%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL045-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 01:06:39 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.87s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 33 ( 15 unt; 2 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 48 ( 25 ~; 21 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 46 ( 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : is_a_theorem(implies(X,implies(not(X),Y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : is_a_theorem(implies(X,implies(Y,X))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z] : is_a_theorem(implies(implies(X,implies(Y,Z)),implies(Y,implies(X,Z)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Y,Z,X] : is_a_theorem(implies(implies(Y,Z),implies(implies(X,Y),implies(X,Z)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(not(X),Y),Y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
~ is_a_theorem(implies(implies(a,b),implies(not(b),not(a)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,plain,
! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f9,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f10,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f11,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f12,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2)))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f13,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1)))),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f14,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(not(X0),X1),X1))),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f15,plain,
~ is_a_theorem(implies(implies(a,b),implies(not(b),not(a)))),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f27,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X1,implies(X0,X2)))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f12,f9]) ).
fof(f28,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X2,X0),implies(X2,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f13,f9]) ).
fof(f41,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f27,f9]) ).
fof(f42,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(X2,X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f28,f9]) ).
fof(f50,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),X1))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[f41,f14]) ).
fof(f67,plain,
! [X0] :
( ~ is_a_theorem(implies(implies(a,b),X0))
| ~ is_a_theorem(implies(X0,implies(not(b),not(a)))) ),
inference(resolution,[status(thm)],[f42,f15]) ).
fof(f152,plain,
! [X0] :
( ~ is_a_theorem(implies(b,X0))
| ~ is_a_theorem(implies(implies(a,X0),implies(not(b),not(a)))) ),
inference(resolution,[status(thm)],[f67,f28]) ).
fof(f173,definition,
( sQ11_spl
<=> is_a_theorem(implies(b,implies(not(b),not(a)))) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f175,plain,
( sQ11_spl
| ~ is_a_theorem(implies(b,implies(not(b),not(a)))) ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f200,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f175,f10]) ).
fof(f201,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f200]) ).
fof(f683,plain,
( ~ is_a_theorem(implies(not(a),implies(not(b),not(a))))
| ~ is_a_theorem(implies(b,implies(not(b),not(a)))) ),
inference(resolution,[status(thm)],[f152,f50]) ).
fof(f696,definition,
( sQ35_spl
<=> is_a_theorem(implies(not(a),implies(not(b),not(a)))) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f698,plain,
( sQ35_spl
| ~ is_a_theorem(implies(not(a),implies(not(b),not(a)))) ),
inference(component_clause,[status(thm)],[f696]) ).
fof(f699,plain,
( ~ sQ35_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f683,f173,f696]) ).
fof(f713,plain,
( sQ35_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f698,f11]) ).
fof(f714,plain,
sQ35_spl,
inference(contradiction_clause,[status(thm)],[f713]) ).
fof(f715,plain,
$false,
inference(sat_refutation,[status(thm)],[f201,f699,f714]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL045-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.56 % Computer : n011.cluster.edu
% 0.08/0.56 % Model : x86_64 x86_64
% 0.08/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.56 % Memory : 8046.5625MB
% 0.08/0.56 % OS : Linux 6.8.0-71-generic
% 0.08/0.56 % CPULimit : 300
% 0.08/0.56 % WCLimit : 300
% 0.08/0.56 % DateTime : Mon Sep 21 00:01:40 UTC 2026
% 0.08/0.56 % CPUTime :
% 0.08/0.57 % Drodi V4.1.1
% 0.12/0.87 % Refutation found
% 0.12/0.87 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.87 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.88 % Elapsed time: 0.315200 seconds
% 0.12/0.88 % CPU time: 2.327158 seconds
% 0.12/0.88 % Total memory used: 93.817 MB
% 0.12/0.88 % Net memory used: 85.942 MB
%------------------------------------------------------------------------------