%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL066-3 : TPTP v9.3.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 0.20s 0.49s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 18 unt; 0 def)
% Number of atoms : 18 ( 17 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 : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 21 ( 21 !; 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,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(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,plain,
! [X0,X1,X2] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f1]) ).
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(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f22,plain,
apply(apply(apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(forward_demodulation,[status(thm)],[f7,f8]) ).
fof(f23,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)],[f5,f22]) ).
fof(f51,plain,
! [X0,X1] : apply(apply(w,apply(q,X0)),X1) = apply(X1,apply(X0,X1)),
inference(paramodulation,[status(thm)],[f7,f6]) ).
fof(f56,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(f57,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)],[f51,f23]) ).
fof(f59,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)],[f56,f57]) ).
fof(f60,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,f59]) ).
fof(f61,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,f60]) ).
fof(f62,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,f61]) ).
fof(f63,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL066-3 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.44 % Computer : n004.cluster.edu
% 0.20/0.44 % Model : x86_64 x86_64
% 0.20/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.44 % Memory : 8046.5625MB
% 0.20/0.44 % OS : Linux 6.8.0-71-generic
% 0.20/0.44 % CPULimit : 300
% 0.20/0.44 % WCLimit : 300
% 0.20/0.44 % DateTime : Mon Sep 21 14:08:35 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.46 % Drodi V4.1.1
% 0.20/0.49 % Refutation found
% 0.20/0.49 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.20/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.52 % Elapsed time: 0.054677 seconds
% 0.20/0.52 % CPU time: 0.040367 seconds
% 0.20/0.52 % Total memory used: 630.992 KB
% 0.20/0.52 % Net memory used: 628.224 KB
%------------------------------------------------------------------------------