0.06/0.09	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.06/0.09	% Command  : tptp2X_and_run_prover9 %d %s
0.09/0.29	% Computer : n008.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 : 960
0.09/0.29	% WCLimit  : 120
0.09/0.29	% DateTime : Tue Aug  9 02:25:38 EDT 2022
0.09/0.29	% CPUTime  : 
0.88/1.16	============================== Prover9 ===============================
0.88/1.16	Prover9 (32) version 2009-11A, November 2009.
0.88/1.16	Process 7275 was started by sandbox on n008.cluster.edu,
0.88/1.16	Tue Aug  9 02:25:39 2022
0.88/1.16	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 960 -f /tmp/Prover9_7118_n008.cluster.edu".
0.88/1.16	============================== end of head ===========================
0.88/1.16	
0.88/1.16	============================== INPUT =================================
0.88/1.16	
0.88/1.16	% Reading from file /tmp/Prover9_7118_n008.cluster.edu
0.88/1.16	
0.88/1.16	set(prolog_style_variables).
0.88/1.16	set(auto2).
0.88/1.16	    % set(auto2) -> set(auto).
0.88/1.16	    % set(auto) -> set(auto_inference).
0.88/1.16	    % set(auto) -> set(auto_setup).
0.88/1.16	    % set(auto_setup) -> set(predicate_elim).
0.88/1.16	    % set(auto_setup) -> assign(eq_defs, unfold).
0.88/1.16	    % set(auto) -> set(auto_limits).
0.88/1.16	    % set(auto_limits) -> assign(max_weight, "100.000").
0.88/1.16	    % set(auto_limits) -> assign(sos_limit, 20000).
0.88/1.16	    % set(auto) -> set(auto_denials).
0.88/1.16	    % set(auto) -> set(auto_process).
0.88/1.16	    % set(auto2) -> assign(new_constants, 1).
0.88/1.16	    % set(auto2) -> assign(fold_denial_max, 3).
0.88/1.16	    % set(auto2) -> assign(max_weight, "200.000").
0.88/1.16	    % set(auto2) -> assign(max_hours, 1).
0.88/1.16	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.88/1.16	    % set(auto2) -> assign(max_seconds, 0).
0.88/1.16	    % set(auto2) -> assign(max_minutes, 5).
0.88/1.16	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.88/1.16	    % set(auto2) -> set(sort_initial_sos).
0.88/1.16	    % set(auto2) -> assign(sos_limit, -1).
0.88/1.16	    % set(auto2) -> assign(lrs_ticks, 3000).
0.88/1.16	    % set(auto2) -> assign(max_megs, 400).
0.88/1.16	    % set(auto2) -> assign(stats, some).
0.88/1.16	    % set(auto2) -> clear(echo_input).
0.88/1.16	    % set(auto2) -> set(quiet).
0.88/1.16	    % set(auto2) -> clear(print_initial_clauses).
0.88/1.16	    % set(auto2) -> clear(print_given).
0.88/1.16	assign(lrs_ticks,-1).
0.88/1.16	assign(sos_limit,10000).
0.88/1.16	assign(order,kbo).
0.88/1.16	set(lex_order_vars).
0.88/1.16	clear(print_given).
0.88/1.16	
0.88/1.16	% formulas(sos).  % not echoed (161 formulas)
0.88/1.16	
0.88/1.16	============================== end of input ==========================
0.88/1.16	
0.88/1.16	% From the command line: assign(max_seconds, 960).
0.88/1.16	
0.88/1.16	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.88/1.16	
0.88/1.16	% Formulas that are not ordinary clauses:
0.88/1.16	1 (all W0 (W0 = slcrc0 <-> aSet0(W0) & -(exists W1 aElementOf0(W1,W0)))) # label(mDefEmp) # label(definition) # label(non_clause).  [assumption].
0.88/1.16	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].
0.88/1.16	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].
0.88/1.16	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].
0.88/1.16	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].
0.88/1.16	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].
0.88/1.16	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].
0.88/1.16	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].
0.88/1.16	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].
0.88/1.16	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].
0.88/1.16	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].
0.88/1.16	12 (all W0 all W1 (aElementOf0(W0,szNzAzT0) & aElementOf0(W1,szNzAzT0) -> (sdtlseqdt0(W0,W1) -> $T))) # label(mLessRel) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	13 (all W0 (aSet0(W0) & isCountable0(W0) -> -isFinite0(W0))) # label(mCountNFin) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	14 (all W0 (aElementOf0(W0,sdtlcdtrc0(xd,szDzozmdt0(xd))) <-> (exists W1 (aElementOf0(W1,szDzozmdt0(xd)) & sdtlpdtrp0(xd,W1) = W0)))) # label(m__4758_AndLHS) # label(hypothesis) # label(non_clause).  [assumption].
0.88/1.16	15 (all W0 (aElementOf0(W0,sdtlcdtrc0(xd,szDzozmdt0(xd))) -> aElementOf0(W0,xT))) # label(m__4758_AndRHS_AndLHS) # label(hypothesis) # label(non_clause).  [assumption].
