%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL043-2 : TPTP v9.3.1. Bugfixed v2.3.0.
% 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 12:08:33 PM UTC 2026
% Result : Unsatisfiable 1.30s 0.71s
% Output : CNFRefutation 2.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 27 unt; 0 def)
% Number of atoms : 31 ( 26 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 20 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 27 !; 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(h,X),Y),Z) = apply(apply(apply(X,Y),Z),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [Strong_fixed_point] :
( fixed_point(Strong_fixed_point)
| apply(Strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(Strong_fixed_point,fixed_pt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
~ 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/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(h,X0),X1),X2) = apply(apply(apply(X0,X1),X2),X1),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
! [X0] :
( fixed_point(X0)
| apply(X0,fixed_pt) != apply(fixed_pt,apply(X0,fixed_pt)) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f8,plain,
~ 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)],[f4]) ).
fof(f15,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(f18,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(f51,plain,
apply(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),fixed_pt) != apply(fixed_pt,apply(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),fixed_pt)),
inference(resolution,[status(thm)],[f7,f8]) ).
fof(f52,plain,
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,fixed_pt)) != apply(fixed_pt,apply(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),fixed_pt)),
inference(forward_demodulation,[status(thm)],[f5,f51]) ).
fof(f53,plain,
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,fixed_pt))) != apply(fixed_pt,apply(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),fixed_pt)),
inference(forward_demodulation,[status(thm)],[f5,f52]) ).
fof(f54,plain,
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,fixed_pt))),h) != apply(fixed_pt,apply(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),fixed_pt)),
inference(forward_demodulation,[status(thm)],[f18,f53]) ).
fof(f55,plain,
apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h) != apply(fixed_pt,apply(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),fixed_pt)),
inference(forward_demodulation,[status(thm)],[f5,f54]) ).
fof(f56,plain,
apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h) != apply(fixed_pt,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,fixed_pt))),
inference(forward_demodulation,[status(thm)],[f5,f55]) ).
fof(f57,plain,
apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h) != apply(fixed_pt,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,fixed_pt)))),
inference(forward_demodulation,[status(thm)],[f5,f56]) ).
fof(f58,plain,
apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h) != apply(fixed_pt,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,fixed_pt))),h)),
inference(forward_demodulation,[status(thm)],[f18,f57]) ).
fof(f59,plain,
apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h) != apply(fixed_pt,apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h)),
inference(forward_demodulation,[status(thm)],[f5,f58]) ).
fof(f138,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,f15]) ).
fof(f368,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,f18]) ).
fof(f452,plain,
apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h) != apply(fixed_pt,apply(apply(apply(apply(h,apply(apply(b,h),apply(b,b))),h),apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt))))),
inference(backward_demodulation,[status(thm)],[f368,f59]) ).
fof(f481,plain,
apply(apply(apply(apply(h,apply(apply(b,h),apply(b,b))),h),apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(apply(h,apply(apply(b,h),apply(b,b))),h),apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt))))),
inference(forward_demodulation,[status(thm)],[f368,f452]) ).
fof(f482,plain,
apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(apply(h,apply(apply(b,h),apply(b,b))),h),apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt))))),
inference(forward_demodulation,[status(thm)],[f18,f481]) ).
fof(f483,plain,
apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(apply(h,apply(apply(b,h),apply(b,b))),h),apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt))))),
inference(forward_demodulation,[status(thm)],[f368,f482]) ).
fof(f484,plain,
apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt))))),
inference(forward_demodulation,[status(thm)],[f18,f483]) ).
fof(f485,plain,
apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt))))),
inference(forward_demodulation,[status(thm)],[f368,f484]) ).
fof(f486,plain,
apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt)))) != apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt)))),
inference(forward_demodulation,[status(thm)],[f138,f485]) ).
fof(f487,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f486]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL043-2 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n004.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
% 1.30/0.71 % Refutation found
% 1.30/0.71 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.30/0.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.14/0.75 % Elapsed time: 0.381192 seconds
% 2.14/0.75 % CPU time: 2.709196 seconds
% 2.14/0.75 % Total memory used: 126.033 MB
% 2.14/0.75 % Net memory used: 125.352 MB
%------------------------------------------------------------------------------