0.06/0.11	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.06/0.11	% Command  : tptp2X_and_run_prover9 %d %s
0.11/0.30	% Computer : n005.cluster.edu
0.11/0.30	% Model    : x86_64 x86_64
0.11/0.30	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.30	% Memory   : 8042.1875MB
0.11/0.30	% OS       : Linux 3.10.0-693.el7.x86_64
0.11/0.30	% CPULimit : 1440
0.11/0.30	% WCLimit  : 180
0.11/0.30	% DateTime : Mon Jul  3 08:38:00 EDT 2023
0.11/0.31	% CPUTime  : 
0.82/1.15	============================== Prover9 ===============================
0.82/1.15	Prover9 (32) version 2009-11A, November 2009.
0.82/1.15	Process 7414 was started by sandbox on n005.cluster.edu,
0.82/1.15	Mon Jul  3 08:38:01 2023
0.82/1.15	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1440 -f /tmp/Prover9_7261_n005.cluster.edu".
0.82/1.15	============================== end of head ===========================
0.82/1.15	
0.82/1.15	============================== INPUT =================================
0.82/1.15	
0.82/1.15	% Reading from file /tmp/Prover9_7261_n005.cluster.edu
0.82/1.15	
0.82/1.15	set(prolog_style_variables).
0.82/1.15	set(auto2).
0.82/1.15	    % set(auto2) -> set(auto).
0.82/1.15	    % set(auto) -> set(auto_inference).
0.82/1.15	    % set(auto) -> set(auto_setup).
0.82/1.15	    % set(auto_setup) -> set(predicate_elim).
0.82/1.15	    % set(auto_setup) -> assign(eq_defs, unfold).
0.82/1.15	    % set(auto) -> set(auto_limits).
0.82/1.15	    % set(auto_limits) -> assign(max_weight, "100.000").
0.82/1.15	    % set(auto_limits) -> assign(sos_limit, 20000).
0.82/1.15	    % set(auto) -> set(auto_denials).
0.82/1.15	    % set(auto) -> set(auto_process).
0.82/1.15	    % set(auto2) -> assign(new_constants, 1).
0.82/1.15	    % set(auto2) -> assign(fold_denial_max, 3).
0.82/1.15	    % set(auto2) -> assign(max_weight, "200.000").
0.82/1.15	    % set(auto2) -> assign(max_hours, 1).
0.82/1.15	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.82/1.15	    % set(auto2) -> assign(max_seconds, 0).
0.82/1.15	    % set(auto2) -> assign(max_minutes, 5).
0.82/1.15	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.82/1.15	    % set(auto2) -> set(sort_initial_sos).
0.82/1.15	    % set(auto2) -> assign(sos_limit, -1).
0.82/1.15	    % set(auto2) -> assign(lrs_ticks, 3000).
0.82/1.15	    % set(auto2) -> assign(max_megs, 400).
0.82/1.15	    % set(auto2) -> assign(stats, some).
0.82/1.15	    % set(auto2) -> clear(echo_input).
0.82/1.15	    % set(auto2) -> set(quiet).
0.82/1.15	    % set(auto2) -> clear(print_initial_clauses).
0.82/1.15	    % set(auto2) -> clear(print_given).
0.82/1.15	assign(lrs_ticks,-1).
0.82/1.15	assign(sos_limit,10000).
0.82/1.15	assign(order,kbo).
0.82/1.15	set(lex_order_vars).
0.82/1.15	clear(print_given).
0.82/1.15	
0.82/1.15	% formulas(sos).  % not echoed (96 formulas)
0.82/1.15	
0.82/1.15	============================== end of input ==========================
0.82/1.15	
0.82/1.15	% From the command line: assign(max_seconds, 1440).
0.82/1.15	
0.82/1.15	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.82/1.15	
0.82/1.15	% Formulas that are not ordinary clauses:
0.82/1.15	1 (all U (ssItem(U) -> totalorderedP(cons(U,nil)))) # label(ax65) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	2 (all U (ssList(U) -> (all V (ssList(V) -> (segmentP(U,V) & segmentP(V,U) -> V = U))))) # label(ax54) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	3 (all U (ssList(U) -> (all V (ssList(V) -> (all W (ssList(W) -> (app(V,U) = app(V,W) -> U = W))))))) # label(ax80) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	4 (all U (ssList(U) -> (all V (ssList(V) -> (nil != U -> hd(U) = hd(app(U,V))))))) # label(ax85) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	5 (all U (ssList(U) -> (U != nil -> (exists V (ssList(V) & V = tl(U)))))) # label(ax76) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	6 (all U (ssList(U) -> (frontsegP(nil,U) <-> nil = U))) # label(ax46) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	7 (all U (ssList(U) -> (all V (ssList(V) -> (all W (ssList(W) -> (all X (ssList(X) -> (segmentP(U,V) -> segmentP(app(app(W,U),X),V)))))))))) # label(ax56) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	8 (all U (ssList(U) -> (all V (ssList(V) -> (frontsegP(U,V) <-> (exists W (ssList(W) & U = app(V,W)))))))) # label(ax5) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	9 (all U (ssItem(U) -> (all V (ssItem(V) -> (all W (ssItem(W) -> (gt(V,W) & gt(U,V) -> gt(U,W)))))))) # label(ax95) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	10 (all U (ssItem(U) -> totalorderP(cons(U,nil)))) # label(ax61) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	11 (all U (ssList(U) -> U = app(U,nil))) # label(ax84) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	12 (all U (ssList(U) -> (all V (ssItem(V) -> cons(V,U) != U)))) # label(ax18) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	13 (all U (ssItem(U) -> (all V (ssItem(V) -> (leq(V,U) <-> geq(U,V)))))) # label(ax32) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	14 (all U (ssItem(U) -> (all V (ssItem(V) -> (leq(U,V) -> lt(U,V) | U = V))))) # label(ax92) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	15 (all U (ssList(U) -> ((all V (ssItem(V) -> (all W (ssItem(W) -> (all X (ssList(X) -> (all Y (ssList(Y) -> (all Z (ssList(Z) -> (U = app(app(X,cons(V,Y)),cons(W,Z)) -> leq(W,V) | leq(V,W)))))))))))) <-> totalorderP(U)))) # label(ax9) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	16 (all U (ssList(U) -> (all V (ssList(V) -> (nil != U -> app(tl(U),V) = tl(app(U,V))))))) # label(ax86) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	17 (all U (ssItem(U) -> geq(U,U))) # label(ax89) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	18 (all U (ssList(U) -> ((all V (ssItem(V) -> (all W (ssItem(W) -> (all X (ssList(X) -> (all Y (ssList(Y) -> (all Z (ssList(Z) -> (U = app(app(X,cons(V,Y)),cons(W,Z)) -> leq(V,W)))))))))))) <-> totalorderedP(U)))) # label(ax11) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	19 (all U (ssList(U) -> (all V (ssList(V) -> (frontsegP(V,U) & frontsegP(U,V) -> U = V))))) # label(ax41) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	20 (all U (ssList(U) -> (all V (ssList(V) -> (all W (ssItem(W) -> (all X (ssItem(X) -> (cons(X,V) = cons(W,U) -> V = U & W = X))))))))) # label(ax19) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	21 (all U (ssList(U) -> (all V (ssList(V) -> (all W (ssList(W) -> (frontsegP(V,W) & frontsegP(U,V) -> frontsegP(U,W)))))))) # label(ax40) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	22 (all U (ssItem(U) -> (all V (ssItem(V) -> (neq(U,V) <-> U != V))))) # label(ax1) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	23 (all U (ssList(U) -> ((all V (ssItem(V) -> (all W (ssItem(W) -> (all X (ssList(X) -> (all Y (ssList(Y) -> (all Z (ssList(Z) -> (app(app(X,cons(V,Y)),cons(W,Z)) = U -> lt(V,W)))))))))))) <-> strictorderedP(U)))) # label(ax12) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	24 (all U (ssItem(U) -> cyclefreeP(cons(U,nil)))) # label(ax59) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	25 (all U (ssList(U) -> segmentP(U,U))) # label(ax55) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	26 (all U (ssItem(U) -> (all V (ssItem(V) -> (all W (ssList(W) -> (memberP(cons(V,W),U) <-> memberP(W,U) | V = U))))))) # label(ax37) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	27 (all U (ssList(U) -> (all V (ssList(V) -> (rearsegP(U,V) & rearsegP(V,U) -> V = U))))) # label(ax48) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	28 (all U (ssItem(U) -> duplicatefreeP(cons(U,nil)))) # label(ax71) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	29 (all U (ssItem(U) -> (all V (ssItem(V) -> (lt(U,V) <-> V != U & leq(U,V)))))) # label(ax93) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	30 (all U (ssItem(U) -> (all V (ssList(V) -> (all W (ssList(W) -> (memberP(app(V,W),U) <-> memberP(W,U) | memberP(V,U)))))))) # label(ax36) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	31 (all U (ssList(U) -> (singletonP(U) <-> (exists V (ssItem(V) & U = cons(V,nil)))))) # label(ax4) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	32 (all U (ssList(U) -> ((all V (ssItem(V) -> (all W (ssItem(W) -> (all X (ssList(X) -> (all Y (ssList(Y) -> (all Z (ssList(Z) -> (U = app(app(X,cons(V,Y)),cons(W,Z)) -> W != V))))))))))) <-> duplicatefreeP(U)))) # label(ax13) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	33 (all U (ssList(U) -> rearsegP(U,nil))) # label(ax51) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	34 (all U (ssList(U) -> (all V (ssItem(V) -> cons(V,U) != nil)))) # label(ax21) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	35 (all U (ssItem(U) -> (all V (ssItem(V) -> (all W (ssItem(W) -> (geq(V,W) & geq(U,V) -> geq(U,W)))))))) # label(ax88) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	36 (all U (ssItem(U) -> -memberP(nil,U))) # label(ax38) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	37 (all U (ssList(U) -> ((all V (ssItem(V) -> (all W (ssItem(W) -> (all X (ssList(X) -> (all Y (ssList(Y) -> (all Z (ssList(Z) -> (U = app(app(X,cons(V,Y)),cons(W,Z)) -> lt(V,W) | lt(W,V)))))))))))) <-> strictorderP(U)))) # label(ax10) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	38 (all U (ssList(U) -> (all V (ssItem(V) -> V = hd(cons(V,U)))))) # label(ax23) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	39 (all U (ssList(U) -> (all V (ssList(V) -> (U != nil & hd(U) = hd(V) & tl(V) = tl(U) & nil != V -> U = V))))) # label(ax77) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	40 (all U (ssItem(U) -> (all V (ssItem(V) -> (all W (ssItem(W) -> (leq(V,W) & leq(U,V) -> leq(U,W)))))))) # label(ax30) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	41 (all U (ssList(U) -> (all V (ssList(V) -> (nil = V & nil = U <-> app(U,V) = nil))))) # label(ax83) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	42 (all U (ssList(U) -> (nil = U <-> rearsegP(nil,U)))) # label(ax52) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	43 (all U (ssItem(U) -> (all V (ssItem(V) -> (lt(V,U) <-> gt(U,V)))))) # label(ax35) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	44 (all U (ssList(U) -> (all V (ssItem(V) -> ssList(cons(V,U)))))) # label(ax16) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	45 (all U (ssList(U) -> (all V (ssList(V) -> ssList(app(U,V)))))) # label(ax26) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	46 (all U (ssList(U) -> (all V (ssList(V) -> ((exists W (U = app(W,V) & ssList(W))) <-> rearsegP(U,V)))))) # label(ax6) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	47 (all U (ssList(U) -> (all V (ssItem(V) -> (memberP(U,V) <-> (exists W ((exists X (app(W,cons(V,X)) = U & ssList(X))) & ssList(W)))))))) # label(ax3) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	48 (all U (ssList(U) -> (nil != U -> (exists V (hd(U) = V & ssItem(V)))))) # label(ax75) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	49 (all U (ssList(U) -> ((all V (ssItem(V) -> (all W (ssItem(W) -> (all X (ssList(X) -> (all Y (ssList(Y) -> (all Z (ssList(Z) -> (app(app(X,cons(V,Y)),cons(W,Z)) = U -> -(leq(W,V) & leq(V,W))))))))))))) <-> cyclefreeP(U)))) # label(ax8) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	50 (all U (ssList(U) -> frontsegP(U,U))) # label(ax42) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	51 (all U (ssList(U) -> (all V (ssItem(V) -> tl(cons(V,U)) = U)))) # label(ax25) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	52 (all U (ssItem(U) -> (all V (ssItem(V) -> (leq(V,U) & leq(U,V) -> V = U))))) # label(ax29) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	53 (all U (ssItem(U) -> (all V (ssItem(V) -> (geq(V,U) & geq(U,V) -> U = V))))) # label(ax87) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	54 (all U (ssList(U) -> (all V (ssList(V) -> (all W (ssItem(W) -> cons(W,app(V,U)) = app(cons(W,V),U))))))) # label(ax27) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	55 (all U (ssItem(U) -> (all V (ssItem(V) -> (all W (ssItem(W) -> (leq(U,V) & lt(V,W) -> lt(U,W)))))))) # label(ax91) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	56 (all U (ssList(U) -> (all V (ssList(V) -> (all W (ssList(W) -> (frontsegP(U,V) -> frontsegP(app(U,W),V)))))))) # label(ax43) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	57 (all U (ssList(U) -> (nil != U -> ssList(tl(U))))) # label(ax24) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	58 (all U (ssItem(U) -> strictorderP(cons(U,nil)))) # label(ax63) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	59 (all U (ssList(U) -> (all V (ssList(V) -> (neq(U,V) <-> V != U))))) # label(ax15) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	60 (all U (ssList(U) -> U = nil | (exists V ((exists W (ssItem(W) & U = cons(W,V))) & ssList(V))))) # label(ax20) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	61 (all U (ssList(U) -> segmentP(U,nil))) # label(ax57) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	62 (all U (ssItem(U) -> (all V (ssList(V) -> (totalorderedP(cons(U,V)) <-> nil != V & leq(U,hd(V)) & totalorderedP(V) | nil = V))))) # label(ax67) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	63 (all U (ssList(U) -> rearsegP(U,U))) # label(ax49) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	64 (all U (ssItem(U) -> equalelemsP(cons(U,nil)))) # label(ax73) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	65 (all U (ssList(U) -> (nil != U -> cons(hd(U),tl(U)) = U))) # label(ax78) # label(axiom) # label(non_clause).  [assumption].
