%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : RNG092+2 : 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 : 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 02:05:20 PM UTC 2026
% Result : Theorem 16.97s 7.73s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG092+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/5.42 % Computer : n016.cluster.edu
% 0.15/5.42 % Model : x86_64 x86_64
% 0.15/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.42 % Memory : 8046.5625MB
% 0.15/5.42 % OS : Linux 6.8.0-71-generic
% 0.15/5.43 % CPULimit : 300
% 0.15/5.43 % WCLimit : 300
% 0.15/5.43 % DateTime : Mon Sep 21 04:23:43 UTC 2026
% 0.15/5.43 % CPUTime :
% 0.15/5.45 % Drodi V4.1.1
% 16.97/7.73 % Refutation found
% 16.97/7.73 % SZS status Theorem for theBenchmark: Theorem is valid
% 16.97/7.73 % SZS output start CNFRefutation for theBenchmark
% 16.97/7.73 fof(f20,axiom,(
% 16.97/7.73 (! [W0] :( aSet0(W0)=> (! [W1] :( aElementOf0(W1,W0)=> aElement0(W1) ) )) )),
% 16.97/7.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 16.97/7.73 fof(f24,definition,(
% 16.97/7.73 (! [W0] :( aIdeal0(W0)<=> ( aSet0(W0)& (! [W1] :( aElementOf0(W1,W0)=> ( (! [W2] :( aElementOf0(W2,W0)=> aElementOf0(sdtpldt0(W1,W2),W0) ))& (! [W2] :( aElement0(W2)=> aElementOf0(sdtasdt0(W2,W1),W0) ) )) ) )) ) )),
% 16.97/7.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 16.97/7.73 fof(f26,conjecture,(
% 16.97/7.73 ( (! [W0,W1,W2] :( ( ( (? [W3,W4] :( aElementOf0(W3,xI)& aElementOf0(W4,xJ)& sdtpldt0(W3,W4) = W0 ))| aElementOf0(W0,sdtpldt1(xI,xJ)) )& ( (? [W3,W4] :( aElementOf0(W3,xI)& aElementOf0(W4,xJ)& sdtpldt0(W3,W4) = W1 ))| aElementOf0(W1,sdtpldt1(xI,xJ)) )& aElement0(W2) )=> (? [W3,W4] :( aElementOf0(W3,xI)& aElementOf0(W4,xJ)& W0 = sdtpldt0(W3,W4)& (? [W5,W6] :( aElementOf0(W5,xI)& aElementOf0(W6,xJ)& W1 = sdtpldt0(W5,W6)& aElementOf0(sdtpldt0(W3,W5),xI)& aElementOf0(sdtpldt0(W4,W6),xJ)& aElementOf0(sdtasdt0(W2,W3),xI)& aElementOf0(sdtasdt0(W2,W4),xJ)& sdtpldt0(W0,W1) = sdtpldt0(sdtpldt0(W3,W5),sdtpldt0(W4,W6))& (? [W7,W8] :( aElementOf0(W7,xI)& aElementOf0(W8,xJ)& sdtpldt0(W7,W8) = sdtpldt0(W0,W1) ))& aElementOf0(sdtpldt0(W0,W1),sdtpldt1(xI,xJ))& (? [W7,W8] :( aElementOf0(W7,xI)& aElementOf0(W8,xJ)& sdtpldt0(W7,W8) = sdtasdt0(W2,W0) ))& aElementOf0(sdtasdt0(W2,W0),sdtpldt1(xI,xJ)) ) )) )))=> ( ( aSet0(sdtpldt1(xI,xJ))& (! [W0] :( aElementOf0(W0,sdtpldt1(xI,xJ))<=> (? [W1,W2] :( aElementOf0(W1,xI)& aElementOf0(W2,xJ)& sdtpldt0(W1,W2) = W0 ) )) ))=> ( (! [W0] :( aElementOf0(W0,sdtpldt1(xI,xJ))=> ( (! [W1] :( aElementOf0(W1,sdtpldt1(xI,xJ))=> aElementOf0(sdtpldt0(W0,W1),sdtpldt1(xI,xJ)) ))& (! [W1] :( aElement0(W1)=> aElementOf0(sdtasdt0(W1,W0),sdtpldt1(xI,xJ)) ) )) ))| aIdeal0(sdtpldt1(xI,xJ)) ) ) ) ),
% 16.97/7.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 16.97/7.73 fof(f27,negated_conjecture,(
