%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : COL002-1 : 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 : 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 12:08:53 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.47s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 14:03:53 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.14/0.47 % Refutation found
% 0.14/0.47 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.47 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.47 fof(f1,axiom,(
% 0.14/0.47 (![X,Y,Z]: (apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)) ))),
% 0.14/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f2,axiom,(
% 0.14/0.47 (![X,Y,Z]: (apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ))),
% 0.14/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f4,axiom,(
% 0.14/0.47 (![X]: (apply(i,X) = X ))),
% 0.14/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f5,negated_conjecture,(
% 0.14/0.47 (![Y]: (Y != apply(fixed_pt,Y) ))),
% 0.14/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f6,plain,(
% 0.14/0.47 ![X0,X1,X2]: (apply(apply(apply(s,X0),X1),X2)=apply(apply(X0,X2),apply(X1,X2)))),
% 0.14/0.47 inference(cnf_transformation,[status(thm)],[f1])).
% 0.14/0.47 fof(f7,plain,(
% 0.14/0.47 ![X0,X1,X2]: (apply(apply(apply(b,X0),X1),X2)=apply(X0,apply(X1,X2)))),
% 0.14/0.47 inference(cnf_transformation,[status(thm)],[f2])).
% 0.14/0.47 fof(f9,plain,(
% 0.14/0.47 ![X0]: (apply(i,X0)=X0)),
% 0.14/0.47 inference(cnf_transformation,[status(thm)],[f4])).
% 0.14/0.47 fof(f10,plain,(
% 0.14/0.47 ![X0]: (~X0=apply(fixed_pt,X0))),
% 0.14/0.47 inference(cnf_transformation,[status(thm)],[f5])).
% 0.14/0.47 fof(f11,definition,(
% 0.14/0.47 ![X0]: (sF0_fnc(X0)=apply(fixed_pt,X0))),
% 0.14/0.47 introduced(definition,[new_symbols(definition,[sF0_fnc(X0)])],[function_definition])).
% 0.14/0.47 fof(f12,plain,(
% 0.14/0.47 ![X0]: (~X0=sF0_fnc(X0))),
% 0.14/0.47 inference(definition_folding,[],[f10,f11])).
% 0.14/0.47 fof(f22,plain,(
% 0.14/0.47 ![X0,X1]: (apply(apply(apply(s,X0),i),X1)=apply(apply(X0,X1),X1))),
% 0.14/0.47 inference(paramodulation,[status(thm)],[f9,f6])).
% 0.14/0.47 fof(f318,plain,(
% 0.14/0.47 ![X0,X1]: (apply(apply(apply(s,apply(b,X0)),i),X1)=apply(X0,apply(X1,X1)))),
% 0.14/0.47 inference(paramodulation,[status(thm)],[f7,f22])).
% 0.14/0.47 fof(f520,plain,(
% 0.14/0.47 ![X0]: (apply(apply(apply(s,apply(b,fixed_pt)),i),X0)=sF0_fnc(apply(X0,X0)))),
% 0.14/0.47 inference(paramodulation,[status(thm)],[f11,f318])).
% 0.14/0.47 fof(f1266,plain,(
% 0.14/0.47 ![X0]: (~apply(X0,X0)=apply(apply(apply(s,apply(b,fixed_pt)),i),X0))),
% 0.14/0.47 inference(paramodulation,[status(thm)],[f520,f12])).
% 0.14/0.47 fof(f1276,plain,(
% 0.14/0.47 $false),
% 0.14/0.47 inference(destructive_equality_resolution,[status(thm)],[f1266])).
% 0.14/0.47 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.48 % Elapsed time: 0.099353 seconds
% 0.14/0.48 % CPU time: 0.650982 seconds
% 0.14/0.48 % Total memory used: 23.057 MB
% 0.14/0.48 % Net memory used: 22.811 MB
%------------------------------------------------------------------------------