%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LAT382+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 01:03:56 PM UTC 2026
% Result : Theorem 0.16s 5.48s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LAT382+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.43 % Computer : n019.cluster.edu
% 0.16/5.43 % Model : x86_64 x86_64
% 0.16/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.43 % Memory : 8046.5625MB
% 0.16/5.43 % OS : Linux 6.8.0-71-generic
% 0.16/5.43 % CPULimit : 300
% 0.16/5.43 % WCLimit : 300
% 0.16/5.43 % DateTime : Sun Sep 20 23:57:25 UTC 2026
% 0.16/5.43 % CPUTime :
% 0.16/5.45 % Drodi V4.1.1
% 0.16/5.48 % Refutation found
% 0.16/5.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/5.48 % SZS output start CNFRefutation for theBenchmark
% 0.16/5.48 fof(f3,axiom,(
% 0.16/5.48 (! [W0] :( aSet0(W0)=> (! [W1] :( aElementOf0(W1,W0)=> aElement0(W1) ) )) )),
% 0.16/5.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/5.48 fof(f8,axiom,(
% 0.16/5.48 (! [W0,W1] :( ( aElement0(W0)& aElement0(W1) )=> ( ( sdtlseqdt0(W0,W1)& sdtlseqdt0(W1,W0) )=> W0 = W1 ) ) )),
% 0.16/5.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/5.48 fof(f12,definition,(
% 0.16/5.48 (! [W0] :( aSet0(W0)=> (! [W1] :( aSubsetOf0(W1,W0)=> (! [W2] :( aInfimumOfIn0(W2,W1,W0)<=> ( aElementOf0(W2,W0)& aLowerBoundOfIn0(W2,W1,W0)& (! [W3] :( aLowerBoundOfIn0(W3,W1,W0)=> sdtlseqdt0(W3,W2) ) )) ) )) )) )),
% 0.16/5.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/5.48 fof(f15,hypothesis,(
% 0.16/5.48 aSet0(xT) ),
% 0.16/5.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/5.48 fof(f16,hypothesis,(
% 0.16/5.48 aSubsetOf0(xS,xT) ),
% 0.16/5.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/5.48 fof(f17,hypothesis,(
% 0.16/5.48 ( aInfimumOfIn0(xu,xS,xT)& aInfimumOfIn0(xv,xS,xT) ) ),
% 0.16/5.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/5.48 fof(f18,conjecture,(
% 0.16/5.48 xu = xv ),
% 0.16/5.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/5.48 fof(f19,negated_conjecture,(
% 0.16/5.48 ~(xu = xv )),
% 0.16/5.48 inference(negated_conjecture,[status(cth)],[f18])).
% 0.16/5.48 fof(f26,plain,(
% 0.16/5.48 ![W0]: (~aSet0(W0)|(![W1]: (~aElementOf0(W1,W0)|aElement0(W1))))),
% 0.16/5.48 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 0.16/5.48 fof(f27,plain,(
% 0.16/5.48 ![X0,X1]: (~aSet0(X0)|~aElementOf0(X1,X0)|aElement0(X1))),
% 0.16/5.48 inference(cnf_transformation,[status(thm)],[f26])).
% 0.16/5.48 fof(f45,plain,(
% 0.16/5.48 ![W0,W1]: ((~aElement0(W0)|~aElement0(W1))|((~sdtlseqdt0(W0,W1)|~sdtlseqdt0(W1,W0))|W0=W1))),
% 0.16/5.48 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.16/5.48 fof(f46,plain,(
% 0.16/5.48 ![X0,X1]: (~aElement0(X0)|~aElement0(X1)|~sdtlseqdt0(X0,X1)|~sdtlseqdt0(X1,X0)|X0=X1)),
% 0.16/5.48 inference(cnf_transformation,[status(thm)],[f45])).
