%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : COL004-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 12:08:55 PM UTC 2026
% Result : Unsatisfiable 0.21s 5.70s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL004-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/5.66 % Computer : n020.cluster.edu
% 0.18/5.66 % Model : x86_64 x86_64
% 0.18/5.66 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.66 % Memory : 8046.5625MB
% 0.18/5.66 % OS : Linux 6.8.0-71-generic
% 0.18/5.66 % CPULimit : 300
% 0.18/5.66 % WCLimit : 300
% 0.18/5.66 % DateTime : Mon Sep 21 14:05:08 UTC 2026
% 0.18/5.66 % CPUTime :
% 0.18/5.67 % Drodi V4.1.1
% 0.21/5.70 % Refutation found
% 0.21/5.70 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.21/5.70 % SZS output start CNFRefutation for theBenchmark
% 0.21/5.70 fof(f1,axiom,(
% 0.21/5.70 (![X,Y,Z]: (apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)) ))),
% 0.21/5.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/5.70 fof(f2,axiom,(
% 0.21/5.70 (![X,Y]: (apply(apply(k,X),Y) = X ))),
% 0.21/5.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/5.70 fof(f3,negated_conjecture,(
% 0.21/5.70 apply(apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x),y) != apply(y,apply(apply(x,x),y)) ),
% 0.21/5.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/5.70 fof(f4,plain,(
% 0.21/5.70 ![X0,X1,X2]: (apply(apply(apply(s,X0),X1),X2)=apply(apply(X0,X2),apply(X1,X2)))),
% 0.21/5.70 inference(cnf_transformation,[status(thm)],[f1])).
% 0.21/5.70 fof(f5,plain,(
% 0.21/5.70 ![X0,X1]: (apply(apply(k,X0),X1)=X0)),
% 0.21/5.70 inference(cnf_transformation,[status(thm)],[f2])).
% 0.21/5.70 fof(f6,plain,(
% 0.21/5.70 ~apply(apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x),y)=apply(y,apply(apply(x,x),y))),
% 0.21/5.70 inference(cnf_transformation,[status(thm)],[f3])).
% 0.21/5.70 fof(f30,plain,(
% 0.21/5.70 ~apply(apply(apply(apply(k,apply(s,apply(apply(s,k),k))),x),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x)),y)=apply(y,apply(apply(x,x),y))),
% 0.21/5.70 inference(paramodulation,[status(thm)],[f4,f6])).
% 0.21/5.70 fof(f31,plain,(
% 0.21/5.70 ~apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x)),y)=apply(y,apply(apply(x,x),y))),
% 0.21/5.70 inference(forward_demodulation,[status(thm)],[f5,f30])).
% 0.21/5.70 fof(f33,plain,(
% 0.21/5.70 ~apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(apply(apply(s,k),k),x),apply(apply(apply(s,k),k),x))),y)=apply(y,apply(apply(x,x),y))),
% 0.21/5.70 inference(paramodulation,[status(thm)],[f4,f31])).
% 0.21/5.70 fof(f34,plain,(
% 0.21/5.70 ![X0,X1]: (apply(apply(apply(s,k),X0),X1)=X1)),
% 0.21/5.70 inference(paramodulation,[status(thm)],[f4,f5])).
% 0.21/5.70 fof(f38,plain,(
% 0.21/5.70 ~apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(apply(apply(s,k),k),x),x)),y)=apply(y,apply(apply(x,x),y))),
% 0.21/5.70 inference(backward_demodulation,[status(thm)],[f34,f33])).
% 0.21/5.70 fof(f41,plain,(
% 0.21/5.70 ~apply(apply(apply(s,apply(apply(s,k),k)),apply(x,x)),y)=apply(y,apply(apply(x,x),y))),
% 0.21/5.70 inference(forward_demodulation,[status(thm)],[f34,f38])).
% 0.21/5.70 fof(f47,plain,(
% 0.21/5.70 ![X0,X1,X2]: (apply(apply(apply(s,apply(apply(s,k),X0)),X1),X2)=apply(X2,apply(X1,X2)))),
% 0.21/5.70 inference(paramodulation,[status(thm)],[f34,f4])).
% 0.21/5.70 fof(f49,plain,(
% 0.21/5.70 $false),
% 0.21/5.70 inference(backward_subsumption_resolution,[status(thm)],[f41,f47])).
% 0.21/5.70 % SZS output end CNFRefutation for theBenchmark.p
% 1.43/6.93 % Elapsed time: 1.040030 seconds
% 1.43/6.93 % CPU time: 0.036936 seconds
% 1.43/6.93 % Total memory used: 587.184 KB
% 1.43/6.93 % Net memory used: 566.976 KB
%------------------------------------------------------------------------------