%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU348+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:20:14 PM UTC 2026
% Result : Theorem 0.23s 1.21s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 28
% Syntax : Number of formulae : 131 ( 17 unt; 21 def)
% Number of atoms : 464 ( 21 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 557 ( 224 ~; 240 |; 56 &)
% ( 25 <=>; 11 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 36 ( 34 usr; 22 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 91 ( 80 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,axiom,
! [A] :
( ( latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> cast_to_el_of_LattPOSet(A,B) = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f105,axiom,
! [A] :
( ( latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(poset_of_lattice(A)))
=> cast_to_el_of_lattice(A,B) = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f189,axiom,
! [A,B] :
( ( element(B,the_carrier(poset_of_lattice(A)))
& latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> element(cast_to_el_of_lattice(A,B),the_carrier(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f367,axiom,
? [A] :
( strict_latt_str(A)
& ~ empty_carrier(A)
& latt_str(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f370,axiom,
? [A] :
( lattice(A)
& join_absorbing(A)
& meet_absorbing(A)
& meet_associative(A)
& meet_commutative(A)
& join_associative(A)
& join_commutative(A)
& strict_latt_str(A)
& ~ empty_carrier(A)
& latt_str(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f519,lemma,
! [A,B] :
( ( latt_str(B)
& lattice(B)
& ~ empty_carrier(B) )
=> ! [C] :
( element(C,the_carrier(B))
=> ( latt_set_smaller(B,C,A)
<=> relstr_element_smaller(poset_of_lattice(B),A,cast_to_el_of_LattPOSet(B,C)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f522,conjecture,
! [A,B] :
( ( latt_str(B)
& lattice(B)
& ~ empty_carrier(B) )
=> ! [C] :
( element(C,the_carrier(poset_of_lattice(B)))
=> ( relstr_element_smaller(poset_of_lattice(B),A,C)
<=> latt_set_smaller(B,cast_to_el_of_lattice(B,C),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f523,negated_conjecture,
~ ! [A,B] :
( ( latt_str(B)
& lattice(B)
& ~ empty_carrier(B) )
=> ! [C] :
( element(C,the_carrier(poset_of_lattice(B)))
=> ( relstr_element_smaller(poset_of_lattice(B),A,C)
<=> latt_set_smaller(B,cast_to_el_of_lattice(B,C),A) ) ) ),
inference(negated_conjecture,[status(cth)],[f522]) ).
fof(f1151,plain,
! [A] :
( ! [B] :
( cast_to_el_of_LattPOSet(A,B) = B
| ~ element(B,the_carrier(A)) )
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f1152,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,[status(thm)],[f1151]) ).
fof(f1207,plain,
! [A] :
( ! [B] :
( cast_to_el_of_lattice(A,B) = B
| ~ element(B,the_carrier(poset_of_lattice(A))) )
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f105]) ).
fof(f1208,plain,
! [X0,X1] :
( cast_to_el_of_lattice(X0,X1) = X1
| ~ element(X1,the_carrier(poset_of_lattice(X0)))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f1207]) ).
fof(f1501,plain,
! [A,B] :
( element(cast_to_el_of_lattice(A,B),the_carrier(A))
| ~ element(B,the_carrier(poset_of_lattice(A)))
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f189]) ).
fof(f1502,plain,
! [X0,X1] :
( element(cast_to_el_of_lattice(X0,X1),the_carrier(X0))
| ~ element(X1,the_carrier(poset_of_lattice(X0)))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f1501]) ).
fof(f2111,plain,
( strict_latt_str(sK164_skl)
& ~ empty_carrier(sK164_skl)
& latt_str(sK164_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK164_skl]),skolemize(A,sK164_skl)],[f367]) ).
fof(f2113,plain,
~ empty_carrier(sK164_skl),
inference(cnf_transformation,[status(thm)],[f2111]) ).
fof(f2124,plain,
( lattice(sK167_skl)
& join_absorbing(sK167_skl)
& meet_absorbing(sK167_skl)
& meet_associative(sK167_skl)
& meet_commutative(sK167_skl)
& join_associative(sK167_skl)
& join_commutative(sK167_skl)
& strict_latt_str(sK167_skl)
& ~ empty_carrier(sK167_skl)
& latt_str(sK167_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK167_skl]),skolemize(A,sK167_skl)],[f370]) ).
