%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM141-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/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 01:42:17 PM UTC 2026
% Result : Unsatisfiable 7.52s 1.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM141-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % 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 02:07:28 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.39 % Drodi V4.1.1
% 7.52/1.40 % Refutation found
% 7.52/1.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 7.52/1.40 % SZS output start CNFRefutation for theBenchmark
% 7.52/1.40 fof(f1,axiom,(
% 7.52/1.40 (![X,Y,U]: (( ~ subclass(X,Y)| ~ member(U,X)| member(U,Y) ) ))),
% 7.52/1.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.52/1.40 fof(f4,axiom,(
% 7.52/1.40 (![X]: (subclass(X,universal_class) ))),
% 7.52/1.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.52/1.40 fof(f8,axiom,(
% 7.52/1.40 (![U,X,Y]: (( ~ member(U,unordered_pair(X,Y))| U = X| U = Y ) ))),
% 7.52/1.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.52/1.40 fof(f10,axiom,(
% 7.52/1.40 (![Y,X]: (( ~ member(Y,universal_class)| member(Y,unordered_pair(X,Y)) ) ))),
% 7.52/1.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.52/1.40 fof(f12,axiom,(
% 7.52/1.40 (![X]: (unordered_pair(X,X) = singleton(X) ))),
% 7.52/1.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.52/1.40 fof(f15,axiom,(
% 7.52/1.40 (![U,V,X,Y]: (( ~ member(ordered_pair(U,V),cross_product(X,Y))| member(V,Y) ) ))),
% 7.52/1.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.52/1.40 fof(f16,axiom,(
% 7.52/1.40 (![U,X,V,Y]: (( ~ member(U,X)| ~ member(V,Y)| member(ordered_pair(U,V),cross_product(X,Y)) ) ))),
% 7.52/1.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.52/1.40 fof(f17,axiom,(
% 7.52/1.40 (![Z,X,Y]: (( ~ member(Z,cross_product(X,Y))| ordered_pair(first(Z),second(Z)) = Z ) ))),
% 7.52/1.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.52/1.40 fof(f22,axiom,(
% 7.52/1.40 (![Z,X,Y]: (( ~ member(Z,intersection(X,Y))| member(Z,Y) ) ))),
% 7.52/1.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.52/1.40 fof(f24,axiom,(
% 7.52/1.40 (![Z,X]: (( ~ member(Z,complement(X))| ~ member(Z,X) ) ))),
% 7.52/1.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.52/1.40 fof(f25,axiom,(
% 7.52/1.40 (![Z,X]: (( ~ member(Z,universal_class)| member(Z,complement(X))| member(Z,X) ) ))),
% 7.52/1.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.52/1.40 fof(f26,axiom,(
% 7.52/1.40 (![X,Y]: (complement(intersection(complement(X),complement(Y))) = union(X,Y) ))),
% 7.52/1.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.52/1.40 fof(f43,axiom,(
% 7.52/1.40 (![X]: (union(X,singleton(X)) = successor(X) ))),
% 7.52/1.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.52/1.40 fof(f47,axiom,(
% 7.52/1.40 (![X]: (( ~ inductive(X)| member(null_class,X) ) ))),
% 7.52/1.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.52/1.40 fof(f49,axiom,(
% 7.52/1.40 (![X]: (( ~ member(null_class,X)| ~ subclass(image(successor_relation,X),X)| inductive(X) ) ))),
% 7.52/1.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.52/1.40 fof(f50,axiom,(
% 7.52/1.40 inductive(omega) ),
% 7.52/1.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.52/1.40 fof(f159,negated_conjecture,(
% 7.52/1.40 member(x,universal_class) ),
% 7.52/1.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.52/1.40 fof(f160,negated_conjecture,(
% 7.52/1.40 ~ member(x,successor(x)) ),
% 7.52/1.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.52/1.40 fof(f161,plain,(
% 7.52/1.40 ![Y,U]: ((![X]: (~subclass(X,Y)|~member(U,X)))|member(U,Y))),
% 7.52/1.40 inference(miniscoping,[status(thm)],[f1])).
% 7.52/1.40 fof(f162,plain,(
% 7.52/1.40 ![X0,X1,X2]: (~subclass(X0,X1)|~member(X2,X0)|member(X2,X1))),
% 7.52/1.40 inference(cnf_transformation,[status(thm)],[f161])).
