0.00/0.09	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.08/0.09	% Command    : tptp2X_and_run_prover9 %d %s
0.09/0.29	% Computer   : n025.cluster.edu
0.09/0.29	% Model      : x86_64 x86_64
0.09/0.29	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.09/0.29	% Memory     : 8042.1875MB
0.09/0.29	% OS         : Linux 3.10.0-693.el7.x86_64
0.09/0.29	% CPULimit   : 1200
0.09/0.29	% DateTime   : Tue Jul 13 16:39:12 EDT 2021
0.09/0.29	% CPUTime    : 
0.77/1.06	============================== Prover9 ===============================
0.77/1.06	Prover9 (32) version 2009-11A, November 2009.
0.77/1.06	Process 19589 was started by sandbox2 on n025.cluster.edu,
0.77/1.06	Tue Jul 13 16:39:13 2021
0.77/1.06	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1200 -f /tmp/Prover9_19435_n025.cluster.edu".
0.77/1.06	============================== end of head ===========================
0.77/1.06	
0.77/1.06	============================== INPUT =================================
0.77/1.06	
0.77/1.06	% Reading from file /tmp/Prover9_19435_n025.cluster.edu
0.77/1.06	
0.77/1.06	set(prolog_style_variables).
0.77/1.06	set(auto2).
0.77/1.06	    % set(auto2) -> set(auto).
0.77/1.06	    % set(auto) -> set(auto_inference).
0.77/1.06	    % set(auto) -> set(auto_setup).
0.77/1.06	    % set(auto_setup) -> set(predicate_elim).
0.77/1.06	    % set(auto_setup) -> assign(eq_defs, unfold).
0.77/1.06	    % set(auto) -> set(auto_limits).
0.77/1.06	    % set(auto_limits) -> assign(max_weight, "100.000").
0.77/1.06	    % set(auto_limits) -> assign(sos_limit, 20000).
0.77/1.06	    % set(auto) -> set(auto_denials).
0.77/1.06	    % set(auto) -> set(auto_process).
0.77/1.06	    % set(auto2) -> assign(new_constants, 1).
0.77/1.06	    % set(auto2) -> assign(fold_denial_max, 3).
0.77/1.06	    % set(auto2) -> assign(max_weight, "200.000").
0.77/1.06	    % set(auto2) -> assign(max_hours, 1).
0.77/1.06	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.77/1.06	    % set(auto2) -> assign(max_seconds, 0).
0.77/1.06	    % set(auto2) -> assign(max_minutes, 5).
0.77/1.06	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.77/1.06	    % set(auto2) -> set(sort_initial_sos).
0.77/1.06	    % set(auto2) -> assign(sos_limit, -1).
0.77/1.06	    % set(auto2) -> assign(lrs_ticks, 3000).
0.77/1.06	    % set(auto2) -> assign(max_megs, 400).
0.77/1.06	    % set(auto2) -> assign(stats, some).
0.77/1.06	    % set(auto2) -> clear(echo_input).
0.77/1.06	    % set(auto2) -> set(quiet).
0.77/1.06	    % set(auto2) -> clear(print_initial_clauses).
0.77/1.06	    % set(auto2) -> clear(print_given).
0.77/1.06	assign(lrs_ticks,-1).
0.77/1.06	assign(sos_limit,10000).
0.77/1.06	assign(order,kbo).
0.77/1.06	set(lex_order_vars).
0.77/1.06	clear(print_given).
0.77/1.06	
0.77/1.06	% formulas(sos).  % not echoed (96 formulas)
0.77/1.06	
0.77/1.06	============================== end of input ==========================
0.77/1.06	
0.77/1.06	% From the command line: assign(max_seconds, 1200).
0.77/1.06	
0.77/1.06	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.77/1.06	
0.77/1.06	% Formulas that are not ordinary clauses:
0.77/1.06	1 (all W0 (W0 = slcrc0 <-> aSet0(W0) & -(exists W1 aElementOf0(W1,W0)))) # label(mDefEmp) # label(definition) # label(non_clause).  [assumption].
0.77/1.06	2 (all W0 (aSet0(W0) -> (all W1 (aSubsetOf0(W1,W0) <-> aSet0(W1) & (all W2 (aElementOf0(W2,W1) -> aElementOf0(W2,W0))))))) # label(mDefSub) # label(definition) # label(non_clause).  [assumption].
0.77/1.06	3 (all W0 all W1 (aSet0(W0) & aElement0(W1) -> (all W2 (W2 = sdtpldt0(W0,W1) <-> aSet0(W2) & (all W3 (aElementOf0(W3,W2) <-> aElement0(W3) & (aElementOf0(W3,W0) | W3 = W1))))))) # label(mDefCons) # label(definition) # label(non_clause).  [assumption].
0.77/1.06	4 (all W0 all W1 (aSet0(W0) & aElement0(W1) -> (all W2 (W2 = sdtmndt0(W0,W1) <-> aSet0(W2) & (all W3 (aElementOf0(W3,W2) <-> aElement0(W3) & aElementOf0(W3,W0) & W3 != W1)))))) # label(mDefDiff) # label(definition) # label(non_clause).  [assumption].