0.88/1.16	16 (all W0 (aSet0(W0) -> (all W1 (aElementOf0(W1,W0) -> sdtpldt0(sdtmndt0(W0,W1),W1) = W0)))) # label(mConsDiff) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	17 (all W0 (aElement0(W0) -> $T)) # label(mElmSort) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	18 (all W0 all W1 (aSet0(W0) & aElementOf0(W1,szNzAzT0) -> (isFinite0(W0) & sdtlseqdt0(W1,sbrdtbr0(W0)) -> (exists W2 (W1 = sbrdtbr0(W2) & aSubsetOf0(W2,W0)))))) # label(mCardSubEx) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	19 (all W0 all W1 (aFunction0(W0) & aElement0(W1) -> aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)))) # label(mPttSet) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	20 (all W0 (aFunction0(W0) -> $T)) # label(mFunSort) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	21 (all W0 (aSet0(W0) & -isFinite0(W0) -> (all W1 (aElementOf0(W1,szNzAzT0) -> slcrc0 != slbdtsldtrb0(W0,W1))))) # label(mSelNSet) # label(axiom) # label(non_clause).  [assumption].
0.88/1.16	22 (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].
0.88/1.16	23 (all W0 (aElementOf0(W0,xP) -> aElementOf0(W0,xO))) # label(m__5208_AndRHS) # label(hypothesis) # label(non_clause).  [assumption].
0.88/1.16	24 (all W0 (aElementOf0(W0,szNzAzT0) -> (all W1 ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) & (all W2 (aElementOf0(W2,sdtlpdtrp0(xN,W0)) -> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2))) -> ((all W2 (aElementOf0(W2,sdtlpdtrp0(xN,W0)) & szmzizndt0(sdtlpdtrp0(xN,W0)) != W2 & aElement0(W2) <-> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))))) & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) -> aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) | xk = sbrdtbr0(W1) & (aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) | (all W2 (aElementOf0(W2,W1) -> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))))))) & aSet0(W1) -> aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) & (all W2 (aElementOf0(W2,sdtlpdtrp0(xN,W0)) -> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2))) & aSet0(sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) & (all W2 (aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) -> aElementOf0(W2,xS))) & aSubsetOf0(sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))),xS) & aElementOf0(sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))),slbdtsldtrb0(xS,xK)) & sbrdtbr0(sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) = xK & (all W2 ((szmzizndt0(sdtlpdtrp0(xN,W0)) = W2 | aElementOf0(W2,W1)) & aElement0(W2) <-> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))))))))) # label(m__3965) # label(hypothesis) # label(non_clause).  [assumption].
2.73/3.00	25 (all W0 (aElementOf0(W0,xQ) -> sdtlseqdt0(xp,W0))) # label(m__5147_AndRHS_AndLHS) # label(hypothesis) # label(non_clause).  [assumption].
2.73/3.00	26 (all W0 all W1 (aElementOf0(W1,szNzAzT0) & aElementOf0(W0,szNzAzT0) -> (sdtlseqdt0(W1,W0) & sdtlseqdt0(W0,W1) -> W1 = W0))) # label(mLessASymm) # label(axiom) # label(non_clause).  [assumption].
2.73/3.00	27 (all W0 all W1 (aElementOf0(W0,szNzAzT0) & aElementOf0(W1,szNzAzT0) -> sdtlseqdt0(W0,W1) | sdtlseqdt0(szszuzczcdt0(W1),W0))) # label(mLessTotal) # label(axiom) # label(non_clause).  [assumption].
2.73/3.00	28 (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].
2.73/3.00	29 (all W0 (aSet0(W0) -> (all W1 (aElementOf0(W1,W0) -> aElement0(W1))))) # label(mEOfElem) # label(axiom) # label(non_clause).  [assumption].
2.73/3.00	30 (all W0 all W1 (aElementOf0(W0,szNzAzT0) & aElementOf0(W1,szNzAzT0) -> (szszuzczcdt0(W0) = szszuzczcdt0(W1) -> W1 = W0))) # label(mSuccEquSucc) # label(axiom) # label(non_clause).  [assumption].
2.73/3.00	31 (all W0 (aElementOf0(W0,szNzAzT0) -> (all W1 ((aSubsetOf0(W1,szNzAzT0) | (all W2 (aElementOf0(W2,W1) -> aElementOf0(W2,szNzAzT0))) & aSet0(W1)) & isCountable0(W1) -> (all W2 (aFunction0(W2) & ((all W3 (aElementOf0(W3,sdtlcdtrc0(W2,szDzozmdt0(W2))) <-> (exists W4 (aElementOf0(W4,szDzozmdt0(W2)) & sdtlpdtrp0(W2,W4) = W3)))) & aSet0(sdtlcdtrc0(W2,szDzozmdt0(W2))) -> (all W3 (aElementOf0(W3,sdtlcdtrc0(W2,szDzozmdt0(W2))) -> aElementOf0(W3,xT))) | aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)) & (szDzozmdt0(W2) = slbdtsldtrb0(W1,W0) | (all W3 ((aElementOf0(W3,szDzozmdt0(W2)) -> W0 = sbrdtbr0(W3) & (aSubsetOf0(W3,W1) | (all W4 (aElementOf0(W4,W3) -> aElementOf0(W4,W1))) & aSet0(W3))) & (sbrdtbr0(W3) = W0 & aSubsetOf0(W3,W1) & (all W4 (aElementOf0(W4,W3) -> aElementOf0(W4,W1))) & aSet0(W3) -> aElementOf0(W3,szDzozmdt0(W2)))))) -> (iLess0(W0,xK) -> (exists W3 ((exists W4 ((all W5 (sbrdtbr0(W5) = W0 & (aSet0(W5) & (all W6 (aElementOf0(W6,W5) -> aElementOf0(W6,W4))) | aSubsetOf0(W5,W4)) | aElementOf0(W5,slbdtsldtrb0(W4,W0)) -> sdtlpdtrp0(W2,W5) = W3)) & isCountable0(W4) & aSubsetOf0(W4,W1) & (all W5 (aElementOf0(W5,W4) -> aElementOf0(W5,W1))) & aSet0(W4))) & aElementOf0(W3,xT)))))))))) # label(m__3398) # label(hypothesis) # label(non_clause).  [assumption].
