0.02/0.03	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.02/0.04	% Command    : vampire --mode casc -t %d %s
0.03/0.23	% Computer   : n152.star.cs.uiowa.edu
0.03/0.23	% Model      : x86_64 x86_64
0.03/0.23	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.03/0.23	% Memory     : 32218.625MB
0.03/0.23	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.03/0.23	% CPULimit   : 300
0.03/0.23	% DateTime   : Sat Jul 14 04:21:40 CDT 2018
0.03/0.23	% CPUTime    : 
0.07/0.27	% lrs+1011_2:1_add=large:afr=on:afp=4000:afq=1.1:amm=off:anc=none:cond=on:fsr=off:gs=on:irw=on:nm=64:nwc=1:sas=z3:stl=30:sos=on:sp=reverse_arity:thf=on:urr=on:updr=off_2 on theBenchmark
0.07/0.34	% Refutation found. Thanks to Tanya!
0.07/0.34	% SZS status Theorem for theBenchmark
0.07/0.34	% SZS output start Proof for theBenchmark
0.07/0.34	tff(func_def_4, type, sK0: $int).
0.07/0.34	tff(func_def_5, type, sK1: $int > $int).
0.07/0.34	tff(f1,conjecture,(
0.07/0.34	  ! [X0 : $int] : ? [X1 : $int] : ($less(X1,X0) & ~? [X2 : $int] : ($less(X2,X0) & $less(X1,X2)))),
0.07/0.34	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1)).
0.07/0.34	tff(f2,negated_conjecture,(
0.07/0.34	  ~! [X0 : $int] : ? [X1 : $int] : ($less(X1,X0) & ~? [X2 : $int] : ($less(X2,X0) & $less(X1,X2)))),
0.07/0.34	  inference(negated_conjecture,[],[f1])).
0.07/0.34	tff(f3,plain,(
0.07/0.34	  ( ! [X0:$int,X1:$int] : ($sum(X0,X1) = $sum(X1,X0)) )),
0.07/0.34	  introduced(theory_axiom,[])).
0.07/0.34	tff(f4,plain,(
0.07/0.34	  ( ! [X2:$int,X0:$int,X1:$int] : ($sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2)) )),
0.07/0.34	  introduced(theory_axiom,[])).
0.07/0.34	tff(f5,plain,(
0.07/0.34	  ( ! [X0:$int] : ($sum(X0,0) = X0) )),
0.07/0.34	  introduced(theory_axiom,[])).
0.07/0.34	tff(f7,plain,(
0.07/0.34	  ( ! [X0:$int] : (0 = $sum(X0,$uminus(X0))) )),
0.07/0.34	  introduced(theory_axiom,[])).
0.07/0.34	tff(f8,plain,(
0.07/0.34	  ( ! [X0:$int] : (~$less(X0,X0)) )),
0.07/0.34	  introduced(theory_axiom,[])).
0.07/0.34	tff(f9,plain,(
0.07/0.34	  ( ! [X2:$int,X0:$int,X1:$int] : ($less(X0,X2) | ~$less(X1,X2) | ~$less(X0,X1)) )),
0.07/0.34	  introduced(theory_axiom,[])).
0.07/0.34	tff(f10,plain,(
0.07/0.34	  ( ! [X0:$int,X1:$int] : ($less(X0,X1) | $less(X1,X0) | X0 = X1) )),
0.07/0.34	  introduced(theory_axiom,[])).
0.07/0.34	tff(f12,plain,(
0.07/0.34	  ( ! [X0:$int,X1:$int] : ($less(X1,$sum(X0,1)) | $less(X0,X1)) )),
0.07/0.34	  introduced(theory_axiom,[])).
0.07/0.34	tff(f13,plain,(
0.07/0.34	  ( ! [X0:$int] : ($uminus($uminus(X0)) = X0) )),
0.07/0.34	  introduced(theory_axiom,[])).
0.07/0.34	tff(f14,plain,(
0.07/0.34	  ( ! [X0:$int,X1:$int] : (~$less(X1,$sum(X0,1)) | ~$less(X0,X1)) )),
0.07/0.34	  introduced(theory_axiom,[])).
0.07/0.34	tff(f15,plain,(
0.07/0.34	  ? [X0 : $int] : ! [X1 : $int] : (~$less(X1,X0) | ? [X2 : $int] : ($less(X2,X0) & $less(X1,X2)))),
0.07/0.34	  inference(ennf_transformation,[],[f2])).
0.07/0.34	tff(f16,plain,(
0.07/0.34	  ? [X0 : $int] : ! [X1 : $int] : (~$less(X1,X0) | ? [X2 : $int] : ($less(X2,X0) & $less(X1,X2))) => ! [X1 : $int] : (~$less(X1,sK0) | ? [X2 : $int] : ($less(X2,sK0) & $less(X1,X2)))),
0.07/0.34	  introduced(choice_axiom,[])).
0.07/0.34	tff(f17,plain,(
0.07/0.34	  ( ! [X0:$int] : (! [X1 : $int] : (? [X2 : $int] : ($less(X2,X0) & $less(X1,X2)) => ($less(sK1(X1),X0) & $less(X1,sK1(X1))))) )),
0.07/0.34	  introduced(choice_axiom,[])).
0.07/0.34	tff(f18,plain,(
0.07/0.34	  ! [X1 : $int] : (~$less(X1,sK0) | ($less(sK1(X1),sK0) & $less(X1,sK1(X1))))),
0.07/0.34	  inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f15,f17,f16])).
0.07/0.34	tff(f19,plain,(
0.07/0.34	  ( ! [X1:$int] : (~$less(X1,sK0) | $less(X1,sK1(X1))) )),
0.07/0.34	  inference(cnf_transformation,[],[f18])).
0.07/0.34	tff(f20,plain,(
0.07/0.34	  ( ! [X1:$int] : (~$less(X1,sK0) | $less(sK1(X1),sK0)) )),
0.07/0.34	  inference(cnf_transformation,[],[f18])).
