%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU305+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 : n007.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 02:22:16 PM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU305+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n007.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 06:08:06 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 0.17/0.47 % Refutation found
% 0.17/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.47 % SZS output start CNFRefutation for theBenchmark
% 0.17/0.47 fof(f4,axiom,(
% 0.17/0.47 (! [A,B,C] :( ( ~ empty_carrier(A)& join_commutative(A)& join_semilatt_str(A)& element(B,the_carrier(A))& element(C,the_carrier(A)) )=> join_commut(A,B,C) = join_commut(A,C,B) ) )),
% 0.17/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.47 fof(f6,axiom,(
% 0.17/0.47 (! [A] :( ( ~ empty_carrier(A)& join_semilatt_str(A) )=> (! [B] :( element(B,the_carrier(A))=> (! [C] :( element(C,the_carrier(A))=> ( below(A,B,C)<=> join(A,B,C) = C ) ) )) )) )),
% 0.17/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.47 fof(f31,axiom,(
% 0.17/0.47 (! [A,B,C] :( ( ~ empty_carrier(A)& join_commutative(A)& join_semilatt_str(A)& element(B,the_carrier(A))& element(C,the_carrier(A)) )=> join_commut(A,B,C) = join(A,B,C) ) )),
% 0.17/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.47 fof(f35,conjecture,(
% 0.17/0.47 (! [A] :( ( ~ empty_carrier(A)& join_commutative(A)& join_semilatt_str(A) )=> (! [B] :( element(B,the_carrier(A))=> (! [C] :( element(C,the_carrier(A))=> ( ( below(A,B,C)& below(A,C,B) )=> B = C ) ) )) )) )),
% 0.17/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.47 fof(f36,negated_conjecture,(
% 0.17/0.47 ~((! [A] :( ( ~ empty_carrier(A)& join_commutative(A)& join_semilatt_str(A) )=> (! [B] :( element(B,the_carrier(A))=> (! [C] :( element(C,the_carrier(A))=> ( ( below(A,B,C)& below(A,C,B) )=> B = C ) ) )) )) ))),
% 0.17/0.47 inference(negated_conjecture,[status(cth)],[f35])).
% 0.17/0.47 fof(f51,plain,(
% 0.17/0.47 ![A,B,C]: (((((empty_carrier(A)|~join_commutative(A))|~join_semilatt_str(A))|~element(B,the_carrier(A)))|~element(C,the_carrier(A)))|join_commut(A,B,C)=join_commut(A,C,B))),
% 0.17/0.47 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.17/0.47 fof(f52,plain,(
% 0.17/0.47 ![X0,X1,X2]: (empty_carrier(X0)|~join_commutative(X0)|~join_semilatt_str(X0)|~element(X1,the_carrier(X0))|~element(X2,the_carrier(X0))|join_commut(X0,X1,X2)=join_commut(X0,X2,X1))),
% 0.17/0.47 inference(cnf_transformation,[status(thm)],[f51])).
% 0.17/0.47 fof(f55,plain,(
% 0.17/0.47 ![A]: ((empty_carrier(A)|~join_semilatt_str(A))|(![B]: (~element(B,the_carrier(A))|(![C]: (~element(C,the_carrier(A))|(below(A,B,C)<=>join(A,B,C)=C))))))),
% 0.17/0.47 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.17/0.47 fof(f56,plain,(
% 0.17/0.47 ![A]: ((empty_carrier(A)|~join_semilatt_str(A))|(![B]: (~element(B,the_carrier(A))|(![C]: (~element(C,the_carrier(A))|((~below(A,B,C)|join(A,B,C)=C)&(below(A,B,C)|~join(A,B,C)=C)))))))),
% 0.17/0.47 inference(NNF_transformation,[status(thm)],[f55])).
% 0.17/0.47 fof(f57,plain,(
% 0.17/0.47 ![X0,X1,X2]: (empty_carrier(X0)|~join_semilatt_str(X0)|~element(X1,the_carrier(X0))|~element(X2,the_carrier(X0))|~below(X0,X1,X2)|join(X0,X1,X2)=X2)),
% 0.17/0.47 inference(cnf_transformation,[status(thm)],[f56])).
% 0.17/0.47 fof(f99,plain,(
% 0.17/0.47 ![A,B,C]: (((((empty_carrier(A)|~join_commutative(A))|~join_semilatt_str(A))|~element(B,the_carrier(A)))|~element(C,the_carrier(A)))|join_commut(A,B,C)=join(A,B,C))),
% 0.17/0.47 inference(pre_NNF_transformation,[status(thm)],[f31])).
