%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL115-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 01:06:51 PM UTC 2026
% Result : Unsatisfiable 1.58s 0.72s
% Output : CNFRefutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 16 unt; 2 def)
% Number of atoms : 89 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 83 ( 43 ~; 38 |; 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 : 89 ( 89 !; 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(Y,X))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : is_a_theorem(implies(implies(implies(X,Y),Y),implies(implies(Y,X),X))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
~ is_a_theorem(implies(not(implies(a,b)),not(b))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,plain,
! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f8,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f9,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f10,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f11,plain,
! [X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),X1),implies(implies(X1,X0),X0))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f12,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f13,plain,
~ is_a_theorem(implies(not(implies(a,b)),not(b))),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f14,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f8,f9]) ).
fof(f15,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(X2,X1)))),
inference(resolution,[status(thm)],[f14,f9]) ).
fof(f16,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X1,X2),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f10,f8]) ).
fof(f18,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X1,implies(X2,X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f15,f8]) ).
fof(f20,definition,
! [X0] :
( sQ0_spl
<=> ~ is_a_theorem(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f21,plain,
! [X0] :
( ~ sQ0_spl
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f20]) ).
fof(f23,definition,
! [X1,X2] :
( sQ1_spl
<=> is_a_theorem(implies(X1,implies(X2,X1))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f24,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(component_clause,[status(thm)],[f23]) ).
fof(f26,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f18,f20,f23]) ).
fof(f27,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f10,f21]) ).
fof(f30,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f27]) ).
fof(f33,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X1,X0),X0))
| ~ is_a_theorem(implies(implies(X0,X1),X1)) ),
inference(resolution,[status(thm)],[f8,f11]) ).
fof(f35,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(not(X0),not(X1))) ),
inference(resolution,[status(thm)],[f12,f8]) ).
fof(f46,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(implies(not(X1),not(X0)),X2))),
inference(resolution,[status(thm)],[f16,f12]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(implies(X0,X1),X2),implies(X1,X2))) ),
inference(resolution,[status(thm)],[f16,f24]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f50,f8]) ).
fof(f57,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(not(X0),implies(X0,X1))) ),
inference(resolution,[status(thm)],[f55,f12]) ).
fof(f58,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,implies(implies(X0,X1),X1))) ),
inference(resolution,[status(thm)],[f55,f11]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(implies(X0,X1),X2),implies(not(X0),X2))) ),
inference(resolution,[status(thm)],[f57,f16]) ).
fof(f68,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,implies(X1,X0)),X2),X2)),
inference(resolution,[status(thm)],[f33,f15]) ).
fof(f71,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(X0,X1),X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f58,f8]) ).
fof(f137,plain,
! [X0] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,X0)) ),
inference(resolution,[status(thm)],[f68,f55]) ).
fof(f148,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(implies(X0,X0),X1),X1)) ),
inference(resolution,[status(thm)],[f137,f71]) ).
fof(f192,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(not(X1),not(X0)),X2))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f46,f8]) ).
fof(f563,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(not(X0),X2))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f64,f8]) ).
fof(f1285,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(not(X0),not(implies(X1,X1))),X0)) ),
inference(resolution,[status(thm)],[f192,f148]) ).
fof(f1891,plain,
! [X0] :
( ~ sQ1_spl
| is_a_theorem(implies(not(not(X0)),X0)) ),
inference(resolution,[status(thm)],[f563,f1285]) ).
fof(f1925,plain,
! [X0] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,not(not(X0)))) ),
inference(resolution,[status(thm)],[f1891,f35]) ).
fof(f1927,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(X0,X1),implies(not(not(X0)),X1))) ),
inference(resolution,[status(thm)],[f1891,f16]) ).
fof(f1975,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,not(not(implies(X1,X0))))) ),
inference(resolution,[status(thm)],[f1925,f55]) ).
fof(f3143,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(not(not(X0)),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f1927,f8]) ).
fof(f4264,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(not(not(X0)),not(not(implies(X1,X0))))) ),
inference(resolution,[status(thm)],[f3143,f1975]) ).
fof(f11142,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(not(implies(X0,X1)),not(X1))) ),
inference(resolution,[status(thm)],[f4264,f35]) ).
fof(f11206,plain,
( ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f13,f11142]) ).
fof(f11238,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f11206]) ).
fof(f11239,plain,
$false,
inference(sat_refutation,[status(thm)],[f26,f30,f11238]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL115-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.32 % Computer : n005.cluster.edu
% 0.08/0.32 % Model : x86_64 x86_64
% 0.08/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.32 % Memory : 8046.5625MB
% 0.08/0.32 % OS : Linux 6.8.0-71-generic
% 0.08/0.32 % CPULimit : 300
% 0.08/0.32 % WCLimit : 300
% 0.08/0.32 % DateTime : Mon Sep 21 00:05:48 UTC 2026
% 0.08/0.32 % CPUTime :
% 0.08/0.33 % Drodi V4.1.1
% 1.58/0.72 % Refutation found
% 1.58/0.72 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.58/0.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.33/0.75 % Elapsed time: 0.408739 seconds
% 1.33/0.75 % CPU time: 2.973329 seconds
% 1.33/0.75 % Total memory used: 100.719 MB
% 1.33/0.75 % Net memory used: 90.625 MB
%------------------------------------------------------------------------------