2.73/3.00	32 (all W0 ((sbrdtbr0(W0) = xK & (aSet0(W0) & (all W1 (aElementOf0(W1,W0) -> aElementOf0(W1,xS))) | aSubsetOf0(W0,xS)) -> aElementOf0(W0,szDzozmdt0(xc))) & (aElementOf0(W0,szDzozmdt0(xc)) -> (all W1 (aElementOf0(W1,W0) -> aElementOf0(W1,xS))) & xK = sbrdtbr0(W0) & aSubsetOf0(W0,xS) & aSet0(W0)))) # label(m__3453_AndLHS) # label(hypothesis) # label(non_clause).  [assumption].
2.73/3.00	33 (all W0 (aElementOf0(W0,sdtlcdtrc0(xc,szDzozmdt0(xc))) -> aElementOf0(W0,xT))) # label(m__3453_AndRHS_AndRHS_AndRHS_AndLHS) # label(hypothesis) # label(non_clause).  [assumption].
2.73/3.00	34 (all W0 ((exists W1 (sdtlpdtrp0(xc,W1) = W0 & aElementOf0(W1,szDzozmdt0(xc)))) <-> aElementOf0(W0,sdtlcdtrc0(xc,szDzozmdt0(xc))))) # label(m__3453_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(hypothesis) # label(non_clause).  [assumption].
2.73/3.00	35 (all W0 (aElementOf0(W0,szNzAzT0) -> (all W1 all W2 (aSet0(W2) & sz00 != W0 & aSet0(W1) -> (aSubsetOf0(slbdtsldtrb0(W1,W0),slbdtsldtrb0(W2,W0)) & slcrc0 != slbdtsldtrb0(W1,W0) -> aSubsetOf0(W1,W2)))))) # label(mSelSub) # label(axiom) # label(non_clause).  [assumption].
2.73/3.00	36 (all W0 (aElementOf0(W0,szNzAzT0) -> sz00 = W0 | (exists W1 (szszuzczcdt0(W1) = W0 & aElementOf0(W1,szNzAzT0))))) # label(mNatExtra) # label(axiom) # label(non_clause).  [assumption].
2.73/3.00	37 (all W0 ((exists W1 (sdtlpdtrp0(xe,W1) = W0 & aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd))))) <-> aElementOf0(W0,xO))) # label(m__4891_AndRHS_AndRHS_AndLHS) # label(hypothesis) # label(non_clause).  [assumption].
2.73/3.00	38 (all W0 (aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd))) <-> aElementOf0(W0,szDzozmdt0(xd)) & szDzizrdt0(xd) = sdtlpdtrp0(xd,W0))) # label(m__4891_AndRHS_AndRHS_AndRHS_AndRHS) # label(hypothesis) # label(non_clause).  [assumption].
2.73/3.03	39 (all W0 (aElementOf0(W0,szNzAzT0) -> (exists W1 ((exists W2 (isCountable0(W2) & (all W3 (aSet0(W3) & ((aSubsetOf0(W3,W2) | (all W4 (aElementOf0(W4,W3) -> aElementOf0(W4,W2)))) & sbrdtbr0(W3) = xk | aElementOf0(W3,slbdtsldtrb0(W2,xk))) -> sdtlpdtrp0(sdtlpdtrp0(xC,W0),W3) = W1)) & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) & (all W3 (aElementOf0(W3,W2) -> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))))) & aSet0(W2) & (all W3 (aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) <-> W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) & aElementOf0(W3,sdtlpdtrp0(xN,W0)) & aElement0(W3))) & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) & (all W3 (aElementOf0(W3,sdtlpdtrp0(xN,W0)) -> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)))) & aElementOf0(W1,xT))))) # label(m__4411) # label(hypothesis) # label(non_clause).  [assumption].
