%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : COL079-1 : 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 : n011.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 12.19s 7.06s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL079-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/5.44 % Computer : n011.cluster.edu
% 0.18/5.44 % Model : x86_64 x86_64
% 0.18/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.44 % Memory : 8046.5625MB
% 0.18/5.44 % OS : Linux 6.8.0-71-generic
% 0.18/5.44 % CPULimit : 300
% 0.18/5.44 % WCLimit : 300
% 0.18/5.44 % DateTime : Mon Sep 21 14:09:31 UTC 2026
% 0.18/5.45 % CPUTime :
% 0.18/5.46 % Drodi V4.1.1
% 12.19/7.06 % Refutation found
% 12.19/7.06 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 12.19/7.06 % SZS output start CNFRefutation for theBenchmark
% 12.19/7.06 fof(f1,axiom,(
% 12.19/7.06 (![X,Y]: (apply(k(X),Y) = X ))),
% 12.19/7.06 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.19/7.06 fof(f4,axiom,(
% 12.19/7.06 (![X]: (pair(apply(projection1,X),apply(projection2,X)) = X ))),
% 12.19/7.06 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.19/7.06 fof(f5,axiom,(
% 12.19/7.06 (![X,Y,Z]: (apply(pair(X,Y),Z) = pair(apply(X,Z),apply(Y,Z)) ))),
% 12.19/7.06 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.19/7.06 fof(f6,axiom,(
% 12.19/7.06 (![X,Y,Z]: (apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,k(Z)),apply(Y,Z)) ))),
% 12.19/7.06 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.19/7.06 fof(f9,axiom,(
% 12.19/7.06 (![X,Y]: (( X = Y| apply(X,n(X,Y)) != apply(Y,n(X,Y)) ) ))),
% 12.19/7.06 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.19/7.06 fof(f11,negated_conjecture,(
% 12.19/7.06 apply(abstraction,apply(abstraction,apply(abstraction,b))) != apply(abstraction,b) ),
% 12.19/7.06 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.19/7.06 fof(f12,plain,(
% 12.19/7.06 ![X0,X1]: (apply(k(X0),X1)=X0)),
% 12.19/7.06 inference(cnf_transformation,[status(thm)],[f1])).
% 12.19/7.06 fof(f15,plain,(
% 12.19/7.06 ![X0]: (pair(apply(projection1,X0),apply(projection2,X0))=X0)),
% 12.19/7.06 inference(cnf_transformation,[status(thm)],[f4])).
% 12.19/7.06 fof(f16,plain,(
% 12.19/7.06 ![X0,X1,X2]: (apply(pair(X0,X1),X2)=pair(apply(X0,X2),apply(X1,X2)))),
% 12.19/7.06 inference(cnf_transformation,[status(thm)],[f5])).
% 12.19/7.06 fof(f17,plain,(
% 12.19/7.06 ![X0,X1,X2]: (apply(apply(apply(abstraction,X0),X1),X2)=apply(apply(X0,k(X2)),apply(X1,X2)))),
% 12.19/7.06 inference(cnf_transformation,[status(thm)],[f6])).
% 12.19/7.06 fof(f20,plain,(
% 12.19/7.06 ![X0,X1]: (X0=X1|~apply(X0,n(X0,X1))=apply(X1,n(X0,X1)))),
% 12.19/7.06 inference(cnf_transformation,[status(thm)],[f9])).
% 12.19/7.06 fof(f22,plain,(
% 12.19/7.06 ~apply(abstraction,apply(abstraction,apply(abstraction,b)))=apply(abstraction,b)),
% 12.19/7.06 inference(cnf_transformation,[status(thm)],[f11])).
% 12.19/7.06 fof(f24,plain,(
% 12.19/7.06 ![X0,X1,X2,X3]: (apply(apply(apply(abstraction,X0),apply(X1,k(X2))),apply(X3,X2))=apply(apply(X0,k(apply(X3,X2))),apply(apply(apply(abstraction,X1),X3),X2)))),
% 12.19/7.06 inference(paramodulation,[status(thm)],[f17,f17])).
