%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : COM013+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 : n020.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 12:10:42 PM UTC 2026
% Result : Theorem 0.10s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM013+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 14:15:19 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.41 % Refutation found
% 0.10/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.41 fof(f3,axiom,(
% 0.10/0.41 (! [W0,W1] :( ( aElement0(W0)& aRewritingSystem0(W1) )=> (! [W2] :( aReductOfIn0(W2,W0,W1)=> aElement0(W2) ) )) )),
% 0.10/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f6,definition,(
% 0.10/0.41 (! [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) ) )) ) ) )),
% 0.10/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f8,definition,(
% 0.10/0.41 (! [W0,W1,W2] :( ( aElement0(W0)& aRewritingSystem0(W1)& aElement0(W2) )=> ( sdtmndtasgtdt0(W0,W1,W2)<=> ( W0 = W2| sdtmndtplgtdt0(W0,W1,W2) ) ) ) )),
% 0.10/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f9,axiom,(
% 0.10/0.41 (! [W0,W1,W2,W3] :( ( aElement0(W0)& aRewritingSystem0(W1)& aElement0(W2)& aElement0(W3) )=> ( ( sdtmndtasgtdt0(W0,W1,W2)& sdtmndtasgtdt0(W2,W1,W3) )=> sdtmndtasgtdt0(W0,W1,W3) ) ) )),
% 0.10/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f12,definition,(
% 0.10/0.41 (! [W0] :( aRewritingSystem0(W0)=> ( isTerminating0(W0)<=> (! [W1,W2] :( ( aElement0(W1)& aElement0(W2) )=> ( sdtmndtplgtdt0(W1,W0,W2)=> iLess0(W2,W1) ) ) )) ) )),
% 0.10/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f13,definition,(
% 0.10/0.41 (! [W0,W1] :( ( aElement0(W0)& aRewritingSystem0(W1) )=> (! [W2] :( aNormalFormOfIn0(W2,W0,W1)<=> ( aElement0(W2)& sdtmndtasgtdt0(W0,W1,W2)& ~ (? [W3] : aReductOfIn0(W3,W2,W1) )) ) )) )),
% 0.10/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f14,hypothesis,(
% 0.10/0.41 ( aRewritingSystem0(xR)& isTerminating0(xR) ) ),
% 0.10/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f15,conjecture,(
% 0.10/0.41 (! [W0] :( aElement0(W0)=> ( (! [W1] :( aElement0(W1)=> ( iLess0(W1,W0)=> (? [W2] : aNormalFormOfIn0(W2,W1,xR) )) ))=> (? [W1] : aNormalFormOfIn0(W1,W0,xR) )) ) )),
% 0.10/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f16,negated_conjecture,(
% 0.10/0.41 ~((! [W0] :( aElement0(W0)=> ( (! [W1] :( aElement0(W1)=> ( iLess0(W1,W0)=> (? [W2] : aNormalFormOfIn0(W2,W1,xR) )) ))=> (? [W1] : aNormalFormOfIn0(W1,W0,xR) )) ) ))),
% 0.10/0.41 inference(negated_conjecture,[status(cth)],[f15])).
% 0.10/0.41 fof(f23,plain,(
% 0.10/0.41 ![W0,W1]: ((~aElement0(W0)|~aRewritingSystem0(W1))|(![W2]: (~aReductOfIn0(W2,W0,W1)|aElement0(W2))))),
% 0.10/0.41 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 0.10/0.41 fof(f24,plain,(
% 0.10/0.41 ![X0,X1,X2]: (~aElement0(X0)|~aRewritingSystem0(X1)|~aReductOfIn0(X2,X0,X1)|aElement0(X2))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f23])).
% 0.10/0.41 fof(f29,plain,(
% 0.10/0.41 ![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))))))),
% 0.10/0.41 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.10/0.41 fof(f30,plain,(
% 0.10/0.41 ![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)))))))),
% 0.10/0.41 inference(NNF_transformation,[status(thm)],[f29])).
% 0.10/0.41 fof(f31,plain,(
% 0.10/0.41 ![W0,W1,W2]: (((~aElement0(W0)|~aRewritingSystem0(W1))|~aElement0(W2))|((~sdtmndtplgtdt0(W0,W1,W2)|(aReductOfIn0(W2,W0,W1)|((aElement0(sK0_skl(W2,W1,W0))&aReductOfIn0(sK0_skl(W2,W1,W0),W0,W1))&sdtmndtplgtdt0(sK0_skl(W2,W1,W0),W1,W2))))&(sdtmndtplgtdt0(W0,W1,W2)|(~aReductOfIn0(W2,W0,W1)&(![W3]: ((~aElement0(W3)|~aReductOfIn0(W3,W0,W1))|~sdtmndtplgtdt0(W3,W1,W2)))))))),
% 0.10/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(W3,sK0_skl(W2,W1,W0))],[f30])).
