TSTP Solution File: COM019+4 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : COM019+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:14:03 EDT 2024
% Result : Theorem 22.69s 3.26s
% Output : CNFRefutation 22.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COM019+4 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Apr 30 00:56:19 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % Drodi V3.6.0
% 22.69/3.26 % Refutation found
% 22.69/3.26 % SZS status Theorem for theBenchmark: Theorem is valid
% 22.69/3.26 % SZS output start CNFRefutation for theBenchmark
% 22.69/3.26 fof(f6,definition,(
% 22.69/3.26 (! [W0,W1,W2] :( ( aElement0(W0)& aRewritingSystem0(W1)& aElement0(W2) )=> ( sdtmndtplgtdt0(W0,W1,W2)<=> ( aReductOfIn0(W2,W0,W1)| (? [W3] :( aElement0(W3)& aReductOfIn0(W3,W0,W1)& sdtmndtplgtdt0(W3,W1,W2) ) )) ) ) )),
% 22.69/3.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 22.69/3.26 fof(f9,axiom,(
% 22.69/3.26 (! [W0,W1,W2,W3] :( ( aElement0(W0)& aRewritingSystem0(W1)& aElement0(W2)& aElement0(W3) )=> ( ( sdtmndtasgtdt0(W0,W1,W2)& sdtmndtasgtdt0(W2,W1,W3) )=> sdtmndtasgtdt0(W0,W1,W3) ) ) )),
% 22.69/3.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 22.69/3.26 fof(f15,hypothesis,(
% 22.69/3.26 aRewritingSystem0(xR) ),
% 22.69/3.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 22.69/3.26 fof(f16,hypothesis,(
% 22.69/3.26 ( (! [W0,W1,W2] :( ( aElement0(W0)& aElement0(W1)& aElement0(W2)& aReductOfIn0(W1,W0,xR)& aReductOfIn0(W2,W0,xR) )=> (? [W3] :( aElement0(W3)& ( W1 = W3| ( ( aReductOfIn0(W3,W1,xR)| (? [W4] :( aElement0(W4)& aReductOfIn0(W4,W1,xR)& sdtmndtplgtdt0(W4,xR,W3) ) ))& sdtmndtplgtdt0(W1,xR,W3) ) )& sdtmndtasgtdt0(W1,xR,W3)& ( W2 = W3| ( ( aReductOfIn0(W3,W2,xR)| (? [W4] :( aElement0(W4)& aReductOfIn0(W4,W2,xR)& sdtmndtplgtdt0(W4,xR,W3) ) ))& sdtmndtplgtdt0(W2,xR,W3) ) )& sdtmndtasgtdt0(W2,xR,W3) ) )))& isLocallyConfluent0(xR)& (! [W0,W1] :( ( aElement0(W0)& aElement0(W1) )=> ( ( aReductOfIn0(W1,W0,xR)| (? [W2] :( aElement0(W2)& aReductOfIn0(W2,W0,xR)& sdtmndtplgtdt0(W2,xR,W1) ))| sdtmndtplgtdt0(W0,xR,W1) )=> iLess0(W1,W0) ) ))& isTerminating0(xR) ) ),
% 22.69/3.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 22.69/3.26 fof(f17,hypothesis,(
% 22.69/3.26 ( aElement0(xa)& aElement0(xb)& aElement0(xc) ) ),
% 22.69/3.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 22.69/3.26 fof(f18,hypothesis,(
% 22.69/3.26 (! [W0,W1,W2] :( ( aElement0(W0)& aElement0(W1)& aElement0(W2)& ( W0 = W1| aReductOfIn0(W1,W0,xR)| (? [W3] :( aElement0(W3)& aReductOfIn0(W3,W0,xR)& sdtmndtplgtdt0(W3,xR,W1) ))| sdtmndtplgtdt0(W0,xR,W1)| sdtmndtasgtdt0(W0,xR,W1) )& ( W0 = W2| aReductOfIn0(W2,W0,xR)| (? [W3] :( aElement0(W3)& aReductOfIn0(W3,W0,xR)& sdtmndtplgtdt0(W3,xR,W2) ))| sdtmndtplgtdt0(W0,xR,W2)| sdtmndtasgtdt0(W0,xR,W2) ) )=> ( iLess0(W0,xa)=> (? [W3] :( aElement0(W3)& ( W1 = W3| ( ( aReductOfIn0(W3,W1,xR)| (? [W4] :( aElement0(W4)& aReductOfIn0(W4,W1,xR)& sdtmndtplgtdt0(W4,xR,W3) ) ))& sdtmndtplgtdt0(W1,xR,W3) ) )& sdtmndtasgtdt0(W1,xR,W3)& ( W2 = W3| ( ( aReductOfIn0(W3,W2,xR)| (? [W4] :( aElement0(W4)& aReductOfIn0(W4,W2,xR)& sdtmndtplgtdt0(W4,xR,W3) ) ))& sdtmndtplgtdt0(W2,xR,W3) ) )& sdtmndtasgtdt0(W2,xR,W3) ) )) ) )),
% 22.69/3.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 22.69/3.26 fof(f20,hypothesis,(
% 22.69/3.26 ( aElement0(xu)& aReductOfIn0(xu,xa,xR)& ( xu = xb| ( ( aReductOfIn0(xb,xu,xR)| (? [W0] :( aElement0(W0)& aReductOfIn0(W0,xu,xR)& sdtmndtplgtdt0(W0,xR,xb) ) ))& sdtmndtplgtdt0(xu,xR,xb) ) )& sdtmndtasgtdt0(xu,xR,xb) ) ),
% 22.69/3.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 22.69/3.26 fof(f22,hypothesis,(