2.73/3.03	40 (all W0 all W1 (aElementOf0(W0,szNzAzT0) & aElementOf0(W1,szNzAzT0) -> (aSubsetOf0(slbdtrb0(W0),slbdtrb0(W1)) <-> sdtlseqdt0(W0,W1)))) # label(mSegLess) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	41 (all W0 all W1 all W2 (aSet0(W0) & aSet0(W1) & aSet0(W2) -> (aSubsetOf0(W0,W1) & aSubsetOf0(W1,W2) -> aSubsetOf0(W0,W2)))) # label(mSubTrans) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	42 (all W0 (aFunction0(W0) -> (all W1 (aElementOf0(W1,szDzozmdt0(W0)) -> aElement0(sdtlpdtrp0(W0,W1)))))) # label(mImgElm) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	43 (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].
2.73/3.03	44 (all W0 (aSet0(W0) & isFinite0(W0) -> (all W1 (aElementOf0(W1,szNzAzT0) -> isFinite0(slbdtsldtrb0(W0,W1)))))) # label(mSelFSet) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	45 (all W0 (aElementOf0(W0,szNzAzT0) -> sdtlseqdt0(W0,W0))) # label(mLessRefl) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	46 (all W0 (aSet0(W0) -> (isCountable0(W0) -> $T))) # label(mCntRel) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	47 (all W0 (aSet0(W0) & isCountable0(W0) -> slcrc0 != W0)) # label(mCountNFin_01) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	48 (all W0 (aSet0(W0) -> aElement0(sbrdtbr0(W0)))) # label(mCardS) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	49 (all W0 all W1 (aElementOf0(W1,szNzAzT0) & aSet0(W0) -> (all W2 (aSubsetOf0(W2,slbdtsldtrb0(W0,W1)) & isFinite0(W2) -> (exists W3 (aSubsetOf0(W3,W0) & aSubsetOf0(W2,slbdtsldtrb0(W3,W1)) & isFinite0(W3))))))) # label(mSelExtra) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	50 (all W0 all W1 (aElementOf0(W0,szNzAzT0) & aElementOf0(W1,szNzAzT0) -> (sdtlseqdt0(W1,W0) -> (all W2 (aElementOf0(W2,sdtlpdtrp0(xN,W0)) -> aElementOf0(W2,sdtlpdtrp0(xN,W1)))) & aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))))) # label(m__3754) # label(hypothesis) # label(non_clause).  [assumption].
2.73/3.03	51 (all W0 ((exists W1 (aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd))) & sdtlpdtrp0(xe,W1) = W0)) | aElementOf0(W0,xO) -> (exists W1 (sdtlpdtrp0(xd,W1) = szDzizrdt0(xd) & sdtlpdtrp0(xe,W1) = W0 & aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd))) & aElementOf0(W1,szNzAzT0))))) # label(m__4982) # label(hypothesis) # label(non_clause).  [assumption].
2.73/3.03	52 (all W0 (isFinite0(W0) & aSet0(W0) -> (all W1 (aSubsetOf0(W1,W0) -> isFinite0(W1))))) # label(mSubFSet) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	53 (all W0 (aSet0(W0) -> (sz00 = sbrdtbr0(W0) <-> slcrc0 = W0))) # label(mCardEmpty) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	54 (all W0 (aElementOf0(W0,szNzAzT0) -> (all W1 (isCountable0(W1) & ((all W2 (aElementOf0(W2,sdtlpdtrp0(xN,W0)) -> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) -> (aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) & (all W2 (aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) <-> aElement0(W2) & W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) & aElementOf0(W2,sdtlpdtrp0(xN,W0)))) -> aSet0(W1) & (all W2 (aElementOf0(W2,W1) -> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))))) | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))))) -> (all W2 (aSet0(W2) & (xk = sbrdtbr0(W2) & ((all W3 (aElementOf0(W3,W2) -> aElementOf0(W3,W1))) | aSubsetOf0(W2,W1)) | aElementOf0(W2,slbdtsldtrb0(W1,xk))) -> aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) & (all W3 (aElementOf0(W3,W2) -> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))))) & (all W3 (aElementOf0(W3,sdtlpdtrp0(xN,W0)) & W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) & aElement0(W3) <-> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))))) & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) & (all W3 (aElementOf0(W3,sdtlpdtrp0(xN,W0)) -> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3))))))))) # label(m__4331) # label(hypothesis) # label(non_clause).  [assumption].
2.73/3.03	55 (all W0 (aElementOf0(W0,szNzAzT0) -> sdtlseqdt0(sz00,W0))) # label(mZeroLess) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	56 (all W0 all W1 (aElementOf0(W0,szNzAzT0) & W1 != W0 & aElementOf0(W1,szNzAzT0) -> -(aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) & (all W2 (aElementOf0(W2,sdtlpdtrp0(xN,W0)) -> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2))) -> (all W2 (aElementOf0(W2,sdtlpdtrp0(xN,W1)) -> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W1)) | szmzizndt0(sdtlpdtrp0(xN,W0)) = szmzizndt0(sdtlpdtrp0(xN,W1))))) # label(m__3821) # label(hypothesis) # label(non_clause).  [assumption].
2.73/3.03	57 (all W0 (aElement0(W0) -> (all W1 (isCountable0(W1) & aSet0(W1) -> isCountable0(sdtpldt0(W1,W0)))))) # label(mCConsSet) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	58 (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].
