%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : COL003-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 2.46s 1.04s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL003-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 14:08:44 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 2.46/1.04 % Refutation found
% 2.46/1.04 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.46/1.04 % SZS output start CNFRefutation for theBenchmark
% 2.46/1.04 fof(f1,axiom,(
% 2.46/1.04 (![A,B,C]: (ifeq(A,A,B,C) = B ))),
% 2.46/1.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.46/1.04 fof(f2,axiom,(
% 2.46/1.04 (![X,Y,Z]: (apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ))),
% 2.46/1.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.46/1.04 fof(f3,axiom,(
% 2.46/1.04 (![X,Y]: (apply(apply(w,X),Y) = apply(apply(X,Y),Y) ))),
% 2.46/1.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.46/1.04 fof(f4,axiom,(
% 2.46/1.04 (![Strong_fixed_point]: (ifeq(apply(Strong_fixed_point,fixed_pt),apply(fixed_pt,apply(Strong_fixed_point,fixed_pt)),fixed_point(Strong_fixed_point),true) = true ))),
% 2.46/1.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.46/1.04 fof(f5,negated_conjecture,(
% 2.46/1.04 fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b)) != true ),
% 2.46/1.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.46/1.04 fof(f6,plain,(
% 2.46/1.04 ![X0,X1,X2]: (ifeq(X0,X0,X1,X2)=X1)),
% 2.46/1.04 inference(cnf_transformation,[status(thm)],[f1])).
% 2.46/1.04 fof(f7,plain,(
% 2.46/1.04 ![X0,X1,X2]: (apply(apply(apply(b,X0),X1),X2)=apply(X0,apply(X1,X2)))),
% 2.46/1.04 inference(cnf_transformation,[status(thm)],[f2])).
% 2.46/1.04 fof(f8,plain,(
% 2.46/1.04 ![X0,X1]: (apply(apply(w,X0),X1)=apply(apply(X0,X1),X1))),
% 2.46/1.04 inference(cnf_transformation,[status(thm)],[f3])).
% 2.46/1.04 fof(f9,plain,(
% 2.46/1.04 ![X0]: (ifeq(apply(X0,fixed_pt),apply(fixed_pt,apply(X0,fixed_pt)),fixed_point(X0),true)=true)),
% 2.46/1.04 inference(cnf_transformation,[status(thm)],[f4])).
% 2.46/1.04 fof(f10,plain,(
% 2.46/1.04 ~fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b))=true),
% 2.46/1.04 inference(cnf_transformation,[status(thm)],[f5])).
% 2.46/1.04 fof(f11,definition,(
% 2.46/1.04 sF5_fnc=apply(w,w)),
% 2.46/1.04 introduced(definition,[new_symbols(definition,[sF5_fnc])],[function_definition])).
% 2.46/1.04 fof(f12,definition,(
% 2.46/1.04 sF4_fnc=apply(b,sF5_fnc)),
% 2.46/1.04 introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition])).
% 2.46/1.04 fof(f13,definition,(
% 2.46/1.04 sF8_fnc=apply(b,w)),
% 2.46/1.04 introduced(definition,[new_symbols(definition,[sF8_fnc])],[function_definition])).
% 2.46/1.04 fof(f14,definition,(
% 2.46/1.04 sF7_fnc=apply(b,sF8_fnc)),
% 2.46/1.04 introduced(definition,[new_symbols(definition,[sF7_fnc])],[function_definition])).
% 2.46/1.04 fof(f15,definition,(
% 2.46/1.04 sF6_fnc=apply(sF7_fnc,b)),
% 2.46/1.04 introduced(definition,[new_symbols(definition,[sF6_fnc])],[function_definition])).
% 2.46/1.04 fof(f16,definition,(
% 2.46/1.04 sF3_fnc=apply(sF4_fnc,sF6_fnc)),
% 2.46/1.04 introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition])).
% 2.46/1.04 fof(f17,definition,(
% 2.46/1.04 sF2_fnc=apply(b,sF3_fnc)),
% 2.46/1.04 introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition])).
% 2.46/1.04 fof(f18,definition,(
% 2.46/1.04 sF1_fnc=apply(sF2_fnc,b)),
% 2.46/1.04 introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition])).