% 0.10/0.41 fof(f35,plain,(
% 0.10/0.41 ![X0,X1,X2]: (~aElement0(X0)|~aRewritingSystem0(X1)|~aElement0(X2)|sdtmndtplgtdt0(X0,X1,X2)|~aReductOfIn0(X2,X0,X1))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f31])).
% 0.10/0.41 fof(f39,plain,(
% 0.10/0.41 ![W0,W1,W2]: (((~aElement0(W0)|~aRewritingSystem0(W1))|~aElement0(W2))|(sdtmndtasgtdt0(W0,W1,W2)<=>(W0=W2|sdtmndtplgtdt0(W0,W1,W2))))),
% 0.10/0.41 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.10/0.41 fof(f40,plain,(
% 0.10/0.41 ![W0,W1,W2]: (((~aElement0(W0)|~aRewritingSystem0(W1))|~aElement0(W2))|((~sdtmndtasgtdt0(W0,W1,W2)|(W0=W2|sdtmndtplgtdt0(W0,W1,W2)))&(sdtmndtasgtdt0(W0,W1,W2)|(~W0=W2&~sdtmndtplgtdt0(W0,W1,W2)))))),
% 0.10/0.41 inference(NNF_transformation,[status(thm)],[f39])).
% 0.10/0.41 fof(f42,plain,(
% 0.10/0.41 ![X0,X1,X2]: (~aElement0(X0)|~aRewritingSystem0(X1)|~aElement0(X2)|sdtmndtasgtdt0(X0,X1,X2)|~X0=X2)),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f40])).
% 0.10/0.41 fof(f43,plain,(
% 0.10/0.41 ![X0,X1,X2]: (~aElement0(X0)|~aRewritingSystem0(X1)|~aElement0(X2)|sdtmndtasgtdt0(X0,X1,X2)|~sdtmndtplgtdt0(X0,X1,X2))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f40])).
% 0.10/0.41 fof(f44,plain,(
% 0.10/0.41 ![W0,W1,W2,W3]: ((((~aElement0(W0)|~aRewritingSystem0(W1))|~aElement0(W2))|~aElement0(W3))|((~sdtmndtasgtdt0(W0,W1,W2)|~sdtmndtasgtdt0(W2,W1,W3))|sdtmndtasgtdt0(W0,W1,W3)))),
% 0.10/0.41 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.10/0.41 fof(f45,plain,(
% 0.10/0.41 ![X0,X1,X2,X3]: (~aElement0(X0)|~aRewritingSystem0(X1)|~aElement0(X2)|~aElement0(X3)|~sdtmndtasgtdt0(X0,X1,X2)|~sdtmndtasgtdt0(X2,X1,X3)|sdtmndtasgtdt0(X0,X1,X3))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f44])).
% 0.10/0.41 fof(f72,plain,(
% 0.10/0.41 ![W0]: (~aRewritingSystem0(W0)|(isTerminating0(W0)<=>(![W1,W2]: ((~aElement0(W1)|~aElement0(W2))|(~sdtmndtplgtdt0(W1,W0,W2)|iLess0(W2,W1))))))),
% 0.10/0.41 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.10/0.41 fof(f73,plain,(
% 0.10/0.41 ![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)))))))),
% 0.10/0.41 inference(NNF_transformation,[status(thm)],[f72])).
% 0.10/0.41 fof(f74,plain,(
% 0.10/0.41 ![W0]: (~aRewritingSystem0(W0)|((~isTerminating0(W0)|(![W1,W2]: ((~aElement0(W1)|~aElement0(W2))|(~sdtmndtplgtdt0(W1,W0,W2)|iLess0(W2,W1)))))&(isTerminating0(W0)|((aElement0(sK9_skl(W0))&aElement0(sK10_skl(W0)))&(sdtmndtplgtdt0(sK9_skl(W0),W0,sK10_skl(W0))&~iLess0(sK10_skl(W0),sK9_skl(W0)))))))),
% 0.10/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl]),skolemize(W1,sK9_skl(W0)),skolemize(W2,sK10_skl(W0))],[f73])).
% 0.10/0.41 fof(f75,plain,(
% 0.10/0.41 ![X0,X1,X2]: (~aRewritingSystem0(X0)|~isTerminating0(X0)|~aElement0(X1)|~aElement0(X2)|~sdtmndtplgtdt0(X1,X0,X2)|iLess0(X2,X1))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f74])).
