TSTP Solution File: COM020+4 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : COM020+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n032.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 : Wed May 31 12:03:56 EDT 2023
% Result : Theorem 6.27s 1.09s
% Output : CNFRefutation 6.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : COM020+4 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.08 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.27 % Computer : n032.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 300
% 0.07/0.27 % DateTime : Tue May 30 11:50:01 EDT 2023
% 0.07/0.27 % CPUTime :
% 0.07/0.28 % Drodi V3.5.1
% 6.27/1.09 % Refutation found
% 6.27/1.09 % SZS status Theorem for theBenchmark: Theorem is valid
% 6.27/1.09 % SZS output start CNFRefutation for theBenchmark
% 6.27/1.09 fof(f3,axiom,(
% 6.27/1.09 (! [W0,W1] :( ( aElement0(W0)& aRewritingSystem0(W1) )=> (! [W2] :( aReductOfIn0(W2,W0,W1)=> aElement0(W2) ) )) )),
% 6.27/1.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 6.27/1.09 fof(f6,definition,(
% 6.27/1.09 (! [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) ) )) ) ) )),
% 6.27/1.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 6.27/1.09 fof(f9,axiom,(
% 6.27/1.09 (! [W0,W1,W2,W3] :( ( aElement0(W0)& aRewritingSystem0(W1)& aElement0(W2)& aElement0(W3) )=> ( ( sdtmndtasgtdt0(W0,W1,W2)& sdtmndtasgtdt0(W2,W1,W3) )=> sdtmndtasgtdt0(W0,W1,W3) ) ) )),
% 6.27/1.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 6.27/1.09 fof(f12,definition,(
% 6.27/1.09 (! [W0] :( aRewritingSystem0(W0)=> ( isTerminating0(W0)<=> (! [W1,W2] :( ( aElement0(W1)& aElement0(W2) )=> ( sdtmndtplgtdt0(W1,W0,W2)=> iLess0(W2,W1) ) ) )) ) )),
% 6.27/1.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 6.27/1.09 fof(f15,hypothesis,(
% 6.27/1.09 aRewritingSystem0(xR) ),
% 6.27/1.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 6.27/1.09 fof(f16,hypothesis,(
% 6.27/1.09 ( (! [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) ) ),
% 6.27/1.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 6.27/1.09 fof(f17,hypothesis,(
% 6.27/1.09 ( aElement0(xa)& aElement0(xb)& aElement0(xc) ) ),
% 6.27/1.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 6.27/1.09 fof(f18,hypothesis,(
% 6.27/1.09 (! [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) ) )) ) )),
% 6.27/1.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 6.27/1.09 fof(f20,hypothesis,(
% 6.27/1.09 ( 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) ) ),
% 6.27/1.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 6.27/1.09 fof(f21,hypothesis,(
% 6.27/1.09 ( aElement0(xv)& aReductOfIn0(xv,xa,xR)& ( xv = xc| ( ( aReductOfIn0(xc,xv,xR)| (? [W0] :( aElement0(W0)& aReductOfIn0(W0,xv,xR)& sdtmndtplgtdt0(W0,xR,xc) ) ))& sdtmndtplgtdt0(xv,xR,xc) ) )& sdtmndtasgtdt0(xv,xR,xc) ) ),
% 6.27/1.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 6.27/1.09 fof(f22,hypothesis,(
% 6.27/1.09 ( 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) ) ),
% 6.27/1.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 6.27/1.09 fof(f23,hypothesis,(
% 6.27/1.09 ( 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) ) ),
% 6.27/1.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 6.27/1.09 fof(f24,conjecture,(
% 6.27/1.09 (? [W0] :( aElement0(W0)& ( xb = W0| aReductOfIn0(W0,xb,xR)| (? [W1] :( aElement0(W1)& aReductOfIn0(W1,xb,xR)& sdtmndtplgtdt0(W1,xR,W0) ))| sdtmndtplgtdt0(xb,xR,W0)| sdtmndtasgtdt0(xb,xR,W0) )& ( xd = W0| aReductOfIn0(W0,xd,xR)| (? [W1] :( aElement0(W1)& aReductOfIn0(W1,xd,xR)& sdtmndtplgtdt0(W1,xR,W0) ))| sdtmndtplgtdt0(xd,xR,W0)| sdtmndtasgtdt0(xd,xR,W0) ) ) )),
% 6.27/1.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 6.27/1.09 fof(f25,negated_conjecture,(
% 6.27/1.09 ~((? [W0] :( aElement0(W0)& ( xb = W0| aReductOfIn0(W0,xb,xR)| (? [W1] :( aElement0(W1)& aReductOfIn0(W1,xb,xR)& sdtmndtplgtdt0(W1,xR,W0) ))| sdtmndtplgtdt0(xb,xR,W0)| sdtmndtasgtdt0(xb,xR,W0) )& ( xd = W0| aReductOfIn0(W0,xd,xR)| (? [W1] :( aElement0(W1)& aReductOfIn0(W1,xd,xR)& sdtmndtplgtdt0(W1,xR,W0) ))| sdtmndtplgtdt0(xd,xR,W0)| sdtmndtasgtdt0(xd,xR,W0) ) ) ))),
% 6.27/1.09 inference(negated_conjecture,[status(cth)],[f24])).
