnf(c_29469,plain,
the_carrier(sP11_iProver_def) = sP12_iProver_def,
definition ).
cnf(c_29470,negated_conjecture,
element(sK31,sP12_iProver_def),
inference(demodulation,[status(thm)],[c_411,c_29467,c_29468,c_29469]) ).
cnf(c_29471,negated_conjecture,
element(sK32,sP12_iProver_def),
inference(demodulation,[status(thm)],[c_410]) ).
cnf(c_29472,negated_conjecture,
( related_reflexive(sP11_iProver_def,sK31,sK32)
| subset(sK31,sK32) ),
inference(demodulation,[status(thm)],[c_409]) ).
cnf(c_29473,negated_conjecture,
( ~ related_reflexive(sP11_iProver_def,sK31,sK32)
| ~ subset(sK31,sK32) ),
inference(demodulation,[status(thm)],[c_408]) ).
cnf(c_32684,plain,
strict_rel_str(poset_of_lattice(sP10_iProver_def)),
inference(superposition,[status(thm)],[c_29467,c_259]) ).
cnf(c_32689,plain,
rel_str(poset_of_lattice(sP10_iProver_def)),
inference(superposition,[status(thm)],[c_29467,c_118]) ).
cnf(c_32692,plain,
( ~ related_reflexive(poset_of_lattice(sP10_iProver_def),cast_to_el_of_LattPOSet(sP10_iProver_def,X0),cast_to_el_of_LattPOSet(sP10_iProver_def,X1))
| ~ element(X0,the_carrier(boole_lattice(sK30)))
| ~ element(X1,the_carrier(boole_lattice(sK30)))
| subset(X0,X1) ),
inference(superposition,[status(thm)],[c_29467,c_5114]) ).
cnf(c_32695,plain,
( ~ element(X0,the_carrier(boole_lattice(sK30)))
| ~ element(X1,the_carrier(boole_lattice(sK30)))
| ~ subset(X0,X1)
| related_reflexive(poset_of_lattice(sP10_iProver_def),cast_to_el_of_LattPOSet(sP10_iProver_def,X0),cast_to_el_of_LattPOSet(sP10_iProver_def,X1)) ),
inference(superposition,[status(thm)],[c_29467,c_5144]) ).
cnf(c_32696,plain,
rel_str(sP11_iProver_def),
inference(light_normalisation,[status(thm)],[c_32689,c_29468]) ).
cnf(c_32700,plain,
strict_rel_str(sP11_iProver_def),
inference(light_normalisation,[status(thm)],[c_32684,c_29468]) ).
cnf(c_32708,plain,
( ~ element(X0,the_carrier(sP10_iProver_def))
| ~ element(X1,the_carrier(sP10_iProver_def))
| ~ subset(X0,X1)
| related_reflexive(sP11_iProver_def,cast_to_el_of_LattPOSet(sP10_iProver_def,X0),cast_to_el_of_LattPOSet(sP10_iProver_def,X1)) ),
inference(light_normalisation,[status(thm)],[c_32695,c_29467,c_29468]) ).
cnf(c_32713,plain,
( ~ related_reflexive(sP11_iProver_def,cast_to_el_of_LattPOSet(sP10_iProver_def,X0),cast_to_el_of_LattPOSet(sP10_iProver_def,X1))
| ~ element(X0,the_carrier(sP10_iProver_def))
| ~ element(X1,the_carrier(sP10_iProver_def))
| subset(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_32692,c_29467,c_29468]) ).
cnf(c_32879,plain,
rel_str_of(the_carrier(sP10_iProver_def),k2_lattice3(sP10_iProver_def)) = poset_of_lattice(sP10_iProver_def),
inference(superposition,[status(thm)],[c_29467,c_5863]) ).
cnf(c_32881,plain,
rel_str_of(the_carrier(sP10_iProver_def),k2_lattice3(sP10_iProver_def)) = sP11_iProver_def,
inference(light_normalisation,[status(thm)],[c_32879,c_29468]) ).
cnf(c_33001,plain,
( ~ rel_str(sP11_iProver_def)
| relation_of2_as_subset(the_InternalRel(sP11_iProver_def),sP12_iProver_def,sP12_iProver_def) ),
inference(superposition,[status(thm)],[c_29469,c_130]) ).
cnf(c_33004,plain,
relation_of2_as_subset(the_InternalRel(sP11_iProver_def),sP12_iProver_def,sP12_iProver_def),
inference(forward_subsumption_resolution,[status(thm)],[c_33001,c_32696]) ).
