%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL066-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 12:08:40 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 16 unt; 0 def)
% Number of atoms : 16 ( 15 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 9 ( 9 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 9 ( 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 : 15 ( 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X,Y,Z] : apply(apply(apply(q,X),Y),Z) = apply(Y,apply(X,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : apply(apply(w,X),Y) = apply(apply(X,Y),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2] : apply(apply(apply(q,X0),X1),X2) = apply(X1,apply(X0,X2)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
! [X0,X1] : apply(apply(w,X0),X1) = apply(apply(X0,X1),X1),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f8,plain,
apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f21,plain,
apply(apply(apply(w,apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x)),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(forward_demodulation,[status(thm)],[f7,f8]) ).
fof(f22,plain,
apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(forward_demodulation,[status(thm)],[f6,f21]) ).
fof(f42,plain,
! [X0,X1] : apply(apply(w,apply(q,X0)),X1) = apply(X1,apply(X0,X1)),
inference(paramodulation,[status(thm)],[f7,f6]) ).
fof(f47,plain,
! [X0,X1,X2] : apply(apply(w,apply(apply(q,X0),X1)),X2) = apply(apply(X1,apply(X0,X2)),X2),
inference(paramodulation,[status(thm)],[f6,f7]) ).
fof(f48,plain,
apply(apply(apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(backward_demodulation,[status(thm)],[f42,f22]) ).
fof(f50,plain,
apply(apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(forward_demodulation,[status(thm)],[f47,f48]) ).
fof(f51,plain,
apply(apply(apply(apply(q,x),apply(q,apply(x,y))),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(forward_demodulation,[status(thm)],[f6,f50]) ).
fof(f52,plain,
apply(apply(apply(q,apply(x,y)),apply(x,y)),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(forward_demodulation,[status(thm)],[f6,f51]) ).
fof(f53,plain,
apply(apply(x,y),apply(apply(x,y),z)) != apply(apply(x,y),apply(apply(x,y),z)),
inference(forward_demodulation,[status(thm)],[f6,f52]) ).
fof(f54,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL066-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 14:14:29 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.12/0.36 % Refutation found
% 0.12/0.36 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.38 % Elapsed time: 0.022467 seconds
% 0.12/0.38 % CPU time: 0.029032 seconds
% 0.12/0.38 % Total memory used: 735.680 KB
% 0.12/0.38 % Net memory used: 725.856 KB
%------------------------------------------------------------------------------