% 6.27/1.09 fof(f32,plain,(
% 6.27/1.09 ![W0,W1]: ((~aElement0(W0)|~aRewritingSystem0(W1))|(![W2]: (~aReductOfIn0(W2,W0,W1)|aElement0(W2))))),
% 6.27/1.09 inference(pre_NNF_transformation,[status(esa)],[f3])).
% 6.27/1.09 fof(f33,plain,(
% 6.27/1.09 ![X0,X1,X2]: (~aElement0(X0)|~aRewritingSystem0(X1)|~aReductOfIn0(X2,X0,X1)|aElement0(X2))),
% 6.27/1.09 inference(cnf_transformation,[status(esa)],[f32])).
% 6.27/1.09 fof(f38,plain,(
% 6.27/1.09 ![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))))))),
% 6.27/1.09 inference(pre_NNF_transformation,[status(esa)],[f6])).
% 6.27/1.09 fof(f39,plain,(
% 6.27/1.09 ![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)))))))),
% 6.27/1.09 inference(NNF_transformation,[status(esa)],[f38])).
% 6.27/1.09 fof(f40,plain,(
% 6.27/1.09 ![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)))))))),
% 6.27/1.09 inference(skolemization,[status(esa)],[f39])).
% 6.27/1.09 fof(f44,plain,(
% 6.27/1.09 ![X0,X1,X2]: (~aElement0(X0)|~aRewritingSystem0(X1)|~aElement0(X2)|sdtmndtplgtdt0(X0,X1,X2)|~aReductOfIn0(X2,X0,X1))),
% 6.27/1.09 inference(cnf_transformation,[status(esa)],[f40])).
% 6.27/1.09 fof(f53,plain,(
% 6.27/1.09 ![W0,W1,W2,W3]: ((((~aElement0(W0)|~aRewritingSystem0(W1))|~aElement0(W2))|~aElement0(W3))|((~sdtmndtasgtdt0(W0,W1,W2)|~sdtmndtasgtdt0(W2,W1,W3))|sdtmndtasgtdt0(W0,W1,W3)))),
% 6.27/1.09 inference(pre_NNF_transformation,[status(esa)],[f9])).
% 6.27/1.09 fof(f54,plain,(
% 6.27/1.09 ![X0,X1,X2,X3]: (~aElement0(X0)|~aRewritingSystem0(X1)|~aElement0(X2)|~aElement0(X3)|~sdtmndtasgtdt0(X0,X1,X2)|~sdtmndtasgtdt0(X2,X1,X3)|sdtmndtasgtdt0(X0,X1,X3))),
% 6.27/1.09 inference(cnf_transformation,[status(esa)],[f53])).
% 6.27/1.09 fof(f81,plain,(
% 6.27/1.09 ![W0]: (~aRewritingSystem0(W0)|(isTerminating0(W0)<=>(![W1,W2]: ((~aElement0(W1)|~aElement0(W2))|(~sdtmndtplgtdt0(W1,W0,W2)|iLess0(W2,W1))))))),
% 6.27/1.09 inference(pre_NNF_transformation,[status(esa)],[f12])).
% 6.27/1.09 fof(f82,plain,(
% 6.27/1.09 ![W0]: (~aRewritingSystem0(W0)|((~isTerminating0(W0)|(![W1,W2]: ((~aElement0(W1)|~aElement0(W2))|(~sdtmndtplgtdt0(W1,W0,W2)|iLess0(W2,W1)))))&(isTerminating0(W0)|(?[W1,W2]: ((aElement0(W1)&aElement0(W2))&(sdtmndtplgtdt0(W1,W0,W2)&~iLess0(W2,W1)))))))),
% 6.27/1.09 inference(NNF_transformation,[status(esa)],[f81])).
% 6.27/1.09 fof(f83,plain,(
% 6.27/1.09 ![W0]: (~aRewritingSystem0(W0)|((~isTerminating0(W0)|(![W1,W2]: ((~aElement0(W1)|~aElement0(W2))|(~sdtmndtplgtdt0(W1,W0,W2)|iLess0(W2,W1)))))&(isTerminating0(W0)|((aElement0(sk0_9(W0))&aElement0(sk0_10(W0)))&(sdtmndtplgtdt0(sk0_9(W0),W0,sk0_10(W0))&~iLess0(sk0_10(W0),sk0_9(W0)))))))),
% 6.27/1.09 inference(skolemization,[status(esa)],[f82])).
% 6.27/1.09 fof(f84,plain,(
% 6.27/1.09 ![X0,X1,X2]: (~aRewritingSystem0(X0)|~isTerminating0(X0)|~aElement0(X1)|~aElement0(X2)|~sdtmndtplgtdt0(X1,X0,X2)|iLess0(X2,X1))),
% 6.27/1.09 inference(cnf_transformation,[status(esa)],[f83])).
% 6.27/1.09 fof(f100,plain,(
% 6.27/1.09 aRewritingSystem0(xR)),
% 6.27/1.09 inference(cnf_transformation,[status(esa)],[f15])).
% 6.27/1.09 fof(f101,plain,(
% 6.27/1.09 (((![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)),
% 6.27/1.09 inference(pre_NNF_transformation,[status(esa)],[f16])).
% 6.27/1.09 fof(f102,plain,(
% 6.27/1.09 (((![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)),
% 6.27/1.09 inference(miniscoping,[status(esa)],[f101])).
% 6.27/1.09 fof(f103,plain,(
% 6.27/1.09 (((![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)),
% 6.27/1.09 inference(skolemization,[status(esa)],[f102])).
