%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL068-1 : TPTP v9.3.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 01:06:43 PM UTC 2026
% Result : Unsatisfiable 51.83s 7.13s
% Output : CNFRefutation 18.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 7
% Syntax : Number of formulae : 73 ( 31 unt; 2 def)
% Number of atoms : 124 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 105 ( 54 ~; 49 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 6 ( 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 : 173 ( 173 !; 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,Z,Y] : is_a_theorem(implies(implies(not(X),Z),implies(implies(Y,Z),implies(implies(X,Y),Z)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
~ is_a_theorem(implies(implies(not(a),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,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] : is_a_theorem(implies(implies(not(X0),X1),implies(implies(X2,X1),implies(implies(X0,X2),X1)))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f11,plain,
~ is_a_theorem(implies(implies(not(a),a),a)),
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,X2] :
( is_a_theorem(implies(not(X0),X2))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f9,f7]) ).
fof(f15,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(resolution,[status(thm)],[f12,f8]) ).
fof(f16,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(X2,X0)))),
inference(resolution,[status(thm)],[f15,f12]) ).
fof(f17,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f15,f7]) ).
fof(f20,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(X2,X1)))),
inference(resolution,[status(thm)],[f17,f15]) ).
fof(f22,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X2,X1),implies(implies(X0,X2),X1)))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[f10,f7]) ).
fof(f24,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(X0,implies(X1,implies(X2,implies(X3,X0))))),
inference(resolution,[status(thm)],[f16,f12]) ).
fof(f28,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X1,implies(X2,X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f20,f7]) ).
fof(f30,definition,
! [X0] :
( sQ0_spl
<=> ~ is_a_theorem(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f31,plain,
! [X0] :
( ~ sQ0_spl
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f30]) ).
fof(f33,definition,
! [X1,X2] :
( sQ1_spl
<=> is_a_theorem(implies(X1,implies(X2,X1))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f34,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(component_clause,[status(thm)],[f33]) ).
fof(f36,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f28,f30,f33]) ).
fof(f37,plain,
! [X0,X1,X2] : is_a_theorem(implies(not(not(X0)),implies(implies(X1,X2),implies(implies(X0,X1),X2)))),
inference(resolution,[status(thm)],[f13,f10]) ).
fof(f39,plain,
! [X0,X1,X2] : is_a_theorem(implies(not(implies(X0,X1)),implies(X1,X2))),
inference(resolution,[status(thm)],[f13,f8]) ).
fof(f42,plain,
! [X0,X1,X2] : is_a_theorem(implies(not(X0),implies(X1,implies(X0,X2)))),
inference(resolution,[status(thm)],[f13,f15]) ).
fof(f43,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f10,f31]) ).
fof(f49,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f43]) ).
fof(f101,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(implies(implies(X3,X1),X0),implies(X1,X2)))),
inference(resolution,[status(thm)],[f22,f39]) ).
fof(f102,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(X0,implies(X1,implies(X2,X3))),implies(implies(X2,X0),implies(X1,implies(X2,X3))))),
inference(resolution,[status(thm)],[f22,f42]) ).
fof(f240,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(implies(implies(X3,X1),X0),implies(X1,X2)))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f101,f7]) ).
fof(f393,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(implies(X2,X0),implies(X1,implies(X2,X3))))
| ~ is_a_theorem(implies(X0,implies(X1,implies(X2,X3)))) ),
inference(resolution,[status(thm)],[f102,f7]) ).
fof(f444,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(implies(X0,X1),implies(implies(X2,X1),X3)),implies(X1,X3))),
inference(resolution,[status(thm)],[f240,f8]) ).
fof(f458,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(implies(X0,X1),not(X2)),implies(X1,implies(X2,X3)))),
inference(resolution,[status(thm)],[f240,f42]) ).
fof(f754,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(X1,X3))
| ~ is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),X3))) ),
inference(resolution,[status(thm)],[f444,f7]) ).
fof(f914,plain,
! [X0,X1] : is_a_theorem(implies(not(X0),implies(X0,X1))),
inference(resolution,[status(thm)],[f754,f458]) ).
fof(f918,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(resolution,[status(thm)],[f754,f8]) ).
fof(f959,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,X1),implies(X1,X2)),implies(X1,X2))),
inference(resolution,[status(thm)],[f918,f240]) ).
fof(f1220,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X0,X1),implies(X1,X2))) ),
inference(resolution,[status(thm)],[f959,f7]) ).
fof(f2105,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,not(X1)),implies(X1,implies(X0,X2)))),
inference(resolution,[status(thm)],[f393,f914]) ).