0.77/1.06	5 (all W0 (aSubsetOf0(W0,szNzAzT0) & W0 != slcrc0 -> (all W1 (W1 = szmzizndt0(W0) <-> aElementOf0(W1,W0) & (all W2 (aElementOf0(W2,W0) -> sdtlseqdt0(W1,W2))))))) # label(mDefMin) # label(definition) # label(non_clause).  [assumption].
0.77/1.06	6 (all W0 (aSubsetOf0(W0,szNzAzT0) & isFinite0(W0) & W0 != slcrc0 -> (all W1 (W1 = szmzazxdt0(W0) <-> aElementOf0(W1,W0) & (all W2 (aElementOf0(W2,W0) -> sdtlseqdt0(W2,W1))))))) # label(mDefMax) # label(definition) # label(non_clause).  [assumption].
0.77/1.06	7 (all W0 (aElementOf0(W0,szNzAzT0) -> (all W1 (W1 = slbdtrb0(W0) <-> aSet0(W1) & (all W2 (aElementOf0(W2,W1) <-> aElementOf0(W2,szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W2),W0))))))) # label(mDefSeg) # label(definition) # label(non_clause).  [assumption].
0.77/1.06	8 (all W0 all W1 (aSet0(W0) & aElementOf0(W1,szNzAzT0) -> (all W2 (W2 = slbdtsldtrb0(W0,W1) <-> aSet0(W2) & (all W3 (aElementOf0(W3,W2) <-> aSubsetOf0(W3,W0) & sbrdtbr0(W3) = W1)))))) # label(mDefSel) # label(definition) # label(non_clause).  [assumption].
0.77/1.06	9 (all W0 all W1 (aFunction0(W0) & aElement0(W1) -> (all W2 (W2 = sdtlbdtrb0(W0,W1) <-> aSet0(W2) & (all W3 (aElementOf0(W3,W2) <-> aElementOf0(W3,szDzozmdt0(W0)) & sdtlpdtrp0(W0,W3) = W1)))))) # label(mDefPtt) # label(definition) # label(non_clause).  [assumption].
0.77/1.07	10 (all W0 (aFunction0(W0) -> (all W1 (aSubsetOf0(W1,szDzozmdt0(W0)) -> (all W2 (W2 = sdtlcdtrc0(W0,W1) <-> aSet0(W2) & (all W3 (aElementOf0(W3,W2) <-> (exists W4 (aElementOf0(W4,W1) & sdtlpdtrp0(W0,W4) = W3)))))))))) # label(mDefSImg) # label(definition) # label(non_clause).  [assumption].
0.77/1.07	11 (all W0 (aFunction0(W0) -> (all W1 (aSubsetOf0(W1,szDzozmdt0(W0)) -> (all W2 (W2 = sdtexdt0(W0,W1) <-> aFunction0(W2) & szDzozmdt0(W2) = W1 & (all W3 (aElementOf0(W3,W1) -> sdtlpdtrp0(W2,W3) = sdtlpdtrp0(W0,W3))))))))) # label(mDefRst) # label(definition) # label(non_clause).  [assumption].
0.77/1.07	12 (all W0 (aFunction0(W0) -> (all W1 (aElementOf0(W1,szDzozmdt0(W0)) -> aElement0(sdtlpdtrp0(W0,W1)))))) # label(mImgElm) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	13 (all W0 (aElementOf0(W0,szNzAzT0) -> sz00 != szszuzczcdt0(W0) & aElementOf0(szszuzczcdt0(W0),szNzAzT0))) # label(mSuccNum) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	14 (all W0 all W1 (aElementOf0(W1,szNzAzT0) & aSet0(W0) -> (sdtlseqdt0(W1,sbrdtbr0(W0)) & isFinite0(W0) -> (exists W2 (aSubsetOf0(W2,W0) & W1 = sbrdtbr0(W2)))))) # label(mCardSubEx) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	15 (all W0 (isFinite0(W0) & aSet0(W0) -> (all W1 (aElementOf0(W1,szNzAzT0) -> isFinite0(slbdtsldtrb0(W0,W1)))))) # label(mSelFSet) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	16 (all W0 (aSet0(W0) -> (isFinite0(W0) <-> aElementOf0(sbrdtbr0(W0),szNzAzT0)))) # label(mCardNum) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	17 (all W0 (aSet0(W0) -> (all W1 (isFinite0(W0) & aSubsetOf0(W1,W0) -> sdtlseqdt0(sbrdtbr0(W1),sbrdtbr0(W0)))))) # label(mCardSub) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	18 (all W0 (aElement0(W0) -> $T)) # label(mElmSort) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	19 (all W0 (aElementOf0(W0,szNzAzT0) -> sdtlseqdt0(W0,szszuzczcdt0(W0)))) # label(mLessSucc) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	20 (all W0 (aElementOf0(W0,szNzAzT0) -> W0 = sbrdtbr0(slbdtrb0(W0)))) # label(mCardSeg) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	21 (all W0 (aSet0(W0) -> aSubsetOf0(W0,W0))) # label(mSubRefl) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	22 (all W0 (aElementOf0(W0,szNzAzT0) -> (isCountable0(sdtlpdtrp0(xN,W0)) & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) -> aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))))) # label(m__3623_AndRHS_AndRHS_AndLHS) # label(hypothesis) # label(non_clause).  [assumption].