% 6.27/1.09 fof(f115,plain,(
% 6.27/1.09 isLocallyConfluent0(xR)),
% 6.27/1.09 inference(cnf_transformation,[status(esa)],[f103])).
% 6.27/1.09 fof(f119,plain,(
% 6.27/1.09 isTerminating0(xR)),
% 6.27/1.09 inference(cnf_transformation,[status(esa)],[f103])).
% 6.27/1.09 fof(f120,plain,(
% 6.27/1.09 aElement0(xa)),
% 6.27/1.09 inference(cnf_transformation,[status(esa)],[f17])).
% 6.27/1.09 fof(f121,plain,(
% 6.27/1.09 aElement0(xb)),
% 6.27/1.09 inference(cnf_transformation,[status(esa)],[f17])).
% 6.27/1.09 fof(f123,plain,(
% 6.27/1.09 ![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)))))),
% 6.27/1.09 inference(pre_NNF_transformation,[status(esa)],[f18])).
% 6.27/1.09 fof(f124,plain,(
% 6.27/1.09 ![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)))),
% 6.27/1.09 introduced(predicate_definition,[f123])).
% 6.27/1.09 fof(f125,plain,(
% 6.27/1.09 ![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)))))),
% 6.27/1.09 inference(formula_renaming,[status(thm)],[f123,f124])).
% 6.27/1.09 fof(f126,plain,(
% 6.27/1.09 ![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)))))),
% 6.27/1.09 inference(skolemization,[status(esa)],[f125])).
% 6.27/1.09 fof(f171,plain,(
% 6.27/1.09 ![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)))),
% 6.27/1.09 inference(cnf_transformation,[status(esa)],[f126])).
% 6.27/1.09 fof(f176,plain,(
% 6.27/1.09 ![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)))),
% 6.27/1.09 inference(cnf_transformation,[status(esa)],[f126])).
% 6.27/1.09 fof(f181,plain,(
% 6.27/1.09 ![X0,X1,X2]: (~aElement0(X0)|~aElement0(X1)|~aElement0(X2)|pd0_0(X1,X0)|~sdtmndtasgtdt0(X0,xR,X2)|~iLess0(X0,xa)|sdtmndtasgtdt0(X2,xR,sk0_16(X2,X1,X0)))),
% 6.27/1.09 inference(cnf_transformation,[status(esa)],[f126])).
% 6.27/1.09 fof(f191,plain,(
% 6.27/1.09 ((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)),
% 6.27/1.09 inference(skolemization,[status(esa)],[f20])).
% 6.27/1.09 fof(f192,plain,(
% 6.27/1.09 aElement0(xu)),
% 6.27/1.09 inference(cnf_transformation,[status(esa)],[f191])).
% 6.27/1.09 fof(f193,plain,(
% 6.27/1.09 aReductOfIn0(xu,xa,xR)),
% 6.27/1.09 inference(cnf_transformation,[status(esa)],[f191])).
% 6.27/1.09 fof(f198,plain,(
% 6.27/1.09 sdtmndtasgtdt0(xu,xR,xb)),
% 6.27/1.09 inference(cnf_transformation,[status(esa)],[f191])).
% 6.27/1.09 fof(f199,plain,(
% 6.27/1.09 ((aElement0(xv)&aReductOfIn0(xv,xa,xR))&(xv=xc|((aReductOfIn0(xc,xv,xR)|((aElement0(sk0_22)&aReductOfIn0(sk0_22,xv,xR))&sdtmndtplgtdt0(sk0_22,xR,xc)))&sdtmndtplgtdt0(xv,xR,xc))))&sdtmndtasgtdt0(xv,xR,xc)),
% 6.27/1.09 inference(skolemization,[status(esa)],[f21])).
% 6.27/1.09 fof(f200,plain,(
% 6.27/1.09 aElement0(xv)),
% 6.27/1.09 inference(cnf_transformation,[status(esa)],[f199])).
% 6.27/1.09 fof(f201,plain,(
% 6.27/1.09 aReductOfIn0(xv,xa,xR)),
% 6.27/1.09 inference(cnf_transformation,[status(esa)],[f199])).
% 6.27/1.09 fof(f207,plain,(
% 6.27/1.09 (((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)),
% 6.27/1.09 inference(skolemization,[status(esa)],[f22])).
% 6.27/1.09 fof(f208,plain,(
% 6.27/1.09 aElement0(xw)),
% 6.27/1.09 inference(cnf_transformation,[status(esa)],[f207])).
% 6.27/1.09 fof(f213,plain,(
% 6.27/1.09 sdtmndtasgtdt0(xu,xR,xw)),
% 6.27/1.09 inference(cnf_transformation,[status(esa)],[f207])).
% 6.27/1.09 fof(f219,plain,(
% 6.27/1.09 (((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)),
% 6.27/1.09 inference(pre_NNF_transformation,[status(esa)],[f23])).
% 6.27/1.09 fof(f220,plain,(
% 6.27/1.09 (((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)),
% 6.27/1.09 inference(skolemization,[status(esa)],[f219])).
% 6.27/1.09 fof(f221,plain,(
% 6.27/1.09 aElement0(xd)),
% 6.27/1.09 inference(cnf_transformation,[status(esa)],[f220])).
% 6.27/1.09 fof(f226,plain,(
% 6.27/1.09 sdtmndtasgtdt0(xw,xR,xd)),
% 6.27/1.09 inference(cnf_transformation,[status(esa)],[f220])).