fof(f2125,plain,
latt_str(sK167_skl),
inference(cnf_transformation,[status(thm)],[f2124]) ).
fof(f2126,plain,
~ empty_carrier(sK167_skl),
inference(cnf_transformation,[status(thm)],[f2124]) ).
fof(f2134,plain,
lattice(sK167_skl),
inference(cnf_transformation,[status(thm)],[f2124]) ).
fof(f2928,plain,
! [A,B] :
( ! [C] :
( ( latt_set_smaller(B,C,A)
<=> relstr_element_smaller(poset_of_lattice(B),A,cast_to_el_of_LattPOSet(B,C)) )
| ~ element(C,the_carrier(B)) )
| ~ latt_str(B)
| ~ lattice(B)
| empty_carrier(B) ),
inference(pre_NNF_transformation,[status(thm)],[f519]) ).
fof(f2929,plain,
! [A,B] :
( ! [C] :
( ( ( ~ relstr_element_smaller(poset_of_lattice(B),A,cast_to_el_of_LattPOSet(B,C))
| latt_set_smaller(B,C,A) )
& ( relstr_element_smaller(poset_of_lattice(B),A,cast_to_el_of_LattPOSet(B,C))
| ~ latt_set_smaller(B,C,A) ) )
| ~ element(C,the_carrier(B)) )
| ~ latt_str(B)
| ~ lattice(B)
| empty_carrier(B) ),
inference(NNF_transformation,[status(thm)],[f2928]) ).
fof(f2930,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ~ relstr_element_smaller(poset_of_lattice(B),A,cast_to_el_of_LattPOSet(B,C))
| latt_set_smaller(B,C,A) )
& ! [A] :
( relstr_element_smaller(poset_of_lattice(B),A,cast_to_el_of_LattPOSet(B,C))
| ~ latt_set_smaller(B,C,A) ) )
| ~ element(C,the_carrier(B)) )
| ~ latt_str(B)
| ~ lattice(B)
| empty_carrier(B) ),
inference(miniscoping,[status(thm)],[f2929]) ).
fof(f2931,plain,
! [X0,X1,X2] :
( relstr_element_smaller(poset_of_lattice(X0),X2,cast_to_el_of_LattPOSet(X0,X1))
| ~ latt_set_smaller(X0,X1,X2)
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f2930]) ).
fof(f2932,plain,
! [X0,X1,X2] :
( ~ relstr_element_smaller(poset_of_lattice(X0),X2,cast_to_el_of_LattPOSet(X0,X1))
| latt_set_smaller(X0,X1,X2)
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f2930]) ).
fof(f2943,plain,
? [A,B] :
( ? [C] :
( ( relstr_element_smaller(poset_of_lattice(B),A,C)
<~> latt_set_smaller(B,cast_to_el_of_lattice(B,C),A) )
& element(C,the_carrier(poset_of_lattice(B))) )
& latt_str(B)
& lattice(B)
& ~ empty_carrier(B) ),
inference(pre_NNF_transformation,[status(thm)],[f523]) ).
fof(f2944,plain,
? [A,B] :
( ? [C] :
( ( ~ latt_set_smaller(B,cast_to_el_of_lattice(B,C),A)
| ~ relstr_element_smaller(poset_of_lattice(B),A,C) )
& ( latt_set_smaller(B,cast_to_el_of_lattice(B,C),A)
| relstr_element_smaller(poset_of_lattice(B),A,C) )
& element(C,the_carrier(poset_of_lattice(B))) )
& latt_str(B)
& lattice(B)
& ~ empty_carrier(B) ),
inference(NNF_transformation,[status(thm)],[f2943]) ).
fof(f2945,plain,
? [B] :
( ? [C] :
( ? [A] :
( ( ~ latt_set_smaller(B,cast_to_el_of_lattice(B,C),A)
| ~ relstr_element_smaller(poset_of_lattice(B),A,C) )
& ( latt_set_smaller(B,cast_to_el_of_lattice(B,C),A)
| relstr_element_smaller(poset_of_lattice(B),A,C) ) )
& element(C,the_carrier(poset_of_lattice(B))) )
& latt_str(B)
& lattice(B)
& ~ empty_carrier(B) ),
inference(miniscoping,[status(thm)],[f2944]) ).
