%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL072-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 4.64s 1.10s
% Output : CNFRefutation 4.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 16 unt; 2 def)
% Number of atoms : 110 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 125 ( 64 ~; 59 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 6 ( 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 : 113 ( 113 !; 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] : is_a_theorem(implies(implies(implies(X,Y),Z),implies(Y,Z))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : is_a_theorem(implies(implies(implies(X,Y),Z),implies(not(X),Z))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z,U] : is_a_theorem(implies(implies(X,implies(not(Y),Z)),implies(X,implies(implies(U,Z),implies(implies(Y,U),Z))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
~ is_a_theorem(implies(a,implies(not(a),b))),
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,X2] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(X1,X2))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f9,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(not(X0),X2))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f10,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(X0,implies(not(X1),X2)),implies(X0,implies(implies(X3,X2),implies(implies(X1,X3),X2))))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f11,plain,
~ is_a_theorem(implies(a,implies(not(a),b))),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f12,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f8,f7]) ).
fof(f13,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(resolution,[status(thm)],[f12,f8]) ).
fof(f14,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(X2,X0)))),
inference(resolution,[status(thm)],[f13,f12]) ).
fof(f17,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(not(X0),X2))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f9,f7]) ).
fof(f24,definition,
! [X1] :
( sQ1_spl
<=> ~ is_a_theorem(X1) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f25,plain,
! [X0] :
( ~ sQ1_spl
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f24]) ).
fof(f29,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(not(X0),X1),implies(X2,implies(implies(X3,X1),implies(implies(X0,X3),X1))))),
inference(resolution,[status(thm)],[f10,f12]) ).
fof(f30,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(X0,implies(implies(X3,X2),implies(implies(X1,X3),X2))))
| ~ is_a_theorem(implies(X0,implies(not(X1),X2))) ),
inference(resolution,[status(thm)],[f10,f7]) ).
fof(f33,plain,
! [X0,X1,X2] : is_a_theorem(implies(not(implies(X0,X1)),implies(not(X0),X2))),
inference(resolution,[status(thm)],[f17,f9]) ).
fof(f34,plain,
! [X0,X1,X2] : is_a_theorem(implies(not(implies(X0,X1)),implies(X1,X2))),
inference(resolution,[status(thm)],[f17,f8]) ).
fof(f47,plain,
( ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f9,f25]) ).
fof(f52,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f47]) ).
fof(f67,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(implies(X3,X2),implies(implies(X1,X3),X2)))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,implies(not(X1),X2))) ),
inference(resolution,[status(thm)],[f30,f7]) ).
fof(f116,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(X2,implies(implies(X3,X1),implies(implies(X0,X3),X1))))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[f29,f7]) ).
fof(f121,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(implies(X1,X3),X2))
| ~ is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,implies(not(X1),X2))) ),
inference(resolution,[status(thm)],[f67,f7]) ).
fof(f176,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(implies(X3,X1),implies(implies(X0,X3),X1)))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[f116,f7]) ).
fof(f177,definition,
! [X0,X1,X3] :
( sQ12_spl
<=> ( is_a_theorem(implies(implies(X3,X1),implies(implies(X0,X3),X1)))
| ~ is_a_theorem(implies(not(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f178,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| is_a_theorem(implies(implies(X2,X1),implies(implies(X0,X2),X1)))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(component_clause,[status(thm)],[f177]) ).
fof(f180,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f176,f177,f24]) ).
fof(f183,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| is_a_theorem(implies(implies(X0,X2),X1))
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[f178,f7]) ).
fof(f252,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(implies(X0,X3),X2))
| ~ is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f121,f9]) ).
fof(f511,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[f183,f7]) ).
fof(f514,plain,
! [X0,X1,X2,X3] :
( ~ sQ12_spl
| is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X3,X1),X0))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f511,f34]) ).
fof(f588,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X0,X1),implies(X1,X2))) ),
inference(resolution,[status(thm)],[f514,f8]) ).
fof(f635,plain,
! [X0] :
( ~ sQ12_spl
| is_a_theorem(implies(X0,X0)) ),
inference(resolution,[status(thm)],[f588,f8]) ).
fof(f660,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| is_a_theorem(implies(implies(X1,X0),implies(X1,X2)))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f635,f252]) ).
fof(f662,plain,
! [X0,X1] :
( ~ sQ12_spl
| is_a_theorem(implies(not(X0),implies(X0,X1))) ),
inference(resolution,[status(thm)],[f635,f17]) ).
fof(f674,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f662,f511]) ).
fof(f880,plain,
! [X0,X1] :
( ~ sQ12_spl
| is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(X0,X1))) ),
inference(resolution,[status(thm)],[f660,f588]) ).
fof(f894,plain,
! [X0] :
( ~ sQ12_spl
| ~ is_a_theorem(implies(not(X0),X0))
| is_a_theorem(implies(implies(X0,X0),X0)) ),
inference(resolution,[status(thm)],[f880,f178]) ).
fof(f955,plain,
! [X0] :
( ~ sQ12_spl
| is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X0))
| ~ is_a_theorem(implies(not(X0),X0)) ),
inference(resolution,[status(thm)],[f894,f7]) ).
fof(f957,plain,
! [X0] :
( ~ sQ12_spl
| is_a_theorem(X0)
| ~ is_a_theorem(implies(not(X0),X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f955,f635]) ).
fof(f1008,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| is_a_theorem(implies(X0,implies(X2,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f674,f14]) ).
fof(f1027,plain,
! [X0,X1] :
( ~ sQ12_spl
| is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(not(implies(X0,X1)),X1)) ),
inference(resolution,[status(thm)],[f1008,f957]) ).
fof(f1237,plain,
! [X0,X1] :
( ~ sQ12_spl
| is_a_theorem(implies(X0,implies(not(X0),X1))) ),
inference(resolution,[status(thm)],[f1027,f33]) ).
fof(f1254,plain,
( ~ sQ12_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f11,f1237]) ).
fof(f1271,plain,
~ sQ12_spl,
inference(contradiction_clause,[status(thm)],[f1254]) ).
fof(f1272,plain,
$false,
inference(sat_refutation,[status(thm)],[f52,f180,f1271]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL072-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n015.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Mon Sep 21 00:06:35 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 4.64/1.10 % Refutation found
% 4.64/1.10 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 4.64/1.10 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.64/1.13 % Elapsed time: 0.743723 seconds
% 4.64/1.13 % CPU time: 5.609430 seconds
% 4.64/1.13 % Total memory used: 108.578 MB
% 4.64/1.13 % Net memory used: 98.062 MB
%------------------------------------------------------------------------------