%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU325+1 : 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 : n016.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 02:22:20 PM UTC 2026
% Result : Theorem 0.13s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU325+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 06:16:37 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.41 fof(f17,axiom,(
% 0.13/0.41 (! [A] :( one_sorted_str(A)=> cast_as_carrier_subset(A) = the_carrier(A) ) )),
% 0.13/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f18,axiom,(
% 0.13/0.41 (! [A,B] :( B = union(A)<=> (! [C] :( in(C,B)<=> (? [D] :( in(C,D)& in(D,A) ) )) )) )),
% 0.13/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f19,axiom,(
% 0.13/0.41 (! [A] :( one_sorted_str(A)=> (! [B] :( element(B,powerset(powerset(the_carrier(A))))=> ( is_a_cover_of_carrier(A,B)<=> cast_as_carrier_subset(A) = union_of_subsets(the_carrier(A),B) ) ) )) )),
% 0.13/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f30,axiom,(
% 0.13/0.41 (! [A] :( ( ~ empty_carrier(A)& one_sorted_str(A) )=> ~ empty(the_carrier(A)) ) )),
% 0.13/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f33,axiom,(
% 0.13/0.41 ( empty(empty_set)& v1_membered(empty_set)& v2_membered(empty_set)& v3_membered(empty_set)& v4_membered(empty_set)& v5_membered(empty_set) ) ),
% 0.13/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f36,axiom,(
% 0.13/0.41 (! [A] :(? [B] :( element(B,powerset(A))& empty(B) ) ))),
% 0.13/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f39,axiom,(
% 0.13/0.41 (! [A,B] :( element(B,powerset(powerset(A)))=> union_of_subsets(A,B) = union(B) ) )),
% 0.13/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f46,conjecture,(
% 0.13/0.41 (! [A] :( ( ~ empty_carrier(A)& one_sorted_str(A) )=> (! [B] :( element(B,powerset(powerset(the_carrier(A))))=> ~ ( is_a_cover_of_carrier(A,B)& B = empty_set ) ) )) )),
% 0.13/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f47,negated_conjecture,(
% 0.13/0.41 ~((! [A] :( ( ~ empty_carrier(A)& one_sorted_str(A) )=> (! [B] :( element(B,powerset(powerset(the_carrier(A))))=> ~ ( is_a_cover_of_carrier(A,B)& B = empty_set ) ) )) ))),
% 0.13/0.41 inference(negated_conjecture,[status(cth)],[f46])).
% 0.13/0.41 fof(f48,axiom,(
% 0.13/0.41 (! [A] :( empty(A)=> A = empty_set ) )),
% 0.13/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f49,axiom,(
% 0.13/0.41 (! [A,B] :~ ( in(A,B)& empty(B) ) )),
% 0.13/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f107,plain,(
% 0.13/0.41 ![A]: (~one_sorted_str(A)|cast_as_carrier_subset(A)=the_carrier(A))),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f17])).
% 0.13/0.41 fof(f108,plain,(
% 0.13/0.41 ![X0]: (~one_sorted_str(X0)|cast_as_carrier_subset(X0)=the_carrier(X0))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f107])).
% 0.13/0.41 fof(f109,plain,(
% 0.13/0.41 ![A,B]: ((~B=union(A)|(![C]: ((~in(C,B)|(?[D]: (in(C,D)&in(D,A))))&(in(C,B)|(![D]: (~in(C,D)|~in(D,A)))))))&(B=union(A)|(?[C]: ((~in(C,B)|(![D]: (~in(C,D)|~in(D,A))))&(in(C,B)|(?[D]: (in(C,D)&in(D,A))))))))),
% 0.13/0.41 inference(NNF_transformation,[status(thm)],[f18])).