% 0.10/0.41 fof(f80,plain,(
% 0.10/0.41 ![W0,W1]: ((~aElement0(W0)|~aRewritingSystem0(W1))|(![W2]: (aNormalFormOfIn0(W2,W0,W1)<=>((aElement0(W2)&sdtmndtasgtdt0(W0,W1,W2))&(![W3]: ~aReductOfIn0(W3,W2,W1))))))),
% 0.10/0.41 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 0.10/0.41 fof(f81,plain,(
% 0.10/0.41 ![W0,W1]: ((~aElement0(W0)|~aRewritingSystem0(W1))|(![W2]: ((~aNormalFormOfIn0(W2,W0,W1)|((aElement0(W2)&sdtmndtasgtdt0(W0,W1,W2))&(![W3]: ~aReductOfIn0(W3,W2,W1))))&(aNormalFormOfIn0(W2,W0,W1)|((~aElement0(W2)|~sdtmndtasgtdt0(W0,W1,W2))|(?[W3]: aReductOfIn0(W3,W2,W1)))))))),
% 0.10/0.41 inference(NNF_transformation,[status(thm)],[f80])).
% 0.10/0.41 fof(f82,plain,(
% 0.10/0.41 ![W0,W1]: ((~aElement0(W0)|~aRewritingSystem0(W1))|((![W2]: (~aNormalFormOfIn0(W2,W0,W1)|((aElement0(W2)&sdtmndtasgtdt0(W0,W1,W2))&(![W3]: ~aReductOfIn0(W3,W2,W1)))))&(![W2]: (aNormalFormOfIn0(W2,W0,W1)|((~aElement0(W2)|~sdtmndtasgtdt0(W0,W1,W2))|(?[W3]: aReductOfIn0(W3,W2,W1)))))))),
% 0.10/0.41 inference(miniscoping,[status(thm)],[f81])).
% 0.10/0.41 fof(f83,plain,(
% 0.10/0.41 ![W0,W1]: ((~aElement0(W0)|~aRewritingSystem0(W1))|((![W2]: (~aNormalFormOfIn0(W2,W0,W1)|((aElement0(W2)&sdtmndtasgtdt0(W0,W1,W2))&(![W3]: ~aReductOfIn0(W3,W2,W1)))))&(![W2]: (aNormalFormOfIn0(W2,W0,W1)|((~aElement0(W2)|~sdtmndtasgtdt0(W0,W1,W2))|aReductOfIn0(sK11_skl(W2,W1,W0),W2,W1))))))),
% 0.10/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl]),skolemize(W3,sK11_skl(W2,W1,W0))],[f82])).
% 0.10/0.41 fof(f84,plain,(
% 0.10/0.41 ![X0,X1,X2]: (~aElement0(X0)|~aRewritingSystem0(X1)|~aNormalFormOfIn0(X2,X0,X1)|aElement0(X2))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f83])).
% 0.10/0.41 fof(f85,plain,(
% 0.10/0.41 ![X0,X1,X2]: (~aElement0(X0)|~aRewritingSystem0(X1)|~aNormalFormOfIn0(X2,X0,X1)|sdtmndtasgtdt0(X0,X1,X2))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f83])).
% 0.10/0.41 fof(f86,plain,(
% 0.10/0.41 ![X0,X1,X2,X3]: (~aElement0(X0)|~aRewritingSystem0(X1)|~aNormalFormOfIn0(X2,X0,X1)|~aReductOfIn0(X3,X2,X1))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f83])).
% 0.10/0.41 fof(f87,plain,(
% 0.10/0.41 ![X0,X1,X2]: (~aElement0(X0)|~aRewritingSystem0(X1)|aNormalFormOfIn0(X2,X0,X1)|~aElement0(X2)|~sdtmndtasgtdt0(X0,X1,X2)|aReductOfIn0(sK11_skl(X2,X1,X0),X2,X1))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f83])).
% 0.10/0.41 fof(f88,plain,(
% 0.10/0.41 aRewritingSystem0(xR)),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f14])).
% 0.10/0.41 fof(f89,plain,(
% 0.10/0.41 isTerminating0(xR)),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f14])).
% 0.10/0.41 fof(f90,plain,(
% 0.10/0.41 (?[W0]: (aElement0(W0)&((![W1]: (~aElement0(W1)|(~iLess0(W1,W0)|(?[W2]: aNormalFormOfIn0(W2,W1,xR)))))&(![W1]: ~aNormalFormOfIn0(W1,W0,xR)))))),
% 0.10/0.41 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.10/0.41 fof(f91,plain,(
% 0.10/0.41 (aElement0(sK12_skl)&((![W1]: (~aElement0(W1)|(~iLess0(W1,sK12_skl)|aNormalFormOfIn0(sK13_skl(W1),W1,xR))))&(![W1]: ~aNormalFormOfIn0(W1,sK12_skl,xR))))),
% 0.10/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl]),skolemize(W0,sK12_skl),skolemize(W2,sK13_skl(W1))],[f90])).
% 0.10/0.42 fof(f92,plain,(
% 0.10/0.42 aElement0(sK12_skl)),
% 0.10/0.42 inference(cnf_transformation,[status(thm)],[f91])).