% 0.16/5.48 fof(f65,plain,(
% 0.16/5.48 ![W0]: (~aSet0(W0)|(![W1]: (~aSubsetOf0(W1,W0)|(![W2]: (aInfimumOfIn0(W2,W1,W0)<=>((aElementOf0(W2,W0)&aLowerBoundOfIn0(W2,W1,W0))&(![W3]: (~aLowerBoundOfIn0(W3,W1,W0)|sdtlseqdt0(W3,W2)))))))))),
% 0.16/5.48 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.16/5.48 fof(f66,plain,(
% 0.16/5.48 ![W0]: (~aSet0(W0)|(![W1]: (~aSubsetOf0(W1,W0)|(![W2]: ((~aInfimumOfIn0(W2,W1,W0)|((aElementOf0(W2,W0)&aLowerBoundOfIn0(W2,W1,W0))&(![W3]: (~aLowerBoundOfIn0(W3,W1,W0)|sdtlseqdt0(W3,W2)))))&(aInfimumOfIn0(W2,W1,W0)|((~aElementOf0(W2,W0)|~aLowerBoundOfIn0(W2,W1,W0))|(?[W3]: (aLowerBoundOfIn0(W3,W1,W0)&~sdtlseqdt0(W3,W2))))))))))),
% 0.16/5.48 inference(NNF_transformation,[status(thm)],[f65])).
% 0.16/5.48 fof(f67,plain,(
% 0.16/5.48 ![W0]: (~aSet0(W0)|(![W1]: (~aSubsetOf0(W1,W0)|((![W2]: (~aInfimumOfIn0(W2,W1,W0)|((aElementOf0(W2,W0)&aLowerBoundOfIn0(W2,W1,W0))&(![W3]: (~aLowerBoundOfIn0(W3,W1,W0)|sdtlseqdt0(W3,W2))))))&(![W2]: (aInfimumOfIn0(W2,W1,W0)|((~aElementOf0(W2,W0)|~aLowerBoundOfIn0(W2,W1,W0))|(?[W3]: (aLowerBoundOfIn0(W3,W1,W0)&~sdtlseqdt0(W3,W2))))))))))),
% 0.16/5.48 inference(miniscoping,[status(thm)],[f66])).
% 0.16/5.48 fof(f68,plain,(
% 0.16/5.48 ![W0]: (~aSet0(W0)|(![W1]: (~aSubsetOf0(W1,W0)|((![W2]: (~aInfimumOfIn0(W2,W1,W0)|((aElementOf0(W2,W0)&aLowerBoundOfIn0(W2,W1,W0))&(![W3]: (~aLowerBoundOfIn0(W3,W1,W0)|sdtlseqdt0(W3,W2))))))&(![W2]: (aInfimumOfIn0(W2,W1,W0)|((~aElementOf0(W2,W0)|~aLowerBoundOfIn0(W2,W1,W0))|(aLowerBoundOfIn0(sK4_skl(W2,W1,W0),W1,W0)&~sdtlseqdt0(sK4_skl(W2,W1,W0),W2)))))))))),
% 0.16/5.48 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(W3,sK4_skl(W2,W1,W0))],[f67])).
% 0.16/5.48 fof(f69,plain,(
% 0.16/5.48 ![X0,X1,X2]: (~aSet0(X0)|~aSubsetOf0(X1,X0)|~aInfimumOfIn0(X2,X1,X0)|aElementOf0(X2,X0))),
% 0.16/5.48 inference(cnf_transformation,[status(thm)],[f68])).
% 0.16/5.48 fof(f70,plain,(
% 0.16/5.48 ![X0,X1,X2]: (~aSet0(X0)|~aSubsetOf0(X1,X0)|~aInfimumOfIn0(X2,X1,X0)|aLowerBoundOfIn0(X2,X1,X0))),
% 0.16/5.48 inference(cnf_transformation,[status(thm)],[f68])).
% 0.16/5.48 fof(f71,plain,(
% 0.16/5.48 ![X0,X1,X2,X3]: (~aSet0(X0)|~aSubsetOf0(X1,X0)|~aInfimumOfIn0(X2,X1,X0)|~aLowerBoundOfIn0(X3,X1,X0)|sdtlseqdt0(X3,X2))),
% 0.16/5.48 inference(cnf_transformation,[status(thm)],[f68])).
% 0.16/5.48 fof(f85,plain,(
% 0.16/5.48 aSet0(xT)),
% 0.16/5.48 inference(cnf_transformation,[status(thm)],[f15])).
% 0.16/5.48 fof(f86,plain,(
% 0.16/5.48 aSubsetOf0(xS,xT)),
% 0.16/5.48 inference(cnf_transformation,[status(thm)],[f16])).
% 0.16/5.48 fof(f87,plain,(
% 0.16/5.48 aInfimumOfIn0(xu,xS,xT)),
% 0.16/5.48 inference(cnf_transformation,[status(thm)],[f17])).
