%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU188+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 : n001.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 02:21:56 PM UTC 2026
% Result : Theorem 0.12s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU188+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n001.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
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 06:01:43 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.38 fof(f2,axiom,(
% 0.12/0.38 (! [A] :( empty(A)=> relation(A) ) )),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f20,axiom,(
% 0.12/0.38 (! [A] :( ( ~ empty(A)& relation(A) )=> ~ empty(relation_dom(A)) ) )),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f21,axiom,(
% 0.12/0.38 (! [A] :( ( ~ empty(A)& relation(A) )=> ~ empty(relation_rng(A)) ) )),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f22,axiom,(
% 0.12/0.38 (! [A] :( empty(A)=> ( empty(relation_dom(A))& relation(relation_dom(A)) ) ) )),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f24,axiom,(
% 0.12/0.38 (? [A] :( empty(A)& relation(A) ) )),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f25,axiom,(
% 0.12/0.38 (? [A] : empty(A) )),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f31,conjecture,(
% 0.12/0.38 (! [A] :( relation(A)=> ( ( relation_dom(A) = empty_set| relation_rng(A) = empty_set )=> A = empty_set ) ) )),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f32,negated_conjecture,(
% 0.12/0.38 ~((! [A] :( relation(A)=> ( ( relation_dom(A) = empty_set| relation_rng(A) = empty_set )=> A = empty_set ) ) ))),
% 0.12/0.38 inference(negated_conjecture,[status(cth)],[f31])).
% 0.12/0.38 fof(f33,axiom,(
% 0.12/0.38 (! [A] :( empty(A)=> A = empty_set ) )),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f38,plain,(
% 0.12/0.38 ![A]: (~empty(A)|relation(A))),
% 0.12/0.38 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.12/0.38 fof(f39,plain,(
% 0.12/0.38 ![X0]: (~empty(X0)|relation(X0))),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f38])).
% 0.12/0.38 fof(f66,plain,(
% 0.12/0.38 ![A]: ((empty(A)|~relation(A))|~empty(relation_dom(A)))),
% 0.12/0.38 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 0.12/0.38 fof(f67,plain,(
% 0.12/0.38 ![X0]: (empty(X0)|~relation(X0)|~empty(relation_dom(X0)))),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f66])).
% 0.12/0.38 fof(f68,plain,(
% 0.12/0.38 ![A]: ((empty(A)|~relation(A))|~empty(relation_rng(A)))),
% 0.12/0.38 inference(pre_NNF_transformation,[status(thm)],[f21])).
% 0.12/0.38 fof(f69,plain,(
% 0.12/0.38 ![X0]: (empty(X0)|~relation(X0)|~empty(relation_rng(X0)))),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f68])).
% 0.12/0.38 fof(f70,plain,(
% 0.12/0.38 ![A]: (~empty(A)|(empty(relation_dom(A))&relation(relation_dom(A))))),
% 0.12/0.38 inference(pre_NNF_transformation,[status(thm)],[f22])).
% 0.12/0.38 fof(f71,plain,(
% 0.12/0.38 ![X0]: (~empty(X0)|empty(relation_dom(X0)))),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f70])).
% 0.12/0.38 fof(f76,plain,(
% 0.12/0.38 (empty(sK7_skl)&relation(sK7_skl))),
% 0.12/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(A,sK7_skl)],[f24])).
% 0.12/0.38 fof(f77,plain,(
% 0.12/0.38 empty(sK7_skl)),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f76])).
% 0.12/0.38 fof(f79,plain,(
% 0.12/0.38 empty(sK8_skl)),
% 0.12/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(A,sK8_skl)],[f25])).
% 0.12/0.38 fof(f80,plain,(
% 0.12/0.38 empty(sK8_skl)),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f79])).
% 0.12/0.38 fof(f93,plain,(
% 0.12/0.38 (?[A]: (relation(A)&((relation_dom(A)=empty_set|relation_rng(A)=empty_set)&~A=empty_set)))),
% 0.12/0.38 inference(pre_NNF_transformation,[status(thm)],[f32])).
% 0.12/0.38 fof(f94,plain,(
% 0.12/0.38 (relation(sK13_skl)&((relation_dom(sK13_skl)=empty_set|relation_rng(sK13_skl)=empty_set)&~sK13_skl=empty_set))),
% 0.12/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl]),skolemize(A,sK13_skl)],[f93])).
% 0.12/0.38 fof(f95,plain,(
% 0.12/0.38 relation(sK13_skl)),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f94])).
% 0.12/0.38 fof(f96,plain,(
% 0.12/0.38 relation_dom(sK13_skl)=empty_set|relation_rng(sK13_skl)=empty_set),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f94])).
