%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU244+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 : n008.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 02:19:53 PM UTC 2026
% Result : Theorem 0.08s 0.37s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 21
% Syntax : Number of formulae : 127 ( 3 unt; 13 def)
% Number of atoms : 428 ( 0 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 522 ( 221 ~; 221 |; 41 &)
% ( 29 <=>; 9 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 27 ( 26 usr; 14 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 59 ( 57 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A] :
( relation(A)
=> ( antisymmetric(A)
<=> is_antisymmetric_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] :
( relation(A)
=> ( connected(A)
<=> is_connected_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] :
( relation(A)
=> ( transitive(A)
<=> is_transitive_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] :
( relation(A)
=> ( well_ordering(A)
<=> ( well_founded_relation(A)
& connected(A)
& antisymmetric(A)
& transitive(A)
& reflexive(A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] :
( relation(A)
=> ! [B] :
( well_orders(A,B)
<=> ( is_well_founded_in(A,B)
& is_connected_in(A,B)
& is_antisymmetric_in(A,B)
& is_transitive_in(A,B)
& is_reflexive_in(A,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A] :
( relation(A)
=> ( reflexive(A)
<=> is_reflexive_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A] :
( relation(A)
=> ( well_founded_relation(A)
<=> is_well_founded_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,conjecture,
! [A] :
( relation(A)
=> ( well_orders(A,relation_field(A))
<=> well_ordering(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( well_orders(A,relation_field(A))
<=> well_ordering(A) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f18,plain,
! [A] :
( ( antisymmetric(A)
<=> is_antisymmetric_in(A,relation_field(A)) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f19,plain,
! [A] :
( ( ( ~ is_antisymmetric_in(A,relation_field(A))
| antisymmetric(A) )
& ( is_antisymmetric_in(A,relation_field(A))
| ~ antisymmetric(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
! [X0] :
( is_antisymmetric_in(X0,relation_field(X0))
| ~ antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
! [X0] :
( ~ is_antisymmetric_in(X0,relation_field(X0))
| antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f22,plain,
! [A] :
( ( connected(A)
<=> is_connected_in(A,relation_field(A)) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f23,plain,
! [A] :
( ( ( ~ is_connected_in(A,relation_field(A))
| connected(A) )
& ( is_connected_in(A,relation_field(A))
| ~ connected(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [X0] :
( is_connected_in(X0,relation_field(X0))
| ~ connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
! [X0] :
( ~ is_connected_in(X0,relation_field(X0))
| connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f26,plain,
! [A] :
( ( transitive(A)
<=> is_transitive_in(A,relation_field(A)) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f27,plain,
! [A] :
( ( ( ~ is_transitive_in(A,relation_field(A))
| transitive(A) )
& ( is_transitive_in(A,relation_field(A))
| ~ transitive(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
! [X0] :
( is_transitive_in(X0,relation_field(X0))
| ~ transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
! [X0] :
( ~ is_transitive_in(X0,relation_field(X0))
| transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f30,plain,
! [A] :
( ( well_ordering(A)
<=> ( well_founded_relation(A)
& connected(A)
& antisymmetric(A)
& transitive(A)
& reflexive(A) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f31,plain,
! [A] :
( ( ( ~ well_founded_relation(A)
| ~ connected(A)
| ~ antisymmetric(A)
| ~ transitive(A)
| ~ reflexive(A)
| well_ordering(A) )
& ( ( well_founded_relation(A)
& connected(A)
& antisymmetric(A)
& transitive(A)
& reflexive(A) )
| ~ well_ordering(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
! [X0] :
( reflexive(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [X0] :
( transitive(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f34,plain,
! [X0] :
( antisymmetric(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f35,plain,
! [X0] :
( connected(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f36,plain,
! [X0] :
( well_founded_relation(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f37,plain,
! [X0] :
( ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0)
| well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f38,plain,
! [A] :
( ! [B] :
( well_orders(A,B)
<=> ( is_well_founded_in(A,B)
& is_connected_in(A,B)
& is_antisymmetric_in(A,B)
& is_transitive_in(A,B)
& is_reflexive_in(A,B) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f39,plain,
