%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : COL033-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 12:08:58 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.45s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL033-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 14:06:26 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.14/0.45 % Refutation found
% 0.14/0.45 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.45 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.45 fof(f1,axiom,(
% 0.14/0.45 (![X,Y,Z]: (apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ))),
% 0.14/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.45 fof(f2,axiom,(
% 0.14/0.45 (![X,Y]: (apply(apply(l,X),Y) = apply(X,apply(Y,Y)) ))),
% 0.14/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.45 fof(f3,axiom,(
% 0.14/0.45 (![X]: (apply(m,X) = apply(X,X) ))),
% 0.14/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.45 fof(f4,negated_conjecture,(
% 0.14/0.45 (![Y]: (apply(Y,f(Y)) != apply(f(Y),apply(Y,f(Y))) ))),
% 0.14/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.45 fof(f5,plain,(
% 0.14/0.45 ![X0,X1,X2]: (apply(apply(apply(b,X0),X1),X2)=apply(X0,apply(X1,X2)))),
% 0.14/0.45 inference(cnf_transformation,[status(thm)],[f1])).
% 0.14/0.45 fof(f6,plain,(
% 0.14/0.45 ![X0,X1]: (apply(apply(l,X0),X1)=apply(X0,apply(X1,X1)))),
% 0.14/0.45 inference(cnf_transformation,[status(thm)],[f2])).
% 0.14/0.45 fof(f7,plain,(
% 0.14/0.45 ![X0]: (apply(m,X0)=apply(X0,X0))),
% 0.14/0.45 inference(cnf_transformation,[status(thm)],[f3])).
% 0.14/0.45 fof(f8,plain,(
% 0.14/0.45 ![X0]: (~apply(X0,f(X0))=apply(f(X0),apply(X0,f(X0))))),
% 0.14/0.45 inference(cnf_transformation,[status(thm)],[f4])).
% 0.14/0.45 fof(f9,definition,(
% 0.14/0.45 ![X0]: (sF0_fnc(X0)=apply(X0,f(X0)))),
% 0.14/0.45 introduced(definition,[new_symbols(definition,[sF0_fnc(X0)])],[function_definition])).
% 0.14/0.45 fof(f10,definition,(
% 0.14/0.45 ![X0]: (sF1_fnc(X0)=apply(f(X0),sF0_fnc(X0)))),
% 0.14/0.45 introduced(definition,[new_symbols(definition,[sF1_fnc(X0)])],[function_definition])).
% 0.14/0.45 fof(f11,plain,(
% 0.14/0.45 ![X0]: (~sF0_fnc(X0)=sF1_fnc(X0))),
% 0.14/0.45 inference(definition_folding,[],[f8,f10,f9])).
% 0.14/0.45 fof(f12,plain,(
% 0.14/0.45 ![X0,X1]: (sF0_fnc(apply(apply(b,X0),X1))=apply(X0,apply(X1,f(apply(apply(b,X0),X1)))))),
% 0.14/0.45 inference(paramodulation,[status(thm)],[f9,f5])).
% 0.14/0.45 fof(f131,plain,(
% 0.14/0.45 ![X0,X1]: (apply(apply(l,X0),X1)=apply(X0,apply(m,X1)))),
% 0.14/0.45 inference(paramodulation,[status(thm)],[f7,f6])).
% 0.14/0.45 fof(f151,plain,(
% 0.14/0.45 ![X0]: (apply(m,apply(l,X0))=apply(X0,apply(m,apply(l,X0))))),
% 0.14/0.45 inference(paramodulation,[status(thm)],[f7,f131])).
% 0.14/0.45 fof(f2261,plain,(
% 0.14/0.45 apply(m,apply(l,f(apply(apply(b,m),l))))=apply(f(apply(apply(b,m),l)),sF0_fnc(apply(apply(b,m),l)))),
% 0.14/0.45 inference(paramodulation,[status(thm)],[f12,f151])).
% 0.14/0.45 fof(f2326,plain,(
% 0.14/0.45 sF0_fnc(apply(apply(b,m),l))=apply(f(apply(apply(b,m),l)),sF0_fnc(apply(apply(b,m),l)))),
% 0.14/0.45 inference(forward_demodulation,[status(thm)],[f12,f2261])).
% 0.14/0.45 fof(f2327,plain,(
% 0.14/0.45 sF0_fnc(apply(apply(b,m),l))=sF1_fnc(apply(apply(b,m),l))),
% 0.14/0.45 inference(forward_demodulation,[status(thm)],[f10,f2326])).
% 0.14/0.45 fof(f2328,plain,(
% 0.14/0.45 $false),
% 0.14/0.45 inference(forward_subsumption_resolution,[status(thm)],[f2327,f11])).
% 0.14/0.45 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.46 % Elapsed time: 0.084486 seconds
% 0.14/0.46 % CPU time: 0.516992 seconds
% 0.14/0.46 % Total memory used: 22.514 MB
% 0.14/0.46 % Net memory used: 22.287 MB
%------------------------------------------------------------------------------