%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : COL044-8 : 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 : n004.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 12:09:00 PM UTC 2026
% Result : Unsatisfiable 103.48s 30.65s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL044-8 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.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 14:06:52 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 103.48/30.65 % Refutation found
% 103.48/30.65 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 103.48/30.65 % SZS output start CNFRefutation for theBenchmark
% 103.48/30.65 fof(f1,axiom,(
% 103.48/30.65 (![X,Y,Z]: (apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ))),
% 103.48/30.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 103.48/30.65 fof(f2,axiom,(
% 103.48/30.65 (![X,Y,Z]: (apply(apply(apply(n,X),Y),Z) = apply(apply(apply(X,Z),Y),Z) ))),
% 103.48/30.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 103.48/30.65 fof(f3,axiom,(
% 103.48/30.65 strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(apply(b,b),n))))),n)),b)),b) ),
% 103.48/30.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 103.48/30.65 fof(f4,negated_conjecture,(
% 103.48/30.65 apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) ),
% 103.48/30.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 103.48/30.65 fof(f5,plain,(
% 103.48/30.65 ![X0,X1,X2]: (apply(apply(apply(b,X0),X1),X2)=apply(X0,apply(X1,X2)))),
% 103.48/30.65 inference(cnf_transformation,[status(thm)],[f1])).
% 103.48/30.65 fof(f6,plain,(
% 103.48/30.65 ![X0,X1,X2]: (apply(apply(apply(n,X0),X1),X2)=apply(apply(apply(X0,X2),X1),X2))),
% 103.48/30.66 inference(cnf_transformation,[status(thm)],[f2])).
% 103.48/30.66 fof(f7,plain,(
% 103.48/30.66 strong_fixed_point=apply(apply(b,apply(apply(b,apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(apply(b,b),n))))),n)),b)),b)),
% 103.48/30.66 inference(cnf_transformation,[status(thm)],[f3])).
% 103.48/30.66 fof(f8,plain,(
% 103.48/30.66 ~apply(strong_fixed_point,fixed_pt)=apply(fixed_pt,apply(strong_fixed_point,fixed_pt))),
% 103.48/30.66 inference(cnf_transformation,[status(thm)],[f4])).
% 103.48/30.66 fof(f9,definition,(
% 103.48/30.66 sF0_fnc=apply(strong_fixed_point,fixed_pt)),
% 103.48/30.66 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 103.48/30.66 fof(f10,definition,(
% 103.48/30.66 sF1_fnc=apply(fixed_pt,sF0_fnc)),
% 103.48/30.66 introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition])).
% 103.48/30.66 fof(f11,plain,(
% 103.48/30.66 ~sF0_fnc=sF1_fnc),
% 103.48/30.66 inference(definition_folding,[],[f8,f10,f9])).
% 103.48/30.66 fof(f12,plain,(
% 103.48/30.66 ![X0]: (apply(strong_fixed_point,X0)=apply(apply(apply(b,apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(apply(b,b),n))))),n)),b),apply(b,X0)))),
% 103.48/30.66 inference(paramodulation,[status(thm)],[f7,f5])).
% 103.48/30.66 fof(f13,plain,(
% 103.48/30.66 ![X0]: (apply(strong_fixed_point,X0)=apply(apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(apply(b,b),n))))),n),apply(b,apply(b,X0))))),
% 103.48/30.66 inference(forward_demodulation,[status(thm)],[f5,f12])).
% 103.48/30.66 fof(f20,plain,(
% 103.48/30.66 ![X0,X1,X2]: (apply(apply(apply(n,apply(n,X0)),X1),X2)=apply(apply(apply(apply(X0,X1),X2),X1),X2))),
% 103.48/30.66 inference(paramodulation,[status(thm)],[f6,f6])).
% 103.48/30.66 fof(f21,plain,(
% 103.48/30.66 ![X0,X1,X2]: (apply(apply(apply(n,apply(b,X0)),X1),X2)=apply(apply(X0,apply(X2,X1)),X2))),
% 103.48/30.66 inference(paramodulation,[status(thm)],[f5,f6])).
% 103.48/30.66 fof(f26,plain,(
% 103.48/30.66 ![X0,X1,X2,X3]: (apply(apply(apply(n,apply(apply(b,X0),X1)),X2),X3)=apply(apply(apply(X0,apply(X1,X3)),X2),X3))),
% 103.48/30.66 inference(paramodulation,[status(thm)],[f5,f6])).
% 103.48/30.66 fof(f30,plain,(
% 103.48/30.66 ![X0,X1,X2]: (apply(apply(apply(n,apply(n,X0)),X1),X2)=apply(apply(apply(n,apply(X0,X1)),X1),X2))),
% 103.48/30.66 inference(forward_demodulation,[status(thm)],[f6,f20])).
% 103.48/30.66 fof(f563,plain,(
% 103.48/30.66 ![X0,X1,X2,X3]: (apply(apply(apply(n,apply(n,apply(apply(b,X0),X1))),X2),X3)=apply(apply(apply(n,apply(X0,apply(X1,X2))),X2),X3))),
% 103.48/30.66 inference(paramodulation,[status(thm)],[f5,f30])).