0.07/0.34	tff(f21,plain,(
0.07/0.34	  ( ! [X4:$int,X2:$int,X3:$int,X1:$int] : ($less(X3,X4) | ~$less(X1,X2) | sK1(X1) != X3 | sK0 != X4 | sK0 != X2) )),
0.07/0.34	  inference(theory_flattening,[],[f20])).
0.07/0.34	tff(f22,plain,(
0.07/0.34	  ( ! [X2:$int,X3:$int,X1:$int] : ($less(X1,X3) | ~$less(X1,X2) | sK1(X1) != X3 | sK0 != X2) )),
0.07/0.34	  inference(theory_flattening,[],[f19])).
0.07/0.34	tff(f23,plain,(
0.07/0.34	  ( ! [X2:$int,X0:$int,X1:$int] : ($sum(X2,1) != sK1(X0) | ~$less(X0,X1) | sK0 != X1 | ~$less(X2,X0)) )),
0.07/0.34	  inference(resolution,[],[f22,f14])).
0.07/0.34	tff(f25,plain,(
0.07/0.34	  ( ! [X2:$int,X0:$int,X3:$int,X1:$int] : ($sum(X3,1) != sK0 | sK1(X0) != X2 | ~$less(X0,X1) | sK0 != X1 | ~$less(X3,X2)) )),
0.07/0.34	  inference(resolution,[],[f21,f14])).
0.07/0.34	tff(f30,plain,(
0.07/0.34	  ( ! [X6:$int,X8:$int,X7:$int,X9:$int] : (sK0 != X9 | ~$less(X8,X9) | $sum(X6,$sum(X7,1)) != sK1(X8) | ~$less($sum(X6,X7),X8)) )),
0.07/0.34	  inference(superposition,[],[f23,f4])).
0.07/0.34	tff(f31,plain,(
0.07/0.34	  ( ! [X2:$int,X0:$int,X3:$int,X1:$int] : (sK0 != X3 | sK1(X1) != X2 | ~$less(X1,X3) | $sum(1,X0) != sK0 | ~$less(X0,X2)) )),
0.07/0.34	  inference(superposition,[],[f25,f3])).
0.07/0.34	tff(f33,plain,(
0.07/0.34	  ( ! [X12:$int,X10:$int,X8:$int,X11:$int,X9:$int] : (sK0 != X12 | sK1(X10) != X11 | ~$less(X10,X12) | $sum(X8,$sum(X9,1)) != sK0 | ~$less($sum(X8,X9),X11)) )),
0.07/0.34	  inference(superposition,[],[f25,f4])).
0.07/0.34	tff(f35,plain,(
0.07/0.34	  ( ! [X2:$int,X0:$int,X1:$int] : (sK1(X0) != X1 | ~$less(X0,sK0) | $sum(1,X2) != sK0 | ~$less(X2,X1)) )),
0.07/0.34	  inference(equality_resolution,[],[f31])).
0.07/0.34	tff(f36,plain,(
0.07/0.34	  ( ! [X2:$int,X0:$int,X1:$int] : (~$less(X0,sK0) | $sum(X1,$sum(X2,1)) != sK1(X0) | ~$less($sum(X1,X2),X0)) )),
0.07/0.34	  inference(equality_resolution,[],[f30])).
0.07/0.34	tff(f42,plain,(
0.07/0.34	  ( ! [X2:$int,X0:$int,X3:$int,X1:$int] : (sK1(X0) != X1 | ~$less(X0,sK0) | $sum(X2,$sum(X3,1)) != sK0 | ~$less($sum(X2,X3),X1)) )),
0.07/0.34	  inference(equality_resolution,[],[f33])).
0.07/0.34	tff(f43,plain,(
0.07/0.34	  ( ! [X0:$int,X1:$int] : ($sum(1,X1) != sK0 | ~$less(X0,sK0) | ~$less(X1,sK1(X0))) )),
0.07/0.34	  inference(equality_resolution,[],[f35])).
0.07/0.34	tff(f46,plain,(
0.07/0.34	  ( ! [X12:$int,X10:$int,X11:$int,X9:$int] : (~$less(X12,sK0) | ~$less($sum(X9,X10),X11) | $sum(X9,$sum(X10,1)) != sK1(X11) | ~$less(X11,X12)) )),
0.07/0.34	  inference(resolution,[],[f36,f9])).
0.07/0.34	tff(f47,plain,(
0.07/0.34	  ( ! [X14:$int,X15:$int,X13:$int] : ($less(sK0,X15) | ~$less($sum(X13,X14),X15) | $sum(X13,$sum(X14,1)) != sK1(X15) | sK0 = X15) )),
0.07/0.34	  inference(resolution,[],[f36,f10])).
0.07/0.34	tff(f49,plain,(
0.07/0.34	  ( ! [X2:$int,X0:$int,X1:$int] : (~$less(X0,sK0) | $sum(X1,$sum(X2,1)) != sK0 | ~$less($sum(X1,X2),sK1(X0))) )),
0.07/0.34	  inference(equality_resolution,[],[f42])).
0.07/0.34	tff(f55,plain,(
0.07/0.34	  ( ! [X4:$int] : (1 != sK0 | ~$less(X4,sK0) | ~$less(0,sK1(X4))) )),
0.07/0.34	  inference(superposition,[],[f43,f5])).
0.07/0.34	tff(f56,plain,(
0.07/0.34	  ( ! [X5:$int] : (0 != sK0 | ~$less(X5,sK0) | ~$less($uminus(1),sK1(X5))) )),
0.07/0.34	  inference(superposition,[],[f43,f7])).
0.07/0.34	tff(f57,plain,(
0.07/0.34	  ( ! [X5:$int] : (0 != sK0 | ~$less(X5,sK0) | ~$less(-1,sK1(X5))) )),
0.07/0.34	  inference(evaluation,[],[f56])).