% 0.17/0.47 fof(f100,plain,(
% 0.17/0.47 ![X0,X1,X2]: (empty_carrier(X0)|~join_commutative(X0)|~join_semilatt_str(X0)|~element(X1,the_carrier(X0))|~element(X2,the_carrier(X0))|join_commut(X0,X1,X2)=join(X0,X1,X2))),
% 0.17/0.47 inference(cnf_transformation,[status(thm)],[f99])).
% 0.17/0.47 fof(f109,plain,(
% 0.17/0.47 (?[A]: (((~empty_carrier(A)&join_commutative(A))&join_semilatt_str(A))&(?[B]: (element(B,the_carrier(A))&(?[C]: (element(C,the_carrier(A))&((below(A,B,C)&below(A,C,B))&~B=C)))))))),
% 0.17/0.47 inference(pre_NNF_transformation,[status(thm)],[f36])).
% 0.17/0.47 fof(f110,plain,(
% 0.17/0.47 (((~empty_carrier(sK7_skl)&join_commutative(sK7_skl))&join_semilatt_str(sK7_skl))&(element(sK8_skl,the_carrier(sK7_skl))&(element(sK9_skl,the_carrier(sK7_skl))&((below(sK7_skl,sK8_skl,sK9_skl)&below(sK7_skl,sK9_skl,sK8_skl))&~sK8_skl=sK9_skl))))),
% 0.17/0.47 inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl,sK9_skl]),skolemize(A,sK7_skl),skolemize(B,sK8_skl),skolemize(C,sK9_skl)],[f109])).
% 0.17/0.47 fof(f111,plain,(
% 0.17/0.47 ~empty_carrier(sK7_skl)),
% 0.17/0.47 inference(cnf_transformation,[status(thm)],[f110])).
% 0.17/0.47 fof(f112,plain,(
% 0.17/0.47 join_commutative(sK7_skl)),
% 0.17/0.47 inference(cnf_transformation,[status(thm)],[f110])).
% 0.17/0.47 fof(f113,plain,(
% 0.17/0.47 join_semilatt_str(sK7_skl)),
% 0.17/0.47 inference(cnf_transformation,[status(thm)],[f110])).
% 0.17/0.47 fof(f114,plain,(
% 0.17/0.47 element(sK8_skl,the_carrier(sK7_skl))),
% 0.17/0.47 inference(cnf_transformation,[status(thm)],[f110])).
% 0.17/0.47 fof(f115,plain,(
% 0.17/0.47 element(sK9_skl,the_carrier(sK7_skl))),
% 0.17/0.47 inference(cnf_transformation,[status(thm)],[f110])).
% 0.17/0.47 fof(f116,plain,(
% 0.17/0.47 below(sK7_skl,sK8_skl,sK9_skl)),
% 0.17/0.47 inference(cnf_transformation,[status(thm)],[f110])).
% 0.17/0.47 fof(f117,plain,(
% 0.17/0.47 below(sK7_skl,sK9_skl,sK8_skl)),
% 0.17/0.47 inference(cnf_transformation,[status(thm)],[f110])).
% 0.17/0.47 fof(f118,plain,(
% 0.17/0.47 ~sK8_skl=sK9_skl),
% 0.17/0.47 inference(cnf_transformation,[status(thm)],[f110])).
% 0.17/0.47 fof(f139,plain,(
% 0.17/0.47 ![X0]: (empty_carrier(sK7_skl)|~join_commutative(sK7_skl)|~join_semilatt_str(sK7_skl)|~element(X0,the_carrier(sK7_skl))|join_commut(sK7_skl,X0,sK9_skl)=join_commut(sK7_skl,sK9_skl,X0))),
% 0.17/0.47 inference(resolution,[status(thm)],[f52,f115])).
% 0.17/0.47 fof(f141,definition,(
% 0.17/0.47 sQ0_spl <=> (empty_carrier(sK7_skl))),
% 0.17/0.47 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.17/0.47 fof(f142,plain,(
% 0.17/0.47 empty_carrier(sK7_skl)|~sQ0_spl),
% 0.17/0.47 inference(component_clause,[status(thm)],[f141])).
