%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : COL042-4 : 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 : n006.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 12:08:58 PM UTC 2026
% Result : Unsatisfiable 124.65s 26.13s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL042-4 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/10.37 % Computer : n006.cluster.edu
% 0.10/10.37 % Model : x86_64 x86_64
% 0.10/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.37 % Memory : 8046.5625MB
% 0.10/10.37 % OS : Linux 6.8.0-71-generic
% 0.10/10.37 % CPULimit : 300
% 0.10/10.37 % WCLimit : 300
% 0.10/10.37 % DateTime : Mon Sep 21 14:06:08 UTC 2026
% 0.10/10.38 % CPUTime :
% 0.10/10.39 % Drodi V4.1.1
% 124.65/26.13 % Refutation found
% 124.65/26.13 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 124.65/26.13 % SZS output start CNFRefutation for theBenchmark
% 124.65/26.13 fof(f1,axiom,(
% 124.65/26.13 (![X,Y,Z]: (apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ))),
% 124.65/26.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 124.65/26.13 fof(f2,axiom,(
% 124.65/26.13 (![X,Y]: (apply(apply(w1,X),Y) = apply(apply(Y,X),X) ))),
% 124.65/26.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 124.65/26.13 fof(f3,axiom,(
% 124.65/26.13 (![Strong_fixed_point]: (( apply(Strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(Strong_fixed_point,fixed_pt))| fixed_point(Strong_fixed_point) ) ))),
% 124.65/26.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 124.65/26.13 fof(f4,negated_conjecture,(
% 124.65/26.13 ~ fixed_point(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b)) ),
% 124.65/26.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 124.65/26.13 fof(f5,plain,(
% 124.65/26.13 ![X0,X1,X2]: (apply(apply(apply(b,X0),X1),X2)=apply(X0,apply(X1,X2)))),
% 124.65/26.13 inference(cnf_transformation,[status(thm)],[f1])).
% 124.65/26.13 fof(f6,plain,(
% 124.65/26.13 ![X0,X1]: (apply(apply(w1,X0),X1)=apply(apply(X1,X0),X0))),
% 124.65/26.13 inference(cnf_transformation,[status(thm)],[f2])).
% 124.65/26.13 fof(f7,plain,(
% 124.65/26.13 ![X0]: (~apply(X0,fixed_pt)=apply(fixed_pt,apply(X0,fixed_pt))|fixed_point(X0))),
% 124.65/26.13 inference(cnf_transformation,[status(thm)],[f3])).
% 124.65/26.13 fof(f8,plain,(
% 124.65/26.13 ~fixed_point(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b))),
% 124.65/26.13 inference(cnf_transformation,[status(thm)],[f4])).
% 124.65/26.13 fof(f10,plain,(
% 124.65/26.13 ![X0]: (apply(apply(w1,X0),w1)=apply(apply(X0,X0),X0))),
% 124.65/26.13 inference(paramodulation,[status(thm)],[f6,f6])).
% 124.65/26.13 fof(f15,plain,(
% 124.65/26.13 ![X0,X1,X2]: (apply(apply(w1,X0),apply(apply(b,X1),X2))=apply(apply(X1,apply(X2,X0)),X0))),
% 124.65/26.13 inference(paramodulation,[status(thm)],[f5,f6])).
% 124.65/26.13 fof(f24,plain,(
% 124.65/26.13 ![X0,X1]: (apply(apply(w1,apply(apply(b,X0),X1)),w1)=apply(apply(X0,apply(X1,apply(apply(b,X0),X1))),apply(apply(b,X0),X1)))),
% 124.65/26.13 inference(paramodulation,[status(thm)],[f5,f10])).
% 124.65/26.13 fof(f30,plain,(
% 124.65/26.13 ~apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),fixed_pt)=apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),fixed_pt))),
% 124.65/26.13 inference(resolution,[status(thm)],[f7,f8])).
% 124.65/26.13 fof(f34,plain,(
% 124.65/26.13 ~apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),fixed_pt)=apply(fixed_pt,apply(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b)),apply(b,fixed_pt)))),
% 124.65/26.13 inference(forward_demodulation,[status(thm)],[f5,f30])).
% 124.65/26.13 fof(f35,plain,(
% 124.65/26.13 ~apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),fixed_pt)=apply(fixed_pt,apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),b),apply(b,fixed_pt))))),
% 124.65/26.13 inference(forward_demodulation,[status(thm)],[f5,f34])).
% 124.65/26.13 fof(f36,plain,(
% 124.65/26.13 ~apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),fixed_pt)=apply(fixed_pt,apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt)))))),
% 124.65/26.13 inference(forward_demodulation,[status(thm)],[f5,f35])).
% 124.65/26.13 fof(f237,plain,(
% 124.65/26.13 ~apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),fixed_pt)=apply(fixed_pt,apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1))),
% 124.65/26.13 inference(forward_demodulation,[status(thm)],[f15,f36])).
% 124.65/26.13 fof(f238,plain,(
% 124.65/26.13 ~apply(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b)),apply(b,fixed_pt))=apply(fixed_pt,apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1))),
% 124.65/26.13 inference(paramodulation,[status(thm)],[f5,f237])).
% 124.65/26.13 fof(f286,plain,(
% 124.65/26.13 ![X0,X1]: (apply(apply(w1,apply(apply(b,apply(b,X0)),X1)),w1)=apply(X0,apply(apply(X1,apply(apply(b,apply(b,X0)),X1)),apply(apply(b,apply(b,X0)),X1))))),
% 124.65/26.13 inference(paramodulation,[status(thm)],[f5,f24])).
% 124.65/26.13 fof(f328,plain,(
% 124.65/26.13 ![X0,X1]: (apply(apply(w1,apply(apply(b,apply(b,X0)),X1)),w1)=apply(X0,apply(apply(w1,apply(apply(b,apply(b,X0)),X1)),X1)))),
% 124.65/26.13 inference(forward_demodulation,[status(thm)],[f6,f286])).
% 124.65/26.13 fof(f1354,plain,(
% 124.65/26.13 ~apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),b),apply(b,fixed_pt)))=apply(fixed_pt,apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1))),
% 124.65/26.13 inference(paramodulation,[status(thm)],[f5,f238])).
% 124.65/26.18 fof(f1355,plain,(
% 124.65/26.18 ~apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt))))=apply(fixed_pt,apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1))),
% 124.65/26.18 inference(forward_demodulation,[status(thm)],[f5,f1354])).
% 124.65/26.18 fof(f1356,plain,(
% 124.65/26.18 ~apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1)=apply(fixed_pt,apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1))),
% 124.65/26.18 inference(paramodulation,[status(thm)],[f15,f1355])).
% 124.65/26.18 fof(f59148,plain,(
% 124.65/26.18 $false),
% 124.65/26.18 inference(backward_subsumption_resolution,[status(thm)],[f1356,f328])).
% 124.65/26.18 % SZS output end CNFRefutation for theBenchmark.p
% 45.31/26.29 % Elapsed time: 15.895398 seconds
% 45.31/26.29 % CPU time: 125.709525 seconds
% 45.31/26.29 % Total memory used: 699.318 MB
% 45.31/26.29 % Net memory used: 676.591 MB
%------------------------------------------------------------------------------