%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL006-7 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 12:08:27 PM UTC 2026
% Result : Unsatisfiable 70.50s 9.44s
% Output : CNFRefutation 71.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 29 unt; 0 def)
% Number of atoms : 29 ( 28 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 8 ( 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 : 43 ( 43 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : apply(apply(k,X),Y) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
strong_fixed_point = apply(apply(s,apply(k,apply(apply(apply(s,s),apply(apply(s,k),k)),apply(apply(s,s),apply(s,k))))),apply(apply(s,apply(k,s)),k)),
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(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f6,plain,
! [X0,X1] : apply(apply(k,X0),X1) = X0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
strong_fixed_point = apply(apply(s,apply(k,apply(apply(apply(s,s),apply(apply(s,k),k)),apply(apply(s,s),apply(s,k))))),apply(apply(s,apply(k,s)),k)),
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(f13,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(k,apply(apply(apply(s,s),apply(apply(s,k),k)),apply(apply(s,s),apply(s,k)))),X0),apply(apply(apply(s,apply(k,s)),k),X0)),
inference(paramodulation,[status(thm)],[f7,f5]) ).
fof(f18,plain,
! [X0,X1,X2] : apply(apply(apply(s,apply(k,X0)),X1),X2) = apply(X0,apply(X1,X2)),
inference(paramodulation,[status(thm)],[f6,f5]) ).
fof(f22,plain,
! [X0,X1,X2] : apply(apply(apply(s,X0),apply(k,X1)),X2) = apply(apply(X0,X2),X1),
inference(paramodulation,[status(thm)],[f6,f5]) ).
fof(f24,plain,
! [X0,X1,X2,X3] : apply(apply(apply(s,X0),apply(X1,X2)),apply(X3,X2)) = apply(apply(X0,apply(X3,X2)),apply(apply(apply(s,X1),X3),X2)),
inference(paramodulation,[status(thm)],[f5,f5]) ).
fof(f25,plain,
! [X0,X1] : apply(apply(apply(s,k),X0),X1) = X1,
inference(paramodulation,[status(thm)],[f5,f6]) ).
fof(f26,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(apply(s,s),apply(apply(s,k),k)),apply(apply(s,s),apply(s,k))),apply(apply(apply(s,apply(k,s)),k),X0)),
inference(forward_demodulation,[status(thm)],[f6,f13]) ).
fof(f27,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(apply(s,s),apply(apply(s,k),k)),apply(apply(s,s),apply(s,k))),apply(s,apply(k,X0))),
inference(forward_demodulation,[status(thm)],[f18,f26]) ).
fof(f34,plain,
! [X0,X1,X2] : apply(apply(apply(s,X0),apply(apply(s,k),X1)),X2) = apply(apply(X0,X2),X2),
inference(paramodulation,[status(thm)],[f25,f5]) ).
fof(f36,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(s,apply(apply(s,s),apply(s,k))),apply(apply(s,s),apply(s,k))),apply(s,apply(k,X0))),
inference(backward_demodulation,[status(thm)],[f34,f27]) ).
fof(f196,plain,
! [X0,X1] : apply(apply(apply(s,X0),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,X1)))),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,X1)))) = apply(apply(X0,apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,X1)))),apply(strong_fixed_point,X1)),
inference(paramodulation,[status(thm)],[f36,f24]) ).
fof(f334,plain,
! [X0,X1] : apply(apply(apply(apply(s,s),k),X0),X1) = apply(apply(X0,X1),X0),
inference(paramodulation,[status(thm)],[f5,f22]) ).
fof(f486,plain,
! [X0,X1] : apply(apply(apply(apply(s,s),apply(s,k)),X0),X1) = apply(apply(X0,X1),X1),
inference(paramodulation,[status(thm)],[f5,f34]) ).
fof(f574,plain,
! [X0,X1] : apply(apply(apply(apply(s,s),apply(s,k)),apply(s,X0)),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,X1)))) = apply(apply(X0,apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,X1)))),apply(strong_fixed_point,X1)),
inference(backward_demodulation,[status(thm)],[f486,f196]) ).
fof(f853,plain,
! [X0] : apply(apply(apply(apply(s,s),k),apply(apply(s,s),apply(s,k))),X0) = apply(apply(X0,apply(apply(s,s),apply(s,k))),apply(apply(s,s),apply(s,k))),
inference(paramodulation,[status(thm)],[f334,f486]) ).
fof(f1040,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(apply(apply(s,s),k),apply(apply(s,s),apply(s,k))),s),apply(s,apply(k,X0))),
inference(backward_demodulation,[status(thm)],[f853,f36]) ).
fof(f2982,plain,
! [X0] : apply(apply(apply(s,apply(apply(s,s),apply(s,k))),apply(apply(s,s),apply(s,k))),apply(s,apply(k,X0))) = apply(apply(apply(k,X0),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,X0)))),apply(strong_fixed_point,X0)),
inference(paramodulation,[status(thm)],[f5,f574]) ).
fof(f3066,plain,
! [X0] : apply(apply(apply(apply(apply(s,s),k),apply(apply(s,s),apply(s,k))),s),apply(s,apply(k,X0))) = apply(apply(apply(k,X0),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,X0)))),apply(strong_fixed_point,X0)),
inference(forward_demodulation,[status(thm)],[f853,f2982]) ).
fof(f3067,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(k,X0),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,X0)))),apply(strong_fixed_point,X0)),
inference(forward_demodulation,[status(thm)],[f1040,f3066]) ).
fof(f3068,plain,
apply(strong_fixed_point,fixed_pt) != apply(strong_fixed_point,fixed_pt),
inference(backward_demodulation,[status(thm)],[f3070,f8]) ).
fof(f3070,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(X0,apply(strong_fixed_point,X0)),
inference(forward_demodulation,[status(thm)],[f6,f3067]) ).
fof(f3080,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f3068]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL006-7 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 14:04:34 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 70.50/9.44 % Refutation found
% 70.50/9.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 70.50/9.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 40.50/10.72 % Elapsed time: 10.137229 seconds
% 40.50/10.72 % CPU time: 58.850459 seconds
% 40.50/10.72 % Total memory used: 330.988 MB
% 40.50/10.72 % Net memory used: 323.401 MB
%------------------------------------------------------------------------------