%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL050-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 01:06:40 PM UTC 2026
% Result : Unsatisfiable 7.10s 6.36s
% Output : CNFRefutation 7.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 5
% Syntax : Number of formulae : 57 ( 33 unt; 0 def)
% Number of atoms : 87 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 63 ( 33 ~; 30 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 133 ( 133 !; 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] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : is_a_theorem(implies(implies(not(X),X),X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : is_a_theorem(implies(X,implies(not(X),Y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
~ is_a_theorem(implies(implies(a,implies(b,c)),implies(b,implies(a,c)))),
file('/export/starexec/sandbox/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(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f9,plain,
! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f10,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f11,plain,
~ is_a_theorem(implies(implies(a,implies(b,c)),implies(b,implies(a,c)))),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f12,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X1,X2),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f8,f7]) ).
fof(f13,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)],[f12,f8]) ).
fof(f15,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)],[f13,f7]) ).
fof(f16,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(implies(X3,X1),implies(X0,implies(X3,X2))))),
inference(resolution,[status(thm)],[f15,f13]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(implies(X3,X1),implies(X0,implies(X3,X2))))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f16,f7]) ).
fof(f31,plain,
~ is_a_theorem(implies(b,implies(implies(b,c),c))),
inference(resolution,[status(thm)],[f23,f11]) ).
fof(f59,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(not(X0),X0),X1))),
inference(resolution,[status(thm)],[f9,f12]) ).
fof(f63,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(not(X0),X1),X2),implies(X0,X2))),
inference(resolution,[status(thm)],[f10,f12]) ).
fof(f64,plain,
! [X0,X1] :
( is_a_theorem(implies(not(X0),X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f10,f7]) ).
fof(f67,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X1,X2),implies(not(X0),X2)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f64,f12]) ).
fof(f78,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(implies(not(X0),X0),X1),X2),implies(implies(X0,X1),X2))),
inference(resolution,[status(thm)],[f59,f12]) ).
fof(f79,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X0),X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f59,f7]) ).
fof(f80,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,not(X1)),implies(X1,implies(X0,X2)))),
inference(resolution,[status(thm)],[f63,f15]) ).
fof(f82,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(implies(not(X0),X1),X2)) ),
inference(resolution,[status(thm)],[f63,f7]) ).
fof(f87,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(not(X0),X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f79,f7]) ).
fof(f91,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(resolution,[status(thm)],[f82,f9]) ).
fof(f92,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(not(X0),X2)))),
inference(resolution,[status(thm)],[f82,f80]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ~ is_a_theorem(X1)
| is_a_theorem(implies(X0,implies(not(X1),X2))) ),
inference(resolution,[status(thm)],[f82,f67]) ).
fof(f192,plain,
! [X0,X1] : is_a_theorem(implies(not(implies(X0,X0)),X1)),
inference(resolution,[status(thm)],[f64,f91]) ).
fof(f204,plain,
! [X0,X1] : is_a_theorem(implies(not(implies(implies(not(X0),X0),X0)),X1)),
inference(resolution,[status(thm)],[f9,f64]) ).
fof(f240,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(implies(not(X0),X0),X0),X1)) ),
inference(resolution,[status(thm)],[f87,f204]) ).
fof(f244,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X0,X0),X1)) ),
inference(resolution,[status(thm)],[f87,f192]) ).
fof(f250,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(not(implies(X1,X1)),X2))),
inference(resolution,[status(thm)],[f244,f92]) ).
fof(f262,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)],[f12,f7]) ).
fof(f374,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(not(X1),X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f240,f12]) ).
fof(f477,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(X0,implies(X1,X3)))
| ~ is_a_theorem(implies(X0,implies(implies(not(X1),X2),X3))) ),
inference(resolution,[status(thm)],[f63,f262]) ).
fof(f532,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(not(X1),X0))
| is_a_theorem(implies(implies(X0,X1),X1)) ),
inference(resolution,[status(thm)],[f374,f12]) ).
fof(f542,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X1))),
inference(resolution,[status(thm)],[f374,f250]) ).
fof(f543,plain,
! [X0,X1] :
( ~ is_a_theorem(X1)
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f374,f95]) ).
fof(f587,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(X2,X2)))),
inference(resolution,[status(thm)],[f543,f542]) ).
fof(f649,plain,
! [X0,X1,X2] :
( is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(X0,implies(X1,X1)),X2)) ),
inference(resolution,[status(thm)],[f587,f87]) ).
fof(f707,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,X0),X1),implies(X2,X1))),
inference(resolution,[status(thm)],[f649,f8]) ).
fof(f760,plain,
! [X0,X1] : is_a_theorem(implies(implies(implies(X0,X0),X1),X1)),
inference(resolution,[status(thm)],[f707,f374]) ).
fof(f771,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(X0,implies(implies(X1,X1),X2))) ),
inference(resolution,[status(thm)],[f760,f262]) ).
fof(f938,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[f532,f7]) ).
fof(f2689,plain,
! [X0,X1] : is_a_theorem(implies(implies(implies(implies(not(X0),X0),X0),X1),X1)),
inference(resolution,[status(thm)],[f771,f78]) ).
fof(f2817,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,implies(not(X1),X1)),implies(X0,X1))),
inference(resolution,[status(thm)],[f2689,f15]) ).
fof(f3115,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X0),X1),implies(implies(X1,X0),X0))),
inference(resolution,[status(thm)],[f2817,f15]) ).
fof(f3613,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(implies(X1,X0),X0))),
inference(resolution,[status(thm)],[f3115,f82]) ).
fof(f3643,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(resolution,[status(thm)],[f3613,f477]) ).
fof(f3675,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(X2,X1)))),
inference(resolution,[status(thm)],[f3643,f543]) ).
fof(f3788,plain,
! [X0,X1,X2] :
( is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(X0,implies(X1,X0)),X2)) ),
inference(resolution,[status(thm)],[f3675,f938]) ).
fof(f4473,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(X1,X2))),
inference(resolution,[status(thm)],[f3788,f8]) ).
fof(f4803,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f4473,f7]) ).
fof(f4861,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(implies(X0,X1),X1))),
inference(resolution,[status(thm)],[f4803,f3115]) ).
fof(f4929,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f31,f4861]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL050-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n009.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Mon Sep 21 00:02:18 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.39 % Drodi V4.1.1
% 7.10/6.36 % Refutation found
% 7.10/6.36 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 7.10/6.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.10/6.39 % Elapsed time: 0.993640 seconds
% 7.10/6.39 % CPU time: 7.681104 seconds
% 7.10/6.39 % Total memory used: 158.508 MB
% 7.10/6.39 % Net memory used: 141.596 MB
%------------------------------------------------------------------------------