0.07/0.34	tff(f58,plain,(
0.07/0.34	  ( ! [X4:$int] : (1 != sK0 | ~$less(X4,1) | ~$less(0,sK1(X4))) )),
0.07/0.34	  inference(inner_rewriting,[],[f55])).
0.07/0.34	tff(f60,plain,(
0.07/0.34	  spl2_0 <=> ! [X4 : $int] : (~$less(X4,1) | ~$less(0,sK1(X4)))),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_0])])).
0.07/0.34	tff(f66,plain,(
0.07/0.34	  spl2_3 <=> 1 != sK0),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_3])])).
0.07/0.34	tff(f68,plain,(
0.07/0.34	  spl2_0 | ~spl2_3),
0.07/0.34	  inference(avatar_split_clause,[],[f58,f66,f60])).
0.07/0.34	tff(f69,plain,(
0.07/0.34	  ( ! [X5:$int] : (0 != sK0 | ~$less(X5,0) | ~$less(-1,sK1(X5))) )),
0.07/0.34	  inference(inner_rewriting,[],[f57])).
0.07/0.34	tff(f71,plain,(
0.07/0.34	  spl2_4 <=> ! [X5 : $int] : (~$less(X5,0) | ~$less(-1,sK1(X5)))),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_4])])).
0.07/0.34	tff(f77,plain,(
0.07/0.34	  spl2_7 <=> 0 != sK0),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_7])])).
0.07/0.34	tff(f79,plain,(
0.07/0.34	  spl2_4 | ~spl2_7),
0.07/0.34	  inference(avatar_split_clause,[],[f69,f77,f71])).
0.07/0.34	tff(f83,plain,(
0.07/0.34	  ( ! [X14:$int,X15:$int,X13:$int] : ($sum(X13,$sum(X14,1)) != sK0 | ~$less($sum(X13,X14),sK1(X15)) | $less(sK0,X15) | sK0 = X15) )),
0.07/0.34	  inference(resolution,[],[f49,f10])).
0.07/0.34	tff(f91,plain,(
0.07/0.34	  ( ! [X19:$int,X17:$int,X18:$int,X16:$int] : ($sum(X16,$sum(X17,1)) != sK1(X18) | ~$less($sum(X16,X17),X18) | ~$less(X18,X19) | $less(sK0,X19) | sK0 = X19) )),
0.07/0.34	  inference(resolution,[],[f46,f10])).
0.07/0.34	tff(f93,plain,(
0.07/0.34	  ( ! [X2:$int,X0:$int,X1:$int] : (~$less(X2,sK0) | $sum(X0,$sum(X1,1)) != sK1($sum(X2,1)) | $sum(X2,1) = sK0 | ~$less($sum(X0,X1),$sum(X2,1))) )),
0.07/0.34	  inference(resolution,[],[f47,f14])).
0.07/0.34	tff(f105,plain,(
0.07/0.34	  ( ! [X2:$int,X0:$int,X1:$int] : ($less(sK0,X2) | ~$less($sum(X1,X0),sK1(X2)) | $sum(X1,$sum(1,X0)) != sK0 | sK0 = X2) )),
0.07/0.34	  inference(superposition,[],[f83,f3])).
0.07/0.34	tff(f108,plain,(
0.07/0.34	  ( ! [X2:$int,X0:$int,X1:$int] : ($sum($sum(X1,1),X0) != sK0 | ~$less($sum(X0,X1),sK1(X2)) | $less(sK0,X2) | sK0 = X2) )),
0.07/0.34	  inference(superposition,[],[f83,f3])).
0.07/0.34	tff(f111,plain,(
0.07/0.34	  ( ! [X2:$int,X0:$int,X1:$int] : ($sum(X1,$sum(1,X0)) != sK0 | ~$less($sum(X0,X1),sK1(X2)) | $less(sK0,X2) | sK0 = X2) )),
0.07/0.34	  inference(forward_demodulation,[],[f108,f4])).
0.07/0.34	tff(f141,plain,(
0.07/0.34	  ( ! [X12:$int,X10:$int,X8:$int,X11:$int,X9:$int] : (~$less(X11,X12) | ~$less($sum(X10,$sum(X8,X9)),X11) | $sum(X10,$sum(X8,$sum(X9,1))) != sK1(X11) | $less(sK0,X12) | sK0 = X12) )),
0.07/0.34	  inference(superposition,[],[f91,f4])).
0.07/0.34	tff(f174,plain,(
0.07/0.34	  ( ! [X8:$int,X9:$int] : ($sum(X8,0) != sK0 | ~$less($sum($uminus(1),X8),sK1(X9)) | $less(sK0,X9) | sK0 = X9) )),
0.07/0.34	  inference(superposition,[],[f111,f7])).
0.07/0.34	tff(f178,plain,(
0.07/0.34	  ( ! [X8:$int,X9:$int] : (sK0 != X8 | ~$less($sum(-1,X8),sK1(X9)) | $less(sK0,X9) | sK0 = X9) )),
0.07/0.34	  inference(evaluation,[],[f174])).
0.07/0.34	tff(f183,plain,(
0.07/0.34	  ( ! [X0:$int] : (~$less($sum(-1,sK0),sK1(X0)) | $less(sK0,X0) | sK0 = X0) )),
0.07/0.34	  inference(equality_resolution,[],[f178])).
0.07/0.34	tff(f202,plain,(
0.07/0.34	  ( ! [X2:$int,X0:$int,X1:$int] : ($less(sK0,X0) | sK0 = X0 | ~$less(X1,X2) | $sum(-1,sK0) != sK1(X1) | sK0 != sK1(X0) | sK0 != X2) )),
0.07/0.34	  inference(resolution,[],[f183,f21])).
