0.00/0.04	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.04	% Command    : tptp2X_and_run_prover9 %d %s
0.02/0.24	% Computer   : n187.star.cs.uiowa.edu
0.02/0.24	% Model      : x86_64 x86_64
0.02/0.24	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.02/0.24	% Memory     : 32218.625MB
0.02/0.24	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.02/0.24	% CPULimit   : 300
0.02/0.24	% DateTime   : Sat Jul 14 05:23:39 CDT 2018
0.02/0.24	% CPUTime    : 
0.56/0.85	============================== Prover9 ===============================
0.56/0.85	Prover9 (32) version 2009-11A, November 2009.
0.56/0.85	Process 5978 was started by sandbox on n187.star.cs.uiowa.edu,
0.56/0.85	Sat Jul 14 05:23:40 2018
0.56/0.85	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_5926_n187.star.cs.uiowa.edu".
0.56/0.85	============================== end of head ===========================
0.56/0.85	
0.56/0.85	============================== INPUT =================================
0.56/0.85	
0.56/0.85	% Reading from file /tmp/Prover9_5926_n187.star.cs.uiowa.edu
0.56/0.85	
0.56/0.85	set(prolog_style_variables).
0.56/0.85	set(auto2).
0.56/0.85	    % set(auto2) -> set(auto).
0.56/0.85	    % set(auto) -> set(auto_inference).
0.56/0.85	    % set(auto) -> set(auto_setup).
0.56/0.85	    % set(auto_setup) -> set(predicate_elim).
0.56/0.85	    % set(auto_setup) -> assign(eq_defs, unfold).
0.56/0.85	    % set(auto) -> set(auto_limits).
0.56/0.85	    % set(auto_limits) -> assign(max_weight, "100.000").
0.56/0.85	    % set(auto_limits) -> assign(sos_limit, 20000).
0.56/0.85	    % set(auto) -> set(auto_denials).
0.56/0.85	    % set(auto) -> set(auto_process).
0.56/0.85	    % set(auto2) -> assign(new_constants, 1).
0.56/0.85	    % set(auto2) -> assign(fold_denial_max, 3).
0.56/0.85	    % set(auto2) -> assign(max_weight, "200.000").
0.56/0.85	    % set(auto2) -> assign(max_hours, 1).
0.56/0.85	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.56/0.85	    % set(auto2) -> assign(max_seconds, 0).
0.56/0.85	    % set(auto2) -> assign(max_minutes, 5).
0.56/0.85	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.56/0.85	    % set(auto2) -> set(sort_initial_sos).
0.56/0.85	    % set(auto2) -> assign(sos_limit, -1).
0.56/0.85	    % set(auto2) -> assign(lrs_ticks, 3000).
0.56/0.85	    % set(auto2) -> assign(max_megs, 400).
0.56/0.85	    % set(auto2) -> assign(stats, some).
0.56/0.85	    % set(auto2) -> clear(echo_input).
0.56/0.85	    % set(auto2) -> set(quiet).
0.56/0.85	    % set(auto2) -> clear(print_initial_clauses).
0.56/0.85	    % set(auto2) -> clear(print_given).
0.56/0.85	assign(lrs_ticks,-1).
0.56/0.85	assign(sos_limit,10000).
0.56/0.85	assign(order,kbo).
0.56/0.85	set(lex_order_vars).
0.56/0.85	clear(print_given).
0.56/0.85	
0.56/0.85	% formulas(sos).  % not echoed (212 formulas)
0.56/0.85	
0.56/0.85	============================== end of input ==========================
0.56/0.85	
0.56/0.85	% From the command line: assign(max_seconds, 300).
