%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU307+2 : TPTP v9.3.1. Released v3.3.0.
% 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 02:22:17 PM UTC 2026
% Result : Theorem 13.17s 2.26s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU307+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 06:11:31 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.42 % Drodi V4.1.1
% 13.17/2.26 % Refutation found
% 13.17/2.26 % SZS status Theorem for theBenchmark: Theorem is valid
% 13.17/2.26 % SZS output start CNFRefutation for theBenchmark
% 13.17/2.26 fof(f65,axiom,(
% 13.17/2.26 (! [A,B] :( B = powerset(A)<=> (! [C] :( in(C,B)<=> subset(C,A) ) )) )),
% 13.17/2.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.17/2.26 fof(f70,axiom,(
% 13.17/2.26 (! [A,B] :( ( ~ empty(A)=> ( element(B,A)<=> in(B,A) ) )& ( empty(A)=> ( element(B,A)<=> empty(B) ) ) ) )),
% 13.17/2.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.17/2.26 fof(f77,axiom,(
% 13.17/2.26 (! [A] :( one_sorted_str(A)=> cast_as_carrier_subset(A) = the_carrier(A) ) )),
% 13.17/2.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.17/2.26 fof(f130,axiom,(
% 13.17/2.26 (! [A] :( one_sorted_str(A)=> element(cast_as_carrier_subset(A),powerset(the_carrier(A))) ) )),
% 13.17/2.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.17/2.26 fof(f185,axiom,(
% 13.17/2.26 (! [A] :( ~ empty(powerset(A))& cup_closed(powerset(A))& diff_closed(powerset(A))& preboolean(powerset(A)) ) )),
% 13.17/2.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.17/2.26 fof(f284,axiom,(
% 13.17/2.26 (! [A,B,C] :( ( element(B,powerset(A))& element(C,powerset(A)) )=> subset_intersection2(A,B,C) = set_intersection2(B,C) ) )),
% 13.17/2.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.17/2.26 fof(f347,conjecture,(
% 13.17/2.26 (! [A] :( one_sorted_str(A)=> (! [B] :( element(B,powerset(the_carrier(A)))=> subset_intersection2(the_carrier(A),B,cast_as_carrier_subset(A)) = B ) )) )),
% 13.17/2.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.17/2.26 fof(f348,negated_conjecture,(
% 13.17/2.26 ~((! [A] :( one_sorted_str(A)=> (! [B] :( element(B,powerset(the_carrier(A)))=> subset_intersection2(the_carrier(A),B,cast_as_carrier_subset(A)) = B ) )) ))),
% 13.17/2.26 inference(negated_conjecture,[status(cth)],[f347])).
% 13.17/2.26 fof(f392,lemma,(
% 13.17/2.26 (! [A,B] :( subset(A,B)=> set_intersection2(A,B) = A ) )),
% 13.17/2.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.17/2.26 fof(f797,plain,(
% 13.17/2.26 ![A,B]: ((~B=powerset(A)|(![C]: ((~in(C,B)|subset(C,A))&(in(C,B)|~subset(C,A)))))&(B=powerset(A)|(?[C]: ((~in(C,B)|~subset(C,A))&(in(C,B)|subset(C,A))))))),
% 13.17/2.26 inference(NNF_transformation,[status(thm)],[f65])).
% 13.17/2.26 fof(f798,plain,(
% 13.17/2.26 (![A,B]: (~B=powerset(A)|((![C]: (~in(C,B)|subset(C,A)))&(![C]: (in(C,B)|~subset(C,A))))))&(![A,B]: (B=powerset(A)|(?[C]: ((~in(C,B)|~subset(C,A))&(in(C,B)|subset(C,A))))))),
% 13.17/2.26 inference(miniscoping,[status(thm)],[f797])).
% 13.17/2.26 fof(f799,plain,(
% 13.17/2.26 (![A,B]: (~B=powerset(A)|((![C]: (~in(C,B)|subset(C,A)))&(![C]: (in(C,B)|~subset(C,A))))))&(![A,B]: (B=powerset(A)|((~in(sK35_skl(B,A),B)|~subset(sK35_skl(B,A),A))&(in(sK35_skl(B,A),B)|subset(sK35_skl(B,A),A)))))),
% 13.17/2.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK35_skl]),skolemize(C,sK35_skl(B,A))],[f798])).
% 13.17/2.26 fof(f800,plain,(
% 13.17/2.26 ![X0,X1,X2]: (~X0=powerset(X1)|~in(X2,X0)|subset(X2,X1))),
% 13.17/2.26 inference(cnf_transformation,[status(thm)],[f799])).
% 13.17/2.26 fof(f828,plain,(
% 13.17/2.26 ![A,B]: ((empty(A)|(element(B,A)<=>in(B,A)))&(~empty(A)|(element(B,A)<=>empty(B))))),
% 13.17/2.26 inference(pre_NNF_transformation,[status(thm)],[f70])).
