%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : COL076-1 : 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 : 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 83.56s 26.43s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL076-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 14:10:02 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.15/0.38 % Drodi V4.1.1
% 83.56/26.43 % Refutation found
% 83.56/26.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 83.56/26.43 % SZS output start CNFRefutation for theBenchmark
% 83.56/26.43 fof(f1,axiom,(
% 83.56/26.43 (![X,Y]: (apply(apply(k,X),Y) = X ))),
% 83.56/26.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 83.56/26.43 fof(f3,axiom,(
% 83.56/26.43 (![X,Y]: (apply(projection2,pair(X,Y)) = Y ))),
% 83.56/26.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 83.56/26.43 fof(f5,axiom,(
% 83.56/26.43 (![X,Y,Z]: (apply(pair(X,Y),Z) = pair(apply(X,Z),apply(Y,Z)) ))),
% 83.56/26.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 83.56/26.43 fof(f6,axiom,(
% 83.56/26.43 (![X,Y,Z]: (apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,apply(k,Z)),apply(Y,Z)) ))),
% 83.56/26.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 83.56/26.43 fof(f9,axiom,(
% 83.56/26.43 (![X,Y]: (( X = Y| apply(X,n(X,Y)) != apply(Y,n(X,Y)) ) ))),
% 83.56/26.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 83.56/26.43 fof(f11,axiom,(
% 83.56/26.43 (![X,Y]: (apply(apply(f,X),Y) = apply(X,X) ))),
% 83.56/26.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 83.56/26.43 fof(f12,negated_conjecture,(
% 83.56/26.43 (![Y]: (Y != apply(eq,pair(apply(k,Y),apply(k,projection2))) ))),
% 83.56/26.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 83.56/26.43 fof(f13,plain,(
% 83.56/26.43 ![X0,X1]: (apply(apply(k,X0),X1)=X0)),
% 83.56/26.43 inference(cnf_transformation,[status(thm)],[f1])).
% 83.56/26.43 fof(f15,plain,(
% 83.56/26.43 ![X0,X1]: (apply(projection2,pair(X0,X1))=X1)),
% 83.56/26.43 inference(cnf_transformation,[status(thm)],[f3])).
% 83.56/26.43 fof(f17,plain,(
% 83.56/26.43 ![X0,X1,X2]: (apply(pair(X0,X1),X2)=pair(apply(X0,X2),apply(X1,X2)))),
% 83.56/26.43 inference(cnf_transformation,[status(thm)],[f5])).
% 83.56/26.43 fof(f18,plain,(
% 83.56/26.43 ![X0,X1,X2]: (apply(apply(apply(abstraction,X0),X1),X2)=apply(apply(X0,apply(k,X2)),apply(X1,X2)))),
% 83.56/26.43 inference(cnf_transformation,[status(thm)],[f6])).
% 83.56/26.43 fof(f21,plain,(
% 83.56/26.43 ![X0,X1]: (X0=X1|~apply(X0,n(X0,X1))=apply(X1,n(X0,X1)))),
% 83.56/26.43 inference(cnf_transformation,[status(thm)],[f9])).
% 83.56/26.43 fof(f23,plain,(
% 83.56/26.43 ![X0,X1]: (apply(apply(f,X0),X1)=apply(X0,X0))),
% 83.56/26.43 inference(cnf_transformation,[status(thm)],[f11])).
% 83.56/26.43 fof(f24,plain,(
% 83.56/26.43 ![X0]: (~X0=apply(eq,pair(apply(k,X0),apply(k,projection2))))),
% 83.56/26.43 inference(cnf_transformation,[status(thm)],[f12])).
% 83.56/26.43 fof(f28,plain,(
% 83.56/26.43 ![X0,X1,X2]: (apply(pair(apply(k,X0),X1),X2)=pair(X0,apply(X1,X2)))),
% 83.56/26.43 inference(paramodulation,[status(thm)],[f13,f17])).