% 6.27/1.09 fof(f229,plain,(
% 6.27/1.09 (![W0]: ((~aElement0(W0)|((((~xb=W0&~aReductOfIn0(W0,xb,xR))&(![W1]: ((~aElement0(W1)|~aReductOfIn0(W1,xb,xR))|~sdtmndtplgtdt0(W1,xR,W0))))&~sdtmndtplgtdt0(xb,xR,W0))&~sdtmndtasgtdt0(xb,xR,W0)))|((((~xd=W0&~aReductOfIn0(W0,xd,xR))&(![W1]: ((~aElement0(W1)|~aReductOfIn0(W1,xd,xR))|~sdtmndtplgtdt0(W1,xR,W0))))&~sdtmndtplgtdt0(xd,xR,W0))&~sdtmndtasgtdt0(xd,xR,W0))))),
% 6.27/1.09 inference(pre_NNF_transformation,[status(esa)],[f25])).
% 6.27/1.09 fof(f230,plain,(
% 6.27/1.09 ![W0]: (pd0_1(W0)=>((((~xb=W0&~aReductOfIn0(W0,xb,xR))&(![W1]: ((~aElement0(W1)|~aReductOfIn0(W1,xb,xR))|~sdtmndtplgtdt0(W1,xR,W0))))&~sdtmndtplgtdt0(xb,xR,W0))&~sdtmndtasgtdt0(xb,xR,W0)))),
% 6.27/1.09 introduced(predicate_definition,[f229])).
% 6.27/1.09 fof(f231,plain,(
% 6.27/1.09 ![W0]: ((~aElement0(W0)|pd0_1(W0))|((((~xd=W0&~aReductOfIn0(W0,xd,xR))&(![W1]: ((~aElement0(W1)|~aReductOfIn0(W1,xd,xR))|~sdtmndtplgtdt0(W1,xR,W0))))&~sdtmndtplgtdt0(xd,xR,W0))&~sdtmndtasgtdt0(xd,xR,W0)))),
% 6.27/1.09 inference(formula_renaming,[status(thm)],[f229,f230])).
% 6.27/1.09 fof(f236,plain,(
% 6.27/1.09 ![X0]: (~aElement0(X0)|pd0_1(X0)|~sdtmndtasgtdt0(xd,xR,X0))),
% 6.27/1.09 inference(cnf_transformation,[status(esa)],[f231])).
% 6.27/1.09 fof(f237,plain,(
% 6.27/1.09 ![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)))),
% 6.27/1.09 inference(pre_NNF_transformation,[status(esa)],[f124])).
% 6.27/1.09 fof(f242,plain,(
% 6.27/1.09 ![X0,X1]: (~pd0_0(X0,X1)|~sdtmndtasgtdt0(X1,xR,X0))),
% 6.27/1.09 inference(cnf_transformation,[status(esa)],[f237])).
% 6.27/1.09 fof(f243,plain,(
% 6.27/1.09 ![W0]: (~pd0_1(W0)|((((~xb=W0&~aReductOfIn0(W0,xb,xR))&(![W1]: ((~aElement0(W1)|~aReductOfIn0(W1,xb,xR))|~sdtmndtplgtdt0(W1,xR,W0))))&~sdtmndtplgtdt0(xb,xR,W0))&~sdtmndtasgtdt0(xb,xR,W0)))),
% 6.27/1.09 inference(pre_NNF_transformation,[status(esa)],[f230])).
% 6.27/1.09 fof(f248,plain,(
% 6.27/1.09 ![X0]: (~pd0_1(X0)|~sdtmndtasgtdt0(xb,xR,X0))),
% 6.27/1.09 inference(cnf_transformation,[status(esa)],[f243])).
% 6.27/1.09 fof(f389,plain,(
% 6.27/1.09 ![X0,X1,X2]: (~aElement0(X0)|~aRewritingSystem0(X1)|sdtmndtplgtdt0(X0,X1,X2)|~aReductOfIn0(X2,X0,X1))),
% 6.27/1.09 inference(forward_subsumption_resolution,[status(thm)],[f44,f33])).
% 6.27/1.09 fof(f523,plain,(
% 6.27/1.09 spl0_39 <=> aElement0(xa)),
% 6.27/1.09 introduced(split_symbol_definition)).
% 6.27/1.09 fof(f525,plain,(
% 6.27/1.09 ~aElement0(xa)|spl0_39),
% 6.27/1.09 inference(component_clause,[status(thm)],[f523])).
% 6.27/1.09 fof(f534,plain,(
% 6.27/1.09 spl0_42 <=> aElement0(xb)),
% 6.27/1.09 introduced(split_symbol_definition)).
% 6.27/1.09 fof(f536,plain,(
% 6.27/1.09 ~aElement0(xb)|spl0_42),
% 6.27/1.09 inference(component_clause,[status(thm)],[f534])).
% 6.27/1.09 fof(f540,plain,(
% 6.27/1.09 $false|spl0_42),
% 6.27/1.09 inference(forward_subsumption_resolution,[status(thm)],[f536,f121])).
% 6.27/1.09 fof(f541,plain,(
% 6.27/1.09 spl0_42),
% 6.27/1.09 inference(contradiction_clause,[status(thm)],[f540])).
% 6.27/1.09 fof(f554,plain,(
% 6.27/1.09 spl0_45 <=> ~aElement0(X0)|~aElement0(X1)|pd0_0(X1,X0)|~sdtmndtasgtdt0(X0,xR,xb)|~iLess0(X0,xa)|~pd0_1(sk0_16(xb,X1,X0))),
% 6.27/1.09 introduced(split_symbol_definition)).