% 0.17/0.47 fof(f144,definition,(
% 0.17/0.47 sQ1_spl <=> (join_commutative(sK7_skl))),
% 0.17/0.47 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.17/0.47 fof(f146,plain,(
% 0.17/0.47 ~join_commutative(sK7_skl)|sQ1_spl),
% 0.17/0.47 inference(component_clause,[status(thm)],[f144])).
% 0.17/0.47 fof(f147,definition,(
% 0.17/0.47 sQ2_spl <=> (join_semilatt_str(sK7_skl))),
% 0.17/0.47 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.17/0.47 fof(f149,plain,(
% 0.17/0.47 ~join_semilatt_str(sK7_skl)|sQ2_spl),
% 0.17/0.47 inference(component_clause,[status(thm)],[f147])).
% 0.17/0.47 fof(f150,definition,(
% 0.17/0.47 ![X0]: (sQ3_spl <=> (~element(X0,the_carrier(sK7_skl))|join_commut(sK7_skl,X0,sK9_skl)=join_commut(sK7_skl,sK9_skl,X0)))),
% 0.17/0.47 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.17/0.47 fof(f151,plain,(
% 0.17/0.47 ![X0]: (~element(X0,the_carrier(sK7_skl))|join_commut(sK7_skl,X0,sK9_skl)=join_commut(sK7_skl,sK9_skl,X0)|~sQ3_spl)),
% 0.17/0.47 inference(component_clause,[status(thm)],[f150])).
% 0.17/0.47 fof(f153,plain,(
% 0.17/0.47 sQ0_spl|~sQ1_spl|~sQ2_spl|sQ3_spl),
% 0.17/0.47 inference(split_clause,[status(thm)],[f139,f141,f144,f147,f150])).
% 0.17/0.47 fof(f158,plain,(
% 0.17/0.47 $false|sQ2_spl),
% 0.17/0.47 inference(forward_subsumption_resolution,[status(thm)],[f149,f113])).
% 0.17/0.47 fof(f159,plain,(
% 0.17/0.47 sQ2_spl),
% 0.17/0.47 inference(contradiction_clause,[status(thm)],[f158])).
% 0.17/0.47 fof(f160,plain,(
% 0.17/0.47 $false|sQ1_spl),
% 0.17/0.47 inference(forward_subsumption_resolution,[status(thm)],[f146,f112])).
% 0.17/0.47 fof(f161,plain,(
% 0.17/0.47 sQ1_spl),
% 0.17/0.47 inference(contradiction_clause,[status(thm)],[f160])).
% 0.17/0.47 fof(f162,plain,(
% 0.17/0.47 $false|~sQ0_spl),
% 0.17/0.47 inference(forward_subsumption_resolution,[status(thm)],[f142,f111])).
% 0.17/0.47 fof(f163,plain,(
% 0.17/0.47 ~sQ0_spl),
% 0.17/0.47 inference(contradiction_clause,[status(thm)],[f162])).
% 0.17/0.47 fof(f174,plain,(
% 0.17/0.47 ![X0]: (empty_carrier(sK7_skl)|~join_commutative(sK7_skl)|~join_semilatt_str(sK7_skl)|~element(X0,the_carrier(sK7_skl))|join_commut(sK7_skl,X0,sK9_skl)=join(sK7_skl,X0,sK9_skl))),
% 0.17/0.47 inference(resolution,[status(thm)],[f100,f115])).
% 0.17/0.47 fof(f175,plain,(
% 0.17/0.47 ![X0]: (empty_carrier(sK7_skl)|~join_commutative(sK7_skl)|~join_semilatt_str(sK7_skl)|~element(X0,the_carrier(sK7_skl))|join_commut(sK7_skl,X0,sK8_skl)=join(sK7_skl,X0,sK8_skl))),
% 0.17/0.47 inference(resolution,[status(thm)],[f100,f114])).
% 0.17/0.47 fof(f176,definition,(
% 0.17/0.47 ![X0]: (sQ7_spl <=> (~element(X0,the_carrier(sK7_skl))|join_commut(sK7_skl,X0,sK9_skl)=join(sK7_skl,X0,sK9_skl)))),
% 0.17/0.47 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.17/0.47 fof(f177,plain,(
% 0.17/0.47 ![X0]: (~element(X0,the_carrier(sK7_skl))|join_commut(sK7_skl,X0,sK9_skl)=join(sK7_skl,X0,sK9_skl)|~sQ7_spl)),
% 0.17/0.47 inference(component_clause,[status(thm)],[f176])).
