%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : COL030-1 : 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 : n020.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 12:08:57 PM UTC 2026
% Result : Unsatisfiable 20.12s 3.19s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL030-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.54 % Computer : n020.cluster.edu
% 0.09/0.54 % Model : x86_64 x86_64
% 0.09/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.54 % Memory : 8046.5625MB
% 0.09/0.54 % OS : Linux 6.8.0-71-generic
% 0.09/0.54 % CPULimit : 300
% 0.09/0.54 % WCLimit : 300
% 0.09/0.54 % DateTime : Mon Sep 21 14:06:32 UTC 2026
% 0.09/0.54 % CPUTime :
% 0.09/0.55 % Drodi V4.1.1
% 20.12/3.19 % Refutation found
% 20.12/3.19 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 20.12/3.19 % SZS output start CNFRefutation for theBenchmark
% 20.12/3.19 fof(f1,axiom,(
% 20.12/3.19 (![X,Y,Z]: (apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)) ))),
% 20.12/3.19 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 20.12/3.19 fof(f2,axiom,(
% 20.12/3.19 (![X,Y]: (apply(apply(l,X),Y) = apply(X,apply(Y,Y)) ))),
% 20.12/3.19 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 20.12/3.19 fof(f3,negated_conjecture,(
% 20.12/3.19 (![Y]: (apply(Y,f(Y)) != apply(f(Y),apply(Y,f(Y))) ))),
% 20.12/3.19 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 20.12/3.19 fof(f4,plain,(
% 20.12/3.19 ![X0,X1,X2]: (apply(apply(apply(s,X0),X1),X2)=apply(apply(X0,X2),apply(X1,X2)))),
% 20.12/3.19 inference(cnf_transformation,[status(thm)],[f1])).
% 20.12/3.19 fof(f5,plain,(
% 20.12/3.19 ![X0,X1]: (apply(apply(l,X0),X1)=apply(X0,apply(X1,X1)))),
% 20.12/3.19 inference(cnf_transformation,[status(thm)],[f2])).
% 20.12/3.19 fof(f6,plain,(
% 20.12/3.19 ![X0]: (~apply(X0,f(X0))=apply(f(X0),apply(X0,f(X0))))),
% 20.12/3.19 inference(cnf_transformation,[status(thm)],[f3])).
% 20.12/3.19 fof(f7,definition,(
% 20.12/3.19 ![X0]: (sF0_fnc(X0)=apply(X0,f(X0)))),
% 20.12/3.19 introduced(definition,[new_symbols(definition,[sF0_fnc(X0)])],[function_definition])).
% 20.12/3.19 fof(f8,definition,(
% 20.12/3.19 ![X0]: (sF1_fnc(X0)=apply(f(X0),sF0_fnc(X0)))),
% 20.12/3.19 introduced(definition,[new_symbols(definition,[sF1_fnc(X0)])],[function_definition])).
% 20.12/3.19 fof(f9,plain,(
% 20.12/3.19 ![X0]: (~sF0_fnc(X0)=sF1_fnc(X0))),
% 20.12/3.19 inference(definition_folding,[],[f6,f8,f7])).
% 20.12/3.19 fof(f120,plain,(
% 20.12/3.19 ![X0,X1,X2]: (apply(apply(l,X0),apply(X1,X2))=apply(X0,apply(apply(apply(s,X1),X1),X2)))),
% 20.12/3.19 inference(paramodulation,[status(thm)],[f4,f5])).
% 20.12/3.19 fof(f1063,plain,(
% 20.12/3.19 ![X0,X1]: (apply(apply(l,X0),apply(X1,f(apply(apply(s,X1),X1))))=apply(X0,sF0_fnc(apply(apply(s,X1),X1))))),
% 20.12/3.19 inference(paramodulation,[status(thm)],[f7,f120])).
% 20.12/3.19 fof(f18615,plain,(
% 20.12/3.19 ![X0]: (apply(apply(apply(s,l),X0),f(apply(apply(s,X0),X0)))=apply(f(apply(apply(s,X0),X0)),sF0_fnc(apply(apply(s,X0),X0))))),
% 20.12/3.19 inference(paramodulation,[status(thm)],[f4,f1063])).
% 20.12/3.19 fof(f18774,plain,(
% 20.12/3.19 ![X0]: (apply(apply(apply(s,l),X0),f(apply(apply(s,X0),X0)))=sF1_fnc(apply(apply(s,X0),X0)))),
% 20.12/3.19 inference(forward_demodulation,[status(thm)],[f8,f18615])).
% 20.12/3.19 fof(f19572,plain,(
% 20.12/3.19 sF0_fnc(apply(apply(s,l),l))=sF1_fnc(apply(apply(s,l),l))),
% 20.12/3.19 inference(paramodulation,[status(thm)],[f7,f18774])).
% 20.12/3.19 fof(f19663,plain,(
% 20.12/3.19 $false),
% 20.12/3.19 inference(forward_subsumption_resolution,[status(thm)],[f19572,f9])).
% 20.12/3.19 % SZS output end CNFRefutation for theBenchmark.p
% 20.12/3.23 % Elapsed time: 2.666574 seconds
% 20.12/3.23 % CPU time: 21.032499 seconds
% 20.12/3.23 % Total memory used: 303.724 MB
% 20.12/3.23 % Net memory used: 300.906 MB
%------------------------------------------------------------------------------