fof(f2946,plain,
( ( ~ latt_set_smaller(sK359_skl,cast_to_el_of_lattice(sK359_skl,sK360_skl),sK361_skl)
| ~ relstr_element_smaller(poset_of_lattice(sK359_skl),sK361_skl,sK360_skl) )
& ( latt_set_smaller(sK359_skl,cast_to_el_of_lattice(sK359_skl,sK360_skl),sK361_skl)
| relstr_element_smaller(poset_of_lattice(sK359_skl),sK361_skl,sK360_skl) )
& element(sK360_skl,the_carrier(poset_of_lattice(sK359_skl)))
& latt_str(sK359_skl)
& lattice(sK359_skl)
& ~ empty_carrier(sK359_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK359_skl,sK360_skl,sK361_skl]),skolemize(B,sK359_skl),skolemize(C,sK360_skl),skolemize(A,sK361_skl)],[f2945]) ).
fof(f2947,plain,
~ empty_carrier(sK359_skl),
inference(cnf_transformation,[status(thm)],[f2946]) ).
fof(f2948,plain,
lattice(sK359_skl),
inference(cnf_transformation,[status(thm)],[f2946]) ).
fof(f2949,plain,
latt_str(sK359_skl),
inference(cnf_transformation,[status(thm)],[f2946]) ).
fof(f2950,plain,
element(sK360_skl,the_carrier(poset_of_lattice(sK359_skl))),
inference(cnf_transformation,[status(thm)],[f2946]) ).
fof(f2951,plain,
( latt_set_smaller(sK359_skl,cast_to_el_of_lattice(sK359_skl,sK360_skl),sK361_skl)
| relstr_element_smaller(poset_of_lattice(sK359_skl),sK361_skl,sK360_skl) ),
inference(cnf_transformation,[status(thm)],[f2946]) ).
fof(f2952,plain,
( ~ latt_set_smaller(sK359_skl,cast_to_el_of_lattice(sK359_skl,sK360_skl),sK361_skl)
| ~ relstr_element_smaller(poset_of_lattice(sK359_skl),sK361_skl,sK360_skl) ),
inference(cnf_transformation,[status(thm)],[f2946]) ).
fof(f3993,definition,
( sQ31_spl
<=> relstr_element_smaller(poset_of_lattice(sK359_skl),sK361_skl,sK360_skl) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f3995,plain,
( sQ31_spl
| ~ relstr_element_smaller(poset_of_lattice(sK359_skl),sK361_skl,sK360_skl) ),
inference(component_clause,[status(thm)],[f3993]) ).
fof(f3996,definition,
( sQ32_spl
<=> latt_set_smaller(sK359_skl,cast_to_el_of_lattice(sK359_skl,sK360_skl),sK361_skl) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f3997,plain,
( ~ sQ32_spl
| latt_set_smaller(sK359_skl,cast_to_el_of_lattice(sK359_skl,sK360_skl),sK361_skl) ),
inference(component_clause,[status(thm)],[f3996]) ).
fof(f3998,plain,
( sQ32_spl
| ~ latt_set_smaller(sK359_skl,cast_to_el_of_lattice(sK359_skl,sK360_skl),sK361_skl) ),
inference(component_clause,[status(thm)],[f3996]) ).
fof(f3999,plain,
( sQ32_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f2951,f3993,f3996]) ).
fof(f4000,plain,
( ~ sQ32_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f2952,f3993,f3996]) ).
fof(f4448,plain,
! [X0] :
( cast_to_el_of_lattice(sK359_skl,X0) = X0
| ~ element(X0,the_carrier(poset_of_lattice(sK359_skl)))
| ~ latt_str(sK359_skl)
| empty_carrier(sK359_skl) ),
inference(resolution,[status(thm)],[f1208,f2948]) ).
fof(f4450,definition,
( sQ63_spl
<=> empty_carrier(sK359_skl) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f4451,plain,
( ~ sQ63_spl
| empty_carrier(sK359_skl) ),
inference(component_clause,[status(thm)],[f4450]) ).
fof(f4453,definition,
( sQ64_spl
<=> latt_str(sK359_skl) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f4455,plain,
( sQ64_spl
| ~ latt_str(sK359_skl) ),
inference(component_clause,[status(thm)],[f4453]) ).