% 0.12/0.38 fof(f97,plain,(
% 0.12/0.38 ~sK13_skl=empty_set),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f94])).
% 0.12/0.38 fof(f98,plain,(
% 0.12/0.38 ![A]: (~empty(A)|A=empty_set)),
% 0.12/0.38 inference(pre_NNF_transformation,[status(thm)],[f33])).
% 0.12/0.38 fof(f99,plain,(
% 0.12/0.38 ![X0]: (~empty(X0)|X0=empty_set)),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f98])).
% 0.12/0.38 fof(f106,definition,(
% 0.12/0.38 sQ0_spl <=> (relation_dom(sK13_skl)=empty_set)),
% 0.12/0.38 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.12/0.38 fof(f107,plain,(
% 0.12/0.38 relation_dom(sK13_skl)=empty_set|~sQ0_spl),
% 0.12/0.38 inference(component_clause,[status(thm)],[f106])).
% 0.12/0.38 fof(f109,definition,(
% 0.12/0.38 sQ1_spl <=> (relation_rng(sK13_skl)=empty_set)),
% 0.12/0.38 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.12/0.38 fof(f110,plain,(
% 0.12/0.38 relation_rng(sK13_skl)=empty_set|~sQ1_spl),
% 0.12/0.38 inference(component_clause,[status(thm)],[f109])).
% 0.12/0.38 fof(f112,plain,(
% 0.12/0.38 sQ0_spl|sQ1_spl),
% 0.12/0.38 inference(split_clause,[status(thm)],[f96,f106,f109])).
% 0.12/0.38 fof(f135,plain,(
% 0.12/0.38 empty(relation_dom(sK7_skl))),
% 0.12/0.38 inference(resolution,[status(thm)],[f77,f71])).
% 0.12/0.38 fof(f136,plain,(
% 0.12/0.38 sK7_skl=empty_set),
% 0.12/0.38 inference(resolution,[status(thm)],[f77,f99])).
% 0.12/0.38 fof(f141,plain,(
% 0.12/0.38 sK8_skl=empty_set),
% 0.12/0.38 inference(resolution,[status(thm)],[f80,f99])).
% 0.12/0.38 fof(f142,plain,(
% 0.12/0.38 relation(sK8_skl)),
% 0.12/0.38 inference(resolution,[status(thm)],[f80,f39])).
% 0.12/0.38 fof(f145,plain,(
% 0.12/0.38 ![X0]: (~empty(X0)|X0=sK7_skl)),
% 0.12/0.38 inference(backward_demodulation,[status(thm)],[f136,f99])).
% 0.12/0.38 fof(f148,plain,(
% 0.12/0.38 relation_dom(sK13_skl)=sK7_skl|~sQ0_spl),
% 0.12/0.38 inference(backward_demodulation,[status(thm)],[f136,f107])).
% 0.12/0.38 fof(f149,plain,(
% 0.12/0.38 ~sK13_skl=sK7_skl),
% 0.12/0.38 inference(backward_demodulation,[status(thm)],[f136,f97])).
% 0.12/0.38 fof(f151,plain,(
% 0.12/0.38 sK7_skl=sK8_skl),
% 0.12/0.38 inference(backward_demodulation,[status(thm)],[f141,f136])).
% 0.12/0.38 fof(f152,plain,(
% 0.12/0.38 ~sK13_skl=sK8_skl),
% 0.12/0.38 inference(backward_demodulation,[status(thm)],[f151,f149])).
% 0.12/0.38 fof(f159,plain,(
% 0.12/0.38 relation_dom(sK13_skl)=sK8_skl|~sQ0_spl),
% 0.12/0.38 inference(forward_demodulation,[status(thm)],[f151,f148])).
% 0.12/0.38 fof(f161,definition,(
% 0.12/0.38 sQ2_spl <=> (relation(sK13_skl))),
% 0.12/0.38 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.12/0.38 fof(f163,plain,(
% 0.12/0.38 ~relation(sK13_skl)|sQ2_spl),
% 0.12/0.38 inference(component_clause,[status(thm)],[f161])).
% 0.12/0.38 fof(f168,plain,(
% 0.12/0.38 relation_rng(sK13_skl)=sK8_skl|~sQ1_spl),
% 0.12/0.38 inference(forward_demodulation,[status(thm)],[f141,f110])).
% 0.12/0.38 fof(f176,plain,(
% 0.12/0.38 empty(relation_dom(sK8_skl))),
% 0.12/0.38 inference(forward_demodulation,[status(thm)],[f151,f135])).