% 16.97/7.73 ~(( (! [W0,W1,W2] :( ( ( (? [W3,W4] :( aElementOf0(W3,xI)& aElementOf0(W4,xJ)& sdtpldt0(W3,W4) = W0 ))| aElementOf0(W0,sdtpldt1(xI,xJ)) )& ( (? [W3,W4] :( aElementOf0(W3,xI)& aElementOf0(W4,xJ)& sdtpldt0(W3,W4) = W1 ))| aElementOf0(W1,sdtpldt1(xI,xJ)) )& aElement0(W2) )=> (? [W3,W4] :( aElementOf0(W3,xI)& aElementOf0(W4,xJ)& W0 = sdtpldt0(W3,W4)& (? [W5,W6] :( aElementOf0(W5,xI)& aElementOf0(W6,xJ)& W1 = sdtpldt0(W5,W6)& aElementOf0(sdtpldt0(W3,W5),xI)& aElementOf0(sdtpldt0(W4,W6),xJ)& aElementOf0(sdtasdt0(W2,W3),xI)& aElementOf0(sdtasdt0(W2,W4),xJ)& sdtpldt0(W0,W1) = sdtpldt0(sdtpldt0(W3,W5),sdtpldt0(W4,W6))& (? [W7,W8] :( aElementOf0(W7,xI)& aElementOf0(W8,xJ)& sdtpldt0(W7,W8) = sdtpldt0(W0,W1) ))& aElementOf0(sdtpldt0(W0,W1),sdtpldt1(xI,xJ))& (? [W7,W8] :( aElementOf0(W7,xI)& aElementOf0(W8,xJ)& sdtpldt0(W7,W8) = sdtasdt0(W2,W0) ))& aElementOf0(sdtasdt0(W2,W0),sdtpldt1(xI,xJ)) ) )) )))=> ( ( aSet0(sdtpldt1(xI,xJ))& (! [W0] :( aElementOf0(W0,sdtpldt1(xI,xJ))<=> (? [W1,W2] :( aElementOf0(W1,xI)& aElementOf0(W2,xJ)& sdtpldt0(W1,W2) = W0 ) )) ))=> ( (! [W0] :( aElementOf0(W0,sdtpldt1(xI,xJ))=> ( (! [W1] :( aElementOf0(W1,sdtpldt1(xI,xJ))=> aElementOf0(sdtpldt0(W0,W1),sdtpldt1(xI,xJ)) ))& (! [W1] :( aElement0(W1)=> aElementOf0(sdtasdt0(W1,W0),sdtpldt1(xI,xJ)) ) )) ))| aIdeal0(sdtpldt1(xI,xJ)) ) ) ) )),
% 16.97/7.73 inference(negated_conjecture,[status(cth)],[f26])).
% 16.97/7.73 fof(f71,plain,(
% 16.97/7.73 ![W0]: (~aSet0(W0)|(![W1]: (~aElementOf0(W1,W0)|aElement0(W1))))),
% 16.97/7.73 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 16.97/7.73 fof(f72,plain,(
% 16.97/7.73 ![X0,X1]: (~aSet0(X0)|~aElementOf0(X1,X0)|aElement0(X1))),
% 16.97/7.73 inference(cnf_transformation,[status(thm)],[f71])).
% 16.97/7.73 fof(f101,plain,(
% 16.97/7.73 ![W0]: (aIdeal0(W0)<=>(aSet0(W0)&(![W1]: (~aElementOf0(W1,W0)|((![W2]: (~aElementOf0(W2,W0)|aElementOf0(sdtpldt0(W1,W2),W0)))&(![W2]: (~aElement0(W2)|aElementOf0(sdtasdt0(W2,W1),W0))))))))),
% 16.97/7.73 inference(pre_NNF_transformation,[status(thm)],[f24])).
% 16.97/7.73 fof(f102,plain,(
% 16.97/7.73 ![W0]: ((~aIdeal0(W0)|(aSet0(W0)&(![W1]: (~aElementOf0(W1,W0)|((![W2]: (~aElementOf0(W2,W0)|aElementOf0(sdtpldt0(W1,W2),W0)))&(![W2]: (~aElement0(W2)|aElementOf0(sdtasdt0(W2,W1),W0))))))))&(aIdeal0(W0)|(~aSet0(W0)|(?[W1]: (aElementOf0(W1,W0)&((?[W2]: (aElementOf0(W2,W0)&~aElementOf0(sdtpldt0(W1,W2),W0)))|(?[W2]: (aElement0(W2)&~aElementOf0(sdtasdt0(W2,W1),W0)))))))))),
% 16.97/7.73 inference(NNF_transformation,[status(thm)],[f101])).
% 16.97/7.73 fof(f103,plain,(
% 16.97/7.73 (![W0]: (~aIdeal0(W0)|(aSet0(W0)&(![W1]: (~aElementOf0(W1,W0)|((![W2]: (~aElementOf0(W2,W0)|aElementOf0(sdtpldt0(W1,W2),W0)))&(![W2]: (~aElement0(W2)|aElementOf0(sdtasdt0(W2,W1),W0)))))))))&(![W0]: (aIdeal0(W0)|(~aSet0(W0)|(?[W1]: (aElementOf0(W1,W0)&((?[W2]: (aElementOf0(W2,W0)&~aElementOf0(sdtpldt0(W1,W2),W0)))|(?[W2]: (aElement0(W2)&~aElementOf0(sdtasdt0(W2,W1),W0)))))))))),
% 16.97/7.73 inference(miniscoping,[status(thm)],[f102])).
