%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL083-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 01:06:46 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.55s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 9 unt; 2 def)
% Number of atoms : 78 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 89 ( 46 ~; 41 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 81 ( 81 !; 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,Z,U] : is_a_theorem(implies(implies(implies(X,Y),Z),implies(implies(Z,X),implies(U,X)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : is_a_theorem(implies(X,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
~ is_a_theorem(implies(implies(implies(a,b),a),a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,plain,
! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f6,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f7,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(implies(X2,X0),implies(X3,X0)))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f8,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f9,plain,
~ is_a_theorem(implies(implies(implies(a,b),a),a)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f11,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(implies(X2,X0),implies(X3,X0)))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f7,f6]) ).
fof(f12,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(X3,X0))
| ~ is_a_theorem(implies(X2,X0))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f11,f6]) ).
fof(f14,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(X0)
| ~ is_a_theorem(X3)
| ~ is_a_theorem(implies(X2,X0))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f12,f6]) ).
fof(f15,definition,
! [X0,X1,X2] :
( sQ0_spl
<=> ( is_a_theorem(X0)
| ~ is_a_theorem(implies(X2,X0))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| is_a_theorem(X0)
| ~ is_a_theorem(implies(X2,X0))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(component_clause,[status(thm)],[f15]) ).
fof(f18,definition,
! [X3] :
( sQ1_spl
<=> ~ is_a_theorem(X3) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f19,plain,
! [X0] :
( ~ sQ1_spl
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f18]) ).
fof(f21,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f14,f15,f18]) ).
fof(f31,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ0_spl
| is_a_theorem(implies(implies(X0,X1),implies(X2,X1)))
| ~ is_a_theorem(implies(implies(implies(implies(X0,X1),implies(X2,X1)),X3),implies(implies(X1,X4),X0))) ),
inference(resolution,[status(thm)],[f16,f7]) ).
fof(f32,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ0_spl
| ~ is_a_theorem(implies(implies(X1,X4),X3))
| is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(implies(implies(X0,X1),X2),implies(X3,X1))) ),
inference(resolution,[status(thm)],[f16,f11]) ).
fof(f34,plain,
! [X0,X1] :
( ~ sQ0_spl
| is_a_theorem(X0)
| ~ is_a_theorem(implies(implies(X0,X1),X0)) ),
inference(resolution,[status(thm)],[f16,f8]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ is_a_theorem(implies(implies(X1,X2),implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f34,f11]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( ~ sQ0_spl
| is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(implies(implies(X0,X1),X2),implies(implies(X1,X3),X1))) ),
inference(resolution,[status(thm)],[f32,f8]) ).
fof(f52,plain,
! [X0,X1] :
( ~ sQ0_spl
| is_a_theorem(implies(implies(X0,X1),implies(X1,X1))) ),
inference(resolution,[status(thm)],[f41,f7]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ is_a_theorem(implies(implies(X1,X2),X1))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f41,f11]) ).
fof(f62,plain,
! [X0,X1] :
( ~ sQ0_spl
| is_a_theorem(implies(X0,implies(X1,X1))) ),
inference(resolution,[status(thm)],[f53,f52]) ).
fof(f81,plain,
( ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f7,f19]) ).
fof(f83,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f81]) ).
fof(f97,plain,
! [X0,X1,X2,X3,X4,X5] :
( is_a_theorem(implies(X5,implies(implies(X0,X1),implies(X2,X1))))
| ~ is_a_theorem(implies(implies(implies(implies(X0,X1),implies(X2,X1)),X3),implies(implies(X1,X4),X0))) ),
inference(resolution,[status(thm)],[f12,f7]) ).
fof(f112,plain,
! [X0,X1,X2,X3] :
( ~ sQ0_spl
| is_a_theorem(implies(X0,implies(implies(implies(X1,X2),X1),implies(X3,X1)))) ),
inference(resolution,[status(thm)],[f97,f62]) ).
fof(f167,plain,
! [X0,X1,X2,X3] :
( ~ sQ0_spl
| is_a_theorem(implies(implies(implies(X0,X1),implies(X1,X2)),implies(X3,implies(X1,X2)))) ),
inference(resolution,[status(thm)],[f31,f112]) ).
fof(f302,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| is_a_theorem(implies(implies(implies(implies(X0,X1),X2),X1),implies(X0,X1))) ),
inference(resolution,[status(thm)],[f167,f31]) ).
fof(f725,plain,
! [X0,X1] :
( ~ sQ0_spl
| is_a_theorem(implies(implies(implies(X0,X1),X0),X0)) ),
inference(resolution,[status(thm)],[f51,f302]) ).
fof(f765,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f9,f725]) ).
fof(f779,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f765]) ).
fof(f780,plain,
$false,
inference(sat_refutation,[status(thm)],[f21,f83,f779]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL083-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n003.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 00:05:30 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 % Drodi V4.1.1
% 0.14/0.55 % Refutation found
% 0.14/0.55 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.56 % Elapsed time: 0.197927 seconds
% 0.14/0.56 % CPU time: 1.284977 seconds
% 0.14/0.56 % Total memory used: 77.435 MB
% 0.14/0.56 % Net memory used: 73.363 MB
%------------------------------------------------------------------------------