%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : COL043-2 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 12:08:59 PM UTC 2026
% Result : Unsatisfiable 1.66s 0.87s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL043-2 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n018.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 14:08:28 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 1.66/0.87 % Refutation found
% 1.66/0.87 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.66/0.87 % SZS output start CNFRefutation for theBenchmark
% 1.66/0.87 fof(f1,axiom,(
% 1.66/0.87 (![X,Y,Z]: (apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ))),
% 1.66/0.87 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.66/0.87 fof(f2,axiom,(
% 1.66/0.87 (![X,Y,Z]: (apply(apply(apply(h,X),Y),Z) = apply(apply(apply(X,Y),Z),Y) ))),
% 1.66/0.87 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.66/0.87 fof(f3,axiom,(
% 1.66/0.87 (![Strong_fixed_point]: (( apply(Strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(Strong_fixed_point,fixed_pt))| fixed_point(Strong_fixed_point) ) ))),
% 1.66/0.87 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.66/0.87 fof(f4,negated_conjecture,(
% 1.66/0.87 ~ fixed_point(apply(apply(b,apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b)),b)) ),
% 1.66/0.87 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.66/0.87 fof(f5,plain,(
% 1.66/0.87 ![X0,X1,X2]: (apply(apply(apply(b,X0),X1),X2)=apply(X0,apply(X1,X2)))),
% 1.66/0.87 inference(cnf_transformation,[status(thm)],[f1])).
% 1.66/0.88 fof(f6,plain,(
% 1.66/0.88 ![X0,X1,X2]: (apply(apply(apply(h,X0),X1),X2)=apply(apply(apply(X0,X1),X2),X1))),
% 1.66/0.88 inference(cnf_transformation,[status(thm)],[f2])).
% 1.66/0.88 fof(f7,plain,(
% 1.66/0.88 ![X0]: (~apply(X0,fixed_pt)=apply(fixed_pt,apply(X0,fixed_pt))|fixed_point(X0))),
% 1.66/0.88 inference(cnf_transformation,[status(thm)],[f3])).
% 1.66/0.88 fof(f8,plain,(
% 1.66/0.88 ~fixed_point(apply(apply(b,apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b)),b))),
% 1.66/0.88 inference(cnf_transformation,[status(thm)],[f4])).
% 1.66/0.88 fof(f15,plain,(
% 1.66/0.88 ![X0,X1,X2]: (apply(apply(apply(h,apply(b,X0)),X1),X2)=apply(apply(X0,apply(X1,X2)),X1))),
% 1.66/0.88 inference(paramodulation,[status(thm)],[f5,f6])).
% 1.66/0.88 fof(f18,plain,(
% 1.66/0.88 ![X0,X1,X2,X3]: (apply(apply(apply(h,apply(apply(b,X0),X1)),X2),X3)=apply(apply(apply(X0,apply(X1,X2)),X3),X2))),
% 1.66/0.88 inference(paramodulation,[status(thm)],[f5,f6])).
% 1.66/0.88 fof(f21,plain,(
% 1.66/0.88 ~apply(apply(apply(b,apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b)),b),fixed_pt)=apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b)),b),fixed_pt))),
% 1.66/0.88 inference(resolution,[status(thm)],[f7,f8])).
% 1.66/0.88 fof(f22,plain,(
% 1.66/0.88 ~apply(apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b),apply(b,fixed_pt))=apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b)),b),fixed_pt))),
% 1.66/0.88 inference(forward_demodulation,[status(thm)],[f5,f21])).
% 1.66/0.88 fof(f23,plain,(
% 1.66/0.88 ~apply(apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h),apply(b,apply(b,fixed_pt)))=apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b)),b),fixed_pt))),
% 1.66/0.88 inference(forward_demodulation,[status(thm)],[f5,f22])).
% 1.66/0.88 fof(f24,plain,(
% 1.66/0.88 ~apply(apply(apply(apply(apply(b,h),apply(b,b)),apply(apply(h,apply(apply(b,h),apply(b,b))),h)),apply(b,apply(b,fixed_pt))),h)=apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b)),b),fixed_pt))),
% 1.66/0.88 inference(forward_demodulation,[status(thm)],[f18,f23])).
% 1.66/0.88 fof(f25,plain,(
% 1.66/0.88 ~apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h)=apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b)),b),fixed_pt))),
% 1.66/0.88 inference(forward_demodulation,[status(thm)],[f5,f24])).