% 12.19/7.06 fof(f25,plain,(
% 12.19/7.06 ![X0,X1,X2]: (apply(apply(apply(abstraction,X0),k(X1)),X2)=apply(apply(X0,k(X2)),X1))),
% 12.19/7.06 inference(paramodulation,[status(thm)],[f12,f17])).
% 12.19/7.06 fof(f122,plain,(
% 12.19/7.06 ![X0]: (apply(pair(projection1,projection2),X0)=X0)),
% 12.19/7.06 inference(backward_demodulation,[status(thm)],[f16,f15])).
% 12.19/7.06 fof(f166,plain,(
% 12.19/7.06 ![X0,X1]: (apply(apply(apply(abstraction,pair(projection1,projection2)),X0),X1)=apply(k(X1),apply(X0,X1)))),
% 12.19/7.06 inference(paramodulation,[status(thm)],[f122,f17])).
% 12.19/7.06 fof(f171,plain,(
% 12.19/7.06 ![X0,X1]: (apply(apply(apply(abstraction,pair(projection1,projection2)),X0),X1)=X1)),
% 12.19/7.06 inference(forward_demodulation,[status(thm)],[f12,f166])).
% 12.19/7.06 fof(f657,plain,(
% 12.19/7.06 ![X0,X1,X2]: (apply(apply(apply(abstraction,X0),apply(pair(projection1,projection2),k(X1))),apply(X2,X1))=apply(apply(X0,k(apply(X2,X1))),X1))),
% 12.19/7.06 inference(paramodulation,[status(thm)],[f171,f24])).
% 12.19/7.06 fof(f743,plain,(
% 12.19/7.06 ![X0,X1,X2]: (apply(apply(apply(abstraction,X0),k(X1)),apply(X2,X1))=apply(apply(X0,k(apply(X2,X1))),X1))),
% 12.19/7.06 inference(forward_demodulation,[status(thm)],[f122,f657])).
% 12.19/7.06 fof(f744,plain,(
% 12.19/7.06 ![X0,X1,X2]: (apply(apply(apply(abstraction,apply(abstraction,X0)),X1),X2)=apply(apply(X0,k(apply(X1,X2))),X2))),
% 12.19/7.06 inference(forward_demodulation,[status(thm)],[f17,f743])).
% 12.19/7.06 fof(f1218,plain,(
% 12.19/7.06 ![X0,X1,X2]: (apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,X0))),X1),X2)=apply(apply(X0,k(X2)),apply(X1,X2)))),
% 12.19/7.06 inference(paramodulation,[status(thm)],[f25,f744])).
% 12.19/7.06 fof(f1334,plain,(
% 12.19/7.06 ![X0,X1,X2]: (apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,X0))),X1),X2)=apply(apply(apply(abstraction,X0),X1),X2))),
% 12.19/7.06 inference(forward_demodulation,[status(thm)],[f17,f1218])).
% 12.19/7.06 fof(f8152,plain,(
% 12.19/7.06 ![X0,X1]: (apply(apply(abstraction,apply(abstraction,apply(abstraction,X0))),X1)=apply(apply(abstraction,X0),X1))),
% 12.19/7.06 inference(resolution,[status(thm)],[f1334,f20])).
% 12.19/7.06 fof(f8313,plain,(
% 12.19/7.06 ![X0]: (apply(abstraction,apply(abstraction,apply(abstraction,X0)))=apply(abstraction,X0))),
% 12.19/7.06 inference(resolution,[status(thm)],[f8152,f20])).
% 12.19/7.07 fof(f8421,plain,(
% 12.19/7.07 ~apply(abstraction,b)=apply(abstraction,b)),
% 12.19/7.07 inference(backward_demodulation,[status(thm)],[f8313,f22])).
% 12.19/7.07 fof(f8459,plain,(
% 12.19/7.07 $false),
% 12.19/7.07 inference(trivial_equality_resolution,[status(thm)],[f8421])).
% 12.19/7.07 % SZS output end CNFRefutation for theBenchmark.p
% 1.86/7.12 % Elapsed time: 1.653682 seconds
% 1.86/7.12 % CPU time: 12.786169 seconds
% 1.86/7.12 % Total memory used: 253.384 MB
% 1.86/7.12 % Net memory used: 240.067 MB
%------------------------------------------------------------------------------