% 6.27/1.09 fof(f555,plain,(
% 6.27/1.09 ![X0,X1]: (~aElement0(X0)|~aElement0(X1)|pd0_0(X1,X0)|~sdtmndtasgtdt0(X0,xR,xb)|~iLess0(X0,xa)|~pd0_1(sk0_16(xb,X1,X0))|~spl0_45)),
% 6.27/1.09 inference(component_clause,[status(thm)],[f554])).
% 6.27/1.09 fof(f557,plain,(
% 6.27/1.09 ![X0,X1]: (~aElement0(X0)|~aElement0(X1)|~aElement0(xb)|pd0_0(X1,X0)|~sdtmndtasgtdt0(X0,xR,xb)|~iLess0(X0,xa)|~pd0_1(sk0_16(xb,X1,X0)))),
% 6.27/1.09 inference(resolution,[status(thm)],[f181,f248])).
% 6.27/1.09 fof(f558,plain,(
% 6.27/1.09 spl0_45|~spl0_42),
% 6.27/1.09 inference(split_clause,[status(thm)],[f557,f554,f534])).
% 6.27/1.09 fof(f576,plain,(
% 6.27/1.09 spl0_49 <=> aRewritingSystem0(xR)),
% 6.27/1.09 introduced(split_symbol_definition)).
% 6.27/1.09 fof(f578,plain,(
% 6.27/1.09 ~aRewritingSystem0(xR)|spl0_49),
% 6.27/1.09 inference(component_clause,[status(thm)],[f576])).
% 6.27/1.09 fof(f586,plain,(
% 6.27/1.09 $false|spl0_49),
% 6.27/1.09 inference(forward_subsumption_resolution,[status(thm)],[f578,f100])).
% 6.27/1.09 fof(f587,plain,(
% 6.27/1.09 spl0_49),
% 6.27/1.09 inference(contradiction_clause,[status(thm)],[f586])).
% 6.27/1.09 fof(f590,plain,(
% 6.27/1.09 $false|spl0_39),
% 6.27/1.09 inference(forward_subsumption_resolution,[status(thm)],[f525,f120])).
% 6.27/1.09 fof(f591,plain,(
% 6.27/1.09 spl0_39),
% 6.27/1.09 inference(contradiction_clause,[status(thm)],[f590])).
% 6.27/1.09 fof(f633,plain,(
% 6.27/1.09 spl0_58 <=> isTerminating0(xR)),
% 6.27/1.09 introduced(split_symbol_definition)).
% 6.27/1.09 fof(f635,plain,(
% 6.27/1.09 ~isTerminating0(xR)|spl0_58),
% 6.27/1.09 inference(component_clause,[status(thm)],[f633])).
% 6.27/1.09 fof(f739,plain,(
% 6.27/1.09 $false|spl0_58),
% 6.27/1.09 inference(forward_subsumption_resolution,[status(thm)],[f635,f119])).
% 6.27/1.09 fof(f740,plain,(
% 6.27/1.09 spl0_58),
% 6.27/1.09 inference(contradiction_clause,[status(thm)],[f739])).
% 6.27/1.09 fof(f741,plain,(
% 6.27/1.09 spl0_73 <=> aElement0(xw)),
% 6.27/1.09 introduced(split_symbol_definition)).
% 6.27/1.09 fof(f743,plain,(
% 6.27/1.09 ~aElement0(xw)|spl0_73),
% 6.27/1.09 inference(component_clause,[status(thm)],[f741])).
% 6.27/1.09 fof(f887,plain,(
% 6.27/1.09 spl0_79 <=> aElement0(xu)),
% 6.27/1.09 introduced(split_symbol_definition)).
% 6.27/1.09 fof(f889,plain,(
% 6.27/1.09 ~aElement0(xu)|spl0_79),
% 6.27/1.09 inference(component_clause,[status(thm)],[f887])).
% 6.27/1.09 fof(f903,plain,(
% 6.27/1.09 $false|spl0_79),
% 6.27/1.09 inference(forward_subsumption_resolution,[status(thm)],[f889,f192])).
% 6.27/1.09 fof(f904,plain,(
% 6.27/1.09 spl0_79),
% 6.27/1.09 inference(contradiction_clause,[status(thm)],[f903])).
% 6.27/1.09 fof(f1024,plain,(
% 6.27/1.09 $false|spl0_73),
% 6.27/1.09 inference(forward_subsumption_resolution,[status(thm)],[f743,f208])).
% 6.27/1.09 fof(f1025,plain,(
% 6.27/1.09 spl0_73),
% 6.27/1.09 inference(contradiction_clause,[status(thm)],[f1024])).
% 6.27/1.09 fof(f1026,plain,(
% 6.27/1.09 spl0_94 <=> aElement0(xd)),
% 6.27/1.09 introduced(split_symbol_definition)).
% 6.27/1.09 fof(f1028,plain,(
% 6.27/1.09 ~aElement0(xd)|spl0_94),
% 6.27/1.09 inference(component_clause,[status(thm)],[f1026])).
% 6.27/1.09 fof(f1042,plain,(
% 6.27/1.09 $false|spl0_94),
% 6.27/1.09 inference(forward_subsumption_resolution,[status(thm)],[f1028,f221])).
