%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET012-2 : 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 : n005.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 02:11:09 PM UTC 2026
% Result : Unsatisfiable 8.34s 1.47s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET012-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.33 % Computer : n005.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.33 % CPULimit : 300
% 0.07/0.33 % WCLimit : 300
% 0.07/0.33 % DateTime : Mon Sep 21 04:41:33 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 % Drodi V4.1.1
% 8.34/1.47 % Refutation found
% 8.34/1.47 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 8.34/1.47 % SZS output start CNFRefutation for theBenchmark
% 8.34/1.47 fof(f2,axiom,(
% 8.34/1.47 (![Element,Subset,Superset]: (( ~ member(Element,Subset)| ~ subset(Subset,Superset)| member(Element,Superset) ) ))),
% 8.34/1.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.34/1.47 fof(f3,axiom,(
% 8.34/1.47 (![Subset,Superset]: (( subset(Subset,Superset)| member(member_of_1_not_of_2(Subset,Superset),Subset) ) ))),
% 8.34/1.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.34/1.47 fof(f4,axiom,(
% 8.34/1.47 (![Subset,Superset]: (( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)| subset(Subset,Superset) ) ))),
% 8.34/1.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.34/1.47 fof(f5,axiom,(
% 8.34/1.47 (![X,Xs]: (( member(X,Xs)| member(X,complement(Xs)) ) ))),
% 8.34/1.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.34/1.47 fof(f6,axiom,(
% 8.34/1.47 (![X,Xs]: (( ~ member(X,Xs)| ~ member(X,complement(Xs)) ) ))),
% 8.34/1.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.34/1.47 fof(f13,axiom,(
% 8.34/1.47 (![Subset,Superset]: (( ~ equal_sets(Subset,Superset)| subset(Subset,Superset) ) ))),
% 8.34/1.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.34/1.47 fof(f15,axiom,(
% 8.34/1.47 (![Set1,Set2]: (( ~ subset(Set1,Set2)| ~ subset(Set2,Set1)| equal_sets(Set2,Set1) ) ))),
% 8.34/1.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.34/1.47 fof(f17,axiom,(
% 8.34/1.47 (![Xs,Ys]: (( ~ equal_sets(Xs,Ys)| equal_sets(Ys,Xs) ) ))),
% 8.34/1.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.34/1.47 fof(f22,hypothesis,(
% 8.34/1.47 equal_sets(complement(a),b) ),
% 8.34/1.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.34/1.47 fof(f23,hypothesis,(
% 8.34/1.47 equal_sets(complement(b),c) ),
% 8.34/1.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.34/1.47 fof(f24,negated_conjecture,(
% 8.34/1.47 ~ equal_sets(a,c) ),
% 8.34/1.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.34/1.47 fof(f26,plain,(
% 8.34/1.47 ![Element,Superset]: ((![Subset]: (~member(Element,Subset)|~subset(Subset,Superset)))|member(Element,Superset))),
% 8.34/1.47 inference(miniscoping,[status(thm)],[f2])).
% 8.34/1.47 fof(f27,plain,(
% 8.34/1.47 ![X0,X1,X2]: (~member(X0,X1)|~subset(X1,X2)|member(X0,X2))),
% 8.34/1.47 inference(cnf_transformation,[status(thm)],[f26])).
% 8.34/1.47 fof(f28,plain,(
% 8.34/1.47 ![X0,X1]: (subset(X0,X1)|member(member_of_1_not_of_2(X0,X1),X0))),
% 8.34/1.47 inference(cnf_transformation,[status(thm)],[f3])).
% 8.34/1.47 fof(f29,plain,(
% 8.34/1.47 ![X0,X1]: (~member(member_of_1_not_of_2(X0,X1),X1)|subset(X0,X1))),
% 8.34/1.47 inference(cnf_transformation,[status(thm)],[f4])).
% 8.34/1.47 fof(f30,plain,(
% 8.34/1.47 ![X0,X1]: (member(X0,X1)|member(X0,complement(X1)))),
% 8.34/1.47 inference(cnf_transformation,[status(thm)],[f5])).
% 8.34/1.47 fof(f31,plain,(
% 8.34/1.47 ![X0,X1]: (~member(X0,X1)|~member(X0,complement(X1)))),
% 8.34/1.47 inference(cnf_transformation,[status(thm)],[f6])).
% 8.34/1.47 fof(f43,plain,(
% 8.34/1.47 ![X0,X1]: (~equal_sets(X0,X1)|subset(X0,X1))),
% 8.34/1.47 inference(cnf_transformation,[status(thm)],[f13])).
