%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : COL078-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 12:09:05 PM UTC 2026
% Result : Unsatisfiable 56.97s 7.69s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL078-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n003.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 14:11:02 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.15/0.39 % Drodi V4.1.1
% 56.97/7.69 % Refutation found
% 56.97/7.69 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 56.97/7.69 % SZS output start CNFRefutation for theBenchmark
% 56.97/7.69 fof(f1,axiom,(
% 56.97/7.69 (![X,Y]: (apply(k(X),Y) = X ))),
% 56.97/7.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 56.97/7.69 fof(f6,axiom,(
% 56.97/7.69 (![X,Y,Z]: (apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,k(Z)),apply(Y,Z)) ))),
% 56.97/7.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 56.97/7.69 fof(f9,axiom,(
% 56.97/7.69 (![X,Y]: (( X = Y| apply(X,n(X,Y)) != apply(Y,n(X,Y)) ) ))),
% 56.97/7.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 56.97/7.69 fof(f11,axiom,(
% 56.97/7.69 (![X]: (apply(identity,X) = X ))),
% 56.97/7.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 56.97/7.69 fof(f12,negated_conjecture,(
% 56.97/7.69 apply(apply(apply(abstraction,abstraction),abstraction),abstraction) != k(k(identity)) ),
% 56.97/7.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 56.97/7.69 fof(f13,plain,(
% 56.97/7.69 ![X0,X1]: (apply(k(X0),X1)=X0)),
% 56.97/7.69 inference(cnf_transformation,[status(thm)],[f1])).
% 56.97/7.69 fof(f18,plain,(
% 56.97/7.69 ![X0,X1,X2]: (apply(apply(apply(abstraction,X0),X1),X2)=apply(apply(X0,k(X2)),apply(X1,X2)))),
% 56.97/7.69 inference(cnf_transformation,[status(thm)],[f6])).
% 56.97/7.69 fof(f21,plain,(
% 56.97/7.69 ![X0,X1]: (X0=X1|~apply(X0,n(X0,X1))=apply(X1,n(X0,X1)))),
% 56.97/7.69 inference(cnf_transformation,[status(thm)],[f9])).
% 56.97/7.69 fof(f23,plain,(
% 56.97/7.69 ![X0]: (apply(identity,X0)=X0)),
% 56.97/7.69 inference(cnf_transformation,[status(thm)],[f11])).
% 56.97/7.69 fof(f24,plain,(
% 56.97/7.69 ~apply(apply(apply(abstraction,abstraction),abstraction),abstraction)=k(k(identity))),
% 56.97/7.69 inference(cnf_transformation,[status(thm)],[f12])).
% 56.97/7.69 fof(f25,plain,(
% 56.97/7.69 ![X0,X1,X2]: (apply(apply(apply(abstraction,k(X0)),X1),X2)=apply(X0,apply(X1,X2)))),
% 56.97/7.69 inference(paramodulation,[status(thm)],[f13,f18])).
% 56.97/7.69 fof(f37,plain,(
% 56.97/7.69 ![X0,X1,X2]: (apply(apply(apply(apply(abstraction,abstraction),X0),X1),X2)=apply(X1,apply(apply(X0,X1),X2)))),
% 56.97/7.69 inference(paramodulation,[status(thm)],[f18,f25])).
% 56.97/7.69 fof(f419,plain,(
% 56.97/7.69 ![X0,X1,X2]: (apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),X0)),X1),X2)=apply(k(X2),apply(apply(X0,k(X2)),apply(X1,X2))))),
% 56.97/7.69 inference(paramodulation,[status(thm)],[f18,f37])).
% 56.97/7.69 fof(f508,plain,(
% 56.97/7.69 ![X0,X1,X2]: (apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),X0)),X1),X2)=X2)),
% 56.97/7.69 inference(forward_demodulation,[status(thm)],[f13,f419])).
% 56.97/7.69 fof(f566,plain,(
% 56.97/7.69 ![X0,X1]: (k(X0)=X1|~X0=apply(X1,n(k(X0),X1)))),
% 56.97/7.69 inference(paramodulation,[status(thm)],[f13,f21])).
% 56.97/7.69 fof(f578,plain,(
% 56.97/7.69 ![X0,X1]: (X0=k(X1)|~apply(X0,n(X0,k(X1)))=X1)),
% 56.97/7.69 inference(paramodulation,[status(thm)],[f13,f21])).
% 56.97/7.69 fof(f579,plain,(
% 56.97/7.69 ![X0]: (X0=identity|~apply(X0,n(X0,identity))=n(X0,identity))),
% 56.97/7.69 inference(paramodulation,[status(thm)],[f23,f21])).
% 56.97/7.69 fof(f616,plain,(
% 56.97/7.69 ![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)))))),
% 56.97/7.69 inference(paramodulation,[status(thm)],[f25,f566])).
% 56.97/7.69 fof(f13122,plain,(
% 56.97/7.69 ![X0,X1]: (apply(apply(abstraction,apply(apply(abstraction,abstraction),X0)),X1)=identity)),
% 56.97/7.69 inference(resolution,[status(thm)],[f508,f579])).
% 56.97/7.69 fof(f13356,plain,(
% 56.97/7.69 ![X0]: (apply(abstraction,apply(apply(abstraction,abstraction),X0))=k(identity))),
% 56.97/7.69 inference(resolution,[status(thm)],[f13122,f578])).
% 56.97/7.69 fof(f47127,plain,(
% 56.97/7.69 k(k(identity))=apply(apply(abstraction,k(abstraction)),apply(abstraction,abstraction))),
% 56.97/7.69 inference(resolution,[status(thm)],[f616,f13356])).
% 56.97/7.69 fof(f47238,plain,(
% 56.97/7.69 k(k(identity))=apply(apply(apply(abstraction,abstraction),abstraction),abstraction)),
% 56.97/7.69 inference(forward_demodulation,[status(thm)],[f18,f47127])).
% 56.97/7.69 fof(f47239,plain,(
% 56.97/7.69 $false),
% 56.97/7.69 inference(forward_subsumption_resolution,[status(thm)],[f47238,f24])).
% 56.97/7.69 % SZS output end CNFRefutation for theBenchmark.p
% 26.18/7.75 % Elapsed time: 7.359136 seconds
% 26.18/7.75 % CPU time: 57.957231 seconds
% 26.18/7.75 % Total memory used: 853.901 MB
% 26.18/7.75 % Net memory used: 812.557 MB
%------------------------------------------------------------------------------