% 0.10/0.42 fof(f93,plain,(
% 0.10/0.42 ![X0]: (~aElement0(X0)|~iLess0(X0,sK12_skl)|aNormalFormOfIn0(sK13_skl(X0),X0,xR))),
% 0.10/0.42 inference(cnf_transformation,[status(thm)],[f91])).
% 0.10/0.42 fof(f94,plain,(
% 0.10/0.42 ![X0]: (~aNormalFormOfIn0(X0,sK12_skl,xR))),
% 0.10/0.42 inference(cnf_transformation,[status(thm)],[f91])).
% 0.10/0.42 fof(f95,plain,(
% 0.10/0.42 ![X0,X1,X2]: (~aElement0(X0)|~aRewritingSystem0(X1)|sdtmndtplgtdt0(X0,X1,X2)|~aReductOfIn0(X2,X0,X1))),
% 0.10/0.42 inference(forward_subsumption_resolution,[status(thm)],[f35,f24])).
% 0.10/0.42 fof(f97,plain,(
% 0.10/0.42 ![X2,X1]: (~aElement0(X2)|~aRewritingSystem0(X1)|~aElement0(X2)|sdtmndtasgtdt0(X2,X1,X2))),
% 0.10/0.42 inference(destructive_equality_resolution,[status(thm)],[f42])).
% 0.10/0.42 fof(f98,plain,(
% 0.10/0.42 ![X0,X1]: (~aElement0(X0)|~aRewritingSystem0(X1)|sdtmndtasgtdt0(X0,X1,X0))),
% 0.10/0.42 inference(duplicate_literals_removal,[status(thm)],[f97])).
% 0.10/0.42 fof(f102,plain,(
% 0.10/0.42 ![X0]: (~aRewritingSystem0(X0)|sdtmndtasgtdt0(sK12_skl,X0,sK12_skl))),
% 0.10/0.42 inference(resolution,[status(thm)],[f98,f92])).
% 0.10/0.42 fof(f103,plain,(
% 0.10/0.42 sdtmndtasgtdt0(sK12_skl,xR,sK12_skl)),
% 0.10/0.42 inference(resolution,[status(thm)],[f102,f88])).
% 0.10/0.42 fof(f105,definition,(
% 0.10/0.42 sQ0_spl <=> (aElement0(sK12_skl))),
% 0.10/0.42 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.10/0.42 fof(f107,plain,(
% 0.10/0.42 ~aElement0(sK12_skl)|sQ0_spl),
% 0.10/0.42 inference(component_clause,[status(thm)],[f105])).
% 0.10/0.42 fof(f108,definition,(
% 0.10/0.42 sQ1_spl <=> (aRewritingSystem0(xR))),
% 0.10/0.42 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.10/0.42 fof(f110,plain,(
% 0.10/0.42 ~aRewritingSystem0(xR)|sQ1_spl),
% 0.10/0.42 inference(component_clause,[status(thm)],[f108])).
% 0.10/0.42 fof(f149,plain,(
% 0.10/0.42 $false|sQ1_spl),
% 0.10/0.42 inference(forward_subsumption_resolution,[status(thm)],[f110,f88])).
% 0.10/0.42 fof(f150,plain,(
% 0.10/0.42 sQ1_spl),
% 0.10/0.42 inference(contradiction_clause,[status(thm)],[f149])).
% 0.10/0.42 fof(f151,plain,(
% 0.10/0.42 $false|sQ0_spl),
% 0.10/0.42 inference(forward_subsumption_resolution,[status(thm)],[f107,f92])).
% 0.10/0.42 fof(f152,plain,(
% 0.10/0.42 sQ0_spl),
% 0.10/0.42 inference(contradiction_clause,[status(thm)],[f151])).
% 0.10/0.42 fof(f174,definition,(
% 0.10/0.42 sQ15_spl <=> (isTerminating0(xR))),
% 0.10/0.42 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 0.10/0.42 fof(f176,plain,(
% 0.10/0.42 ~isTerminating0(xR)|sQ15_spl),
% 0.10/0.42 inference(component_clause,[status(thm)],[f174])).
% 0.10/0.42 fof(f201,plain,(
% 0.10/0.42 ~aElement0(sK12_skl)|~aRewritingSystem0(xR)|aNormalFormOfIn0(sK12_skl,sK12_skl,xR)|~aElement0(sK12_skl)|aReductOfIn0(sK11_skl(sK12_skl,xR,sK12_skl),sK12_skl,xR)),
% 0.10/0.42 inference(resolution,[status(thm)],[f87,f103])).
% 0.10/0.42 fof(f202,definition,(
% 0.10/0.42 sQ21_spl <=> (aNormalFormOfIn0(sK12_skl,sK12_skl,xR))),
% 0.10/0.42 introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition])).
% 0.10/0.42 fof(f203,plain,(
% 0.10/0.42 aNormalFormOfIn0(sK12_skl,sK12_skl,xR)|~sQ21_spl),
% 0.10/0.42 inference(component_clause,[status(thm)],[f202])).