0.07/0.34	tff(f203,plain,(
0.07/0.34	  ( ! [X4:$int,X3:$int] : ($less(sK0,X3) | sK0 = X3 | ~$less($sum(-1,sK0),X4) | sK1(X3) != sK1($sum(-1,sK0)) | sK0 != X4) )),
0.07/0.34	  inference(resolution,[],[f183,f22])).
0.07/0.34	tff(f207,plain,(
0.07/0.34	  spl2_8 <=> ! [X1 : $int,X2 : $int] : (~$less(X1,X2) | sK0 != X2 | $sum(-1,sK0) != sK1(X1))),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_8])])).
0.07/0.34	tff(f210,plain,(
0.07/0.34	  spl2_10 <=> ! [X0 : $int] : ($less(sK0,X0) | sK0 != sK1(X0) | sK0 = X0)),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_10])])).
0.07/0.34	tff(f211,plain,(
0.07/0.34	  ( ! [X0:$int] : (sK0 != sK1(X0) | $less(sK0,X0) | sK0 = X0) ) | ~spl2_10),
0.07/0.34	  inference(avatar_component_clause,[],[f210])).
0.07/0.34	tff(f212,plain,(
0.07/0.34	  spl2_8 | spl2_10),
0.07/0.34	  inference(avatar_split_clause,[],[f202,f210,f207])).
0.07/0.34	tff(f214,plain,(
0.07/0.34	  spl2_12 <=> ! [X4 : $int] : (~$less($sum(-1,sK0),X4) | sK0 != X4)),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_12])])).
0.07/0.34	tff(f215,plain,(
0.07/0.34	  ( ! [X4:$int] : (sK0 != X4 | ~$less($sum(-1,sK0),X4)) ) | ~spl2_12),
0.07/0.34	  inference(avatar_component_clause,[],[f214])).
0.07/0.34	tff(f217,plain,(
0.07/0.34	  spl2_14 <=> ! [X3 : $int] : ($less(sK0,X3) | sK1(X3) != sK1($sum(-1,sK0)) | sK0 = X3)),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_14])])).
0.07/0.34	tff(f218,plain,(
0.07/0.34	  ( ! [X3:$int] : (sK1(X3) != sK1($sum(-1,sK0)) | $less(sK0,X3) | sK0 = X3) ) | ~spl2_14),
0.07/0.34	  inference(avatar_component_clause,[],[f217])).
0.07/0.34	tff(f219,plain,(
0.07/0.34	  spl2_12 | spl2_14),
0.07/0.34	  inference(avatar_split_clause,[],[f203,f217,f214])).
0.07/0.34	tff(f257,plain,(
0.07/0.34	  $less(sK0,$sum(-1,sK0)) | $sum(-1,sK0) = sK0 | ~spl2_14),
0.07/0.34	  inference(equality_resolution,[],[f218])).
0.07/0.34	tff(f259,plain,(
0.07/0.34	  spl2_17 <=> $sum(-1,sK0) != sK0),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_17])])).
0.07/0.34	tff(f260,plain,(
0.07/0.34	  $sum(-1,sK0) != sK0 | ~spl2_17),
0.07/0.34	  inference(avatar_component_clause,[],[f259])).
0.07/0.34	tff(f262,plain,(
0.07/0.34	  spl2_16 <=> $sum(-1,sK0) = sK0),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_16])])).
0.07/0.34	tff(f265,plain,(
0.07/0.34	  spl2_19 <=> ~$less(sK0,$sum(-1,sK0))),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_19])])).
0.07/0.34	tff(f266,plain,(
0.07/0.34	  ~$less(sK0,$sum(-1,sK0)) | ~spl2_19),
0.07/0.34	  inference(avatar_component_clause,[],[f265])).
0.07/0.34	tff(f268,plain,(
0.07/0.34	  spl2_18 <=> $less(sK0,$sum(-1,sK0))),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_18])])).
0.07/0.34	tff(f270,plain,(
0.07/0.34	  spl2_16 | spl2_18 | ~spl2_14),
0.07/0.34	  inference(avatar_split_clause,[],[f257,f217,f268,f262])).
0.07/0.34	tff(f297,plain,(
0.07/0.34	  ~$less($sum(-1,$uminus($uminus(sK0))),sK1($sum(-1,sK0))) | (~spl2_17 | ~spl2_19)),
0.07/0.34	  inference(unit_resulting_resolution,[],[f13,f260,f266,f178])).
0.07/0.34	tff(f298,plain,(
0.07/0.34	  ~$less($sum(-1,$sum(sK0,0)),sK1($sum(-1,sK0))) | (~spl2_17 | ~spl2_19)),
0.07/0.34	  inference(unit_resulting_resolution,[],[f5,f260,f266,f178])).
0.07/0.34	tff(f299,plain,(
0.07/0.34	  ~$less($sum(-1,sK0),sK1($sum(-1,sK0))) | (~spl2_17 | ~spl2_19)),
0.07/0.34	  inference(unit_resulting_resolution,[],[f260,f266,f183])).
0.07/0.34	tff(f300,plain,(
0.07/0.34	  sK0 != sK1($sum(-1,sK0)) | (~spl2_10 | ~spl2_17 | ~spl2_19)),
0.07/0.34	  inference(unit_resulting_resolution,[],[f260,f266,f211])).
0.07/0.34	tff(f301,plain,(
0.07/0.34	  $less($sum(-1,sK0),sK0) | (~spl2_17 | ~spl2_19)),
0.07/0.34	  inference(unit_resulting_resolution,[],[f260,f266,f10])).
0.07/0.34	tff(f302,plain,(
0.07/0.34	  $less($sum(-1,sK0),sK0) | (~spl2_17 | ~spl2_19)),
0.07/0.34	  inference(unit_resulting_resolution,[],[f260,f266,f10])).
0.07/0.34	tff(f303,plain,(
0.07/0.34	  $less($sum(-1,sK0),$sum(sK0,1)) | ~spl2_19),
0.07/0.34	  inference(unit_resulting_resolution,[],[f266,f12])).
