%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU348+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 0.08s 0.37s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 34
% Syntax : Number of formulae : 143 ( 20 unt; 24 def)
% Number of atoms : 473 ( 30 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 544 ( 214 ~; 239 |; 48 &)
% ( 28 <=>; 14 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 37 ( 35 usr; 25 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 92 ( 80 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A] :
( rel_str(A)
=> ( strict_rel_str(A)
=> A = rel_str_of(the_carrier(A),the_InternalRel(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] :
( ( latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> poset_of_lattice(A) = rel_str_of(the_carrier(A),k2_lattice3(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,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(f8,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(f16,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(f34,axiom,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,axiom,
? [A] :
( strict_rel_str(A)
& rel_str(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,axiom,
? [A] :
( antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& strict_rel_str(A)
& ~ empty_carrier(A)
& rel_str(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [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(f58,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(f59,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)],[f58]) ).
fof(f67,plain,
! [A] :
( A = rel_str_of(the_carrier(A),the_InternalRel(A))
| ~ strict_rel_str(A)
| ~ rel_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f68,plain,
! [X0] :
( X0 = rel_str_of(the_carrier(X0),the_InternalRel(X0))
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f85,plain,
! [A] :
( poset_of_lattice(A) = rel_str_of(the_carrier(A),k2_lattice3(A))
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f86,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,[status(thm)],[f85]) ).
fof(f87,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)],[f7]) ).
fof(f88,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)],[f87]) ).
fof(f89,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)],[f8]) ).
fof(f90,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)],[f89]) ).
fof(f108,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)],[f16]) ).
fof(f109,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)],[f108]) ).
fof(f137,plain,
! [A] : element(sK6_skl(A),A),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(B,sK6_skl(A))],[f34]) ).
fof(f138,plain,
! [X0] : element(sK6_skl(X0),X0),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f170,plain,
( strict_rel_str(sK8_skl)
& rel_str(sK8_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(A,sK8_skl)],[f45]) ).
fof(f171,plain,
rel_str(sK8_skl),
inference(cnf_transformation,[status(thm)],[f170]) ).
fof(f172,plain,
strict_rel_str(sK8_skl),
inference(cnf_transformation,[status(thm)],[f170]) ).
fof(f179,plain,
( antisymmetric_relstr(sK11_skl)
& transitive_relstr(sK11_skl)
& reflexive_relstr(sK11_skl)
& strict_rel_str(sK11_skl)
& ~ empty_carrier(sK11_skl)
& rel_str(sK11_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl]),skolemize(A,sK11_skl)],[f48]) ).
fof(f180,plain,
rel_str(sK11_skl),
inference(cnf_transformation,[status(thm)],[f179]) ).
fof(f182,plain,
strict_rel_str(sK11_skl),
inference(cnf_transformation,[status(thm)],[f179]) ).
fof(f208,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)],[f57]) ).
fof(f209,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)],[f208]) ).
fof(f210,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)],[f209]) ).
fof(f211,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)],[f210]) ).
fof(f212,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)],[f210]) ).
fof(f213,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)],[f59]) ).
fof(f214,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)],[f213]) ).
fof(f215,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)],[f214]) ).
fof(f216,plain,
( ( ~ latt_set_smaller(sK16_skl,cast_to_el_of_lattice(sK16_skl,sK17_skl),sK18_skl)
| ~ relstr_element_smaller(poset_of_lattice(sK16_skl),sK18_skl,sK17_skl) )
& ( latt_set_smaller(sK16_skl,cast_to_el_of_lattice(sK16_skl,sK17_skl),sK18_skl)
| relstr_element_smaller(poset_of_lattice(sK16_skl),sK18_skl,sK17_skl) )
& element(sK17_skl,the_carrier(poset_of_lattice(sK16_skl)))
& latt_str(sK16_skl)
& lattice(sK16_skl)
& ~ empty_carrier(sK16_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl,sK17_skl,sK18_skl]),skolemize(B,sK16_skl),skolemize(C,sK17_skl),skolemize(A,sK18_skl)],[f215]) ).
fof(f217,plain,
~ empty_carrier(sK16_skl),
inference(cnf_transformation,[status(thm)],[f216]) ).