% 13.17/2.26 fof(f829,plain,(
% 13.17/2.26 ![A,B]: ((empty(A)|((~element(B,A)|in(B,A))&(element(B,A)|~in(B,A))))&(~empty(A)|((~element(B,A)|empty(B))&(element(B,A)|~empty(B)))))),
% 13.17/2.26 inference(NNF_transformation,[status(thm)],[f828])).
% 13.17/2.26 fof(f830,plain,(
% 13.17/2.26 (![A]: (empty(A)|((![B]: (~element(B,A)|in(B,A)))&(![B]: (element(B,A)|~in(B,A))))))&(![A]: (~empty(A)|((![B]: (~element(B,A)|empty(B)))&(![B]: (element(B,A)|~empty(B))))))),
% 13.17/2.26 inference(miniscoping,[status(thm)],[f829])).
% 13.17/2.26 fof(f831,plain,(
% 13.17/2.26 ![X0,X1]: (empty(X0)|~element(X1,X0)|in(X1,X0))),
% 13.17/2.26 inference(cnf_transformation,[status(thm)],[f830])).
% 13.17/2.26 fof(f884,plain,(
% 13.17/2.26 ![A]: (~one_sorted_str(A)|cast_as_carrier_subset(A)=the_carrier(A))),
% 13.17/2.26 inference(pre_NNF_transformation,[status(thm)],[f77])).
% 13.17/2.26 fof(f885,plain,(
% 13.17/2.26 ![X0]: (~one_sorted_str(X0)|cast_as_carrier_subset(X0)=the_carrier(X0))),
% 13.17/2.26 inference(cnf_transformation,[status(thm)],[f884])).
% 13.17/2.26 fof(f1133,plain,(
% 13.17/2.26 ![A]: (~one_sorted_str(A)|element(cast_as_carrier_subset(A),powerset(the_carrier(A))))),
% 13.17/2.26 inference(pre_NNF_transformation,[status(thm)],[f130])).
% 13.17/2.26 fof(f1134,plain,(
% 13.17/2.26 ![X0]: (~one_sorted_str(X0)|element(cast_as_carrier_subset(X0),powerset(the_carrier(X0))))),
% 13.17/2.26 inference(cnf_transformation,[status(thm)],[f1133])).
% 13.17/2.30 fof(f1228,plain,(
% 13.17/2.30 (((![A]: ~empty(powerset(A)))&(![A]: cup_closed(powerset(A))))&(![A]: diff_closed(powerset(A))))&(![A]: preboolean(powerset(A)))),
% 13.17/2.30 inference(miniscoping,[status(thm)],[f185])).
% 13.17/2.30 fof(f1229,plain,(
% 13.17/2.30 ![X0]: (~empty(powerset(X0)))),
% 13.17/2.30 inference(cnf_transformation,[status(thm)],[f1228])).
% 13.17/2.30 fof(f1589,plain,(
% 13.17/2.30 ![A,B,C]: ((~element(B,powerset(A))|~element(C,powerset(A)))|subset_intersection2(A,B,C)=set_intersection2(B,C))),
% 13.17/2.30 inference(pre_NNF_transformation,[status(thm)],[f284])).
% 13.17/2.30 fof(f1590,plain,(
% 13.17/2.30 ![X0,X1,X2]: (~element(X0,powerset(X1))|~element(X2,powerset(X1))|subset_intersection2(X1,X0,X2)=set_intersection2(X0,X2))),
% 13.17/2.30 inference(cnf_transformation,[status(thm)],[f1589])).
% 13.17/2.30 fof(f2001,plain,(
% 13.17/2.30 (?[A]: (one_sorted_str(A)&(?[B]: (element(B,powerset(the_carrier(A)))&~subset_intersection2(the_carrier(A),B,cast_as_carrier_subset(A))=B))))),
% 13.17/2.30 inference(pre_NNF_transformation,[status(thm)],[f348])).
% 13.17/2.30 fof(f2002,plain,(
% 13.17/2.30 (one_sorted_str(sK251_skl)&(element(sK252_skl,powerset(the_carrier(sK251_skl)))&~subset_intersection2(the_carrier(sK251_skl),sK252_skl,cast_as_carrier_subset(sK251_skl))=sK252_skl))),
% 13.17/2.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK251_skl,sK252_skl]),skolemize(A,sK251_skl),skolemize(B,sK252_skl)],[f2001])).
% 13.17/2.30 fof(f2003,plain,(
% 13.17/2.30 one_sorted_str(sK251_skl)),
% 13.17/2.30 inference(cnf_transformation,[status(thm)],[f2002])).
% 13.17/2.30 fof(f2004,plain,(
% 13.17/2.30 element(sK252_skl,powerset(the_carrier(sK251_skl)))),
% 13.17/2.30 inference(cnf_transformation,[status(thm)],[f2002])).