% 0.17/0.47 fof(f179,plain,(
% 0.17/0.47 sQ0_spl|~sQ1_spl|~sQ2_spl|sQ7_spl),
% 0.17/0.47 inference(split_clause,[status(thm)],[f174,f141,f144,f147,f176])).
% 0.17/0.47 fof(f180,definition,(
% 0.17/0.47 ![X0]: (sQ8_spl <=> (~element(X0,the_carrier(sK7_skl))|join_commut(sK7_skl,X0,sK8_skl)=join(sK7_skl,X0,sK8_skl)))),
% 0.17/0.47 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.17/0.47 fof(f181,plain,(
% 0.17/0.47 ![X0]: (~element(X0,the_carrier(sK7_skl))|join_commut(sK7_skl,X0,sK8_skl)=join(sK7_skl,X0,sK8_skl)|~sQ8_spl)),
% 0.17/0.47 inference(component_clause,[status(thm)],[f180])).
% 0.17/0.47 fof(f183,plain,(
% 0.17/0.47 sQ0_spl|~sQ1_spl|~sQ2_spl|sQ8_spl),
% 0.17/0.47 inference(split_clause,[status(thm)],[f175,f141,f144,f147,f180])).
% 0.17/0.47 fof(f235,plain,(
% 0.17/0.47 empty_carrier(sK7_skl)|~join_semilatt_str(sK7_skl)|~element(sK8_skl,the_carrier(sK7_skl))|~element(sK9_skl,the_carrier(sK7_skl))|join(sK7_skl,sK8_skl,sK9_skl)=sK9_skl),
% 0.17/0.47 inference(resolution,[status(thm)],[f116,f57])).
% 0.17/0.47 fof(f236,definition,(
% 0.17/0.47 sQ20_spl <=> (element(sK8_skl,the_carrier(sK7_skl)))),
% 0.17/0.47 introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition])).
% 0.17/0.47 fof(f238,plain,(
% 0.17/0.47 ~element(sK8_skl,the_carrier(sK7_skl))|sQ20_spl),
% 0.17/0.47 inference(component_clause,[status(thm)],[f236])).
% 0.17/0.47 fof(f239,definition,(
% 0.17/0.47 sQ21_spl <=> (element(sK9_skl,the_carrier(sK7_skl)))),
% 0.17/0.47 introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition])).
% 0.17/0.47 fof(f241,plain,(
% 0.17/0.47 ~element(sK9_skl,the_carrier(sK7_skl))|sQ21_spl),
% 0.17/0.47 inference(component_clause,[status(thm)],[f239])).
% 0.17/0.47 fof(f242,definition,(
% 0.17/0.47 sQ22_spl <=> (join(sK7_skl,sK8_skl,sK9_skl)=sK9_skl)),
% 0.17/0.47 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 0.17/0.47 fof(f243,plain,(
% 0.17/0.47 join(sK7_skl,sK8_skl,sK9_skl)=sK9_skl|~sQ22_spl),
% 0.17/0.47 inference(component_clause,[status(thm)],[f242])).
% 0.17/0.47 fof(f245,plain,(
% 0.17/0.47 sQ0_spl|~sQ2_spl|~sQ20_spl|~sQ21_spl|sQ22_spl),
% 0.17/0.47 inference(split_clause,[status(thm)],[f235,f141,f147,f236,f239,f242])).
% 0.17/0.47 fof(f246,plain,(
% 0.17/0.47 empty_carrier(sK7_skl)|~join_semilatt_str(sK7_skl)|~element(sK9_skl,the_carrier(sK7_skl))|~element(sK8_skl,the_carrier(sK7_skl))|join(sK7_skl,sK9_skl,sK8_skl)=sK8_skl),
% 0.17/0.47 inference(resolution,[status(thm)],[f117,f57])).
% 0.17/0.47 fof(f247,definition,(
% 0.17/0.47 sQ23_spl <=> (join(sK7_skl,sK9_skl,sK8_skl)=sK8_skl)),
% 0.17/0.47 introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition])).
% 0.17/0.47 fof(f248,plain,(
% 0.17/0.47 join(sK7_skl,sK9_skl,sK8_skl)=sK8_skl|~sQ23_spl),
% 0.17/0.47 inference(component_clause,[status(thm)],[f247])).