% 6.27/1.09 fof(f1043,plain,(
% 6.27/1.09 spl0_94),
% 6.27/1.09 inference(contradiction_clause,[status(thm)],[f1042])).
% 6.27/1.09 fof(f1044,plain,(
% 6.27/1.09 spl0_97 <=> aElement0(xv)),
% 6.27/1.09 introduced(split_symbol_definition)).
% 6.27/1.09 fof(f1046,plain,(
% 6.27/1.09 ~aElement0(xv)|spl0_97),
% 6.27/1.09 inference(component_clause,[status(thm)],[f1044])).
% 6.27/1.09 fof(f1060,plain,(
% 6.27/1.09 $false|spl0_97),
% 6.27/1.09 inference(forward_subsumption_resolution,[status(thm)],[f1046,f200])).
% 6.27/1.09 fof(f1061,plain,(
% 6.27/1.09 spl0_97),
% 6.27/1.09 inference(contradiction_clause,[status(thm)],[f1060])).
% 6.27/1.09 fof(f1184,plain,(
% 6.27/1.09 spl0_109 <=> ~aElement0(sk0_16(X0,xd,X1))|pd0_1(sk0_16(X0,xd,X1))|~aElement0(X1)|~aElement0(X0)|pd0_0(xd,X1)|~sdtmndtasgtdt0(X1,xR,X0)|~iLess0(X1,xa)),
% 6.27/1.09 introduced(split_symbol_definition)).
% 6.27/1.09 fof(f1185,plain,(
% 6.27/1.09 ![X0,X1]: (~aElement0(sk0_16(X0,xd,X1))|pd0_1(sk0_16(X0,xd,X1))|~aElement0(X1)|~aElement0(X0)|pd0_0(xd,X1)|~sdtmndtasgtdt0(X1,xR,X0)|~iLess0(X1,xa)|~spl0_109)),
% 6.27/1.09 inference(component_clause,[status(thm)],[f1184])).
% 6.27/1.09 fof(f1187,plain,(
% 6.27/1.09 ![X0,X1]: (~aElement0(sk0_16(X0,xd,X1))|pd0_1(sk0_16(X0,xd,X1))|~aElement0(X1)|~aElement0(xd)|~aElement0(X0)|pd0_0(xd,X1)|~sdtmndtasgtdt0(X1,xR,X0)|~iLess0(X1,xa))),
% 6.27/1.09 inference(resolution,[status(thm)],[f236,f176])).
% 6.27/1.09 fof(f1188,plain,(
% 6.27/1.09 spl0_109|~spl0_94),
% 6.27/1.09 inference(split_clause,[status(thm)],[f1187,f1184,f1026])).
% 6.27/1.09 fof(f1277,plain,(
% 6.27/1.09 spl0_125 <=> iLess0(xu,xa)),
% 6.27/1.09 introduced(split_symbol_definition)).
% 6.27/1.09 fof(f1282,plain,(
% 6.27/1.09 spl0_126 <=> sdtmndtplgtdt0(xa,xR,xu)),
% 6.27/1.09 introduced(split_symbol_definition)).
% 6.27/1.09 fof(f1283,plain,(
% 6.27/1.09 sdtmndtplgtdt0(xa,xR,xu)|~spl0_126),
% 6.27/1.09 inference(component_clause,[status(thm)],[f1282])).
% 6.27/1.09 fof(f1285,plain,(
% 6.27/1.09 ~aElement0(xa)|~aRewritingSystem0(xR)|sdtmndtplgtdt0(xa,xR,xu)),
% 6.27/1.09 inference(resolution,[status(thm)],[f193,f389])).
% 6.27/1.09 fof(f1286,plain,(
% 6.27/1.09 ~spl0_39|~spl0_49|spl0_126),
% 6.27/1.09 inference(split_clause,[status(thm)],[f1285,f523,f576,f1282])).
% 6.27/1.09 fof(f1346,plain,(
% 6.27/1.09 spl0_139 <=> isLocallyConfluent0(xR)),
% 6.27/1.09 introduced(split_symbol_definition)).
% 6.27/1.09 fof(f1348,plain,(
% 6.27/1.09 ~isLocallyConfluent0(xR)|spl0_139),
% 6.27/1.09 inference(component_clause,[status(thm)],[f1346])).
% 6.27/1.09 fof(f1673,plain,(
% 6.27/1.09 spl0_174 <=> pd0_1(sk0_16(X0,xd,X1))|~aElement0(X1)|~aElement0(X0)|pd0_0(xd,X1)|~sdtmndtasgtdt0(X1,xR,X0)|~iLess0(X1,xa)|~aElement0(X1)|~aElement0(X0)|pd0_0(xd,X1)|~sdtmndtasgtdt0(X1,xR,X0)|~iLess0(X1,xa)),
% 6.27/1.09 introduced(split_symbol_definition)).
% 6.27/1.09 fof(f1674,plain,(
% 6.27/1.09 ![X0,X1]: (pd0_1(sk0_16(X0,xd,X1))|~aElement0(X1)|~aElement0(X0)|pd0_0(xd,X1)|~sdtmndtasgtdt0(X1,xR,X0)|~iLess0(X1,xa)|~aElement0(X1)|~aElement0(X0)|pd0_0(xd,X1)|~sdtmndtasgtdt0(X1,xR,X0)|~iLess0(X1,xa)|~spl0_174)),
% 6.27/1.09 inference(component_clause,[status(thm)],[f1673])).