% 1.66/0.88 fof(f26,plain,(
% 1.66/0.88 ~apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h)=apply(fixed_pt,apply(apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b),apply(b,fixed_pt)))),
% 1.66/0.90 inference(forward_demodulation,[status(thm)],[f5,f25])).
% 1.66/0.90 fof(f27,plain,(
% 1.66/0.90 ~apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h)=apply(fixed_pt,apply(apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h),apply(b,apply(b,fixed_pt))))),
% 1.66/0.90 inference(forward_demodulation,[status(thm)],[f5,f26])).
% 1.66/0.90 fof(f28,plain,(
% 1.66/0.90 ~apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h)=apply(fixed_pt,apply(apply(apply(apply(apply(b,h),apply(b,b)),apply(apply(h,apply(apply(b,h),apply(b,b))),h)),apply(b,apply(b,fixed_pt))),h))),
% 1.66/0.90 inference(forward_demodulation,[status(thm)],[f18,f27])).
% 1.66/0.90 fof(f29,plain,(
% 1.66/0.90 ~apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h)=apply(fixed_pt,apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h))),
% 1.66/0.90 inference(forward_demodulation,[status(thm)],[f5,f28])).
% 1.66/0.90 fof(f138,plain,(
% 1.66/0.90 ![X0,X1,X2]: (apply(apply(apply(h,apply(b,apply(b,X0))),X1),X2)=apply(X0,apply(apply(X1,X2),X1)))),
% 1.66/0.90 inference(paramodulation,[status(thm)],[f5,f15])).
% 1.66/0.90 fof(f643,plain,(
% 1.66/0.90 ![X0,X1,X2]: (apply(apply(apply(h,apply(apply(b,b),X0)),X1),X2)=apply(apply(X0,X1),apply(X2,X1)))),
% 1.66/0.90 inference(paramodulation,[status(thm)],[f5,f18])).
% 1.66/0.90 fof(f754,plain,(
% 1.66/0.90 ~apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h)=apply(fixed_pt,apply(apply(apply(apply(h,apply(apply(b,h),apply(b,b))),h),apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))))),
% 1.66/0.90 inference(backward_demodulation,[status(thm)],[f643,f29])).
% 1.66/0.90 fof(f797,plain,(
% 1.66/0.90 ~apply(apply(apply(apply(h,apply(apply(b,h),apply(b,b))),h),apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt))))=apply(fixed_pt,apply(apply(apply(apply(h,apply(apply(b,h),apply(b,b))),h),apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))))),
% 1.66/0.90 inference(forward_demodulation,[status(thm)],[f643,f754])).
% 1.66/0.90 fof(f798,plain,(
% 1.66/0.90 ~apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt))))=apply(fixed_pt,apply(apply(apply(apply(h,apply(apply(b,h),apply(b,b))),h),apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))))),
% 1.66/0.90 inference(forward_demodulation,[status(thm)],[f18,f797])).
% 1.66/0.90 fof(f799,plain,(
% 1.66/0.90 ~apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt))))=apply(fixed_pt,apply(apply(apply(apply(h,apply(apply(b,h),apply(b,b))),h),apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))))),
% 1.66/0.90 inference(forward_demodulation,[status(thm)],[f643,f798])).
% 1.66/0.90 fof(f800,plain,(
% 1.66/0.90 ~apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt))))=apply(fixed_pt,apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt)))))),
% 1.66/0.90 inference(forward_demodulation,[status(thm)],[f18,f799])).
% 1.66/0.90 fof(f801,plain,(
% 1.66/0.90 ~apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt))))=apply(fixed_pt,apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt)))))),
% 1.66/0.90 inference(forward_demodulation,[status(thm)],[f643,f800])).
% 1.66/0.90 fof(f802,plain,(
% 1.66/0.90 ~apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt))))=apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt))))),
% 1.66/0.90 inference(forward_demodulation,[status(thm)],[f138,f801])).
% 1.66/0.90 fof(f803,plain,(
% 1.66/0.90 $false),
% 1.66/0.90 inference(trivial_equality_resolution,[status(thm)],[f802])).
% 1.66/0.90 % SZS output end CNFRefutation for theBenchmark.p
% 1.66/0.92 % Elapsed time: 0.529674 seconds
% 1.66/0.92 % CPU time: 3.904257 seconds
% 1.66/0.92 % Total memory used: 114.847 MB
% 1.66/0.92 % Net memory used: 114.023 MB
%------------------------------------------------------------------------------