fof(f4456,definition,
! [X0] :
( sQ65_spl
<=> ( cast_to_el_of_lattice(sK359_skl,X0) = X0
| ~ element(X0,the_carrier(poset_of_lattice(sK359_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f4457,plain,
! [X0] :
( ~ sQ65_spl
| cast_to_el_of_lattice(sK359_skl,X0) = X0
| ~ element(X0,the_carrier(poset_of_lattice(sK359_skl))) ),
inference(component_clause,[status(thm)],[f4456]) ).
fof(f4459,plain,
( sQ65_spl
| ~ sQ64_spl
| sQ63_spl ),
inference(split_clause,[status(thm)],[f4448,f4450,f4453,f4456]) ).
fof(f4460,definition,
( sQ66_spl
<=> lattice(sK359_skl) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f4462,plain,
( sQ66_spl
| ~ lattice(sK359_skl) ),
inference(component_clause,[status(thm)],[f4460]) ).
fof(f4466,plain,
( ~ sQ65_spl
| cast_to_el_of_lattice(sK359_skl,sK360_skl) = sK360_skl ),
inference(resolution,[status(thm)],[f4457,f2950]) ).
fof(f4468,plain,
! [X0] :
( element(cast_to_el_of_lattice(sK359_skl,X0),the_carrier(sK359_skl))
| ~ element(X0,the_carrier(poset_of_lattice(sK359_skl)))
| ~ latt_str(sK359_skl)
| empty_carrier(sK359_skl) ),
inference(resolution,[status(thm)],[f1502,f2948]) ).
fof(f4470,definition,
! [X0] :
( sQ67_spl
<=> ( element(cast_to_el_of_lattice(sK359_skl,X0),the_carrier(sK359_skl))
| ~ element(X0,the_carrier(poset_of_lattice(sK359_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f4471,plain,
! [X0] :
( ~ sQ67_spl
| element(cast_to_el_of_lattice(sK359_skl,X0),the_carrier(sK359_skl))
| ~ element(X0,the_carrier(poset_of_lattice(sK359_skl))) ),
inference(component_clause,[status(thm)],[f4470]) ).
fof(f4473,plain,
( sQ67_spl
| ~ sQ64_spl
| sQ63_spl ),
inference(split_clause,[status(thm)],[f4468,f4450,f4453,f4470]) ).
fof(f4475,plain,
( ~ sQ63_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4451,f2947]) ).
fof(f4476,plain,
~ sQ63_spl,
inference(contradiction_clause,[status(thm)],[f4475]) ).
fof(f4477,plain,
( sQ64_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4455,f2949]) ).
fof(f4478,plain,
sQ64_spl,
inference(contradiction_clause,[status(thm)],[f4477]) ).
fof(f4496,plain,
( sQ32_spl
| ~ sQ65_spl
| ~ latt_set_smaller(sK359_skl,sK360_skl,sK361_skl) ),
inference(forward_demodulation,[status(thm)],[f4466,f3998]) ).
fof(f4498,plain,
! [X0,X1] :
( ~ relstr_element_smaller(poset_of_lattice(sK359_skl),X1,cast_to_el_of_LattPOSet(sK359_skl,X0))
| latt_set_smaller(sK359_skl,X0,X1)
| ~ element(X0,the_carrier(sK359_skl))
| ~ latt_str(sK359_skl)
| empty_carrier(sK359_skl) ),
inference(resolution,[status(thm)],[f2932,f2948]) ).
fof(f4499,definition,
! [X0,X1] :
( sQ72_spl
<=> ( ~ relstr_element_smaller(poset_of_lattice(sK359_skl),X1,cast_to_el_of_LattPOSet(sK359_skl,X0))
| latt_set_smaller(sK359_skl,X0,X1)
| ~ element(X0,the_carrier(sK359_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f4500,plain,
! [X0,X1] :
( ~ sQ72_spl
| ~ relstr_element_smaller(poset_of_lattice(sK359_skl),X1,cast_to_el_of_LattPOSet(sK359_skl,X0))
| latt_set_smaller(sK359_skl,X0,X1)
| ~ element(X0,the_carrier(sK359_skl)) ),
inference(component_clause,[status(thm)],[f4499]) ).
fof(f4502,plain,
( sQ72_spl
| ~ sQ64_spl
| sQ63_spl ),
inference(split_clause,[status(thm)],[f4498,f4450,f4453,f4499]) ).