% 22.69/3.26 ( aElement0(xw)& ( xu = xw| ( ( aReductOfIn0(xw,xu,xR)| (? [W0] :( aElement0(W0)& aReductOfIn0(W0,xu,xR)& sdtmndtplgtdt0(W0,xR,xw) ) ))& sdtmndtplgtdt0(xu,xR,xw) ) )& sdtmndtasgtdt0(xu,xR,xw)& ( xv = xw| ( ( aReductOfIn0(xw,xv,xR)| (? [W0] :( aElement0(W0)& aReductOfIn0(W0,xv,xR)& sdtmndtplgtdt0(W0,xR,xw) ) ))& sdtmndtplgtdt0(xv,xR,xw) ) )& sdtmndtasgtdt0(xv,xR,xw) ) ),
% 22.69/3.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 22.69/3.26 fof(f23,hypothesis,(
% 22.69/3.26 ( aElement0(xd)& ( xw = xd| ( ( aReductOfIn0(xd,xw,xR)| (? [W0] :( aElement0(W0)& aReductOfIn0(W0,xw,xR)& sdtmndtplgtdt0(W0,xR,xd) ) ))& sdtmndtplgtdt0(xw,xR,xd) ) )& sdtmndtasgtdt0(xw,xR,xd)& ~ (? [W0] : aReductOfIn0(W0,xd,xR))& aNormalFormOfIn0(xd,xw,xR) ) ),
% 22.69/3.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 22.69/3.26 fof(f24,conjecture,(
% 22.69/3.26 ( xb = xd| aReductOfIn0(xd,xb,xR)| (? [W0] :( aElement0(W0)& aReductOfIn0(W0,xb,xR)& sdtmndtplgtdt0(W0,xR,xd) ))| sdtmndtplgtdt0(xb,xR,xd)| sdtmndtasgtdt0(xb,xR,xd) ) ),
% 22.69/3.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 22.69/3.26 fof(f25,negated_conjecture,(
% 22.69/3.26 ~(( xb = xd| aReductOfIn0(xd,xb,xR)| (? [W0] :( aElement0(W0)& aReductOfIn0(W0,xb,xR)& sdtmndtplgtdt0(W0,xR,xd) ))| sdtmndtplgtdt0(xb,xR,xd)| sdtmndtasgtdt0(xb,xR,xd) ) )),
% 22.69/3.26 inference(negated_conjecture,[status(cth)],[f24])).
% 22.69/3.26 fof(f38,plain,(
% 22.69/3.26 ![W0,W1,W2]: (((~aElement0(W0)|~aRewritingSystem0(W1))|~aElement0(W2))|(sdtmndtplgtdt0(W0,W1,W2)<=>(aReductOfIn0(W2,W0,W1)|(?[W3]: ((aElement0(W3)&aReductOfIn0(W3,W0,W1))&sdtmndtplgtdt0(W3,W1,W2))))))),
% 22.69/3.26 inference(pre_NNF_transformation,[status(esa)],[f6])).
% 22.69/3.26 fof(f39,plain,(
% 22.69/3.26 ![W0,W1,W2]: (((~aElement0(W0)|~aRewritingSystem0(W1))|~aElement0(W2))|((~sdtmndtplgtdt0(W0,W1,W2)|(aReductOfIn0(W2,W0,W1)|(?[W3]: ((aElement0(W3)&aReductOfIn0(W3,W0,W1))&sdtmndtplgtdt0(W3,W1,W2)))))&(sdtmndtplgtdt0(W0,W1,W2)|(~aReductOfIn0(W2,W0,W1)&(![W3]: ((~aElement0(W3)|~aReductOfIn0(W3,W0,W1))|~sdtmndtplgtdt0(W3,W1,W2)))))))),
% 22.69/3.26 inference(NNF_transformation,[status(esa)],[f38])).
% 22.69/3.26 fof(f40,plain,(
% 22.69/3.26 ![W0,W1,W2]: (((~aElement0(W0)|~aRewritingSystem0(W1))|~aElement0(W2))|((~sdtmndtplgtdt0(W0,W1,W2)|(aReductOfIn0(W2,W0,W1)|((aElement0(sk0_0(W2,W1,W0))&aReductOfIn0(sk0_0(W2,W1,W0),W0,W1))&sdtmndtplgtdt0(sk0_0(W2,W1,W0),W1,W2))))&(sdtmndtplgtdt0(W0,W1,W2)|(~aReductOfIn0(W2,W0,W1)&(![W3]: ((~aElement0(W3)|~aReductOfIn0(W3,W0,W1))|~sdtmndtplgtdt0(W3,W1,W2)))))))),
% 22.69/3.26 inference(skolemization,[status(esa)],[f39])).
% 22.69/3.26 fof(f42,plain,(
% 22.69/3.26 ![X0,X1,X2]: (~aElement0(X0)|~aRewritingSystem0(X1)|~aElement0(X2)|~sdtmndtplgtdt0(X0,X1,X2)|aReductOfIn0(X2,X0,X1)|aReductOfIn0(sk0_0(X2,X1,X0),X0,X1))),
% 22.69/3.26 inference(cnf_transformation,[status(esa)],[f40])).
% 22.69/3.26 fof(f53,plain,(
% 22.69/3.26 ![W0,W1,W2,W3]: ((((~aElement0(W0)|~aRewritingSystem0(W1))|~aElement0(W2))|~aElement0(W3))|((~sdtmndtasgtdt0(W0,W1,W2)|~sdtmndtasgtdt0(W2,W1,W3))|sdtmndtasgtdt0(W0,W1,W3)))),
% 22.69/3.26 inference(pre_NNF_transformation,[status(esa)],[f9])).
% 22.69/3.26 fof(f54,plain,(
% 22.69/3.26 ![X0,X1,X2,X3]: (~aElement0(X0)|~aRewritingSystem0(X1)|~aElement0(X2)|~aElement0(X3)|~sdtmndtasgtdt0(X0,X1,X2)|~sdtmndtasgtdt0(X2,X1,X3)|sdtmndtasgtdt0(X0,X1,X3))),
% 22.69/3.26 inference(cnf_transformation,[status(esa)],[f53])).
% 22.69/3.26 fof(f100,plain,(
% 22.69/3.26 aRewritingSystem0(xR)),
% 22.69/3.26 inference(cnf_transformation,[status(esa)],[f15])).