% 16.97/7.73 fof(f104,plain,(
% 16.97/7.73 (![W0]: (~aIdeal0(W0)|(aSet0(W0)&(![W1]: (~aElementOf0(W1,W0)|((![W2]: (~aElementOf0(W2,W0)|aElementOf0(sdtpldt0(W1,W2),W0)))&(![W2]: (~aElement0(W2)|aElementOf0(sdtasdt0(W2,W1),W0)))))))))&(![W0]: (aIdeal0(W0)|(~aSet0(W0)|(aElementOf0(sK8_skl(W0),W0)&((aElementOf0(sK9_skl(W0),W0)&~aElementOf0(sdtpldt0(sK8_skl(W0),sK9_skl(W0)),W0))|(aElement0(sK10_skl(W0))&~aElementOf0(sdtasdt0(sK10_skl(W0),sK8_skl(W0)),W0)))))))),
% 16.97/7.73 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl,sK10_skl]),skolemize(W1,sK8_skl(W0)),skolemize(W2,sK9_skl(W0)),skolemize(W2,sK10_skl(W0))],[f103])).
% 16.97/7.73 fof(f108,plain,(
% 16.97/7.73 ![X0]: (aIdeal0(X0)|~aSet0(X0)|aElementOf0(sK8_skl(X0),X0))),
% 16.97/7.73 inference(cnf_transformation,[status(thm)],[f104])).
% 16.97/7.73 fof(f122,plain,(
% 16.97/7.73 ((![W0,W1,W2]: (((((![W3,W4]: ((~aElementOf0(W3,xI)|~aElementOf0(W4,xJ))|~sdtpldt0(W3,W4)=W0))&~aElementOf0(W0,sdtpldt1(xI,xJ)))|((![W3,W4]: ((~aElementOf0(W3,xI)|~aElementOf0(W4,xJ))|~sdtpldt0(W3,W4)=W1))&~aElementOf0(W1,sdtpldt1(xI,xJ))))|~aElement0(W2))|(?[W3,W4]: (((aElementOf0(W3,xI)&aElementOf0(W4,xJ))&W0=sdtpldt0(W3,W4))&(?[W5,W6]: (((((((((((aElementOf0(W5,xI)&aElementOf0(W6,xJ))&W1=sdtpldt0(W5,W6))&aElementOf0(sdtpldt0(W3,W5),xI))&aElementOf0(sdtpldt0(W4,W6),xJ))&aElementOf0(sdtasdt0(W2,W3),xI))&aElementOf0(sdtasdt0(W2,W4),xJ))&sdtpldt0(W0,W1)=sdtpldt0(sdtpldt0(W3,W5),sdtpldt0(W4,W6)))&(?[W7,W8]: ((aElementOf0(W7,xI)&aElementOf0(W8,xJ))&sdtpldt0(W7,W8)=sdtpldt0(W0,W1))))&aElementOf0(sdtpldt0(W0,W1),sdtpldt1(xI,xJ)))&(?[W7,W8]: ((aElementOf0(W7,xI)&aElementOf0(W8,xJ))&sdtpldt0(W7,W8)=sdtasdt0(W2,W0))))&aElementOf0(sdtasdt0(W2,W0),sdtpldt1(xI,xJ))))))))&((aSet0(sdtpldt1(xI,xJ))&(![W0]: (aElementOf0(W0,sdtpldt1(xI,xJ))<=>(?[W1,W2]: ((aElementOf0(W1,xI)&aElementOf0(W2,xJ))&sdtpldt0(W1,W2)=W0)))))&((?[W0]: (aElementOf0(W0,sdtpldt1(xI,xJ))&((?[W1]: (aElementOf0(W1,sdtpldt1(xI,xJ))&~aElementOf0(sdtpldt0(W0,W1),sdtpldt1(xI,xJ))))|(?[W1]: (aElement0(W1)&~aElementOf0(sdtasdt0(W1,W0),sdtpldt1(xI,xJ)))))))&~aIdeal0(sdtpldt1(xI,xJ)))))),
% 16.97/7.73 inference(pre_NNF_transformation,[status(thm)],[f27])).
% 16.97/7.73 fof(f123,definition,(
% 16.97/7.73 ![W0,W1,W2]: (sP2_prd(W2,W1,W0)<=>((((![W3,W4]: ((~aElementOf0(W3,xI)|~aElementOf0(W4,xJ))|~sdtpldt0(W3,W4)=W0))&~aElementOf0(W0,sdtpldt1(xI,xJ)))|((![W3,W4]: ((~aElementOf0(W3,xI)|~aElementOf0(W4,xJ))|~sdtpldt0(W3,W4)=W1))&~aElementOf0(W1,sdtpldt1(xI,xJ))))|~aElement0(W2)))),
% 16.97/7.73 introduced(definition,[new_symbols(definition,[sP2_prd])],[])).
