%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV006-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 02:46:25 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 11 unt; 2 def)
% Number of atoms : 46 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 20 ~; 18 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 16 ( 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X] : less_than(X,successor(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Z,Y] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] : ~ less_than(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
less_than(i,n),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
less_than(a(i),a(m)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
! [X] :
( ~ less_than(a(X),a(m))
| ~ less_than(X,successor(n))
| less_than(X,i) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,plain,
! [X0] : less_than(X0,successor(X0)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f27,plain,
! [Z,Y] :
( ~ less_than(Y,Z)
| ! [X] :
( ~ less_than(X,Y)
| less_than(X,Z) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ~ less_than(X2,X1)
| ~ less_than(X0,X2)
| less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f30,plain,
! [X0] : ~ less_than(X0,X0),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f38,plain,
less_than(i,n),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f40,plain,
less_than(a(i),a(m)),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f41,plain,
! [X0] :
( ~ less_than(a(X0),a(m))
| ~ less_than(X0,successor(n))
| less_than(X0,i) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f75,plain,
! [X0] :
( ~ less_than(n,X0)
| less_than(i,X0) ),
inference(resolution,[status(thm)],[f28,f38]) ).
fof(f122,plain,
( ~ less_than(i,successor(n))
| less_than(i,i) ),
inference(resolution,[status(thm)],[f41,f40]) ).
fof(f124,definition,
( sQ9_spl
<=> less_than(i,i) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f125,plain,
( ~ sQ9_spl
| less_than(i,i) ),
inference(component_clause,[status(thm)],[f124]) ).
fof(f127,definition,
( sQ10_spl
<=> less_than(i,successor(n)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f129,plain,
( sQ10_spl
| ~ less_than(i,successor(n)) ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f130,plain,
( ~ sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f122,f124,f127]) ).
fof(f131,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f125,f30]) ).
fof(f132,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f131]) ).
fof(f167,plain,
( sQ10_spl
| ~ less_than(n,successor(n)) ),
inference(resolution,[status(thm)],[f75,f129]) ).
fof(f176,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f167,f26]) ).
fof(f177,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f176]) ).
fof(f178,plain,
$false,
inference(sat_refutation,[status(thm)],[f130,f132,f177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 08:27:17 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.42 % Elapsed time: 0.048195 seconds
% 0.09/0.42 % CPU time: 0.132052 seconds
% 0.09/0.42 % Total memory used: 66.903 MB
% 0.09/0.42 % Net memory used: 66.674 MB
%------------------------------------------------------------------------------