% 8.34/1.47 fof(f45,plain,(
% 8.34/1.47 ![X0,X1]: (~subset(X0,X1)|~subset(X1,X0)|equal_sets(X1,X0))),
% 8.34/1.47 inference(cnf_transformation,[status(thm)],[f15])).
% 8.34/1.47 fof(f47,plain,(
% 8.34/1.47 ![X0,X1]: (~equal_sets(X0,X1)|equal_sets(X1,X0))),
% 8.34/1.47 inference(cnf_transformation,[status(thm)],[f17])).
% 8.34/1.47 fof(f54,plain,(
% 8.34/1.47 equal_sets(complement(a),b)),
% 8.34/1.47 inference(cnf_transformation,[status(thm)],[f22])).
% 8.34/1.47 fof(f55,plain,(
% 8.34/1.47 equal_sets(complement(b),c)),
% 8.34/1.47 inference(cnf_transformation,[status(thm)],[f23])).
% 8.34/1.47 fof(f56,plain,(
% 8.34/1.47 ~equal_sets(a,c)),
% 8.34/1.47 inference(cnf_transformation,[status(thm)],[f24])).
% 8.34/1.47 fof(f58,plain,(
% 8.34/1.47 equal_sets(b,complement(a))),
% 8.34/1.47 inference(resolution,[status(thm)],[f54,f47])).
% 8.34/1.47 fof(f62,plain,(
% 8.34/1.47 equal_sets(c,complement(b))),
% 8.34/1.47 inference(resolution,[status(thm)],[f55,f47])).
% 8.34/1.47 fof(f75,plain,(
% 8.34/1.47 subset(c,complement(b))),
% 8.34/1.47 inference(resolution,[status(thm)],[f43,f62])).
% 8.34/1.47 fof(f76,plain,(
% 8.34/1.47 subset(b,complement(a))),
% 8.34/1.47 inference(resolution,[status(thm)],[f43,f58])).
% 8.34/1.47 fof(f77,plain,(
% 8.34/1.47 subset(complement(b),c)),
% 8.34/1.47 inference(resolution,[status(thm)],[f43,f55])).
% 8.34/1.47 fof(f78,plain,(
% 8.34/1.47 subset(complement(a),b)),
% 8.34/1.47 inference(resolution,[status(thm)],[f43,f54])).
% 8.34/1.47 fof(f90,plain,(
% 8.34/1.47 ![X0,X1,X2]: (member(X0,X1)|~subset(complement(X1),X2)|member(X0,X2))),
% 8.34/1.47 inference(resolution,[status(thm)],[f30,f27])).
% 8.34/1.47 fof(f92,plain,(
% 8.34/1.47 ![X0,X1]: (subset(complement(X0),X1)|~member(member_of_1_not_of_2(complement(X0),X1),X0))),
% 8.34/1.49 inference(resolution,[status(thm)],[f28,f31])).
% 8.34/1.49 fof(f97,plain,(
% 8.34/1.49 ![X0,X1,X2]: (subset(X0,X1)|~subset(X0,X2)|member(member_of_1_not_of_2(X0,X1),X2))),
% 8.34/1.49 inference(resolution,[status(thm)],[f28,f27])).
% 8.34/1.49 fof(f109,plain,(
% 8.34/1.49 ![X0]: (member(X0,a)|member(X0,b))),
% 8.34/1.49 inference(resolution,[status(thm)],[f90,f78])).
% 8.34/1.49 fof(f110,plain,(
% 8.34/1.49 ![X0]: (member(X0,b)|member(X0,c))),
% 8.34/1.49 inference(resolution,[status(thm)],[f90,f77])).
% 8.34/1.49 fof(f112,plain,(
% 8.34/1.49 ![X0]: (member(member_of_1_not_of_2(X0,a),b)|subset(X0,a))),
% 8.34/1.49 inference(resolution,[status(thm)],[f109,f29])).
% 8.34/1.49 fof(f121,plain,(
% 8.34/1.49 ![X0,X1]: (member(X0,c)|~subset(b,X1)|member(X0,X1))),
% 8.34/1.49 inference(resolution,[status(thm)],[f110,f27])).
% 8.34/1.49 fof(f151,plain,(
% 8.34/1.49 ![X0]: (member(X0,c)|member(X0,complement(a)))),
% 8.34/1.49 inference(resolution,[status(thm)],[f121,f76])).
% 8.34/1.49 fof(f154,plain,(
% 8.34/1.49 ![X0]: (member(X0,c)|~member(X0,a))),
% 8.34/1.49 inference(resolution,[status(thm)],[f151,f31])).
% 8.34/1.49 fof(f831,plain,(
% 8.34/1.49 ![X0]: (subset(c,X0)|member(member_of_1_not_of_2(c,X0),complement(b)))),
% 8.34/1.49 inference(resolution,[status(thm)],[f97,f75])).
