%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : COL039-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 21.95s 18.34s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL039-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/15.44 % CPULimit : 300
% 0.09/15.44 % WCLimit : 300
% 0.09/15.44 % DateTime : Mon Sep 21 14:07:03 UTC 2026
% 0.09/15.44 % CPUTime :
% 0.09/15.45 % Drodi V4.1.1
% 21.95/18.34 % Refutation found
% 21.95/18.34 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 21.95/18.34 % SZS output start CNFRefutation for theBenchmark
% 21.95/18.34 fof(f1,axiom,(
% 21.95/18.34 (![X,Y,Z]: (apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ))),
% 21.95/18.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.95/18.34 fof(f2,axiom,(
% 21.95/18.34 (![X]: (apply(m,X) = apply(X,X) ))),
% 21.95/18.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.95/18.34 fof(f3,axiom,(
% 21.95/18.34 (![X,Y]: (apply(apply(o,X),Y) = apply(Y,apply(X,Y)) ))),
% 21.95/18.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.95/18.34 fof(f4,negated_conjecture,(
% 21.95/18.34 (![Y]: (apply(Y,f(Y)) != apply(f(Y),apply(Y,f(Y))) ))),
% 21.95/18.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.95/18.34 fof(f5,plain,(
% 21.95/18.34 ![X0,X1,X2]: (apply(apply(apply(b,X0),X1),X2)=apply(X0,apply(X1,X2)))),
% 21.95/18.34 inference(cnf_transformation,[status(thm)],[f1])).
% 21.95/18.34 fof(f6,plain,(
% 21.95/18.34 ![X0]: (apply(m,X0)=apply(X0,X0))),
% 21.95/18.34 inference(cnf_transformation,[status(thm)],[f2])).
% 21.95/18.34 fof(f7,plain,(
% 21.95/18.34 ![X0,X1]: (apply(apply(o,X0),X1)=apply(X1,apply(X0,X1)))),
% 21.95/18.34 inference(cnf_transformation,[status(thm)],[f3])).
% 21.95/18.34 fof(f8,plain,(
% 21.95/18.34 ![X0]: (~apply(X0,f(X0))=apply(f(X0),apply(X0,f(X0))))),
% 21.95/18.34 inference(cnf_transformation,[status(thm)],[f4])).
% 21.95/18.34 fof(f9,definition,(
% 21.95/18.34 ![X0]: (sF0_fnc(X0)=apply(X0,f(X0)))),
% 21.95/18.34 introduced(definition,[new_symbols(definition,[sF0_fnc(X0)])],[function_definition])).
% 21.95/18.34 fof(f10,definition,(
% 21.95/18.34 ![X0]: (sF1_fnc(X0)=apply(f(X0),sF0_fnc(X0)))),
% 21.95/18.34 introduced(definition,[new_symbols(definition,[sF1_fnc(X0)])],[function_definition])).
% 21.95/18.34 fof(f11,plain,(
% 21.95/18.34 ![X0]: (~sF0_fnc(X0)=sF1_fnc(X0))),
% 21.95/18.34 inference(definition_folding,[],[f8,f10,f9])).
% 21.95/18.34 fof(f107,plain,(
% 21.95/18.34 ![X0,X1]: (apply(m,apply(apply(b,X0),X1))=apply(X0,apply(X1,apply(apply(b,X0),X1))))),
% 21.95/18.34 inference(paramodulation,[status(thm)],[f5,f6])).
% 21.95/18.34 fof(f137,plain,(
% 21.95/18.34 ![X0]: (apply(apply(o,X0),f(X0))=apply(f(X0),sF0_fnc(X0)))),
% 21.95/18.34 inference(paramodulation,[status(thm)],[f9,f7])).
% 21.95/18.34 fof(f149,plain,(
% 21.95/18.34 ![X0]: (apply(apply(o,X0),f(X0))=sF1_fnc(X0))),
% 21.95/18.34 inference(forward_demodulation,[status(thm)],[f10,f137])).
% 21.95/18.34 fof(f270,plain,(
% 21.95/18.34 ![X0]: (apply(apply(m,apply(apply(b,o),X0)),f(apply(X0,apply(apply(b,o),X0))))=sF1_fnc(apply(X0,apply(apply(b,o),X0))))),
% 21.95/18.34 inference(paramodulation,[status(thm)],[f107,f149])).
% 21.95/18.34 fof(f26537,plain,(
% 21.95/18.34 sF0_fnc(apply(m,apply(apply(b,o),m)))=sF1_fnc(apply(m,apply(apply(b,o),m)))),
% 21.95/18.34 inference(paramodulation,[status(thm)],[f9,f270])).
% 21.95/18.34 fof(f26660,plain,(
% 21.95/18.34 $false),
% 21.95/18.34 inference(forward_subsumption_resolution,[status(thm)],[f26537,f11])).
% 21.95/18.34 % SZS output end CNFRefutation for theBenchmark.p
% 22.75/18.42 % Elapsed time: 2.957547 seconds
% 22.75/18.42 % CPU time: 23.100433 seconds
% 22.75/18.42 % Total memory used: 433.879 MB
% 22.75/18.42 % Net memory used: 432.767 MB
%------------------------------------------------------------------------------