% 0.13/0.41 fof(f110,plain,(
% 0.13/0.41 (![A,B]: (~B=union(A)|((![C]: (~in(C,B)|(?[D]: (in(C,D)&in(D,A)))))&(![C]: (in(C,B)|(![D]: (~in(C,D)|~in(D,A))))))))&(![A,B]: (B=union(A)|(?[C]: ((~in(C,B)|(![D]: (~in(C,D)|~in(D,A))))&(in(C,B)|(?[D]: (in(C,D)&in(D,A))))))))),
% 0.13/0.41 inference(miniscoping,[status(thm)],[f109])).
% 0.13/0.41 fof(f111,plain,(
% 0.13/0.41 (![A,B]: (~B=union(A)|((![C]: (~in(C,B)|(in(C,sK0_skl(C,B,A))&in(sK0_skl(C,B,A),A))))&(![C]: (in(C,B)|(![D]: (~in(C,D)|~in(D,A))))))))&(![A,B]: (B=union(A)|((~in(sK1_skl(B,A),B)|(![D]: (~in(sK1_skl(B,A),D)|~in(D,A))))&(in(sK1_skl(B,A),B)|(in(sK1_skl(B,A),sK2_skl(B,A))&in(sK2_skl(B,A),A))))))),
% 0.13/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(D,sK0_skl(C,B,A)),skolemize(C,sK1_skl(B,A)),skolemize(D,sK2_skl(B,A))],[f110])).
% 0.13/0.41 fof(f117,plain,(
% 0.13/0.41 ![X0,X1]: (X0=union(X1)|in(sK1_skl(X0,X1),X0)|in(sK2_skl(X0,X1),X1))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f111])).
% 0.13/0.41 fof(f118,plain,(
% 0.13/0.41 ![A]: (~one_sorted_str(A)|(![B]: (~element(B,powerset(powerset(the_carrier(A))))|(is_a_cover_of_carrier(A,B)<=>cast_as_carrier_subset(A)=union_of_subsets(the_carrier(A),B)))))),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 0.13/0.41 fof(f119,plain,(
% 0.13/0.41 ![A]: (~one_sorted_str(A)|(![B]: (~element(B,powerset(powerset(the_carrier(A))))|((~is_a_cover_of_carrier(A,B)|cast_as_carrier_subset(A)=union_of_subsets(the_carrier(A),B))&(is_a_cover_of_carrier(A,B)|~cast_as_carrier_subset(A)=union_of_subsets(the_carrier(A),B))))))),
% 0.13/0.41 inference(NNF_transformation,[status(thm)],[f118])).
% 0.13/0.41 fof(f120,plain,(
% 0.13/0.41 ![X0,X1]: (~one_sorted_str(X0)|~element(X1,powerset(powerset(the_carrier(X0))))|~is_a_cover_of_carrier(X0,X1)|cast_as_carrier_subset(X0)=union_of_subsets(the_carrier(X0),X1))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f119])).
% 0.13/0.41 fof(f130,plain,(
% 0.13/0.41 ![A]: ((empty_carrier(A)|~one_sorted_str(A))|~empty(the_carrier(A)))),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f30])).
% 0.13/0.41 fof(f131,plain,(
% 0.13/0.41 ![X0]: (empty_carrier(X0)|~one_sorted_str(X0)|~empty(the_carrier(X0)))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f130])).
% 0.13/0.41 fof(f135,plain,(
% 0.13/0.41 empty(empty_set)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f33])).
% 0.13/0.41 fof(f152,plain,(
% 0.13/0.41 ![A]: (element(sK7_skl(A),powerset(A))&empty(sK7_skl(A)))),
% 0.13/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(B,sK7_skl(A))],[f36])).
% 0.13/0.41 fof(f153,plain,(
% 0.13/0.41 ![X0]: (element(sK7_skl(X0),powerset(X0)))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f152])).
% 0.13/0.41 fof(f154,plain,(
% 0.13/0.41 ![X0]: (empty(sK7_skl(X0)))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f152])).
% 0.13/0.41 fof(f162,plain,(
% 0.13/0.41 ![A,B]: (~element(B,powerset(powerset(A)))|union_of_subsets(A,B)=union(B))),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f39])).