0.82/1.16	66 (exists U ((exists V (U != V & ssItem(V))) & ssItem(U))) # label(ax2) # label(axiom) # label(non_clause).  [assumption].
0.82/1.16	67 (all U (ssItem(U) -> strictorderedP(cons(U,nil)))) # label(ax68) # label(axiom) # label(non_clause).  [assumption].
0.82/1.16	68 (all U (ssList(U) -> (all V (ssList(V) -> (all W (ssList(W) -> app(U,app(V,W)) = app(app(U,V),W))))))) # label(ax82) # label(axiom) # label(non_clause).  [assumption].
0.82/1.16	69 (all U (ssItem(U) -> -lt(U,U))) # label(ax90) # label(axiom) # label(non_clause).  [assumption].
0.82/1.16	70 (all U (ssItem(U) -> leq(U,U))) # label(ax31) # label(axiom) # label(non_clause).  [assumption].
0.82/1.16	71 (all U (ssItem(U) -> (all V (ssItem(V) -> (lt(U,V) -> -lt(V,U)))))) # label(ax33) # label(axiom) # label(non_clause).  [assumption].
0.82/1.16	72 (all U (ssItem(U) -> (all V (ssItem(V) -> (all W (ssItem(W) -> (lt(U,V) & lt(V,W) -> lt(U,W)))))))) # label(ax34) # label(axiom) # label(non_clause).  [assumption].
0.82/1.16	73 (all U (ssList(U) -> (all V (ssList(V) -> (all W (ssList(W) -> (app(W,V) = app(U,V) -> U = W))))))) # label(ax79) # label(axiom) # label(non_clause).  [assumption].
0.82/1.16	74 (all U (ssItem(U) -> (all V (ssItem(V) -> (gt(U,V) -> -gt(V,U)))))) # label(ax94) # label(axiom) # label(non_clause).  [assumption].
0.82/1.16	75 (all U (ssList(U) -> app(nil,U) = U)) # label(ax28) # label(axiom) # label(non_clause).  [assumption].
0.82/1.16	76 (all U (ssItem(U) -> (all V (ssList(V) -> (V = nil | V != nil & lt(U,hd(V)) & strictorderedP(V) <-> strictorderedP(cons(U,V))))))) # label(ax70) # label(axiom) # label(non_clause).  [assumption].
0.82/1.16	77 (all U (ssList(U) -> (all V (ssList(V) -> (all W (ssList(W) -> (segmentP(V,W) & segmentP(U,V) -> segmentP(U,W)))))))) # label(ax53) # label(axiom) # label(non_clause).  [assumption].
0.82/1.16	78 (all U (ssList(U) -> (all V (ssList(V) -> ((exists W (ssList(W) & (exists X (ssList(X) & U = app(app(W,V),X))))) <-> segmentP(U,V)))))) # label(ax7) # label(axiom) # label(non_clause).  [assumption].
0.82/1.16	79 (all U (ssList(U) -> (nil != U -> ssItem(hd(U))))) # label(ax22) # label(axiom) # label(non_clause).  [assumption].
0.82/1.16	80 (all U (ssList(U) -> frontsegP(U,nil))) # label(ax45) # label(axiom) # label(non_clause).  [assumption].
0.82/1.16	81 (all U (ssItem(U) -> (all V (ssItem(V) -> (all W (ssList(W) -> (all X (ssList(X) -> (frontsegP(cons(U,W),cons(V,X)) <-> U = V & frontsegP(W,X)))))))))) # label(ax44) # label(axiom) # label(non_clause).  [assumption].
0.82/1.16	82 (all U (ssList(U) -> (all V (ssList(V) -> (all W (ssList(W) -> (rearsegP(U,V) & rearsegP(V,W) -> rearsegP(U,W)))))))) # label(ax47) # label(axiom) # label(non_clause).  [assumption].
0.82/1.16	83 (all U (ssList(U) -> (all V (ssItem(V) -> cons(V,U) = app(cons(V,nil),U))))) # label(ax81) # label(axiom) # label(non_clause).  [assumption].
0.82/1.16	84 (all U (ssList(U) -> (segmentP(nil,U) <-> nil = U))) # label(ax58) # label(axiom) # label(non_clause).  [assumption].
0.82/1.16	85 (all U (ssList(U) -> (all V (ssList(V) -> (all W (ssList(W) -> (rearsegP(U,V) -> rearsegP(app(W,U),V)))))))) # label(ax50) # label(axiom) # label(non_clause).  [assumption].
0.82/1.16	86 (all U (ssList(U) -> (equalelemsP(U) <-> (all V (ssItem(V) -> (all W (ssItem(W) -> (all X (ssList(X) -> (all Y (ssList(Y) -> (U = app(X,cons(V,cons(W,Y))) -> V = W)))))))))))) # label(ax14) # label(axiom) # label(non_clause).  [assumption].
0.82/1.16	87 -(all U (ssList(U) -> (all V (ssList(V) -> (all W (ssList(W) -> (all X (ssList(X) -> -neq(V,nil) | -frontsegP(X,W) | neq(U,nil) | (exists Y (neq(W,Y) & strictorderedP(Y) & segmentP(Y,W) & frontsegP(X,Y) & ssList(Y))) | -strictorderedP(W) | W != U | V != X)))))))) # label(co1) # label(negated_conjecture) # label(non_clause).  [assumption].