% 0.17/0.47 fof(f250,plain,(
% 0.17/0.47 sQ0_spl|~sQ2_spl|~sQ21_spl|~sQ20_spl|sQ23_spl),
% 0.17/0.47 inference(split_clause,[status(thm)],[f246,f141,f147,f239,f236,f247])).
% 0.17/0.47 fof(f251,plain,(
% 0.17/0.47 $false|sQ20_spl),
% 0.17/0.47 inference(forward_subsumption_resolution,[status(thm)],[f238,f114])).
% 0.17/0.47 fof(f252,plain,(
% 0.17/0.47 sQ20_spl),
% 0.17/0.47 inference(contradiction_clause,[status(thm)],[f251])).
% 0.17/0.47 fof(f253,plain,(
% 0.17/0.47 $false|sQ21_spl),
% 0.17/0.47 inference(forward_subsumption_resolution,[status(thm)],[f241,f115])).
% 0.17/0.47 fof(f254,plain,(
% 0.17/0.47 sQ21_spl),
% 0.17/0.47 inference(contradiction_clause,[status(thm)],[f253])).
% 0.17/0.47 fof(f276,plain,(
% 0.17/0.47 join_commut(sK7_skl,sK8_skl,sK9_skl)=join_commut(sK7_skl,sK9_skl,sK8_skl)|~sQ3_spl),
% 0.17/0.47 inference(resolution,[status(thm)],[f151,f114])).
% 0.17/0.47 fof(f285,plain,(
% 0.17/0.47 join_commut(sK7_skl,sK8_skl,sK9_skl)=join(sK7_skl,sK8_skl,sK9_skl)|~sQ7_spl),
% 0.17/0.47 inference(resolution,[status(thm)],[f177,f114])).
% 0.17/0.47 fof(f288,plain,(
% 0.17/0.47 sK9_skl=join_commut(sK7_skl,sK9_skl,sK8_skl)|~sQ22_spl|~sQ7_spl|~sQ3_spl),
% 0.17/0.47 inference(backward_demodulation,[status(thm)],[f289,f276])).
% 0.17/0.47 fof(f289,plain,(
% 0.17/0.47 join_commut(sK7_skl,sK8_skl,sK9_skl)=sK9_skl|~sQ22_spl|~sQ7_spl),
% 0.17/0.47 inference(forward_demodulation,[status(thm)],[f243,f285])).
% 0.17/0.47 fof(f290,plain,(
% 0.17/0.47 join_commut(sK7_skl,sK9_skl,sK8_skl)=join(sK7_skl,sK9_skl,sK8_skl)|~sQ8_spl),
% 0.17/0.47 inference(resolution,[status(thm)],[f181,f115])).
% 0.17/0.47 fof(f292,plain,(
% 0.17/0.47 sK9_skl=join(sK7_skl,sK9_skl,sK8_skl)|~sQ22_spl|~sQ7_spl|~sQ3_spl|~sQ8_spl),
% 0.17/0.47 inference(forward_demodulation,[status(thm)],[f288,f290])).
% 0.17/0.47 fof(f293,plain,(
% 0.17/0.47 sK9_skl=sK8_skl|~sQ23_spl|~sQ22_spl|~sQ7_spl|~sQ3_spl|~sQ8_spl),
% 0.17/0.47 inference(forward_demodulation,[status(thm)],[f248,f292])).
% 0.17/0.47 fof(f294,plain,(
% 0.17/0.47 $false|~sQ23_spl|~sQ22_spl|~sQ7_spl|~sQ3_spl|~sQ8_spl),
% 0.17/0.47 inference(forward_subsumption_resolution,[status(thm)],[f293,f118])).
% 0.17/0.47 fof(f295,plain,(
% 0.17/0.47 ~sQ23_spl|~sQ22_spl|~sQ7_spl|~sQ3_spl|~sQ8_spl),
% 0.17/0.47 inference(contradiction_clause,[status(thm)],[f294])).
% 0.17/0.47 fof(f296,plain,(
% 0.17/0.47 $false),
% 0.17/0.47 inference(sat_refutation,[status(thm)],[f153,f159,f161,f163,f179,f183,f245,f250,f252,f254,f295])).
% 0.17/0.47 % SZS output end CNFRefutation for theBenchmark.p
% 0.17/0.51 % Elapsed time: 0.066889 seconds
% 0.17/0.51 % CPU time: 0.189491 seconds
% 0.17/0.51 % Total memory used: 69.503 MB
% 0.17/0.51 % Net memory used: 69.470 MB
%------------------------------------------------------------------------------