%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET022-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 0.13s 0.48s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 11 unt; 0 def)
% Number of atoms : 31 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 14 ~; 11 |; 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/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] :
( little_set(f3(X))
| ~ ordered_pair_predicate(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X] :
( X = ordered_pair(f2(X),f3(X))
| ~ ordered_pair_predicate(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f146,axiom,
! [X,Y] :
( first(ordered_pair(X,Y)) = X
| ~ little_set(Y)
| ~ little_set(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f148,hypothesis,
ordered_pair_predicate(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f149,negated_conjecture,
~ little_set(first(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f164,plain,
! [X0] :
( little_set(f2(X0))
| ~ ordered_pair_predicate(X0) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f165,plain,
! [X0] :
( little_set(f3(X0))
| ~ ordered_pair_predicate(X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f166,plain,
! [X0] :
( X0 = ordered_pair(f2(X0),f3(X0))
| ~ ordered_pair_predicate(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f334,plain,
! [X0,X1] :
( first(ordered_pair(X0,X1)) = X0
| ~ little_set(X1)
| ~ little_set(X0) ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f336,plain,
ordered_pair_predicate(a),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f337,plain,
~ little_set(first(a)),
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f417,plain,
little_set(f2(a)),
inference(resolution,[status(thm)],[f164,f336]) ).
fof(f424,plain,
little_set(f3(a)),
inference(resolution,[status(thm)],[f165,f336]) ).
fof(f429,plain,
! [X0] :
( first(ordered_pair(X0,f3(a))) = X0
| ~ little_set(X0) ),
inference(resolution,[status(thm)],[f424,f334]) ).
fof(f538,plain,
a = ordered_pair(f2(a),f3(a)),
inference(resolution,[status(thm)],[f166,f336]) ).
fof(f742,plain,
first(ordered_pair(f2(a),f3(a))) = f2(a),
inference(resolution,[status(thm)],[f429,f417]) ).
fof(f748,plain,
first(a) = f2(a),
inference(forward_demodulation,[status(thm)],[f538,f742]) ).
fof(f749,plain,
~ little_set(f2(a)),
inference(backward_demodulation,[status(thm)],[f748,f337]) ).
fof(f751,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f749,f417]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET022-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n006.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 04:43:27 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.37 % Drodi V4.1.1
% 0.13/0.48 % Refutation found
% 0.13/0.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.50 % Elapsed time: 0.130638 seconds
% 0.13/0.50 % CPU time: 0.721536 seconds
% 0.13/0.50 % Total memory used: 116.641 MB
% 0.13/0.50 % Net memory used: 115.574 MB
%------------------------------------------------------------------------------