2.73/3.03	59 (all W0 (aFunction0(W0) -> (all W1 (aSubsetOf0(W1,szDzozmdt0(W0)) & isCountable0(W1) -> ((all W2 all W3 (W3 != W2 & aElementOf0(W3,szDzozmdt0(W0)) & aElementOf0(W2,szDzozmdt0(W0)) -> sdtlpdtrp0(W0,W3) != sdtlpdtrp0(W0,W2))) -> isCountable0(sdtlcdtrc0(W0,W1))))))) # label(mImgCount) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	60 (all W0 (aElementOf0(W0,szDzozmdt0(xd)) & szDzizrdt0(xd) = sdtlpdtrp0(xd,W0) <-> aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd))))) # label(m__4854_AndRHS_AndRHS) # label(hypothesis) # label(non_clause).  [assumption].
2.73/3.03	61 (all W0 all W1 (aElementOf0(W0,szNzAzT0) & aElementOf0(W1,szNzAzT0) -> (aElementOf0(W0,slbdtrb0(szszuzczcdt0(W1))) <-> aElementOf0(W0,slbdtrb0(W1)) | W1 = W0))) # label(mSegSucc) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	62 (all W0 (aSet0(W0) -> $T)) # label(mSetSort) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	63 (all W0 (aElementOf0(W0,xQ) -> aElementOf0(W0,xS))) # label(m__5116_AndLHS) # label(hypothesis) # label(non_clause).  [assumption].
2.73/3.03	64 (all W0 (aElementOf0(W0,xQ) -> aElementOf0(W0,xS))) # label(m__5116_AndRHS_AndRHS_AndRHS_AndRHS) # label(hypothesis) # label(non_clause).  [assumption].
2.73/3.03	65 (all W0 (aElement0(W0) -> (all W1 (aSet0(W1) & isFinite0(W1) -> isFinite0(sdtmndt0(W1,W0)))))) # label(mFDiffSet) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	66 (all W0 (aSet0(W0) -> aSubsetOf0(W0,W0))) # label(mSubRefl) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	67 (all W0 (aElementOf0(W0,szNzAzT0) -> (all W1 (((aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) | (all W2 (aElementOf0(W2,W1) -> aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0)))))) & xk = sbrdtbr0(W1) | aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))) & aSet0(W1) -> sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1))))) # label(m__4730_AndLHS) # label(hypothesis) # label(non_clause).  [assumption].
2.73/3.03	68 (all W0 (aElementOf0(W0,xQ) -> aElementOf0(W0,xO))) # label(m__5078_AndRHS_AndRHS_AndRHS_AndRHS) # label(hypothesis) # label(non_clause).  [assumption].
2.73/3.03	69 (all W0 (aElementOf0(W0,szNzAzT0) -> szszuzczcdt0(W0) != W0)) # label(mNatNSucc) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	70 (all W0 (aSet0(W0) -> (isFinite0(W0) <-> aElementOf0(sbrdtbr0(W0),szNzAzT0)))) # label(mCardNum) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	71 (all W0 (aElementOf0(W0,szNzAzT0) -> sdtlseqdt0(W0,szszuzczcdt0(W0)))) # label(mLessSucc) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	72 (all W0 all W1 (aElementOf0(W1,szNzAzT0) & aElementOf0(W0,szNzAzT0) -> (iLess0(W0,W1) -> $T))) # label(mIHSort) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	73 (all W0 (aElementOf0(W0,szNzAzT0) -> aElementOf0(szszuzczcdt0(W0),szNzAzT0) & sz00 != szszuzczcdt0(W0))) # label(mSuccNum) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	74 (all W0 (aFunction0(W0) -> (isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) & isCountable0(szDzozmdt0(W0)) -> aElement0(szDzizrdt0(W0)) & isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0)))))) # label(mDirichlet) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	75 (all W0 (isFinite0(W0) & aSubsetOf0(W0,szNzAzT0) -> (exists W1 (aElementOf0(W1,szNzAzT0) & aSubsetOf0(W0,slbdtrb0(W1)))))) # label(mFinSubSeg) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	76 (all W0 (aElementOf0(W0,szNzAzT0) -> isFinite0(slbdtrb0(W0)))) # label(mSegFin) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	77 (all W0 (aElementOf0(W0,szNzAzT0) -> (((all W1 (aElementOf0(W1,sdtlpdtrp0(xN,W0)) -> aElementOf0(W1,szNzAzT0))) & aSet0(sdtlpdtrp0(xN,W0)) | aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)) & isCountable0(sdtlpdtrp0(xN,W0)) -> (all W1 (aElementOf0(W1,sdtlpdtrp0(xN,W0)) -> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1))) & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) & (all W1 (aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) -> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))))) & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) & (all W1 (szmzizndt0(sdtlpdtrp0(xN,W0)) != W1 & aElementOf0(W1,sdtlpdtrp0(xN,W0)) & aElement0(W1) <-> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))))) & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))))) # label(m__3623_AndRHS_AndRHS_AndLHS) # label(hypothesis) # label(non_clause).  [assumption].