% 2.46/1.04 fof(f19,definition,(
% 2.46/1.04 sF0_fnc=fixed_point(sF1_fnc)),
% 2.46/1.04 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 2.46/1.04 fof(f20,plain,(
% 2.46/1.04 ~sF0_fnc=true),
% 2.46/1.04 inference(definition_folding,[],[f10,f19,f18,f17,f16,f15,f14,f13,f12,f11])).
% 2.46/1.04 fof(f21,plain,(
% 2.46/1.04 ![X0,X1]: (apply(apply(sF8_fnc,X0),X1)=apply(w,apply(X0,X1)))),
% 2.46/1.04 inference(paramodulation,[status(thm)],[f13,f7])).
% 2.46/1.04 fof(f22,plain,(
% 2.46/1.04 ![X0,X1]: (apply(apply(sF4_fnc,X0),X1)=apply(sF5_fnc,apply(X0,X1)))),
% 2.46/1.04 inference(paramodulation,[status(thm)],[f12,f7])).
% 2.46/1.04 fof(f23,plain,(
% 2.46/1.04 ![X0,X1]: (apply(apply(sF7_fnc,X0),X1)=apply(sF8_fnc,apply(X0,X1)))),
% 2.46/1.04 inference(paramodulation,[status(thm)],[f14,f7])).
% 2.46/1.04 fof(f24,plain,(
% 2.46/1.04 ![X0,X1]: (apply(apply(sF2_fnc,X0),X1)=apply(sF3_fnc,apply(X0,X1)))),
% 2.46/1.04 inference(paramodulation,[status(thm)],[f17,f7])).
% 2.46/1.04 fof(f26,plain,(
% 2.46/1.04 ![X0]: (apply(apply(w,w),X0)=apply(apply(X0,X0),X0))),
% 2.46/1.04 inference(paramodulation,[status(thm)],[f8,f8])).
% 2.46/1.04 fof(f27,plain,(
% 2.46/1.04 ![X0]: (apply(sF5_fnc,X0)=apply(apply(w,X0),X0))),
% 2.46/1.04 inference(paramodulation,[status(thm)],[f11,f8])).
% 2.46/1.04 fof(f37,plain,(
% 2.46/1.04 ![X0,X1,X2]: (apply(apply(w,apply(apply(b,X0),X1)),X2)=apply(apply(X0,apply(X1,X2)),X2))),
% 2.46/1.04 inference(paramodulation,[status(thm)],[f7,f8])).
% 2.46/1.04 fof(f42,plain,(
% 2.46/1.04 ![X0]: (apply(sF5_fnc,X0)=apply(apply(X0,X0),X0))),
% 2.46/1.04 inference(forward_demodulation,[status(thm)],[f11,f26])).
% 5.09/1.07 fof(f81,plain,(
% 5.09/1.07 ifeq(apply(sF1_fnc,fixed_pt),apply(fixed_pt,apply(sF1_fnc,fixed_pt)),sF0_fnc,true)=true),
% 5.09/1.07 inference(paramodulation,[status(thm)],[f19,f9])).
% 5.09/1.07 fof(f92,plain,(
% 5.09/1.07 ![X0]: (apply(sF3_fnc,X0)=apply(sF5_fnc,apply(sF6_fnc,X0)))),
% 5.09/1.07 inference(paramodulation,[status(thm)],[f16,f22])).
% 5.09/1.07 fof(f106,plain,(
% 5.09/1.07 ![X0]: (apply(sF6_fnc,X0)=apply(sF8_fnc,apply(b,X0)))),
% 5.09/1.07 inference(paramodulation,[status(thm)],[f15,f23])).
% 5.09/1.07 fof(f121,plain,(
% 5.09/1.07 ![X0,X1]: (apply(apply(sF6_fnc,X0),X1)=apply(w,apply(apply(b,X0),X1)))),
% 5.09/1.07 inference(paramodulation,[status(thm)],[f106,f21])).
% 5.09/1.07 fof(f125,plain,(
% 5.09/1.07 ![X0,X1,X2]: (apply(apply(apply(sF6_fnc,X0),X1),X2)=apply(apply(X0,apply(X1,X2)),X2))),
% 5.09/1.07 inference(backward_demodulation,[status(thm)],[f121,f37])).