0.77/1.07	23 (all W0 all W1 (aElementOf0(W1,szNzAzT0) & aElementOf0(W0,szNzAzT0) -> (iLess0(W0,W1) -> $T))) # label(mIHSort) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	24 (all W0 (aSet0(W0) -> $T)) # label(mSetSort) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	25 (all W0 (aFunction0(W0) -> aSet0(szDzozmdt0(W0)))) # label(mDomSet) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	26 (all W0 (aElementOf0(W0,szNzAzT0) -> isFinite0(slbdtrb0(W0)))) # label(mSegFin) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	27 (all W0 (aElement0(W0) -> (all W1 (isCountable0(W1) & aSet0(W1) -> isCountable0(sdtmndt0(W1,W0)))))) # label(mCDiffSet) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	28 (all W0 all W1 all W2 (aSet0(W0) & aSet0(W1) & aSet0(W2) -> (aSubsetOf0(W1,W2) & aSubsetOf0(W0,W1) -> aSubsetOf0(W0,W2)))) # label(mSubTrans) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	29 (all W0 (aSet0(W0) -> (isFinite0(W0) -> $T))) # label(mFinRel) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	30 (all W0 (aSet0(W0) -> (all W1 (aElementOf0(W1,W0) -> W0 = sdtpldt0(sdtmndt0(W0,W1),W1))))) # label(mConsDiff) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	31 (all W0 (aSet0(W0) -> (isCountable0(W0) -> $T))) # label(mCntRel) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	32 (all W0 (aElementOf0(W0,szNzAzT0) -> W0 = sz00 | (exists W1 (szszuzczcdt0(W1) = W0 & aElementOf0(W1,szNzAzT0))))) # label(mNatExtra) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	33 (all W0 all W1 (aElementOf0(W1,szNzAzT0) & aElementOf0(W0,szNzAzT0) -> sdtlseqdt0(W0,W1) | sdtlseqdt0(szszuzczcdt0(W1),W0))) # label(mLessTotal) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	34 (all W0 all W1 (aElementOf0(W0,szNzAzT0) & aElementOf0(W1,szNzAzT0) -> (sdtlseqdt0(W1,W0) -> (iLess0(W0,xi) -> aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)))))) # label(m__3754) # label(hypothesis) # label(non_clause).  [assumption].
0.77/1.07	35 (all W0 (aElementOf0(W0,szNzAzT0) -> (all W1 (isCountable0(W1) & aSubsetOf0(W1,szNzAzT0) -> (all W2 (aFunction0(W2) & szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) & aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) -> (iLess0(W0,xK) -> (exists W3 ((exists W4 (aSubsetOf0(W4,W1) & isCountable0(W4) & (all W5 (aElementOf0(W5,slbdtsldtrb0(W4,W0)) -> sdtlpdtrp0(W2,W5) = W3)))) & aElementOf0(W3,xT)))))))))) # label(m__3398) # label(hypothesis) # label(non_clause).  [assumption].
0.77/1.07	36 (all W0 (aSet0(W0) -> (all W1 (aElementOf0(W1,W0) -> aElement0(W1))))) # label(mEOfElem) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	37 (all W0 (isCountable0(W0) & aSet0(W0) -> W0 != slcrc0)) # label(mCountNFin_01) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	38 (all W0 (aElementOf0(W0,szNzAzT0) -> iLess0(W0,szszuzczcdt0(W0)))) # label(mIH) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	39 (all W0 (aElementOf0(W0,szNzAzT0) -> szszuzczcdt0(W0) != W0)) # label(mNatNSucc) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	40 (all W0 (aSet0(W0) & isCountable0(W0) -> -isFinite0(W0))) # label(mCountNFin) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	41 (all W0 (aFunction0(W0) -> (isCountable0(szDzozmdt0(W0)) & isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) -> aElement0(szDzizrdt0(W0)) & isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0)))))) # label(mDirichlet) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	42 (all W0 all W1 (aSet0(W0) & aSet0(W1) -> (aSubsetOf0(W0,W1) & aSubsetOf0(W1,W0) -> W0 = W1))) # label(mSubASymm) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	43 (all W0 (aElementOf0(W0,szNzAzT0) -> sdtlseqdt0(sz00,W0))) # label(mZeroLess) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	44 (all W0 all W1 (aElementOf0(W1,szNzAzT0) & aElementOf0(W0,szNzAzT0) -> (sdtlseqdt0(W0,W1) <-> aSubsetOf0(slbdtrb0(W0),slbdtrb0(W1))))) # label(mSegLess) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	45 (all W0 (aSet0(W0) -> (slcrc0 = W0 <-> sz00 = sbrdtbr0(W0)))) # label(mCardEmpty) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	46 (all W0 (aElementOf0(W0,szNzAzT0) -> -sdtlseqdt0(szszuzczcdt0(W0),sz00))) # label(mNoScLessZr) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	47 (all W0 (aFunction0(W0) -> (all W1 (isCountable0(W1) & aSubsetOf0(W1,szDzozmdt0(W0)) -> ((all W2 all W3 (aElementOf0(W2,szDzozmdt0(W0)) & aElementOf0(W3,szDzozmdt0(W0)) & W2 != W3 -> sdtlpdtrp0(W0,W3) != sdtlpdtrp0(W0,W2))) -> isCountable0(sdtlcdtrc0(W0,W1))))))) # label(mImgCount) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	48 (all W0 all W1 (aElementOf0(W1,szNzAzT0) & aElementOf0(W0,szNzAzT0) -> (W1 = W0 | aElementOf0(W0,slbdtrb0(W1)) <-> aElementOf0(W0,slbdtrb0(szszuzczcdt0(W1)))))) # label(mSegSucc) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	49 (all W0 all W1 (aElementOf0(W1,szNzAzT0) & aSet0(W0) -> (all W2 (isFinite0(W2) & aSubsetOf0(W2,slbdtsldtrb0(W0,W1)) -> (exists W3 (isFinite0(W3) & aSubsetOf0(W2,slbdtsldtrb0(W3,W1)) & aSubsetOf0(W3,W0))))))) # label(mSelExtra) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	50 (all W0 all W1 (aSubsetOf0(W0,szNzAzT0) & W1 != slcrc0 & W0 != slcrc0 & aSubsetOf0(W1,szNzAzT0) -> (aElementOf0(szmzizndt0(W0),W1) & aElementOf0(szmzizndt0(W1),W0) -> szmzizndt0(W0) = szmzizndt0(W1)))) # label(mMinMin) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	51 (all W0 (aElement0(W0) -> (all W1 (isFinite0(W1) & aSet0(W1) -> isFinite0(sdtpldt0(W1,W0)))))) # label(mFConsSet) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	52 (all W0 (isFinite0(W0) & aSet0(W0) -> (all W1 (aElement0(W1) -> (-aElementOf0(W1,W0) -> sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0))))))) # label(mCardCons) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	53 (all W0 (aElement0(W0) -> (all W1 (aSet0(W1) & isCountable0(W1) -> isCountable0(sdtpldt0(W1,W0)))))) # label(mCConsSet) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	54 (all W0 all W1 (aElement0(W0) & aSet0(W1) -> (-aElementOf0(W0,W1) -> W1 = sdtmndt0(sdtpldt0(W1,W0),W0)))) # label(mDiffCons) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	55 (all W0 (aFunction0(W0) -> $T)) # label(mFunSort) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	56 (all W0 (aSet0(W0) -> aElement0(sbrdtbr0(W0)))) # label(mCardS) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	57 (all W0 (aElementOf0(W0,szNzAzT0) -> sdtlseqdt0(W0,W0))) # label(mLessRefl) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	58 (all W0 all W1 all W2 (aElementOf0(W0,szNzAzT0) & aElementOf0(W2,szNzAzT0) & aElementOf0(W1,szNzAzT0) -> (sdtlseqdt0(W1,W2) & sdtlseqdt0(W0,W1) -> sdtlseqdt0(W0,W2)))) # label(mLessTrans) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	59 (all W0 (aElement0(W0) -> (all W1 (aSet0(W1) & isFinite0(W1) -> isFinite0(sdtmndt0(W1,W0)))))) # label(mFDiffSet) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	60 (all W0 (aSet0(W0) & -isFinite0(W0) -> (all W1 (aElementOf0(W1,szNzAzT0) -> slbdtsldtrb0(W0,W1) != slcrc0)))) # label(mSelNSet) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	61 (all W0 all W1 (aElementOf0(W1,szNzAzT0) & aElementOf0(W0,szNzAzT0) -> (szszuzczcdt0(W0) = szszuzczcdt0(W1) -> W1 = W0))) # label(mSuccEquSucc) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	62 (all W0 all W1 (aElement0(W1) & aFunction0(W0) -> aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)))) # label(mPttSet) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	63 (all W0 (aSubsetOf0(W0,szNzAzT0) & isFinite0(W0) -> (exists W1 (aSubsetOf0(W0,slbdtrb0(W1)) & aElementOf0(W1,szNzAzT0))))) # label(mFinSubSeg) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	64 (all W0 (aSet0(W0) & isCountable0(W0) -> (all W1 (aElementOf0(W1,szNzAzT0) & W1 != sz00 -> isCountable0(slbdtsldtrb0(W0,W1)))))) # label(mSelCSet) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	65 (all W0 all W1 (aElementOf0(W1,szNzAzT0) & aElementOf0(W0,szNzAzT0) -> (sdtlseqdt0(W0,W1) -> $T))) # label(mLessRel) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	66 sdtlseqdt0(xj,xi) & (exists W0 (xi = szszuzczcdt0(W0) & aElementOf0(W0,szNzAzT0))) -> (sdtlseqdt0(xj,xi) -> aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))) # label(m__3786_02) # label(hypothesis) # label(non_clause).  [assumption].
