%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : COL002-4 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 0.24s 0.35s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : COL002-4 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.02 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Mon Sep 21 14:02:51 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 % Drodi V4.1.1
% 0.24/0.35 % Refutation found
% 0.24/0.35 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.24/0.35 % SZS output start CNFRefutation for theBenchmark
% 0.24/0.35 fof(f1,axiom,(
% 0.24/0.35 (![X,Y,Z]: (apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)) ))),
% 0.24/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.35 fof(f2,axiom,(
% 0.24/0.35 (![X,Y,Z]: (apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ))),
% 0.24/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.35 fof(f4,axiom,(
% 0.24/0.35 (![X]: (apply(i,X) = X ))),
% 0.24/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.35 fof(f5,axiom,(
% 0.24/0.35 (![X]: (weak_fixed_point(X) = apply(apply(apply(s,apply(b,X)),i),apply(apply(s,apply(b,X)),i)) ))),
% 0.24/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.35 fof(f6,negated_conjecture,(
% 0.24/0.35 weak_fixed_point(fixed_pt) != apply(fixed_pt,weak_fixed_point(fixed_pt)) ),
% 0.24/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.35 fof(f7,plain,(
% 0.24/0.35 ![X0,X1,X2]: (apply(apply(apply(s,X0),X1),X2)=apply(apply(X0,X2),apply(X1,X2)))),
% 0.24/0.35 inference(cnf_transformation,[status(thm)],[f1])).
% 0.24/0.35 fof(f8,plain,(
% 0.24/0.35 ![X0,X1,X2]: (apply(apply(apply(b,X0),X1),X2)=apply(X0,apply(X1,X2)))),
% 0.24/0.35 inference(cnf_transformation,[status(thm)],[f2])).
% 0.24/0.35 fof(f10,plain,(
% 0.24/0.35 ![X0]: (apply(i,X0)=X0)),
% 0.24/0.35 inference(cnf_transformation,[status(thm)],[f4])).
% 0.24/0.35 fof(f11,plain,(
% 0.24/0.35 ![X0]: (weak_fixed_point(X0)=apply(apply(apply(s,apply(b,X0)),i),apply(apply(s,apply(b,X0)),i)))),
% 0.24/0.35 inference(cnf_transformation,[status(thm)],[f5])).
% 0.24/0.35 fof(f12,plain,(
% 0.24/0.35 ~weak_fixed_point(fixed_pt)=apply(fixed_pt,weak_fixed_point(fixed_pt))),
% 0.24/0.35 inference(cnf_transformation,[status(thm)],[f6])).
% 0.24/0.35 fof(f13,definition,(
% 0.24/0.35 sF0_fnc=weak_fixed_point(fixed_pt)),
% 0.24/0.35 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 0.24/0.35 fof(f14,definition,(
% 0.24/0.35 sF1_fnc=apply(fixed_pt,sF0_fnc)),
% 0.24/0.35 introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition])).
% 0.24/0.35 fof(f15,plain,(
% 0.24/0.35 ~sF0_fnc=sF1_fnc),
% 0.24/0.35 inference(definition_folding,[],[f12,f14,f13])).
% 0.24/0.35 fof(f30,plain,(
% 0.24/0.35 ![X0,X1]: (apply(apply(apply(s,X0),i),X1)=apply(apply(X0,X1),X1))),
% 0.24/0.35 inference(paramodulation,[status(thm)],[f10,f7])).
% 0.24/0.35 fof(f39,plain,(
% 0.24/0.35 ![X0,X1]: (apply(apply(apply(s,apply(b,X0)),i),X1)=apply(X0,apply(X1,X1)))),
% 0.24/0.35 inference(paramodulation,[status(thm)],[f8,f30])).
% 0.24/0.35 fof(f458,plain,(
% 0.24/0.35 ![X0,X1]: (apply(apply(apply(s,apply(b,X0)),i),apply(apply(s,apply(b,X1)),i))=apply(X0,weak_fixed_point(X1)))),
% 0.24/0.35 inference(paramodulation,[status(thm)],[f11,f39])).
% 0.24/0.35 fof(f520,plain,(
% 0.24/0.35 ![X0]: (weak_fixed_point(X0)=apply(X0,weak_fixed_point(X0)))),
% 0.24/0.35 inference(backward_demodulation,[status(thm)],[f458,f11])).
% 0.24/0.35 fof(f615,plain,(
% 0.24/0.35 weak_fixed_point(fixed_pt)=apply(fixed_pt,sF0_fnc)),
% 0.24/0.35 inference(paramodulation,[status(thm)],[f13,f520])).
% 0.24/0.35 fof(f638,plain,(
% 0.24/0.35 sF1_fnc=sF0_fnc),
% 0.24/0.35 inference(backward_demodulation,[status(thm)],[f639,f14])).
% 0.24/0.35 fof(f639,plain,(
% 0.24/0.35 sF0_fnc=apply(fixed_pt,sF0_fnc)),
% 0.24/0.35 inference(forward_demodulation,[status(thm)],[f13,f615])).
% 0.24/0.35 fof(f644,plain,(
% 0.24/0.35 $false),
% 0.24/0.35 inference(forward_subsumption_resolution,[status(thm)],[f638,f15])).
% 0.24/0.35 % SZS output end CNFRefutation for theBenchmark.p
% 0.24/0.35 % Elapsed time: 0.054455 seconds
% 0.24/0.35 % CPU time: 0.319858 seconds
% 0.24/0.35 % Total memory used: 25.819 MB
% 0.24/0.35 % Net memory used: 25.560 MB
%------------------------------------------------------------------------------