2.73/3.03	78 (all W0 (aElementOf0(W0,szNzAzT0) -> (exists W1 ((all W2 ((aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) | (aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) | (all W3 (aElementOf0(W3,W2) -> aElementOf0(W3,sdtlpdtrp0(xN,szszuzczcdt0(W0)))))) & xk = sbrdtbr0(W2)) & aSet0(W2) -> W1 = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W2))) & aElementOf0(W1,xT))))) # label(m__4618) # label(hypothesis) # label(non_clause).  [assumption].
2.73/3.03	79 (all W0 all W1 (aSet0(W1) & aElement0(W0) -> (-aElementOf0(W0,W1) -> sdtmndt0(sdtpldt0(W1,W0),W0) = W1))) # label(mDiffCons) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	80 (all W0 (aElementOf0(W0,szNzAzT0) -> iLess0(W0,szszuzczcdt0(W0)))) # label(mIH) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	81 (exists W0 (aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd))) & sdtlpdtrp0(xe,W0) = xp)) # label(m__5182) # label(hypothesis) # label(non_clause).  [assumption].
2.73/3.03	82 (all W0 (aElementOf0(W0,xO) -> aElementOf0(W0,xS))) # label(m__4998_AndLHS) # label(hypothesis) # label(non_clause).  [assumption].
2.73/3.03	83 (all W0 (aElementOf0(W0,szNzAzT0) -> aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0)) & szmzizndt0(sdtlpdtrp0(xN,W0)) = sdtlpdtrp0(xe,W0) & (all W1 (aElementOf0(W1,sdtlpdtrp0(xN,W0)) -> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1))))) # label(m__4660_AndRHS_AndLHS) # label(hypothesis) # label(non_clause).  [assumption].
2.73/3.03	84 (all W0 (aSet0(W0) -> (all W1 (isFinite0(W0) & aElementOf0(W1,W0) -> sbrdtbr0(W0) = szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))))))) # label(mCardDiff) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	85 (all W0 (aElementOf0(W0,szNzAzT0) -> W0 = sbrdtbr0(slbdtrb0(W0)))) # label(mCardSeg) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	86 (all W0 all W1 all W2 (aElementOf0(W2,szNzAzT0) & aElementOf0(W1,szNzAzT0) & aElementOf0(W0,szNzAzT0) -> (sdtlseqdt0(W0,W1) & sdtlseqdt0(W1,W2) -> sdtlseqdt0(W0,W2)))) # label(mLessTrans) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	87 (all W0 (aElementOf0(W0,xP) <-> aElementOf0(W0,xQ) & szmzizndt0(xQ) != W0 & aElement0(W0))) # label(m__5164_AndLHS) # label(hypothesis) # label(non_clause).  [assumption].
2.73/3.03	88 (all W0 (aElementOf0(W0,xQ) -> sdtlseqdt0(szmzizndt0(xQ),W0))) # label(m__5164_AndRHS_AndRHS_AndLHS) # label(hypothesis) # label(non_clause).  [assumption].
2.73/3.03	89 (all W0 (aElementOf0(W0,szNzAzT0) -> aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) & (all W1 (aElementOf0(W1,sdtlpdtrp0(xN,W0)) -> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1))) & (all W1 (W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) & aElementOf0(W1,sdtlpdtrp0(xN,W0)) & aElement0(W1) <-> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))))) & (all W1 ((aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) -> (all W2 (aElementOf0(W2,W1) -> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))))) & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) & sbrdtbr0(W1) = xk & aSet0(W1)) & (xk = sbrdtbr0(W1) & (aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) | aSet0(W1) & (all W2 (aElementOf0(W2,W1) -> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))))) -> aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))))) & szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) & (all W1 (aSet0(W1) & ((all W2 (aElementOf0(W2,sdtlpdtrp0(xN,W0)) -> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) -> ((all W2 (aElement0(W2) & szmzizndt0(sdtlpdtrp0(xN,W0)) != W2 & aElementOf0(W2,sdtlpdtrp0(xN,W0)) <-> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))))) & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) -> aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) | (aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) | (all W2 (aElementOf0(W2,W1) -> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))))) & sbrdtbr0(W1) = xk)) -> (all W2 (aElementOf0(W2,sdtlpdtrp0(xN,W0)) -> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2))) & (all W2 ((aElementOf0(W2,W1) | W2 = szmzizndt0(sdtlpdtrp0(xN,W0))) & aElement0(W2) <-> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))))) & sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)))) & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) & aFunction0(sdtlpdtrp0(xC,W0)))) # label(m__4151_AndRHS_AndRHS) # label(hypothesis) # label(non_clause).  [assumption].
2.73/3.03	90 (all W0 (aSet0(W0) -> (all W1 (isFinite0(W0) & aSubsetOf0(W1,W0) -> sdtlseqdt0(sbrdtbr0(W1),sbrdtbr0(W0)))))) # label(mCardSub) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	91 (all W0 (aElement0(W0) -> (all W1 (isCountable0(W1) & aSet0(W1) -> isCountable0(sdtmndt0(W1,W0)))))) # label(mCDiffSet) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	92 (all W0 (aElementOf0(W0,xS) -> aElementOf0(W0,szNzAzT0))) # label(m__3435_AndLHS) # label(hypothesis) # label(non_clause).  [assumption].
