%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL077-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 01:06:44 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.44s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 44 ( 16 unt; 2 def)
% Number of atoms : 79 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 73 ( 38 ~; 33 |; 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 : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 82 ( 82 !; 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,Z] : is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
~ is_a_theorem(implies(not(not(a)),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,X2] : is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(implies(X0,X1),implies(X0,X2)))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f10,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f11,plain,
~ is_a_theorem(implies(not(not(a)),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)],[f7,f8]) ).
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,X2] :
( is_a_theorem(implies(implies(X0,X1),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f9,f7]) ).
fof(f16,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X1,implies(X2,X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f13,f7]) ).
fof(f17,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(X0,implies(X1,implies(X2,implies(X3,X2))))),
inference(resolution,[status(thm)],[f13,f12]) ).
fof(f18,definition,
! [X0] :
( sQ0_spl
<=> ~ is_a_theorem(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f19,plain,
! [X0] :
( ~ sQ0_spl
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f18]) ).
fof(f21,definition,
! [X1,X2] :
( sQ1_spl
<=> is_a_theorem(implies(X1,implies(X2,X1))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f22,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(component_clause,[status(thm)],[f21]) ).
fof(f24,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f16,f18,f21]) ).
fof(f25,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f9,f19]) ).
fof(f28,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f25]) ).
fof(f29,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(implies(not(X1),not(X2)),implies(X2,X1)))),
inference(resolution,[status(thm)],[f12,f10]) ).
fof(f45,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,implies(X1,X2)),implies(X0,X1)),implies(implies(X0,implies(X1,X2)),implies(X0,X2)))),
inference(resolution,[status(thm)],[f14,f9]) ).
fof(f48,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(X0,X1),implies(X0,X0))) ),
inference(resolution,[status(thm)],[f14,f22]) ).
fof(f50,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f48,f7]) ).
fof(f55,plain,
! [X0] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,X0)) ),
inference(resolution,[status(thm)],[f50,f17]) ).
fof(f59,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(implies(X0,X1),X0),implies(implies(X0,X1),X1))) ),
inference(resolution,[status(thm)],[f55,f14]) ).
fof(f61,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,implies(X1,X1))) ),
inference(resolution,[status(thm)],[f55,f12]) ).
fof(f86,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,implies(not(X1),not(X2))),implies(X0,implies(X2,X1)))),
inference(resolution,[status(thm)],[f29,f14]) ).
fof(f176,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X0,X2)))
| ~ is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X0,X1))) ),
inference(resolution,[status(thm)],[f45,f7]) ).
fof(f182,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(X0,X1),X1))
| ~ is_a_theorem(implies(implies(X0,X1),X0)) ),
inference(resolution,[status(thm)],[f59,f7]) ).
fof(f240,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X0,implies(X2,X1)))
| ~ is_a_theorem(implies(X0,implies(not(X1),not(X2)))) ),
inference(resolution,[status(thm)],[f86,f7]) ).
fof(f330,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(implies(X0,implies(X1,X0)),X2),X2)) ),
inference(resolution,[status(thm)],[f182,f13]) ).
fof(f387,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(X0,implies(X1,X0)),X2)) ),
inference(resolution,[status(thm)],[f330,f7]) ).
fof(f419,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(resolution,[status(thm)],[f176,f61]) ).
fof(f475,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(not(X0),implies(X0,X1))) ),
inference(resolution,[status(thm)],[f387,f86]) ).
fof(f604,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(X0,X1))) ),
inference(resolution,[status(thm)],[f419,f7]) ).
fof(f1512,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(not(not(X0)),implies(X1,X0))) ),
inference(resolution,[status(thm)],[f240,f475]) ).
fof(f1531,plain,
! [X0] :
( ~ sQ1_spl
| is_a_theorem(implies(not(not(X0)),X0)) ),
inference(resolution,[status(thm)],[f1512,f604]) ).
fof(f1538,plain,
( ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f11,f1531]) ).
fof(f1548,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f1538]) ).
fof(f1549,plain,
$false,
inference(sat_refutation,[status(thm)],[f24,f28,f1548]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL077-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 00:06:22 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.15/0.44 % Refutation found
% 0.15/0.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.48 % Elapsed time: 0.094967 seconds
% 0.15/0.48 % CPU time: 0.510731 seconds
% 0.15/0.48 % Total memory used: 61.388 MB
% 0.15/0.48 % Net memory used: 60.181 MB
%------------------------------------------------------------------------------