% 5.09/1.07 fof(f133,plain,(
% 5.09/1.07 ![X0]: (apply(sF1_fnc,X0)=apply(sF3_fnc,apply(b,X0)))),
% 5.09/1.07 inference(paramodulation,[status(thm)],[f18,f24])).
% 5.09/1.07 fof(f3917,plain,(
% 5.09/1.07 ![X0,X1]: (apply(apply(w,apply(sF6_fnc,X0)),X1)=apply(apply(X0,apply(X1,X1)),X1))),
% 5.09/1.07 inference(paramodulation,[status(thm)],[f8,f125])).
% 5.09/1.07 fof(f5074,plain,(
% 5.09/1.07 ![X0,X1]: (apply(apply(w,apply(sF6_fnc,apply(b,X0))),X1)=apply(X0,apply(apply(X1,X1),X1)))),
% 5.09/1.07 inference(paramodulation,[status(thm)],[f7,f3917])).
% 5.09/1.07 fof(f5232,plain,(
% 5.09/1.07 ![X0,X1]: (apply(apply(w,apply(sF6_fnc,apply(b,X0))),X1)=apply(X0,apply(sF5_fnc,X1)))),
% 5.09/1.07 inference(forward_demodulation,[status(thm)],[f42,f5074])).
% 5.09/1.07 fof(f10014,plain,(
% 5.09/1.07 ![X0]: (apply(sF5_fnc,apply(sF6_fnc,apply(b,X0)))=apply(X0,apply(sF5_fnc,apply(sF6_fnc,apply(b,X0)))))),
% 5.09/1.07 inference(paramodulation,[status(thm)],[f27,f5232])).
% 5.09/1.07 fof(f10097,plain,(
% 5.09/1.07 ![X0]: (apply(sF3_fnc,apply(b,X0))=apply(X0,apply(sF5_fnc,apply(sF6_fnc,apply(b,X0)))))),
% 5.09/1.07 inference(forward_demodulation,[status(thm)],[f92,f10014])).
% 5.09/1.07 fof(f10098,plain,(
% 5.09/1.07 ![X0]: (apply(sF1_fnc,X0)=apply(X0,apply(sF5_fnc,apply(sF6_fnc,apply(b,X0)))))),
% 5.09/1.07 inference(forward_demodulation,[status(thm)],[f133,f10097])).
% 5.09/1.07 fof(f10099,plain,(
% 5.09/1.07 ![X0]: (apply(sF1_fnc,X0)=apply(X0,apply(sF3_fnc,apply(b,X0))))),
% 5.09/1.07 inference(forward_demodulation,[status(thm)],[f92,f10098])).
% 5.09/1.07 fof(f10100,plain,(
% 5.09/1.07 ifeq(apply(sF1_fnc,fixed_pt),apply(sF1_fnc,fixed_pt),sF0_fnc,true)=true),
% 5.09/1.07 inference(backward_demodulation,[status(thm)],[f10105,f81])).
% 5.09/1.07 fof(f10105,plain,(
% 5.09/1.07 ![X0]: (apply(sF1_fnc,X0)=apply(X0,apply(sF1_fnc,X0)))),
% 5.09/1.07 inference(forward_demodulation,[status(thm)],[f133,f10099])).
% 5.09/1.07 fof(f10207,plain,(
% 5.09/1.07 sF0_fnc=true),
% 5.09/1.07 inference(forward_demodulation,[status(thm)],[f6,f10100])).
% 5.09/1.07 fof(f10208,plain,(
% 5.09/1.07 $false),
% 5.09/1.07 inference(forward_subsumption_resolution,[status(thm)],[f10207,f20])).
% 5.09/1.07 % SZS output end CNFRefutation for theBenchmark.p
% 1.87/1.11 % Elapsed time: 0.728155 seconds
% 1.87/1.11 % CPU time: 5.487402 seconds
% 1.87/1.11 % Total memory used: 112.757 MB
% 1.87/1.11 % Net memory used: 111.484 MB
%------------------------------------------------------------------------------