fof(f218,plain,
lattice(sK16_skl),
inference(cnf_transformation,[status(thm)],[f216]) ).
fof(f219,plain,
latt_str(sK16_skl),
inference(cnf_transformation,[status(thm)],[f216]) ).
fof(f220,plain,
element(sK17_skl,the_carrier(poset_of_lattice(sK16_skl))),
inference(cnf_transformation,[status(thm)],[f216]) ).
fof(f221,plain,
( latt_set_smaller(sK16_skl,cast_to_el_of_lattice(sK16_skl,sK17_skl),sK18_skl)
| relstr_element_smaller(poset_of_lattice(sK16_skl),sK18_skl,sK17_skl) ),
inference(cnf_transformation,[status(thm)],[f216]) ).
fof(f222,plain,
( ~ latt_set_smaller(sK16_skl,cast_to_el_of_lattice(sK16_skl,sK17_skl),sK18_skl)
| ~ relstr_element_smaller(poset_of_lattice(sK16_skl),sK18_skl,sK17_skl) ),
inference(cnf_transformation,[status(thm)],[f216]) ).
fof(f243,definition,
( sQ0_spl
<=> relstr_element_smaller(poset_of_lattice(sK16_skl),sK18_skl,sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f244,plain,
( ~ sQ0_spl
| relstr_element_smaller(poset_of_lattice(sK16_skl),sK18_skl,sK17_skl) ),
inference(component_clause,[status(thm)],[f243]) ).
fof(f246,definition,
( sQ1_spl
<=> latt_set_smaller(sK16_skl,cast_to_el_of_lattice(sK16_skl,sK17_skl),sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f247,plain,
( ~ sQ1_spl
| latt_set_smaller(sK16_skl,cast_to_el_of_lattice(sK16_skl,sK17_skl),sK18_skl) ),
inference(component_clause,[status(thm)],[f246]) ).
fof(f248,plain,
( sQ1_spl
| ~ latt_set_smaller(sK16_skl,cast_to_el_of_lattice(sK16_skl,sK17_skl),sK18_skl) ),
inference(component_clause,[status(thm)],[f246]) ).
fof(f249,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f221,f243,f246]) ).
fof(f250,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f222,f243,f246]) ).
fof(f251,plain,
! [X0] :
( cast_to_el_of_lattice(sK16_skl,X0) = X0
| ~ element(X0,the_carrier(poset_of_lattice(sK16_skl)))
| ~ latt_str(sK16_skl)
| empty_carrier(sK16_skl) ),
inference(resolution,[status(thm)],[f90,f218]) ).
fof(f252,definition,
( sQ2_spl
<=> empty_carrier(sK16_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f253,plain,
( ~ sQ2_spl
| empty_carrier(sK16_skl) ),
inference(component_clause,[status(thm)],[f252]) ).
fof(f255,definition,
( sQ3_spl
<=> latt_str(sK16_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f257,plain,
( sQ3_spl
| ~ latt_str(sK16_skl) ),
inference(component_clause,[status(thm)],[f255]) ).
fof(f258,definition,
! [X0] :
( sQ4_spl
<=> ( cast_to_el_of_lattice(sK16_skl,X0) = X0
| ~ element(X0,the_carrier(poset_of_lattice(sK16_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f259,plain,
! [X0] :
( ~ sQ4_spl
| cast_to_el_of_lattice(sK16_skl,X0) = X0
| ~ element(X0,the_carrier(poset_of_lattice(sK16_skl))) ),
inference(component_clause,[status(thm)],[f258]) ).
fof(f261,plain,
( sQ4_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f251,f252,f255,f258]) ).
fof(f262,plain,
( sK8_skl = rel_str_of(the_carrier(sK8_skl),the_InternalRel(sK8_skl))
| ~ rel_str(sK8_skl) ),
inference(resolution,[status(thm)],[f68,f172]) ).
fof(f263,definition,
( sQ5_spl
<=> rel_str(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f265,plain,
( sQ5_spl
| ~ rel_str(sK8_skl) ),
inference(component_clause,[status(thm)],[f263]) ).
fof(f266,definition,
( sQ6_spl
<=> sK8_skl = rel_str_of(the_carrier(sK8_skl),the_InternalRel(sK8_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f269,plain,
( sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f262,f263,f266]) ).