0.82/1.16	
0.82/1.16	============================== end of process non-clausal formulas ===
0.82/1.16	
0.82/1.16	============================== PROCESS INITIAL CLAUSES ===============
0.82/1.16	
0.82/1.16	============================== PREDICATE ELIMINATION =================
0.82/1.16	88 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | C != B | -duplicatefreeP(A) # label(ax13) # label(axiom).  [clausify(32)].
0.82/1.16	89 duplicatefreeP(nil) # label(ax72) # label(axiom).  [assumption].
0.91/1.21	90 -ssItem(A) | duplicatefreeP(cons(A,nil)) # label(ax71) # label(axiom).  [clausify(28)].
0.91/1.21	91 -ssList(A) | ssItem(f19(A)) | duplicatefreeP(A) # label(ax13) # label(axiom).  [clausify(32)].
0.91/1.21	92 -ssList(A) | ssItem(f20(A)) | duplicatefreeP(A) # label(ax13) # label(axiom).  [clausify(32)].
0.91/1.21	93 -ssList(A) | ssList(f21(A)) | duplicatefreeP(A) # label(ax13) # label(axiom).  [clausify(32)].
0.91/1.21	94 -ssList(A) | ssList(f22(A)) | duplicatefreeP(A) # label(ax13) # label(axiom).  [clausify(32)].
0.91/1.21	95 -ssList(A) | ssList(f23(A)) | duplicatefreeP(A) # label(ax13) # label(axiom).  [clausify(32)].
0.91/1.21	96 -ssList(A) | app(app(f21(A),cons(f19(A),f22(A))),cons(f20(A),f23(A))) = A | duplicatefreeP(A) # label(ax13) # label(axiom).  [clausify(32)].
0.91/1.21	97 -ssList(A) | f20(A) = f19(A) | duplicatefreeP(A) # label(ax13) # label(axiom).  [clausify(32)].
0.91/1.21	Derived: -ssList(nil) | -ssItem(A) | -ssItem(B) | -ssList(C) | -ssList(D) | -ssList(E) | app(app(C,cons(A,D)),cons(B,E)) != nil | B != A.  [resolve(88,i,89,a)].
0.91/1.21	Derived: -ssList(cons(A,nil)) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != cons(A,nil) | C != B | -ssItem(A).  [resolve(88,i,90,b)].
0.91/1.21	Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | C != B | -ssList(A) | ssItem(f19(A)).  [resolve(88,i,91,c)].
0.91/1.21	Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | C != B | -ssList(A) | ssItem(f20(A)).  [resolve(88,i,92,c)].
0.91/1.21	Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | C != B | -ssList(A) | ssList(f21(A)).  [resolve(88,i,93,c)].
0.91/1.21	Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | C != B | -ssList(A) | ssList(f22(A)).  [resolve(88,i,94,c)].
0.91/1.21	Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | C != B | -ssList(A) | ssList(f23(A)).  [resolve(88,i,95,c)].
0.91/1.21	Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | C != B | -ssList(A) | app(app(f21(A),cons(f19(A),f22(A))),cons(f20(A),f23(A))) = A.  [resolve(88,i,96,c)].
0.91/1.21	Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | C != B | -ssList(A) | f20(A) = f19(A).  [resolve(88,i,97,c)].
0.91/1.21	98 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | leq(C,B) | leq(B,C) | -totalorderP(A) # label(ax9) # label(axiom).  [clausify(15)].
0.91/1.21	99 -ssItem(A) | totalorderP(cons(A,nil)) # label(ax61) # label(axiom).  [clausify(10)].
0.91/1.21	100 -ssList(A) | ssItem(f3(A)) | totalorderP(A) # label(ax9) # label(axiom).  [clausify(15)].
0.91/1.21	101 -ssList(A) | ssItem(f4(A)) | totalorderP(A) # label(ax9) # label(axiom).  [clausify(15)].
0.91/1.21	102 -ssList(A) | ssList(f5(A)) | totalorderP(A) # label(ax9) # label(axiom).  [clausify(15)].
0.91/1.21	103 -ssList(A) | ssList(f6(A)) | totalorderP(A) # label(ax9) # label(axiom).  [clausify(15)].
0.91/1.21	104 -ssList(A) | ssList(f7(A)) | totalorderP(A) # label(ax9) # label(axiom).  [clausify(15)].
0.91/1.21	105 -ssList(A) | app(app(f5(A),cons(f3(A),f6(A))),cons(f4(A),f7(A))) = A | totalorderP(A) # label(ax9) # label(axiom).  [clausify(15)].
0.91/1.21	106 -ssList(A) | -leq(f4(A),f3(A)) | totalorderP(A) # label(ax9) # label(axiom).  [clausify(15)].
0.91/1.21	107 -ssList(A) | -leq(f3(A),f4(A)) | totalorderP(A) # label(ax9) # label(axiom).  [clausify(15)].
0.91/1.21	Derived: -ssList(cons(A,nil)) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != cons(A,nil) | leq(C,B) | leq(B,C) | -ssItem(A).  [resolve(98,j,99,b)].
0.91/1.21	Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | leq(C,B) | leq(B,C) | -ssList(A) | ssItem(f3(A)).  [resolve(98,j,100,c)].
0.91/1.21	Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | leq(C,B) | leq(B,C) | -ssList(A) | ssItem(f4(A)).  [resolve(98,j,101,c)].
1.07/1.36	Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | leq(C,B) | leq(B,C) | -ssList(A) | ssList(f5(A)).  [resolve(98,j,102,c)].
1.07/1.36	Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | leq(C,B) | leq(B,C) | -ssList(A) | ssList(f6(A)).  [resolve(98,j,103,c)].
1.07/1.36	Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | leq(C,B) | leq(B,C) | -ssList(A) | ssList(f7(A)).  [resolve(98,j,104,c)].
1.07/1.36	Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | leq(C,B) | leq(B,C) | -ssList(A) | app(app(f5(A),cons(f3(A),f6(A))),cons(f4(A),f7(A))) = A.  [resolve(98,j,105,c)].
1.07/1.36	Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | leq(C,B) | leq(B,C) | -ssList(A) | -leq(f4(A),f3(A)).  [resolve(98,j,106,c)].
1.07/1.36	Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | leq(C,B) | leq(B,C) | -ssList(A) | -leq(f3(A),f4(A)).  [resolve(98,j,107,c)].
1.07/1.36	108 totalorderP(nil) # label(ax62) # label(axiom).  [assumption].
