%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV008-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 0.37s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of formulae : 43 ( 11 unt; 6 def)
% Number of atoms : 101 ( 5 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 103 ( 45 ~; 52 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 15 ( 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X,Y] :
( X = Y
| less_than(Y,X)
| less_than(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] : ~ less_than(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ less_than(n,l),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
less_than(one,l),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
less_than(a(l),a(predecessor(l))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
! [X] :
( ~ less_than(a(X),a(predecessor(n)))
| ~ less_than(one,n)
| less_than(n,X)
| less_than(X,n) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
! [X] :
( ~ less_than(a(X),a(predecessor(X)))
| ~ less_than(X,n)
| ~ less_than(one,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,plain,
! [X0,X1] :
( X0 = X1
| less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f27,plain,
! [X0] : ~ less_than(X0,X0),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f33,plain,
~ less_than(n,l),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f34,plain,
less_than(one,l),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f35,plain,
less_than(a(l),a(predecessor(l))),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f36,plain,
! [X0] :
( ~ less_than(a(X0),a(predecessor(n)))
| ~ less_than(one,n)
| less_than(n,X0)
| less_than(X0,n) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f37,plain,
! [X0] :
( ~ less_than(a(X0),a(predecessor(X0)))
| ~ less_than(X0,n)
| ~ less_than(one,X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f38,definition,
! [X0] :
( sQ0_spl
<=> ( ~ less_than(a(X0),a(predecessor(n)))
| less_than(n,X0)
| less_than(X0,n) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f39,plain,
! [X0] :
( ~ sQ0_spl
| ~ less_than(a(X0),a(predecessor(n)))
| less_than(n,X0)
| less_than(X0,n) ),
inference(component_clause,[status(thm)],[f38]) ).
fof(f41,definition,
( sQ1_spl
<=> less_than(one,n) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f43,plain,
( sQ1_spl
| ~ less_than(one,n) ),
inference(component_clause,[status(thm)],[f41]) ).
fof(f44,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f36,f38,f41]) ).
fof(f45,plain,
( ~ less_than(l,n)
| ~ less_than(one,l) ),
inference(resolution,[status(thm)],[f37,f35]) ).
fof(f46,definition,
( sQ2_spl
<=> less_than(one,l) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f48,plain,
( sQ2_spl
| ~ less_than(one,l) ),
inference(component_clause,[status(thm)],[f46]) ).
fof(f49,definition,
( sQ3_spl
<=> less_than(l,n) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f52,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f45,f46,f49]) ).
fof(f53,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f48,f34]) ).
fof(f54,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f53]) ).
fof(f63,plain,
( l = n
| less_than(l,n) ),
inference(resolution,[status(thm)],[f26,f33]) ).
fof(f74,definition,
( sQ6_spl
<=> n = l ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f75,plain,
( ~ sQ6_spl
| n = l ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f78,plain,
( sQ6_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f63,f49,f74]) ).
fof(f79,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| ~ less_than(a(X0),a(predecessor(l)))
| less_than(n,X0)
| less_than(X0,n) ),
inference(backward_demodulation,[status(thm)],[f75,f39]) ).
fof(f83,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| ~ less_than(a(X0),a(predecessor(l)))
| less_than(n,X0)
| less_than(X0,l) ),
inference(forward_demodulation,[status(thm)],[f75,f79]) ).
fof(f84,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| ~ less_than(a(X0),a(predecessor(l)))
| less_than(l,X0)
| less_than(X0,l) ),
inference(forward_demodulation,[status(thm)],[f75,f83]) ).
fof(f91,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| less_than(l,l)
| less_than(l,l) ),
inference(resolution,[status(thm)],[f84,f35]) ).
fof(f93,definition,
( sQ7_spl
<=> less_than(l,l) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ7_spl
| less_than(l,l) ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f91,f93,f74,f38]) ).
fof(f97,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f94,f27]) ).
fof(f98,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f97]) ).
fof(f99,plain,
( sQ1_spl
| ~ sQ6_spl
| ~ less_than(one,l) ),
inference(forward_demodulation,[status(thm)],[f75,f43]) ).
fof(f100,plain,
( sQ1_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f99,f34]) ).
fof(f101,plain,
( sQ1_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f100]) ).
fof(f102,plain,
$false,
inference(sat_refutation,[status(thm)],[f44,f52,f54,f78,f96,f98,f101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n015.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 08:29:36 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.37 % Refutation found
% 0.09/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.41 % Elapsed time: 0.043015 seconds
% 0.09/0.41 % CPU time: 0.079110 seconds
% 0.09/0.41 % Total memory used: 12.791 MB
% 0.09/0.41 % Net memory used: 12.758 MB
%------------------------------------------------------------------------------