%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL416-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 01:07:39 PM UTC 2026
% Result : Unsatisfiable 10.44s 1.97s
% Output : CNFRefutation 10.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 6 unt; 0 def)
% Number of atoms : 92 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 126 ( 65 ~; 61 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 93 ( 93 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( is_a_theorem(B)
| ~ is_a_theorem(A)
| ~ is_a_theorem(equivalent(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] : is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(A,B),equivalent(C,B)),C))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
~ is_a_theorem(equivalent(a,a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [B] :
( is_a_theorem(B)
| ! [A] :
( ~ is_a_theorem(A)
| ~ is_a_theorem(equivalent(A,B)) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f5,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f6,plain,
! [X0,X1,X2] : is_a_theorem(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
~ is_a_theorem(equivalent(a,a)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f8,plain,
! [X0,X1,X2] :
( is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f6,f5]) ).
fof(f9,plain,
! [X0,X1,X2] :
( is_a_theorem(X2)
| ~ is_a_theorem(equivalent(equivalent(X0,X1),equivalent(X2,X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f8,f5]) ).
fof(f10,plain,
! [X0,X1,X2] :
( is_a_theorem(equivalent(equivalent(equivalent(X0,X1),X2),equivalent(X1,X2)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f9,f6]) ).
fof(f12,plain,
! [X0,X1,X2] :
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(equivalent(X0,X1),X2))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f10,f5]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ~ is_a_theorem(X0)
| is_a_theorem(equivalent(equivalent(X2,X1),X2))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(resolution,[status(thm)],[f12,f8]) ).
fof(f15,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(equivalent(X0,X1),X2),equivalent(X3,X2)),X3)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f12,f6]) ).
fof(f16,plain,
! [X0,X1,X2] :
( is_a_theorem(X2)
| ~ is_a_theorem(equivalent(X2,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(resolution,[status(thm)],[f13,f9]) ).
fof(f17,plain,
! [X0,X1,X2] :
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(resolution,[status(thm)],[f13,f12]) ).
fof(f24,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(equivalent(X0,equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),X3))) ),
inference(resolution,[status(thm)],[f16,f6]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X0,X2),equivalent(X3,X2)),X3),X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f17,f6]) ).
fof(f32,plain,
! [X0,X1,X2,X3,X4] :
( is_a_theorem(equivalent(X2,equivalent(equivalent(equivalent(equivalent(X0,equivalent(X1,X2)),X3),equivalent(X4,X3)),X4)))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f15,f12]) ).
fof(f129,plain,
! [X0,X1,X2] :
( ~ is_a_theorem(X2)
| ~ is_a_theorem(X1)
| is_a_theorem(equivalent(X1,equivalent(X2,X0)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f24,f32]) ).
fof(f156,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(X2)
| ~ is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(X2,X3),equivalent(X0,X3)))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f129,f24]) ).
fof(f163,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(X2)
| ~ is_a_theorem(equivalent(equivalent(X2,X3),equivalent(X0,X3)))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f156]) ).
fof(f276,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(X0)
| ~ is_a_theorem(X3)
| ~ is_a_theorem(equivalent(equivalent(equivalent(X0,X1),X2),equivalent(X1,X2))) ),
inference(resolution,[status(thm)],[f163,f6]) ).
fof(f417,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(equivalent(X0,X2))
| ~ is_a_theorem(X3)
| ~ is_a_theorem(equivalent(equivalent(X1,X2),X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f29,f276]) ).
fof(f524,plain,
! [X0,X1,X2,X3] :
( ~ is_a_theorem(X2)
| is_a_theorem(equivalent(X0,equivalent(equivalent(X2,X3),X3)))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f417,f8]) ).
fof(f674,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(equivalent(equivalent(X2,X3),X3))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f524,f5]) ).
fof(f685,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(equivalent(equivalent(X2,X3),X3))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f674]) ).
fof(f798,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(equivalent(X3,X3))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f685,f12]) ).
fof(f818,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(equivalent(X3,X3))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f798]) ).
fof(f828,plain,
! [X0,X1,X2] :
( ~ is_a_theorem(X2)
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f818,f7]) ).
fof(f867,plain,
! [X0] : ~ is_a_theorem(X0),
inference(resolution,[status(thm)],[f828,f6]) ).
fof(f875,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f6,f867]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL416-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 % Computer : n008.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Mon Sep 21 00:30:24 UTC 2026
% 0.19/0.47 % CPUTime :
% 0.19/0.48 % Drodi V4.1.1
% 10.44/1.97 % Refutation found
% 10.44/1.97 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 10.44/1.97 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 6.99/2.03 % Elapsed time: 1.544764 seconds
% 6.99/2.03 % CPU time: 11.564747 seconds
% 6.99/2.03 % Total memory used: 168.577 MB
% 6.99/2.03 % Net memory used: 159.745 MB
%------------------------------------------------------------------------------