% 22.69/3.26 fof(f101,plain,(
% 22.69/3.26 (((![W0,W1,W2]: (((((~aElement0(W0)|~aElement0(W1))|~aElement0(W2))|~aReductOfIn0(W1,W0,xR))|~aReductOfIn0(W2,W0,xR))|(?[W3]: ((((aElement0(W3)&(W1=W3|((aReductOfIn0(W3,W1,xR)|(?[W4]: ((aElement0(W4)&aReductOfIn0(W4,W1,xR))&sdtmndtplgtdt0(W4,xR,W3))))&sdtmndtplgtdt0(W1,xR,W3))))&sdtmndtasgtdt0(W1,xR,W3))&(W2=W3|((aReductOfIn0(W3,W2,xR)|(?[W4]: ((aElement0(W4)&aReductOfIn0(W4,W2,xR))&sdtmndtplgtdt0(W4,xR,W3))))&sdtmndtplgtdt0(W2,xR,W3))))&sdtmndtasgtdt0(W2,xR,W3)))))&isLocallyConfluent0(xR))&(![W0,W1]: ((~aElement0(W0)|~aElement0(W1))|(((~aReductOfIn0(W1,W0,xR)&(![W2]: ((~aElement0(W2)|~aReductOfIn0(W2,W0,xR))|~sdtmndtplgtdt0(W2,xR,W1))))&~sdtmndtplgtdt0(W0,xR,W1))|iLess0(W1,W0)))))&isTerminating0(xR)),
% 22.69/3.26 inference(pre_NNF_transformation,[status(esa)],[f16])).
% 22.69/3.26 fof(f102,plain,(
% 22.69/3.26 (((![W1,W2]: ((![W0]: ((((~aElement0(W0)|~aElement0(W1))|~aElement0(W2))|~aReductOfIn0(W1,W0,xR))|~aReductOfIn0(W2,W0,xR)))|(?[W3]: ((((aElement0(W3)&(W1=W3|((aReductOfIn0(W3,W1,xR)|(?[W4]: ((aElement0(W4)&aReductOfIn0(W4,W1,xR))&sdtmndtplgtdt0(W4,xR,W3))))&sdtmndtplgtdt0(W1,xR,W3))))&sdtmndtasgtdt0(W1,xR,W3))&(W2=W3|((aReductOfIn0(W3,W2,xR)|(?[W4]: ((aElement0(W4)&aReductOfIn0(W4,W2,xR))&sdtmndtplgtdt0(W4,xR,W3))))&sdtmndtplgtdt0(W2,xR,W3))))&sdtmndtasgtdt0(W2,xR,W3)))))&isLocallyConfluent0(xR))&(![W0,W1]: ((~aElement0(W0)|~aElement0(W1))|(((~aReductOfIn0(W1,W0,xR)&(![W2]: ((~aElement0(W2)|~aReductOfIn0(W2,W0,xR))|~sdtmndtplgtdt0(W2,xR,W1))))&~sdtmndtplgtdt0(W0,xR,W1))|iLess0(W1,W0)))))&isTerminating0(xR)),
% 22.69/3.26 inference(miniscoping,[status(esa)],[f101])).
% 22.69/3.26 fof(f103,plain,(
% 22.69/3.26 (((![W1,W2]: ((![W0]: ((((~aElement0(W0)|~aElement0(W1))|~aElement0(W2))|~aReductOfIn0(W1,W0,xR))|~aReductOfIn0(W2,W0,xR)))|((((aElement0(sk0_13(W2,W1))&(W1=sk0_13(W2,W1)|((aReductOfIn0(sk0_13(W2,W1),W1,xR)|((aElement0(sk0_14(W2,W1))&aReductOfIn0(sk0_14(W2,W1),W1,xR))&sdtmndtplgtdt0(sk0_14(W2,W1),xR,sk0_13(W2,W1))))&sdtmndtplgtdt0(W1,xR,sk0_13(W2,W1)))))&sdtmndtasgtdt0(W1,xR,sk0_13(W2,W1)))&(W2=sk0_13(W2,W1)|((aReductOfIn0(sk0_13(W2,W1),W2,xR)|((aElement0(sk0_15(W2,W1))&aReductOfIn0(sk0_15(W2,W1),W2,xR))&sdtmndtplgtdt0(sk0_15(W2,W1),xR,sk0_13(W2,W1))))&sdtmndtplgtdt0(W2,xR,sk0_13(W2,W1)))))&sdtmndtasgtdt0(W2,xR,sk0_13(W2,W1)))))&isLocallyConfluent0(xR))&(![W0,W1]: ((~aElement0(W0)|~aElement0(W1))|(((~aReductOfIn0(W1,W0,xR)&(![W2]: ((~aElement0(W2)|~aReductOfIn0(W2,W0,xR))|~sdtmndtplgtdt0(W2,xR,W1))))&~sdtmndtplgtdt0(W0,xR,W1))|iLess0(W1,W0)))))&isTerminating0(xR)),
% 22.69/3.26 inference(skolemization,[status(esa)],[f102])).
% 22.69/3.26 fof(f116,plain,(
% 22.69/3.26 ![X0,X1]: (~aElement0(X0)|~aElement0(X1)|~aReductOfIn0(X1,X0,xR)|iLess0(X1,X0))),
% 22.69/3.26 inference(cnf_transformation,[status(esa)],[f103])).
% 22.69/3.26 fof(f120,plain,(
% 22.69/3.26 aElement0(xa)),
% 22.69/3.26 inference(cnf_transformation,[status(esa)],[f17])).
% 22.69/3.26 fof(f121,plain,(
% 22.69/3.26 aElement0(xb)),
% 22.69/3.26 inference(cnf_transformation,[status(esa)],[f17])).
