%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL080-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 32.47s 4.49s
% Output : CNFRefutation 32.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 18 unt; 2 def)
% Number of atoms : 72 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 65 ( 36 ~; 27 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 4 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/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : is_a_theorem(implies(X,implies(Y,X))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : is_a_theorem(implies(implies(implies(X,Y),X),X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
~ is_a_theorem(implies(implies(implies(a,b),c),implies(implies(c,a),implies(e,a)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f7,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f8,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f9,plain,
! [X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),X0),X0)),
inference(cnf_transformation,[status(thm)],[f3]) ).
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)],[f4]) ).
fof(f11,plain,
~ is_a_theorem(implies(implies(implies(a,b),c),implies(implies(c,a),implies(e,a)))),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f12,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f8,f7]) ).
fof(f13,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(X2,X1)))),
inference(resolution,[status(thm)],[f12,f8]) ).
fof(f14,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(implies(implies(X0,X1),X0)) ),
inference(resolution,[status(thm)],[f9,f7]) ).
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,f7]) ).
fof(f18,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(implies(X0,X2),X0),X1))),
inference(resolution,[status(thm)],[f16,f9]) ).
fof(f19,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(implies(implies(X0,X1),implies(X2,X1)),X3),implies(implies(X2,X0),X3))),
inference(resolution,[status(thm)],[f16,f10]) ).
fof(f20,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(X1,X2))),
inference(resolution,[status(thm)],[f16,f8]) ).
fof(f23,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X1,implies(X2,X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f13,f7]) ).
fof(f25,definition,
! [X0] :
( sQ0_spl
<=> ~ is_a_theorem(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f26,plain,
! [X0] :
( ~ sQ0_spl
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f25]) ).
fof(f28,definition,
! [X1,X2] :
( sQ1_spl
<=> is_a_theorem(implies(X1,implies(X2,X1))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f29,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(component_clause,[status(thm)],[f28]) ).
fof(f31,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f23,f25,f28]) ).
fof(f32,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f9,f26]) ).
fof(f36,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f32]) ).
fof(f53,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(X0,X1))) ),
inference(resolution,[status(thm)],[f16,f14]) ).
fof(f54,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f16,f7]) ).
fof(f69,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f20,f7]) ).
fof(f70,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(implies(X0,X2),X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f18,f7]) ).
fof(f72,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(implies(X2,X0),X3))
| ~ is_a_theorem(implies(implies(implies(X0,X1),implies(X2,X1)),X3)) ),
inference(resolution,[status(thm)],[f19,f7]) ).
fof(f74,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X1),X0))
| is_a_theorem(implies(implies(X0,X1),X1)) ),
inference(resolution,[status(thm)],[f53,f16]) ).
fof(f83,plain,
! [X0] :
( ~ is_a_theorem(implies(X0,implies(implies(c,a),implies(e,a))))
| ~ is_a_theorem(implies(implies(implies(a,b),c),X0)) ),
inference(resolution,[status(thm)],[f54,f11]) ).
fof(f152,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,implies(X1,implies(X2,X0)))) ),
inference(resolution,[status(thm)],[f69,f29]) ).
fof(f161,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(implies(X0,X1),X0),X2))
| ~ is_a_theorem(implies(X0,implies(implies(implies(X0,X1),X0),X2))) ),
inference(resolution,[status(thm)],[f70,f53]) ).
fof(f169,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(X0,X1),implies(implies(implies(X0,X2),X3),implies(implies(X1,X2),X3)))),
inference(resolution,[status(thm)],[f72,f10]) ).
fof(f195,plain,
! [X0] :
( ~ is_a_theorem(implies(implies(implies(a,b),c),implies(X0,implies(implies(c,a),implies(e,a)))))
| ~ is_a_theorem(implies(implies(X0,implies(implies(c,a),implies(e,a))),X0)) ),
inference(resolution,[status(thm)],[f74,f83]) ).
fof(f604,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(implies(X0,X1),X0),implies(X2,X0))) ),
inference(resolution,[status(thm)],[f161,f152]) ).
fof(f845,plain,
~ is_a_theorem(implies(implies(implies(implies(implies(a,b),a),implies(e,a)),implies(implies(c,a),implies(e,a))),implies(implies(implies(a,b),a),implies(e,a)))),
inference(resolution,[status(thm)],[f195,f169]) ).
fof(f10854,plain,
~ is_a_theorem(implies(implies(implies(a,b),a),implies(e,a))),
inference(resolution,[status(thm)],[f845,f12]) ).
fof(f10855,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10854,f604]) ).
fof(f10856,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f10855]) ).
fof(f10857,plain,
$false,
inference(sat_refutation,[status(thm)],[f31,f36,f10856]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL080-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Mon Sep 21 00:03:22 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.31 % Drodi V4.1.1
% 32.47/4.49 % Refutation found
% 32.47/4.49 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 32.47/4.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 32.47/4.54 % Elapsed time: 4.228533 seconds
% 32.47/4.54 % CPU time: 33.278586 seconds
% 32.47/4.54 % Total memory used: 314.348 MB
% 32.47/4.54 % Net memory used: 272.499 MB
%------------------------------------------------------------------------------