0.07/0.34	tff(f305,plain,(
0.07/0.34	  ( ! [X2:$int] : (~$less(sK0,X2) | $sum(-1,sK0) != sK1(sK0) | sK0 != X2) ) | ~spl2_19),
0.07/0.34	  inference(resolution,[],[f266,f22])).
0.07/0.34	tff(f307,plain,(
0.07/0.34	  $less($sum(-1,sK0),sK0) | $sum(-1,sK0) = sK0 | ~spl2_19),
0.07/0.34	  inference(resolution,[],[f266,f10])).
0.07/0.34	tff(f308,plain,(
0.07/0.34	  ( ! [X4:$int,X5:$int] : (~$less($sum(X4,X5),sK1($sum(-1,sK0))) | $sum(X4,$sum(1,X5)) != sK0 | $sum(-1,sK0) = sK0) ) | ~spl2_19),
0.07/0.34	  inference(resolution,[],[f266,f105])).
0.07/0.34	tff(f309,plain,(
0.07/0.34	  ( ! [X6:$int,X7:$int] : (~$less($sum(X6,X7),$sum(-1,sK0)) | $sum(X6,$sum(X7,1)) != sK1($sum(-1,sK0)) | $sum(-1,sK0) = sK0) ) | ~spl2_19),
0.07/0.34	  inference(resolution,[],[f266,f47])).
0.07/0.34	tff(f310,plain,(
0.07/0.34	  ~$less($sum(-1,sK0),sK1($sum(-1,sK0))) | (~spl2_17 | ~spl2_19)),
0.07/0.34	  inference(evaluation,[],[f298])).
0.07/0.34	tff(f311,plain,(
0.07/0.34	  $less($sum(-1,sK0),$sum(1,sK0)) | ~spl2_19),
0.07/0.34	  inference(forward_demodulation,[],[f303,f3])).
0.07/0.34	tff(f316,plain,(
0.07/0.34	  spl2_20 <=> $less($sum(-1,sK0),$sum(1,sK0))),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_20])])).
0.07/0.34	tff(f317,plain,(
0.07/0.34	  $less($sum(-1,sK0),$sum(1,sK0)) | ~spl2_20),
0.07/0.34	  inference(avatar_component_clause,[],[f316])).
0.07/0.34	tff(f318,plain,(
0.07/0.34	  spl2_20 | spl2_19),
0.07/0.34	  inference(avatar_split_clause,[],[f311,f265,f316])).
0.07/0.34	tff(f323,plain,(
0.07/0.34	  spl2_22 <=> $less($sum(-1,sK0),sK0)),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_22])])).
0.07/0.34	tff(f324,plain,(
0.07/0.34	  $less($sum(-1,sK0),sK0) | ~spl2_22),
0.07/0.34	  inference(avatar_component_clause,[],[f323])).
0.07/0.34	tff(f325,plain,(
0.07/0.34	  spl2_22 | spl2_17 | spl2_19),
0.07/0.34	  inference(avatar_split_clause,[],[f302,f265,f259,f323])).
0.07/0.34	tff(f326,plain,(
0.07/0.34	  spl2_22 | spl2_17 | spl2_19),
0.07/0.34	  inference(avatar_split_clause,[],[f301,f265,f259,f323])).
0.07/0.34	tff(f331,plain,(
0.07/0.34	  spl2_25 <=> sK0 != sK1($sum(-1,sK0))),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_25])])).
0.07/0.34	tff(f333,plain,(
0.07/0.34	  ~spl2_25 | ~spl2_10 | spl2_17 | spl2_19),
0.07/0.34	  inference(avatar_split_clause,[],[f300,f265,f259,f210,f331])).
0.07/0.34	tff(f338,plain,(
0.07/0.34	  spl2_27 <=> ~$less($sum(-1,sK0),sK1($sum(-1,sK0)))),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_27])])).
0.07/0.34	tff(f340,plain,(
0.07/0.34	  ~spl2_27 | spl2_17 | spl2_19),
0.07/0.34	  inference(avatar_split_clause,[],[f299,f265,f259,f338])).
0.07/0.34	tff(f341,plain,(
0.07/0.34	  ~spl2_27 | spl2_17 | spl2_19),
0.07/0.34	  inference(avatar_split_clause,[],[f310,f265,f259,f338])).
0.07/0.34	tff(f342,plain,(
0.07/0.34	  ~$less($sum(-1,sK0),sK1($sum(-1,sK0))) | (~spl2_17 | ~spl2_19)),
0.07/0.34	  inference(forward_demodulation,[],[f297,f13])).
0.07/0.34	tff(f343,plain,(
0.07/0.34	  ~spl2_27 | spl2_17 | spl2_19),
0.07/0.34	  inference(avatar_split_clause,[],[f342,f265,f259,f338])).
0.07/0.34	tff(f348,plain,(
0.07/0.34	  spl2_29 <=> $sum(-1,sK0) != sK1(sK0)),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_29])])).
0.07/0.34	tff(f351,plain,(
0.07/0.34	  spl2_30 <=> ! [X2 : $int] : (~$less(sK0,X2) | sK0 != X2)),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_30])])).
0.07/0.34	tff(f353,plain,(
0.07/0.34	  ~spl2_29 | spl2_30 | spl2_19),
0.07/0.34	  inference(avatar_split_clause,[],[f305,f265,f351,f348])).
0.07/0.34	tff(f354,plain,(
0.07/0.34	  spl2_16 | spl2_22 | spl2_19),
0.07/0.34	  inference(avatar_split_clause,[],[f307,f265,f323,f262])).
0.07/0.34	tff(f356,plain,(
0.07/0.34	  spl2_32 <=> ! [X5 : $int,X4 : $int] : (~$less($sum(X4,X5),sK1($sum(-1,sK0))) | $sum(X4,$sum(1,X5)) != sK0)),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_32])])).