cnf(c_33046,plain,
relation_of2(the_InternalRel(sP11_iProver_def),sP12_iProver_def,sP12_iProver_def),
inference(superposition,[status(thm)],[c_33004,c_396]) ).
cnf(c_33469,plain,
( ~ element(X0,the_carrier(sP10_iProver_def))
| cast_to_el_of_LattPOSet(boole_lattice(sK30),X0) = X0 ),
inference(superposition,[status(thm)],[c_29467,c_21257]) ).
cnf(c_33470,plain,
( ~ element(X0,the_carrier(sP10_iProver_def))
| cast_to_el_of_LattPOSet(sP10_iProver_def,X0) = X0 ),
inference(light_normalisation,[status(thm)],[c_33469,c_29467]) ).
cnf(c_33492,plain,
( ~ rel_str(sP11_iProver_def)
| rel_str_of(the_carrier(sP11_iProver_def),the_InternalRel(sP11_iProver_def)) = sP11_iProver_def ),
inference(superposition,[status(thm)],[c_32700,c_49]) ).
cnf(c_33498,plain,
( ~ rel_str(sP11_iProver_def)
| rel_str_of(sP12_iProver_def,the_InternalRel(sP11_iProver_def)) = sP11_iProver_def ),
inference(light_normalisation,[status(thm)],[c_33492,c_29469]) ).
cnf(c_33499,plain,
rel_str_of(sP12_iProver_def,the_InternalRel(sP11_iProver_def)) = sP11_iProver_def,
inference(forward_subsumption_resolution,[status(thm)],[c_33498,c_32696]) ).
cnf(c_33731,plain,
( rel_str_of(X0,X1) != sP11_iProver_def
| ~ relation_of2(the_InternalRel(sP11_iProver_def),sP12_iProver_def,sP12_iProver_def)
| X0 = sP12_iProver_def ),
inference(superposition,[status(thm)],[c_33499,c_262]) ).
cnf(c_33767,plain,
( rel_str_of(X0,X1) != sP11_iProver_def
| X0 = sP12_iProver_def ),
inference(forward_subsumption_resolution,[status(thm)],[c_33731,c_33046]) ).
cnf(c_35860,plain,
the_carrier(sP10_iProver_def) = sP12_iProver_def,
inference(superposition,[status(thm)],[c_32881,c_33767]) ).
cnf(c_35901,plain,
( ~ element(X0,sP12_iProver_def)
| cast_to_el_of_LattPOSet(sP10_iProver_def,X0) = X0 ),
inference(demodulation,[status(thm)],[c_33470,c_35860]) ).
cnf(c_35908,plain,
( ~ related_reflexive(sP11_iProver_def,cast_to_el_of_LattPOSet(sP10_iProver_def,X0),cast_to_el_of_LattPOSet(sP10_iProver_def,X1))
| ~ element(X0,sP12_iProver_def)
| ~ element(X1,sP12_iProver_def)
| subset(X0,X1) ),
inference(demodulation,[status(thm)],[c_32713,c_35860]) ).
cnf(c_35909,plain,
( ~ subset(X0,X1)
| ~ element(X0,sP12_iProver_def)
| ~ element(X1,sP12_iProver_def)
| related_reflexive(sP11_iProver_def,cast_to_el_of_LattPOSet(sP10_iProver_def,X0),cast_to_el_of_LattPOSet(sP10_iProver_def,X1)) ),
inference(demodulation,[status(thm)],[c_32708,c_35860]) ).
cnf(c_36505,plain,
cast_to_el_of_LattPOSet(sP10_iProver_def,sK31) = sK31,
inference(superposition,[status(thm)],[c_29470,c_35901]) ).
cnf(c_36506,plain,
cast_to_el_of_LattPOSet(sP10_iProver_def,sK32) = sK32,
inference(superposition,[status(thm)],[c_29471,c_35901]) ).
cnf(c_39314,plain,
( ~ related_reflexive(sP11_iProver_def,cast_to_el_of_LattPOSet(sP10_iProver_def,X0),sK32)
| ~ element(X0,sP12_iProver_def)
| ~ element(sK32,sP12_iProver_def)
| subset(X0,sK32) ),
inference(superposition,[status(thm)],[c_36506,c_35908]) ).