2.73/3.03	93 (all W0 (aSet0(W0) -> (isFinite0(W0) -> $T))) # label(mFinRel) # label(axiom) # label(non_clause).  [assumption].
2.73/3.03	94 (all W0 (aElementOf0(W0,xQ) -> aElementOf0(W0,szNzAzT0))) # label(m__5106_AndLHS) # label(hypothesis) # label(non_clause).  [assumption].
2.73/3.03	95 (all W0 all W1 (aSubsetOf0(W0,szNzAzT0) & aSubsetOf0(W1,szNzAzT0) & W0 != slcrc0 & slcrc0 != W1 -> (aElementOf0(szmzizndt0(W0),W1) & aElementOf0(szmzizndt0(W1),W0) -> szmzizndt0(W0) = szmzizndt0(W1)))) # label(mMinMin) # label(axiom) # label(non_clause).  [assumption].
25.73/26.08	96 (all W0 (aElementOf0(W0,szNzAzT0) -> (all W1 (aElementOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,W0),szDzozmdt0(sdtlpdtrp0(xC,W0)))) <-> (exists W2 (W1 = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W2) & aElementOf0(W2,szDzozmdt0(sdtlpdtrp0(xC,W0))))))) & aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,W0),szDzozmdt0(sdtlpdtrp0(xC,W0))),xT) & (all W1 (aElementOf0(W1,sdtlcdtrc0(sdtlpdtrp0(xC,W0),szDzozmdt0(sdtlpdtrp0(xC,W0)))) -> aElementOf0(W1,xT))) & aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,W0),szDzozmdt0(sdtlpdtrp0(xC,W0)))))) # label(m__4182) # label(hypothesis) # label(non_clause).  [assumption].
25.73/26.08	97 (all W0 (aElementOf0(W0,szNzAzT0) -> -sdtlseqdt0(szszuzczcdt0(W0),sz00))) # label(mNoScLessZr) # label(axiom) # label(non_clause).  [assumption].
25.73/26.08	98 (all W0 all W1 (aSet0(W0) & aSet0(W1) -> (aSubsetOf0(W0,W1) & aSubsetOf0(W1,W0) -> W0 = W1))) # label(mSubASymm) # label(axiom) # label(non_clause).  [assumption].
25.73/26.08	99 (all W0 (aFunction0(W0) -> aSet0(szDzozmdt0(W0)))) # label(mDomSet) # label(axiom) # label(non_clause).  [assumption].
25.73/26.08	100 (all W0 (aElementOf0(W0,xP) -> aElementOf0(W0,xQ))) # label(m__5195_AndRHS) # label(hypothesis) # label(non_clause).  [assumption].
25.73/26.08	101 (all W0 (aElementOf0(W0,szNzAzT0) -> isCountable0(sdtlpdtrp0(xN,W0)) & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) & (all W1 (aElementOf0(W1,sdtlpdtrp0(xN,W0)) -> aElementOf0(W1,szNzAzT0))) & aSet0(sdtlpdtrp0(xN,W0)))) # label(m__3671) # label(hypothesis) # label(non_clause).  [assumption].
25.73/26.08	102 (all W0 (aElementOf0(W0,xQ) -> aElementOf0(W0,xO))) # label(m__5093_AndLHS) # label(hypothesis) # label(non_clause).  [assumption].
25.73/26.08	103 -(xQ = slcrc0 | -(exists W0 aElementOf0(W0,xQ))) # label(m__5093_AndRHS) # label(hypothesis) # label(non_clause).  [assumption].
25.73/26.08	104 (all W0 (aElement0(W0) -> (all W1 (aSet0(W1) & isFinite0(W1) -> isFinite0(sdtpldt0(W1,W0)))))) # label(mFConsSet) # label(axiom) # label(non_clause).  [assumption].
25.73/26.08	
25.73/26.08	============================== end of process non-clausal formulas ===
25.73/26.08	
25.73/26.08	============================== PROCESS INITIAL CLAUSES ===============
25.73/26.08	
25.73/26.08	============================== PREDICATE ELIMINATION =================
25.73/26.08	
25.73/26.08	============================== end predicate elimination =============
25.73/26.08	
25.73/26.08	Auto_denials:  (non-Horn, no changes).
25.73/26.08	
25.73/26.08	Term ordering decisions:
25.73/26.08	Function symbol KB weights:  szNzAzT0=1. xK=1. xN=1. xT=1. xk=1. xd=1. xC=1. xS=1. xc=1. xQ=1. xO=1. slcrc0=1. xe=1. xP=1. sz00=1. xp=1. c1=1. c2=1. sdtlpdtrp0=1. sdtlcdtrc0=1. slbdtsldtrb0=1. sdtmndt0=1. sdtpldt0=1. sdtlbdtrb0=1. sdtexdt0=1. f2=1. f5=1. f6=1. f7=1. f15=1. f16=1. f17=1. f31=1. f34=1. f36=1. f37=1. f38=1. f39=1. f43=1. f44=1. f45=1. f46=1. szDzozmdt0=1. sbrdtbr0=1. szmzizndt0=1. szszuzczcdt0=1. szDzizrdt0=1. slbdtrb0=1. szmzazxdt0=1. f1=1. f14=1. f25=1. f26=1. f27=1. f28=1. f29=1. f30=1. f33=1. f40=1. f41=1. f42=1. f3=1. f4=1. f8=1. f9=1. f11=1. f12=1. f13=1. f19=1. f20=1. f21=1. f22=1. f23=1. f32=1. f35=1. f10=1. f18=1. f24=1.