fof(f270,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f265,f171]) ).
fof(f271,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f270]) ).
fof(f273,plain,
( ~ sQ4_spl
| cast_to_el_of_lattice(sK16_skl,sK17_skl) = sK17_skl ),
inference(resolution,[status(thm)],[f259,f220]) ).
fof(f287,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f257,f219]) ).
fof(f288,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f287]) ).
fof(f289,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f253,f217]) ).
fof(f290,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f289]) ).
fof(f291,plain,
( sQ1_spl
| ~ sQ4_spl
| ~ latt_set_smaller(sK16_skl,sK17_skl,sK18_skl) ),
inference(backward_demodulation,[status(thm)],[f273,f248]) ).
fof(f292,plain,
( ~ sQ4_spl
| element(sK17_skl,the_carrier(sK16_skl))
| ~ element(sK17_skl,the_carrier(poset_of_lattice(sK16_skl)))
| ~ latt_str(sK16_skl)
| ~ lattice(sK16_skl)
| empty_carrier(sK16_skl) ),
inference(paramodulation,[status(thm)],[f273,f109]) ).
fof(f293,definition,
( sQ11_spl
<=> lattice(sK16_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f295,plain,
( sQ11_spl
| ~ lattice(sK16_skl) ),
inference(component_clause,[status(thm)],[f293]) ).
fof(f296,definition,
( sQ12_spl
<=> element(sK17_skl,the_carrier(poset_of_lattice(sK16_skl))) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f298,plain,
( sQ12_spl
| ~ element(sK17_skl,the_carrier(poset_of_lattice(sK16_skl))) ),
inference(component_clause,[status(thm)],[f296]) ).
fof(f299,definition,
( sQ13_spl
<=> element(sK17_skl,the_carrier(sK16_skl)) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f300,plain,
( ~ sQ13_spl
| element(sK17_skl,the_carrier(sK16_skl)) ),
inference(component_clause,[status(thm)],[f299]) ).
fof(f302,plain,
( ~ sQ4_spl
| sQ13_spl
| ~ sQ12_spl
| ~ sQ3_spl
| ~ sQ11_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f292,f252,f293,f255,f296,f299,f258]) ).
fof(f303,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f298,f220]) ).
fof(f304,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f303]) ).
fof(f305,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f295,f218]) ).
fof(f306,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f305]) ).
fof(f310,plain,
! [X0,X1] :
( ~ relstr_element_smaller(poset_of_lattice(sK16_skl),X1,cast_to_el_of_LattPOSet(sK16_skl,X0))
| latt_set_smaller(sK16_skl,X0,X1)
| ~ element(X0,the_carrier(sK16_skl))
| ~ latt_str(sK16_skl)
| empty_carrier(sK16_skl) ),
inference(resolution,[status(thm)],[f212,f218]) ).
fof(f311,definition,
! [X0,X1] :
( sQ14_spl
<=> ( ~ relstr_element_smaller(poset_of_lattice(sK16_skl),X1,cast_to_el_of_LattPOSet(sK16_skl,X0))
| latt_set_smaller(sK16_skl,X0,X1)
| ~ element(X0,the_carrier(sK16_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f312,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ relstr_element_smaller(poset_of_lattice(sK16_skl),X1,cast_to_el_of_LattPOSet(sK16_skl,X0))
| latt_set_smaller(sK16_skl,X0,X1)
| ~ element(X0,the_carrier(sK16_skl)) ),
inference(component_clause,[status(thm)],[f311]) ).
fof(f314,plain,
( sQ14_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f310,f252,f255,f311]) ).
fof(f315,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ latt_set_smaller(sK16_skl,X0,X1)
| ~ element(X0,the_carrier(sK16_skl))
| ~ latt_str(sK16_skl)
| ~ lattice(sK16_skl)
| empty_carrier(sK16_skl)
| latt_set_smaller(sK16_skl,X0,X1)
| ~ element(X0,the_carrier(sK16_skl)) ),
inference(resolution,[status(thm)],[f312,f211]) ).