% 0.10/0.42 fof(f205,definition,(
% 0.10/0.42 sQ22_spl <=> (aReductOfIn0(sK11_skl(sK12_skl,xR,sK12_skl),sK12_skl,xR))),
% 0.10/0.42 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 0.10/0.42 fof(f206,plain,(
% 0.10/0.42 aReductOfIn0(sK11_skl(sK12_skl,xR,sK12_skl),sK12_skl,xR)|~sQ22_spl),
% 0.10/0.42 inference(component_clause,[status(thm)],[f205])).
% 0.10/0.42 fof(f208,plain,(
% 0.10/0.42 ~sQ0_spl|~sQ1_spl|sQ21_spl|sQ22_spl),
% 0.10/0.42 inference(split_clause,[status(thm)],[f201,f105,f108,f202,f205])).
% 0.10/0.42 fof(f209,plain,(
% 0.10/0.42 $false|~sQ21_spl),
% 0.10/0.42 inference(forward_subsumption_resolution,[status(thm)],[f203,f94])).
% 0.10/0.42 fof(f210,plain,(
% 0.10/0.42 ~sQ21_spl),
% 0.10/0.42 inference(contradiction_clause,[status(thm)],[f209])).
% 0.10/0.42 fof(f212,plain,(
% 0.10/0.42 ~aElement0(sK12_skl)|~aRewritingSystem0(xR)|sdtmndtplgtdt0(sK12_skl,xR,sK11_skl(sK12_skl,xR,sK12_skl))|~sQ22_spl),
% 0.10/0.42 inference(resolution,[status(thm)],[f206,f95])).
% 0.10/0.42 fof(f213,plain,(
% 0.10/0.42 ~aElement0(sK12_skl)|~aRewritingSystem0(xR)|aElement0(sK11_skl(sK12_skl,xR,sK12_skl))|~sQ22_spl),
% 0.10/0.42 inference(resolution,[status(thm)],[f206,f24])).
% 0.10/0.42 fof(f218,definition,(
% 0.10/0.42 sQ24_spl <=> (sdtmndtplgtdt0(sK12_skl,xR,sK11_skl(sK12_skl,xR,sK12_skl)))),
% 0.10/0.42 introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition])).
% 0.10/0.42 fof(f219,plain,(
% 0.10/0.42 sdtmndtplgtdt0(sK12_skl,xR,sK11_skl(sK12_skl,xR,sK12_skl))|~sQ24_spl),
% 0.10/0.42 inference(component_clause,[status(thm)],[f218])).
% 0.10/0.42 fof(f221,plain,(
% 0.10/0.42 ~sQ0_spl|~sQ1_spl|sQ24_spl|~sQ22_spl),
% 0.10/0.42 inference(split_clause,[status(thm)],[f212,f105,f108,f218,f205])).
% 0.10/0.42 fof(f222,definition,(
% 0.10/0.42 sQ25_spl <=> (aElement0(sK11_skl(sK12_skl,xR,sK12_skl)))),
% 0.10/0.42 introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition])).
% 0.10/0.42 fof(f225,plain,(
% 0.10/0.42 ~sQ0_spl|~sQ1_spl|sQ25_spl|~sQ22_spl),
% 0.10/0.42 inference(split_clause,[status(thm)],[f213,f105,f108,f222,f205])).
% 0.10/0.42 fof(f230,plain,(
% 0.10/0.42 ~aElement0(sK12_skl)|~aRewritingSystem0(xR)|~aElement0(sK11_skl(sK12_skl,xR,sK12_skl))|sdtmndtasgtdt0(sK12_skl,xR,sK11_skl(sK12_skl,xR,sK12_skl))|~sQ24_spl),
% 0.10/0.42 inference(resolution,[status(thm)],[f219,f43])).
% 0.10/0.42 fof(f232,plain,(
% 0.10/0.42 ~aRewritingSystem0(xR)|~isTerminating0(xR)|~aElement0(sK12_skl)|~aElement0(sK11_skl(sK12_skl,xR,sK12_skl))|iLess0(sK11_skl(sK12_skl,xR,sK12_skl),sK12_skl)|~sQ24_spl),
% 0.10/0.42 inference(resolution,[status(thm)],[f219,f75])).
% 0.10/0.42 fof(f245,definition,(
% 0.10/0.42 sQ29_spl <=> (sdtmndtasgtdt0(sK12_skl,xR,sK11_skl(sK12_skl,xR,sK12_skl)))),
% 0.10/0.42 introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition])).
% 0.10/0.42 fof(f246,plain,(
% 0.10/0.42 sdtmndtasgtdt0(sK12_skl,xR,sK11_skl(sK12_skl,xR,sK12_skl))|~sQ29_spl),
% 0.10/0.42 inference(component_clause,[status(thm)],[f245])).
