%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET023-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 02:08:56 PM UTC 2026
% Result : Unsatisfiable 0.07s 0.36s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 10 unt; 0 def)
% Number of atoms : 32 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 27 ( 15 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 11 ( 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [X] :
( little_set(f2(X))
| ~ ordered_pair_predicate(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] :
( little_set(f3(X))
| ~ ordered_pair_predicate(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X] :
( X = ordered_pair(f2(X),f3(X))
| ~ ordered_pair_predicate(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f147,axiom,
! [X,Y] :
( second(ordered_pair(X,Y)) = Y
| ~ little_set(Y)
| ~ little_set(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f149,hypothesis,
ordered_pair_predicate(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f150,negated_conjecture,
~ little_set(second(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f165,plain,
! [X0] :
( little_set(f2(X0))
| ~ ordered_pair_predicate(X0) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f166,plain,
! [X0] :
( little_set(f3(X0))
| ~ ordered_pair_predicate(X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f167,plain,
! [X0] :
( X0 = ordered_pair(f2(X0),f3(X0))
| ~ ordered_pair_predicate(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f336,plain,
! [X0,X1] :
( second(ordered_pair(X0,X1)) = X1
| ~ little_set(X1)
| ~ little_set(X0) ),
inference(cnf_transformation,[status(thm)],[f147]) ).
fof(f338,plain,
ordered_pair_predicate(a),
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f339,plain,
~ little_set(second(a)),
inference(cnf_transformation,[status(thm)],[f150]) ).
fof(f427,plain,
little_set(f2(a)),
inference(resolution,[status(thm)],[f165,f338]) ).
fof(f434,plain,
little_set(f3(a)),
inference(resolution,[status(thm)],[f166,f338]) ).
fof(f440,plain,
! [X0] :
( second(ordered_pair(X0,f3(a))) = f3(a)
| ~ little_set(X0) ),
inference(resolution,[status(thm)],[f434,f336]) ).
fof(f463,plain,
a = ordered_pair(f2(a),f3(a)),
inference(resolution,[status(thm)],[f167,f338]) ).
fof(f985,plain,
( second(a) = f3(a)
| ~ little_set(f2(a)) ),
inference(paramodulation,[status(thm)],[f463,f440]) ).
fof(f987,plain,
second(a) = f3(a),
inference(forward_subsumption_resolution,[status(thm)],[f985,f427]) ).
fof(f991,plain,
~ little_set(f3(a)),
inference(backward_demodulation,[status(thm)],[f987,f339]) ).
fof(f993,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f991,f434]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET023-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Mon Sep 21 04:43:51 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.31 % Drodi V4.1.1
% 0.07/0.36 % Refutation found
% 0.07/0.36 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.07/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.07/0.37 % Elapsed time: 0.066293 seconds
% 0.07/0.37 % CPU time: 0.286063 seconds
% 0.07/0.37 % Total memory used: 114.806 MB
% 0.07/0.37 % Net memory used: 113.699 MB
%------------------------------------------------------------------------------