% 0.16/5.48 fof(f88,plain,(
% 0.16/5.48 aInfimumOfIn0(xv,xS,xT)),
% 0.16/5.48 inference(cnf_transformation,[status(thm)],[f17])).
% 0.16/5.48 fof(f89,plain,(
% 0.16/5.48 ~xu=xv),
% 0.16/5.48 inference(cnf_transformation,[status(thm)],[f19])).
% 0.16/5.48 fof(f103,definition,(
% 0.16/5.48 sQ2_spl <=> (aSet0(xT))),
% 0.16/5.48 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.16/5.48 fof(f105,plain,(
% 0.16/5.48 ~aSet0(xT)|sQ2_spl),
% 0.16/5.48 inference(component_clause,[status(thm)],[f103])).
% 0.16/5.48 fof(f110,plain,(
% 0.16/5.48 $false|sQ2_spl),
% 0.16/5.48 inference(forward_subsumption_resolution,[status(thm)],[f105,f85])).
% 0.16/5.48 fof(f111,plain,(
% 0.16/5.48 sQ2_spl),
% 0.16/5.48 inference(contradiction_clause,[status(thm)],[f110])).
% 0.16/5.48 fof(f133,plain,(
% 0.16/5.48 ~aSet0(xT)|~aSubsetOf0(xS,xT)|aElementOf0(xv,xT)),
% 0.16/5.48 inference(resolution,[status(thm)],[f69,f88])).
% 0.16/5.48 fof(f134,plain,(
% 0.16/5.48 ~aSet0(xT)|~aSubsetOf0(xS,xT)|aElementOf0(xu,xT)),
% 0.16/5.48 inference(resolution,[status(thm)],[f69,f87])).
% 0.16/5.48 fof(f135,definition,(
% 0.16/5.48 sQ7_spl <=> (aSubsetOf0(xS,xT))),
% 0.16/5.48 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.16/5.48 fof(f137,plain,(
% 0.16/5.48 ~aSubsetOf0(xS,xT)|sQ7_spl),
% 0.16/5.48 inference(component_clause,[status(thm)],[f135])).
% 0.16/5.48 fof(f138,definition,(
% 0.16/5.48 sQ8_spl <=> (aElementOf0(xv,xT))),
% 0.16/5.48 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.16/5.48 fof(f139,plain,(
% 0.16/5.48 aElementOf0(xv,xT)|~sQ8_spl),
% 0.16/5.48 inference(component_clause,[status(thm)],[f138])).
% 0.16/5.48 fof(f141,plain,(
% 0.16/5.48 ~sQ2_spl|~sQ7_spl|sQ8_spl),
% 0.16/5.48 inference(split_clause,[status(thm)],[f133,f103,f135,f138])).
% 0.16/5.48 fof(f142,definition,(
% 0.16/5.48 sQ9_spl <=> (aElementOf0(xu,xT))),
% 0.16/5.48 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.16/5.48 fof(f143,plain,(
% 0.16/5.48 aElementOf0(xu,xT)|~sQ9_spl),
% 0.16/5.48 inference(component_clause,[status(thm)],[f142])).
% 0.16/5.48 fof(f145,plain,(
% 0.16/5.48 ~sQ2_spl|~sQ7_spl|sQ9_spl),
% 0.16/5.48 inference(split_clause,[status(thm)],[f134,f103,f135,f142])).
% 0.16/5.48 fof(f146,plain,(
% 0.16/5.48 $false|sQ7_spl),
% 0.16/5.48 inference(forward_subsumption_resolution,[status(thm)],[f137,f86])).
% 0.16/5.48 fof(f147,plain,(
% 0.16/5.48 sQ7_spl),
% 0.16/5.48 inference(contradiction_clause,[status(thm)],[f146])).
% 0.16/5.48 fof(f149,plain,(
% 0.16/5.48 ~aSet0(xT)|aElement0(xv)|~sQ8_spl),
% 0.16/5.48 inference(resolution,[status(thm)],[f139,f27])).
% 0.16/5.48 fof(f151,definition,(
% 0.16/5.48 sQ10_spl <=> (aElement0(xv))),
% 0.16/5.48 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.16/5.48 fof(f154,plain,(
% 0.16/5.48 ~sQ2_spl|sQ10_spl|~sQ8_spl),
% 0.16/5.48 inference(split_clause,[status(thm)],[f149,f103,f151,f138])).
