%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : COL002-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 0.09s 10.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL002-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/10.36 % Computer : n003.cluster.edu
% 0.09/10.36 % Model : x86_64 x86_64
% 0.09/10.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.36 % Memory : 8046.5625MB
% 0.09/10.36 % OS : Linux 6.8.0-71-generic
% 0.09/10.36 % CPULimit : 300
% 0.09/10.36 % WCLimit : 300
% 0.09/10.36 % DateTime : Mon Sep 21 14:04:42 UTC 2026
% 0.09/10.36 % CPUTime :
% 0.09/10.37 % Drodi V4.1.1
% 0.09/10.40 % Refutation found
% 0.09/10.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/10.40 % SZS output start CNFRefutation for theBenchmark
% 0.09/10.40 fof(f1,axiom,(
% 0.09/10.40 (![A,B,C]: (ifeq(A,A,B,C) = B ))),
% 0.09/10.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/10.40 fof(f2,axiom,(
% 0.09/10.40 (![X,Y,Z]: (apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)) ))),
% 0.09/10.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/10.40 fof(f3,axiom,(
% 0.09/10.40 (![X,Y,Z]: (apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ))),
% 0.09/10.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/10.40 fof(f5,axiom,(
% 0.09/10.40 (![X]: (apply(i,X) = X ))),
% 0.09/10.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/10.40 fof(f6,axiom,(
% 0.09/10.40 (![Weak_sage]: (ifeq(Weak_sage,apply(fixed_pt,Weak_sage),fixed_point(Weak_sage),true) = true ))),
% 0.09/10.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/10.40 fof(f7,negated_conjecture,(
% 0.09/10.40 (![X]: (fixed_point(apply(apply(apply(s,apply(b,X)),i),apply(apply(s,apply(b,X)),i))) != true ))),
% 0.09/10.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/10.40 fof(f8,plain,(
% 0.09/10.40 ![X0,X1,X2]: (ifeq(X0,X0,X1,X2)=X1)),
% 0.09/10.40 inference(cnf_transformation,[status(thm)],[f1])).
% 0.09/10.40 fof(f9,plain,(
% 0.09/10.40 ![X0,X1,X2]: (apply(apply(apply(s,X0),X1),X2)=apply(apply(X0,X2),apply(X1,X2)))),
% 0.09/10.40 inference(cnf_transformation,[status(thm)],[f2])).
% 0.09/10.40 fof(f10,plain,(
% 0.09/10.40 ![X0,X1,X2]: (apply(apply(apply(b,X0),X1),X2)=apply(X0,apply(X1,X2)))),
% 0.09/10.40 inference(cnf_transformation,[status(thm)],[f3])).
% 0.09/10.40 fof(f12,plain,(
% 0.09/10.40 ![X0]: (apply(i,X0)=X0)),
% 0.09/10.40 inference(cnf_transformation,[status(thm)],[f5])).
% 0.09/10.40 fof(f13,plain,(
% 0.09/10.40 ![X0]: (ifeq(X0,apply(fixed_pt,X0),fixed_point(X0),true)=true)),
% 0.09/10.40 inference(cnf_transformation,[status(thm)],[f6])).
% 0.09/10.40 fof(f14,plain,(
% 0.09/10.40 ![X0]: (~fixed_point(apply(apply(apply(s,apply(b,X0)),i),apply(apply(s,apply(b,X0)),i)))=true)),
% 0.09/10.40 inference(cnf_transformation,[status(thm)],[f7])).
% 0.09/10.40 fof(f15,definition,(
% 0.09/10.40 ![X0]: (sF4_fnc(X0)=apply(b,X0))),
% 0.09/10.40 introduced(definition,[new_symbols(definition,[sF4_fnc(X0)])],[function_definition])).
% 0.09/10.40 fof(f16,definition,(
% 0.09/10.40 ![X0]: (sF3_fnc(X0)=apply(s,sF4_fnc(X0)))),
% 0.09/10.40 introduced(definition,[new_symbols(definition,[sF3_fnc(X0)])],[function_definition])).
% 0.09/10.40 fof(f17,definition,(
% 0.09/10.40 ![X0]: (sF2_fnc(X0)=apply(sF3_fnc(X0),i))),
% 0.09/10.40 introduced(definition,[new_symbols(definition,[sF2_fnc(X0)])],[function_definition])).
% 0.09/10.40 fof(f18,definition,(
% 0.09/10.40 ![X0]: (sF6_fnc(X0)=apply(s,sF4_fnc(X0)))),
% 0.09/10.40 introduced(definition,[new_symbols(definition,[sF6_fnc(X0)])],[function_definition])).
% 0.09/10.40 fof(f19,definition,(
% 0.09/10.40 ![X0]: (sF5_fnc(X0)=apply(sF6_fnc(X0),i))),
% 0.09/10.40 introduced(definition,[new_symbols(definition,[sF5_fnc(X0)])],[function_definition])).
% 0.09/10.40 fof(f20,definition,(
% 0.09/10.40 ![X0]: (sF1_fnc(X0)=apply(sF2_fnc(X0),sF5_fnc(X0)))),
% 0.09/10.40 introduced(definition,[new_symbols(definition,[sF1_fnc(X0)])],[function_definition])).