0.07/0.34	tff(f358,plain,(
0.07/0.34	  spl2_16 | spl2_32 | spl2_19),
0.07/0.34	  inference(avatar_split_clause,[],[f308,f265,f356,f262])).
0.07/0.34	tff(f360,plain,(
0.07/0.34	  spl2_34 <=> ! [X7 : $int,X6 : $int] : (~$less($sum(X6,X7),$sum(-1,sK0)) | $sum(X6,$sum(X7,1)) != sK1($sum(-1,sK0)))),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_34])])).
0.07/0.34	tff(f362,plain,(
0.07/0.34	  spl2_16 | spl2_34 | spl2_19),
0.07/0.34	  inference(avatar_split_clause,[],[f309,f265,f360,f262])).
0.07/0.34	tff(f384,plain,(
0.07/0.34	  ~$less(sK0,$sum($sum(-1,sK0),1)) | ~spl2_22),
0.07/0.34	  inference(unit_resulting_resolution,[],[f324,f14])).
0.07/0.34	tff(f389,plain,(
0.07/0.34	  ( ! [X10:$int,X11:$int] : ($sum(X10,$sum(X11,1)) != sK1($sum($sum(-1,sK0),1)) | $sum($sum(-1,sK0),1) = sK0 | ~$less($sum(X10,X11),$sum($sum(-1,sK0),1))) ) | ~spl2_22),
0.07/0.34	  inference(resolution,[],[f324,f93])).
0.07/0.34	tff(f397,plain,(
0.07/0.34	  ~$less(sK0,$sum(1,$sum(-1,sK0))) | ~spl2_22),
0.07/0.34	  inference(forward_demodulation,[],[f384,f3])).
0.07/0.34	tff(f402,plain,(
0.07/0.34	  spl2_37 <=> ~$less(sK0,$sum(1,$sum(-1,sK0)))),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_37])])).
0.07/0.34	tff(f404,plain,(
0.07/0.34	  ~spl2_37 | ~spl2_22),
0.07/0.34	  inference(avatar_split_clause,[],[f397,f323,f402])).
0.07/0.34	tff(f406,plain,(
0.07/0.34	  ( ! [X10:$int,X11:$int] : ($sum(X10,$sum(X11,1)) != sK1($sum(1,$sum(-1,sK0))) | $sum($sum(-1,sK0),1) = sK0 | ~$less($sum(X10,X11),$sum($sum(-1,sK0),1))) ) | ~spl2_22),
0.07/0.34	  inference(forward_demodulation,[],[f389,f3])).
0.07/0.34	tff(f407,plain,(
0.07/0.34	  ( ! [X10:$int,X11:$int] : ($sum(1,$sum(-1,sK0)) = sK0 | $sum(X10,$sum(X11,1)) != sK1($sum(1,$sum(-1,sK0))) | ~$less($sum(X10,X11),$sum($sum(-1,sK0),1))) ) | ~spl2_22),
0.07/0.34	  inference(forward_demodulation,[],[f406,f3])).
0.07/0.34	tff(f408,plain,(
0.07/0.34	  ( ! [X10:$int,X11:$int] : (~$less($sum(X10,X11),$sum(1,$sum(-1,sK0))) | $sum(1,$sum(-1,sK0)) = sK0 | $sum(X10,$sum(X11,1)) != sK1($sum(1,$sum(-1,sK0)))) ) | ~spl2_22),
0.07/0.34	  inference(forward_demodulation,[],[f407,f3])).
0.07/0.34	tff(f413,plain,(
0.07/0.34	  spl2_38 <=> $sum(1,$sum(-1,sK0)) = sK0),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_38])])).
0.07/0.34	tff(f414,plain,(
0.07/0.34	  $sum(1,$sum(-1,sK0)) = sK0 | ~spl2_38),
0.07/0.34	  inference(avatar_component_clause,[],[f413])).
0.07/0.34	tff(f416,plain,(
0.07/0.34	  spl2_40 <=> ! [X11 : $int,X10 : $int] : (~$less($sum(X10,X11),$sum(1,$sum(-1,sK0))) | $sum(X10,$sum(X11,1)) != sK1($sum(1,$sum(-1,sK0))))),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_40])])).
0.07/0.34	tff(f418,plain,(
0.07/0.34	  spl2_38 | spl2_40 | ~spl2_22),
0.07/0.34	  inference(avatar_split_clause,[],[f408,f323,f416,f413])).
0.07/0.34	tff(f452,plain,(
0.07/0.34	  ~$less($sum(1,sK0),$sum(-1,sK0)) | ~spl2_20),
0.07/0.34	  inference(unit_resulting_resolution,[],[f8,f317,f9])).
0.07/0.34	tff(f453,plain,(
0.07/0.34	  ~$less($sum(1,sK0),$sum(-1,sK0)) | ~spl2_20),
0.07/0.34	  inference(unit_resulting_resolution,[],[f8,f317,f9])).
0.07/0.34	tff(f455,plain,(
0.07/0.34	  ~$less($sum(1,sK0),$sum($sum(-1,sK0),1)) | ~spl2_20),
0.07/0.34	  inference(unit_resulting_resolution,[],[f317,f14])).
0.07/0.34	tff(f456,plain,(
0.07/0.34	  ( ! [X2:$int,X0:$int,X1:$int] : (~$less($sum(X0,$sum(X1,X2)),$sum(-1,sK0)) | $sum(X0,$sum(X1,$sum(X2,1))) != sK1($sum(-1,sK0)) | $less(sK0,$sum(1,sK0)) | $sum(1,sK0) = sK0) ) | ~spl2_20),
0.07/0.34	  inference(resolution,[],[f317,f141])).
0.07/0.34	tff(f457,plain,(
0.07/0.34	  ~$less($sum(1,sK0),$sum(1,$sum(-1,sK0))) | ~spl2_20),
0.07/0.34	  inference(forward_demodulation,[],[f455,f3])).