% 0.16/5.48 fof(f156,plain,(
% 0.16/5.48 ~aSet0(xT)|aElement0(xu)|~sQ9_spl),
% 0.16/5.48 inference(resolution,[status(thm)],[f143,f27])).
% 0.16/5.48 fof(f158,definition,(
% 0.16/5.48 sQ11_spl <=> (aElement0(xu))),
% 0.16/5.48 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.16/5.48 fof(f161,plain,(
% 0.16/5.48 ~sQ2_spl|sQ11_spl|~sQ9_spl),
% 0.16/5.48 inference(split_clause,[status(thm)],[f156,f103,f158,f142])).
% 0.16/5.48 fof(f208,plain,(
% 0.16/5.48 ~aSet0(xT)|~aSubsetOf0(xS,xT)|aLowerBoundOfIn0(xv,xS,xT)),
% 0.16/5.48 inference(resolution,[status(thm)],[f70,f88])).
% 0.16/5.48 fof(f209,plain,(
% 0.16/5.48 ~aSet0(xT)|~aSubsetOf0(xS,xT)|aLowerBoundOfIn0(xu,xS,xT)),
% 0.16/5.48 inference(resolution,[status(thm)],[f70,f87])).
% 0.16/5.48 fof(f210,definition,(
% 0.16/5.48 sQ20_spl <=> (aLowerBoundOfIn0(xv,xS,xT))),
% 0.16/5.48 introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition])).
% 0.16/5.48 fof(f211,plain,(
% 0.16/5.48 aLowerBoundOfIn0(xv,xS,xT)|~sQ20_spl),
% 0.16/5.48 inference(component_clause,[status(thm)],[f210])).
% 0.16/5.48 fof(f213,plain,(
% 0.16/5.48 ~sQ2_spl|~sQ7_spl|sQ20_spl),
% 0.16/5.48 inference(split_clause,[status(thm)],[f208,f103,f135,f210])).
% 0.16/5.48 fof(f214,definition,(
% 0.16/5.48 sQ21_spl <=> (aLowerBoundOfIn0(xu,xS,xT))),
% 0.16/5.48 introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition])).
% 0.16/5.48 fof(f215,plain,(
% 0.16/5.48 aLowerBoundOfIn0(xu,xS,xT)|~sQ21_spl),
% 0.16/5.48 inference(component_clause,[status(thm)],[f214])).
% 0.16/5.48 fof(f217,plain,(
% 0.16/5.48 ~sQ2_spl|~sQ7_spl|sQ21_spl),
% 0.16/5.48 inference(split_clause,[status(thm)],[f209,f103,f135,f214])).
% 0.16/5.48 fof(f239,plain,(
% 0.16/5.48 ![X0]: (~aSet0(xT)|~aSubsetOf0(xS,xT)|~aLowerBoundOfIn0(X0,xS,xT)|sdtlseqdt0(X0,xv))),
% 0.16/5.48 inference(resolution,[status(thm)],[f71,f88])).
% 0.16/5.49 fof(f240,plain,(
% 0.16/5.49 ![X0]: (~aSet0(xT)|~aSubsetOf0(xS,xT)|~aLowerBoundOfIn0(X0,xS,xT)|sdtlseqdt0(X0,xu))),
% 0.16/5.49 inference(resolution,[status(thm)],[f71,f87])).
% 0.16/5.49 fof(f241,definition,(
% 0.16/5.49 ![X0]: (sQ25_spl <=> (~aLowerBoundOfIn0(X0,xS,xT)|sdtlseqdt0(X0,xv)))),
% 0.16/5.49 introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition])).
% 0.16/5.49 fof(f242,plain,(
% 0.16/5.49 ![X0]: (~aLowerBoundOfIn0(X0,xS,xT)|sdtlseqdt0(X0,xv)|~sQ25_spl)),
% 0.16/5.49 inference(component_clause,[status(thm)],[f241])).
% 0.16/5.49 fof(f244,plain,(
% 0.16/5.49 ~sQ2_spl|~sQ7_spl|sQ25_spl),
% 0.16/5.49 inference(split_clause,[status(thm)],[f239,f103,f135,f241])).