% 0.13/0.41 fof(f163,plain,(
% 0.13/0.41 ![X0,X1]: (~element(X0,powerset(powerset(X1)))|union_of_subsets(X1,X0)=union(X0))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f162])).
% 0.13/0.41 fof(f180,plain,(
% 0.13/0.41 (?[A]: ((~empty_carrier(A)&one_sorted_str(A))&(?[B]: (element(B,powerset(powerset(the_carrier(A))))&(is_a_cover_of_carrier(A,B)&B=empty_set)))))),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f47])).
% 0.13/0.41 fof(f181,plain,(
% 0.13/0.41 ((~empty_carrier(sK10_skl)&one_sorted_str(sK10_skl))&(element(sK11_skl,powerset(powerset(the_carrier(sK10_skl))))&(is_a_cover_of_carrier(sK10_skl,sK11_skl)&sK11_skl=empty_set)))),
% 0.13/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl]),skolemize(A,sK10_skl),skolemize(B,sK11_skl)],[f180])).
% 0.13/0.41 fof(f182,plain,(
% 0.13/0.41 ~empty_carrier(sK10_skl)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f181])).
% 0.13/0.41 fof(f183,plain,(
% 0.13/0.41 one_sorted_str(sK10_skl)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f181])).
% 0.13/0.41 fof(f184,plain,(
% 0.13/0.41 element(sK11_skl,powerset(powerset(the_carrier(sK10_skl))))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f181])).
% 0.13/0.41 fof(f185,plain,(
% 0.13/0.41 is_a_cover_of_carrier(sK10_skl,sK11_skl)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f181])).
% 0.13/0.41 fof(f186,plain,(
% 0.13/0.41 sK11_skl=empty_set),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f181])).
% 0.13/0.41 fof(f187,plain,(
% 0.13/0.41 ![A]: (~empty(A)|A=empty_set)),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f48])).
% 0.13/0.41 fof(f188,plain,(
% 0.13/0.41 ![X0]: (~empty(X0)|X0=empty_set)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f187])).
% 0.13/0.41 fof(f189,plain,(
% 0.13/0.41 ![A,B]: (~in(A,B)|~empty(B))),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f49])).
% 0.13/0.41 fof(f190,plain,(
% 0.13/0.41 ![B]: ((![A]: ~in(A,B))|~empty(B))),
% 0.13/0.41 inference(miniscoping,[status(thm)],[f189])).
% 0.13/0.41 fof(f191,plain,(
% 0.13/0.41 ![X0,X1]: (~in(X0,X1)|~empty(X1))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f190])).
% 0.13/0.41 fof(f207,plain,(
% 0.13/0.41 empty(sK11_skl)),
% 0.13/0.41 inference(backward_demodulation,[status(thm)],[f186,f135])).
% 0.13/0.41 fof(f208,plain,(
% 0.13/0.41 ~one_sorted_str(sK10_skl)|~element(sK11_skl,powerset(powerset(the_carrier(sK10_skl))))|cast_as_carrier_subset(sK10_skl)=union_of_subsets(the_carrier(sK10_skl),sK11_skl)),
% 0.13/0.41 inference(resolution,[status(thm)],[f185,f120])).
% 0.13/0.41 fof(f209,plain,(
% 0.13/0.41 ~element(sK11_skl,powerset(powerset(the_carrier(sK10_skl))))|cast_as_carrier_subset(sK10_skl)=union_of_subsets(the_carrier(sK10_skl),sK11_skl)),
% 0.13/0.41 inference(forward_subsumption_resolution,[status(thm)],[f208,f183])).
% 0.13/0.41 fof(f213,plain,(
% 0.13/0.41 ![X0]: (~empty(X0)|X0=sK11_skl)),
% 0.13/0.41 inference(forward_demodulation,[status(thm)],[f186,f188])).
% 0.13/0.41 fof(f227,plain,(
% 0.13/0.41 cast_as_carrier_subset(sK10_skl)=union_of_subsets(the_carrier(sK10_skl),sK11_skl)),
% 0.13/0.41 inference(forward_subsumption_resolution,[status(thm)],[f209,f184])).