% 83.56/26.43 fof(f105,plain,(
% 83.56/26.43 ![X0,X1]: (apply(k,X0)=X1|~X0=apply(X1,n(apply(k,X0),X1)))),
% 83.56/26.43 inference(paramodulation,[status(thm)],[f13,f21])).
% 83.56/26.43 fof(f108,plain,(
% 83.56/26.43 ![X0,X1]: (X0=apply(k,X1)|~apply(X0,n(X0,apply(k,X1)))=X1)),
% 83.56/26.43 inference(paramodulation,[status(thm)],[f13,f21])).
% 83.56/26.43 fof(f180,plain,(
% 83.56/26.43 ![X0,X1,X2]: (apply(k,X0)=pair(apply(k,X1),X2)|~X0=pair(X1,apply(X2,n(apply(k,X0),pair(apply(k,X1),X2)))))),
% 83.56/26.43 inference(paramodulation,[status(thm)],[f28,f105])).
% 83.56/26.43 fof(f325,plain,(
% 83.56/26.43 ![X0]: (apply(f,X0)=apply(k,apply(X0,X0)))),
% 83.56/26.43 inference(resolution,[status(thm)],[f23,f108])).
% 83.56/26.43 fof(f6427,plain,(
% 83.56/26.43 ![X0,X1,X2]: (apply(apply(apply(abstraction,apply(k,X0)),X1),X2)=apply(X0,apply(X1,X2)))),
% 83.56/26.43 inference(paramodulation,[status(thm)],[f13,f18])).
% 83.56/26.43 fof(f6449,plain,(
% 83.56/26.43 ![X0,X1,X2]: (apply(pair(X0,projection2),pair(X1,X2))=pair(apply(X0,pair(X1,X2)),X2))),
% 83.56/26.43 inference(paramodulation,[status(thm)],[f15,f17])).
% 83.56/26.43 fof(f49820,plain,(
% 83.56/26.43 ![X0,X1,X2]: (apply(k,X0)=pair(apply(k,X1),apply(k,X2))|~X0=pair(X1,X2))),
% 83.56/26.43 inference(paramodulation,[status(thm)],[f13,f180])).
% 83.56/26.43 fof(f49869,plain,(
% 83.56/26.43 ![X0,X1]: (apply(k,pair(X0,X1))=pair(apply(k,X0),apply(k,X1)))),
% 83.56/26.43 inference(destructive_equality_resolution,[status(thm)],[f49820])).
% 83.56/26.43 fof(f77041,plain,(
% 83.56/26.43 ![X0]: (~X0=apply(eq,apply(k,pair(X0,projection2))))),
% 83.56/26.43 inference(backward_demodulation,[status(thm)],[f49869,f24])).
% 83.56/26.43 fof(f77511,plain,(
% 83.56/26.43 ![X0,X1]: (~apply(X0,pair(X1,projection2))=apply(eq,apply(k,apply(pair(X0,projection2),pair(X1,projection2)))))),
% 83.56/26.43 inference(paramodulation,[status(thm)],[f6449,f77041])).
% 83.56/26.43 fof(f82157,plain,(
% 83.56/26.43 ![X0]: (~apply(X0,pair(X0,projection2))=apply(eq,apply(f,pair(X0,projection2))))),
% 83.56/26.43 inference(paramodulation,[status(thm)],[f325,f77511])).
% 83.56/26.43 fof(f82514,plain,(
% 83.56/26.43 $false),
% 83.56/26.43 inference(resolution,[status(thm)],[f82157,f6427])).
% 83.56/26.43 % SZS output end CNFRefutation for theBenchmark.p
% 83.56/26.56 % Elapsed time: 26.151608 seconds
% 83.56/26.56 % CPU time: 206.054290 seconds
% 83.56/26.56 % Total memory used: 1.730 GB
% 83.56/26.56 % Net memory used: 1.583 GB
%------------------------------------------------------------------------------