% 6.27/1.09 fof(f1676,plain,(
% 6.27/1.09 ![X0,X1]: (pd0_1(sk0_16(X0,xd,X1))|~aElement0(X1)|~aElement0(X0)|pd0_0(xd,X1)|~sdtmndtasgtdt0(X1,xR,X0)|~iLess0(X1,xa)|~aElement0(X1)|~aElement0(xd)|~aElement0(X0)|pd0_0(xd,X1)|~sdtmndtasgtdt0(X1,xR,X0)|~iLess0(X1,xa)|~spl0_109)),
% 6.27/1.09 inference(resolution,[status(thm)],[f1185,f171])).
% 6.27/1.09 fof(f1677,plain,(
% 6.27/1.09 spl0_174|~spl0_94|~spl0_109),
% 6.27/1.09 inference(split_clause,[status(thm)],[f1676,f1673,f1026,f1184])).
% 6.27/1.09 fof(f1680,plain,(
% 6.27/1.09 ![X0,X1]: (pd0_1(sk0_16(X0,xd,X1))|~aElement0(X1)|~aElement0(X0)|pd0_0(xd,X1)|~sdtmndtasgtdt0(X1,xR,X0)|~iLess0(X1,xa)|~spl0_174)),
% 6.27/1.09 inference(duplicate_literals_removal,[status(esa)],[f1674])).
% 6.27/1.09 fof(f1754,plain,(
% 6.27/1.09 spl0_186 <=> aReductOfIn0(xu,xa,xR)),
% 6.27/1.09 introduced(split_symbol_definition)).
% 6.27/1.09 fof(f1756,plain,(
% 6.27/1.09 ~aReductOfIn0(xu,xa,xR)|spl0_186),
% 6.27/1.09 inference(component_clause,[status(thm)],[f1754])).
% 6.27/1.09 fof(f1787,plain,(
% 6.27/1.09 $false|spl0_186),
% 6.27/1.09 inference(forward_subsumption_resolution,[status(thm)],[f1756,f193])).
% 6.27/1.09 fof(f1788,plain,(
% 6.27/1.09 spl0_186),
% 6.27/1.09 inference(contradiction_clause,[status(thm)],[f1787])).
% 6.27/1.09 fof(f1880,plain,(
% 6.27/1.09 ~aRewritingSystem0(xR)|~isTerminating0(xR)|~aElement0(xa)|~aElement0(xu)|iLess0(xu,xa)|~spl0_126),
% 6.27/1.09 inference(resolution,[status(thm)],[f1283,f84])).
% 6.27/1.09 fof(f1881,plain,(
% 6.27/1.09 ~spl0_49|~spl0_58|~spl0_39|~spl0_79|spl0_125|~spl0_126),
% 6.27/1.09 inference(split_clause,[status(thm)],[f1880,f576,f633,f523,f887,f1277,f1282])).
% 6.27/1.09 fof(f1887,plain,(
% 6.27/1.09 spl0_204 <=> aReductOfIn0(xv,xa,xR)),
% 6.27/1.09 introduced(split_symbol_definition)).
% 6.27/1.09 fof(f1889,plain,(
% 6.27/1.09 ~aReductOfIn0(xv,xa,xR)|spl0_204),
% 6.27/1.09 inference(component_clause,[status(thm)],[f1887])).
% 6.27/1.09 fof(f1914,plain,(
% 6.27/1.09 $false|spl0_204),
% 6.27/1.09 inference(forward_subsumption_resolution,[status(thm)],[f1889,f201])).
% 6.27/1.09 fof(f1915,plain,(
% 6.27/1.09 spl0_204),
% 6.27/1.09 inference(contradiction_clause,[status(thm)],[f1914])).
% 6.27/1.09 fof(f2111,plain,(
% 6.27/1.09 spl0_224 <=> ~aElement0(X0)|~sdtmndtasgtdt0(X0,xR,xw)|sdtmndtasgtdt0(X0,xR,xd)),
% 6.27/1.09 introduced(split_symbol_definition)).
% 6.27/1.09 fof(f2112,plain,(
% 6.27/1.09 ![X0]: (~aElement0(X0)|~sdtmndtasgtdt0(X0,xR,xw)|sdtmndtasgtdt0(X0,xR,xd)|~spl0_224)),
% 6.27/1.09 inference(component_clause,[status(thm)],[f2111])).
% 6.27/1.09 fof(f2114,plain,(
% 6.27/1.09 ![X0]: (~aElement0(X0)|~aRewritingSystem0(xR)|~aElement0(xw)|~aElement0(xd)|~sdtmndtasgtdt0(X0,xR,xw)|sdtmndtasgtdt0(X0,xR,xd))),
% 6.27/1.09 inference(resolution,[status(thm)],[f226,f54])).
% 6.27/1.09 fof(f2115,plain,(
% 6.27/1.09 spl0_224|~spl0_49|~spl0_73|~spl0_94),
% 6.27/1.09 inference(split_clause,[status(thm)],[f2114,f2111,f576,f741,f1026])).
% 6.27/1.09 fof(f2693,plain,(
% 6.27/1.09 spl0_298 <=> sdtmndtasgtdt0(xu,xR,xd)),
% 6.27/1.09 introduced(split_symbol_definition)).
% 6.27/1.09 fof(f2694,plain,(
% 6.27/1.09 sdtmndtasgtdt0(xu,xR,xd)|~spl0_298),
% 6.27/1.09 inference(component_clause,[status(thm)],[f2693])).
