%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL081-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 12:08:42 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 14 unt; 0 def)
% Number of atoms : 18 ( 17 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 10 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 17 ( 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : apply(k(X),Y) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z] : apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,k(Z)),apply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y] :
( apply(X,n(X,Y)) != apply(Y,n(X,Y))
| X = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
k(k(b)) != apply(abstraction,k(k(b))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,plain,
! [X0,X1] : apply(k(X0),X1) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
! [X0,X1,X2] : apply(apply(apply(abstraction,X0),X1),X2) = apply(apply(X0,k(X2)),apply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f21,plain,
! [X0,X1] :
( apply(X0,n(X0,X1)) != apply(X1,n(X0,X1))
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f24,plain,
k(k(b)) != apply(abstraction,k(k(b))),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f25,plain,
! [X0,X1,X2] : apply(apply(apply(abstraction,k(X0)),X1),X2) = apply(X0,apply(X1,X2)),
inference(paramodulation,[status(thm)],[f13,f18]) ).
fof(f374,plain,
apply(k(k(b)),n(k(k(b)),apply(abstraction,k(k(b))))) != apply(apply(abstraction,k(k(b))),n(k(k(b)),apply(abstraction,k(k(b))))),
inference(resolution,[status(thm)],[f21,f24]) ).
fof(f377,plain,
k(b) != apply(apply(abstraction,k(k(b))),n(k(k(b)),apply(abstraction,k(k(b))))),
inference(forward_demodulation,[status(thm)],[f13,f374]) ).
fof(f451,plain,
apply(k(b),n(k(b),apply(apply(abstraction,k(k(b))),n(k(k(b)),apply(abstraction,k(k(b))))))) != apply(apply(apply(abstraction,k(k(b))),n(k(k(b)),apply(abstraction,k(k(b))))),n(k(b),apply(apply(abstraction,k(k(b))),n(k(k(b)),apply(abstraction,k(k(b))))))),
inference(resolution,[status(thm)],[f377,f21]) ).
fof(f453,plain,
b != apply(apply(apply(abstraction,k(k(b))),n(k(k(b)),apply(abstraction,k(k(b))))),n(k(b),apply(apply(abstraction,k(k(b))),n(k(k(b)),apply(abstraction,k(k(b))))))),
inference(forward_demodulation,[status(thm)],[f13,f451]) ).
fof(f454,plain,
b != apply(k(b),apply(n(k(k(b)),apply(abstraction,k(k(b)))),n(k(b),apply(apply(abstraction,k(k(b))),n(k(k(b)),apply(abstraction,k(k(b)))))))),
inference(forward_demodulation,[status(thm)],[f25,f453]) ).
fof(f455,plain,
b != b,
inference(forward_demodulation,[status(thm)],[f13,f454]) ).
fof(f456,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f455]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL081-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 14:15:15 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.44 % Elapsed time: 0.059995 seconds
% 0.13/0.44 % CPU time: 0.267255 seconds
% 0.13/0.44 % Total memory used: 92.214 MB
% 0.13/0.44 % Net memory used: 92.003 MB
%------------------------------------------------------------------------------