%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : COL078-2 : 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 : n012.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 0.08s 10.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL078-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/10.36 % Computer : n012.cluster.edu
% 0.08/10.36 % Model : x86_64 x86_64
% 0.08/10.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.36 % Memory : 8046.5625MB
% 0.08/10.36 % OS : Linux 6.8.0-71-generic
% 0.08/10.36 % CPULimit : 300
% 0.08/10.36 % WCLimit : 300
% 0.08/10.36 % DateTime : Mon Sep 21 14:09:17 UTC 2026
% 0.08/10.36 % CPUTime :
% 0.08/10.36 % Drodi V4.1.1
% 0.08/10.40 % Refutation found
% 0.08/10.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/10.40 % SZS output start CNFRefutation for theBenchmark
% 0.08/10.40 fof(f1,axiom,(
% 0.08/10.40 (![X,Y]: (apply(k(X),Y) = X ))),
% 0.08/10.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/10.40 fof(f2,axiom,(
% 0.08/10.40 (![X,Y,Z]: (apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,k(Z)),apply(Y,Z)) ))),
% 0.08/10.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/10.40 fof(f3,axiom,(
% 0.08/10.40 (![X,Y]: (( X = Y| apply(X,n(X,Y)) != apply(Y,n(X,Y)) ) ))),
% 0.08/10.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/10.40 fof(f4,axiom,(
% 0.08/10.40 (![X]: (apply(identity,X) = X ))),
% 0.08/10.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/10.40 fof(f5,negated_conjecture,(
% 0.08/10.40 apply(apply(apply(abstraction,abstraction),abstraction),abstraction) != k(k(identity)) ),
% 0.08/10.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/10.40 fof(f6,plain,(
% 0.08/10.40 ![X0,X1]: (apply(k(X0),X1)=X0)),
% 0.08/10.40 inference(cnf_transformation,[status(thm)],[f1])).
% 0.08/10.40 fof(f7,plain,(
% 0.08/10.40 ![X0,X1,X2]: (apply(apply(apply(abstraction,X0),X1),X2)=apply(apply(X0,k(X2)),apply(X1,X2)))),
% 0.08/10.40 inference(cnf_transformation,[status(thm)],[f2])).
% 0.08/10.40 fof(f8,plain,(
% 0.08/10.40 ![X0,X1]: (X0=X1|~apply(X0,n(X0,X1))=apply(X1,n(X0,X1)))),
% 0.08/10.40 inference(cnf_transformation,[status(thm)],[f3])).
% 0.08/10.40 fof(f9,plain,(
% 0.08/10.40 ![X0]: (apply(identity,X0)=X0)),
% 0.08/10.40 inference(cnf_transformation,[status(thm)],[f4])).
% 0.08/10.40 fof(f10,plain,(
% 0.08/10.40 ~apply(apply(apply(abstraction,abstraction),abstraction),abstraction)=k(k(identity))),
% 0.08/10.40 inference(cnf_transformation,[status(thm)],[f5])).
% 0.08/10.40 fof(f11,plain,(
% 0.08/10.40 ![X0,X1]: (k(X0)=X1|~X0=apply(X1,n(k(X0),X1)))),
% 0.08/10.40 inference(paramodulation,[status(thm)],[f6,f8])).
% 0.08/10.40 fof(f13,plain,(
% 0.08/10.40 ![X0,X1]: (X0=k(X1)|~apply(X0,n(X0,k(X1)))=X1)),
% 0.08/10.40 inference(paramodulation,[status(thm)],[f6,f8])).
% 0.08/10.40 fof(f14,plain,(
% 0.08/10.40 ![X0]: (X0=identity|~apply(X0,n(X0,identity))=n(X0,identity))),
% 0.08/10.40 inference(paramodulation,[status(thm)],[f9,f8])).
% 0.08/10.40 fof(f19,plain,(
% 0.08/10.40 ![X0,X1,X2]: (apply(apply(apply(abstraction,k(X0)),X1),X2)=apply(X0,apply(X1,X2)))),
% 0.08/10.40 inference(paramodulation,[status(thm)],[f6,f7])).
% 0.08/10.40 fof(f118,plain,(
% 0.08/10.40 ![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)))))),
% 0.08/10.40 inference(paramodulation,[status(thm)],[f19,f11])).
% 0.08/10.40 fof(f120,plain,(
% 0.08/10.40 ![X0,X1,X2]: (apply(apply(abstraction,k(X0)),X1)=k(X2)|~apply(X0,apply(X1,n(apply(apply(abstraction,k(X0)),X1),k(X2))))=X2)),
% 0.08/10.40 inference(paramodulation,[status(thm)],[f19,f13])).
% 0.08/10.40 fof(f126,plain,(
% 0.08/10.40 ![X0,X1]: (k(X0)=apply(apply(abstraction,k(k(X0))),X1))),
% 0.08/10.40 inference(resolution,[status(thm)],[f118,f6])).
% 0.08/10.40 fof(f147,plain,(
% 0.08/10.40 ![X0,X1]: (k(X0)=apply(apply(apply(abstraction,abstraction),X1),k(X0)))),
% 0.08/10.40 inference(paramodulation,[status(thm)],[f7,f126])).
% 0.08/10.40 fof(f274,plain,(
% 0.08/10.40 ![X0,X1,X2]: (apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),X0)),X1),X2)=apply(k(X2),apply(X1,X2)))),
% 0.08/10.40 inference(paramodulation,[status(thm)],[f147,f7])).
% 0.08/10.40 fof(f281,plain,(
% 0.08/10.40 ![X0,X1,X2]: (apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),X0)),X1),X2)=X2)),
% 0.08/10.40 inference(forward_demodulation,[status(thm)],[f6,f274])).
% 0.08/10.40 fof(f284,plain,(
% 0.08/10.40 ![X0,X1]: (apply(apply(abstraction,apply(apply(abstraction,abstraction),X0)),X1)=identity)),
% 0.08/10.40 inference(resolution,[status(thm)],[f281,f14])).
% 0.08/10.40 fof(f341,plain,(
% 0.08/10.40 ![X0]: (apply(abstraction,apply(apply(abstraction,abstraction),X0))=k(identity))),
% 0.08/10.40 inference(resolution,[status(thm)],[f284,f13])).
% 0.08/10.40 fof(f386,plain,(
% 0.08/10.40 apply(apply(abstraction,k(abstraction)),apply(abstraction,abstraction))=k(k(identity))),
% 0.08/10.40 inference(resolution,[status(thm)],[f341,f120])).
% 0.08/10.40 fof(f393,plain,(
% 0.08/10.40 apply(apply(apply(abstraction,abstraction),abstraction),abstraction)=k(k(identity))),
% 0.08/10.40 inference(forward_demodulation,[status(thm)],[f7,f386])).
% 0.08/10.40 fof(f394,plain,(
% 0.08/10.40 $false),
% 0.08/10.40 inference(forward_subsumption_resolution,[status(thm)],[f393,f10])).
% 0.08/10.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/10.41 % Elapsed time: 0.047695 seconds
% 0.12/10.41 % CPU time: 0.169843 seconds
% 0.12/10.41 % Total memory used: 70.851 MB
% 0.12/10.41 % Net memory used: 70.149 MB
%------------------------------------------------------------------------------