%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : COL006-6 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 12:08:55 PM UTC 2026
% Result : Unsatisfiable 24.97s 3.58s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL006-6 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n001.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 14:10:15 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 24.97/3.58 % Refutation found
% 24.97/3.58 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 24.97/3.58 % SZS output start CNFRefutation for theBenchmark
% 24.97/3.58 fof(f1,axiom,(
% 24.97/3.58 (![X,Y,Z]: (apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)) ))),
% 24.97/3.58 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 24.97/3.58 fof(f2,axiom,(
% 24.97/3.58 (![X,Y]: (apply(apply(k,X),Y) = X ))),
% 24.97/3.58 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 24.97/3.58 fof(f3,axiom,(
% 24.97/3.58 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))))) ),
% 24.97/3.58 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 24.97/3.58 fof(f4,negated_conjecture,(
% 24.97/3.58 apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) ),
% 24.97/3.58 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 24.97/3.58 fof(f5,plain,(
% 24.97/3.58 ![X0,X1,X2]: (apply(apply(apply(s,X0),X1),X2)=apply(apply(X0,X2),apply(X1,X2)))),
% 24.97/3.58 inference(cnf_transformation,[status(thm)],[f1])).
% 24.97/3.58 fof(f6,plain,(
% 24.97/3.58 ![X0,X1]: (apply(apply(k,X0),X1)=X0)),
% 24.97/3.58 inference(cnf_transformation,[status(thm)],[f2])).
% 24.97/3.58 fof(f7,plain,(
% 24.97/3.58 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)))))),
% 24.97/3.58 inference(cnf_transformation,[status(thm)],[f3])).
% 24.97/3.58 fof(f8,plain,(
% 24.97/3.58 ~apply(strong_fixed_point,fixed_pt)=apply(fixed_pt,apply(strong_fixed_point,fixed_pt))),
% 24.97/3.58 inference(cnf_transformation,[status(thm)],[f4])).
% 24.97/3.58 fof(f13,plain,(
% 24.97/3.58 ![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)))),
% 24.97/3.58 inference(paramodulation,[status(thm)],[f7,f5])).
% 24.97/3.58 fof(f15,plain,(
% 24.97/3.58 ![X0,X1]: (apply(apply(apply(s,k),X0),X1)=X1)),
% 24.97/3.58 inference(paramodulation,[status(thm)],[f6,f5])).
% 24.97/3.58 fof(f19,plain,(
% 24.97/3.58 ![X0,X1,X2]: (apply(apply(apply(s,apply(k,X0)),X1),X2)=apply(X0,apply(X1,X2)))),
% 24.97/3.58 inference(paramodulation,[status(thm)],[f6,f5])).
% 24.97/3.58 fof(f23,plain,(
% 24.97/3.58 ![X0,X1,X2]: (apply(apply(apply(s,X0),apply(k,X1)),X2)=apply(apply(X0,X2),X1))),
% 24.97/3.58 inference(paramodulation,[status(thm)],[f6,f5])).
% 24.97/3.58 fof(f28,plain,(
% 24.97/3.58 ![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)))),
% 24.97/3.58 inference(forward_demodulation,[status(thm)],[f6,f13])).
% 24.97/3.58 fof(f29,plain,(
% 24.97/3.58 ![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)))))),
% 24.97/3.58 inference(backward_demodulation,[status(thm)],[f23,f28])).
% 24.97/3.58 fof(f30,plain,(
% 24.97/3.58 ![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)))))),
% 24.97/3.58 inference(forward_demodulation,[status(thm)],[f19,f29])).
% 24.97/3.58 fof(f33,plain,(
% 24.97/3.58 ![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)))),
% 24.97/3.58 inference(paramodulation,[status(thm)],[f30,f5])).
% 24.97/3.58 fof(f60,plain,(
% 24.97/3.58 ![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)))),
% 24.97/3.58 inference(paramodulation,[status(thm)],[f5,f33])).
% 24.97/3.58 fof(f84,plain,(
% 24.97/3.58 ![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)))),
% 24.97/3.58 inference(paramodulation,[status(thm)],[f6,f60])).
% 22.37/3.66 fof(f87,plain,(
% 22.37/3.66 ![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)))),
% 22.37/3.66 inference(paramodulation,[status(thm)],[f60,f5])).
% 22.37/3.66 fof(f90,plain,(
% 22.37/3.66 ![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)))),
% 22.37/3.66 inference(forward_demodulation,[status(thm)],[f19,f87])).
% 22.37/3.66 fof(f117,plain,(
% 22.37/3.66 ![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))),
% 22.37/3.66 inference(paramodulation,[status(thm)],[f6,f90])).
% 22.37/3.66 fof(f122,plain,(
% 22.37/3.66 ![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)))),
% 22.37/3.66 inference(paramodulation,[status(thm)],[f5,f90])).
% 22.37/3.66 fof(f135,plain,(
% 22.37/3.66 ![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)))),
% 22.37/3.66 inference(forward_demodulation,[status(thm)],[f15,f122])).
% 22.37/3.66 fof(f136,plain,(
% 22.37/3.66 ![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)))),
% 22.37/3.66 inference(forward_demodulation,[status(thm)],[f15,f135])).
% 22.37/3.66 fof(f141,plain,(
% 22.37/3.66 ![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))),
% 22.37/3.66 inference(paramodulation,[status(thm)],[f6,f136])).
% 22.37/3.66 fof(f177,plain,(
% 22.37/3.66 ![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))),
% 22.37/3.66 inference(paramodulation,[status(thm)],[f5,f141])).
% 22.37/3.66 fof(f205,plain,(
% 22.37/3.66 ![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))),
% 22.37/3.66 inference(forward_demodulation,[status(thm)],[f117,f177])).
% 22.37/3.66 fof(f2289,plain,(
% 22.37/3.66 ![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))))),
% 22.37/3.66 inference(paramodulation,[status(thm)],[f30,f205])).
% 22.37/3.66 fof(f2422,plain,(
% 22.37/3.66 ~apply(strong_fixed_point,fixed_pt)=apply(strong_fixed_point,fixed_pt)),
% 22.37/3.66 inference(backward_demodulation,[status(thm)],[f2427,f8])).
% 22.37/3.66 fof(f2427,plain,(
% 22.37/3.66 ![X0]: (apply(strong_fixed_point,X0)=apply(X0,apply(strong_fixed_point,X0)))),
% 22.37/3.66 inference(forward_demodulation,[status(thm)],[f84,f2289])).
% 22.37/3.66 fof(f2640,plain,(
% 22.37/3.66 $false),
% 22.37/3.66 inference(trivial_equality_resolution,[status(thm)],[f2422])).
% 22.37/3.66 % SZS output end CNFRefutation for theBenchmark.p
% 23.60/4.84 % Elapsed time: 4.263705 seconds
% 23.60/4.84 % CPU time: 12.229308 seconds
% 23.60/4.84 % Total memory used: 146.125 MB
% 23.60/4.84 % Net memory used: 144.653 MB
%------------------------------------------------------------------------------