% 7.52/1.40 fof(f165,plain,(
% 7.52/1.40 ![X0]: (subclass(X0,universal_class))),
% 7.52/1.40 inference(cnf_transformation,[status(thm)],[f4])).
% 7.52/1.40 fof(f169,plain,(
% 7.52/1.40 ![U,Y]: ((![X]: (~member(U,unordered_pair(X,Y))|U=X))|U=Y)),
% 7.52/1.40 inference(miniscoping,[status(thm)],[f8])).
% 7.52/1.40 fof(f170,plain,(
% 7.52/1.40 ![X0,X1,X2]: (~member(X0,unordered_pair(X1,X2))|X0=X1|X0=X2)),
% 7.52/1.40 inference(cnf_transformation,[status(thm)],[f169])).
% 7.52/1.40 fof(f173,plain,(
% 7.52/1.40 ![Y]: (~member(Y,universal_class)|(![X]: member(Y,unordered_pair(X,Y))))),
% 7.52/1.40 inference(miniscoping,[status(thm)],[f10])).
% 7.52/1.40 fof(f174,plain,(
% 7.52/1.40 ![X0,X1]: (~member(X0,universal_class)|member(X0,unordered_pair(X1,X0)))),
% 7.52/1.40 inference(cnf_transformation,[status(thm)],[f173])).
% 7.52/1.40 fof(f176,plain,(
% 7.52/1.40 ![X0]: (unordered_pair(X0,X0)=singleton(X0))),
% 7.52/1.40 inference(cnf_transformation,[status(thm)],[f12])).
% 7.52/1.40 fof(f180,plain,(
% 7.52/1.40 ![V,Y]: ((![U,X]: ~member(ordered_pair(U,V),cross_product(X,Y)))|member(V,Y))),
% 7.52/1.40 inference(miniscoping,[status(thm)],[f15])).
% 7.52/1.40 fof(f181,plain,(
% 7.52/1.40 ![X0,X1,X2,X3]: (~member(ordered_pair(X0,X1),cross_product(X2,X3))|member(X1,X3))),
% 7.52/1.40 inference(cnf_transformation,[status(thm)],[f180])).
% 7.52/1.40 fof(f182,plain,(
% 7.52/1.40 ![X0,X1,X2,X3]: (~member(X0,X1)|~member(X2,X3)|member(ordered_pair(X0,X2),cross_product(X1,X3)))),
% 7.52/1.40 inference(cnf_transformation,[status(thm)],[f16])).
% 7.52/1.40 fof(f183,plain,(
% 7.52/1.40 ![Z]: ((![X,Y]: ~member(Z,cross_product(X,Y)))|ordered_pair(first(Z),second(Z))=Z)),
% 7.52/1.40 inference(miniscoping,[status(thm)],[f17])).
% 7.52/1.40 fof(f184,plain,(
% 7.52/1.40 ![X0,X1,X2]: (~member(X0,cross_product(X1,X2))|ordered_pair(first(X0),second(X0))=X0)),
% 7.52/1.40 inference(cnf_transformation,[status(thm)],[f183])).
% 7.52/1.40 fof(f190,plain,(
% 7.52/1.40 ![Z,Y]: ((![X]: ~member(Z,intersection(X,Y)))|member(Z,Y))),
% 7.52/1.40 inference(miniscoping,[status(thm)],[f22])).
% 7.52/1.40 fof(f191,plain,(
% 7.52/1.40 ![X0,X1,X2]: (~member(X0,intersection(X1,X2))|member(X0,X2))),
% 7.52/1.40 inference(cnf_transformation,[status(thm)],[f190])).
% 7.52/1.40 fof(f193,plain,(
% 7.52/1.40 ![X0,X1]: (~member(X0,complement(X1))|~member(X0,X1))),
% 7.52/1.40 inference(cnf_transformation,[status(thm)],[f24])).
% 7.52/1.40 fof(f194,plain,(
% 7.52/1.40 ![X0,X1]: (~member(X0,universal_class)|member(X0,complement(X1))|member(X0,X1))),
% 7.52/1.40 inference(cnf_transformation,[status(thm)],[f25])).
% 7.52/1.40 fof(f195,plain,(
% 7.52/1.40 ![X0,X1]: (complement(intersection(complement(X0),complement(X1)))=union(X0,X1))),
% 7.52/1.40 inference(cnf_transformation,[status(thm)],[f26])).