% 16.97/7.73 fof(f124,definition,(
% 16.97/7.73 ![W0,W1]: (sP3_prd(W1,W0)<=>(aElementOf0(W1,sdtpldt1(xI,xJ))&~aElementOf0(sdtpldt0(W0,W1),sdtpldt1(xI,xJ))))),
% 16.97/7.73 introduced(definition,[new_symbols(definition,[sP3_prd])],[])).
% 16.97/7.73 fof(f125,plain,(
% 16.97/7.73 (![W0,W1,W2]: (sP2_prd(W2,W1,W0)|(?[W3,W4]: (((aElementOf0(W3,xI)&aElementOf0(W4,xJ))&W0=sdtpldt0(W3,W4))&(?[W5,W6]: (((((((((((aElementOf0(W5,xI)&aElementOf0(W6,xJ))&W1=sdtpldt0(W5,W6))&aElementOf0(sdtpldt0(W3,W5),xI))&aElementOf0(sdtpldt0(W4,W6),xJ))&aElementOf0(sdtasdt0(W2,W3),xI))&aElementOf0(sdtasdt0(W2,W4),xJ))&sdtpldt0(W0,W1)=sdtpldt0(sdtpldt0(W3,W5),sdtpldt0(W4,W6)))&(?[W7,W8]: ((aElementOf0(W7,xI)&aElementOf0(W8,xJ))&sdtpldt0(W7,W8)=sdtpldt0(W0,W1))))&aElementOf0(sdtpldt0(W0,W1),sdtpldt1(xI,xJ)))&(?[W7,W8]: ((aElementOf0(W7,xI)&aElementOf0(W8,xJ))&sdtpldt0(W7,W8)=sdtasdt0(W2,W0))))&aElementOf0(sdtasdt0(W2,W0),sdtpldt1(xI,xJ))))))))&((aSet0(sdtpldt1(xI,xJ))&(![W0]: (aElementOf0(W0,sdtpldt1(xI,xJ))<=>(?[W1,W2]: ((aElementOf0(W1,xI)&aElementOf0(W2,xJ))&sdtpldt0(W1,W2)=W0)))))&((?[W0]: (aElementOf0(W0,sdtpldt1(xI,xJ))&((?[W1]: sP3_prd(W1,W0))|(?[W1]: (aElement0(W1)&~aElementOf0(sdtasdt0(W1,W0),sdtpldt1(xI,xJ)))))))&~aIdeal0(sdtpldt1(xI,xJ))))),
% 16.97/7.73 inference(formula_renaming,[status(thm)],[f122,f124,f123])).
% 16.97/7.73 fof(f126,plain,(
% 16.97/7.73 (![W0,W1,W2]: (sP2_prd(W2,W1,W0)|(?[W3,W4]: (((aElementOf0(W3,xI)&aElementOf0(W4,xJ))&W0=sdtpldt0(W3,W4))&(?[W5,W6]: (((((((((((aElementOf0(W5,xI)&aElementOf0(W6,xJ))&W1=sdtpldt0(W5,W6))&aElementOf0(sdtpldt0(W3,W5),xI))&aElementOf0(sdtpldt0(W4,W6),xJ))&aElementOf0(sdtasdt0(W2,W3),xI))&aElementOf0(sdtasdt0(W2,W4),xJ))&sdtpldt0(W0,W1)=sdtpldt0(sdtpldt0(W3,W5),sdtpldt0(W4,W6)))&(?[W7,W8]: ((aElementOf0(W7,xI)&aElementOf0(W8,xJ))&sdtpldt0(W7,W8)=sdtpldt0(W0,W1))))&aElementOf0(sdtpldt0(W0,W1),sdtpldt1(xI,xJ)))&(?[W7,W8]: ((aElementOf0(W7,xI)&aElementOf0(W8,xJ))&sdtpldt0(W7,W8)=sdtasdt0(W2,W0))))&aElementOf0(sdtasdt0(W2,W0),sdtpldt1(xI,xJ))))))))&((aSet0(sdtpldt1(xI,xJ))&(![W0]: ((~aElementOf0(W0,sdtpldt1(xI,xJ))|(?[W1,W2]: ((aElementOf0(W1,xI)&aElementOf0(W2,xJ))&sdtpldt0(W1,W2)=W0)))&(aElementOf0(W0,sdtpldt1(xI,xJ))|(![W1,W2]: ((~aElementOf0(W1,xI)|~aElementOf0(W2,xJ))|~sdtpldt0(W1,W2)=W0))))))&((?[W0]: (aElementOf0(W0,sdtpldt1(xI,xJ))&((?[W1]: sP3_prd(W1,W0))|(?[W1]: (aElement0(W1)&~aElementOf0(sdtasdt0(W1,W0),sdtpldt1(xI,xJ)))))))&~aIdeal0(sdtpldt1(xI,xJ))))),
% 16.97/7.73 inference(NNF_transformation,[status(thm)],[f125])).