% 13.17/2.30 fof(f2005,plain,(
% 13.17/2.30 ~subset_intersection2(the_carrier(sK251_skl),sK252_skl,cast_as_carrier_subset(sK251_skl))=sK252_skl),
% 13.17/2.30 inference(cnf_transformation,[status(thm)],[f2002])).
% 13.17/2.30 fof(f2147,plain,(
% 13.17/2.30 ![A,B]: (~subset(A,B)|set_intersection2(A,B)=A)),
% 13.17/2.30 inference(pre_NNF_transformation,[status(thm)],[f392])).
% 13.17/2.30 fof(f2148,plain,(
% 13.17/2.30 ![X0,X1]: (~subset(X0,X1)|set_intersection2(X0,X1)=X0)),
% 13.17/2.30 inference(cnf_transformation,[status(thm)],[f2147])).
% 13.17/2.30 fof(f2890,plain,(
% 13.17/2.30 cast_as_carrier_subset(sK251_skl)=the_carrier(sK251_skl)),
% 13.17/2.30 inference(resolution,[status(thm)],[f885,f2003])).
% 13.17/2.30 fof(f2891,plain,(
% 13.17/2.30 ~subset_intersection2(the_carrier(sK251_skl),sK252_skl,the_carrier(sK251_skl))=sK252_skl),
% 13.17/2.30 inference(backward_demodulation,[status(thm)],[f2890,f2005])).
% 13.17/2.30 fof(f2892,plain,(
% 13.17/2.30 element(cast_as_carrier_subset(sK251_skl),powerset(the_carrier(sK251_skl)))),
% 13.17/2.30 inference(resolution,[status(thm)],[f1134,f2003])).
% 13.17/2.30 fof(f2893,plain,(
% 13.17/2.30 element(the_carrier(sK251_skl),powerset(the_carrier(sK251_skl)))),
% 13.17/2.30 inference(forward_demodulation,[status(thm)],[f2890,f2892])).
% 13.17/2.30 fof(f2960,plain,(
% 13.17/2.30 ![X0]: (~element(X0,powerset(the_carrier(sK251_skl)))|subset_intersection2(the_carrier(sK251_skl),sK252_skl,X0)=set_intersection2(sK252_skl,X0))),
% 13.17/2.30 inference(resolution,[status(thm)],[f1590,f2004])).
% 13.17/2.30 fof(f2990,plain,(
% 13.17/2.30 subset_intersection2(the_carrier(sK251_skl),sK252_skl,the_carrier(sK251_skl))=set_intersection2(sK252_skl,the_carrier(sK251_skl))),
% 13.17/2.30 inference(resolution,[status(thm)],[f2960,f2893])).
% 13.17/2.30 fof(f3089,plain,(
% 13.17/2.30 ~set_intersection2(sK252_skl,the_carrier(sK251_skl))=sK252_skl),
% 13.17/2.30 inference(backward_demodulation,[status(thm)],[f2990,f2891])).
% 13.17/2.30 fof(f15207,plain,(
% 13.17/2.30 empty(powerset(the_carrier(sK251_skl)))|in(sK252_skl,powerset(the_carrier(sK251_skl)))),
% 13.17/2.30 inference(resolution,[status(thm)],[f831,f2004])).
% 13.17/2.30 fof(f15225,plain,(
% 13.17/2.30 in(sK252_skl,powerset(the_carrier(sK251_skl)))),
% 13.17/2.30 inference(forward_subsumption_resolution,[status(thm)],[f15207,f1229])).
% 13.17/2.30 fof(f15227,plain,(
% 13.17/2.30 ![X0]: (~powerset(the_carrier(sK251_skl))=powerset(X0)|subset(sK252_skl,X0))),
% 13.17/2.30 inference(resolution,[status(thm)],[f15225,f800])).
% 13.17/2.30 fof(f15612,plain,(
% 13.17/2.30 subset(sK252_skl,the_carrier(sK251_skl))),
% 13.17/2.30 inference(equality_resolution,[status(thm)],[f15227])).
% 13.17/2.30 fof(f15613,plain,(
% 13.17/2.30 set_intersection2(sK252_skl,the_carrier(sK251_skl))=sK252_skl),
% 13.17/2.30 inference(resolution,[status(thm)],[f15612,f2148])).
% 13.17/2.30 fof(f15618,plain,(
% 13.17/2.30 $false),
% 13.17/2.30 inference(forward_subsumption_resolution,[status(thm)],[f15613,f3089])).
% 13.17/2.30 % SZS output end CNFRefutation for theBenchmark.p
% 14.10/2.31 % Elapsed time: 1.928694 seconds
% 14.10/2.31 % CPU time: 14.680884 seconds
% 14.10/2.31 % Total memory used: 337.976 MB
% 14.10/2.31 % Net memory used: 322.587 MB
%------------------------------------------------------------------------------