0.77/1.07	67 (all W0 (aSet0(W0) -> (all W1 (isFinite0(W0) & aElementOf0(W1,W0) -> szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0))))) # label(mCardDiff) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	68 (all W0 all W1 (aElementOf0(W0,szNzAzT0) & aElementOf0(W1,szNzAzT0) -> (sdtlseqdt0(W0,W1) & sdtlseqdt0(W1,W0) -> W1 = W0))) # label(mLessASymm) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	69 (all W0 (aElementOf0(W0,szNzAzT0) -> (all W1 all W2 (aSet0(W1) & W0 != sz00 & aSet0(W2) -> (slcrc0 != slbdtsldtrb0(W1,W0) & aSubsetOf0(slbdtsldtrb0(W1,W0),slbdtsldtrb0(W2,W0)) -> aSubsetOf0(W1,W2)))))) # label(mSelSub) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	70 (all W0 (aFunction0(W0) -> (all W1 (aElementOf0(W1,szDzozmdt0(W0)) -> aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))))))) # label(mImgRng) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	71 (all W0 (aSet0(W0) & isFinite0(W0) -> (all W1 (aSubsetOf0(W1,W0) -> isFinite0(W1))))) # label(mSubFSet) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	72 (all W0 (aElementOf0(W0,szNzAzT0) -> isCountable0(sdtlpdtrp0(xN,W0)) & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0))) # label(m__3671) # label(hypothesis) # label(non_clause).  [assumption].
0.77/1.07	73 (all W0 all W1 (aElementOf0(W1,szNzAzT0) & aElementOf0(W0,szNzAzT0) -> (sdtlseqdt0(W0,W1) <-> sdtlseqdt0(szszuzczcdt0(W0),szszuzczcdt0(W1))))) # label(mSuccLess) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	74 -(sdtlseqdt0(xj,xi) -> aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))) # label(m__) # label(negated_conjecture) # label(non_clause).  [assumption].
16.74/17.14	
16.74/17.14	============================== end of process non-clausal formulas ===
16.74/17.14	
16.74/17.14	============================== PROCESS INITIAL CLAUSES ===============
16.74/17.14	
16.74/17.14	============================== PREDICATE ELIMINATION =================
16.74/17.14	
16.74/17.14	============================== end predicate elimination =============
16.74/17.14	
16.74/17.14	Auto_denials:  (non-Horn, no changes).
16.74/17.14	
16.74/17.14	Term ordering decisions:
16.74/17.14	Function symbol KB weights:  szNzAzT0=1. slcrc0=1. xN=1. sz00=1. xT=1. xK=1. xi=1. xS=1. xc=1. xj=1. xk=1. sdtlpdtrp0=1. slbdtsldtrb0=1. sdtlcdtrc0=1. sdtmndt0=1. sdtpldt0=1. sdtlbdtrb0=1. sdtexdt0=1. f2=1. f5=1. f6=1. f7=1. f14=1. f18=1. f19=1. szDzozmdt0=1. szszuzczcdt0=1. slbdtrb0=1. sbrdtbr0=1. szmzizndt0=1. szmzazxdt0=1. szDzizrdt0=1. f1=1. f15=1. f21=1. f3=1. f4=1. f8=1. f9=1. f11=1. f12=1. f13=1. f16=1. f17=1. f20=1. f10=1.
16.74/17.14	
16.74/17.14	============================== end of process initial clauses ========
16.74/17.14	
16.74/17.14	============================== CLAUSES FOR SEARCH ====================
16.74/17.14	
16.74/17.14	============================== end of clauses for search =============
16.74/17.14	
16.74/17.14	============================== SEARCH ================================
16.74/17.14	
16.74/17.14	% Starting search at 0.03 seconds.
16.74/17.14	
16.74/17.14	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 84 (0.00 of 0.30 sec).