% 16.97/7.73 fof(f127,plain,(
% 16.97/7.73 (![W0,W1,W2]: (sP2_prd(W2,W1,W0)|(?[W3,W4]: (((aElementOf0(W3,xI)&aElementOf0(W4,xJ))&W0=sdtpldt0(W3,W4))&(((((?[W5,W6]: (((((((aElementOf0(W5,xI)&aElementOf0(W6,xJ))&W1=sdtpldt0(W5,W6))&aElementOf0(sdtpldt0(W3,W5),xI))&aElementOf0(sdtpldt0(W4,W6),xJ))&aElementOf0(sdtasdt0(W2,W3),xI))&aElementOf0(sdtasdt0(W2,W4),xJ))&sdtpldt0(W0,W1)=sdtpldt0(sdtpldt0(W3,W5),sdtpldt0(W4,W6))))&(?[W7,W8]: ((aElementOf0(W7,xI)&aElementOf0(W8,xJ))&sdtpldt0(W7,W8)=sdtpldt0(W0,W1))))&aElementOf0(sdtpldt0(W0,W1),sdtpldt1(xI,xJ)))&(?[W7,W8]: ((aElementOf0(W7,xI)&aElementOf0(W8,xJ))&sdtpldt0(W7,W8)=sdtasdt0(W2,W0))))&aElementOf0(sdtasdt0(W2,W0),sdtpldt1(xI,xJ)))))))&((aSet0(sdtpldt1(xI,xJ))&((![W0]: (~aElementOf0(W0,sdtpldt1(xI,xJ))|(?[W1,W2]: ((aElementOf0(W1,xI)&aElementOf0(W2,xJ))&sdtpldt0(W1,W2)=W0))))&(![W0]: (aElementOf0(W0,sdtpldt1(xI,xJ))|(![W1,W2]: ((~aElementOf0(W1,xI)|~aElementOf0(W2,xJ))|~sdtpldt0(W1,W2)=W0))))))&((?[W0]: (aElementOf0(W0,sdtpldt1(xI,xJ))&((?[W1]: sP3_prd(W1,W0))|(?[W1]: (aElement0(W1)&~aElementOf0(sdtasdt0(W1,W0),sdtpldt1(xI,xJ)))))))&~aIdeal0(sdtpldt1(xI,xJ))))),
% 16.97/7.73 inference(miniscoping,[status(thm)],[f126])).
% 16.97/7.73 fof(f128,plain,(
% 16.97/7.73 (![W0,W1,W2]: (sP2_prd(W2,W1,W0)|(((aElementOf0(sK11_skl(W2,W1,W0),xI)&aElementOf0(sK12_skl(W2,W1,W0),xJ))&W0=sdtpldt0(sK11_skl(W2,W1,W0),sK12_skl(W2,W1,W0)))&(((((((((((aElementOf0(sK13_skl(W2,W1,W0),xI)&aElementOf0(sK14_skl(W2,W1,W0),xJ))&W1=sdtpldt0(sK13_skl(W2,W1,W0),sK14_skl(W2,W1,W0)))&aElementOf0(sdtpldt0(sK11_skl(W2,W1,W0),sK13_skl(W2,W1,W0)),xI))&aElementOf0(sdtpldt0(sK12_skl(W2,W1,W0),sK14_skl(W2,W1,W0)),xJ))&aElementOf0(sdtasdt0(W2,sK11_skl(W2,W1,W0)),xI))&aElementOf0(sdtasdt0(W2,sK12_skl(W2,W1,W0)),xJ))&sdtpldt0(W0,W1)=sdtpldt0(sdtpldt0(sK11_skl(W2,W1,W0),sK13_skl(W2,W1,W0)),sdtpldt0(sK12_skl(W2,W1,W0),sK14_skl(W2,W1,W0))))&((aElementOf0(sK15_skl(W2,W1,W0),xI)&aElementOf0(sK16_skl(W2,W1,W0),xJ))&sdtpldt0(sK15_skl(W2,W1,W0),sK16_skl(W2,W1,W0))=sdtpldt0(W0,W1)))&aElementOf0(sdtpldt0(W0,W1),sdtpldt1(xI,xJ)))&((aElementOf0(sK17_skl(W2,W1,W0),xI)&aElementOf0(sK18_skl(W2,W1,W0),xJ))&sdtpldt0(sK17_skl(W2,W1,W0),sK18_skl(W2,W1,W0))=sdtasdt0(W2,W0)))&aElementOf0(sdtasdt0(W2,W0),sdtpldt1(xI,xJ))))))&((aSet0(sdtpldt1(xI,xJ))&((![W0]: (~aElementOf0(W0,sdtpldt1(xI,xJ))|((aElementOf0(sK19_skl(W0),xI)&aElementOf0(sK20_skl(W0),xJ))&sdtpldt0(sK19_skl(W0),sK20_skl(W0))=W0)))&(![W0]: (aElementOf0(W0,sdtpldt1(xI,xJ))|(![W1,W2]: ((~aElementOf0(W1,xI)|~aElementOf0(W2,xJ))|~sdtpldt0(W1,W2)=W0))))))&((aElementOf0(sK21_skl,sdtpldt1(xI,xJ))&(sP3_prd(sK22_skl,sK21_skl)|(aElement0(sK23_skl)&~aElementOf0(sdtasdt0(sK23_skl,sK21_skl),sdtpldt1(xI,xJ)))))&~aIdeal0(sdtpldt1(xI,xJ))))),