fof(f2163,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(X0,X1),implies(X2,implies(X0,implies(X3,X1))))),
inference(resolution,[status(thm)],[f393,f24]) ).
fof(f2168,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X2,implies(X0,X1)))) ),
inference(resolution,[status(thm)],[f393,f34]) ).
fof(f2180,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X1,implies(X0,X2)))
| ~ is_a_theorem(implies(X0,not(X1))) ),
inference(resolution,[status(thm)],[f2105,f7]) ).
fof(f2189,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))),
inference(resolution,[status(thm)],[f2180,f918]) ).
fof(f2200,plain,
! [X0,X1] :
( is_a_theorem(implies(not(X0),X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f2189,f7]) ).
fof(f2345,plain,
! [X0,X1] : is_a_theorem(implies(not(implies(X0,X0)),X1)),
inference(resolution,[status(thm)],[f2200,f918]) ).
fof(f2346,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(implies(X2,X2),X0),X1))),
inference(resolution,[status(thm)],[f2345,f22]) ).
fof(f4625,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(X2,implies(X0,X1)))
| ~ is_a_theorem(implies(X0,implies(X0,X1))) ),
inference(resolution,[status(thm)],[f2168,f7]) ).
fof(f4718,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(implies(X2,X2),X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f2346,f7]) ).
fof(f6335,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,implies(implies(X1,implies(X1,X2)),implies(X1,X2)))) ),
inference(resolution,[status(thm)],[f4625,f2168]) ).
fof(f6524,plain,
! [X0,X1] : is_a_theorem(implies(implies(implies(X0,X0),X1),X1)),
inference(resolution,[status(thm)],[f4718,f918]) ).
fof(f6561,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X0,X0),X1)) ),
inference(resolution,[status(thm)],[f6524,f7]) ).
fof(f7474,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(resolution,[status(thm)],[f6335,f1220]) ).
fof(f7516,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(X0,X1))) ),
inference(resolution,[status(thm)],[f7474,f7]) ).
fof(f7581,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(X0,X1),implies(X0,implies(X2,X1)))) ),
inference(resolution,[status(thm)],[f7516,f2163]) ).
fof(f9547,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2)))) ),
inference(resolution,[status(thm)],[f393,f7581]) ).
fof(f9620,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,implies(implies(X0,X1),X1))) ),
inference(resolution,[status(thm)],[f9547,f6561]) ).
fof(f9634,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(X1,implies(X0,X2)))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f9547,f7]) ).
fof(f9667,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(X0,X1),X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f9620,f7]) ).
fof(f12058,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,implies(implies(X1,implies(X0,X2)),implies(X1,X2)))) ),
inference(resolution,[status(thm)],[f9634,f9547]) ).
fof(f16805,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(X0,implies(implies(X1,X1),X2)),implies(X0,X2))) ),
inference(resolution,[status(thm)],[f12058,f6561]) ).
fof(f32955,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(X0,implies(implies(X1,X1),X2))) ),
inference(resolution,[status(thm)],[f16805,f7]) ).
fof(f41812,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(not(not(X0)),implies(implies(X0,X1),X1))) ),
inference(resolution,[status(thm)],[f32955,f37]) ).
fof(f41867,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(not(X0),X1),implies(implies(X0,X1),X1))) ),
inference(resolution,[status(thm)],[f32955,f10]) ).
fof(f42066,plain,
! [X0] :
( ~ sQ1_spl
| is_a_theorem(implies(not(not(X0)),X0)) ),
inference(resolution,[status(thm)],[f41812,f32955]) ).
fof(f42314,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(implies(not(not(X0)),X0),X1),X1)) ),
inference(resolution,[status(thm)],[f42066,f9667]) ).
fof(f43601,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(not(not(X0)),X0),X1)) ),
inference(resolution,[status(thm)],[f42314,f7]) ).
fof(f48441,plain,
! [X0] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(not(X0),X0),X0)) ),
inference(resolution,[status(thm)],[f41867,f43601]) ).
fof(f48541,plain,
( ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f11,f48441]) ).
fof(f48636,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f48541]) ).
fof(f48637,plain,
$false,
inference(sat_refutation,[status(thm)],[f36,f49,f48636]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL068-1 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n002.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 00:05:33 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.47 % Drodi V4.1.1
% 51.83/7.13 % Refutation found
% 51.83/7.13 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 51.83/7.13 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 18.10/7.20 % Elapsed time: 6.734340 seconds
% 18.10/7.20 % CPU time: 52.736307 seconds
% 18.10/7.20 % Total memory used: 350.042 MB
% 18.10/7.20 % Net memory used: 292.936 MB
%------------------------------------------------------------------------------