%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM552+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 01:43:11 PM UTC 2026
% Result : Theorem 3.17s 0.82s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM552+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.33 % Computer : n011.cluster.edu
% 0.09/0.33 % Model : x86_64 x86_64
% 0.09/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.33 % Memory : 8046.5625MB
% 0.09/0.33 % OS : Linux 6.8.0-71-generic
% 0.09/0.33 % CPULimit : 300
% 0.09/0.33 % WCLimit : 300
% 0.09/0.33 % DateTime : Mon Sep 21 02:39:40 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.35 % Drodi V4.1.1
% 3.17/0.82 % Refutation found
% 3.17/0.82 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.17/0.82 % SZS output start CNFRefutation for theBenchmark
% 3.17/0.82 fof(f10,definition,(
% 3.17/0.82 (! [W0] :( aSet0(W0)=> (! [W1] :( aSubsetOf0(W1,W0)<=> ( aSet0(W1)& (! [W2] :( aElementOf0(W2,W1)=> aElementOf0(W2,W0) ) )) ) )) )),
% 3.17/0.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.17/0.82 fof(f57,definition,(
% 3.17/0.82 (! [W0,W1] :( ( aSet0(W0)& aElementOf0(W1,szNzAzT0) )=> (! [W2] :( W2 = slbdtsldtrb0(W0,W1)<=> ( aSet0(W2)& (! [W3] :( aElementOf0(W3,W2)<=> ( aSubsetOf0(W3,W0)& sbrdtbr0(W3) = W1 ) ) )) ) )) )),
% 3.17/0.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.17/0.82 fof(f61,hypothesis,(
% 3.17/0.82 aElementOf0(xk,szNzAzT0) ),
% 3.17/0.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.17/0.82 fof(f62,hypothesis,(
% 3.17/0.82 ( aSet0(xS)& aSet0(xT)& xk != sz00 ) ),
% 3.17/0.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.17/0.82 fof(f63,hypothesis,(
% 3.17/0.82 ( aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))& slbdtsldtrb0(xS,xk) != slcrc0 ) ),
% 3.17/0.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.17/0.82 fof(f65,hypothesis,(
% 3.17/0.82 aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ),
% 3.17/0.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.17/0.82 fof(f68,conjecture,(
% 3.17/0.82 ( aElementOf0(xx,xQ)=> aElementOf0(xx,xT) ) ),
% 3.17/0.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.17/0.82 fof(f69,negated_conjecture,(
% 3.17/0.82 ~(( aElementOf0(xx,xQ)=> aElementOf0(xx,xT) ) )),
% 3.17/0.82 inference(negated_conjecture,[status(cth)],[f68])).
% 3.17/0.82 fof(f94,plain,(
% 3.17/0.82 ![W0]: (~aSet0(W0)|(![W1]: (aSubsetOf0(W1,W0)<=>(aSet0(W1)&(![W2]: (~aElementOf0(W2,W1)|aElementOf0(W2,W0)))))))),
% 3.17/0.82 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 3.17/0.82 fof(f95,plain,(
% 3.17/0.82 ![W0]: (~aSet0(W0)|(![W1]: ((~aSubsetOf0(W1,W0)|(aSet0(W1)&(![W2]: (~aElementOf0(W2,W1)|aElementOf0(W2,W0)))))&(aSubsetOf0(W1,W0)|(~aSet0(W1)|(?[W2]: (aElementOf0(W2,W1)&~aElementOf0(W2,W0))))))))),
% 3.17/0.82 inference(NNF_transformation,[status(thm)],[f94])).
% 3.17/0.82 fof(f96,plain,(
% 3.17/0.82 ![W0]: (~aSet0(W0)|((![W1]: (~aSubsetOf0(W1,W0)|(aSet0(W1)&(![W2]: (~aElementOf0(W2,W1)|aElementOf0(W2,W0))))))&(![W1]: (aSubsetOf0(W1,W0)|(~aSet0(W1)|(?[W2]: (aElementOf0(W2,W1)&~aElementOf0(W2,W0))))))))),
% 3.17/0.82 inference(miniscoping,[status(thm)],[f95])).
