%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU115+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 02:19:15 PM UTC 2026
% Result : Theorem 0.21s 0.71s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 12 unt; 0 def)
% Number of atoms : 44 ( 13 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 32 ( 8 ~; 4 |; 18 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 12 ( 11 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f22,axiom,
! [A] :
? [B] :
( finite(B)
& natural(B)
& ordinal(B)
& epsilon_connected(B)
& epsilon_transitive(B)
& one_to_one(B)
& function(B)
& relation(B)
& empty(B)
& element(B,powerset(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,conjecture,
finite_subsets(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
finite_subsets(empty_set) != singleton(empty_set),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f35,axiom,
! [A] :
( finite(A)
=> finite_subsets(A) = powerset(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f98,plain,
! [A] :
( finite(sK3_skl(A))
& natural(sK3_skl(A))
& ordinal(sK3_skl(A))
& epsilon_connected(sK3_skl(A))
& epsilon_transitive(sK3_skl(A))
& one_to_one(sK3_skl(A))
& function(sK3_skl(A))
& relation(sK3_skl(A))
& empty(sK3_skl(A))
& element(sK3_skl(A),powerset(A)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(B,sK3_skl(A))],[f22]) ).
fof(f100,plain,
! [X0] : empty(sK3_skl(X0)),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f108,plain,
! [X0] : finite(sK3_skl(X0)),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f133,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f134,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f135,plain,
finite_subsets(empty_set) != singleton(empty_set),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f136,plain,
! [A] :
( finite_subsets(A) = powerset(A)
| ~ finite(A) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f137,plain,
! [X0] :
( finite_subsets(X0) = powerset(X0)
| ~ finite(X0) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f138,plain,
powerset(empty_set) = singleton(empty_set),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f140,plain,
finite_subsets(empty_set) != powerset(empty_set),
inference(backward_demodulation,[status(thm)],[f138,f135]) ).
fof(f143,plain,
~ finite(empty_set),
inference(resolution,[status(thm)],[f140,f137]) ).
fof(f149,plain,
! [X0] : sK3_skl(X0) = empty_set,
inference(resolution,[status(thm)],[f100,f134]) ).
fof(f162,plain,
finite(empty_set),
inference(forward_demodulation,[status(thm)],[f149,f108]) ).
fof(f163,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f162,f143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU115+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.66 % Computer : n001.cluster.edu
% 0.16/0.66 % Model : x86_64 x86_64
% 0.16/0.66 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.66 % Memory : 8046.5625MB
% 0.16/0.66 % OS : Linux 6.8.0-71-generic
% 0.16/0.66 % CPULimit : 300
% 0.16/0.66 % WCLimit : 300
% 0.16/0.66 % DateTime : Mon Sep 21 05:56:44 UTC 2026
% 0.16/0.66 % CPUTime :
% 0.16/0.68 % Drodi V4.1.1
% 0.21/0.71 % Refutation found
% 0.21/0.71 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/0.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.74 % Elapsed time: 0.056675 seconds
% 0.21/0.74 % CPU time: 0.147794 seconds
% 0.21/0.74 % Total memory used: 51.562 MB
% 0.21/0.74 % Net memory used: 51.541 MB
%------------------------------------------------------------------------------