16.74/17.14	
16.74/17.14	Low Water (keep): wt=27.000, iters=3385
16.74/17.14	
16.74/17.14	Low Water (keep): wt=26.000, iters=3440
16.74/17.14	
16.74/17.14	Low Water (keep): wt=23.000, iters=3408
16.74/17.14	
16.74/17.14	Low Water (keep): wt=22.000, iters=3474
16.74/17.14	
16.74/17.14	Low Water (keep): wt=21.000, iters=3425
16.74/17.14	
16.74/17.14	Low Water (keep): wt=19.000, iters=3342
16.74/17.14	
16.74/17.14	Low Water (keep): wt=17.000, iters=3486
16.74/17.14	
16.74/17.14	Low Water (keep): wt=16.000, iters=3448
16.74/17.14	
16.74/17.14	Low Water (keep): wt=15.000, iters=3566
16.74/17.14	
16.74/17.14	Low Water (keep): wt=14.000, iters=3353
16.74/17.14	
16.74/17.14	Low Water (keep): wt=13.000, iters=3361
16.74/17.14	
16.74/17.14	Low Water (keep): wt=12.000, iters=3342
16.74/17.14	
16.74/17.14	Low Water (keep): wt=11.000, iters=3336
16.74/17.14	
16.74/17.14	Low Water (keep): wt=10.000, iters=3335
16.74/17.14	
16.74/17.14	Low Water (keep): wt=9.000, iters=3348
16.74/17.14	
16.74/17.14	Low Water (displace): id=4145, wt=42.000
16.74/17.14	
16.74/17.14	Low Water (displace): id=1763, wt=41.000
16.74/17.14	
16.74/17.14	Low Water (displace): id=2205, wt=40.000
16.74/17.14	
16.74/17.14	Low Water (displace): id=1764, wt=39.000
16.74/17.14	
16.74/17.14	Low Water (displace): id=3399, wt=37.000
16.74/17.14	
16.74/17.14	Low Water (displace): id=15245, wt=21.000
16.74/17.14	
16.74/17.14	Low Water (displace): id=15098, wt=20.000
16.74/17.14	
16.74/17.14	Low Water (displace): id=15426, wt=8.000
16.74/17.14	
16.74/17.14	Low Water (keep): wt=8.000, iters=3335
16.74/17.14	
16.74/17.14	============================== PROOF =================================
16.74/17.14	% SZS status Theorem
16.74/17.14	% SZS output start Refutation
16.74/17.14	
16.74/17.14	% Proof 1 at 15.67 (+ 0.34) seconds.
16.74/17.14	% Length of proof is 58.
16.74/17.14	% Level of proof is 11.
16.74/17.14	% Maximum clause weight is 18.000.
16.74/17.14	% Given clauses 10339.
16.74/17.14	
16.74/17.14	2 (all W0 (aSet0(W0) -> (all W1 (aSubsetOf0(W1,W0) <-> aSet0(W1) & (all W2 (aElementOf0(W2,W1) -> aElementOf0(W2,W0))))))) # label(mDefSub) # label(definition) # label(non_clause).  [assumption].
16.74/17.14	7 (all W0 (aElementOf0(W0,szNzAzT0) -> (all W1 (W1 = slbdtrb0(W0) <-> aSet0(W1) & (all W2 (aElementOf0(W2,W1) <-> aElementOf0(W2,szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W2),W0))))))) # label(mDefSeg) # label(definition) # label(non_clause).  [assumption].
16.74/17.14	13 (all W0 (aElementOf0(W0,szNzAzT0) -> sz00 != szszuzczcdt0(W0) & aElementOf0(szszuzczcdt0(W0),szNzAzT0))) # label(mSuccNum) # label(axiom) # label(non_clause).  [assumption].
16.74/17.14	19 (all W0 (aElementOf0(W0,szNzAzT0) -> sdtlseqdt0(W0,szszuzczcdt0(W0)))) # label(mLessSucc) # label(axiom) # label(non_clause).  [assumption].
16.74/17.14	21 (all W0 (aSet0(W0) -> aSubsetOf0(W0,W0))) # label(mSubRefl) # label(axiom) # label(non_clause).  [assumption].
16.74/17.14	32 (all W0 (aElementOf0(W0,szNzAzT0) -> W0 = sz00 | (exists W1 (szszuzczcdt0(W1) = W0 & aElementOf0(W1,szNzAzT0))))) # label(mNatExtra) # label(axiom) # label(non_clause).  [assumption].
16.74/17.14	43 (all W0 (aElementOf0(W0,szNzAzT0) -> sdtlseqdt0(sz00,W0))) # label(mZeroLess) # label(axiom) # label(non_clause).  [assumption].
16.74/17.14	48 (all W0 all W1 (aElementOf0(W1,szNzAzT0) & aElementOf0(W0,szNzAzT0) -> (W1 = W0 | aElementOf0(W0,slbdtrb0(W1)) <-> aElementOf0(W0,slbdtrb0(szszuzczcdt0(W1)))))) # label(mSegSucc) # label(axiom) # label(non_clause).  [assumption].
16.74/17.14	58 (all W0 all W1 all W2 (aElementOf0(W0,szNzAzT0) & aElementOf0(W2,szNzAzT0) & aElementOf0(W1,szNzAzT0) -> (sdtlseqdt0(W1,W2) & sdtlseqdt0(W0,W1) -> sdtlseqdt0(W0,W2)))) # label(mLessTrans) # label(axiom) # label(non_clause).  [assumption].
16.74/17.14	66 sdtlseqdt0(xj,xi) & (exists W0 (xi = szszuzczcdt0(W0) & aElementOf0(W0,szNzAzT0))) -> (sdtlseqdt0(xj,xi) -> aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))) # label(m__3786_02) # label(hypothesis) # label(non_clause).  [assumption].