% 3.17/0.82 fof(f97,plain,(
% 3.17/0.82 ![W0]: (~aSet0(W0)|((![W1]: (~aSubsetOf0(W1,W0)|(aSet0(W1)&(![W2]: (~aElementOf0(W2,W1)|aElementOf0(W2,W0))))))&(![W1]: (aSubsetOf0(W1,W0)|(~aSet0(W1)|(aElementOf0(sK1_skl(W1,W0),W1)&~aElementOf0(sK1_skl(W1,W0),W0)))))))),
% 3.17/0.82 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W2,sK1_skl(W1,W0))],[f96])).
% 3.17/0.82 fof(f99,plain,(
% 3.17/0.82 ![X0,X1,X2]: (~aSet0(X0)|~aSubsetOf0(X1,X0)|~aElementOf0(X2,X1)|aElementOf0(X2,X0))),
% 3.17/0.82 inference(cnf_transformation,[status(thm)],[f97])).
% 3.17/0.82 fof(f251,plain,(
% 3.17/0.82 ![W0,W1]: ((~aSet0(W0)|~aElementOf0(W1,szNzAzT0))|(![W2]: (W2=slbdtsldtrb0(W0,W1)<=>(aSet0(W2)&(![W3]: (aElementOf0(W3,W2)<=>(aSubsetOf0(W3,W0)&sbrdtbr0(W3)=W1)))))))),
% 3.17/0.82 inference(pre_NNF_transformation,[status(thm)],[f57])).
% 3.17/0.82 fof(f252,plain,(
% 3.17/0.82 ![W0,W1]: ((~aSet0(W0)|~aElementOf0(W1,szNzAzT0))|(![W2]: ((~W2=slbdtsldtrb0(W0,W1)|(aSet0(W2)&(![W3]: ((~aElementOf0(W3,W2)|(aSubsetOf0(W3,W0)&sbrdtbr0(W3)=W1))&(aElementOf0(W3,W2)|(~aSubsetOf0(W3,W0)|~sbrdtbr0(W3)=W1))))))&(W2=slbdtsldtrb0(W0,W1)|(~aSet0(W2)|(?[W3]: ((~aElementOf0(W3,W2)|(~aSubsetOf0(W3,W0)|~sbrdtbr0(W3)=W1))&(aElementOf0(W3,W2)|(aSubsetOf0(W3,W0)&sbrdtbr0(W3)=W1)))))))))),
% 3.17/0.82 inference(NNF_transformation,[status(thm)],[f251])).
% 3.17/0.82 fof(f253,plain,(
% 3.17/0.82 ![W0,W1]: ((~aSet0(W0)|~aElementOf0(W1,szNzAzT0))|((![W2]: (~W2=slbdtsldtrb0(W0,W1)|(aSet0(W2)&((![W3]: (~aElementOf0(W3,W2)|(aSubsetOf0(W3,W0)&sbrdtbr0(W3)=W1)))&(![W3]: (aElementOf0(W3,W2)|(~aSubsetOf0(W3,W0)|~sbrdtbr0(W3)=W1)))))))&(![W2]: (W2=slbdtsldtrb0(W0,W1)|(~aSet0(W2)|(?[W3]: ((~aElementOf0(W3,W2)|(~aSubsetOf0(W3,W0)|~sbrdtbr0(W3)=W1))&(aElementOf0(W3,W2)|(aSubsetOf0(W3,W0)&sbrdtbr0(W3)=W1)))))))))),
% 3.17/0.82 inference(miniscoping,[status(thm)],[f252])).