fof(f316,definition,
! [X0,X1] :
( sQ15_spl
<=> ( ~ latt_set_smaller(sK16_skl,X0,X1)
| ~ element(X0,the_carrier(sK16_skl))
| latt_set_smaller(sK16_skl,X0,X1)
| ~ element(X0,the_carrier(sK16_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f319,plain,
( ~ sQ14_spl
| ~ sQ3_spl
| ~ sQ11_spl
| sQ2_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f315,f316,f252,f293,f255,f311]) ).
fof(f320,plain,
( sK11_skl = rel_str_of(the_carrier(sK11_skl),the_InternalRel(sK11_skl))
| ~ rel_str(sK11_skl) ),
inference(resolution,[status(thm)],[f182,f68]) ).
fof(f321,definition,
( sQ16_spl
<=> rel_str(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f323,plain,
( sQ16_spl
| ~ rel_str(sK11_skl) ),
inference(component_clause,[status(thm)],[f321]) ).
fof(f324,definition,
( sQ17_spl
<=> sK11_skl = rel_str_of(the_carrier(sK11_skl),the_InternalRel(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f327,plain,
( sQ17_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f320,f321,f324]) ).
fof(f328,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f323,f180]) ).
fof(f329,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f328]) ).
fof(f330,plain,
( ~ sQ4_spl
| cast_to_el_of_lattice(sK16_skl,sK6_skl(the_carrier(poset_of_lattice(sK16_skl)))) = sK6_skl(the_carrier(poset_of_lattice(sK16_skl))) ),
inference(resolution,[status(thm)],[f138,f259]) ).
fof(f331,plain,
( ~ sQ4_spl
| element(sK6_skl(the_carrier(poset_of_lattice(sK16_skl))),the_carrier(sK16_skl))
| ~ element(sK6_skl(the_carrier(poset_of_lattice(sK16_skl))),the_carrier(poset_of_lattice(sK16_skl)))
| ~ latt_str(sK16_skl)
| ~ lattice(sK16_skl)
| empty_carrier(sK16_skl) ),
inference(paramodulation,[status(thm)],[f330,f109]) ).
fof(f332,definition,
( sQ18_spl
<=> element(sK6_skl(the_carrier(poset_of_lattice(sK16_skl))),the_carrier(poset_of_lattice(sK16_skl))) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f334,plain,
( sQ18_spl
| ~ element(sK6_skl(the_carrier(poset_of_lattice(sK16_skl))),the_carrier(poset_of_lattice(sK16_skl))) ),
inference(component_clause,[status(thm)],[f332]) ).
fof(f335,definition,
( sQ19_spl
<=> element(sK6_skl(the_carrier(poset_of_lattice(sK16_skl))),the_carrier(sK16_skl)) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f338,plain,
( ~ sQ4_spl
| sQ19_spl
| ~ sQ18_spl
| ~ sQ3_spl
| ~ sQ11_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f331,f252,f293,f255,f332,f335,f258]) ).
fof(f339,plain,
( sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f334,f138]) ).
fof(f340,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f339]) ).
fof(f346,plain,
( poset_of_lattice(sK16_skl) = rel_str_of(the_carrier(sK16_skl),k2_lattice3(sK16_skl))
| ~ latt_str(sK16_skl)
| empty_carrier(sK16_skl) ),
inference(resolution,[status(thm)],[f86,f218]) ).
fof(f347,definition,
( sQ20_spl
<=> poset_of_lattice(sK16_skl) = rel_str_of(the_carrier(sK16_skl),k2_lattice3(sK16_skl)) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f350,plain,
( sQ20_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f346,f252,f255,f347]) ).
fof(f360,plain,
! [X0] :
( cast_to_el_of_LattPOSet(sK16_skl,X0) = X0
| ~ element(X0,the_carrier(sK16_skl))
| ~ latt_str(sK16_skl)
| empty_carrier(sK16_skl) ),
inference(resolution,[status(thm)],[f88,f218]) ).
fof(f361,definition,
! [X0] :
( sQ21_spl
<=> ( cast_to_el_of_LattPOSet(sK16_skl,X0) = X0
| ~ element(X0,the_carrier(sK16_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f362,plain,
! [X0] :
( ~ sQ21_spl
| cast_to_el_of_LattPOSet(sK16_skl,X0) = X0
| ~ element(X0,the_carrier(sK16_skl)) ),
inference(component_clause,[status(thm)],[f361]) ).
