%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : COL044-2 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 2.13s 1.08s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL044-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n014.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 14:06:35 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 2.13/1.08 % Refutation found
% 2.13/1.08 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.13/1.08 % SZS output start CNFRefutation for theBenchmark
% 2.13/1.08 fof(f1,axiom,(
% 2.13/1.08 (![X,Y,Z]: (apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ))),
% 2.13/1.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.13/1.08 fof(f2,axiom,(
% 2.13/1.08 (![X,Y,Z]: (apply(apply(apply(n,X),Y),Z) = apply(apply(apply(X,Z),Y),Z) ))),
% 2.13/1.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.13/1.08 fof(f3,axiom,(
% 2.13/1.08 (![Strong_fixed_point]: (( apply(Strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(Strong_fixed_point,fixed_pt))| fixed_point(Strong_fixed_point) ) ))),
% 2.13/1.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.13/1.08 fof(f4,negated_conjecture,(
% 2.13/1.08 ~ fixed_point(apply(apply(b,apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n)),b)),b)) ),
% 2.13/1.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.13/1.08 fof(f5,plain,(
% 2.13/1.08 ![X0,X1,X2]: (apply(apply(apply(b,X0),X1),X2)=apply(X0,apply(X1,X2)))),
% 2.13/1.08 inference(cnf_transformation,[status(thm)],[f1])).
% 2.13/1.08 fof(f6,plain,(
% 2.13/1.08 ![X0,X1,X2]: (apply(apply(apply(n,X0),X1),X2)=apply(apply(apply(X0,X2),X1),X2))),
% 2.13/1.08 inference(cnf_transformation,[status(thm)],[f2])).
% 2.13/1.08 fof(f7,plain,(
% 2.13/1.08 ![X0]: (~apply(X0,fixed_pt)=apply(fixed_pt,apply(X0,fixed_pt))|fixed_point(X0))),
% 2.13/1.08 inference(cnf_transformation,[status(thm)],[f3])).
% 2.13/1.08 fof(f8,plain,(
% 2.13/1.08 ~fixed_point(apply(apply(b,apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n)),b)),b))),
% 2.13/1.08 inference(cnf_transformation,[status(thm)],[f4])).
% 2.13/1.08 fof(f9,plain,(
% 2.13/1.08 ~apply(apply(apply(b,apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n)),b)),b),fixed_pt)=apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n)),b)),b),fixed_pt))),
% 2.13/1.08 inference(resolution,[status(thm)],[f7,f8])).
% 2.13/1.08 fof(f10,plain,(
% 2.13/1.08 ~apply(apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n)),b),apply(b,fixed_pt))=apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n)),b)),b),fixed_pt))),
% 2.13/1.08 inference(forward_demodulation,[status(thm)],[f5,f9])).
% 2.13/1.08 fof(f11,plain,(
% 2.13/1.08 ~apply(apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n),apply(b,apply(b,fixed_pt)))=apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n)),b)),b),fixed_pt))),
% 2.13/1.08 inference(forward_demodulation,[status(thm)],[f5,f10])).
% 2.13/1.08 fof(f12,plain,(
% 2.13/1.08 ~apply(apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n),apply(b,apply(b,fixed_pt)))=apply(fixed_pt,apply(apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n)),b),apply(b,fixed_pt)))),
% 2.13/1.08 inference(forward_demodulation,[status(thm)],[f5,f11])).
% 2.13/1.08 fof(f13,plain,(
% 2.13/1.08 ~apply(apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n),apply(b,apply(b,fixed_pt)))=apply(fixed_pt,apply(apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n),apply(b,apply(b,fixed_pt))))),
% 2.13/1.08 inference(forward_demodulation,[status(thm)],[f5,f12])).
% 2.13/1.08 fof(f20,plain,(
% 2.13/1.08 ![X0,X1,X2]: (apply(apply(apply(n,apply(b,X0)),X1),X2)=apply(apply(X0,apply(X2,X1)),X2))),
% 2.13/1.08 inference(paramodulation,[status(thm)],[f5,f6])).
% 2.13/1.08 fof(f23,plain,(
% 2.13/1.08 ![X0,X1,X2,X3]: (apply(apply(apply(n,apply(apply(b,X0),X1)),X2),X3)=apply(apply(apply(X0,apply(X1,X3)),X2),X3))),
% 2.13/1.08 inference(paramodulation,[status(thm)],[f5,f6])).
% 2.13/1.08 fof(f128,plain,(
% 2.13/1.08 ![X0,X1,X2]: (apply(apply(apply(n,apply(b,apply(b,X0))),X1),X2)=apply(X0,apply(apply(X2,X1),X2)))),
% 2.13/1.08 inference(paramodulation,[status(thm)],[f5,f20])).
% 2.13/1.08 fof(f287,plain,(
% 2.13/1.08 ![X0,X1,X2]: (apply(apply(apply(n,apply(apply(b,b),X0)),X1),X2)=apply(apply(X0,X2),apply(X1,X2)))),
% 2.13/1.08 inference(paramodulation,[status(thm)],[f5,f23])).
% 2.13/1.08 fof(f1551,plain,(
% 2.13/1.08 ~apply(apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n),apply(b,apply(b,fixed_pt)))=apply(fixed_pt,apply(apply(apply(apply(n,apply(apply(b,b),n)),n),apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))))),
% 2.13/1.09 inference(backward_demodulation,[status(thm)],[f287,f13])).
% 2.13/1.09 fof(f1762,plain,(
% 2.13/1.09 ~apply(apply(apply(apply(n,apply(apply(b,b),n)),n),apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt))))=apply(fixed_pt,apply(apply(apply(apply(n,apply(apply(b,b),n)),n),apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))))),
% 2.13/1.09 inference(forward_demodulation,[status(thm)],[f287,f1551])).
% 2.13/1.09 fof(f1763,plain,(
% 2.13/1.09 ~apply(apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),apply(n,apply(b,apply(b,fixed_pt))))=apply(fixed_pt,apply(apply(apply(apply(n,apply(apply(b,b),n)),n),apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))))),
% 2.13/1.09 inference(forward_demodulation,[status(thm)],[f287,f1762])).
% 2.13/1.09 fof(f1764,plain,(
% 2.13/1.09 ~apply(apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),apply(n,apply(b,apply(b,fixed_pt))))=apply(fixed_pt,apply(apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),apply(n,apply(b,apply(b,fixed_pt)))))),
% 2.13/1.09 inference(forward_demodulation,[status(thm)],[f287,f1763])).
% 2.13/1.09 fof(f1765,plain,(
% 2.13/1.09 ~apply(apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),apply(n,apply(b,apply(b,fixed_pt))))=apply(apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),apply(n,apply(b,apply(b,fixed_pt))))),
% 2.13/1.09 inference(forward_demodulation,[status(thm)],[f128,f1764])).
% 2.13/1.09 fof(f1766,plain,(
% 2.13/1.09 $false),
% 2.13/1.09 inference(trivial_equality_resolution,[status(thm)],[f1765])).
% 2.13/1.09 % SZS output end CNFRefutation for theBenchmark.p
% 0.69/1.11 % Elapsed time: 0.726530 seconds
% 0.69/1.11 % CPU time: 5.466025 seconds
% 0.69/1.11 % Total memory used: 125.295 MB
% 0.69/1.11 % Net memory used: 124.273 MB
%------------------------------------------------------------------------------