% 103.48/30.66 fof(f636,plain,(
% 103.48/30.66 ![X0]: (apply(strong_fixed_point,X0)=apply(apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n),apply(b,apply(b,X0))))),
% 103.48/30.66 inference(backward_demodulation,[status(thm)],[f563,f13])).
% 103.48/30.66 fof(f683,plain,(
% 103.48/30.66 ![X0,X1,X2]: (apply(apply(apply(n,apply(b,apply(b,X0))),X1),X2)=apply(X0,apply(apply(X2,X1),X2)))),
% 103.48/30.66 inference(paramodulation,[status(thm)],[f5,f21])).
% 103.48/30.66 fof(f790,plain,(
% 103.48/30.66 ![X0,X1,X2]: (apply(apply(apply(apply(n,apply(b,b)),X0),X1),X2)=apply(apply(X1,X0),apply(X1,X2)))),
% 103.48/30.66 inference(paramodulation,[status(thm)],[f21,f5])).
% 103.48/30.66 fof(f871,plain,(
% 103.48/30.66 ![X0,X1]: (apply(apply(apply(n,apply(n,apply(b,b))),X0),X1)=apply(apply(X0,X1),apply(X0,X1)))),
% 103.48/30.66 inference(paramodulation,[status(thm)],[f6,f790])).
% 103.48/30.66 fof(f1810,plain,(
% 103.48/30.66 ![X0,X1,X2]: (apply(apply(apply(n,apply(apply(b,b),X0)),X1),X2)=apply(apply(X0,X2),apply(X1,X2)))),
% 103.48/30.68 inference(paramodulation,[status(thm)],[f5,f26])).
% 103.48/30.68 fof(f3747,plain,(
% 103.48/30.68 ![X0]: (apply(strong_fixed_point,X0)=apply(apply(apply(apply(n,apply(apply(b,b),n)),n),apply(b,apply(b,X0))),apply(n,apply(b,apply(b,X0)))))),
% 103.48/30.68 inference(paramodulation,[status(thm)],[f1810,f636])).
% 103.48/30.68 fof(f3770,plain,(
% 103.48/30.68 ![X0]: (apply(strong_fixed_point,X0)=apply(apply(apply(apply(n,apply(n,apply(b,b))),n),apply(b,apply(b,X0))),apply(n,apply(b,apply(b,X0)))))),
% 103.48/30.68 inference(forward_demodulation,[status(thm)],[f30,f3747])).
% 103.48/30.68 fof(f3853,plain,(
% 103.48/30.68 ![X0]: (apply(strong_fixed_point,X0)=apply(apply(apply(n,apply(b,apply(b,X0))),apply(n,apply(b,apply(b,X0)))),apply(n,apply(b,apply(b,X0)))))),
% 103.48/30.68 inference(paramodulation,[status(thm)],[f871,f3770])).
% 103.48/30.68 fof(f5477,plain,(
% 103.48/30.68 ![X0,X1]: (apply(apply(apply(n,apply(b,apply(b,X0))),apply(n,apply(b,apply(b,X1)))),apply(n,apply(b,apply(b,X1))))=apply(X0,apply(strong_fixed_point,X1)))),
% 103.48/30.68 inference(paramodulation,[status(thm)],[f3853,f683])).
% 103.48/30.68 fof(f5801,plain,(
% 103.48/30.68 ![X0]: (apply(strong_fixed_point,X0)=apply(X0,apply(strong_fixed_point,X0)))),
% 103.48/30.68 inference(backward_demodulation,[status(thm)],[f5477,f3853])).
% 103.48/30.68 fof(f5920,plain,(
% 103.48/30.68 apply(strong_fixed_point,fixed_pt)=apply(fixed_pt,sF0_fnc)),
% 103.48/30.68 inference(paramodulation,[status(thm)],[f9,f5801])).
% 103.48/30.68 fof(f6068,plain,(
% 103.48/30.68 sF1_fnc=sF0_fnc),
% 103.48/30.68 inference(backward_demodulation,[status(thm)],[f6069,f10])).
% 103.48/30.68 fof(f6069,plain,(
% 103.48/30.68 sF0_fnc=apply(fixed_pt,sF0_fnc)),
% 103.48/30.68 inference(forward_demodulation,[status(thm)],[f9,f5920])).
% 103.48/30.68 fof(f6284,plain,(
% 103.48/30.68 $false),
% 103.48/30.68 inference(forward_subsumption_resolution,[status(thm)],[f6068,f11])).
% 103.48/30.68 % SZS output end CNFRefutation for theBenchmark.p
% 88.17/30.79 % Elapsed time: 30.410912 seconds
% 88.17/30.79 % CPU time: 240.281307 seconds
% 88.17/30.79 % Total memory used: 66.981 GB
% 88.17/30.79 % Net memory used: 66.972 GB
%------------------------------------------------------------------------------