% 22.69/3.26 fof(f123,plain,(
% 22.69/3.26 ![W0,W1,W2]: (((((~aElement0(W0)|~aElement0(W1))|~aElement0(W2))|((((~W0=W1&~aReductOfIn0(W1,W0,xR))&(![W3]: ((~aElement0(W3)|~aReductOfIn0(W3,W0,xR))|~sdtmndtplgtdt0(W3,xR,W1))))&~sdtmndtplgtdt0(W0,xR,W1))&~sdtmndtasgtdt0(W0,xR,W1)))|((((~W0=W2&~aReductOfIn0(W2,W0,xR))&(![W3]: ((~aElement0(W3)|~aReductOfIn0(W3,W0,xR))|~sdtmndtplgtdt0(W3,xR,W2))))&~sdtmndtplgtdt0(W0,xR,W2))&~sdtmndtasgtdt0(W0,xR,W2)))|(~iLess0(W0,xa)|(?[W3]: ((((aElement0(W3)&(W1=W3|((aReductOfIn0(W3,W1,xR)|(?[W4]: ((aElement0(W4)&aReductOfIn0(W4,W1,xR))&sdtmndtplgtdt0(W4,xR,W3))))&sdtmndtplgtdt0(W1,xR,W3))))&sdtmndtasgtdt0(W1,xR,W3))&(W2=W3|((aReductOfIn0(W3,W2,xR)|(?[W4]: ((aElement0(W4)&aReductOfIn0(W4,W2,xR))&sdtmndtplgtdt0(W4,xR,W3))))&sdtmndtplgtdt0(W2,xR,W3))))&sdtmndtasgtdt0(W2,xR,W3)))))),
% 22.69/3.26 inference(pre_NNF_transformation,[status(esa)],[f18])).
% 22.69/3.26 fof(f124,plain,(
% 22.69/3.26 ![W0,W1]: (pd0_0(W1,W0)=>((((~W0=W1&~aReductOfIn0(W1,W0,xR))&(![W3]: ((~aElement0(W3)|~aReductOfIn0(W3,W0,xR))|~sdtmndtplgtdt0(W3,xR,W1))))&~sdtmndtplgtdt0(W0,xR,W1))&~sdtmndtasgtdt0(W0,xR,W1)))),
% 22.69/3.26 introduced(predicate_definition,[f123])).
% 22.69/3.26 fof(f125,plain,(
% 22.69/3.26 ![W0,W1,W2]: (((((~aElement0(W0)|~aElement0(W1))|~aElement0(W2))|pd0_0(W1,W0))|((((~W0=W2&~aReductOfIn0(W2,W0,xR))&(![W3]: ((~aElement0(W3)|~aReductOfIn0(W3,W0,xR))|~sdtmndtplgtdt0(W3,xR,W2))))&~sdtmndtplgtdt0(W0,xR,W2))&~sdtmndtasgtdt0(W0,xR,W2)))|(~iLess0(W0,xa)|(?[W3]: ((((aElement0(W3)&(W1=W3|((aReductOfIn0(W3,W1,xR)|(?[W4]: ((aElement0(W4)&aReductOfIn0(W4,W1,xR))&sdtmndtplgtdt0(W4,xR,W3))))&sdtmndtplgtdt0(W1,xR,W3))))&sdtmndtasgtdt0(W1,xR,W3))&(W2=W3|((aReductOfIn0(W3,W2,xR)|(?[W4]: ((aElement0(W4)&aReductOfIn0(W4,W2,xR))&sdtmndtplgtdt0(W4,xR,W3))))&sdtmndtplgtdt0(W2,xR,W3))))&sdtmndtasgtdt0(W2,xR,W3)))))),
% 22.69/3.26 inference(formula_renaming,[status(thm)],[f123,f124])).
% 22.69/3.26 fof(f126,plain,(
% 22.69/3.26 ![W0,W1,W2]: (((((~aElement0(W0)|~aElement0(W1))|~aElement0(W2))|pd0_0(W1,W0))|((((~W0=W2&~aReductOfIn0(W2,W0,xR))&(![W3]: ((~aElement0(W3)|~aReductOfIn0(W3,W0,xR))|~sdtmndtplgtdt0(W3,xR,W2))))&~sdtmndtplgtdt0(W0,xR,W2))&~sdtmndtasgtdt0(W0,xR,W2)))|(~iLess0(W0,xa)|((((aElement0(sk0_16(W2,W1,W0))&(W1=sk0_16(W2,W1,W0)|((aReductOfIn0(sk0_16(W2,W1,W0),W1,xR)|((aElement0(sk0_17(W2,W1,W0))&aReductOfIn0(sk0_17(W2,W1,W0),W1,xR))&sdtmndtplgtdt0(sk0_17(W2,W1,W0),xR,sk0_16(W2,W1,W0))))&sdtmndtplgtdt0(W1,xR,sk0_16(W2,W1,W0)))))&sdtmndtasgtdt0(W1,xR,sk0_16(W2,W1,W0)))&(W2=sk0_16(W2,W1,W0)|((aReductOfIn0(sk0_16(W2,W1,W0),W2,xR)|((aElement0(sk0_18(W2,W1,W0))&aReductOfIn0(sk0_18(W2,W1,W0),W2,xR))&sdtmndtplgtdt0(sk0_18(W2,W1,W0),xR,sk0_16(W2,W1,W0))))&sdtmndtplgtdt0(W2,xR,sk0_16(W2,W1,W0)))))&sdtmndtasgtdt0(W2,xR,sk0_16(W2,W1,W0)))))),
% 22.69/3.26 inference(skolemization,[status(esa)],[f125])).
% 22.69/3.26 fof(f171,plain,(
% 22.69/3.26 ![X0,X1,X2]: (~aElement0(X0)|~aElement0(X1)|~aElement0(X2)|pd0_0(X1,X0)|~sdtmndtasgtdt0(X0,xR,X2)|~iLess0(X0,xa)|aElement0(sk0_16(X2,X1,X0)))),
% 22.69/3.26 inference(cnf_transformation,[status(esa)],[f126])).
% 22.69/3.26 fof(f176,plain,(
% 22.69/3.26 ![X0,X1,X2]: (~aElement0(X0)|~aElement0(X1)|~aElement0(X2)|pd0_0(X1,X0)|~sdtmndtasgtdt0(X0,xR,X2)|~iLess0(X0,xa)|sdtmndtasgtdt0(X1,xR,sk0_16(X2,X1,X0)))),
% 22.69/3.26 inference(cnf_transformation,[status(esa)],[f126])).