16.74/17.14	68 (all W0 all W1 (aElementOf0(W0,szNzAzT0) & aElementOf0(W1,szNzAzT0) -> (sdtlseqdt0(W0,W1) & sdtlseqdt0(W1,W0) -> W1 = W0))) # label(mLessASymm) # label(axiom) # label(non_clause).  [assumption].
16.74/17.14	73 (all W0 all W1 (aElementOf0(W1,szNzAzT0) & aElementOf0(W0,szNzAzT0) -> (sdtlseqdt0(W0,W1) <-> sdtlseqdt0(szszuzczcdt0(W0),szszuzczcdt0(W1))))) # label(mSuccLess) # label(axiom) # label(non_clause).  [assumption].
16.74/17.14	74 -(sdtlseqdt0(xj,xi) -> aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))) # label(m__) # label(negated_conjecture) # label(non_clause).  [assumption].
16.74/17.14	78 -aSet0(A) | -aSubsetOf0(B,A) | aSet0(B) # label(mDefSub) # label(definition).  [clausify(2)].
16.74/17.14	110 -aElementOf0(A,szNzAzT0) | slbdtrb0(A) != B | -aElementOf0(C,B) | sdtlseqdt0(szszuzczcdt0(C),A) # label(mDefSeg) # label(definition).  [clausify(7)].
16.74/17.14	111 -aElementOf0(A,szNzAzT0) | slbdtrb0(A) != B | aElementOf0(C,B) | -aElementOf0(C,szNzAzT0) | -sdtlseqdt0(szszuzczcdt0(C),A) # label(mDefSeg) # label(definition).  [clausify(7)].
16.74/17.14	145 -aElementOf0(A,szNzAzT0) | aElementOf0(szszuzczcdt0(A),szNzAzT0) # label(mSuccNum) # label(axiom).  [clausify(13)].
16.74/17.14	154 -aElementOf0(A,szNzAzT0) | sdtlseqdt0(A,szszuzczcdt0(A)) # label(mLessSucc) # label(axiom).  [clausify(19)].
16.74/17.14	156 -aSet0(A) | aSubsetOf0(A,A) # label(mSubRefl) # label(axiom).  [clausify(21)].
16.74/17.14	158 sdtlpdtrp0(xN,sz00) = xS # label(m__3623_AndRHS_AndLHS) # label(hypothesis).  [assumption].
16.74/17.14	169 -aElementOf0(A,szNzAzT0) | sz00 = A | szszuzczcdt0(f15(A)) = A # label(mNatExtra) # label(axiom).  [clausify(32)].
16.74/17.14	170 -aElementOf0(A,szNzAzT0) | sz00 = A | aElementOf0(f15(A),szNzAzT0) # label(mNatExtra) # label(axiom).  [clausify(32)].
16.74/17.14	179 aElementOf0(xi,szNzAzT0) # label(m__3786_AndLHS) # label(hypothesis).  [assumption].
16.74/17.14	180 aElementOf0(xj,szNzAzT0) # label(m__3786_AndRHS) # label(hypothesis).  [assumption].
16.74/17.14	189 -aElementOf0(A,szNzAzT0) | sdtlseqdt0(sz00,A) # label(mZeroLess) # label(axiom).  [clausify(43)].
16.74/17.14	200 aElementOf0(sz00,szNzAzT0) # label(mZeroNum) # label(axiom).  [assumption].
16.74/17.14	203 -aElementOf0(A,szNzAzT0) | -aElementOf0(B,szNzAzT0) | A = B | aElementOf0(B,slbdtrb0(A)) | -aElementOf0(B,slbdtrb0(szszuzczcdt0(A))) # label(mSegSucc) # label(axiom).  [clausify(48)].
16.74/17.14	215 -aElementOf0(A,szNzAzT0) | -aElementOf0(B,szNzAzT0) | -aElementOf0(C,szNzAzT0) | -sdtlseqdt0(C,B) | -sdtlseqdt0(A,C) | sdtlseqdt0(A,B) # label(mLessTrans) # label(axiom).  [clausify(58)].
16.74/17.14	223 aSubsetOf0(xS,szNzAzT0) # label(m__3435_AndLHS) # label(hypothesis).  [assumption].
16.74/17.14	225 -sdtlseqdt0(xj,xi) | szszuzczcdt0(A) != xi | -aElementOf0(A,szNzAzT0) | aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) # label(m__3786_02) # label(hypothesis).  [clausify(66)].
16.74/17.14	228 -aElementOf0(A,szNzAzT0) | -aElementOf0(B,szNzAzT0) | -sdtlseqdt0(A,B) | -sdtlseqdt0(B,A) | B = A # label(mLessASymm) # label(axiom).  [clausify(68)].
16.74/17.14	231 aSet0(szNzAzT0) # label(mNATSet_AndRHS) # label(axiom).  [assumption].
16.74/17.14	240 -aElementOf0(A,szNzAzT0) | -aElementOf0(B,szNzAzT0) | -sdtlseqdt0(B,A) | sdtlseqdt0(szszuzczcdt0(B),szszuzczcdt0(A)) # label(mSuccLess) # label(axiom).  [clausify(73)].