1.07/1.36	Derived: -ssList(nil) | -ssItem(A) | -ssItem(B) | -ssList(C) | -ssList(D) | -ssList(E) | app(app(C,cons(A,D)),cons(B,E)) != nil | leq(B,A) | leq(A,B).  [resolve(108,a,98,j)].
1.07/1.36	109 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | -leq(C,B) | -leq(B,C) | -cyclefreeP(A) # label(ax8) # label(axiom).  [clausify(49)].
1.07/1.36	110 -ssItem(A) | cyclefreeP(cons(A,nil)) # label(ax59) # label(axiom).  [clausify(24)].
1.07/1.36	111 -ssList(A) | ssItem(f33(A)) | cyclefreeP(A) # label(ax8) # label(axiom).  [clausify(49)].
1.07/1.36	112 -ssList(A) | ssItem(f34(A)) | cyclefreeP(A) # label(ax8) # label(axiom).  [clausify(49)].
1.07/1.36	113 -ssList(A) | ssList(f35(A)) | cyclefreeP(A) # label(ax8) # label(axiom).  [clausify(49)].
1.07/1.36	114 -ssList(A) | ssList(f36(A)) | cyclefreeP(A) # label(ax8) # label(axiom).  [clausify(49)].
1.07/1.36	115 -ssList(A) | ssList(f37(A)) | cyclefreeP(A) # label(ax8) # label(axiom).  [clausify(49)].
1.07/1.36	116 -ssList(A) | app(app(f35(A),cons(f33(A),f36(A))),cons(f34(A),f37(A))) = A | cyclefreeP(A) # label(ax8) # label(axiom).  [clausify(49)].
1.07/1.36	117 -ssList(A) | leq(f34(A),f33(A)) | cyclefreeP(A) # label(ax8) # label(axiom).  [clausify(49)].
1.07/1.36	118 -ssList(A) | leq(f33(A),f34(A)) | cyclefreeP(A) # label(ax8) # label(axiom).  [clausify(49)].
1.07/1.36	Derived: -ssList(cons(A,nil)) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != cons(A,nil) | -leq(C,B) | -leq(B,C) | -ssItem(A).  [resolve(109,j,110,b)].
1.07/1.36	Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | -leq(C,B) | -leq(B,C) | -ssList(A) | ssItem(f33(A)).  [resolve(109,j,111,c)].
1.07/1.36	Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | -leq(C,B) | -leq(B,C) | -ssList(A) | ssItem(f34(A)).  [resolve(109,j,112,c)].
1.07/1.36	Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | -leq(C,B) | -leq(B,C) | -ssList(A) | ssList(f35(A)).  [resolve(109,j,113,c)].
1.07/1.36	Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | -leq(C,B) | -leq(B,C) | -ssList(A) | ssList(f36(A)).  [resolve(109,j,114,c)].
1.07/1.36	Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | -leq(C,B) | -leq(B,C) | -ssList(A) | ssList(f37(A)).  [resolve(109,j,115,c)].
1.07/1.36	Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | -leq(C,B) | -leq(B,C) | -ssList(A) | app(app(f35(A),cons(f33(A),f36(A))),cons(f34(A),f37(A))) = A.  [resolve(109,j,116,c)].
1.29/1.58	Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | -leq(C,B) | -leq(B,C) | -ssList(A) | leq(f34(A),f33(A)).  [resolve(109,j,117,c)].
1.29/1.58	Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | -leq(C,B) | -leq(B,C) | -ssList(A) | leq(f33(A),f34(A)).  [resolve(109,j,118,c)].
1.29/1.58	119 cyclefreeP(nil) # label(ax60) # label(axiom).  [assumption].
1.29/1.58	Derived: -ssList(nil) | -ssItem(A) | -ssItem(B) | -ssList(C) | -ssList(D) | -ssList(E) | app(app(C,cons(A,D)),cons(B,E)) != nil | -leq(B,A) | -leq(A,B).  [resolve(119,a,109,j)].
1.29/1.58	120 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | lt(B,C) | lt(C,B) | -strictorderP(A) # label(ax10) # label(axiom).  [clausify(37)].
1.29/1.58	121 -ssList(A) | ssItem(f24(A)) | strictorderP(A) # label(ax10) # label(axiom).  [clausify(37)].
1.29/1.58	122 -ssList(A) | ssItem(f25(A)) | strictorderP(A) # label(ax10) # label(axiom).  [clausify(37)].
1.29/1.58	123 -ssList(A) | ssList(f26(A)) | strictorderP(A) # label(ax10) # label(axiom).  [clausify(37)].
1.29/1.58	124 -ssList(A) | ssList(f27(A)) | strictorderP(A) # label(ax10) # label(axiom).  [clausify(37)].
1.29/1.58	125 -ssList(A) | ssList(f28(A)) | strictorderP(A) # label(ax10) # label(axiom).  [clausify(37)].
1.29/1.58	126 -ssList(A) | app(app(f26(A),cons(f24(A),f27(A))),cons(f25(A),f28(A))) = A | strictorderP(A) # label(ax10) # label(axiom).  [clausify(37)].
1.29/1.58	127 -ssList(A) | -lt(f24(A),f25(A)) | strictorderP(A) # label(ax10) # label(axiom).  [clausify(37)].
1.29/1.58	128 -ssList(A) | -lt(f25(A),f24(A)) | strictorderP(A) # label(ax10) # label(axiom).  [clausify(37)].
1.29/1.58	Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | lt(B,C) | lt(C,B) | -ssList(A) | ssItem(f24(A)).  [resolve(120,j,121,c)].
1.29/1.58	Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | lt(B,C) | lt(C,B) | -ssList(A) | ssItem(f25(A)).  [resolve(120,j,122,c)].
1.29/1.58	Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | lt(B,C) | lt(C,B) | -ssList(A) | ssList(f26(A)).  [resolve(120,j,123,c)].
1.29/1.58	Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | lt(B,C) | lt(C,B) | -ssList(A) | ssList(f27(A)).  [resolve(120,j,124,c)].
1.29/1.58	Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | lt(B,C) | lt(C,B) | -ssList(A) | ssList(f28(A)).  [resolve(120,j,125,c)].
1.29/1.58	Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | lt(B,C) | lt(C,B) | -ssList(A) | app(app(f26(A),cons(f24(A),f27(A))),cons(f25(A),f28(A))) = A.  [resolve(120,j,126,c)].
1.29/1.58	Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | lt(B,C) | lt(C,B) | -ssList(A) | -lt(f24(A),f25(A)).  [resolve(120,j,127,c)].
1.29/1.58	Derived: -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != A | lt(B,C) | lt(C,B) | -ssList(A) | -lt(f25(A),f24(A)).  [resolve(120,j,128,c)].