% 22.69/3.26 fof(f180,plain,(
% 22.69/3.26 ![X0,X1,X2]: (~aElement0(X0)|~aElement0(X1)|~aElement0(X2)|pd0_0(X1,X0)|~sdtmndtasgtdt0(X0,xR,X2)|~iLess0(X0,xa)|X2=sk0_16(X2,X1,X0)|sdtmndtplgtdt0(X2,xR,sk0_16(X2,X1,X0)))),
% 22.69/3.26 inference(cnf_transformation,[status(esa)],[f126])).
% 22.69/3.26 fof(f191,plain,(
% 22.69/3.26 ((aElement0(xu)&aReductOfIn0(xu,xa,xR))&(xu=xb|((aReductOfIn0(xb,xu,xR)|((aElement0(sk0_21)&aReductOfIn0(sk0_21,xu,xR))&sdtmndtplgtdt0(sk0_21,xR,xb)))&sdtmndtplgtdt0(xu,xR,xb))))&sdtmndtasgtdt0(xu,xR,xb)),
% 22.69/3.26 inference(skolemization,[status(esa)],[f20])).
% 22.69/3.26 fof(f192,plain,(
% 22.69/3.26 aElement0(xu)),
% 22.69/3.26 inference(cnf_transformation,[status(esa)],[f191])).
% 22.69/3.26 fof(f193,plain,(
% 22.69/3.26 aReductOfIn0(xu,xa,xR)),
% 22.69/3.26 inference(cnf_transformation,[status(esa)],[f191])).
% 22.69/3.26 fof(f198,plain,(
% 22.69/3.26 sdtmndtasgtdt0(xu,xR,xb)),
% 22.69/3.26 inference(cnf_transformation,[status(esa)],[f191])).
% 22.69/3.26 fof(f207,plain,(
% 22.69/3.26 (((aElement0(xw)&(xu=xw|((aReductOfIn0(xw,xu,xR)|((aElement0(sk0_23)&aReductOfIn0(sk0_23,xu,xR))&sdtmndtplgtdt0(sk0_23,xR,xw)))&sdtmndtplgtdt0(xu,xR,xw))))&sdtmndtasgtdt0(xu,xR,xw))&(xv=xw|((aReductOfIn0(xw,xv,xR)|((aElement0(sk0_24)&aReductOfIn0(sk0_24,xv,xR))&sdtmndtplgtdt0(sk0_24,xR,xw)))&sdtmndtplgtdt0(xv,xR,xw))))&sdtmndtasgtdt0(xv,xR,xw)),
% 22.69/3.26 inference(skolemization,[status(esa)],[f22])).
% 22.69/3.26 fof(f208,plain,(
% 22.69/3.26 aElement0(xw)),
% 22.69/3.26 inference(cnf_transformation,[status(esa)],[f207])).
% 22.69/3.26 fof(f213,plain,(
% 22.69/3.26 sdtmndtasgtdt0(xu,xR,xw)),
% 22.69/3.26 inference(cnf_transformation,[status(esa)],[f207])).
% 22.69/3.26 fof(f219,plain,(
% 22.69/3.26 (((aElement0(xd)&(xw=xd|((aReductOfIn0(xd,xw,xR)|(?[W0]: ((aElement0(W0)&aReductOfIn0(W0,xw,xR))&sdtmndtplgtdt0(W0,xR,xd))))&sdtmndtplgtdt0(xw,xR,xd))))&sdtmndtasgtdt0(xw,xR,xd))&(![W0]: ~aReductOfIn0(W0,xd,xR)))&aNormalFormOfIn0(xd,xw,xR)),
% 22.69/3.26 inference(pre_NNF_transformation,[status(esa)],[f23])).
% 22.69/3.26 fof(f220,plain,(
% 22.69/3.26 (((aElement0(xd)&(xw=xd|((aReductOfIn0(xd,xw,xR)|((aElement0(sk0_25)&aReductOfIn0(sk0_25,xw,xR))&sdtmndtplgtdt0(sk0_25,xR,xd)))&sdtmndtplgtdt0(xw,xR,xd))))&sdtmndtasgtdt0(xw,xR,xd))&(![W0]: ~aReductOfIn0(W0,xd,xR)))&aNormalFormOfIn0(xd,xw,xR)),
% 22.69/3.26 inference(skolemization,[status(esa)],[f219])).
% 22.69/3.26 fof(f221,plain,(
% 22.69/3.26 aElement0(xd)),
% 22.69/3.26 inference(cnf_transformation,[status(esa)],[f220])).
% 22.69/3.26 fof(f226,plain,(
% 22.69/3.26 sdtmndtasgtdt0(xw,xR,xd)),
% 22.69/3.26 inference(cnf_transformation,[status(esa)],[f220])).
% 22.69/3.26 fof(f227,plain,(
% 22.69/3.26 ![X0]: (~aReductOfIn0(X0,xd,xR))),
% 22.69/3.26 inference(cnf_transformation,[status(esa)],[f220])).
% 22.69/3.26 fof(f229,plain,(
% 22.69/3.26 ((((~xb=xd&~aReductOfIn0(xd,xb,xR))&(![W0]: ((~aElement0(W0)|~aReductOfIn0(W0,xb,xR))|~sdtmndtplgtdt0(W0,xR,xd))))&~sdtmndtplgtdt0(xb,xR,xd))&~sdtmndtasgtdt0(xb,xR,xd))),
% 22.69/3.26 inference(pre_NNF_transformation,[status(esa)],[f25])).
% 22.69/3.26 fof(f234,plain,(
% 22.69/3.26 ~sdtmndtasgtdt0(xb,xR,xd)),
% 22.69/3.26 inference(cnf_transformation,[status(esa)],[f229])).
