%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU275+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 : n011.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 02:20:00 PM UTC 2026
% Result : Theorem 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 12 unt; 0 def)
% Number of atoms : 90 ( 0 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 99 ( 41 ~; 36 |; 15 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 27 ( 26 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,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] : relation(inclusion_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : reflexive(inclusion_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] : transitive(inclusion_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A] :
( ordinal(A)
=> connected(inclusion_relation(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A] : antisymmetric(inclusion_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] :
( ordinal(A)
=> well_founded_relation(inclusion_relation(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,conjecture,
! [A] :
( ordinal(A)
=> well_ordering(inclusion_relation(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> well_ordering(inclusion_relation(A)) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f18,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)],[f3]) ).
fof(f19,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)],[f18]) ).
fof(f25,plain,
! [X0] :
( ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0)
| well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f26,plain,
! [X0] : relation(inclusion_relation(X0)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f31,plain,
! [X0] : reflexive(inclusion_relation(X0)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f32,plain,
! [X0] : transitive(inclusion_relation(X0)),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f33,plain,
! [A] :
( connected(inclusion_relation(A))
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f34,plain,
! [X0] :
( connected(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [X0] : antisymmetric(inclusion_relation(X0)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f36,plain,
! [A] :
( well_founded_relation(inclusion_relation(A))
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f37,plain,
! [X0] :
( well_founded_relation(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
? [A] :
( ~ well_ordering(inclusion_relation(A))
& ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f39,plain,
( ~ well_ordering(inclusion_relation(sK1_skl))
& ordinal(sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(A,sK1_skl)],[f38]) ).
fof(f40,plain,
ordinal(sK1_skl),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f41,plain,
~ well_ordering(inclusion_relation(sK1_skl)),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f44,plain,
! [X0] :
( ~ well_founded_relation(inclusion_relation(X0))
| ~ connected(inclusion_relation(X0))
| ~ antisymmetric(inclusion_relation(X0))
| ~ transitive(inclusion_relation(X0))
| ~ reflexive(inclusion_relation(X0))
| well_ordering(inclusion_relation(X0)) ),
inference(resolution,[status(thm)],[f25,f26]) ).
fof(f45,plain,
! [X0] :
( ~ well_founded_relation(inclusion_relation(X0))
| ~ connected(inclusion_relation(X0))
| ~ antisymmetric(inclusion_relation(X0))
| ~ transitive(inclusion_relation(X0))
| well_ordering(inclusion_relation(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f44,f31]) ).
fof(f46,plain,
! [X0] :
( ~ well_founded_relation(inclusion_relation(X0))
| ~ connected(inclusion_relation(X0))
| ~ antisymmetric(inclusion_relation(X0))
| well_ordering(inclusion_relation(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f45,f32]) ).
fof(f47,plain,
! [X0] :
( ~ ordinal(X0)
| ~ well_founded_relation(inclusion_relation(X0))
| ~ antisymmetric(inclusion_relation(X0))
| well_ordering(inclusion_relation(X0)) ),
inference(resolution,[status(thm)],[f46,f34]) ).
fof(f51,plain,
! [X0] :
( ~ ordinal(X0)
| ~ well_founded_relation(inclusion_relation(X0))
| well_ordering(inclusion_relation(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f47,f35]) ).
fof(f53,plain,
! [X0] :
( ~ ordinal(X0)
| well_ordering(inclusion_relation(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f51,f37]) ).
fof(f54,plain,
~ ordinal(sK1_skl),
inference(resolution,[status(thm)],[f53,f41]) ).
fof(f55,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f54,f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU275+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 06:05:40 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.39 % Refutation found
% 0.10/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.41 % Elapsed time: 0.040434 seconds
% 0.10/0.41 % CPU time: 0.107573 seconds
% 0.10/0.41 % Total memory used: 38.304 MB
% 0.10/0.41 % Net memory used: 38.062 MB
%------------------------------------------------------------------------------