% 0.12/0.38 fof(f177,plain,(
% 0.12/0.38 empty(sK8_skl)|~relation(sK8_skl)),
% 0.12/0.38 inference(resolution,[status(thm)],[f176,f67])).
% 0.12/0.38 fof(f182,definition,(
% 0.12/0.38 sQ4_spl <=> (empty(sK8_skl))),
% 0.12/0.38 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.12/0.38 fof(f185,definition,(
% 0.12/0.38 sQ5_spl <=> (relation(sK8_skl))),
% 0.12/0.38 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.12/0.38 fof(f187,plain,(
% 0.12/0.38 ~relation(sK8_skl)|sQ5_spl),
% 0.12/0.38 inference(component_clause,[status(thm)],[f185])).
% 0.12/0.38 fof(f188,plain,(
% 0.12/0.38 sQ4_spl|~sQ5_spl),
% 0.12/0.38 inference(split_clause,[status(thm)],[f177,f182,f185])).
% 0.12/0.38 fof(f189,plain,(
% 0.12/0.38 $false|sQ5_spl),
% 0.12/0.38 inference(forward_subsumption_resolution,[status(thm)],[f187,f142])).
% 0.12/0.38 fof(f190,plain,(
% 0.12/0.38 sQ5_spl),
% 0.12/0.38 inference(contradiction_clause,[status(thm)],[f189])).
% 0.12/0.38 fof(f206,plain,(
% 0.12/0.38 ![X0]: (~empty(X0)|X0=sK8_skl)),
% 0.12/0.38 inference(forward_demodulation,[status(thm)],[f151,f145])).
% 0.12/0.38 fof(f211,plain,(
% 0.12/0.38 empty(sK13_skl)|~relation(sK13_skl)|~empty(sK8_skl)|~sQ1_spl),
% 0.12/0.38 inference(paramodulation,[status(thm)],[f168,f69])).
% 0.12/0.38 fof(f213,definition,(
% 0.12/0.38 sQ7_spl <=> (empty(sK13_skl))),
% 0.12/0.38 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.12/0.38 fof(f214,plain,(
% 0.12/0.38 empty(sK13_skl)|~sQ7_spl),
% 0.12/0.38 inference(component_clause,[status(thm)],[f213])).
% 0.12/0.38 fof(f216,plain,(
% 0.12/0.38 sQ7_spl|~sQ2_spl|~sQ4_spl|~sQ1_spl),
% 0.12/0.38 inference(split_clause,[status(thm)],[f211,f213,f161,f182,f109])).
% 0.12/0.38 fof(f217,plain,(
% 0.12/0.38 $false|sQ2_spl),
% 0.12/0.38 inference(forward_subsumption_resolution,[status(thm)],[f163,f95])).
% 0.12/0.38 fof(f218,plain,(
% 0.12/0.38 sQ2_spl),
% 0.12/0.38 inference(contradiction_clause,[status(thm)],[f217])).
% 0.12/0.38 fof(f219,plain,(
% 0.12/0.38 empty(sK13_skl)|~relation(sK13_skl)|~empty(sK8_skl)|~sQ0_spl),
% 0.12/0.38 inference(paramodulation,[status(thm)],[f159,f67])).
% 0.12/0.38 fof(f221,plain,(
% 0.12/0.38 sQ7_spl|~sQ2_spl|~sQ4_spl|~sQ0_spl),
% 0.12/0.38 inference(split_clause,[status(thm)],[f219,f213,f161,f182,f106])).
% 0.12/0.38 fof(f224,plain,(
% 0.12/0.38 sK13_skl=sK8_skl|~sQ7_spl),
% 0.12/0.38 inference(resolution,[status(thm)],[f214,f206])).
% 0.12/0.38 fof(f229,plain,(
% 0.12/0.38 $false|~sQ7_spl),
% 0.12/0.38 inference(forward_subsumption_resolution,[status(thm)],[f224,f152])).
% 0.12/0.38 fof(f230,plain,(
% 0.12/0.38 ~sQ7_spl),
% 0.12/0.38 inference(contradiction_clause,[status(thm)],[f229])).
% 0.12/0.38 fof(f231,plain,(
% 0.12/0.38 $false),
% 0.12/0.38 inference(sat_refutation,[status(thm)],[f112,f188,f190,f216,f218,f221,f230])).
% 0.12/0.38 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.41 % Elapsed time: 0.050382 seconds
% 0.12/0.41 % CPU time: 0.142012 seconds
% 0.12/0.41 % Total memory used: 86.390 MB
% 0.12/0.41 % Net memory used: 86.261 MB
%------------------------------------------------------------------------------