% 0.10/0.42 fof(f248,plain,(
% 0.10/0.42 ~sQ0_spl|~sQ1_spl|~sQ25_spl|sQ29_spl|~sQ24_spl),
% 0.10/0.42 inference(split_clause,[status(thm)],[f230,f105,f108,f222,f245,f218])).
% 0.10/0.42 fof(f250,definition,(
% 0.10/0.42 sQ30_spl <=> (iLess0(sK11_skl(sK12_skl,xR,sK12_skl),sK12_skl))),
% 0.10/0.42 introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition])).
% 0.10/0.42 fof(f251,plain,(
% 0.10/0.42 iLess0(sK11_skl(sK12_skl,xR,sK12_skl),sK12_skl)|~sQ30_spl),
% 0.10/0.42 inference(component_clause,[status(thm)],[f250])).
% 0.10/0.42 fof(f253,plain,(
% 0.10/0.42 ~sQ1_spl|~sQ15_spl|~sQ0_spl|~sQ25_spl|sQ30_spl|~sQ24_spl),
% 0.10/0.42 inference(split_clause,[status(thm)],[f232,f108,f174,f105,f222,f250,f218])).
% 0.10/0.42 fof(f254,plain,(
% 0.10/0.42 $false|sQ15_spl),
% 0.10/0.42 inference(forward_subsumption_resolution,[status(thm)],[f176,f89])).
% 0.10/0.42 fof(f255,plain,(
% 0.10/0.42 sQ15_spl),
% 0.10/0.42 inference(contradiction_clause,[status(thm)],[f254])).
% 0.10/0.42 fof(f259,plain,(
% 0.10/0.42 ![X0]: (~aElement0(sK12_skl)|~aRewritingSystem0(xR)|~aElement0(sK11_skl(sK12_skl,xR,sK12_skl))|~aElement0(X0)|~sdtmndtasgtdt0(sK11_skl(sK12_skl,xR,sK12_skl),xR,X0)|sdtmndtasgtdt0(sK12_skl,xR,X0)|~sQ29_spl)),
% 0.10/0.42 inference(resolution,[status(thm)],[f246,f45])).
% 0.10/0.42 fof(f271,definition,(
% 0.10/0.42 ![X0]: (sQ34_spl <=> (~aElement0(X0)|~sdtmndtasgtdt0(sK11_skl(sK12_skl,xR,sK12_skl),xR,X0)|sdtmndtasgtdt0(sK12_skl,xR,X0)))),
% 0.10/0.42 introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition])).
% 0.10/0.42 fof(f272,plain,(
% 0.10/0.42 ![X0]: (~aElement0(X0)|~sdtmndtasgtdt0(sK11_skl(sK12_skl,xR,sK12_skl),xR,X0)|sdtmndtasgtdt0(sK12_skl,xR,X0)|~sQ34_spl)),
% 0.10/0.42 inference(component_clause,[status(thm)],[f271])).
% 0.10/0.42 fof(f274,plain,(
% 0.10/0.42 ~sQ0_spl|~sQ1_spl|~sQ25_spl|sQ34_spl|~sQ29_spl),
% 0.10/0.42 inference(split_clause,[status(thm)],[f259,f105,f108,f222,f271,f245])).
% 0.10/0.42 fof(f277,plain,(
% 0.10/0.42 ~aElement0(sK11_skl(sK12_skl,xR,sK12_skl))|aNormalFormOfIn0(sK13_skl(sK11_skl(sK12_skl,xR,sK12_skl)),sK11_skl(sK12_skl,xR,sK12_skl),xR)|~sQ30_spl),
% 0.10/0.42 inference(resolution,[status(thm)],[f251,f93])).
% 0.10/0.42 fof(f278,definition,(
% 0.10/0.42 sQ35_spl <=> (aNormalFormOfIn0(sK13_skl(sK11_skl(sK12_skl,xR,sK12_skl)),sK11_skl(sK12_skl,xR,sK12_skl),xR))),
% 0.10/0.42 introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition])).
% 0.10/0.42 fof(f279,plain,(
% 0.10/0.42 aNormalFormOfIn0(sK13_skl(sK11_skl(sK12_skl,xR,sK12_skl)),sK11_skl(sK12_skl,xR,sK12_skl),xR)|~sQ35_spl),
% 0.10/0.42 inference(component_clause,[status(thm)],[f278])).
% 0.10/0.42 fof(f281,plain,(
% 0.10/0.42 ~sQ25_spl|sQ35_spl|~sQ30_spl),
% 0.10/0.42 inference(split_clause,[status(thm)],[f277,f222,f278,f250])).
% 0.10/0.42 fof(f320,plain,(
% 0.10/0.42 ~aElement0(sK11_skl(sK12_skl,xR,sK12_skl))|~aRewritingSystem0(xR)|sdtmndtasgtdt0(sK11_skl(sK12_skl,xR,sK12_skl),xR,sK13_skl(sK11_skl(sK12_skl,xR,sK12_skl)))|~sQ35_spl),
% 0.10/0.42 inference(resolution,[status(thm)],[f279,f85])).