% 0.13/0.41 fof(f261,plain,(
% 0.13/0.41 ![X0]: (sK7_skl(X0)=sK11_skl)),
% 0.13/0.41 inference(resolution,[status(thm)],[f154,f213])).
% 0.13/0.42 fof(f313,plain,(
% 0.13/0.42 cast_as_carrier_subset(sK10_skl)=the_carrier(sK10_skl)),
% 0.13/0.42 inference(resolution,[status(thm)],[f108,f183])).
% 0.13/0.42 fof(f320,plain,(
% 0.13/0.42 cast_as_carrier_subset(sK10_skl)=union_of_subsets(cast_as_carrier_subset(sK10_skl),sK11_skl)),
% 0.13/0.42 inference(backward_demodulation,[status(thm)],[f313,f227])).
% 0.13/0.42 fof(f322,plain,(
% 0.13/0.42 empty_carrier(sK10_skl)|~one_sorted_str(sK10_skl)|~empty(cast_as_carrier_subset(sK10_skl))),
% 0.13/0.42 inference(paramodulation,[status(thm)],[f313,f131])).
% 0.13/0.42 fof(f324,plain,(
% 0.13/0.42 ~one_sorted_str(sK10_skl)|~empty(cast_as_carrier_subset(sK10_skl))),
% 0.13/0.42 inference(forward_subsumption_resolution,[status(thm)],[f322,f182])).
% 0.13/0.42 fof(f346,plain,(
% 0.13/0.42 ~empty(cast_as_carrier_subset(sK10_skl))),
% 0.13/0.42 inference(forward_subsumption_resolution,[status(thm)],[f324,f183])).
% 0.13/0.42 fof(f347,plain,(
% 0.13/0.42 ![X0]: (~in(X0,sK11_skl))),
% 0.13/0.42 inference(resolution,[status(thm)],[f191,f207])).
% 0.13/0.42 fof(f349,plain,(
% 0.13/0.42 ![X0]: (sK11_skl=union(X0)|in(sK2_skl(sK11_skl,X0),X0))),
% 0.13/0.42 inference(resolution,[status(thm)],[f117,f347])).
% 0.13/0.42 fof(f387,plain,(
% 0.13/0.42 ![X0]: (element(sK11_skl,powerset(X0)))),
% 0.13/0.42 inference(forward_demodulation,[status(thm)],[f261,f153])).
% 0.13/0.42 fof(f439,plain,(
% 0.13/0.42 ![X0]: (union_of_subsets(X0,sK11_skl)=union(sK11_skl))),
% 0.13/0.42 inference(resolution,[status(thm)],[f163,f387])).
% 0.13/0.42 fof(f508,plain,(
% 0.13/0.42 cast_as_carrier_subset(sK10_skl)=union(sK11_skl)),
% 0.13/0.42 inference(backward_demodulation,[status(thm)],[f439,f320])).
% 0.13/0.42 fof(f598,plain,(
% 0.13/0.42 sK11_skl=union(sK11_skl)),
% 0.13/0.42 inference(resolution,[status(thm)],[f349,f347])).
% 0.13/0.42 fof(f626,plain,(
% 0.13/0.42 cast_as_carrier_subset(sK10_skl)=sK11_skl),
% 0.13/0.42 inference(backward_demodulation,[status(thm)],[f598,f508])).
% 0.13/0.42 fof(f638,plain,(
% 0.13/0.42 ~empty(sK11_skl)),
% 0.13/0.42 inference(backward_demodulation,[status(thm)],[f626,f346])).
% 0.13/0.42 fof(f643,plain,(
% 0.13/0.42 $false),
% 0.13/0.42 inference(forward_subsumption_resolution,[status(thm)],[f638,f207])).
% 0.13/0.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.44 % Elapsed time: 0.073512 seconds
% 0.13/0.44 % CPU time: 0.241951 seconds
% 0.13/0.44 % Total memory used: 106.491 MB
% 0.13/0.44 % Net memory used: 106.362 MB
%------------------------------------------------------------------------------