%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL081-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 01:06:45 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 8 unt; 3 def)
% Number of atoms : 58 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 59 ( 30 ~; 26 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 4 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 58 ( 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
~ is_a_theorem(implies(a,a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f5,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f6,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(f7,plain,
~ is_a_theorem(implies(a,a)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f8,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)],[f6,f5]) ).
fof(f9,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)],[f8,f5]) ).
fof(f11,plain,
! [X0,X1,X2,X3,X4] :
( ~ is_a_theorem(implies(implies(X1,X4),X2))
| is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f9,f8]) ).
fof(f13,plain,
! [X0,X1,X2,X3,X4,X5] :
( is_a_theorem(implies(X5,implies(implies(X3,X1),implies(X4,X1))))
| ~ is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(implies(X3,X1),implies(X4,X1)))) ),
inference(resolution,[status(thm)],[f11,f6]) ).
fof(f17,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(X0,implies(implies(implies(X1,X2),X1),implies(X3,X1)))),
inference(resolution,[status(thm)],[f13,f6]) ).
fof(f24,definition,
! [X0] :
( sQ0_spl
<=> ~ is_a_theorem(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f25,plain,
! [X0] :
( ~ sQ0_spl
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f24]) ).
fof(f31,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f6,f25]) ).
fof(f33,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f31]) ).
fof(f37,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(implies(implies(X1,X2),X1),implies(X3,X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f17,f5]) ).
fof(f38,definition,
! [X1,X2,X3] :
( sQ2_spl
<=> is_a_theorem(implies(implies(implies(X1,X2),X1),implies(X3,X1))) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ sQ2_spl
| is_a_theorem(implies(implies(implies(X0,X1),X0),implies(X2,X0))) ),
inference(component_clause,[status(thm)],[f38]) ).
fof(f41,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f37,f24,f38]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ~ sQ2_spl
| is_a_theorem(implies(X2,X0))
| ~ is_a_theorem(implies(implies(X0,X1),X0)) ),
inference(resolution,[status(thm)],[f39,f5]) ).
fof(f44,plain,
! [X0,X1] :
( ~ sQ2_spl
| is_a_theorem(implies(X0,implies(X1,X1))) ),
inference(resolution,[status(thm)],[f43,f39]) ).
fof(f48,plain,
! [X0,X1] :
( ~ sQ2_spl
| is_a_theorem(implies(X1,X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f44,f5]) ).
fof(f49,definition,
! [X1] :
( sQ3_spl
<=> is_a_theorem(implies(X1,X1)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f50,plain,
! [X0] :
( ~ sQ3_spl
| is_a_theorem(implies(X0,X0)) ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f52,plain,
( ~ sQ2_spl
| sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f48,f24,f49,f38]) ).
fof(f53,plain,
( ~ sQ3_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f7,f50]) ).
fof(f55,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f53]) ).
fof(f56,plain,
$false,
inference(sat_refutation,[status(thm)],[f33,f41,f52,f55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL081-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n005.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 00:04:03 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 0.08/0.38 % Refutation found
% 0.08/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.46 % Elapsed time: 0.104945 seconds
% 0.15/0.46 % CPU time: 0.185335 seconds
% 0.15/0.46 % Total memory used: 32.840 MB
% 0.15/0.46 % Net memory used: 32.478 MB
%------------------------------------------------------------------------------