% 16.97/7.73 inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl,sK13_skl,sK14_skl,sK15_skl,sK16_skl,sK17_skl,sK18_skl,sK19_skl,sK20_skl,sK21_skl,sK22_skl,sK23_skl]),skolemize(W3,sK11_skl(W2,W1,W0)),skolemize(W4,sK12_skl(W2,W1,W0)),skolemize(W5,sK13_skl(W2,W1,W0)),skolemize(W6,sK14_skl(W2,W1,W0)),skolemize(W7,sK15_skl(W2,W1,W0)),skolemize(W8,sK16_skl(W2,W1,W0)),skolemize(W7,sK17_skl(W2,W1,W0)),skolemize(W8,sK18_skl(W2,W1,W0)),skolemize(W1,sK19_skl(W0)),skolemize(W2,sK20_skl(W0)),skolemize(W0,sK21_skl),skolemize(W1,sK22_skl),skolemize(W1,sK23_skl)],[f127])).
% 16.97/7.73 fof(f143,plain,(
% 16.97/7.73 ![X0,X1,X2]: (sP2_prd(X0,X1,X2)|aElementOf0(sdtpldt0(X2,X1),sdtpldt1(xI,xJ)))),
% 16.97/7.73 inference(cnf_transformation,[status(thm)],[f128])).
% 16.97/7.73 fof(f147,plain,(
% 16.97/7.73 ![X0,X1,X2]: (sP2_prd(X0,X1,X2)|aElementOf0(sdtasdt0(X0,X2),sdtpldt1(xI,xJ)))),
% 16.97/7.73 inference(cnf_transformation,[status(thm)],[f128])).
% 16.97/7.73 fof(f148,plain,(
% 16.97/7.73 aSet0(sdtpldt1(xI,xJ))),
% 16.97/7.73 inference(cnf_transformation,[status(thm)],[f128])).
% 16.97/7.73 fof(f153,plain,(
% 16.97/7.73 aElementOf0(sK21_skl,sdtpldt1(xI,xJ))),
% 16.97/7.73 inference(cnf_transformation,[status(thm)],[f128])).
% 16.97/7.73 fof(f154,plain,(
% 16.97/7.73 sP3_prd(sK22_skl,sK21_skl)|aElement0(sK23_skl)),
% 16.97/7.73 inference(cnf_transformation,[status(thm)],[f128])).
% 16.97/7.73 fof(f155,plain,(
% 16.97/7.73 sP3_prd(sK22_skl,sK21_skl)|~aElementOf0(sdtasdt0(sK23_skl,sK21_skl),sdtpldt1(xI,xJ))),
% 16.97/7.73 inference(cnf_transformation,[status(thm)],[f128])).
% 16.97/7.73 fof(f156,plain,(
% 16.97/7.73 ~aIdeal0(sdtpldt1(xI,xJ))),
% 16.97/7.73 inference(cnf_transformation,[status(thm)],[f128])).
% 16.97/7.73 fof(f168,plain,(
% 16.97/7.73 ![W0,W1,W2]: ((~sP2_prd(W2,W1,W0)|((((![W3,W4]: ((~aElementOf0(W3,xI)|~aElementOf0(W4,xJ))|~sdtpldt0(W3,W4)=W0))&~aElementOf0(W0,sdtpldt1(xI,xJ)))|((![W3,W4]: ((~aElementOf0(W3,xI)|~aElementOf0(W4,xJ))|~sdtpldt0(W3,W4)=W1))&~aElementOf0(W1,sdtpldt1(xI,xJ))))|~aElement0(W2)))&(sP2_prd(W2,W1,W0)|((((?[W3,W4]: ((aElementOf0(W3,xI)&aElementOf0(W4,xJ))&sdtpldt0(W3,W4)=W0))|aElementOf0(W0,sdtpldt1(xI,xJ)))&((?[W3,W4]: ((aElementOf0(W3,xI)&aElementOf0(W4,xJ))&sdtpldt0(W3,W4)=W1))|aElementOf0(W1,sdtpldt1(xI,xJ))))&aElement0(W2))))),
% 16.97/7.73 inference(NNF_transformation,[status(thm)],[f123])).