% 0.16/5.49 fof(f245,definition,(
% 0.16/5.49 ![X0]: (sQ26_spl <=> (~aLowerBoundOfIn0(X0,xS,xT)|sdtlseqdt0(X0,xu)))),
% 0.16/5.49 introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition])).
% 0.16/5.49 fof(f246,plain,(
% 0.16/5.49 ![X0]: (~aLowerBoundOfIn0(X0,xS,xT)|sdtlseqdt0(X0,xu)|~sQ26_spl)),
% 0.16/5.49 inference(component_clause,[status(thm)],[f245])).
% 0.16/5.49 fof(f248,plain,(
% 0.16/5.49 ~sQ2_spl|~sQ7_spl|sQ26_spl),
% 0.16/5.49 inference(split_clause,[status(thm)],[f240,f103,f135,f245])).
% 0.16/5.49 fof(f249,plain,(
% 0.16/5.49 sdtlseqdt0(xu,xv)|~sQ25_spl|~sQ21_spl),
% 0.16/5.49 inference(resolution,[status(thm)],[f242,f215])).
% 0.16/5.49 fof(f252,plain,(
% 0.16/5.49 sdtlseqdt0(xv,xu)|~sQ26_spl|~sQ20_spl),
% 0.16/5.49 inference(resolution,[status(thm)],[f246,f211])).
% 0.16/5.49 fof(f254,plain,(
% 0.16/5.49 ~aElement0(xv)|~aElement0(xu)|~sdtlseqdt0(xv,xu)|xv=xu|~sQ25_spl|~sQ21_spl),
% 0.16/5.49 inference(resolution,[status(thm)],[f249,f46])).
% 0.16/5.49 fof(f259,definition,(
% 0.16/5.49 sQ28_spl <=> (sdtlseqdt0(xv,xu))),
% 0.16/5.49 introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition])).
% 0.16/5.49 fof(f261,plain,(
% 0.16/5.49 ~sdtlseqdt0(xv,xu)|sQ28_spl),
% 0.16/5.49 inference(component_clause,[status(thm)],[f259])).
% 0.16/5.49 fof(f262,definition,(
% 0.16/5.49 sQ29_spl <=> (xv=xu)),
% 0.16/5.49 introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition])).
% 0.16/5.49 fof(f263,plain,(
% 0.16/5.49 xv=xu|~sQ29_spl),
% 0.16/5.49 inference(component_clause,[status(thm)],[f262])).
% 0.16/5.49 fof(f265,plain,(
% 0.16/5.49 ~sQ10_spl|~sQ11_spl|~sQ28_spl|sQ29_spl|~sQ25_spl|~sQ21_spl),
% 0.16/5.49 inference(split_clause,[status(thm)],[f254,f151,f158,f259,f262,f241,f214])).
% 0.16/5.49 fof(f266,plain,(
% 0.16/5.49 $false|~sQ26_spl|~sQ20_spl|sQ28_spl),
% 0.16/5.49 inference(forward_subsumption_resolution,[status(thm)],[f261,f252])).
% 0.16/5.49 fof(f267,plain,(
% 0.16/5.49 ~sQ26_spl|~sQ20_spl|sQ28_spl),
% 0.16/5.49 inference(contradiction_clause,[status(thm)],[f266])).
% 0.16/5.49 fof(f268,plain,(
% 0.16/5.49 $false|~sQ29_spl),
% 0.16/5.49 inference(forward_subsumption_resolution,[status(thm)],[f263,f89])).
% 0.16/5.49 fof(f269,plain,(
% 0.16/5.49 ~sQ29_spl),
% 0.16/5.49 inference(contradiction_clause,[status(thm)],[f268])).
% 0.16/5.49 fof(f270,plain,(
% 0.16/5.49 $false),
% 0.16/5.49 inference(sat_refutation,[status(thm)],[f111,f141,f145,f147,f154,f161,f213,f217,f244,f248,f265,f267,f269])).
% 0.16/5.49 % SZS output end CNFRefutation for theBenchmark.p
% 0.21/5.52 % Elapsed time: 0.069944 seconds
% 0.21/5.52 % CPU time: 0.235369 seconds
% 0.21/5.52 % Total memory used: 80.072 MB
% 0.21/5.52 % Net memory used: 79.835 MB
%------------------------------------------------------------------------------