%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : COL044-6 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 12:09:00 PM UTC 2026
% Result : Unsatisfiable 116.21s 25.36s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL044-6 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/10.48 % Computer : n019.cluster.edu
% 0.20/10.48 % Model : x86_64 x86_64
% 0.20/10.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/10.48 % Memory : 8046.5625MB
% 0.20/10.48 % OS : Linux 6.8.0-71-generic
% 0.20/10.49 % CPULimit : 300
% 0.20/10.49 % WCLimit : 300
% 0.20/10.49 % DateTime : Mon Sep 21 14:07:01 UTC 2026
% 0.20/10.49 % CPUTime :
% 0.25/10.50 % Drodi V4.1.1
% 116.21/25.36 % Refutation found
% 116.21/25.36 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 116.21/25.36 % SZS output start CNFRefutation for theBenchmark
% 116.21/25.36 fof(f1,axiom,(
% 116.21/25.36 (![X,Y,Z]: (apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ))),
% 116.21/25.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 116.21/25.36 fof(f2,axiom,(
% 116.21/25.36 (![X,Y,Z]: (apply(apply(apply(n,X),Y),Z) = apply(apply(apply(X,Z),Y),Z) ))),
% 116.21/25.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 116.21/25.36 fof(f3,axiom,(
% 116.21/25.36 strong_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) ),
% 116.21/25.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 116.21/25.36 fof(f4,negated_conjecture,(
% 116.21/25.36 apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) ),
% 116.21/25.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 116.21/25.36 fof(f5,plain,(
% 116.21/25.36 ![X0,X1,X2]: (apply(apply(apply(b,X0),X1),X2)=apply(X0,apply(X1,X2)))),
% 116.21/25.36 inference(cnf_transformation,[status(thm)],[f1])).
% 116.21/25.36 fof(f6,plain,(
% 116.21/25.36 ![X0,X1,X2]: (apply(apply(apply(n,X0),X1),X2)=apply(apply(apply(X0,X2),X1),X2))),
% 116.21/25.36 inference(cnf_transformation,[status(thm)],[f2])).
% 116.21/25.36 fof(f7,plain,(
% 116.21/25.36 strong_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)),
% 116.21/25.36 inference(cnf_transformation,[status(thm)],[f3])).
% 116.21/25.36 fof(f8,plain,(
% 116.21/25.36 ~apply(strong_fixed_point,fixed_pt)=apply(fixed_pt,apply(strong_fixed_point,fixed_pt))),
% 116.21/25.36 inference(cnf_transformation,[status(thm)],[f4])).
% 116.21/25.36 fof(f12,plain,(
% 116.21/25.36 ![X0]: (apply(strong_fixed_point,X0)=apply(apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n)),b),apply(b,X0)))),
% 116.21/25.36 inference(paramodulation,[status(thm)],[f7,f5])).
% 116.21/25.36 fof(f13,plain,(
% 116.21/25.36 ![X0]: (apply(strong_fixed_point,X0)=apply(apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n),apply(b,apply(b,X0))))),
% 116.21/25.36 inference(forward_demodulation,[status(thm)],[f5,f12])).
% 116.21/25.36 fof(f21,plain,(
% 116.21/25.36 ![X0,X1,X2]: (apply(apply(apply(n,apply(b,X0)),X1),X2)=apply(apply(X0,apply(X2,X1)),X2))),
% 116.21/25.36 inference(paramodulation,[status(thm)],[f5,f6])).
% 116.21/25.36 fof(f26,plain,(
% 116.21/25.36 ![X0,X1,X2,X3]: (apply(apply(apply(n,apply(apply(b,X0),X1)),X2),X3)=apply(apply(apply(X0,apply(X1,X3)),X2),X3))),
% 116.21/25.36 inference(paramodulation,[status(thm)],[f5,f6])).
% 116.21/25.36 fof(f191,plain,(
% 116.21/25.36 ![X0,X1,X2]: (apply(apply(apply(n,apply(b,apply(b,X0))),X1),X2)=apply(X0,apply(apply(X2,X1),X2)))),
% 116.21/25.36 inference(paramodulation,[status(thm)],[f5,f21])).
% 116.21/25.36 fof(f1787,plain,(
% 116.21/25.36 ![X0,X1,X2]: (apply(apply(apply(n,apply(apply(b,b),X0)),X1),X2)=apply(apply(X0,X2),apply(X1,X2)))),
% 116.21/25.36 inference(paramodulation,[status(thm)],[f5,f26])).
% 116.21/25.36 fof(f5676,plain,(
% 116.21/25.36 ![X0]: (apply(strong_fixed_point,X0)=apply(apply(apply(apply(n,apply(apply(b,b),n)),n),apply(b,apply(b,X0))),apply(n,apply(b,apply(b,X0)))))),
% 116.21/25.36 inference(paramodulation,[status(thm)],[f13,f1787])).
% 116.21/25.36 fof(f9085,plain,(
% 116.21/25.36 ![X0]: (apply(strong_fixed_point,X0)=apply(apply(apply(n,apply(b,apply(b,X0))),apply(n,apply(b,apply(b,X0)))),apply(n,apply(b,apply(b,X0)))))),
% 116.21/25.36 inference(paramodulation,[status(thm)],[f1787,f5676])).
% 116.21/25.36 fof(f9205,plain,(
% 116.21/25.36 ![X0,X1]: (apply(apply(apply(n,apply(b,apply(b,X0))),apply(n,apply(b,apply(b,X1)))),apply(n,apply(b,apply(b,X1))))=apply(X0,apply(strong_fixed_point,X1)))),
% 116.21/25.36 inference(paramodulation,[status(thm)],[f9085,f191])).
% 116.21/25.36 fof(f9269,plain,(
% 116.21/25.36 ![X0]: (apply(strong_fixed_point,X0)=apply(X0,apply(strong_fixed_point,X0)))),
% 116.21/25.36 inference(backward_demodulation,[status(thm)],[f9205,f9085])).
% 116.21/25.36 fof(f9289,plain,(
% 116.21/25.36 ~apply(strong_fixed_point,fixed_pt)=apply(strong_fixed_point,fixed_pt)),
% 116.21/25.36 inference(backward_demodulation,[status(thm)],[f9269,f8])).
% 116.21/25.36 fof(f9297,plain,(
% 116.21/25.36 $false),
% 116.21/25.36 inference(trivial_equality_resolution,[status(thm)],[f9289])).
% 116.21/25.36 % SZS output end CNFRefutation for theBenchmark.p
% 19.38/32.26 % Elapsed time: 21.758868 seconds
% 19.38/32.26 % CPU time: 168.719622 seconds
% 19.38/32.26 % Total memory used: 66.645 GB
% 19.38/32.26 % Net memory used: 66.641 GB
%------------------------------------------------------------------------------