%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD060-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 12:22:05 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 34 ( 12 unt; 0 def)
% Number of atoms : 77 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 88 ( 45 ~; 43 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 51 ( 51 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [Y,X,Z] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| sum(X,Y,add(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Z,Y] :
( ~ less_or_equal(Y,Z)
| ~ less_or_equal(X,Y)
| less_or_equal(X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [U,V,X,Y,Z] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
less_or_equal(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ less_or_equal(add(a,a),add(b,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,plain,
! [X0,X1,X2] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f57,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| sum(X,Y,add(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f58,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| sum(X0,X1,add(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f62,plain,
! [Z,Y] :
( ~ less_or_equal(Y,Z)
| ! [X] :
( ~ less_or_equal(X,Y)
| less_or_equal(X,Z) ) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X0,X2)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f66,plain,
! [V,Y,Z] :
( ~ sum(Y,Z,V)
| ! [U,X] :
( ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f67,plain,
! [X0,X1,X2,X3,X4] :
( ~ sum(X3,X4,X1)
| ~ sum(X2,X4,X0)
| ~ less_or_equal(X2,X3)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f70,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f71,plain,
defined(b),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f72,plain,
less_or_equal(a,b),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f73,plain,
~ less_or_equal(add(a,a),add(b,b)),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ~ sum(b,X2,X1)
| ~ sum(a,X2,X0)
| less_or_equal(X0,X1) ),
inference(resolution,[status(thm)],[f67,f72]) ).
fof(f91,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(b)
| ~ sum(a,X1,X0)
| less_or_equal(X0,add(b,X1)) ),
inference(resolution,[status(thm)],[f80,f58]) ).
fof(f92,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ sum(a,X1,X0)
| less_or_equal(X0,add(b,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f91,f71]) ).
fof(f93,plain,
! [X0] :
( ~ defined(X0)
| ~ defined(a)
| ~ defined(X0)
| less_or_equal(add(a,X0),add(b,X0)) ),
inference(resolution,[status(thm)],[f92,f58]) ).
fof(f94,plain,
! [X0] :
( ~ defined(a)
| ~ defined(X0)
| less_or_equal(add(a,X0),add(b,X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f93]) ).
fof(f95,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(add(a,X0),add(b,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f94,f70]) ).
fof(f98,plain,
! [X0,X1] :
( ~ less_or_equal(add(b,X0),X1)
| less_or_equal(add(a,X0),X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f95,f63]) ).
fof(f217,plain,
! [X0,X1] :
( ~ defined(X0)
| ~ defined(X1)
| sum(X0,X1,add(X1,X0)) ),
inference(resolution,[status(thm)],[f37,f58]) ).
fof(f233,plain,
! [X0] :
( ~ defined(X0)
| sum(X0,b,add(b,X0)) ),
inference(resolution,[status(thm)],[f217,f71]) ).
fof(f242,plain,
sum(a,b,add(b,a)),
inference(resolution,[status(thm)],[f233,f70]) ).
fof(f256,plain,
( ~ defined(b)
| less_or_equal(add(b,a),add(b,b)) ),
inference(resolution,[status(thm)],[f242,f92]) ).
fof(f265,plain,
less_or_equal(add(b,a),add(b,b)),
inference(forward_subsumption_resolution,[status(thm)],[f256,f71]) ).
fof(f349,plain,
( less_or_equal(add(a,a),add(b,b))
| ~ defined(a) ),
inference(resolution,[status(thm)],[f265,f98]) ).
fof(f353,plain,
less_or_equal(add(a,a),add(b,b)),
inference(forward_subsumption_resolution,[status(thm)],[f349,f70]) ).
fof(f362,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f353,f73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD060-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n008.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 15:44:24 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.42 % Refutation found
% 0.13/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.44 % Elapsed time: 0.074589 seconds
% 0.13/0.44 % CPU time: 0.328462 seconds
% 0.13/0.44 % Total memory used: 20.425 MB
% 0.13/0.44 % Net memory used: 19.974 MB
%------------------------------------------------------------------------------