1.29/1.58	129 -ssItem(A) | strictorderP(cons(A,nil)) # label(ax63) # label(axiom).  [clausify(58)].
1.29/1.58	Derived: -ssItem(A) | -ssList(cons(A,nil)) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | -ssList(F) | app(app(D,cons(B,E)),cons(C,F)) != cons(A,nil) | lt(B,C) | lt(C,B).  [resolve(129,b,120,j)].
1.29/1.58	130 strictorderP(nil) # label(ax64) # label(axiom).  [assumption].
1.29/1.58	Derived: -ssList(nil) | -ssItem(A) | -ssItem(B) | -ssList(C) | -ssList(D) | -ssList(E) | app(app(C,cons(A,D)),cons(B,E)) != nil | lt(A,B) | lt(B,A).  [resolve(130,a,120,j)].
1.29/1.58	131 -ssList(A) | -equalelemsP(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(D,cons(B,cons(C,E))) != A | C = B # label(ax14) # label(axiom).  [clausify(86)].
6.13/6.49	132 equalelemsP(nil) # label(ax74) # label(axiom).  [assumption].
6.13/6.49	133 -ssItem(A) | equalelemsP(cons(A,nil)) # label(ax73) # label(axiom).  [clausify(64)].
6.13/6.49	Derived: -ssList(nil) | -ssItem(A) | -ssItem(B) | -ssList(C) | -ssList(D) | app(C,cons(A,cons(B,D))) != nil | B = A.  [resolve(131,b,132,a)].
6.13/6.49	Derived: -ssList(cons(A,nil)) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(D,cons(B,cons(C,E))) != cons(A,nil) | C = B | -ssItem(A).  [resolve(131,b,133,b)].
6.13/6.49	134 -ssList(A) | equalelemsP(A) | ssItem(f42(A)) # label(ax14) # label(axiom).  [clausify(86)].
6.13/6.49	Derived: -ssList(A) | ssItem(f42(A)) | -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(D,cons(B,cons(C,E))) != A | C = B.  [resolve(134,b,131,b)].
6.13/6.49	135 -ssList(A) | equalelemsP(A) | ssItem(f43(A)) # label(ax14) # label(axiom).  [clausify(86)].
6.13/6.49	Derived: -ssList(A) | ssItem(f43(A)) | -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(D,cons(B,cons(C,E))) != A | C = B.  [resolve(135,b,131,b)].
6.13/6.49	136 -ssList(A) | equalelemsP(A) | ssList(f44(A)) # label(ax14) # label(axiom).  [clausify(86)].
6.13/6.49	Derived: -ssList(A) | ssList(f44(A)) | -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(D,cons(B,cons(C,E))) != A | C = B.  [resolve(136,b,131,b)].
6.13/6.49	137 -ssList(A) | equalelemsP(A) | ssList(f45(A)) # label(ax14) # label(axiom).  [clausify(86)].
6.13/6.49	Derived: -ssList(A) | ssList(f45(A)) | -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(D,cons(B,cons(C,E))) != A | C = B.  [resolve(137,b,131,b)].
6.13/6.49	138 -ssList(A) | equalelemsP(A) | app(f44(A),cons(f42(A),cons(f43(A),f45(A)))) = A # label(ax14) # label(axiom).  [clausify(86)].
6.13/6.49	Derived: -ssList(A) | app(f44(A),cons(f42(A),cons(f43(A),f45(A)))) = A | -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(D,cons(B,cons(C,E))) != A | C = B.  [resolve(138,b,131,b)].
6.13/6.49	139 -ssList(A) | equalelemsP(A) | f43(A) != f42(A) # label(ax14) # label(axiom).  [clausify(86)].
6.13/6.49	Derived: -ssList(A) | f43(A) != f42(A) | -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(D,cons(B,cons(C,E))) != A | C = B.  [resolve(139,b,131,b)].
6.13/6.49	
6.13/6.49	============================== end predicate elimination =============
6.13/6.49	
6.13/6.49	Auto_denials:  (non-Horn, no changes).
6.13/6.49	
6.13/6.49	Term ordering decisions:
6.13/6.49	Function symbol KB weights:  nil=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. cons=1. app=1. f2=1. f29=1. f30=1. f31=1. f40=1. f41=1. hd=1. tl=1. f1=1. f3=1. f4=1. f5=1. f6=1. f7=1. f8=1. f9=1. f10=1. f11=1. f12=1. f13=1. f14=1. f15=1. f16=1. f17=1. f18=1. f19=1. f20=1. f21=1. f22=1. f23=1. f24=1. f25=1. f26=1. f27=1. f28=1. f32=1. f33=1. f34=1. f35=1. f36=1. f37=1. f38=1. f39=1. f42=1. f43=1. f44=1. f45=1.
6.13/6.49	
6.13/6.49	============================== end of process initial clauses ========
6.13/6.49	
6.13/6.49	============================== CLAUSES FOR SEARCH ====================
6.13/6.49	
6.13/6.49	============================== end of clauses for search =============
6.13/6.49	
6.13/6.49	============================== SEARCH ================================
6.13/6.49	
6.13/6.49	% Starting search at 1.04 seconds.
6.13/6.49	
6.13/6.49	Low Water (keep): wt=38.000, iters=3493
6.13/6.49	
6.13/6.49	Low Water (keep): wt=35.000, iters=3374
6.13/6.49	
6.13/6.49	Low Water (keep): wt=33.000, iters=3372
6.13/6.49	
6.13/6.49	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 84 (0.00 of 2.12 sec).