% 7.52/1.40 fof(f212,plain,(
% 7.52/1.40 ![X0]: (union(X0,singleton(X0))=successor(X0))),
% 7.52/1.40 inference(cnf_transformation,[status(thm)],[f43])).
% 7.52/1.40 fof(f216,plain,(
% 7.52/1.40 ![X0]: (~inductive(X0)|member(null_class,X0))),
% 7.52/1.40 inference(cnf_transformation,[status(thm)],[f47])).
% 7.52/1.40 fof(f218,plain,(
% 7.52/1.40 ![X0]: (~member(null_class,X0)|~subclass(image(successor_relation,X0),X0)|inductive(X0))),
% 7.52/1.40 inference(cnf_transformation,[status(thm)],[f49])).
% 7.52/1.40 fof(f219,plain,(
% 7.52/1.40 inductive(omega)),
% 7.52/1.40 inference(cnf_transformation,[status(thm)],[f50])).
% 7.52/1.40 fof(f348,plain,(
% 7.52/1.40 member(x,universal_class)),
% 7.52/1.40 inference(cnf_transformation,[status(thm)],[f159])).
% 7.52/1.40 fof(f349,plain,(
% 7.52/1.40 ~member(x,successor(x))),
% 7.52/1.40 inference(cnf_transformation,[status(thm)],[f160])).
% 7.52/1.40 fof(f358,plain,(
% 7.52/1.40 ![X0,X1]: (~member(X0,X1)|member(X0,universal_class))),
% 7.52/1.40 inference(resolution,[status(thm)],[f165,f162])).
% 7.52/1.40 fof(f366,plain,(
% 7.52/1.40 ![X0]: (~member(X0,universal_class)|member(X0,singleton(X0)))),
% 7.52/1.40 inference(paramodulation,[status(thm)],[f176,f174])).
% 7.52/1.40 fof(f368,plain,(
% 7.52/1.40 ![X0,X1]: (~member(X0,singleton(X1))|X0=X1|X0=X1)),
% 7.52/1.40 inference(paramodulation,[status(thm)],[f176,f170])).
% 7.52/1.40 fof(f369,plain,(
% 7.52/1.40 ![X0,X1]: (~member(X0,singleton(X1))|X0=X1)),
% 7.52/1.40 inference(duplicate_literals_removal,[status(thm)],[f368])).
% 7.52/1.40 fof(f380,plain,(
% 7.52/1.40 ![X0,X1,X2,X3]: (ordered_pair(first(ordered_pair(X0,X1)),second(ordered_pair(X0,X1)))=ordered_pair(X0,X1)|~member(X0,X2)|~member(X1,X3))),
% 7.52/1.40 inference(resolution,[status(thm)],[f184,f182])).
% 7.52/1.40 fof(f393,plain,(
% 7.52/1.40 member(null_class,omega)),
% 7.52/1.40 inference(resolution,[status(thm)],[f216,f219])).
% 7.52/1.40 fof(f396,plain,(
% 7.52/1.40 ![X0,X1,X2]: (~member(X0,universal_class)|member(X0,union(X1,X2))|member(X0,intersection(complement(X1),complement(X2))))),
% 7.52/1.40 inference(paramodulation,[status(thm)],[f195,f194])).
% 7.52/1.40 fof(f487,plain,(
% 7.52/1.40 ~member(null_class,universal_class)|inductive(universal_class)),
% 7.52/1.40 inference(resolution,[status(thm)],[f218,f165])).
% 7.52/1.40 fof(f870,plain,(
% 7.52/1.40 ![X0]: (inductive(universal_class)|~member(null_class,X0))),
% 7.52/1.40 inference(resolution,[status(thm)],[f487,f358])).
% 7.52/1.40 fof(f871,plain,(
% 7.52/1.40 inductive(universal_class)),
% 7.52/1.40 inference(resolution,[status(thm)],[f870,f393])).
% 7.52/1.40 fof(f885,plain,(
% 7.52/1.40 member(null_class,universal_class)),
% 7.52/1.40 inference(resolution,[status(thm)],[f871,f216])).
% 7.52/1.40 fof(f1575,plain,(
% 7.52/1.40 ![X0,X1]: (ordered_pair(first(ordered_pair(X0,x)),second(ordered_pair(X0,x)))=ordered_pair(X0,x)|~member(X0,X1))),
% 7.52/1.40 inference(resolution,[status(thm)],[f380,f348])).
