%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL075-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 10.65s 2.01s
% Output : CNFRefutation 10.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 11 unt; 2 def)
% Number of atoms : 55 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 51 ( 27 ~; 22 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 7 ( 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 : 71 ( 71 !; 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,Z,U,V] : is_a_theorem(implies(implies(implies(implies(implies(X,Y),implies(not(Z),not(U))),Z),V),implies(implies(V,X),implies(U,X)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
~ is_a_theorem(implies(a,implies(not(a),b))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f5,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f6,plain,
! [X0,X1,X2,X3,X4] : is_a_theorem(implies(implies(implies(implies(implies(X0,X1),implies(not(X2),not(X3))),X2),X4),implies(implies(X4,X0),implies(X3,X0)))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
~ is_a_theorem(implies(a,implies(not(a),b))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f8,plain,
! [X0,X1,X2,X3,X4] :
( is_a_theorem(implies(implies(X4,X0),implies(X3,X0)))
| ~ is_a_theorem(implies(implies(implies(implies(X0,X1),implies(not(X2),not(X3))),X2),X4)) ),
inference(resolution,[status(thm)],[f6,f5]) ).
fof(f9,plain,
! [X0,X1,X2,X3,X4] : is_a_theorem(implies(implies(implies(implies(X0,X1),implies(X2,X1)),implies(X1,X3)),implies(X4,implies(X1,X3)))),
inference(resolution,[status(thm)],[f8,f6]) ).
fof(f10,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(implies(X0,implies(not(X1),X2)),X3),implies(X1,X3))),
inference(resolution,[status(thm)],[f9,f8]) ).
fof(f11,plain,
! [X0,X1,X2,X3,X4] :
( is_a_theorem(implies(X4,implies(X1,X3)))
| ~ is_a_theorem(implies(implies(implies(X0,X1),implies(X2,X1)),implies(X1,X3))) ),
inference(resolution,[status(thm)],[f9,f5]) ).
fof(f12,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,X0),X1),implies(X2,X1))),
inference(resolution,[status(thm)],[f10,f8]) ).
fof(f15,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(implies(X0,X0),X1)) ),
inference(resolution,[status(thm)],[f12,f5]) ).
fof(f17,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(X2,X1)))),
inference(resolution,[status(thm)],[f11,f12]) ).
fof(f20,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X1,implies(X2,X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f17,f5]) ).
fof(f21,definition,
! [X0] :
( sQ0_spl
<=> ~ is_a_theorem(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f22,plain,
! [X0] :
( ~ sQ0_spl
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f21]) ).
fof(f24,definition,
! [X1,X2] :
( sQ1_spl
<=> is_a_theorem(implies(X1,implies(X2,X1))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f25,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(component_clause,[status(thm)],[f24]) ).
fof(f27,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f20,f21,f24]) ).
fof(f28,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f6,f22]) ).
fof(f33,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f28]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,implies(X1,implies(X2,X2)))) ),
inference(resolution,[status(thm)],[f15,f25]) ).
fof(f74,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(implies(X0,implies(X1,X1)),X2),implies(X3,X2))) ),
inference(resolution,[status(thm)],[f8,f40]) ).
fof(f106,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(implies(X0,X1),X2),implies(X1,X2))) ),
inference(resolution,[status(thm)],[f74,f8]) ).
fof(f113,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(implies(implies(not(X0),not(X1)),X0),X2),implies(X1,X2))) ),
inference(resolution,[status(thm)],[f106,f8]) ).
fof(f4979,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(implies(not(X0),not(X1)),X0),X2)) ),
inference(resolution,[status(thm)],[f113,f5]) ).
fof(f9727,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,implies(not(X0),X1))) ),
inference(resolution,[status(thm)],[f4979,f106]) ).
fof(f9851,plain,
( ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f7,f9727]) ).
fof(f9891,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f9851]) ).
fof(f9892,plain,
$false,
inference(sat_refutation,[status(thm)],[f27,f33,f9891]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL075-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n008.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Mon Sep 21 00:03:54 UTC 2026
% 0.16/0.45 % CPUTime :
% 0.16/0.46 % Drodi V4.1.1
% 10.65/2.01 % Refutation found
% 10.65/2.01 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 10.65/2.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 10.65/2.06 % Elapsed time: 1.597152 seconds
% 10.65/2.06 % CPU time: 12.179456 seconds
% 10.65/2.06 % Total memory used: 175.058 MB
% 10.65/2.06 % Net memory used: 163.877 MB
%------------------------------------------------------------------------------