cnf(c_39315,plain,
( ~ related_reflexive(sP11_iProver_def,cast_to_el_of_LattPOSet(sP10_iProver_def,X0),sK32)
| ~ element(X0,sP12_iProver_def)
| subset(X0,sK32) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39314,c_29471]) ).
cnf(c_39439,plain,
( ~ related_reflexive(sP11_iProver_def,sK31,sK32)
| ~ element(sK31,sP12_iProver_def)
| subset(sK31,sK32) ),
inference(superposition,[status(thm)],[c_36505,c_39315]) ).
cnf(c_39441,plain,
( ~ related_reflexive(sP11_iProver_def,sK31,sK32)
| subset(sK31,sK32) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39439,c_29470]) ).
cnf(c_39445,plain,
subset(sK31,sK32),
inference(global_subsumption_just,[status(thm)],[c_39441,c_29472,c_39441]) ).
cnf(c_39447,plain,
~ related_reflexive(sP11_iProver_def,sK31,sK32),
inference(backward_subsumption_resolution,[status(thm)],[c_29473,c_39445]) ).
cnf(c_39509,plain,
( ~ element(X0,sP12_iProver_def)
| ~ subset(X0,sK32)
| ~ element(sK32,sP12_iProver_def)
| related_reflexive(sP11_iProver_def,cast_to_el_of_LattPOSet(sP10_iProver_def,X0),sK32) ),
inference(superposition,[status(thm)],[c_36506,c_35909]) ).
cnf(c_39511,plain,
( ~ element(X0,sP12_iProver_def)
| ~ subset(X0,sK32)
| related_reflexive(sP11_iProver_def,cast_to_el_of_LattPOSet(sP10_iProver_def,X0),sK32) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39509,c_29471]) ).
cnf(c_39711,plain,
( ~ element(sK31,sP12_iProver_def)
| ~ subset(sK31,sK32)
| related_reflexive(sP11_iProver_def,sK31,sK32) ),
inference(superposition,[status(thm)],[c_36505,c_39511]) ).
cnf(c_39715,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_39711,c_39447,c_39445,c_29470]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU369+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 2 18:03:52 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.22/0.48 Running first-order theorem proving
% 0.22/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.81/1.70 % SZS status Started for theBenchmark.p
% 7.81/1.70 % SZS status Theorem for theBenchmark.p
% 7.81/1.70
% 7.81/1.70 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 7.81/1.70
% 7.81/1.70 ------ iProver source info
% 7.81/1.70
% 7.81/1.70 git: date: 2024-05-02 19:28:25 +0000
% 7.81/1.70 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 7.81/1.70 git: non_committed_changes: false
% 7.81/1.70
% 7.81/1.70 ------ Parsing...
% 7.81/1.70 ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.81/1.70
% 7.81/1.70 ------ 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
% 7.81/1.70
% 7.81/1.70 ------ Preprocessing... gs_s sp: 10 0s gs_e snvd_s sp: 0 0s snvd_e
% 7.81/1.70
% 7.81/1.70 ------ Preprocessing... sf_s rm: 11 0s sf_e sf_s rm: 0 0s sf_e
% 7.81/1.70 ------ Proving...
% 7.81/1.70 ------ Problem Properties
% 7.81/1.70
% 7.81/1.70
% 7.81/1.70 clauses 225
% 7.81/1.70 conjectures 4
% 7.81/1.70 EPR 86
% 7.81/1.70 Horn 210
% 7.81/1.70 unary 142
% 7.81/1.70 binary 49
% 7.81/1.70 lits 393
% 7.81/1.70 lits eq 36
% 7.81/1.70 fd_pure 0
% 7.81/1.70 fd_pseudo 0
% 7.81/1.70 fd_cond 1
% 7.81/1.70 fd_pseudo_cond 6
% 7.81/1.70 AC symbols 0
% 7.81/1.70
% 7.81/1.70 ------ Schedule dynamic 5 is on
% 7.81/1.70
% 7.81/1.70 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.81/1.70
% 7.81/1.70
% 7.81/1.70 ------
% 7.81/1.70 Current options:
% 7.81/1.70 ------
% 7.81/1.70
% 7.81/1.70
% 7.81/1.70
% 7.81/1.70
% 7.81/1.70 ------ Proving...
% 7.81/1.70
% 7.81/1.70
% 7.81/1.70 % SZS status Theorem for theBenchmark.p
% 7.81/1.70
% 7.81/1.70 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.81/1.70
% 7.81/1.70
%------------------------------------------------------------------------------