fof(f364,plain,
( sQ21_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f360,f252,f255,f361]) ).
fof(f367,plain,
( ~ sQ21_spl
| cast_to_el_of_LattPOSet(sK16_skl,sK6_skl(the_carrier(sK16_skl))) = sK6_skl(the_carrier(sK16_skl)) ),
inference(resolution,[status(thm)],[f362,f138]) ).
fof(f368,plain,
! [X0] :
( ~ sQ21_spl
| ~ element(X0,the_carrier(poset_of_lattice(sK16_skl)))
| ~ latt_str(sK16_skl)
| ~ lattice(sK16_skl)
| empty_carrier(sK16_skl)
| cast_to_el_of_LattPOSet(sK16_skl,cast_to_el_of_lattice(sK16_skl,X0)) = cast_to_el_of_lattice(sK16_skl,X0) ),
inference(resolution,[status(thm)],[f362,f109]) ).
fof(f369,plain,
( ~ sQ13_spl
| ~ sQ21_spl
| cast_to_el_of_LattPOSet(sK16_skl,sK17_skl) = sK17_skl ),
inference(resolution,[status(thm)],[f362,f300]) ).
fof(f370,definition,
! [X0] :
( sQ22_spl
<=> ( ~ element(X0,the_carrier(poset_of_lattice(sK16_skl)))
| cast_to_el_of_LattPOSet(sK16_skl,cast_to_el_of_lattice(sK16_skl,X0)) = cast_to_el_of_lattice(sK16_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f373,plain,
( ~ sQ21_spl
| ~ sQ3_spl
| ~ sQ11_spl
| sQ2_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f368,f370,f252,f293,f255,f361]) ).
fof(f374,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ21_spl
| ~ sQ14_spl
| ~ relstr_element_smaller(poset_of_lattice(sK16_skl),X0,sK17_skl)
| latt_set_smaller(sK16_skl,sK17_skl,X0)
| ~ element(sK17_skl,the_carrier(sK16_skl)) ),
inference(paramodulation,[status(thm)],[f369,f312]) ).
fof(f375,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ21_spl
| relstr_element_smaller(poset_of_lattice(sK16_skl),X0,sK17_skl)
| ~ latt_set_smaller(sK16_skl,sK17_skl,X0)
| ~ element(sK17_skl,the_carrier(sK16_skl))
| ~ latt_str(sK16_skl)
| ~ lattice(sK16_skl)
| empty_carrier(sK16_skl) ),
inference(paramodulation,[status(thm)],[f369,f211]) ).
fof(f376,definition,
! [X0] :
( sQ23_spl
<=> ( ~ relstr_element_smaller(poset_of_lattice(sK16_skl),X0,sK17_skl)
| latt_set_smaller(sK16_skl,sK17_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f377,plain,
! [X0] :
( ~ sQ23_spl
| ~ relstr_element_smaller(poset_of_lattice(sK16_skl),X0,sK17_skl)
| latt_set_smaller(sK16_skl,sK17_skl,X0) ),
inference(component_clause,[status(thm)],[f376]) ).
fof(f379,plain,
( ~ sQ21_spl
| ~ sQ14_spl
| sQ23_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f374,f299,f376,f311,f361]) ).
fof(f380,definition,
! [X0] :
( sQ24_spl
<=> ( relstr_element_smaller(poset_of_lattice(sK16_skl),X0,sK17_skl)
| ~ latt_set_smaller(sK16_skl,sK17_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f381,plain,
! [X0] :
( ~ sQ24_spl
| relstr_element_smaller(poset_of_lattice(sK16_skl),X0,sK17_skl)
| ~ latt_set_smaller(sK16_skl,sK17_skl,X0) ),
inference(component_clause,[status(thm)],[f380]) ).
fof(f383,plain,
( ~ sQ21_spl
| sQ24_spl
| ~ sQ13_spl
| ~ sQ3_spl
| ~ sQ11_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f375,f252,f293,f255,f299,f380,f361]) ).
