%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : COL075-2 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/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 12:09:05 PM UTC 2026
% Result : Unsatisfiable 17.25s 2.83s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL075-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.51 % Computer : n004.cluster.edu
% 0.08/0.51 % Model : x86_64 x86_64
% 0.08/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.51 % Memory : 8046.5625MB
% 0.08/0.51 % OS : Linux 6.8.0-71-generic
% 0.08/0.52 % CPULimit : 300
% 0.08/0.52 % WCLimit : 300
% 0.08/0.52 % DateTime : Mon Sep 21 14:08:22 UTC 2026
% 0.08/0.52 % CPUTime :
% 0.08/0.52 % Drodi V4.1.1
% 17.25/2.83 % Refutation found
% 17.25/2.83 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 17.25/2.83 % SZS output start CNFRefutation for theBenchmark
% 17.25/2.83 fof(f1,axiom,(
% 17.25/2.83 (![X,Y]: (apply(apply(k,X),Y) = X ))),
% 17.25/2.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 17.25/2.83 fof(f2,axiom,(
% 17.25/2.83 (![X,Y,Z]: (apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,apply(k,Z)),apply(Y,Z)) ))),
% 17.25/2.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 17.25/2.83 fof(f3,negated_conjecture,(
% 17.25/2.83 (![Y]: (apply(apply(Y,b(Y)),c(Y)) != apply(b(Y),b(Y)) ))),
% 17.25/2.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 17.25/2.83 fof(f4,plain,(
% 17.25/2.83 ![X0,X1]: (apply(apply(k,X0),X1)=X0)),
% 17.25/2.83 inference(cnf_transformation,[status(thm)],[f1])).
% 17.25/2.83 fof(f5,plain,(
% 17.25/2.83 ![X0,X1,X2]: (apply(apply(apply(abstraction,X0),X1),X2)=apply(apply(X0,apply(k,X2)),apply(X1,X2)))),
% 17.25/2.83 inference(cnf_transformation,[status(thm)],[f2])).
% 17.25/2.83 fof(f6,plain,(
% 17.25/2.83 ![X0]: (~apply(apply(X0,b(X0)),c(X0))=apply(b(X0),b(X0)))),
% 17.25/2.83 inference(cnf_transformation,[status(thm)],[f3])).
% 17.25/2.83 fof(f7,definition,(
% 17.25/2.83 ![X0]: (sF1_fnc(X0)=apply(X0,b(X0)))),
% 17.25/2.83 introduced(definition,[new_symbols(definition,[sF1_fnc(X0)])],[function_definition])).
% 17.25/2.83 fof(f8,definition,(
% 17.25/2.83 ![X0]: (sF0_fnc(X0)=apply(sF1_fnc(X0),c(X0)))),
% 17.25/2.83 introduced(definition,[new_symbols(definition,[sF0_fnc(X0)])],[function_definition])).
% 17.25/2.83 fof(f9,definition,(
% 17.25/2.83 ![X0]: (sF2_fnc(X0)=apply(b(X0),b(X0)))),
% 17.25/2.83 introduced(definition,[new_symbols(definition,[sF2_fnc(X0)])],[function_definition])).
% 17.25/2.83 fof(f10,plain,(
% 17.25/2.83 ![X0]: (~sF0_fnc(X0)=sF2_fnc(X0))),
% 17.25/2.83 inference(definition_folding,[],[f6,f9,f8,f7])).
% 17.25/2.83 fof(f46,plain,(
% 17.25/2.83 ![X0,X1,X2]: (apply(apply(apply(abstraction,X0),apply(k,X1)),X2)=apply(apply(X0,apply(k,X2)),X1))),
% 17.25/2.83 inference(paramodulation,[status(thm)],[f4,f5])).
% 17.25/2.83 fof(f337,plain,(
% 17.25/2.83 ![X0,X1]: (apply(apply(apply(apply(abstraction,abstraction),k),X0),X1)=apply(apply(apply(k,X0),apply(k,X1)),X0))),
% 17.25/2.83 inference(paramodulation,[status(thm)],[f5,f46])).
% 17.25/2.83 fof(f362,plain,(
% 17.25/2.83 ![X0,X1]: (apply(apply(apply(apply(abstraction,abstraction),k),X0),X1)=apply(X0,X0))),
% 17.25/2.83 inference(forward_demodulation,[status(thm)],[f4,f337])).
% 17.25/2.83 fof(f881,plain,(
% 17.25/2.83 ![X0]: (apply(sF1_fnc(apply(apply(abstraction,abstraction),k)),X0)=apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k))))),
% 17.25/2.83 inference(paramodulation,[status(thm)],[f7,f362])).
% 17.25/2.83 fof(f939,plain,(
% 17.25/2.83 ![X0]: (apply(sF1_fnc(apply(apply(abstraction,abstraction),k)),X0)=sF2_fnc(apply(apply(abstraction,abstraction),k)))),
% 17.25/2.83 inference(forward_demodulation,[status(thm)],[f9,f881])).
% 17.25/2.83 fof(f24098,plain,(
% 17.25/2.83 sF0_fnc(apply(apply(abstraction,abstraction),k))=sF2_fnc(apply(apply(abstraction,abstraction),k))),
% 17.25/2.83 inference(paramodulation,[status(thm)],[f8,f939])).
% 17.25/2.83 fof(f24180,plain,(
% 17.25/2.83 $false),
% 17.25/2.83 inference(forward_subsumption_resolution,[status(thm)],[f24098,f10])).
% 17.25/2.83 % SZS output end CNFRefutation for theBenchmark.p
% 17.25/2.88 % Elapsed time: 2.344876 seconds
% 17.25/2.88 % CPU time: 18.373017 seconds
% 17.25/2.88 % Total memory used: 368.945 MB
% 17.25/2.88 % Net memory used: 367.286 MB
%------------------------------------------------------------------------------