% 3.17/0.82 fof(f254,plain,(
% 3.17/0.82 ![W0,W1]: ((~aSet0(W0)|~aElementOf0(W1,szNzAzT0))|((![W2]: (~W2=slbdtsldtrb0(W0,W1)|(aSet0(W2)&((![W3]: (~aElementOf0(W3,W2)|(aSubsetOf0(W3,W0)&sbrdtbr0(W3)=W1)))&(![W3]: (aElementOf0(W3,W2)|(~aSubsetOf0(W3,W0)|~sbrdtbr0(W3)=W1)))))))&(![W2]: (W2=slbdtsldtrb0(W0,W1)|(~aSet0(W2)|((~aElementOf0(sK10_skl(W2,W1,W0),W2)|(~aSubsetOf0(sK10_skl(W2,W1,W0),W0)|~sbrdtbr0(sK10_skl(W2,W1,W0))=W1))&(aElementOf0(sK10_skl(W2,W1,W0),W2)|(aSubsetOf0(sK10_skl(W2,W1,W0),W0)&sbrdtbr0(sK10_skl(W2,W1,W0))=W1))))))))),
% 3.17/0.82 inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(W3,sK10_skl(W2,W1,W0))],[f253])).
% 3.17/0.82 fof(f255,plain,(
% 3.17/0.82 ![X0,X1,X2]: (~aSet0(X0)|~aElementOf0(X1,szNzAzT0)|~X2=slbdtsldtrb0(X0,X1)|aSet0(X2))),
% 3.17/0.82 inference(cnf_transformation,[status(thm)],[f254])).
% 3.17/0.82 fof(f256,plain,(
% 3.17/0.82 ![X0,X1,X2,X3]: (~aSet0(X0)|~aElementOf0(X1,szNzAzT0)|~X2=slbdtsldtrb0(X0,X1)|~aElementOf0(X3,X2)|aSubsetOf0(X3,X0))),
% 3.17/0.82 inference(cnf_transformation,[status(thm)],[f254])).
% 3.17/0.82 fof(f268,plain,(
% 3.17/0.82 aElementOf0(xk,szNzAzT0)),
% 3.17/0.82 inference(cnf_transformation,[status(thm)],[f61])).
% 3.17/0.82 fof(f270,plain,(
% 3.17/0.82 aSet0(xT)),
% 3.17/0.82 inference(cnf_transformation,[status(thm)],[f62])).
% 3.17/0.82 fof(f272,plain,(
% 3.17/0.82 aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))),
% 3.17/0.82 inference(cnf_transformation,[status(thm)],[f63])).
% 3.17/0.82 fof(f275,plain,(
% 3.17/0.82 aElementOf0(xQ,slbdtsldtrb0(xS,xk))),
% 3.17/0.82 inference(cnf_transformation,[status(thm)],[f65])).
% 3.17/0.82 fof(f281,plain,(
% 3.17/0.82 (aElementOf0(xx,xQ)&~aElementOf0(xx,xT))),
% 3.17/0.82 inference(pre_NNF_transformation,[status(thm)],[f69])).
% 3.17/0.82 fof(f282,plain,(
% 3.17/0.82 aElementOf0(xx,xQ)),
% 3.17/0.82 inference(cnf_transformation,[status(thm)],[f281])).
% 3.17/0.82 fof(f283,plain,(
% 3.17/0.82 ~aElementOf0(xx,xT)),
% 3.17/0.82 inference(cnf_transformation,[status(thm)],[f281])).
% 3.17/0.82 fof(f322,plain,(
% 3.17/0.82 ![X0,X1]: (~aSet0(X0)|~aElementOf0(X1,szNzAzT0)|aSet0(slbdtsldtrb0(X0,X1)))),
% 3.17/0.82 inference(destructive_equality_resolution,[status(thm)],[f255])).
