%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL006-6 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 87.48s 11.60s
% Output : CNFRefutation 68.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 31 unt; 0 def)
% Number of atoms : 31 ( 30 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 46 ( 46 !; 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/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : apply(apply(k,X),Y) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
strong_fixed_point = apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),
file('/export/starexec/sandbox/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/sandbox/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(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),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(s,apply(apply(s,k),k)),apply(apply(s,k),k))),X0),apply(apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),X0)),
inference(paramodulation,[status(thm)],[f7,f5]) ).
fof(f15,plain,
! [X0,X1] : apply(apply(apply(s,k),X0),X1) = X1,
inference(paramodulation,[status(thm)],[f6,f5]) ).
fof(f19,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(f23,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(f28,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),X0)),
inference(forward_demodulation,[status(thm)],[f6,f13]) ).
fof(f29,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(apply(s,apply(k,s)),k),X0),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),
inference(backward_demodulation,[status(thm)],[f23,f28]) ).
fof(f30,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,X0)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),
inference(forward_demodulation,[status(thm)],[f19,f29]) ).
fof(f33,plain,
! [X0,X1] : apply(apply(apply(s,X0),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),apply(apply(s,apply(k,X1)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))) = apply(apply(X0,apply(apply(s,apply(k,X1)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(strong_fixed_point,X1)),
inference(paramodulation,[status(thm)],[f30,f5]) ).
fof(f60,plain,
! [X0,X1] : apply(apply(apply(s,apply(s,X0)),apply(s,apply(k,X1))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))) = apply(apply(X0,apply(apply(s,apply(k,X1)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(strong_fixed_point,X1)),
inference(paramodulation,[status(thm)],[f5,f33]) ).
fof(f84,plain,
! [X0,X1] : apply(apply(apply(s,apply(s,apply(k,X0))),apply(s,apply(k,X1))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))) = apply(X0,apply(strong_fixed_point,X1)),
inference(paramodulation,[status(thm)],[f6,f60]) ).
fof(f87,plain,
! [X0,X1] : apply(apply(apply(apply(s,apply(s,s)),apply(s,apply(k,X0))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),X1) = apply(apply(apply(apply(s,apply(k,X0)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),X1),apply(apply(strong_fixed_point,X0),X1)),
inference(paramodulation,[status(thm)],[f60,f5]) ).
fof(f90,plain,
! [X0,X1] : apply(apply(apply(apply(s,apply(s,s)),apply(s,apply(k,X0))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),X1) = apply(apply(X0,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),X1)),apply(apply(strong_fixed_point,X0),X1)),
inference(forward_demodulation,[status(thm)],[f19,f87]) ).
fof(f117,plain,
! [X0] : apply(apply(apply(apply(s,apply(s,s)),apply(s,apply(k,k))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),X0) = apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),X0),
inference(paramodulation,[status(thm)],[f6,f90]) ).
fof(f122,plain,
! [X0,X1] : apply(apply(apply(apply(s,apply(s,s)),apply(s,apply(k,X0))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),X1) = apply(apply(X0,apply(apply(apply(apply(s,k),k),X1),apply(apply(apply(s,k),k),X1))),apply(apply(strong_fixed_point,X0),X1)),
inference(paramodulation,[status(thm)],[f5,f90]) ).
fof(f135,plain,
! [X0,X1] : apply(apply(apply(apply(s,apply(s,s)),apply(s,apply(k,X0))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),X1) = apply(apply(X0,apply(X1,apply(apply(apply(s,k),k),X1))),apply(apply(strong_fixed_point,X0),X1)),
inference(forward_demodulation,[status(thm)],[f15,f122]) ).
fof(f136,plain,
! [X0,X1] : apply(apply(apply(apply(s,apply(s,s)),apply(s,apply(k,X0))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),X1) = apply(apply(X0,apply(X1,X1)),apply(apply(strong_fixed_point,X0),X1)),
inference(forward_demodulation,[status(thm)],[f15,f135]) ).
fof(f141,plain,
! [X0] : apply(apply(apply(apply(s,apply(s,s)),apply(s,apply(k,k))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),X0) = apply(X0,X0),
inference(paramodulation,[status(thm)],[f6,f136]) ).
fof(f177,plain,
! [X0,X1] : apply(apply(apply(apply(s,apply(s,s)),apply(s,apply(k,k))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),apply(X0,X1)) = apply(apply(apply(s,X0),X0),X1),
inference(paramodulation,[status(thm)],[f5,f141]) ).
fof(f205,plain,
! [X0,X1] : apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(X0,X1)) = apply(apply(apply(s,X0),X0),X1),
inference(forward_demodulation,[status(thm)],[f117,f177]) ).
fof(f2289,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(s,apply(s,apply(k,X0))),apply(s,apply(k,X0))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),
inference(paramodulation,[status(thm)],[f30,f205]) ).
fof(f2422,plain,
apply(strong_fixed_point,fixed_pt) != apply(strong_fixed_point,fixed_pt),
inference(backward_demodulation,[status(thm)],[f2427,f8]) ).
fof(f2427,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(X0,apply(strong_fixed_point,X0)),
inference(forward_demodulation,[status(thm)],[f84,f2289]) ).
fof(f2640,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f2422]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL006-6 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n018.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 14:06:44 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.44 % Drodi V4.1.1
% 87.48/11.60 % Refutation found
% 87.48/11.60 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 87.48/11.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 50.07/12.85 % Elapsed time: 12.197025 seconds
% 50.07/12.85 % CPU time: 72.929641 seconds
% 50.07/12.85 % Total memory used: 394.486 MB
% 50.07/12.85 % Net memory used: 372.109 MB
%------------------------------------------------------------------------------