0.07/0.34	tff(f458,plain,(
0.07/0.34	  ~$less($sum(1,sK0),sK0) | (~spl2_20 | ~spl2_38)),
0.07/0.34	  inference(forward_demodulation,[],[f457,f414])).
0.07/0.34	tff(f463,plain,(
0.07/0.34	  spl2_43 <=> ~$less($sum(1,sK0),sK0)),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_43])])).
0.07/0.34	tff(f464,plain,(
0.07/0.34	  ~$less($sum(1,sK0),sK0) | ~spl2_43),
0.07/0.34	  inference(avatar_component_clause,[],[f463])).
0.07/0.34	tff(f465,plain,(
0.07/0.34	  ~spl2_43 | ~spl2_20 | ~spl2_38),
0.07/0.34	  inference(avatar_split_clause,[],[f458,f413,f316,f463])).
0.07/0.34	tff(f472,plain,(
0.07/0.34	  spl2_45 <=> ~$less($sum(1,sK0),$sum(-1,sK0))),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_45])])).
0.07/0.34	tff(f473,plain,(
0.07/0.34	  ~$less($sum(1,sK0),$sum(-1,sK0)) | ~spl2_45),
0.07/0.34	  inference(avatar_component_clause,[],[f472])).
0.07/0.34	tff(f474,plain,(
0.07/0.34	  ~spl2_45 | ~spl2_20),
0.07/0.34	  inference(avatar_split_clause,[],[f453,f316,f472])).
0.07/0.34	tff(f475,plain,(
0.07/0.34	  ~spl2_45 | ~spl2_20),
0.07/0.34	  inference(avatar_split_clause,[],[f452,f316,f472])).
0.07/0.34	tff(f480,plain,(
0.07/0.34	  spl2_46 <=> $sum(1,sK0) = sK0),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_46])])).
0.07/0.34	tff(f486,plain,(
0.07/0.34	  spl2_48 <=> $less(sK0,$sum(1,sK0))),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_48])])).
0.07/0.34	tff(f489,plain,(
0.07/0.34	  spl2_50 <=> ! [X1 : $int,X0 : $int,X2 : $int] : (~$less($sum(X0,$sum(X1,X2)),$sum(-1,sK0)) | $sum(X0,$sum(X1,$sum(X2,1))) != sK1($sum(-1,sK0)))),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_50])])).
0.07/0.34	tff(f491,plain,(
0.07/0.34	  spl2_46 | spl2_48 | spl2_50 | ~spl2_20),
0.07/0.34	  inference(avatar_split_clause,[],[f456,f316,f489,f486,f480])).
0.07/0.34	tff(f503,plain,(
0.07/0.34	  $less(sK0,$sum($sum(1,sK0),1)) | ~spl2_43),
0.07/0.34	  inference(unit_resulting_resolution,[],[f464,f12])).
0.07/0.34	tff(f509,plain,(
0.07/0.34	  $less(sK0,$sum(1,$sum(1,sK0))) | ~spl2_43),
0.07/0.34	  inference(forward_demodulation,[],[f503,f3])).
0.07/0.34	tff(f514,plain,(
0.07/0.34	  spl2_52 <=> $less(sK0,$sum(1,$sum(1,sK0)))),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_52])])).
0.07/0.34	tff(f515,plain,(
0.07/0.34	  $less(sK0,$sum(1,$sum(1,sK0))) | ~spl2_52),
0.07/0.34	  inference(avatar_component_clause,[],[f514])).
0.07/0.34	tff(f516,plain,(
0.07/0.34	  spl2_52 | spl2_43),
0.07/0.34	  inference(avatar_split_clause,[],[f509,f463,f514])).
0.07/0.34	tff(f595,plain,(
0.07/0.34	  $sum(1,sK0) != sK1($sum(-1,sK0)) | (~spl2_20 | ~spl2_22 | ~spl2_38)),
0.07/0.34	  inference(unit_resulting_resolution,[],[f324,f317,f414,f35])).
0.07/0.34	tff(f618,plain,(
0.07/0.34	  spl2_55 <=> $sum(1,sK0) != sK1($sum(-1,sK0))),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_55])])).
0.07/0.34	tff(f620,plain,(
0.07/0.34	  ~spl2_55 | ~spl2_20 | ~spl2_22 | ~spl2_38),
0.07/0.34	  inference(avatar_split_clause,[],[f595,f413,f323,f316,f618])).
0.07/0.34	tff(f654,plain,(
0.07/0.34	  $less($sum(-1,sK0),$sum($sum(1,sK0),1)) | ~spl2_45),
0.07/0.34	  inference(unit_resulting_resolution,[],[f473,f12])).
0.07/0.34	tff(f657,plain,(
0.07/0.34	  ( ! [X2:$int] : (~$less($sum(1,sK0),X2) | $sum(-1,sK0) != sK1($sum(1,sK0)) | sK0 != X2) ) | ~spl2_45),
0.07/0.34	  inference(resolution,[],[f473,f22])).
0.07/0.34	tff(f660,plain,(
0.07/0.34	  $less($sum(-1,sK0),$sum(1,$sum(1,sK0))) | ~spl2_45),
0.07/0.34	  inference(forward_demodulation,[],[f654,f3])).
0.07/0.34	tff(f665,plain,(
0.07/0.34	  spl2_56 <=> $less($sum(-1,sK0),$sum(1,$sum(1,sK0)))),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_56])])).
0.07/0.34	tff(f667,plain,(
0.07/0.34	  spl2_56 | spl2_45),
0.07/0.34	  inference(avatar_split_clause,[],[f660,f472,f665])).
0.07/0.34	tff(f672,plain,(
0.07/0.34	  spl2_59 <=> $sum(-1,sK0) != sK1($sum(1,sK0))),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_59])])).
