%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU257+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 : n018.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 02:19:55 PM UTC 2026
% Result : Theorem 0.11s 0.44s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 73 ( 5 unt; 6 def)
% Number of atoms : 260 ( 0 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 337 ( 150 ~; 144 |; 19 &)
% ( 8 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 7 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 85 ( 81 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,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(f4,axiom,
! [A,B] :
( relation(A)
=> relation(relation_restriction(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B] :
( relation(B)
=> ( reflexive(B)
=> reflexive(relation_restriction(B,A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B] :
( relation(B)
=> ( connected(B)
=> connected(relation_restriction(B,A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B] :
( relation(B)
=> ( transitive(B)
=> transitive(relation_restriction(B,A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B] :
( relation(B)
=> ( antisymmetric(B)
=> antisymmetric(relation_restriction(B,A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( relation(B)
=> ( well_founded_relation(B)
=> well_founded_relation(relation_restriction(B,A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,conjecture,
! [A,B] :
( relation(B)
=> ( well_ordering(B)
=> well_ordering(relation_restriction(B,A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> ( well_ordering(B)
=> well_ordering(relation_restriction(B,A)) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f16,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)],[f2]) ).
fof(f17,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)],[f16]) ).
fof(f18,plain,
! [X0] :
( reflexive(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
! [X0] :
( transitive(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f20,plain,
! [X0] :
( antisymmetric(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f21,plain,
! [X0] :
( connected(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f22,plain,
! [X0] :
( well_founded_relation(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f23,plain,
! [X0] :
( ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0)
| well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f26,plain,
! [A,B] :
( relation(relation_restriction(A,B))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f27,plain,
! [A] :
( ! [B] : relation(relation_restriction(A,B))
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f31,plain,
! [A,B] :
( reflexive(relation_restriction(B,A))
| ~ reflexive(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f32,plain,
! [B] :
( ! [A] : reflexive(relation_restriction(B,A))
| ~ reflexive(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( reflexive(relation_restriction(X0,X1))
| ~ reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
! [A,B] :
( connected(relation_restriction(B,A))
| ~ connected(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f35,plain,
! [B] :
( ! [A] : connected(relation_restriction(B,A))
| ~ connected(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( connected(relation_restriction(X0,X1))
| ~ connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
! [A,B] :
( transitive(relation_restriction(B,A))
| ~ transitive(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f38,plain,
! [B] :
( ! [A] : transitive(relation_restriction(B,A))
| ~ transitive(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f37]) ).
fof(f39,plain,
! [X0,X1] :
( transitive(relation_restriction(X0,X1))
| ~ transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
! [A,B] :
( antisymmetric(relation_restriction(B,A))
| ~ antisymmetric(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f41,plain,
! [B] :
( ! [A] : antisymmetric(relation_restriction(B,A))
| ~ antisymmetric(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( antisymmetric(relation_restriction(X0,X1))
| ~ antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
! [A,B] :
( well_founded_relation(relation_restriction(B,A))
| ~ well_founded_relation(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f44,plain,
! [B] :
( ! [A] : well_founded_relation(relation_restriction(B,A))
| ~ well_founded_relation(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( well_founded_relation(relation_restriction(X0,X1))
| ~ well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
? [A,B] :
( ~ well_ordering(relation_restriction(B,A))
& well_ordering(B)
& relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f47,plain,
? [B] :
( ? [A] : ~ well_ordering(relation_restriction(B,A))
& well_ordering(B)
& relation(B) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f48,plain,
( ~ well_ordering(relation_restriction(sK0_skl,sK1_skl))
& well_ordering(sK0_skl)
& relation(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(B,sK0_skl),skolemize(A,sK1_skl)],[f47]) ).
fof(f49,plain,
relation(sK0_skl),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f50,plain,
well_ordering(sK0_skl),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f51,plain,
~ well_ordering(relation_restriction(sK0_skl,sK1_skl)),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f56,plain,
( reflexive(sK0_skl)
| ~ relation(sK0_skl) ),
inference(resolution,[status(thm)],[f18,f50]) ).
fof(f57,definition,
( sQ0_spl
<=> relation(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f59,plain,
( sQ0_spl
| ~ relation(sK0_skl) ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f60,definition,
( sQ1_spl
<=> reflexive(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f63,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f56,f57,f60]) ).
fof(f64,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f59,f49]) ).
fof(f65,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f64]) ).
fof(f66,plain,
( transitive(sK0_skl)
| ~ relation(sK0_skl) ),
inference(resolution,[status(thm)],[f19,f50]) ).
fof(f67,definition,
( sQ2_spl
<=> transitive(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f70,plain,
( sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f66,f57,f67]) ).
fof(f71,plain,
( antisymmetric(sK0_skl)
| ~ relation(sK0_skl) ),
inference(resolution,[status(thm)],[f20,f50]) ).
fof(f72,definition,
( sQ3_spl
<=> antisymmetric(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f75,plain,
( sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f71,f57,f72]) ).
fof(f76,plain,
( connected(sK0_skl)
| ~ relation(sK0_skl) ),
inference(resolution,[status(thm)],[f21,f50]) ).