% 0.09/10.40 fof(f21,definition,(
% 0.09/10.40 ![X0]: (sF0_fnc(X0)=fixed_point(sF1_fnc(X0)))),
% 0.09/10.40 introduced(definition,[new_symbols(definition,[sF0_fnc(X0)])],[function_definition])).
% 0.09/10.40 fof(f22,plain,(
% 0.09/10.40 ![X0]: (~sF0_fnc(X0)=true)),
% 0.09/10.40 inference(definition_folding,[],[f14,f21,f20,f19,f18,f17,f16,f15])).
% 0.09/10.40 fof(f23,plain,(
% 0.09/10.40 ![X0]: (sF6_fnc(X0)=sF3_fnc(X0))),
% 0.09/10.40 inference(forward_demodulation,[status(thm)],[f16,f18])).
% 0.09/10.40 fof(f24,plain,(
% 0.09/10.40 ![X0]: (sF5_fnc(X0)=apply(sF3_fnc(X0),i))),
% 0.09/10.40 inference(forward_demodulation,[status(thm)],[f23,f19])).
% 0.09/10.40 fof(f25,plain,(
% 0.09/10.40 ![X0]: (sF5_fnc(X0)=sF2_fnc(X0))),
% 0.09/10.40 inference(forward_demodulation,[status(thm)],[f17,f24])).
% 0.09/10.40 fof(f26,plain,(
% 0.09/10.40 ![X0]: (sF1_fnc(X0)=apply(sF2_fnc(X0),sF2_fnc(X0)))),
% 0.09/10.40 inference(forward_demodulation,[status(thm)],[f25,f20])).
% 0.09/10.40 fof(f27,plain,(
% 0.09/10.40 ![X0,X1,X2]: (apply(apply(sF4_fnc(X0),X1),X2)=apply(X0,apply(X1,X2)))),
% 0.09/10.40 inference(forward_demodulation,[status(thm)],[f15,f10])).
% 0.09/10.40 fof(f30,plain,(
% 0.09/10.40 ![X0,X1,X2]: (apply(apply(sF3_fnc(X0),X1),X2)=apply(apply(sF4_fnc(X0),X2),apply(X1,X2)))),
% 0.09/10.40 inference(paramodulation,[status(thm)],[f16,f9])).
% 0.09/10.40 fof(f48,plain,(
% 0.09/10.40 ![X0,X1,X2]: (apply(apply(sF3_fnc(X0),X1),X2)=apply(X0,apply(X2,apply(X1,X2))))),
% 0.09/10.40 inference(forward_demodulation,[status(thm)],[f27,f30])).
% 0.09/10.40 fof(f121,plain,(
% 0.09/10.40 ![X0,X1]: (apply(apply(sF3_fnc(X0),i),X1)=apply(X0,apply(X1,X1)))),
% 0.09/10.40 inference(paramodulation,[status(thm)],[f12,f48])).
% 0.13/10.41 fof(f146,plain,(
% 0.13/10.41 ![X0,X1]: (apply(sF2_fnc(X0),X1)=apply(X0,apply(X1,X1)))),
% 0.13/10.41 inference(forward_demodulation,[status(thm)],[f17,f121])).
% 0.13/10.41 fof(f169,plain,(
% 0.13/10.41 ![X0,X1]: (apply(sF2_fnc(X0),sF2_fnc(X1))=apply(X0,sF1_fnc(X1)))),
% 0.13/10.41 inference(paramodulation,[status(thm)],[f26,f146])).
% 0.13/10.41 fof(f543,plain,(
% 0.13/10.41 ![X0]: (sF1_fnc(X0)=apply(X0,sF1_fnc(X0)))),
% 0.13/10.41 inference(backward_demodulation,[status(thm)],[f169,f26])).
% 0.13/10.41 fof(f576,plain,(
% 0.13/10.41 ifeq(sF1_fnc(fixed_pt),sF1_fnc(fixed_pt),fixed_point(sF1_fnc(fixed_pt)),true)=true),
% 0.13/10.41 inference(paramodulation,[status(thm)],[f543,f13])).
% 0.13/10.41 fof(f603,plain,(
% 0.13/10.41 fixed_point(sF1_fnc(fixed_pt))=true),
% 0.13/10.41 inference(forward_demodulation,[status(thm)],[f8,f576])).
% 0.13/10.41 fof(f604,plain,(
% 0.13/10.41 sF0_fnc(fixed_pt)=true),
% 0.13/10.41 inference(forward_demodulation,[status(thm)],[f21,f603])).
% 0.13/10.41 fof(f605,plain,(
% 0.13/10.41 $false),
% 0.13/10.41 inference(forward_subsumption_resolution,[status(thm)],[f604,f22])).
% 0.13/10.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/10.41 % Elapsed time: 0.045304 seconds
% 0.13/10.41 % CPU time: 0.243501 seconds
% 0.13/10.41 % Total memory used: 9.058 MB
% 0.13/10.41 % Net memory used: 8.998 MB
%------------------------------------------------------------------------------