16.74/17.14	244 sdtlseqdt0(xj,xi) # label(m__) # label(negated_conjecture).  [clausify(74)].
16.74/17.14	245 -aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) # label(m__) # label(negated_conjecture).  [clausify(74)].
16.74/17.14	274 szszuzczcdt0(A) != xi | -aElementOf0(A,szNzAzT0).  [back_unit_del(225),unit_del(a,244),unit_del(d,245)].
16.74/17.14	344 xi = sz00 | aElementOf0(f15(xi),szNzAzT0).  [resolve(179,a,170,a),flip(a)].
16.74/17.14	345 xi = sz00 | szszuzczcdt0(f15(xi)) = xi.  [resolve(179,a,169,a),flip(a)].
16.74/17.14	386 aElementOf0(szszuzczcdt0(xj),szNzAzT0).  [resolve(180,a,145,a)].
16.74/17.14	400 slbdtrb0(xj) != A | -aElementOf0(B,A) | sdtlseqdt0(szszuzczcdt0(B),xj).  [resolve(180,a,110,a)].
16.74/17.14	419 sdtlseqdt0(sz00,xj).  [resolve(189,a,180,a)].
16.74/17.15	473 sdtlseqdt0(sz00,szszuzczcdt0(sz00)).  [resolve(200,a,154,a)].
16.74/17.15	475 aElementOf0(szszuzczcdt0(sz00),szNzAzT0).  [resolve(200,a,145,a)].
16.74/17.15	545 aSet0(xS).  [resolve(223,a,78,b),unit_del(a,231)].
16.74/17.15	620 -aElementOf0(A,szNzAzT0) | -sdtlseqdt0(A,xj) | sdtlseqdt0(A,xi).  [resolve(244,a,215,d),unit_del(b,179),unit_del(c,180)].
16.74/17.15	643 szszuzczcdt0(sz00) != xi.  [resolve(274,b,200,a)].
16.74/17.15	722 aSubsetOf0(xS,xS).  [resolve(545,a,156,a)].
16.74/17.15	750 sdtlseqdt0(szszuzczcdt0(sz00),szszuzczcdt0(xj)).  [resolve(419,a,240,c),unit_del(a,180),unit_del(b,200)].
16.74/17.15	2155 slbdtrb0(szszuzczcdt0(xj)) != A | aElementOf0(sz00,A).  [resolve(750,a,111,e),unit_del(a,386),unit_del(d,200)].
16.74/17.15	4248 xi = sz00 | szszuzczcdt0(f15(xi)) != xi.  [resolve(344,b,274,b)].
16.74/17.15	28438 aElementOf0(sz00,slbdtrb0(szszuzczcdt0(xj))).  [xx_res(2155,a)].
16.74/17.15	28439 xj = sz00 | aElementOf0(sz00,slbdtrb0(xj)).  [resolve(28438,a,203,e),unit_del(a,180),unit_del(b,200)].
16.74/17.15	28444 xj = sz00 | sdtlseqdt0(szszuzczcdt0(sz00),xj).  [resolve(28439,b,400,b),xx(b)].
16.74/17.15	28447 xj = sz00 | sdtlseqdt0(szszuzczcdt0(sz00),xi).  [resolve(28444,b,620,b),unit_del(b,475)].
16.74/17.15	28448 xj = sz00 | -sdtlseqdt0(xi,szszuzczcdt0(sz00)).  [resolve(28447,b,228,d),unit_del(b,179),unit_del(c,475),unit_del(e,643)].
16.74/17.15	29046 xi = sz00.  [resolve(4248,b,345,b),merge(b)].
16.74/17.15	29057 xj = sz00.  [back_rewrite(28448),rewrite([29046(4)]),unit_del(b,473)].
16.74/17.15	29139 $F.  [back_rewrite(245),rewrite([29046(2),158(3),29057(3),158(4)]),unit_del(a,722)].
16.74/17.15	
16.74/17.15	% SZS output end Refutation
16.74/17.15	============================== end of proof ==========================
16.74/17.15	
16.74/17.15	============================== STATISTICS ============================
16.74/17.15	
16.74/17.15	Given=10339. Generated=312678. Kept=29058. proofs=1.
16.74/17.15	Usable=7452. Sos=7367. Demods=127. Limbo=93, Disabled=14312. Hints=0.
16.74/17.15	Megabytes=24.62.
16.74/17.15	User_CPU=15.67, System_CPU=0.34, Wall_clock=16.
16.74/17.15	
16.74/17.15	============================== end of statistics =====================
16.74/17.15	
16.74/17.15	============================== end of search =========================
16.74/17.15	
16.74/17.15	THEOREM PROVED
16.74/17.15	% SZS status Theorem
16.74/17.15	
16.74/17.15	Exiting with 1 proof.
16.74/17.15	
16.74/17.15	Process 19589 exit (max_proofs) Tue Jul 13 16:39:29 2021
16.74/17.15	Prover9 interrupted
16.74/17.15	EOF