% 22.69/3.26 fof(f235,plain,(
% 22.69/3.26 ![W0,W1]: (~pd0_0(W1,W0)|((((~W0=W1&~aReductOfIn0(W1,W0,xR))&(![W3]: ((~aElement0(W3)|~aReductOfIn0(W3,W0,xR))|~sdtmndtplgtdt0(W3,xR,W1))))&~sdtmndtplgtdt0(W0,xR,W1))&~sdtmndtasgtdt0(W0,xR,W1)))),
% 22.69/3.26 inference(pre_NNF_transformation,[status(esa)],[f124])).
% 22.69/3.26 fof(f240,plain,(
% 22.69/3.26 ![X0,X1]: (~pd0_0(X0,X1)|~sdtmndtasgtdt0(X1,xR,X0))),
% 22.69/3.26 inference(cnf_transformation,[status(esa)],[f235])).
% 22.69/3.26 fof(f407,plain,(
% 22.69/3.26 ~pd0_0(xb,xu)),
% 22.69/3.26 inference(resolution,[status(thm)],[f240,f198])).
% 22.69/3.26 fof(f409,plain,(
% 22.69/3.26 ![X0,X1]: (~aElement0(X0)|~aElement0(X1)|pd0_0(xb,X0)|~sdtmndtasgtdt0(X0,xR,X1)|~iLess0(X0,xa)|aElement0(sk0_16(X1,xb,X0)))),
% 22.69/3.26 inference(resolution,[status(thm)],[f171,f121])).
% 22.69/3.26 fof(f410,plain,(
% 22.69/3.26 spl0_38 <=> aElement0(xw)),
% 22.69/3.26 introduced(split_symbol_definition)).
% 22.69/3.26 fof(f412,plain,(
% 22.69/3.26 ~aElement0(xw)|spl0_38),
% 22.69/3.26 inference(component_clause,[status(thm)],[f410])).
% 22.69/3.26 fof(f413,plain,(
% 22.69/3.26 spl0_39 <=> aElement0(xd)),
% 22.69/3.26 introduced(split_symbol_definition)).
% 22.69/3.26 fof(f415,plain,(
% 22.69/3.26 ~aElement0(xd)|spl0_39),
% 22.69/3.26 inference(component_clause,[status(thm)],[f413])).
% 22.69/3.26 fof(f427,plain,(
% 22.69/3.26 spl0_43 <=> aElement0(xu)),
% 22.69/3.26 introduced(split_symbol_definition)).
% 22.69/3.26 fof(f429,plain,(
% 22.69/3.26 ~aElement0(xu)|spl0_43),
% 22.69/3.26 inference(component_clause,[status(thm)],[f427])).
% 22.69/3.26 fof(f436,plain,(
% 22.69/3.26 spl0_46 <=> iLess0(xu,xa)),
% 22.69/3.26 introduced(split_symbol_definition)).
% 22.69/3.26 fof(f458,plain,(
% 22.69/3.26 spl0_50 <=> pd0_0(xb,xu)),
% 22.69/3.26 introduced(split_symbol_definition)).
% 22.69/3.26 fof(f459,plain,(
% 22.69/3.26 pd0_0(xb,xu)|~spl0_50),
% 22.69/3.26 inference(component_clause,[status(thm)],[f458])).
% 22.69/3.26 fof(f470,plain,(
% 22.69/3.26 spl0_52 <=> aElement0(xa)),
% 22.69/3.26 introduced(split_symbol_definition)).
% 22.69/3.26 fof(f472,plain,(
% 22.69/3.26 ~aElement0(xa)|spl0_52),
% 22.69/3.26 inference(component_clause,[status(thm)],[f470])).
% 22.69/3.26 fof(f493,plain,(
% 22.69/3.26 ![X0,X1]: (~aElement0(X0)|~aElement0(X1)|pd0_0(xb,X0)|~sdtmndtasgtdt0(X0,xR,X1)|~iLess0(X0,xa)|sdtmndtasgtdt0(xb,xR,sk0_16(X1,xb,X0)))),
% 22.69/3.26 inference(resolution,[status(thm)],[f176,f121])).
% 22.69/3.26 fof(f530,plain,(
% 22.69/3.26 $false|spl0_39),
% 22.69/3.26 inference(forward_subsumption_resolution,[status(thm)],[f415,f221])).
% 22.69/3.26 fof(f531,plain,(
% 22.69/3.26 spl0_39),
% 22.69/3.26 inference(contradiction_clause,[status(thm)],[f530])).
% 22.69/3.26 fof(f551,plain,(
% 22.69/3.26 ![X0,X1]: (~aElement0(X0)|~aElement0(X1)|pd0_0(xb,X0)|~sdtmndtasgtdt0(X0,xR,X1)|~iLess0(X0,xa)|X1=sk0_16(X1,xb,X0)|sdtmndtplgtdt0(X1,xR,sk0_16(X1,xb,X0)))),
% 22.69/3.26 inference(resolution,[status(thm)],[f180,f121])).
% 22.69/3.26 fof(f609,plain,(
% 22.69/3.26 spl0_79 <=> aRewritingSystem0(xR)),
% 22.69/3.26 introduced(split_symbol_definition)).
% 22.69/3.26 fof(f611,plain,(
% 22.69/3.26 ~aRewritingSystem0(xR)|spl0_79),
% 22.69/3.27 inference(component_clause,[status(thm)],[f609])).
% 22.69/3.27 fof(f617,plain,(
% 22.69/3.27 $false|spl0_79),
% 22.69/3.27 inference(forward_subsumption_resolution,[status(thm)],[f100,f611])).
% 22.69/3.27 fof(f618,plain,(
% 22.69/3.27 spl0_79),
% 22.69/3.27 inference(contradiction_clause,[status(thm)],[f617])).
% 22.69/3.27 fof(f619,plain,(
% 22.69/3.27 $false|spl0_52),
% 22.69/3.27 inference(forward_subsumption_resolution,[status(thm)],[f120,f472])).
% 22.69/3.27 fof(f620,plain,(
% 22.69/3.27 spl0_52),
% 22.69/3.27 inference(contradiction_clause,[status(thm)],[f619])).