fof(f4520,plain,
( ~ sQ65_spl
| ~ sQ67_spl
| element(sK360_skl,the_carrier(sK359_skl))
| ~ element(sK360_skl,the_carrier(poset_of_lattice(sK359_skl))) ),
inference(paramodulation,[status(thm)],[f4466,f4471]) ).
fof(f4521,definition,
( sQ77_spl
<=> element(sK360_skl,the_carrier(poset_of_lattice(sK359_skl))) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f4523,plain,
( sQ77_spl
| ~ element(sK360_skl,the_carrier(poset_of_lattice(sK359_skl))) ),
inference(component_clause,[status(thm)],[f4521]) ).
fof(f4524,definition,
( sQ78_spl
<=> element(sK360_skl,the_carrier(sK359_skl)) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f4527,plain,
( ~ sQ65_spl
| ~ sQ67_spl
| sQ78_spl
| ~ sQ77_spl ),
inference(split_clause,[status(thm)],[f4520,f4521,f4524,f4470,f4456]) ).
fof(f4528,plain,
( sQ77_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4523,f2950]) ).
fof(f4529,plain,
sQ77_spl,
inference(contradiction_clause,[status(thm)],[f4528]) ).
fof(f4530,plain,
! [X0,X1] :
( ~ sQ67_spl
| ~ sQ72_spl
| ~ element(X0,the_carrier(poset_of_lattice(sK359_skl)))
| ~ relstr_element_smaller(poset_of_lattice(sK359_skl),X1,cast_to_el_of_LattPOSet(sK359_skl,cast_to_el_of_lattice(sK359_skl,X0)))
| latt_set_smaller(sK359_skl,cast_to_el_of_lattice(sK359_skl,X0),X1) ),
inference(resolution,[status(thm)],[f4500,f4471]) ).
fof(f4531,plain,
! [X0] :
( ~ sQ67_spl
| ~ sQ72_spl
| ~ relstr_element_smaller(poset_of_lattice(sK359_skl),X0,cast_to_el_of_LattPOSet(sK359_skl,cast_to_el_of_lattice(sK359_skl,sK360_skl)))
| latt_set_smaller(sK359_skl,cast_to_el_of_lattice(sK359_skl,sK360_skl),X0) ),
inference(resolution,[status(thm)],[f4530,f2950]) ).
fof(f4532,plain,
! [X0] :
( ~ sQ67_spl
| ~ sQ72_spl
| ~ sQ65_spl
| ~ relstr_element_smaller(poset_of_lattice(sK359_skl),X0,cast_to_el_of_LattPOSet(sK359_skl,cast_to_el_of_lattice(sK359_skl,sK360_skl)))
| latt_set_smaller(sK359_skl,sK360_skl,X0) ),
inference(forward_demodulation,[status(thm)],[f4466,f4531]) ).
fof(f4533,plain,
! [X0] :
( ~ sQ67_spl
| ~ sQ72_spl
| ~ sQ65_spl
| ~ relstr_element_smaller(poset_of_lattice(sK359_skl),X0,cast_to_el_of_LattPOSet(sK359_skl,sK360_skl))
| latt_set_smaller(sK359_skl,sK360_skl,X0) ),
inference(forward_demodulation,[status(thm)],[f4466,f4532]) ).
fof(f4537,definition,
( sQ79_spl
<=> empty_carrier(sK164_skl) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f4538,plain,
( ~ sQ79_spl
| empty_carrier(sK164_skl) ),
inference(component_clause,[status(thm)],[f4537]) ).
fof(f4551,plain,
! [X0] :
( ~ sQ67_spl
| ~ sQ72_spl
| ~ sQ65_spl
| ~ latt_set_smaller(sK359_skl,sK360_skl,X0)
| ~ element(sK360_skl,the_carrier(sK359_skl))
| ~ latt_str(sK359_skl)
| ~ lattice(sK359_skl)
| empty_carrier(sK359_skl)
| latt_set_smaller(sK359_skl,sK360_skl,X0) ),
inference(resolution,[status(thm)],[f4533,f2931]) ).