% 7.52/1.40 fof(f1721,plain,(
% 7.52/1.40 ordered_pair(first(ordered_pair(null_class,x)),second(ordered_pair(null_class,x)))=ordered_pair(null_class,x)),
% 7.52/1.40 inference(resolution,[status(thm)],[f1575,f885])).
% 7.52/1.40 fof(f1889,plain,(
% 7.52/1.40 ![X0,X1]: (~member(ordered_pair(null_class,x),cross_product(X0,X1))|member(second(ordered_pair(null_class,x)),X1))),
% 7.52/1.40 inference(paramodulation,[status(thm)],[f1721,f181])).
% 7.52/1.40 fof(f2288,plain,(
% 7.52/1.40 ![X0,X1]: (member(second(ordered_pair(null_class,x)),X0)|~member(null_class,X1)|~member(x,X0))),
% 7.52/1.40 inference(resolution,[status(thm)],[f1889,f182])).
% 5.78/1.43 fof(f2311,plain,(
% 5.78/1.43 ![X0]: (member(second(ordered_pair(null_class,x)),singleton(x))|~member(null_class,X0)|~member(x,universal_class))),
% 5.78/1.43 inference(resolution,[status(thm)],[f2288,f366])).
% 5.78/1.43 fof(f2325,plain,(
% 5.78/1.43 ![X0]: (member(second(ordered_pair(null_class,x)),singleton(x))|~member(null_class,X0))),
% 5.78/1.43 inference(forward_subsumption_resolution,[status(thm)],[f2311,f348])).
% 5.78/1.43 fof(f2449,plain,(
% 5.78/1.43 ![X0,X1]: (member(x,union(X0,X1))|member(x,intersection(complement(X0),complement(X1))))),
% 5.78/1.43 inference(resolution,[status(thm)],[f396,f348])).
% 5.78/1.43 fof(f2644,plain,(
% 5.78/1.43 ![X0]: (~member(null_class,X0)|second(ordered_pair(null_class,x))=x)),
% 5.78/1.43 inference(resolution,[status(thm)],[f2325,f369])).
% 5.78/1.43 fof(f2650,plain,(
% 5.78/1.43 ![X0,X1]: (member(x,union(X0,X1))|member(x,complement(X1)))),
% 5.78/1.43 inference(resolution,[status(thm)],[f2449,f191])).
% 5.78/1.43 fof(f2683,plain,(
% 5.78/1.43 second(ordered_pair(null_class,x))=x),
% 5.78/1.43 inference(resolution,[status(thm)],[f2644,f885])).
% 5.78/1.43 fof(f2701,plain,(
% 5.78/1.43 ![X0]: (member(x,singleton(x))|~member(null_class,X0))),
% 5.78/1.43 inference(backward_demodulation,[status(thm)],[f2683,f2325])).
% 5.78/1.43 fof(f2971,plain,(
% 5.78/1.43 ![X0]: (member(x,successor(X0))|member(x,complement(singleton(X0))))),
% 5.78/1.43 inference(paramodulation,[status(thm)],[f212,f2650])).
% 5.78/1.43 fof(f5150,plain,(
% 5.78/1.43 ![X0]: (member(x,successor(X0))|~member(x,singleton(X0)))),
% 5.78/1.43 inference(resolution,[status(thm)],[f2971,f193])).
% 5.78/1.43 fof(f5327,plain,(
% 5.78/1.43 ![X0]: (member(x,successor(x))|~member(null_class,X0))),
% 5.78/1.43 inference(resolution,[status(thm)],[f5150,f2701])).
% 5.78/1.43 fof(f5331,plain,(
% 5.78/1.43 ![X0]: (~member(null_class,X0))),
% 5.78/1.43 inference(forward_subsumption_resolution,[status(thm)],[f5327,f349])).
% 5.78/1.43 fof(f5370,plain,(
% 5.78/1.43 $false),
% 5.78/1.43 inference(backward_subsumption_resolution,[status(thm)],[f885,f5331])).
% 5.78/1.43 % SZS output end CNFRefutation for theBenchmark.p
% 5.78/1.46 % Elapsed time: 1.071281 seconds
% 5.78/1.46 % CPU time: 8.167562 seconds
% 5.78/1.46 % Total memory used: 223.068 MB
% 5.78/1.46 % Net memory used: 214.211 MB
%------------------------------------------------------------------------------