fof(f77,definition,
( sQ4_spl
<=> connected(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f80,plain,
( sQ4_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f76,f57,f77]) ).
fof(f81,plain,
( well_founded_relation(sK0_skl)
| ~ relation(sK0_skl) ),
inference(resolution,[status(thm)],[f22,f50]) ).
fof(f82,definition,
( sQ5_spl
<=> well_founded_relation(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f85,plain,
( sQ5_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f81,f57,f82]) ).
fof(f86,plain,
! [X0,X1] :
( ~ reflexive(X0)
| ~ relation(X0)
| ~ well_founded_relation(relation_restriction(X0,X1))
| ~ connected(relation_restriction(X0,X1))
| ~ antisymmetric(relation_restriction(X0,X1))
| ~ transitive(relation_restriction(X0,X1))
| well_ordering(relation_restriction(X0,X1))
| ~ relation(relation_restriction(X0,X1)) ),
inference(resolution,[status(thm)],[f23,f33]) ).
fof(f95,plain,
! [X0,X1] :
( ~ reflexive(X0)
| ~ relation(X0)
| ~ well_founded_relation(relation_restriction(X0,X1))
| ~ connected(relation_restriction(X0,X1))
| ~ antisymmetric(relation_restriction(X0,X1))
| ~ transitive(relation_restriction(X0,X1))
| well_ordering(relation_restriction(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f86,f28]) ).
fof(f115,plain,
! [X0,X1] :
( ~ antisymmetric(X0)
| ~ relation(X0)
| ~ reflexive(X0)
| ~ relation(X0)
| ~ well_founded_relation(relation_restriction(X0,X1))
| ~ connected(relation_restriction(X0,X1))
| ~ transitive(relation_restriction(X0,X1))
| well_ordering(relation_restriction(X0,X1)) ),
inference(resolution,[status(thm)],[f95,f42]) ).
fof(f118,plain,
! [X0,X1] :
( ~ antisymmetric(X0)
| ~ reflexive(X0)
| ~ relation(X0)
| ~ well_founded_relation(relation_restriction(X0,X1))
| ~ connected(relation_restriction(X0,X1))
| ~ transitive(relation_restriction(X0,X1))
| well_ordering(relation_restriction(X0,X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f115]) ).
fof(f121,plain,
! [X0,X1] :
( ~ connected(X0)
| ~ relation(X0)
| ~ antisymmetric(X0)
| ~ reflexive(X0)
| ~ relation(X0)
| ~ well_founded_relation(relation_restriction(X0,X1))
| ~ transitive(relation_restriction(X0,X1))
| well_ordering(relation_restriction(X0,X1)) ),
inference(resolution,[status(thm)],[f118,f36]) ).
fof(f123,plain,
! [X0,X1] :
( ~ connected(X0)
| ~ antisymmetric(X0)
| ~ reflexive(X0)
| ~ relation(X0)
| ~ well_founded_relation(relation_restriction(X0,X1))
| ~ transitive(relation_restriction(X0,X1))
| well_ordering(relation_restriction(X0,X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f121]) ).
fof(f125,plain,
! [X0,X1] :
( ~ well_founded_relation(X0)
| ~ relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ reflexive(X0)
| ~ relation(X0)
| ~ transitive(relation_restriction(X0,X1))
| well_ordering(relation_restriction(X0,X1)) ),
inference(resolution,[status(thm)],[f123,f45]) ).
fof(f126,plain,
! [X0,X1] :
( ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ reflexive(X0)
| ~ relation(X0)
| ~ transitive(relation_restriction(X0,X1))
| well_ordering(relation_restriction(X0,X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f125]) ).
fof(f127,plain,
! [X0,X1] :
( ~ transitive(X0)
| ~ relation(X0)
| ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ reflexive(X0)
| ~ relation(X0)
| well_ordering(relation_restriction(X0,X1)) ),
inference(resolution,[status(thm)],[f126,f39]) ).
fof(f128,plain,
! [X0,X1] :
( ~ transitive(X0)
| ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ reflexive(X0)
| ~ relation(X0)
| well_ordering(relation_restriction(X0,X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f127]) ).
fof(f129,plain,
( ~ transitive(sK0_skl)
| ~ well_founded_relation(sK0_skl)
| ~ connected(sK0_skl)
| ~ antisymmetric(sK0_skl)
| ~ reflexive(sK0_skl)
| ~ relation(sK0_skl) ),
inference(resolution,[status(thm)],[f128,f51]) ).
fof(f135,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f129,f57,f60,f72,f77,f82,f67]) ).
fof(f136,plain,
$false,
inference(sat_refutation,[status(thm)],[f63,f65,f70,f75,f80,f85,f135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU257+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.39 % Computer : n018.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 21 06:06:29 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.40 % Drodi V4.1.1
% 0.11/0.44 % Refutation found
% 0.11/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.47 % Elapsed time: 0.065145 seconds
% 0.11/0.47 % CPU time: 0.185469 seconds
% 0.11/0.47 % Total memory used: 58.849 MB
% 0.11/0.47 % Net memory used: 58.539 MB
%------------------------------------------------------------------------------