fof(f4552,definition,
! [X0] :
( sQ83_spl
<=> ( ~ latt_set_smaller(sK359_skl,sK360_skl,X0)
| latt_set_smaller(sK359_skl,sK360_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f4555,plain,
( ~ sQ67_spl
| ~ sQ72_spl
| ~ sQ65_spl
| ~ sQ78_spl
| ~ sQ64_spl
| ~ sQ66_spl
| sQ63_spl
| sQ83_spl ),
inference(split_clause,[status(thm)],[f4551,f4552,f4450,f4460,f4453,f4524,f4456,f4499,f4470]) ).
fof(f4556,plain,
( sQ66_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4462,f2948]) ).
fof(f4557,plain,
sQ66_spl,
inference(contradiction_clause,[status(thm)],[f4556]) ).
fof(f4558,plain,
( ~ sQ79_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4538,f2113]) ).
fof(f4559,plain,
~ sQ79_spl,
inference(contradiction_clause,[status(thm)],[f4558]) ).
fof(f4560,plain,
! [X0] :
( element(cast_to_el_of_lattice(sK167_skl,X0),the_carrier(sK167_skl))
| ~ element(X0,the_carrier(poset_of_lattice(sK167_skl)))
| ~ lattice(sK167_skl)
| empty_carrier(sK167_skl) ),
inference(resolution,[status(thm)],[f2125,f1502]) ).
fof(f4561,plain,
! [X0] :
( cast_to_el_of_lattice(sK167_skl,X0) = X0
| ~ element(X0,the_carrier(poset_of_lattice(sK167_skl)))
| ~ lattice(sK167_skl)
| empty_carrier(sK167_skl) ),
inference(resolution,[status(thm)],[f2125,f1208]) ).
fof(f4562,definition,
( sQ84_spl
<=> empty_carrier(sK167_skl) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f4563,plain,
( ~ sQ84_spl
| empty_carrier(sK167_skl) ),
inference(component_clause,[status(thm)],[f4562]) ).
fof(f4565,definition,
( sQ85_spl
<=> lattice(sK167_skl) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f4566,plain,
( ~ sQ85_spl
| lattice(sK167_skl) ),
inference(component_clause,[status(thm)],[f4565]) ).
fof(f4567,plain,
( sQ85_spl
| ~ lattice(sK167_skl) ),
inference(component_clause,[status(thm)],[f4565]) ).
fof(f4568,definition,
! [X0] :
( sQ86_spl
<=> ( element(cast_to_el_of_lattice(sK167_skl,X0),the_carrier(sK167_skl))
| ~ element(X0,the_carrier(poset_of_lattice(sK167_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f4571,plain,
( sQ86_spl
| ~ sQ85_spl
| sQ84_spl ),
inference(split_clause,[status(thm)],[f4560,f4562,f4565,f4568]) ).
fof(f4572,definition,
! [X0] :
( sQ87_spl
<=> ( cast_to_el_of_lattice(sK167_skl,X0) = X0
| ~ element(X0,the_carrier(poset_of_lattice(sK167_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f4575,plain,
( sQ87_spl
| ~ sQ85_spl
| sQ84_spl ),
inference(split_clause,[status(thm)],[f4561,f4562,f4565,f4572]) ).
fof(f4576,plain,
( ~ sQ84_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2126,f4563]) ).
fof(f4577,plain,
~ sQ84_spl,
inference(contradiction_clause,[status(thm)],[f4576]) ).
fof(f4578,plain,
( sQ85_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2134,f4567]) ).
fof(f4579,plain,
sQ85_spl,
inference(contradiction_clause,[status(thm)],[f4578]) ).
fof(f4580,plain,
! [X0,X1] :
( ~ sQ85_spl
| ~ relstr_element_smaller(poset_of_lattice(sK167_skl),X1,cast_to_el_of_LattPOSet(sK167_skl,X0))
| latt_set_smaller(sK167_skl,X0,X1)
| ~ element(X0,the_carrier(sK167_skl))
| ~ latt_str(sK167_skl)
| empty_carrier(sK167_skl) ),
inference(resolution,[status(thm)],[f4566,f2932]) ).
fof(f4583,definition,
( sQ88_spl
<=> latt_str(sK167_skl) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f4585,plain,
( sQ88_spl
| ~ latt_str(sK167_skl) ),
inference(component_clause,[status(thm)],[f4583]) ).
