%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : COL003-12 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 282.86s 36.08s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL003-12 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n005.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 21 14:03:02 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Drodi V4.1.1
% 282.86/36.08 % Refutation found
% 282.86/36.08 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 282.86/36.08 % SZS output start CNFRefutation for theBenchmark
% 282.86/36.08 fof(f1,axiom,(
% 282.86/36.08 (![X,Y,Z]: (apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ))),
% 282.86/36.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 282.86/36.08 fof(f2,axiom,(
% 282.86/36.08 (![X,Y]: (apply(apply(w,X),Y) = apply(apply(X,Y),Y) ))),
% 282.86/36.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 282.86/36.08 fof(f3,axiom,(
% 282.86/36.08 strong_fixed_point = apply(apply(b,apply(w,w)),apply(apply(b,w),apply(apply(b,b),b))) ),
% 282.86/36.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 282.86/36.08 fof(f4,negated_conjecture,(
% 282.86/36.08 apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) ),
% 282.86/36.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 282.86/36.08 fof(f5,plain,(
% 282.86/36.08 ![X0,X1,X2]: (apply(apply(apply(b,X0),X1),X2)=apply(X0,apply(X1,X2)))),
% 282.86/36.08 inference(cnf_transformation,[status(thm)],[f1])).
% 282.86/36.08 fof(f6,plain,(
% 282.86/36.08 ![X0,X1]: (apply(apply(w,X0),X1)=apply(apply(X0,X1),X1))),
% 282.86/36.08 inference(cnf_transformation,[status(thm)],[f2])).
% 282.86/36.08 fof(f7,plain,(
% 282.86/36.08 strong_fixed_point=apply(apply(b,apply(w,w)),apply(apply(b,w),apply(apply(b,b),b)))),
% 282.86/36.08 inference(cnf_transformation,[status(thm)],[f3])).
% 282.86/36.08 fof(f8,plain,(
% 282.86/36.08 ~apply(strong_fixed_point,fixed_pt)=apply(fixed_pt,apply(strong_fixed_point,fixed_pt))),
% 282.86/36.08 inference(cnf_transformation,[status(thm)],[f4])).
% 282.86/36.08 fof(f13,plain,(
% 282.86/36.08 ![X0]: (apply(apply(w,w),X0)=apply(apply(X0,X0),X0))),
% 282.86/36.08 inference(paramodulation,[status(thm)],[f6,f6])).
% 282.86/36.08 fof(f27,plain,(
% 282.86/36.08 ![X0,X1]: (apply(apply(w,apply(b,X0)),X1)=apply(X0,apply(X1,X1)))),
% 282.86/36.08 inference(paramodulation,[status(thm)],[f6,f5])).
% 282.86/36.08 fof(f45,plain,(
% 282.86/36.08 ![X0,X1]: (apply(apply(w,apply(w,apply(b,X0))),X1)=apply(apply(X0,apply(X1,X1)),X1))),
% 282.86/36.08 inference(paramodulation,[status(thm)],[f27,f6])).
% 282.86/36.08 fof(f53,plain,(
% 282.86/36.08 ![X0]: (apply(strong_fixed_point,X0)=apply(apply(w,w),apply(apply(apply(b,w),apply(apply(b,b),b)),X0)))),
% 282.86/36.08 inference(paramodulation,[status(thm)],[f7,f5])).
% 282.86/36.08 fof(f55,plain,(
% 282.86/36.08 ![X0]: (apply(strong_fixed_point,X0)=apply(apply(w,w),apply(w,apply(apply(apply(b,b),b),X0))))),
% 282.86/36.08 inference(forward_demodulation,[status(thm)],[f5,f53])).
% 282.86/36.08 fof(f56,plain,(
% 282.86/36.08 ![X0]: (apply(strong_fixed_point,X0)=apply(apply(w,w),apply(w,apply(b,apply(b,X0)))))),
% 282.86/36.08 inference(forward_demodulation,[status(thm)],[f5,f55])).
% 282.86/36.08 fof(f517,plain,(
% 282.86/36.08 ![X0,X1]: (apply(apply(w,apply(w,apply(b,apply(b,X0)))),X1)=apply(X0,apply(apply(X1,X1),X1)))),
% 282.86/36.08 inference(paramodulation,[status(thm)],[f5,f45])).
% 282.86/36.08 fof(f11233,plain,(
% 282.86/36.08 ![X0,X1]: (apply(apply(w,apply(w,apply(b,apply(b,X0)))),X1)=apply(X0,apply(apply(w,w),X1)))),
% 282.86/36.08 inference(paramodulation,[status(thm)],[f13,f517])).
% 282.86/36.08 fof(f124172,plain,(
% 282.86/36.08 ![X0]: (apply(apply(w,w),apply(w,apply(b,apply(b,X0))))=apply(X0,apply(apply(w,w),apply(w,apply(b,apply(b,X0))))))),
% 282.86/36.08 inference(paramodulation,[status(thm)],[f6,f11233])).
% 282.86/36.08 fof(f124642,plain,(
% 282.86/36.08 ![X0]: (apply(strong_fixed_point,X0)=apply(X0,apply(apply(w,w),apply(w,apply(b,apply(b,X0))))))),
% 282.86/36.08 inference(forward_demodulation,[status(thm)],[f56,f124172])).
% 282.86/36.08 fof(f124643,plain,(
% 282.86/36.08 ![X0]: (apply(strong_fixed_point,X0)=apply(X0,apply(strong_fixed_point,X0)))),
% 282.86/36.08 inference(forward_demodulation,[status(thm)],[f56,f124642])).
% 282.86/36.08 fof(f126490,plain,(
% 282.86/36.08 ~apply(strong_fixed_point,fixed_pt)=apply(strong_fixed_point,fixed_pt)),
% 282.86/36.08 inference(backward_demodulation,[status(thm)],[f124643,f8])).
% 282.86/36.08 fof(f126895,plain,(
% 282.86/36.08 $false),
% 282.86/36.08 inference(trivial_equality_resolution,[status(thm)],[f126490])).
% 282.86/36.08 % SZS output end CNFRefutation for theBenchmark.p
% 35.58/36.37 % Elapsed time: 36.002508 seconds
% 35.58/36.37 % CPU time: 284.997972 seconds
% 35.58/36.37 % Total memory used: 1.182 GB
% 35.58/36.37 % Net memory used: 1.147 GB
%------------------------------------------------------------------------------