% 22.69/3.27 fof(f812,plain,(
% 22.69/3.27 $false|spl0_43),
% 22.69/3.27 inference(forward_subsumption_resolution,[status(thm)],[f192,f429])).
% 22.69/3.27 fof(f813,plain,(
% 22.69/3.27 spl0_43),
% 22.69/3.27 inference(contradiction_clause,[status(thm)],[f812])).
% 22.69/3.27 fof(f1592,plain,(
% 22.69/3.27 $false|spl0_38),
% 22.69/3.27 inference(forward_subsumption_resolution,[status(thm)],[f412,f208])).
% 22.69/3.27 fof(f1593,plain,(
% 22.69/3.27 spl0_38),
% 22.69/3.27 inference(contradiction_clause,[status(thm)],[f1592])).
% 22.69/3.27 fof(f2092,plain,(
% 22.69/3.27 $false|~spl0_50),
% 22.69/3.27 inference(forward_subsumption_resolution,[status(thm)],[f459,f407])).
% 22.69/3.27 fof(f2093,plain,(
% 22.69/3.27 ~spl0_50),
% 22.69/3.27 inference(contradiction_clause,[status(thm)],[f2092])).
% 22.69/3.27 fof(f2758,plain,(
% 22.69/3.27 spl0_406 <=> ~aElement0(X0)|~sdtmndtasgtdt0(X0,xR,xw)|sdtmndtasgtdt0(X0,xR,xd)),
% 22.69/3.27 introduced(split_symbol_definition)).
% 22.69/3.27 fof(f2759,plain,(
% 22.69/3.27 ![X0]: (~aElement0(X0)|~sdtmndtasgtdt0(X0,xR,xw)|sdtmndtasgtdt0(X0,xR,xd)|~spl0_406)),
% 22.69/3.27 inference(component_clause,[status(thm)],[f2758])).
% 22.69/3.27 fof(f2761,plain,(
% 22.69/3.27 ![X0]: (~aElement0(X0)|~aRewritingSystem0(xR)|~aElement0(xw)|~aElement0(xd)|~sdtmndtasgtdt0(X0,xR,xw)|sdtmndtasgtdt0(X0,xR,xd))),
% 22.69/3.27 inference(resolution,[status(thm)],[f226,f54])).
% 22.69/3.27 fof(f2762,plain,(
% 22.69/3.27 spl0_406|~spl0_79|~spl0_38|~spl0_39),
% 22.69/3.27 inference(split_clause,[status(thm)],[f2761,f2758,f609,f410,f413])).
% 22.69/3.27 fof(f3112,plain,(
% 22.69/3.27 spl0_440 <=> sdtmndtasgtdt0(xu,xR,xd)),
% 22.69/3.27 introduced(split_symbol_definition)).
% 22.69/3.27 fof(f3113,plain,(
% 22.69/3.27 sdtmndtasgtdt0(xu,xR,xd)|~spl0_440),
% 22.69/3.27 inference(component_clause,[status(thm)],[f3112])).
% 22.69/3.27 fof(f3115,plain,(
% 22.69/3.27 ~aElement0(xu)|sdtmndtasgtdt0(xu,xR,xd)|~spl0_406),
% 22.69/3.27 inference(resolution,[status(thm)],[f2759,f213])).
% 22.69/3.27 fof(f3116,plain,(
% 22.69/3.27 ~spl0_43|spl0_440|~spl0_406),
% 22.69/3.27 inference(split_clause,[status(thm)],[f3115,f427,f3112,f2758])).
% 22.69/3.27 fof(f8893,plain,(
% 22.69/3.27 spl0_1050 <=> xd=sk0_16(xd,xb,xu)),
% 22.69/3.27 introduced(split_symbol_definition)).
% 22.69/3.27 fof(f8894,plain,(
% 22.69/3.27 xd=sk0_16(xd,xb,xu)|~spl0_1050),
% 22.69/3.27 inference(component_clause,[status(thm)],[f8893])).
% 22.69/3.27 fof(f8896,plain,(
% 22.69/3.27 spl0_1051 <=> sdtmndtplgtdt0(xd,xR,sk0_16(xd,xb,xu))),
% 22.69/3.27 introduced(split_symbol_definition)).
% 22.69/3.27 fof(f8897,plain,(
% 22.69/3.27 sdtmndtplgtdt0(xd,xR,sk0_16(xd,xb,xu))|~spl0_1051),
% 22.69/3.27 inference(component_clause,[status(thm)],[f8896])).
% 22.69/3.27 fof(f8899,plain,(
% 22.69/3.27 ~aElement0(xu)|~aElement0(xd)|pd0_0(xb,xu)|~iLess0(xu,xa)|xd=sk0_16(xd,xb,xu)|sdtmndtplgtdt0(xd,xR,sk0_16(xd,xb,xu))|~spl0_440),
% 22.69/3.27 inference(resolution,[status(thm)],[f3113,f551])).
% 22.69/3.27 fof(f8900,plain,(
% 22.69/3.27 ~spl0_43|~spl0_39|spl0_50|~spl0_46|spl0_1050|spl0_1051|~spl0_440),
% 22.69/3.27 inference(split_clause,[status(thm)],[f8899,f427,f413,f458,f436,f8893,f8896,f3112])).
% 22.69/3.27 fof(f8901,plain,(
% 22.69/3.27 spl0_1052 <=> sdtmndtasgtdt0(xb,xR,sk0_16(xd,xb,xu))),
% 22.69/3.27 introduced(split_symbol_definition)).
% 22.69/3.27 fof(f8902,plain,(
% 22.69/3.27 sdtmndtasgtdt0(xb,xR,sk0_16(xd,xb,xu))|~spl0_1052),
% 22.69/3.27 inference(component_clause,[status(thm)],[f8901])).
% 22.69/3.27 fof(f8904,plain,(
% 22.69/3.27 ~aElement0(xu)|~aElement0(xd)|pd0_0(xb,xu)|~iLess0(xu,xa)|sdtmndtasgtdt0(xb,xR,sk0_16(xd,xb,xu))|~spl0_440),
% 22.69/3.27 inference(resolution,[status(thm)],[f3113,f493])).