0.07/0.34	tff(f675,plain,(
0.07/0.34	  spl2_60 <=> ! [X2 : $int] : (~$less($sum(1,sK0),X2) | sK0 != X2)),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_60])])).
0.07/0.34	tff(f677,plain,(
0.07/0.34	  ~spl2_59 | spl2_60 | spl2_45),
0.07/0.34	  inference(avatar_split_clause,[],[f657,f472,f675,f672])).
0.07/0.34	tff(f700,plain,(
0.07/0.34	  ~$less($sum(1,$sum(1,sK0)),$sum(-1,sK0)) | (~spl2_19 | ~spl2_52)),
0.07/0.34	  inference(unit_resulting_resolution,[],[f266,f515,f9])).
0.07/0.34	tff(f701,plain,(
0.07/0.34	  ~$less($sum(1,$sum(1,sK0)),sK0) | ~spl2_52),
0.07/0.34	  inference(unit_resulting_resolution,[],[f8,f515,f9])).
0.07/0.34	tff(f703,plain,(
0.07/0.34	  ~$less($sum(1,$sum(1,sK0)),sK0) | ~spl2_52),
0.07/0.34	  inference(unit_resulting_resolution,[],[f8,f515,f9])).
0.07/0.34	tff(f705,plain,(
0.07/0.34	  ~$less($sum(1,$sum(1,sK0)),$sum(sK0,1)) | ~spl2_52),
0.07/0.34	  inference(unit_resulting_resolution,[],[f515,f14])).
0.07/0.34	tff(f707,plain,(
0.07/0.34	  ~$less($sum(1,$sum(1,sK0)),$sum(1,sK0)) | ~spl2_52),
0.07/0.34	  inference(forward_demodulation,[],[f705,f3])).
0.07/0.34	tff(f712,plain,(
0.07/0.34	  spl2_63 <=> ~$less($sum(1,$sum(1,sK0)),$sum(1,sK0))),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_63])])).
0.07/0.34	tff(f714,plain,(
0.07/0.34	  ~spl2_63 | ~spl2_52),
0.07/0.34	  inference(avatar_split_clause,[],[f707,f514,f712])).
0.07/0.34	tff(f721,plain,(
0.07/0.34	  spl2_65 <=> ~$less($sum(1,$sum(1,sK0)),sK0)),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_65])])).
0.07/0.34	tff(f722,plain,(
0.07/0.34	  ~$less($sum(1,$sum(1,sK0)),sK0) | ~spl2_65),
0.07/0.34	  inference(avatar_component_clause,[],[f721])).
0.07/0.34	tff(f723,plain,(
0.07/0.34	  ~spl2_65 | ~spl2_52),
0.07/0.34	  inference(avatar_split_clause,[],[f703,f514,f721])).
0.07/0.34	tff(f724,plain,(
0.07/0.34	  ~spl2_65 | ~spl2_52),
0.07/0.34	  inference(avatar_split_clause,[],[f701,f514,f721])).
0.07/0.34	tff(f729,plain,(
0.07/0.34	  spl2_67 <=> ~$less($sum(1,$sum(1,sK0)),$sum(-1,sK0))),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_67])])).
0.07/0.34	tff(f731,plain,(
0.07/0.34	  ~spl2_67 | spl2_19 | ~spl2_52),
0.07/0.34	  inference(avatar_split_clause,[],[f700,f514,f265,f729])).
0.07/0.34	tff(f763,plain,(
0.07/0.34	  $less(sK0,$sum($sum(1,$sum(1,sK0)),1)) | ~spl2_65),
0.07/0.34	  inference(unit_resulting_resolution,[],[f722,f12])).
0.07/0.34	tff(f769,plain,(
0.07/0.34	  $less(sK0,$sum(1,$sum(1,$sum(1,sK0)))) | ~spl2_65),
0.07/0.34	  inference(forward_demodulation,[],[f763,f3])).
0.07/0.34	tff(f774,plain,(
0.07/0.34	  spl2_68 <=> $less(sK0,$sum(1,$sum(1,$sum(1,sK0))))),
0.07/0.34	  introduced(avatar_definition,[new_symbols(naming,[spl2_68])])).
0.07/0.34	tff(f776,plain,(
0.07/0.34	  spl2_68 | spl2_65),
0.07/0.34	  inference(avatar_split_clause,[],[f769,f721,f774])).
0.07/0.34	tff(f822,plain,(
0.07/0.34	  sK0 != sK0 | (~spl2_12 | ~spl2_22)),
0.07/0.34	  inference(unit_resulting_resolution,[],[f324,f215])).
0.07/0.34	tff(f826,plain,(
0.07/0.34	  $false | (~spl2_12 | ~spl2_22)),
0.07/0.34	  inference(trivial_inequality_removal,[],[f822])).
0.07/0.34	tff(f827,plain,(
0.07/0.34	  ~spl2_12 | ~spl2_22),
0.07/0.34	  inference(avatar_contradiction_clause,[],[f826])).
0.07/0.34	tff(f830,plain,(
0.07/0.34	  $false),
0.07/0.34	  inference(avatar_sat_refutation,[],[f68,f79,f212,f219,f270,f318,f325,f326,f333,f340,f341,f343,f353,f354,f358,f362,f404,f418,f465,f474,f475,f491,f516,f620,f667,f677,f714,f723,f724,f731,f776,f827])).
0.07/0.34	% SZS output end Proof for theBenchmark
0.07/0.34	% ------------------------------
0.07/0.34	% Version: Vampire 4.2.2 (commit 552c234 on 2018-07-02 14:53:33 +0100)
0.07/0.34	% Termination reason: Refutation
0.07/0.34	
0.07/0.34	% Memory used [KB]: 5884
0.07/0.34	% Time elapsed: 0.072 s
0.07/0.34	% ------------------------------
0.07/0.34	% ------------------------------
0.07/0.34	% Success in time 0.106 s
0.07/0.34	EOF