% 16.97/7.73 fof(f169,plain,(
% 16.97/7.73 (![W0,W1,W2]: (~sP2_prd(W2,W1,W0)|((((![W3,W4]: ((~aElementOf0(W3,xI)|~aElementOf0(W4,xJ))|~sdtpldt0(W3,W4)=W0))&~aElementOf0(W0,sdtpldt1(xI,xJ)))|((![W3,W4]: ((~aElementOf0(W3,xI)|~aElementOf0(W4,xJ))|~sdtpldt0(W3,W4)=W1))&~aElementOf0(W1,sdtpldt1(xI,xJ))))|~aElement0(W2))))&(![W0,W1,W2]: (sP2_prd(W2,W1,W0)|((((?[W3,W4]: ((aElementOf0(W3,xI)&aElementOf0(W4,xJ))&sdtpldt0(W3,W4)=W0))|aElementOf0(W0,sdtpldt1(xI,xJ)))&((?[W3,W4]: ((aElementOf0(W3,xI)&aElementOf0(W4,xJ))&sdtpldt0(W3,W4)=W1))|aElementOf0(W1,sdtpldt1(xI,xJ))))&aElement0(W2))))),
% 16.97/7.73 inference(miniscoping,[status(thm)],[f168])).
% 16.97/7.73 fof(f170,plain,(
% 16.97/7.73 (![W0,W1,W2]: (~sP2_prd(W2,W1,W0)|((((![W3,W4]: ((~aElementOf0(W3,xI)|~aElementOf0(W4,xJ))|~sdtpldt0(W3,W4)=W0))&~aElementOf0(W0,sdtpldt1(xI,xJ)))|((![W3,W4]: ((~aElementOf0(W3,xI)|~aElementOf0(W4,xJ))|~sdtpldt0(W3,W4)=W1))&~aElementOf0(W1,sdtpldt1(xI,xJ))))|~aElement0(W2))))&(![W0,W1,W2]: (sP2_prd(W2,W1,W0)|(((((aElementOf0(sK24_skl(W2,W1,W0),xI)&aElementOf0(sK25_skl(W2,W1,W0),xJ))&sdtpldt0(sK24_skl(W2,W1,W0),sK25_skl(W2,W1,W0))=W0)|aElementOf0(W0,sdtpldt1(xI,xJ)))&(((aElementOf0(sK26_skl(W2,W1,W0),xI)&aElementOf0(sK27_skl(W2,W1,W0),xJ))&sdtpldt0(sK26_skl(W2,W1,W0),sK27_skl(W2,W1,W0))=W1)|aElementOf0(W1,sdtpldt1(xI,xJ))))&aElement0(W2))))),
% 16.97/7.73 inference(skolemize,[status(esa),new_symbols(skolem,[sK24_skl,sK25_skl,sK26_skl,sK27_skl]),skolemize(W3,sK24_skl(W2,W1,W0)),skolemize(W4,sK25_skl(W2,W1,W0)),skolemize(W3,sK26_skl(W2,W1,W0)),skolemize(W4,sK27_skl(W2,W1,W0))],[f169])).
% 16.97/7.73 fof(f174,plain,(
% 16.97/7.73 ![X0,X1,X2]: (~sP2_prd(X0,X1,X2)|~aElementOf0(X2,sdtpldt1(xI,xJ))|~aElementOf0(X1,sdtpldt1(xI,xJ))|~aElement0(X0))),
% 16.97/7.73 inference(cnf_transformation,[status(thm)],[f170])).
% 16.97/7.73 fof(f182,plain,(
% 16.97/7.73 ![W0,W1]: ((~sP3_prd(W1,W0)|(aElementOf0(W1,sdtpldt1(xI,xJ))&~aElementOf0(sdtpldt0(W0,W1),sdtpldt1(xI,xJ))))&(sP3_prd(W1,W0)|(~aElementOf0(W1,sdtpldt1(xI,xJ))|aElementOf0(sdtpldt0(W0,W1),sdtpldt1(xI,xJ)))))),
% 16.97/7.73 inference(NNF_transformation,[status(thm)],[f124])).
% 17.41/7.75 fof(f183,plain,(
% 17.41/7.75 (![W0,W1]: (~sP3_prd(W1,W0)|(aElementOf0(W1,sdtpldt1(xI,xJ))&~aElementOf0(sdtpldt0(W0,W1),sdtpldt1(xI,xJ)))))&(![W0,W1]: (sP3_prd(W1,W0)|(~aElementOf0(W1,sdtpldt1(xI,xJ))|aElementOf0(sdtpldt0(W0,W1),sdtpldt1(xI,xJ)))))),
% 17.41/7.75 inference(miniscoping,[status(thm)],[f182])).
% 17.41/7.75 fof(f184,plain,(
% 17.41/7.75 ![X0,X1]: (~sP3_prd(X0,X1)|aElementOf0(X0,sdtpldt1(xI,xJ)))),
% 17.41/7.75 inference(cnf_transformation,[status(thm)],[f183])).
