%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL043-3 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 12:08:33 PM UTC 2026
% Result : Unsatisfiable 1.24s 0.72s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 22 unt; 0 def)
% Number of atoms : 22 ( 21 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 35 ( 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] : apply(apply(apply(h,X),Y),Z) = apply(apply(apply(X,Y),Z),Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b)),b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
file('/export/starexec/sandbox2/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(h,X0),X1),X2) = apply(apply(apply(X0,X1),X2),X1),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b)),b),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f8,plain,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f12,plain,
! [X0] : apply(apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b),apply(b,X0)) = apply(strong_fixed_point,X0),
inference(paramodulation,[status(thm)],[f7,f5]) ).
fof(f13,plain,
! [X0] : apply(apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h),apply(b,apply(b,X0))) = apply(strong_fixed_point,X0),
inference(forward_demodulation,[status(thm)],[f5,f12]) ).
fof(f17,plain,
! [X0,X1,X2] : apply(apply(apply(h,apply(b,X0)),X1),X2) = apply(apply(X0,apply(X1,X2)),X1),
inference(paramodulation,[status(thm)],[f5,f6]) ).
fof(f22,plain,
! [X0,X1,X2,X3] : apply(apply(apply(h,apply(apply(b,X0),X1)),X2),X3) = apply(apply(apply(X0,apply(X1,X2)),X3),X2),
inference(paramodulation,[status(thm)],[f5,f6]) ).
fof(f213,plain,
! [X0,X1,X2] : apply(apply(apply(h,apply(b,apply(b,X0))),X1),X2) = apply(X0,apply(apply(X1,X2),X1)),
inference(paramodulation,[status(thm)],[f5,f17]) ).
fof(f652,plain,
! [X0] : apply(apply(apply(apply(apply(b,h),apply(b,b)),apply(apply(h,apply(apply(b,h),apply(b,b))),h)),apply(b,apply(b,X0))),h) = apply(strong_fixed_point,X0),
inference(backward_demodulation,[status(thm)],[f22,f13]) ).
fof(f670,plain,
! [X0,X1,X2] : apply(apply(apply(h,apply(apply(b,b),X0)),X1),X2) = apply(apply(X0,X1),apply(X2,X1)),
inference(paramodulation,[status(thm)],[f5,f22]) ).
fof(f800,plain,
! [X0] : apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,X0))),h) = apply(strong_fixed_point,X0),
inference(forward_demodulation,[status(thm)],[f5,f652]) ).
fof(f2404,plain,
! [X0] : apply(apply(apply(apply(h,apply(apply(b,h),apply(b,b))),h),apply(b,apply(b,X0))),apply(h,apply(b,apply(b,X0)))) = apply(strong_fixed_point,X0),
inference(paramodulation,[status(thm)],[f800,f670]) ).
fof(f3244,plain,
! [X0] : apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,X0))),h),apply(h,apply(b,apply(b,X0)))) = apply(strong_fixed_point,X0),
inference(forward_demodulation,[status(thm)],[f22,f2404]) ).
fof(f3245,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(h,apply(b,apply(b,X0))),apply(h,apply(b,apply(b,X0)))),apply(h,apply(b,apply(b,X0)))),
inference(paramodulation,[status(thm)],[f670,f3244]) ).
fof(f3306,plain,
! [X0,X1] : apply(apply(apply(h,apply(b,apply(b,X0))),apply(h,apply(b,apply(b,X1)))),apply(h,apply(b,apply(b,X1)))) = apply(X0,apply(strong_fixed_point,X1)),
inference(paramodulation,[status(thm)],[f3245,f213]) ).
fof(f3342,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(X0,apply(strong_fixed_point,X0)),
inference(backward_demodulation,[status(thm)],[f3306,f3245]) ).
fof(f3389,plain,
$false,
inference(resolution,[status(thm)],[f3342,f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL043-3 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 14:06:19 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 1.24/0.72 % Refutation found
% 1.24/0.72 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.24/0.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 27.58/5.33 % Elapsed time: 4.763891 seconds
% 27.58/5.33 % CPU time: 5.910889 seconds
% 27.58/5.33 % Total memory used: 3.986 GB
% 27.58/5.33 % Net memory used: 3.984 GB
%------------------------------------------------------------------------------