% 6.27/1.09 fof(f2696,plain,(
% 6.27/1.09 ~aElement0(xu)|sdtmndtasgtdt0(xu,xR,xd)|~spl0_224),
% 6.27/1.09 inference(resolution,[status(thm)],[f213,f2112])).
% 6.27/1.09 fof(f2697,plain,(
% 6.27/1.09 ~spl0_79|spl0_298|~spl0_224),
% 6.27/1.09 inference(split_clause,[status(thm)],[f2696,f887,f2693,f2111])).
% 6.27/1.09 fof(f2756,plain,(
% 6.27/1.09 $false|spl0_139),
% 6.27/1.09 inference(forward_subsumption_resolution,[status(thm)],[f1348,f115])).
% 6.27/1.09 fof(f2757,plain,(
% 6.27/1.09 spl0_139),
% 6.27/1.09 inference(contradiction_clause,[status(thm)],[f2756])).
% 6.27/1.09 fof(f3118,plain,(
% 6.27/1.09 spl0_357 <=> ~aElement0(X0)|pd0_0(xd,X0)|~sdtmndtasgtdt0(X0,xR,xb)|~iLess0(X0,xa)|~aElement0(X0)|pd0_0(xd,X0)|~sdtmndtasgtdt0(X0,xR,xb)|~iLess0(X0,xa)),
% 6.27/1.10 introduced(split_symbol_definition)).
% 6.27/1.10 fof(f3119,plain,(
% 6.27/1.10 ![X0]: (~aElement0(X0)|pd0_0(xd,X0)|~sdtmndtasgtdt0(X0,xR,xb)|~iLess0(X0,xa)|~aElement0(X0)|pd0_0(xd,X0)|~sdtmndtasgtdt0(X0,xR,xb)|~iLess0(X0,xa)|~spl0_357)),
% 6.27/1.10 inference(component_clause,[status(thm)],[f3118])).
% 6.27/1.10 fof(f3121,plain,(
% 6.27/1.10 ![X0]: (~aElement0(X0)|~aElement0(xd)|pd0_0(xd,X0)|~sdtmndtasgtdt0(X0,xR,xb)|~iLess0(X0,xa)|~aElement0(X0)|~aElement0(xb)|pd0_0(xd,X0)|~sdtmndtasgtdt0(X0,xR,xb)|~iLess0(X0,xa)|~spl0_45|~spl0_174)),
% 6.27/1.10 inference(resolution,[status(thm)],[f555,f1680])).
% 6.27/1.10 fof(f3122,plain,(
% 6.27/1.10 spl0_357|~spl0_94|~spl0_42|~spl0_45|~spl0_174),
% 6.27/1.10 inference(split_clause,[status(thm)],[f3121,f3118,f1026,f534,f554,f1673])).
% 6.27/1.10 fof(f3131,plain,(
% 6.27/1.10 ![X0]: (~aElement0(X0)|pd0_0(xd,X0)|~sdtmndtasgtdt0(X0,xR,xb)|~iLess0(X0,xa)|~spl0_357)),
% 6.27/1.10 inference(duplicate_literals_removal,[status(esa)],[f3119])).
% 6.27/1.10 fof(f3142,plain,(
% 6.27/1.10 spl0_360 <=> pd0_0(xd,xu)),
% 6.27/1.10 introduced(split_symbol_definition)).
% 6.27/1.10 fof(f3143,plain,(
% 6.27/1.10 pd0_0(xd,xu)|~spl0_360),
% 6.27/1.10 inference(component_clause,[status(thm)],[f3142])).
% 6.27/1.10 fof(f3145,plain,(
% 6.27/1.10 ~aElement0(xu)|pd0_0(xd,xu)|~iLess0(xu,xa)|~spl0_357),
% 6.27/1.10 inference(resolution,[status(thm)],[f3131,f198])).
% 6.27/1.10 fof(f3146,plain,(
% 6.27/1.10 ~spl0_79|spl0_360|~spl0_125|~spl0_357),
% 6.27/1.10 inference(split_clause,[status(thm)],[f3145,f887,f3142,f1277,f3118])).
% 6.27/1.10 fof(f3180,plain,(
% 6.27/1.10 ~pd0_0(xd,xu)|~spl0_298),
% 6.27/1.10 inference(resolution,[status(thm)],[f2694,f242])).
% 6.27/1.10 fof(f3181,plain,(
% 6.27/1.10 $false|~spl0_360|~spl0_298),
% 6.27/1.10 inference(forward_subsumption_resolution,[status(thm)],[f3180,f3143])).
% 6.27/1.10 fof(f3182,plain,(
% 6.27/1.10 ~spl0_360|~spl0_298),
% 6.27/1.10 inference(contradiction_clause,[status(thm)],[f3181])).
% 6.27/1.10 fof(f3183,plain,(
% 6.27/1.10 $false),
% 6.27/1.10 inference(sat_refutation,[status(thm)],[f541,f558,f587,f591,f740,f904,f1025,f1043,f1061,f1188,f1286,f1677,f1788,f1881,f1915,f2115,f2697,f2757,f3122,f3146,f3182])).
% 6.27/1.10 % SZS output end CNFRefutation for theBenchmark.p
% 6.27/1.12 % Elapsed time: 0.834183 seconds
% 6.27/1.12 % CPU time: 6.492855 seconds
% 6.27/1.12 % Memory used: 95.103 MB
%------------------------------------------------------------------------------