%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL060-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 12:08:37 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.36s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 13 unt; 0 def)
% Number of atoms : 13 ( 12 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 10 ( 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : apply(apply(t,X),Y) = apply(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
apply(apply(apply(apply(apply(b,apply(t,b)),apply(apply(b,b),t)),x),y),z) != apply(y,apply(x,z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [X0,X1,X2] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f5,plain,
! [X0,X1] : apply(apply(t,X0),X1) = apply(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f6,plain,
apply(apply(apply(apply(apply(b,apply(t,b)),apply(apply(b,b),t)),x),y),z) != apply(y,apply(x,z)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f18,plain,
apply(apply(apply(apply(t,b),apply(apply(apply(b,b),t),x)),y),z) != apply(y,apply(x,z)),
inference(forward_demodulation,[status(thm)],[f4,f6]) ).
fof(f19,plain,
apply(apply(apply(apply(apply(apply(b,b),t),x),b),y),z) != apply(y,apply(x,z)),
inference(forward_demodulation,[status(thm)],[f5,f18]) ).
fof(f20,plain,
apply(apply(apply(apply(b,apply(t,x)),b),y),z) != apply(y,apply(x,z)),
inference(forward_demodulation,[status(thm)],[f4,f19]) ).
fof(f21,plain,
apply(apply(apply(t,x),apply(b,y)),z) != apply(y,apply(x,z)),
inference(forward_demodulation,[status(thm)],[f4,f20]) ).
fof(f22,plain,
apply(apply(apply(b,y),x),z) != apply(y,apply(x,z)),
inference(forward_demodulation,[status(thm)],[f5,f21]) ).
fof(f23,plain,
apply(y,apply(x,z)) != apply(y,apply(x,z)),
inference(forward_demodulation,[status(thm)],[f4,f22]) ).
fof(f24,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL060-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n003.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 14:09:16 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 0.08/0.36 % Refutation found
% 0.08/0.36 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.38 % Elapsed time: 0.023082 seconds
% 0.08/0.38 % CPU time: 0.025052 seconds
% 0.08/0.38 % Total memory used: 428.656 KB
% 0.08/0.38 % Net memory used: 410.432 KB
%------------------------------------------------------------------------------