25.73/26.08	
25.73/26.08	============================== end of process initial clauses ========
25.73/26.08	
25.73/26.08	============================== CLAUSES FOR SEARCH ====================
25.73/26.08	
25.73/26.08	============================== end of clauses for search =============
25.73/26.08	
25.73/26.08	============================== SEARCH ================================
25.73/26.08	
25.73/26.08	% Starting search at 4.58 seconds.
25.73/26.08	
25.73/26.08	Low Water (keep): wt=2.000, iters=2147483647
25.73/26.08	
25.73/26.08	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 97 (0.00 of 4.64 sec).
25.73/26.08	
25.73/26.08	============================== PROOF =================================
25.73/26.08	% SZS status Theorem
25.73/26.08	% SZS output start Refutation
25.73/26.08	
25.73/26.08	% Proof 1 at 24.85 (+ 0.06) seconds.
25.73/26.08	% Length of proof is 15.
25.73/26.08	% Level of proof is 4.
25.73/26.08	% Maximum clause weight is 14.000.
25.73/26.08	% Given clauses 6495.
25.73/26.08	
25.73/26.08	30 (all W0 all W1 (aElementOf0(W0,szNzAzT0) & aElementOf0(W1,szNzAzT0) -> (szszuzczcdt0(W0) = szszuzczcdt0(W1) -> W1 = W0))) # label(mSuccEquSucc) # label(axiom) # label(non_clause).  [assumption].
25.73/26.08	298 -aElementOf0(A,szNzAzT0) | -aElementOf0(B,szNzAzT0) | szszuzczcdt0(B) != szszuzczcdt0(A) | B = A # label(mSuccEquSucc) # label(axiom).  [clausify(30)].
25.73/26.08	3922 szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ) # label(m__5255_AndLHS) # label(hypothesis).  [assumption].
25.73/26.08	3923 aElementOf0(sbrdtbr0(xP),szNzAzT0) # label(m__5255_AndRHS_AndLHS) # label(hypothesis).  [assumption].
25.73/26.08	3924 sbrdtbr0(xQ) = szszuzczcdt0(xk) # label(m__5255_AndRHS_AndRHS) # label(hypothesis).  [assumption].
25.73/26.08	3925 szszuzczcdt0(xk) = sbrdtbr0(xQ).  [copy(3924),flip(a)].
25.73/26.08	4014 xK = sbrdtbr0(xQ) # label(m__5078_AndRHS_AndRHS_AndLHS) # label(hypothesis).  [assumption].
25.73/26.08	4015 sbrdtbr0(xQ) = xK.  [copy(4014),flip(a)].
25.73/26.08	4117 aElementOf0(xk,szNzAzT0) # label(m__3533_AndLHS) # label(hypothesis).  [assumption].
25.73/26.08	4145 xk != sbrdtbr0(xP) # label(m__) # label(negated_conjecture).  [assumption].
25.73/26.08	4146 sbrdtbr0(xP) != xk.  [copy(4145),flip(a)].
25.73/26.08	6655 szszuzczcdt0(xk) = xK.  [back_rewrite(3925),rewrite([4015(4)])].
25.73/26.08	6656 szszuzczcdt0(sbrdtbr0(xP)) = xK.  [back_rewrite(3922),rewrite([4015(5)])].
25.73/26.08	7524 -aElementOf0(A,szNzAzT0) | szszuzczcdt0(A) != xK | xk = A.  [resolve(4117,a,298,b),rewrite([6655(4)]),flip(b)].
25.73/26.08	18014 $F.  [resolve(7524,a,3923,a),rewrite([6656(3)]),flip(b),xx(a),unit_del(a,4146)].
25.73/26.08	
25.73/26.08	% SZS output end Refutation
25.73/26.08	============================== end of proof ==========================
25.73/26.08	
25.73/26.08	============================== STATISTICS ============================
25.73/26.08	
25.73/26.08	Given=6495. Generated=26403. Kept=16701. proofs=1.
25.73/26.08	Usable=6493. Sos=9751. Demods=104. Limbo=16, Disabled=3840. Hints=0.
25.73/26.08	Megabytes=70.23.
25.73/26.08	User_CPU=24.85, System_CPU=0.06, Wall_clock=25.
25.73/26.08	
25.73/26.08	============================== end of statistics =====================
25.73/26.08	
25.73/26.08	============================== end of search =========================
25.73/26.08	
25.73/26.08	THEOREM PROVED
25.73/26.08	% SZS status Theorem
25.73/26.08	
25.73/26.08	Exiting with 1 proof.
25.73/26.08	
25.73/26.08	Process 7275 exit (max_proofs) Tue Aug  9 02:26:04 2022
25.73/26.08	Prover9 interrupted
25.73/26.08	EOF