% 17.41/7.75 fof(f185,plain,(
% 17.41/7.75 ![X0,X1]: (~sP3_prd(X0,X1)|~aElementOf0(sdtpldt0(X1,X0),sdtpldt1(xI,xJ)))),
% 17.41/7.75 inference(cnf_transformation,[status(thm)],[f183])).
% 17.41/7.75 fof(f593,plain,(
% 17.41/7.75 aIdeal0(sdtpldt1(xI,xJ))|aElementOf0(sK8_skl(sdtpldt1(xI,xJ)),sdtpldt1(xI,xJ))),
% 17.41/7.75 inference(resolution,[status(thm)],[f108,f148])).
% 17.41/7.75 fof(f594,plain,(
% 17.41/7.75 aElementOf0(sK8_skl(sdtpldt1(xI,xJ)),sdtpldt1(xI,xJ))),
% 17.41/7.75 inference(forward_subsumption_resolution,[status(thm)],[f593,f156])).
% 17.41/7.75 fof(f699,plain,(
% 17.41/7.75 ![X0]: (sP3_prd(sK22_skl,sK21_skl)|sP2_prd(sK23_skl,X0,sK21_skl))),
% 17.41/7.75 inference(resolution,[status(thm)],[f155,f147])).
% 17.41/7.75 fof(f820,plain,(
% 17.41/7.75 ![X0,X1]: (~sP2_prd(X0,X1,sK21_skl)|~aElementOf0(X1,sdtpldt1(xI,xJ))|~aElement0(X0))),
% 17.41/7.75 inference(resolution,[status(thm)],[f174,f153])).
% 17.41/7.75 fof(f1041,plain,(
% 17.41/7.75 ![X0,X1,X2]: (~sP3_prd(X0,X1)|sP2_prd(X2,X0,X1))),
% 17.41/7.75 inference(resolution,[status(thm)],[f185,f143])).
% 17.41/7.75 fof(f4650,plain,(
% 17.41/7.75 ~aSet0(sdtpldt1(xI,xJ))|aElement0(sK8_skl(sdtpldt1(xI,xJ)))),
% 17.41/7.75 inference(resolution,[status(thm)],[f594,f72])).
% 17.41/7.75 fof(f4653,plain,(
% 17.41/7.75 aElement0(sK8_skl(sdtpldt1(xI,xJ)))),
% 17.41/7.75 inference(forward_subsumption_resolution,[status(thm)],[f4650,f148])).
% 17.41/7.75 fof(f7437,plain,(
% 17.41/7.75 ![X0]: (~sP2_prd(X0,sK21_skl,sK21_skl)|~aElement0(X0))),
% 17.41/7.75 inference(resolution,[status(thm)],[f820,f153])).
% 17.41/7.75 fof(f7514,plain,(
% 17.41/7.75 ~aElement0(sK23_skl)|sP3_prd(sK22_skl,sK21_skl)),
% 17.41/7.75 inference(resolution,[status(thm)],[f7437,f699])).
% 17.41/7.75 fof(f7535,plain,(
% 17.41/7.75 sP3_prd(sK22_skl,sK21_skl)),
% 17.41/7.75 inference(forward_subsumption_resolution,[status(thm)],[f7514,f154])).
% 17.41/7.75 fof(f7536,plain,(
% 17.41/7.75 ![X0]: (sP2_prd(X0,sK22_skl,sK21_skl))),
% 17.41/7.75 inference(resolution,[status(thm)],[f7535,f1041])).
% 17.41/7.75 fof(f7537,plain,(
% 17.41/7.75 aElementOf0(sK22_skl,sdtpldt1(xI,xJ))),
% 17.41/7.75 inference(resolution,[status(thm)],[f7535,f184])).
% 17.41/7.75 fof(f7764,plain,(
% 17.41/7.75 ![X0]: (~sP2_prd(X0,sK22_skl,sK21_skl)|~aElement0(X0))),
% 17.41/7.75 inference(resolution,[status(thm)],[f7537,f820])).
% 17.41/7.75 fof(f7790,plain,(
% 17.41/7.75 ![X0]: (~aElement0(X0))),
% 17.41/7.75 inference(forward_subsumption_resolution,[status(thm)],[f7764,f7536])).
% 17.41/7.75 fof(f7802,plain,(
% 17.41/7.75 $false),
% 17.41/7.75 inference(backward_subsumption_resolution,[status(thm)],[f4653,f7790])).
% 17.41/7.75 % SZS output end CNFRefutation for theBenchmark.p
% 17.41/7.77 % Elapsed time: 2.325241 seconds
% 17.41/7.77 % CPU time: 18.086031 seconds
% 17.41/7.77 % Total memory used: 201.810 MB
% 17.41/7.77 % Net memory used: 189.112 MB
%------------------------------------------------------------------------------