fof(f397,plain,
! [X0] :
( ~ sQ21_spl
| ~ sQ14_spl
| ~ relstr_element_smaller(poset_of_lattice(sK16_skl),X0,sK6_skl(the_carrier(sK16_skl)))
| latt_set_smaller(sK16_skl,sK6_skl(the_carrier(sK16_skl)),X0)
| ~ element(sK6_skl(the_carrier(sK16_skl)),the_carrier(sK16_skl)) ),
inference(paramodulation,[status(thm)],[f367,f312]) ).
fof(f398,plain,
! [X0] :
( ~ sQ21_spl
| relstr_element_smaller(poset_of_lattice(sK16_skl),X0,sK6_skl(the_carrier(sK16_skl)))
| ~ latt_set_smaller(sK16_skl,sK6_skl(the_carrier(sK16_skl)),X0)
| ~ element(sK6_skl(the_carrier(sK16_skl)),the_carrier(sK16_skl))
| ~ latt_str(sK16_skl)
| ~ lattice(sK16_skl)
| empty_carrier(sK16_skl) ),
inference(paramodulation,[status(thm)],[f367,f211]) ).
fof(f399,definition,
( sQ28_spl
<=> element(sK6_skl(the_carrier(sK16_skl)),the_carrier(sK16_skl)) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f401,plain,
( sQ28_spl
| ~ element(sK6_skl(the_carrier(sK16_skl)),the_carrier(sK16_skl)) ),
inference(component_clause,[status(thm)],[f399]) ).
fof(f402,definition,
! [X0] :
( sQ29_spl
<=> ( ~ relstr_element_smaller(poset_of_lattice(sK16_skl),X0,sK6_skl(the_carrier(sK16_skl)))
| latt_set_smaller(sK16_skl,sK6_skl(the_carrier(sK16_skl)),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f405,plain,
( ~ sQ21_spl
| ~ sQ14_spl
| sQ29_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f397,f399,f402,f311,f361]) ).
fof(f406,definition,
! [X0] :
( sQ30_spl
<=> ( relstr_element_smaller(poset_of_lattice(sK16_skl),X0,sK6_skl(the_carrier(sK16_skl)))
| ~ latt_set_smaller(sK16_skl,sK6_skl(the_carrier(sK16_skl)),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f409,plain,
( ~ sQ21_spl
| sQ30_spl
| ~ sQ28_spl
| ~ sQ3_spl
| ~ sQ11_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f398,f252,f293,f255,f399,f406,f361]) ).
fof(f410,plain,
( sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f401,f138]) ).
fof(f411,plain,
sQ28_spl,
inference(contradiction_clause,[status(thm)],[f410]) ).
fof(f417,plain,
( ~ sQ0_spl
| ~ sQ23_spl
| latt_set_smaller(sK16_skl,sK17_skl,sK18_skl) ),
inference(resolution,[status(thm)],[f377,f244]) ).
fof(f418,plain,
( ~ sQ0_spl
| ~ sQ23_spl
| sQ1_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f417,f291]) ).
fof(f419,plain,
( ~ sQ0_spl
| ~ sQ23_spl
| sQ1_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f418]) ).
fof(f420,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| latt_set_smaller(sK16_skl,sK17_skl,sK18_skl) ),
inference(forward_demodulation,[status(thm)],[f273,f247]) ).
fof(f421,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ24_spl
| relstr_element_smaller(poset_of_lattice(sK16_skl),sK18_skl,sK17_skl) ),
inference(resolution,[status(thm)],[f381,f420]) ).
fof(f422,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ24_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f421,f243,f380,f258,f246]) ).
fof(f423,plain,
$false,
inference(sat_refutation,[status(thm)],[f249,f250,f261,f269,f271,f288,f290,f302,f304,f306,f314,f319,f327,f329,f338,f340,f350,f364,f373,f379,f383,f405,f409,f411,f419,f422]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU348+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n010.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 : Mon Sep 21 06:14:10 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.08/0.37 % Refutation found
% 0.08/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.052483 seconds
% 0.13/0.41 % CPU time: 0.085636 seconds
% 0.13/0.41 % Total memory used: 16.076 MB
% 0.13/0.41 % Net memory used: 16.067 MB
%------------------------------------------------------------------------------