% 3.17/0.82 fof(f323,plain,(
% 3.17/0.82 ![X0,X1,X2]: (~aSet0(X0)|~aElementOf0(X1,szNzAzT0)|~aElementOf0(X2,slbdtsldtrb0(X0,X1))|aSubsetOf0(X2,X0))),
% 3.17/0.82 inference(destructive_equality_resolution,[status(thm)],[f256])).
% 3.17/0.82 fof(f378,definition,(
% 3.17/0.82 sQ10_spl <=> (aSet0(slbdtsldtrb0(xT,xk)))),
% 3.17/0.82 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 3.17/0.82 fof(f380,plain,(
% 3.17/0.82 ~aSet0(slbdtsldtrb0(xT,xk))|sQ10_spl),
% 3.17/0.82 inference(component_clause,[status(thm)],[f378])).
% 3.17/0.82 fof(f392,plain,(
% 3.17/0.82 ![X0]: (~aSet0(slbdtsldtrb0(xT,xk))|~aElementOf0(X0,slbdtsldtrb0(xS,xk))|aElementOf0(X0,slbdtsldtrb0(xT,xk)))),
% 3.17/0.82 inference(resolution,[status(thm)],[f99,f272])).
% 3.17/0.82 fof(f394,definition,(
% 3.17/0.82 ![X0]: (sQ12_spl <=> (~aElementOf0(X0,slbdtsldtrb0(xS,xk))|aElementOf0(X0,slbdtsldtrb0(xT,xk))))),
% 3.17/0.82 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 3.17/0.82 fof(f395,plain,(
% 3.17/0.82 ![X0]: (~aElementOf0(X0,slbdtsldtrb0(xS,xk))|aElementOf0(X0,slbdtsldtrb0(xT,xk))|~sQ12_spl)),
% 3.17/0.82 inference(component_clause,[status(thm)],[f394])).
% 3.17/0.82 fof(f397,plain,(
% 3.17/0.82 ~sQ10_spl|sQ12_spl),
% 3.17/0.82 inference(split_clause,[status(thm)],[f392,f378,f394])).
% 3.17/0.82 fof(f1449,plain,(
% 3.17/0.82 ![X0,X1]: (~aSubsetOf0(X0,xT)|~aElementOf0(X1,X0)|aElementOf0(X1,xT))),
% 3.17/0.82 inference(resolution,[status(thm)],[f99,f270])).
% 3.17/0.82 fof(f1455,definition,(
% 3.17/0.82 sQ123_spl <=> (aElementOf0(xk,szNzAzT0))),
% 3.17/0.82 introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition])).
% 3.17/0.82 fof(f1457,plain,(
% 3.17/0.82 ~aElementOf0(xk,szNzAzT0)|sQ123_spl),
% 3.17/0.82 inference(component_clause,[status(thm)],[f1455])).
% 3.17/0.82 fof(f1464,plain,(
% 3.17/0.82 $false|sQ123_spl),
% 3.17/0.82 inference(forward_subsumption_resolution,[status(thm)],[f1457,f268])).
% 3.17/0.82 fof(f1465,plain,(
% 3.17/0.82 sQ123_spl),
% 3.17/0.82 inference(contradiction_clause,[status(thm)],[f1464])).
% 3.17/0.82 fof(f1501,definition,(
% 3.17/0.82 sQ130_spl <=> (aSet0(xT))),
% 3.17/0.82 introduced(definition,[new_symbols(definition,[sQ130_spl])],[split_symbol_definition])).
% 3.17/0.82 fof(f1503,plain,(
% 3.17/0.82 ~aSet0(xT)|sQ130_spl),
% 3.17/0.82 inference(component_clause,[status(thm)],[f1501])).
% 3.17/0.82 fof(f1632,plain,(
% 3.17/0.82 ![X0]: (~aSet0(X0)|aSet0(slbdtsldtrb0(X0,xk)))),
% 3.17/0.82 inference(resolution,[status(thm)],[f322,f268])).