fof(f4586,definition,
! [X0,X1] :
( sQ89_spl
<=> ( ~ relstr_element_smaller(poset_of_lattice(sK167_skl),X1,cast_to_el_of_LattPOSet(sK167_skl,X0))
| latt_set_smaller(sK167_skl,X0,X1)
| ~ element(X0,the_carrier(sK167_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f4589,plain,
( ~ sQ85_spl
| sQ89_spl
| ~ sQ88_spl
| sQ84_spl ),
inference(split_clause,[status(thm)],[f4580,f4562,f4583,f4586,f4565]) ).
fof(f4592,plain,
( sQ88_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4585,f2125]) ).
fof(f4593,plain,
sQ88_spl,
inference(contradiction_clause,[status(thm)],[f4592]) ).
fof(f4619,plain,
! [X0] :
( ~ sQ85_spl
| cast_to_el_of_LattPOSet(sK167_skl,X0) = X0
| ~ element(X0,the_carrier(sK167_skl))
| ~ latt_str(sK167_skl)
| empty_carrier(sK167_skl) ),
inference(resolution,[status(thm)],[f1152,f4566]) ).
fof(f4620,plain,
! [X0] :
( cast_to_el_of_LattPOSet(sK359_skl,X0) = X0
| ~ element(X0,the_carrier(sK359_skl))
| ~ latt_str(sK359_skl)
| empty_carrier(sK359_skl) ),
inference(resolution,[status(thm)],[f1152,f2948]) ).
fof(f4622,definition,
! [X0] :
( sQ90_spl
<=> ( cast_to_el_of_LattPOSet(sK167_skl,X0) = X0
| ~ element(X0,the_carrier(sK167_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f4625,plain,
( ~ sQ85_spl
| sQ90_spl
| ~ sQ88_spl
| sQ84_spl ),
inference(split_clause,[status(thm)],[f4619,f4562,f4583,f4622,f4565]) ).
fof(f4626,definition,
! [X0] :
( sQ91_spl
<=> ( cast_to_el_of_LattPOSet(sK359_skl,X0) = X0
| ~ element(X0,the_carrier(sK359_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f4627,plain,
! [X0] :
( ~ sQ91_spl
| cast_to_el_of_LattPOSet(sK359_skl,X0) = X0
| ~ element(X0,the_carrier(sK359_skl)) ),
inference(component_clause,[status(thm)],[f4626]) ).
fof(f4629,plain,
( sQ91_spl
| ~ sQ64_spl
| sQ63_spl ),
inference(split_clause,[status(thm)],[f4620,f4450,f4453,f4626]) ).
fof(f4634,plain,
! [X0] :
( ~ sQ67_spl
| ~ sQ91_spl
| ~ element(X0,the_carrier(poset_of_lattice(sK359_skl)))
| cast_to_el_of_LattPOSet(sK359_skl,cast_to_el_of_lattice(sK359_skl,X0)) = cast_to_el_of_lattice(sK359_skl,X0) ),
inference(resolution,[status(thm)],[f4627,f4471]) ).
fof(f4636,plain,
( ~ sQ67_spl
| ~ sQ91_spl
| cast_to_el_of_LattPOSet(sK359_skl,cast_to_el_of_lattice(sK359_skl,sK360_skl)) = cast_to_el_of_lattice(sK359_skl,sK360_skl) ),
inference(resolution,[status(thm)],[f4634,f2950]) ).
fof(f4637,plain,
( ~ sQ67_spl
| ~ sQ91_spl
| ~ sQ65_spl
| cast_to_el_of_LattPOSet(sK359_skl,sK360_skl) = cast_to_el_of_lattice(sK359_skl,sK360_skl) ),
inference(forward_demodulation,[status(thm)],[f4466,f4636]) ).
fof(f4638,plain,
( ~ sQ67_spl
| ~ sQ91_spl
| ~ sQ65_spl
| cast_to_el_of_LattPOSet(sK359_skl,sK360_skl) = sK360_skl ),
inference(forward_demodulation,[status(thm)],[f4466,f4637]) ).
fof(f4639,plain,
! [X0] :
( ~ sQ67_spl
| ~ sQ72_spl
| ~ sQ65_spl
| ~ sQ91_spl
| ~ relstr_element_smaller(poset_of_lattice(sK359_skl),X0,sK360_skl)
| latt_set_smaller(sK359_skl,sK360_skl,X0) ),
inference(backward_demodulation,[status(thm)],[f4638,f4533]) ).