6.13/6.49	
6.13/6.49	Low Water (keep): wt=31.000, iters=3420
6.13/6.49	
6.13/6.49	Low Water (keep): wt=30.000, iters=3496
6.13/6.49	
6.13/6.49	Low Water (keep): wt=29.000, iters=3443
6.13/6.49	
6.13/6.49	Low Water (keep): wt=28.000, iters=3492
6.13/6.49	
6.13/6.49	Low Water (keep): wt=23.000, iters=3427
6.13/6.49	
6.13/6.49	Low Water (keep): wt=22.000, iters=3343
6.13/6.49	
6.13/6.49	Low Water (keep): wt=21.000, iters=3366
6.13/6.49	
6.13/6.49	Low Water (keep): wt=20.000, iters=3624
6.13/6.49	
6.13/6.49	Low Water (keep): wt=19.000, iters=3416
6.13/6.49	
6.13/6.49	Low Water (keep): wt=18.000, iters=3424
6.13/6.49	
6.13/6.49	Low Water (keep): wt=17.000, iters=3362
6.13/6.49	
6.13/6.49	Low Water (keep): wt=16.000, iters=3353
6.13/6.49	
6.13/6.49	Low Water (keep): wt=15.000, iters=3349
6.13/6.49	
6.13/6.49	Low Water (displace): id=6141, wt=46.000
6.13/6.49	
6.13/6.49	Low Water (displace): id=5896, wt=44.000
6.13/6.49	
6.13/6.49	Low Water (displace): id=3450, wt=43.000
6.13/6.49	
6.13/6.49	Low Water (displace): id=6158, wt=42.000
6.13/6.49	
6.13/6.49	Low Water (displace): id=3476, wt=41.000
6.13/6.49	
6.13/6.49	Low Water (keep): wt=14.000, iters=3346
87.86/88.26	
87.86/88.26	Low Water (displace): id=6004, wt=40.000
87.86/88.26	
87.86/88.26	Low Water (displace): id=4941, wt=39.000
87.86/88.26	
87.86/88.26	Low Water (displace): id=5569, wt=38.000
87.86/88.26	
87.86/88.26	Low Water (displace): id=5998, wt=37.000
87.86/88.26	
87.86/88.26	Low Water (displace): id=6154, wt=36.000
87.86/88.26	
87.86/88.26	Low Water (displace): id=13562, wt=13.000
87.86/88.26	
87.86/88.26	Low Water (keep): wt=13.000, iters=3368
87.86/88.26	
87.86/88.26	Low Water (displace): id=14764, wt=12.000
87.86/88.26	
87.86/88.26	Low Water (displace): id=15429, wt=11.000
87.86/88.26	
87.86/88.26	Low Water (keep): wt=12.000, iters=3358
87.86/88.26	
87.86/88.26	Low Water (displace): id=16642, wt=10.000
87.86/88.26	
87.86/88.26	Low Water (displace): id=22498, wt=8.000
87.86/88.26	
87.86/88.26	Low Water (keep): wt=11.000, iters=3345
87.86/88.26	
87.86/88.26	Low Water (displace): id=24740, wt=7.000
87.86/88.26	
87.86/88.26	Low Water (keep): wt=10.000, iters=3353
87.86/88.26	
87.86/88.26	Low Water (keep): wt=9.000, iters=3391
87.86/88.26	
87.86/88.26	============================== PROOF =================================
87.86/88.26	% SZS status Theorem
87.86/88.26	% SZS output start Refutation
87.86/88.26	
87.86/88.26	% Proof 1 at 83.84 (+ 3.16) seconds.
87.86/88.26	% Length of proof is 61.
87.86/88.26	% Level of proof is 9.
87.86/88.26	% Maximum clause weight is 21.000.
87.86/88.26	% Given clauses 15848.
87.86/88.26	
87.86/88.26	34 (all U (ssList(U) -> (all V (ssItem(V) -> cons(V,U) != nil)))) # label(ax21) # label(axiom) # label(non_clause).  [assumption].
87.86/88.26	44 (all U (ssList(U) -> (all V (ssItem(V) -> ssList(cons(V,U)))))) # label(ax16) # label(axiom) # label(non_clause).  [assumption].
87.86/88.26	48 (all U (ssList(U) -> (nil != U -> (exists V (hd(U) = V & ssItem(V)))))) # label(ax75) # label(axiom) # label(non_clause).  [assumption].
87.86/88.26	57 (all U (ssList(U) -> (nil != U -> ssList(tl(U))))) # label(ax24) # label(axiom) # label(non_clause).  [assumption].
87.86/88.26	59 (all U (ssList(U) -> (all V (ssList(V) -> (neq(U,V) <-> V != U))))) # label(ax15) # label(axiom) # label(non_clause).  [assumption].
87.86/88.26	61 (all U (ssList(U) -> segmentP(U,nil))) # label(ax57) # label(axiom) # label(non_clause).  [assumption].
87.86/88.26	65 (all U (ssList(U) -> (nil != U -> cons(hd(U),tl(U)) = U))) # label(ax78) # label(axiom) # label(non_clause).  [assumption].
87.86/88.26	67 (all U (ssItem(U) -> strictorderedP(cons(U,nil)))) # label(ax68) # label(axiom) # label(non_clause).  [assumption].
87.86/88.26	80 (all U (ssList(U) -> frontsegP(U,nil))) # label(ax45) # label(axiom) # label(non_clause).  [assumption].
87.86/88.26	81 (all U (ssItem(U) -> (all V (ssItem(V) -> (all W (ssList(W) -> (all X (ssList(X) -> (frontsegP(cons(U,W),cons(V,X)) <-> U = V & frontsegP(W,X)))))))))) # label(ax44) # label(axiom) # label(non_clause).  [assumption].
87.86/88.26	87 -(all U (ssList(U) -> (all V (ssList(V) -> (all W (ssList(W) -> (all X (ssList(X) -> -neq(V,nil) | -frontsegP(X,W) | neq(U,nil) | (exists Y (neq(W,Y) & strictorderedP(Y) & segmentP(Y,W) & frontsegP(X,Y) & ssList(Y))) | -strictorderedP(W) | W != U | V != X)))))))) # label(co1) # label(negated_conjecture) # label(non_clause).  [assumption].
87.86/88.26	202 -ssList(A) | -ssItem(B) | cons(B,A) != nil # label(ax21) # label(axiom).  [clausify(34)].
87.86/88.26	221 -ssList(A) | -ssItem(B) | ssList(cons(B,A)) # label(ax16) # label(axiom).  [clausify(44)].
87.86/88.26	230 -ssList(A) | A = nil | hd(A) = f32(A) # label(ax75) # label(axiom).  [clausify(48)].
87.86/88.26	231 -ssList(A) | nil = A | f32(A) = hd(A).  [copy(230),flip(b),flip(c)].
87.86/88.26	232 -ssList(A) | A = nil | ssItem(f32(A)) # label(ax75) # label(axiom).  [clausify(48)].
87.86/88.26	233 -ssList(A) | nil = A | ssItem(f32(A)).  [copy(232),flip(b)].
87.86/88.26	241 -ssList(A) | A = nil | ssList(tl(A)) # label(ax24) # label(axiom).  [clausify(57)].
87.86/88.26	242 -ssList(A) | nil = A | ssList(tl(A)).  [copy(241),flip(b)].
87.86/88.26	244 -ssList(A) | -ssList(B) | -neq(A,B) | B != A # label(ax15) # label(axiom).  [clausify(59)].
87.86/88.26	245 -ssList(A) | -ssList(B) | neq(A,B) | B = A # label(ax15) # label(axiom).  [clausify(59)].
87.86/88.26	253 -ssList(A) | segmentP(A,nil) # label(ax57) # label(axiom).  [clausify(61)].