! [A] :
( ! [B] :
( ( ~ is_well_founded_in(A,B)
| ~ is_connected_in(A,B)
| ~ is_antisymmetric_in(A,B)
| ~ is_transitive_in(A,B)
| ~ is_reflexive_in(A,B)
| well_orders(A,B) )
& ( ( is_well_founded_in(A,B)
& is_connected_in(A,B)
& is_antisymmetric_in(A,B)
& is_transitive_in(A,B)
& is_reflexive_in(A,B) )
| ~ well_orders(A,B) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
! [A] :
( ( ! [B] :
( ~ is_well_founded_in(A,B)
| ~ is_connected_in(A,B)
| ~ is_antisymmetric_in(A,B)
| ~ is_transitive_in(A,B)
| ~ is_reflexive_in(A,B)
| well_orders(A,B) )
& ! [B] :
( ( is_well_founded_in(A,B)
& is_connected_in(A,B)
& is_antisymmetric_in(A,B)
& is_transitive_in(A,B)
& is_reflexive_in(A,B) )
| ~ well_orders(A,B) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( is_reflexive_in(X0,X1)
| ~ well_orders(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( is_transitive_in(X0,X1)
| ~ well_orders(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f43,plain,
! [X0,X1] :
( is_antisymmetric_in(X0,X1)
| ~ well_orders(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f44,plain,
! [X0,X1] :
( is_connected_in(X0,X1)
| ~ well_orders(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f45,plain,
! [X0,X1] :
( is_well_founded_in(X0,X1)
| ~ well_orders(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f46,plain,
! [X0,X1] :
( ~ is_well_founded_in(X0,X1)
| ~ is_connected_in(X0,X1)
| ~ is_antisymmetric_in(X0,X1)
| ~ is_transitive_in(X0,X1)
| ~ is_reflexive_in(X0,X1)
| well_orders(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f49,plain,
! [A] :
( ( reflexive(A)
<=> is_reflexive_in(A,relation_field(A)) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f50,plain,
! [A] :
( ( ( ~ is_reflexive_in(A,relation_field(A))
| reflexive(A) )
& ( is_reflexive_in(A,relation_field(A))
| ~ reflexive(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
! [X0] :
( is_reflexive_in(X0,relation_field(X0))
| ~ reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
! [X0] :
( ~ is_reflexive_in(X0,relation_field(X0))
| reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f55,plain,
! [A] :
( ( well_founded_relation(A)
<=> is_well_founded_in(A,relation_field(A)) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f56,plain,
! [A] :
( ( ( ~ is_well_founded_in(A,relation_field(A))
| well_founded_relation(A) )
& ( is_well_founded_in(A,relation_field(A))
| ~ well_founded_relation(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f55]) ).
fof(f57,plain,
! [X0] :
( is_well_founded_in(X0,relation_field(X0))
| ~ well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f58,plain,
! [X0] :
( ~ is_well_founded_in(X0,relation_field(X0))
| well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f59,plain,
? [A] :
( ( well_orders(A,relation_field(A))
<~> well_ordering(A) )
& relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f60,plain,
? [A] :
( ( ~ well_ordering(A)
| ~ well_orders(A,relation_field(A)) )
& ( well_ordering(A)
| well_orders(A,relation_field(A)) )
& relation(A) ),
inference(NNF_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
( ( ~ well_ordering(sK0_skl)
| ~ well_orders(sK0_skl,relation_field(sK0_skl)) )
& ( well_ordering(sK0_skl)
| well_orders(sK0_skl,relation_field(sK0_skl)) )
& relation(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(A,sK0_skl)],[f60]) ).
fof(f62,plain,
relation(sK0_skl),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
( well_ordering(sK0_skl)
| well_orders(sK0_skl,relation_field(sK0_skl)) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f64,plain,
( ~ well_ordering(sK0_skl)
| ~ well_orders(sK0_skl,relation_field(sK0_skl)) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f65,definition,
( sQ0_spl
<=> well_orders(sK0_skl,relation_field(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f67,plain,
( sQ0_spl
| ~ well_orders(sK0_skl,relation_field(sK0_skl)) ),
inference(component_clause,[status(thm)],[f65]) ).
fof(f68,definition,
( sQ1_spl
<=> well_ordering(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f70,plain,
( sQ1_spl
| ~ well_ordering(sK0_skl) ),
inference(component_clause,[status(thm)],[f68]) ).
fof(f71,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f63,f65,f68]) ).
fof(f72,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f64,f65,f68]) ).
fof(f77,plain,
( sQ0_spl
| ~ is_well_founded_in(sK0_skl,relation_field(sK0_skl))
| ~ is_connected_in(sK0_skl,relation_field(sK0_skl))
| ~ is_antisymmetric_in(sK0_skl,relation_field(sK0_skl))
| ~ is_transitive_in(sK0_skl,relation_field(sK0_skl))
| ~ is_reflexive_in(sK0_skl,relation_field(sK0_skl))
| ~ relation(sK0_skl) ),
inference(resolution,[status(thm)],[f46,f67]) ).
fof(f78,definition,
( sQ2_spl
<=> relation(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f80,plain,
( sQ2_spl
| ~ relation(sK0_skl) ),
inference(component_clause,[status(thm)],[f78]) ).