% 22.69/3.27 fof(f8905,plain,(
% 22.69/3.27 ~spl0_43|~spl0_39|spl0_50|~spl0_46|spl0_1052|~spl0_440),
% 22.69/3.27 inference(split_clause,[status(thm)],[f8904,f427,f413,f458,f436,f8901,f3112])).
% 22.69/3.27 fof(f8916,plain,(
% 22.69/3.27 spl0_1055 <=> aElement0(sk0_16(xd,xb,xu))),
% 22.69/3.27 introduced(split_symbol_definition)).
% 22.69/3.27 fof(f8919,plain,(
% 22.69/3.27 ~aElement0(xu)|~aElement0(xd)|pd0_0(xb,xu)|~iLess0(xu,xa)|aElement0(sk0_16(xd,xb,xu))|~spl0_440),
% 22.69/3.27 inference(resolution,[status(thm)],[f3113,f409])).
% 22.69/3.27 fof(f8920,plain,(
% 22.69/3.27 ~spl0_43|~spl0_39|spl0_50|~spl0_46|spl0_1055|~spl0_440),
% 22.69/3.27 inference(split_clause,[status(thm)],[f8919,f427,f413,f458,f436,f8916,f3112])).
% 22.69/3.27 fof(f10093,plain,(
% 22.69/3.27 ~aElement0(xa)|~aElement0(xu)|iLess0(xu,xa)),
% 22.69/3.27 inference(resolution,[status(thm)],[f116,f193])).
% 22.69/3.27 fof(f10094,plain,(
% 22.69/3.27 ~spl0_52|~spl0_43|spl0_46),
% 22.69/3.27 inference(split_clause,[status(thm)],[f10093,f470,f427,f436])).
% 22.69/3.27 fof(f16921,plain,(
% 22.69/3.27 spl0_1981 <=> aReductOfIn0(sk0_16(xd,xb,xu),xd,xR)),
% 22.69/3.27 introduced(split_symbol_definition)).
% 22.69/3.27 fof(f16922,plain,(
% 22.69/3.27 aReductOfIn0(sk0_16(xd,xb,xu),xd,xR)|~spl0_1981),
% 22.69/3.27 inference(component_clause,[status(thm)],[f16921])).
% 22.69/3.27 fof(f16929,plain,(
% 22.69/3.27 spl0_1983 <=> aReductOfIn0(sk0_0(sk0_16(xd,xb,xu),xR,xd),xd,xR)),
% 22.69/3.27 introduced(split_symbol_definition)).
% 22.69/3.27 fof(f16930,plain,(
% 22.69/3.27 aReductOfIn0(sk0_0(sk0_16(xd,xb,xu),xR,xd),xd,xR)|~spl0_1983),
% 22.69/3.27 inference(component_clause,[status(thm)],[f16929])).
% 22.69/3.27 fof(f16932,plain,(
% 22.69/3.27 ~aElement0(xd)|~aRewritingSystem0(xR)|~aElement0(sk0_16(xd,xb,xu))|aReductOfIn0(sk0_16(xd,xb,xu),xd,xR)|aReductOfIn0(sk0_0(sk0_16(xd,xb,xu),xR,xd),xd,xR)|~spl0_1051),
% 22.69/3.27 inference(resolution,[status(thm)],[f8897,f42])).
% 22.69/3.27 fof(f16933,plain,(
% 22.69/3.27 ~spl0_39|~spl0_79|~spl0_1055|spl0_1981|spl0_1983|~spl0_1051),
% 22.69/3.27 inference(split_clause,[status(thm)],[f16932,f413,f609,f8916,f16921,f16929,f8896])).
% 22.69/3.27 fof(f16939,plain,(
% 22.69/3.27 $false|~spl0_1981),
% 22.69/3.27 inference(forward_subsumption_resolution,[status(thm)],[f16922,f227])).
% 22.69/3.27 fof(f16940,plain,(
% 22.69/3.27 ~spl0_1981),
% 22.69/3.27 inference(contradiction_clause,[status(thm)],[f16939])).
% 22.69/3.27 fof(f16941,plain,(
% 22.69/3.27 $false|~spl0_1983),
% 22.69/3.27 inference(forward_subsumption_resolution,[status(thm)],[f16930,f227])).
% 22.69/3.27 fof(f16942,plain,(
% 22.69/3.27 ~spl0_1983),
% 22.69/3.27 inference(contradiction_clause,[status(thm)],[f16941])).
% 22.69/3.27 fof(f16947,plain,(
% 22.69/3.27 sdtmndtasgtdt0(xb,xR,xd)|~spl0_1050|~spl0_1052),
% 22.69/3.27 inference(backward_demodulation,[status(thm)],[f8894,f8902])).
% 22.69/3.27 fof(f16948,plain,(
% 22.69/3.27 $false|~spl0_1050|~spl0_1052),
% 22.69/3.27 inference(forward_subsumption_resolution,[status(thm)],[f16947,f234])).
% 22.69/3.27 fof(f16949,plain,(
% 22.69/3.27 ~spl0_1050|~spl0_1052),
% 22.69/3.27 inference(contradiction_clause,[status(thm)],[f16948])).
% 22.69/3.27 fof(f16950,plain,(
% 22.69/3.27 $false),
% 22.69/3.27 inference(sat_refutation,[status(thm)],[f531,f618,f620,f813,f1593,f2093,f2762,f3116,f8900,f8905,f8920,f10094,f16933,f16940,f16942,f16949])).
% 22.69/3.27 % SZS output end CNFRefutation for theBenchmark.p
% 22.69/3.29 % Elapsed time: 2.935968 seconds
% 22.69/3.29 % CPU time: 23.215760 seconds
% 22.69/3.29 % Total memory used: 171.422 MB
% 22.69/3.29 % Net memory used: 168.498 MB
%------------------------------------------------------------------------------