87.86/88.26	263 -ssList(A) | A = nil | cons(hd(A),tl(A)) = A # label(ax78) # label(axiom).  [clausify(65)].
87.86/88.26	264 -ssList(A) | nil = A | cons(hd(A),tl(A)) = A.  [copy(263),flip(b)].
87.86/88.26	268 -ssItem(A) | strictorderedP(cons(A,nil)) # label(ax68) # label(axiom).  [clausify(67)].
87.86/88.26	292 -ssList(A) | frontsegP(A,nil) # label(ax45) # label(axiom).  [clausify(80)].
87.86/88.26	296 -ssItem(A) | -ssItem(B) | -ssList(C) | -ssList(D) | frontsegP(cons(A,C),cons(B,D)) | B != A | -frontsegP(C,D) # label(ax44) # label(axiom).  [clausify(81)].
87.86/88.26	304 ssList(nil) # label(ax17) # label(axiom).  [assumption].
87.86/88.26	305 ssList(c3) # label(co1) # label(negated_conjecture).  [clausify(87)].
87.86/88.26	306 ssList(c4) # label(co1) # label(negated_conjecture).  [clausify(87)].
87.86/88.26	309 neq(c4,nil) # label(co1) # label(negated_conjecture).  [clausify(87)].
87.86/88.26	311 -neq(c3,nil) # label(co1) # label(negated_conjecture).  [clausify(87)].
87.86/88.26	312 -neq(c5,A) | -strictorderedP(A) | -segmentP(A,c5) | -frontsegP(c6,A) | -ssList(A) # label(co1) # label(negated_conjecture).  [clausify(87)].
87.86/88.26	314 c5 = c3 # label(co1) # label(negated_conjecture).  [clausify(87)].
87.86/88.26	315 c6 = c4 # label(co1) # label(negated_conjecture).  [clausify(87)].
87.86/88.26	472 -ssItem(A) | -ssList(B) | -ssList(C) | frontsegP(cons(A,B),cons(A,C)) | -frontsegP(B,C).  [factor(296,a,b),xx(e)].
87.86/88.26	478 -neq(c3,A) | -strictorderedP(A) | -segmentP(A,c3) | -frontsegP(c4,A) | -ssList(A).  [back_rewrite(312),rewrite([314(1),314(4),315(6)])].
87.86/88.26	1655 -ssList(A) | neq(A,nil) | nil = A.  [resolve(304,a,245,b)].
87.86/88.26	1656 -ssList(A) | neq(nil,A) | nil = A.  [resolve(304,a,245,a),flip(c)].
87.86/88.26	1779 c4 = nil | cons(hd(c4),tl(c4)) = c4.  [resolve(306,a,264,a),flip(a)].
87.86/88.26	1787 c4 = nil | ssList(tl(c4)).  [resolve(306,a,242,a),flip(a)].
87.86/88.26	1789 c4 = nil | ssItem(f32(c4)).  [resolve(306,a,233,a),flip(a)].
87.86/88.26	1790 c4 = nil | f32(c4) = hd(c4).  [resolve(306,a,231,a),flip(a)].
87.86/88.26	1852 c4 != nil.  [resolve(309,a,244,c),flip(c),unit_del(a,306),unit_del(b,304)].
87.86/88.26	1860 f32(c4) = hd(c4).  [back_unit_del(1790),unit_del(a,1852)].
87.86/88.26	1861 ssItem(hd(c4)).  [back_unit_del(1789),rewrite([1860(5)]),unit_del(a,1852)].
87.86/88.26	1862 ssList(tl(c4)).  [back_unit_del(1787),unit_del(a,1852)].
87.86/88.26	1866 cons(hd(c4),tl(c4)) = c4.  [back_unit_del(1779),unit_del(a,1852)].
87.86/88.26	6177 strictorderedP(cons(hd(c4),nil)).  [resolve(1861,a,268,a)].
87.86/88.26	6182 -ssList(A) | ssList(cons(hd(c4),A)).  [resolve(1861,a,221,b)].
87.86/88.26	6184 -ssList(A) | cons(hd(c4),A) != nil.  [resolve(1861,a,202,b)].
87.86/88.26	6229 cons(hd(c4),nil) != nil.  [resolve(6184,a,304,a)].
87.86/88.26	6284 frontsegP(tl(c4),nil).  [resolve(1862,a,292,a)].
87.86/88.26	9644 -ssItem(A) | frontsegP(cons(A,tl(c4)),cons(A,nil)).  [resolve(6284,a,472,e),unit_del(b,1862),unit_del(c,304)].
87.86/88.26	16664 c3 = nil.  [resolve(1655,a,305,a),flip(b),unit_del(a,311)].
87.86/88.26	16686 -neq(nil,A) | -strictorderedP(A) | -segmentP(A,nil) | -frontsegP(c4,A) | -ssList(A).  [back_rewrite(478),rewrite([16664(1),16664(4)])].
87.86/88.26	26820 ssList(cons(hd(c4),nil)).  [resolve(6182,a,304,a)].
87.86/88.26	26961 neq(nil,cons(hd(c4),nil)).  [resolve(26820,a,1656,a),flip(b),unit_del(b,6229)].
87.86/88.26	26977 segmentP(cons(hd(c4),nil),nil).  [resolve(26820,a,253,a)].
87.86/88.26	64249 frontsegP(c4,cons(hd(c4),nil)).  [resolve(9644,a,1861,a),rewrite([1866(5)])].
87.86/88.26	71311 $F.  [resolve(16686,a,26961,a),unit_del(a,6177),unit_del(b,26977),unit_del(c,64249),unit_del(d,26820)].
87.86/88.26	
87.86/88.26	% SZS output end Refutation
87.86/88.26	============================== end of proof ==========================
87.86/88.26	
87.86/88.26	============================== STATISTICS ============================
87.86/88.26	
87.86/88.26	Given=15848. Generated=3907181. Kept=71099. proofs=1.
87.86/88.26	Usable=12689. Sos=7991. Demods=483. Limbo=2, Disabled=50663. Hints=0.
87.86/88.26	Megabytes=48.85.
87.86/88.26	User_CPU=83.84, System_CPU=3.16, Wall_clock=87.
87.86/88.26	
87.86/88.26	============================== end of statistics =====================
87.86/88.26	
87.86/88.26	============================== end of search =========================
87.86/88.26	
87.86/88.26	THEOREM PROVED
87.86/88.26	% SZS status Theorem
87.86/88.26	
87.86/88.26	Exiting with 1 proof.
87.86/88.26	
87.86/88.26	Process 7414 exit (max_proofs) Mon Jul  3 08:39:28 2023
87.86/88.27	Prover9 interrupted
87.86/88.27	EOF