fof(f4640,plain,
! [X0] :
( ~ sQ67_spl
| ~ sQ91_spl
| ~ sQ65_spl
| relstr_element_smaller(poset_of_lattice(sK359_skl),X0,sK360_skl)
| ~ latt_set_smaller(sK359_skl,sK360_skl,X0)
| ~ element(sK360_skl,the_carrier(sK359_skl))
| ~ latt_str(sK359_skl)
| ~ lattice(sK359_skl)
| empty_carrier(sK359_skl) ),
inference(paramodulation,[status(thm)],[f4638,f2931]) ).
fof(f4641,definition,
! [X0] :
( sQ92_spl
<=> ( relstr_element_smaller(poset_of_lattice(sK359_skl),X0,sK360_skl)
| ~ latt_set_smaller(sK359_skl,sK360_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f4642,plain,
! [X0] :
( ~ sQ92_spl
| relstr_element_smaller(poset_of_lattice(sK359_skl),X0,sK360_skl)
| ~ latt_set_smaller(sK359_skl,sK360_skl,X0) ),
inference(component_clause,[status(thm)],[f4641]) ).
fof(f4644,plain,
( ~ sQ67_spl
| ~ sQ91_spl
| ~ sQ65_spl
| sQ92_spl
| ~ sQ78_spl
| ~ sQ64_spl
| ~ sQ66_spl
| sQ63_spl ),
inference(split_clause,[status(thm)],[f4640,f4450,f4460,f4453,f4524,f4641,f4456,f4626,f4470]) ).
fof(f4646,plain,
( sQ32_spl
| ~ sQ65_spl
| ~ sQ67_spl
| ~ sQ72_spl
| ~ sQ91_spl
| ~ relstr_element_smaller(poset_of_lattice(sK359_skl),sK361_skl,sK360_skl) ),
inference(resolution,[status(thm)],[f4639,f4496]) ).
fof(f4647,plain,
( sQ32_spl
| ~ sQ65_spl
| ~ sQ67_spl
| ~ sQ72_spl
| ~ sQ91_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f4646,f3993,f4626,f4499,f4470,f4456,f3996]) ).
fof(f4648,plain,
( ~ sQ32_spl
| ~ sQ65_spl
| latt_set_smaller(sK359_skl,sK360_skl,sK361_skl) ),
inference(forward_demodulation,[status(thm)],[f4466,f3997]) ).
fof(f4649,plain,
( ~ sQ92_spl
| sQ31_spl
| ~ latt_set_smaller(sK359_skl,sK360_skl,sK361_skl) ),
inference(resolution,[status(thm)],[f3995,f4642]) ).
fof(f4650,plain,
( ~ sQ92_spl
| sQ31_spl
| ~ sQ32_spl
| ~ sQ65_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4649,f4648]) ).
fof(f4651,plain,
( ~ sQ92_spl
| sQ31_spl
| ~ sQ32_spl
| ~ sQ65_spl ),
inference(contradiction_clause,[status(thm)],[f4650]) ).
fof(f4652,plain,
$false,
inference(sat_refutation,[status(thm)],[f3999,f4000,f4459,f4473,f4476,f4478,f4502,f4527,f4529,f4555,f4557,f4559,f4571,f4575,f4577,f4579,f4589,f4593,f4625,f4629,f4644,f4647,f4651]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU348+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.86 % Computer : n019.cluster.edu
% 0.17/0.86 % Model : x86_64 x86_64
% 0.17/0.86 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.86 % Memory : 8046.5625MB
% 0.17/0.86 % OS : Linux 6.8.0-71-generic
% 0.17/0.86 % CPULimit : 300
% 0.17/0.86 % WCLimit : 300
% 0.17/0.87 % DateTime : Mon Sep 21 06:14:36 UTC 2026
% 0.17/0.87 % CPUTime :
% 0.23/1.01 % Drodi V4.1.1
% 0.23/1.21 % Refutation found
% 0.23/1.21 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.23/1.21 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.40/1.28 % Elapsed time: 0.393862 seconds
% 0.40/1.28 % CPU time: 1.712473 seconds
% 0.40/1.28 % Total memory used: 207.229 MB
% 0.40/1.28 % Net memory used: 206.205 MB
%------------------------------------------------------------------------------