% 0.10/0.42 fof(f321,plain,(
% 0.10/0.42 ~aElement0(sK11_skl(sK12_skl,xR,sK12_skl))|~aRewritingSystem0(xR)|aElement0(sK13_skl(sK11_skl(sK12_skl,xR,sK12_skl)))|~sQ35_spl),
% 0.10/0.42 inference(resolution,[status(thm)],[f279,f84])).
% 0.10/0.42 fof(f322,definition,(
% 0.10/0.42 sQ44_spl <=> (sdtmndtasgtdt0(sK11_skl(sK12_skl,xR,sK12_skl),xR,sK13_skl(sK11_skl(sK12_skl,xR,sK12_skl))))),
% 0.10/0.42 introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition])).
% 0.10/0.42 fof(f323,plain,(
% 0.10/0.42 sdtmndtasgtdt0(sK11_skl(sK12_skl,xR,sK12_skl),xR,sK13_skl(sK11_skl(sK12_skl,xR,sK12_skl)))|~sQ44_spl),
% 0.10/0.42 inference(component_clause,[status(thm)],[f322])).
% 0.10/0.42 fof(f325,plain,(
% 0.10/0.42 ~sQ25_spl|~sQ1_spl|sQ44_spl|~sQ35_spl),
% 0.10/0.42 inference(split_clause,[status(thm)],[f320,f222,f108,f322,f278])).
% 0.10/0.42 fof(f326,definition,(
% 0.10/0.42 sQ45_spl <=> (aElement0(sK13_skl(sK11_skl(sK12_skl,xR,sK12_skl))))),
% 0.10/0.42 introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition])).
% 0.10/0.42 fof(f329,plain,(
% 0.10/0.42 ~sQ25_spl|~sQ1_spl|sQ45_spl|~sQ35_spl),
% 0.10/0.42 inference(split_clause,[status(thm)],[f321,f222,f108,f326,f278])).
% 0.10/0.42 fof(f370,plain,(
% 0.10/0.42 ~aElement0(sK13_skl(sK11_skl(sK12_skl,xR,sK12_skl)))|sdtmndtasgtdt0(sK12_skl,xR,sK13_skl(sK11_skl(sK12_skl,xR,sK12_skl)))|~sQ44_spl|~sQ34_spl),
% 0.10/0.42 inference(resolution,[status(thm)],[f323,f272])).
% 0.10/0.42 fof(f374,definition,(
% 0.10/0.42 sQ53_spl <=> (sdtmndtasgtdt0(sK12_skl,xR,sK13_skl(sK11_skl(sK12_skl,xR,sK12_skl))))),
% 0.10/0.42 introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition])).
% 0.10/0.42 fof(f375,plain,(
% 0.10/0.42 sdtmndtasgtdt0(sK12_skl,xR,sK13_skl(sK11_skl(sK12_skl,xR,sK12_skl)))|~sQ53_spl),
% 0.10/0.42 inference(component_clause,[status(thm)],[f374])).
% 0.10/0.42 fof(f377,plain,(
% 0.10/0.42 ~sQ45_spl|sQ53_spl|~sQ44_spl|~sQ34_spl),
% 0.10/0.42 inference(split_clause,[status(thm)],[f370,f326,f374,f322,f271])).
% 0.10/0.42 fof(f407,plain,(
% 0.10/0.42 ~aElement0(sK12_skl)|~aRewritingSystem0(xR)|aNormalFormOfIn0(sK13_skl(sK11_skl(sK12_skl,xR,sK12_skl)),sK12_skl,xR)|~aElement0(sK13_skl(sK11_skl(sK12_skl,xR,sK12_skl)))|aReductOfIn0(sK11_skl(sK13_skl(sK11_skl(sK12_skl,xR,sK12_skl)),xR,sK12_skl),sK13_skl(sK11_skl(sK12_skl,xR,sK12_skl)),xR)|~sQ53_spl),
% 0.10/0.42 inference(resolution,[status(thm)],[f375,f87])).
% 0.10/0.42 fof(f410,definition,(
% 0.10/0.42 sQ58_spl <=> (aNormalFormOfIn0(sK13_skl(sK11_skl(sK12_skl,xR,sK12_skl)),sK12_skl,xR))),
% 0.10/0.42 introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition])).
% 0.10/0.42 fof(f411,plain,(
% 0.10/0.42 aNormalFormOfIn0(sK13_skl(sK11_skl(sK12_skl,xR,sK12_skl)),sK12_skl,xR)|~sQ58_spl),
% 0.10/0.42 inference(component_clause,[status(thm)],[f410])).
