%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : COL081-2 : 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 : n016.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 12:09:06 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.42s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL081-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n016.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 14:14:26 UTC 2026
% 0.14/0.37 % CPUTime :
% 0.14/0.39 % Drodi V4.1.1
% 0.14/0.42 % Refutation found
% 0.14/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.42 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.42 fof(f1,axiom,(
% 0.14/0.42 (![X,Y]: (apply(k(X),Y) = X ))),
% 0.14/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.42 fof(f2,axiom,(
% 0.14/0.42 (![X,Y,Z]: (apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,k(Z)),apply(Y,Z)) ))),
% 0.14/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.42 fof(f3,axiom,(
% 0.14/0.42 (![X,Y]: (( X = Y| apply(X,n(X,Y)) != apply(Y,n(X,Y)) ) ))),
% 0.14/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.42 fof(f5,negated_conjecture,(
% 0.14/0.42 k(k(b)) != apply(abstraction,k(k(b))) ),
% 0.14/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.42 fof(f6,plain,(
% 0.14/0.42 ![X0,X1]: (apply(k(X0),X1)=X0)),
% 0.14/0.42 inference(cnf_transformation,[status(thm)],[f1])).
% 0.14/0.42 fof(f7,plain,(
% 0.14/0.42 ![X0,X1,X2]: (apply(apply(apply(abstraction,X0),X1),X2)=apply(apply(X0,k(X2)),apply(X1,X2)))),
% 0.14/0.42 inference(cnf_transformation,[status(thm)],[f2])).
% 0.14/0.42 fof(f8,plain,(
% 0.14/0.42 ![X0,X1]: (X0=X1|~apply(X0,n(X0,X1))=apply(X1,n(X0,X1)))),
% 0.14/0.42 inference(cnf_transformation,[status(thm)],[f3])).
% 0.14/0.42 fof(f10,plain,(
% 0.14/0.42 ~k(k(b))=apply(abstraction,k(k(b)))),
% 0.14/0.42 inference(cnf_transformation,[status(thm)],[f5])).
% 0.14/0.42 fof(f11,plain,(
% 0.14/0.42 ![X0,X1]: (k(X0)=X1|~X0=apply(X1,n(k(X0),X1)))),
% 0.14/0.42 inference(paramodulation,[status(thm)],[f6,f8])).
% 0.14/0.42 fof(f19,plain,(
% 0.14/0.42 ![X0,X1,X2]: (apply(apply(apply(abstraction,k(X0)),X1),X2)=apply(X0,apply(X1,X2)))),
% 0.14/0.42 inference(paramodulation,[status(thm)],[f6,f7])).
% 0.14/0.42 fof(f141,plain,(
% 0.14/0.42 ![X0,X1,X2]: (k(X0)=apply(apply(abstraction,k(X1)),X2)|~X0=apply(X1,apply(X2,n(k(X0),apply(apply(abstraction,k(X1)),X2)))))),
% 0.14/0.42 inference(paramodulation,[status(thm)],[f19,f11])).
% 0.14/0.42 fof(f149,plain,(
% 0.14/0.42 ![X0,X1]: (k(X0)=apply(apply(abstraction,k(k(X0))),X1))),
% 0.14/0.42 inference(resolution,[status(thm)],[f141,f6])).
% 0.14/0.42 fof(f179,plain,(
% 0.14/0.42 ![X0]: (k(k(X0))=apply(abstraction,k(k(X0))))),
% 0.14/0.42 inference(resolution,[status(thm)],[f149,f11])).
% 0.14/0.42 fof(f198,plain,(
% 0.14/0.42 ~k(k(b))=k(k(b))),
% 0.14/0.42 inference(backward_demodulation,[status(thm)],[f179,f10])).
% 0.14/0.42 fof(f216,plain,(
% 0.14/0.42 $false),
% 0.14/0.42 inference(trivial_equality_resolution,[status(thm)],[f198])).
% 0.14/0.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.45 % Elapsed time: 0.074092 seconds
% 0.14/0.45 % CPU time: 0.188511 seconds
% 0.14/0.45 % Total memory used: 68.219 MB
% 0.14/0.45 % Net memory used: 67.659 MB
%------------------------------------------------------------------------------