% 8.34/1.49 fof(f937,plain,(
% 8.34/1.49 ![X0]: (subset(c,X0)|~member(member_of_1_not_of_2(c,X0),b))),
% 8.34/1.49 inference(resolution,[status(thm)],[f831,f31])).
% 8.34/1.49 fof(f955,definition,(
% 8.34/1.49 sQ7_spl <=> (subset(c,a))),
% 8.34/1.49 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 8.34/1.49 fof(f1450,definition,(
% 8.34/1.49 sQ16_spl <=> (subset(complement(b),a))),
% 8.34/1.49 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 8.34/1.49 fof(f2521,plain,(
% 8.34/1.49 ![X0]: (member(member_of_1_not_of_2(a,X0),c)|subset(a,X0))),
% 8.34/1.49 inference(resolution,[status(thm)],[f154,f28])).
% 8.34/1.49 fof(f2892,plain,(
% 8.34/1.49 subset(a,c)|subset(a,c)),
% 8.34/1.49 inference(resolution,[status(thm)],[f2521,f29])).
% 8.34/1.49 fof(f2908,definition,(
% 8.34/1.49 sQ24_spl <=> (subset(a,c))),
% 8.34/1.49 introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition])).
% 8.34/1.49 fof(f2909,plain,(
% 8.34/1.49 subset(a,c)|~sQ24_spl),
% 8.34/1.49 inference(component_clause,[status(thm)],[f2908])).
% 8.34/1.49 fof(f2911,plain,(
% 8.34/1.49 sQ24_spl),
% 8.34/1.49 inference(split_clause,[status(thm)],[f2892,f2908])).
% 8.34/1.49 fof(f4125,plain,(
% 8.34/1.49 ~subset(c,a)|equal_sets(c,a)|~sQ24_spl),
% 8.34/1.49 inference(resolution,[status(thm)],[f2909,f45])).
% 8.34/1.49 fof(f4128,definition,(
% 8.34/1.49 sQ29_spl <=> (equal_sets(c,a))),
% 8.34/1.49 introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition])).
% 8.34/1.49 fof(f4129,plain,(
% 8.34/1.49 equal_sets(c,a)|~sQ29_spl),
% 8.34/1.49 inference(component_clause,[status(thm)],[f4128])).
% 8.34/1.49 fof(f4131,plain,(
% 8.34/1.49 ~sQ7_spl|sQ29_spl|~sQ24_spl),
% 8.34/1.49 inference(split_clause,[status(thm)],[f4125,f955,f4128,f2908])).
% 8.34/1.49 fof(f4136,plain,(
% 8.34/1.49 equal_sets(a,c)|~sQ29_spl),
% 8.34/1.49 inference(resolution,[status(thm)],[f4129,f47])).
% 8.34/1.49 fof(f4137,plain,(
% 8.34/1.49 $false|~sQ29_spl),
% 8.34/1.49 inference(forward_subsumption_resolution,[status(thm)],[f4136,f56])).
% 8.34/1.49 fof(f4138,plain,(
% 8.34/1.49 ~sQ29_spl),
% 8.34/1.49 inference(contradiction_clause,[status(thm)],[f4137])).
% 8.34/1.49 fof(f4663,plain,(
% 8.34/1.49 subset(c,a)|subset(c,a)),
% 8.34/1.49 inference(resolution,[status(thm)],[f112,f937])).
% 8.34/1.49 fof(f4666,plain,(
% 8.34/1.49 subset(complement(b),a)|subset(complement(b),a)),
% 8.34/1.49 inference(resolution,[status(thm)],[f112,f92])).
% 8.34/1.49 fof(f4685,plain,(
% 8.34/1.49 sQ7_spl),
% 8.34/1.49 inference(split_clause,[status(thm)],[f4663,f955])).
% 8.34/1.49 fof(f4691,plain,(
% 8.34/1.49 sQ16_spl),
% 8.34/1.49 inference(split_clause,[status(thm)],[f4666,f1450])).
% 8.34/1.49 fof(f4695,plain,(
% 8.34/1.49 $false),
% 8.34/1.49 inference(sat_refutation,[status(thm)],[f2911,f4131,f4138,f4685,f4691])).
% 8.34/1.49 % SZS output end CNFRefutation for theBenchmark.p
% 8.34/1.51 % Elapsed time: 1.152601 seconds
% 8.34/1.51 % CPU time: 8.901097 seconds
% 8.34/1.51 % Total memory used: 85.386 MB
% 8.34/1.51 % Net memory used: 74.354 MB
%------------------------------------------------------------------------------