fof(f81,definition,
( sQ3_spl
<=> is_reflexive_in(sK0_skl,relation_field(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f83,plain,
( sQ3_spl
| ~ is_reflexive_in(sK0_skl,relation_field(sK0_skl)) ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,definition,
( sQ4_spl
<=> is_transitive_in(sK0_skl,relation_field(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( sQ4_spl
| ~ is_transitive_in(sK0_skl,relation_field(sK0_skl)) ),
inference(component_clause,[status(thm)],[f84]) ).
fof(f87,definition,
( sQ5_spl
<=> is_antisymmetric_in(sK0_skl,relation_field(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f89,plain,
( sQ5_spl
| ~ is_antisymmetric_in(sK0_skl,relation_field(sK0_skl)) ),
inference(component_clause,[status(thm)],[f87]) ).
fof(f90,definition,
( sQ6_spl
<=> is_connected_in(sK0_skl,relation_field(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f92,plain,
( sQ6_spl
| ~ is_connected_in(sK0_skl,relation_field(sK0_skl)) ),
inference(component_clause,[status(thm)],[f90]) ).
fof(f93,definition,
( sQ7_spl
<=> is_well_founded_in(sK0_skl,relation_field(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f95,plain,
( sQ7_spl
| ~ is_well_founded_in(sK0_skl,relation_field(sK0_skl)) ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( sQ0_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f77,f78,f81,f84,f87,f90,f93,f65]) ).
fof(f97,plain,
( sQ1_spl
| ~ well_founded_relation(sK0_skl)
| ~ connected(sK0_skl)
| ~ antisymmetric(sK0_skl)
| ~ transitive(sK0_skl)
| ~ reflexive(sK0_skl)
| ~ relation(sK0_skl) ),
inference(resolution,[status(thm)],[f70,f37]) ).
fof(f98,definition,
( sQ8_spl
<=> reflexive(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f100,plain,
( sQ8_spl
| ~ reflexive(sK0_skl) ),
inference(component_clause,[status(thm)],[f98]) ).
fof(f101,definition,
( sQ9_spl
<=> transitive(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f103,plain,
( sQ9_spl
| ~ transitive(sK0_skl) ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f104,definition,
( sQ10_spl
<=> antisymmetric(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( sQ10_spl
| ~ antisymmetric(sK0_skl) ),
inference(component_clause,[status(thm)],[f104]) ).
fof(f107,definition,
( sQ11_spl
<=> connected(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f109,plain,
( sQ11_spl
| ~ connected(sK0_skl) ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f110,definition,
( sQ12_spl
<=> well_founded_relation(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f112,plain,
( sQ12_spl
| ~ well_founded_relation(sK0_skl) ),
inference(component_clause,[status(thm)],[f110]) ).
fof(f113,plain,
( sQ1_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f97,f78,f98,f101,f104,f107,f110,f68]) ).
fof(f114,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f80,f62]) ).
fof(f115,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f114]) ).
fof(f116,plain,
( sQ12_spl
| ~ is_well_founded_in(sK0_skl,relation_field(sK0_skl))
| ~ relation(sK0_skl) ),
inference(resolution,[status(thm)],[f112,f58]) ).
fof(f117,plain,
( sQ12_spl
| ~ well_ordering(sK0_skl)
| ~ relation(sK0_skl) ),
inference(resolution,[status(thm)],[f112,f36]) ).
fof(f118,plain,
( sQ12_spl
| ~ sQ7_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f116,f78,f93,f110]) ).
fof(f119,plain,
( sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f117,f78,f68,f110]) ).
fof(f120,plain,
( sQ7_spl
| ~ well_founded_relation(sK0_skl)
| ~ relation(sK0_skl) ),
inference(resolution,[status(thm)],[f95,f57]) ).
fof(f121,plain,
( sQ7_spl
| ~ well_orders(sK0_skl,relation_field(sK0_skl))
| ~ relation(sK0_skl) ),
inference(resolution,[status(thm)],[f95,f45]) ).
fof(f122,plain,
( sQ7_spl
| ~ sQ12_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f120,f78,f110,f93]) ).
fof(f123,plain,
( sQ7_spl
| ~ sQ0_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f121,f78,f65,f93]) ).
fof(f124,plain,
( sQ11_spl
| ~ well_ordering(sK0_skl)
| ~ relation(sK0_skl) ),
inference(resolution,[status(thm)],[f109,f35]) ).
fof(f125,plain,
( sQ11_spl
| ~ is_connected_in(sK0_skl,relation_field(sK0_skl))
| ~ relation(sK0_skl) ),
inference(resolution,[status(thm)],[f109,f25]) ).
fof(f126,plain,
( sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f124,f78,f68,f107]) ).
fof(f127,plain,
( sQ11_spl
| ~ sQ6_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f125,f78,f90,f107]) ).
fof(f130,plain,
( sQ6_spl
| ~ connected(sK0_skl)
| ~ relation(sK0_skl) ),
inference(resolution,[status(thm)],[f92,f24]) ).