% 3.17/0.82 fof(f1719,plain,(
% 3.17/0.82 ~aSet0(xT)|sQ10_spl),
% 3.17/0.82 inference(resolution,[status(thm)],[f1632,f380])).
% 3.17/0.82 fof(f1728,plain,(
% 3.17/0.82 $false|sQ10_spl),
% 3.17/0.82 inference(forward_subsumption_resolution,[status(thm)],[f1719,f270])).
% 3.17/0.82 fof(f1729,plain,(
% 3.17/0.82 sQ10_spl),
% 3.17/0.82 inference(contradiction_clause,[status(thm)],[f1728])).
% 3.17/0.82 fof(f1800,plain,(
% 3.17/0.82 aElementOf0(xQ,slbdtsldtrb0(xT,xk))|~sQ12_spl),
% 3.17/0.82 inference(resolution,[status(thm)],[f395,f275])).
% 3.17/0.82 fof(f1803,plain,(
% 3.17/0.82 ~aSet0(xT)|~aElementOf0(xk,szNzAzT0)|aSubsetOf0(xQ,xT)|~sQ12_spl),
% 3.17/0.82 inference(resolution,[status(thm)],[f1800,f323])).
% 3.17/0.82 fof(f1805,definition,(
% 3.17/0.82 sQ162_spl <=> (aSubsetOf0(xQ,xT))),
% 3.17/0.82 introduced(definition,[new_symbols(definition,[sQ162_spl])],[split_symbol_definition])).
% 3.17/0.82 fof(f1806,plain,(
% 3.17/0.82 aSubsetOf0(xQ,xT)|~sQ162_spl),
% 3.17/0.82 inference(component_clause,[status(thm)],[f1805])).
% 3.17/0.82 fof(f1808,plain,(
% 3.17/0.82 ~sQ130_spl|~sQ123_spl|sQ162_spl|~sQ12_spl),
% 3.17/0.82 inference(split_clause,[status(thm)],[f1803,f1501,f1455,f1805,f394])).
% 3.17/0.82 fof(f1809,plain,(
% 3.17/0.82 $false|sQ130_spl),
% 3.17/0.82 inference(forward_subsumption_resolution,[status(thm)],[f1503,f270])).
% 3.17/0.82 fof(f1810,plain,(
% 3.17/0.82 sQ130_spl),
% 3.17/0.82 inference(contradiction_clause,[status(thm)],[f1809])).
% 3.17/0.82 fof(f1812,plain,(
% 3.17/0.82 ![X0]: (~aElementOf0(X0,xQ)|aElementOf0(X0,xT)|~sQ162_spl)),
% 3.17/0.82 inference(resolution,[status(thm)],[f1806,f1449])).
% 3.17/0.82 fof(f1823,plain,(
% 3.17/0.82 aElementOf0(xx,xT)|~sQ162_spl),
% 3.17/0.82 inference(resolution,[status(thm)],[f1812,f282])).
% 3.17/0.82 fof(f1825,plain,(
% 3.17/0.82 $false|~sQ162_spl),
% 3.17/0.82 inference(forward_subsumption_resolution,[status(thm)],[f1823,f283])).
% 3.17/0.82 fof(f1826,plain,(
% 3.17/0.82 ~sQ162_spl),
% 3.17/0.82 inference(contradiction_clause,[status(thm)],[f1825])).
% 3.17/0.82 fof(f1827,plain,(
% 3.17/0.82 $false),
% 3.17/0.82 inference(sat_refutation,[status(thm)],[f397,f1465,f1729,f1808,f1810,f1826])).
% 3.17/0.82 % SZS output end CNFRefutation for theBenchmark.p
% 3.17/0.84 % Elapsed time: 0.487684 seconds
% 3.17/0.84 % CPU time: 3.505577 seconds
% 3.17/0.84 % Total memory used: 161.228 MB
% 3.17/0.84 % Net memory used: 157.381 MB
%------------------------------------------------------------------------------