% 0.10/0.42 fof(f413,definition,(
% 0.10/0.42 sQ59_spl <=> (aReductOfIn0(sK11_skl(sK13_skl(sK11_skl(sK12_skl,xR,sK12_skl)),xR,sK12_skl),sK13_skl(sK11_skl(sK12_skl,xR,sK12_skl)),xR))),
% 0.10/0.42 introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition])).
% 0.10/0.42 fof(f414,plain,(
% 0.10/0.42 aReductOfIn0(sK11_skl(sK13_skl(sK11_skl(sK12_skl,xR,sK12_skl)),xR,sK12_skl),sK13_skl(sK11_skl(sK12_skl,xR,sK12_skl)),xR)|~sQ59_spl),
% 0.10/0.42 inference(component_clause,[status(thm)],[f413])).
% 0.10/0.42 fof(f416,plain,(
% 0.10/0.42 ~sQ0_spl|~sQ1_spl|sQ58_spl|~sQ45_spl|sQ59_spl|~sQ53_spl),
% 0.10/0.42 inference(split_clause,[status(thm)],[f407,f105,f108,f410,f326,f413,f374])).
% 0.10/0.42 fof(f428,plain,(
% 0.10/0.42 $false|~sQ58_spl),
% 0.10/0.42 inference(forward_subsumption_resolution,[status(thm)],[f411,f94])).
% 0.10/0.42 fof(f429,plain,(
% 0.10/0.42 ~sQ58_spl),
% 0.10/0.42 inference(contradiction_clause,[status(thm)],[f428])).
% 0.10/0.42 fof(f616,definition,(
% 0.10/0.42 sQ81_spl <=> (aNormalFormOfIn0(sK13_skl(sK12_skl),sK12_skl,xR))),
% 0.10/0.42 introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition])).
% 0.10/0.42 fof(f617,plain,(
% 0.10/0.42 aNormalFormOfIn0(sK13_skl(sK12_skl),sK12_skl,xR)|~sQ81_spl),
% 0.10/0.42 inference(component_clause,[status(thm)],[f616])).
% 0.10/0.42 fof(f620,plain,(
% 0.10/0.42 $false|~sQ81_spl),
% 0.10/0.42 inference(forward_subsumption_resolution,[status(thm)],[f617,f94])).
% 0.10/0.42 fof(f621,plain,(
% 0.10/0.42 ~sQ81_spl),
% 0.10/0.42 inference(contradiction_clause,[status(thm)],[f620])).
% 0.10/0.42 fof(f740,plain,(
% 0.10/0.42 ![X0]: (~aElement0(sK11_skl(sK12_skl,xR,sK12_skl))|~aRewritingSystem0(xR)|~aReductOfIn0(X0,sK13_skl(sK11_skl(sK12_skl,xR,sK12_skl)),xR)|~sQ35_spl)),
% 0.10/0.42 inference(resolution,[status(thm)],[f86,f279])).
% 0.10/0.42 fof(f741,definition,(
% 0.10/0.42 ![X0]: (sQ96_spl <=> (~aReductOfIn0(X0,sK13_skl(sK11_skl(sK12_skl,xR,sK12_skl)),xR)))),
% 0.10/0.42 introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition])).
% 0.10/0.42 fof(f742,plain,(
% 0.10/0.42 ![X0]: (~aReductOfIn0(X0,sK13_skl(sK11_skl(sK12_skl,xR,sK12_skl)),xR)|~sQ96_spl)),
% 0.10/0.42 inference(component_clause,[status(thm)],[f741])).
% 0.10/0.42 fof(f744,plain,(
% 0.10/0.42 ~sQ25_spl|~sQ1_spl|sQ96_spl|~sQ35_spl),
% 0.10/0.42 inference(split_clause,[status(thm)],[f740,f222,f108,f741,f278])).
% 0.10/0.42 fof(f745,plain,(
% 0.10/0.42 $false|~sQ96_spl|~sQ59_spl),
% 0.10/0.42 inference(backward_subsumption_resolution,[status(thm)],[f414,f742])).
% 0.10/0.42 fof(f746,plain,(
% 0.10/0.42 ~sQ96_spl|~sQ59_spl),
% 0.10/0.42 inference(contradiction_clause,[status(thm)],[f745])).
% 0.10/0.42 fof(f747,plain,(
% 0.10/0.42 $false),
% 0.10/0.42 inference(sat_refutation,[status(thm)],[f150,f152,f208,f210,f221,f225,f248,f253,f255,f274,f281,f325,f329,f377,f416,f429,f621,f744,f746])).
% 0.10/0.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.10/0.44 % Elapsed time: 0.070521 seconds
% 0.10/0.44 % CPU time: 0.220449 seconds
% 0.10/0.44 % Total memory used: 83.664 MB
% 0.10/0.44 % Net memory used: 83.459 MB
%------------------------------------------------------------------------------