fof(f131,plain,
( sQ6_spl
| ~ well_orders(sK0_skl,relation_field(sK0_skl))
| ~ relation(sK0_skl) ),
inference(resolution,[status(thm)],[f92,f44]) ).
fof(f132,plain,
( sQ6_spl
| ~ sQ11_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f130,f78,f107,f90]) ).
fof(f133,plain,
( sQ6_spl
| ~ sQ0_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f131,f78,f65,f90]) ).
fof(f134,plain,
( sQ10_spl
| ~ is_antisymmetric_in(sK0_skl,relation_field(sK0_skl))
| ~ relation(sK0_skl) ),
inference(resolution,[status(thm)],[f106,f21]) ).
fof(f135,plain,
( sQ10_spl
| ~ well_ordering(sK0_skl)
| ~ relation(sK0_skl) ),
inference(resolution,[status(thm)],[f106,f34]) ).
fof(f136,plain,
( sQ10_spl
| ~ sQ5_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f134,f78,f87,f104]) ).
fof(f137,plain,
( sQ10_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f135,f78,f68,f104]) ).
fof(f138,plain,
( sQ5_spl
| ~ antisymmetric(sK0_skl)
| ~ relation(sK0_skl) ),
inference(resolution,[status(thm)],[f89,f20]) ).
fof(f139,plain,
( sQ5_spl
| ~ well_orders(sK0_skl,relation_field(sK0_skl))
| ~ relation(sK0_skl) ),
inference(resolution,[status(thm)],[f89,f43]) ).
fof(f140,plain,
( sQ5_spl
| ~ sQ10_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f138,f78,f104,f87]) ).
fof(f141,plain,
( sQ5_spl
| ~ sQ0_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f139,f78,f65,f87]) ).
fof(f142,plain,
( sQ8_spl
| ~ is_reflexive_in(sK0_skl,relation_field(sK0_skl))
| ~ relation(sK0_skl) ),
inference(resolution,[status(thm)],[f100,f52]) ).
fof(f143,plain,
( sQ8_spl
| ~ well_ordering(sK0_skl)
| ~ relation(sK0_skl) ),
inference(resolution,[status(thm)],[f100,f32]) ).
fof(f144,plain,
( sQ8_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f142,f78,f81,f98]) ).
fof(f145,plain,
( sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f143,f78,f68,f98]) ).
fof(f148,plain,
( sQ3_spl
| ~ reflexive(sK0_skl)
| ~ relation(sK0_skl) ),
inference(resolution,[status(thm)],[f83,f51]) ).
fof(f149,plain,
( sQ3_spl
| ~ well_orders(sK0_skl,relation_field(sK0_skl))
| ~ relation(sK0_skl) ),
inference(resolution,[status(thm)],[f83,f41]) ).
fof(f150,plain,
( sQ3_spl
| ~ sQ8_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f148,f78,f98,f81]) ).
fof(f151,plain,
( sQ3_spl
| ~ sQ0_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f149,f78,f65,f81]) ).
fof(f154,plain,
( sQ9_spl
| ~ is_transitive_in(sK0_skl,relation_field(sK0_skl))
| ~ relation(sK0_skl) ),
inference(resolution,[status(thm)],[f103,f29]) ).
fof(f155,plain,
( sQ9_spl
| ~ well_ordering(sK0_skl)
| ~ relation(sK0_skl) ),
inference(resolution,[status(thm)],[f103,f33]) ).
fof(f156,plain,
( sQ9_spl
| ~ sQ4_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f154,f78,f84,f101]) ).
fof(f157,plain,
( sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f155,f78,f68,f101]) ).
fof(f160,plain,
( sQ4_spl
| ~ transitive(sK0_skl)
| ~ relation(sK0_skl) ),
inference(resolution,[status(thm)],[f86,f28]) ).
fof(f161,plain,
( sQ4_spl
| ~ well_orders(sK0_skl,relation_field(sK0_skl))
| ~ relation(sK0_skl) ),
inference(resolution,[status(thm)],[f86,f42]) ).
fof(f162,plain,
( sQ4_spl
| ~ sQ9_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f160,f78,f101,f84]) ).
fof(f163,plain,
( sQ4_spl
| ~ sQ0_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f161,f78,f65,f84]) ).
fof(f164,plain,
$false,
inference(sat_refutation,[status(thm)],[f71,f72,f96,f113,f115,f118,f119,f122,f123,f126,f127,f132,f133,f136,f137,f140,f141,f144,f145,f150,f151,f156,f157,f162,f163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU244+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n008.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 06:03:39 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % 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
% 0.13/0.40 % Elapsed time: 0.052264 seconds
% 0.13/0.40 % CPU time: 0.148310 seconds
% 0.13/0.40 % Total memory used: 102.300 MB
% 0.13/0.40 % Net memory used: 102.041 MB
%------------------------------------------------------------------------------