0.56/0.85	
0.56/0.85	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.56/0.85	
0.56/0.85	% Formulas that are not ordinary clauses:
0.56/0.85	1 (all X all Y all Z (-s_e(X,Y,Z,Z) | Y = X)) # label(aA3) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	2 (all X all Y all X1 all Y1 all Z all Z1 all V all V1 (-s_e(Y,Z,Y1,Z1) | -s_e(Y,V,Y1,V1) | -s_t(X,Y,Z) | -s_t(X1,Y1,Z1) | X = Y | s_e(Z,V,Z1,V1) | -s_e(X,V,X1,V1) | -s_e(X,Y,X1,Y1))) # label(aA5) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	3 (all X all Y s_e(X,Y,Y,X)) # label(aA1) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	4 (all X all Y (X = Y | -s_t(X,Y,X))) # label(aA6) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	5 (all X all Y all W all V (s_e(Y,ext(X,Y,W,V),W,V) & s_t(X,Y,ext(X,Y,W,V)))) # label(aA4) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	6 (all X all Y all Z all V all Z2 all V2 (-s_e(X,Y,Z,V) | -s_e(X,Y,Z2,V2) | s_e(Z,V,Z2,V2))) # label(aA2) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	7 (all Xa all Xp all Xc all Xb all Xq ((-s_t(Xb,Xq,Xc) | s_t(Xp,ip(Xa,Xp,Xc,Xb,Xq),Xb) | -s_t(Xa,Xp,Xc)) & (-s_t(Xa,Xp,Xc) | -s_t(Xb,Xq,Xc) | s_t(Xq,ip(Xa,Xp,Xc,Xb,Xq),Xa)))) # label(aA7) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	8 (all Xp all Xq all Xcs all Xr (Xp = Xq | Xp = Xcs | s_col(Xp,Xcs,Xr) | -s_col(Xp,Xq,Xr) | -s_col(Xp,Xq,Xcs))) # label(aSatz6_16b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	9 (all Xa1 all Xb1 s_t(Xa1,Xa1,Xb1)) # label(aSatz3_3) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	10 (all Xp all Xq all Xr all Xa (s_t(Xp,Xq,Xr) | -s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr)))) # label(aSatz7_15b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	11 (all Xa all Xb all Xc all Xa1 all Xc1 ((-s_e(Xa,Xc,Xa1,Xc1) | s_t(Xa1,insert(Xa,Xb,Xa1,Xc1),Xc1) | -s_t(Xa,Xb,Xc)) & (-s_t(Xa,Xb,Xc) | s_e3(Xa,Xb,Xc,Xa1,insert(Xa,Xb,Xa1,Xc1),Xc1) | -s_e(Xa,Xc,Xa1,Xc1)))) # label(aSatz4_5) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	12 (all Xa all Xb all Xc (-s_r(Xa,Xb,Xc) | s_r(Xa,Xb,s(Xb,Xc)))) # label(aSatz8_4) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	13 (all Xa all Xb all Xc all Xd all Xe all Xf (le(Xa,Xb,Xe,Xf) | -le(Xc,Xd,Xe,Xf) | -le(Xa,Xb,Xc,Xd))) # label(aSatz5_8) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	14 (all Xp all Xq all Xr all Xa (s_col(Xa,Xp,Xq) | Xa != Xp | -s_t(Xq,Xp,Xr) | Xr = Xp | Xq = Xp)) # label(aSatz6_15d) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	15 (all Xa all Xb all Xc all Xc1 (-s_col(Xa,Xb,Xc) | -s_e(Xb,Xc,Xb,Xc1) | Xc = Xc1 | -s_e(Xa,Xc,Xa,Xc1) | Xb = Xa)) # label(aSatz4_18) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	16 (all Xa all Xb all Xc all Xa1 all Xb1 all Xp ((-s_t(Xa,Xb,Xc) | -s_t(Xa1,Xb1,Xc) | s_t(Xb,crossbar(Xa,Xb,Xc,Xa1,Xb1,Xp),Xb1) | -s_t(Xa,Xp,Xa1)) & (s_t(Xp,crossbar(Xa,Xb,Xc,Xa1,Xb1,Xp),Xc) | -s_t(Xa,Xp,Xa1) | -s_t(Xa1,Xb1,Xc) | -s_t(Xa,Xb,Xc)))) # label(aSatz3_17) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	17 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_col(Xa,Xb,Xc) | s_col(Xa1,Xb1,Xc1) | -s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1))) # label(aSatz4_13) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	18 (all Xa all Xb le(Xa,Xb,Xa,Xb)) # label(aSatz5_7) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	19 (all Xa all Xb all Xp all Xp1 ((Xa = Xb | -s_col(Xa,Xb,midpoint(Xp,Xp1)) | Xp1 = reflect(Xa,Xb,Xp) | Xp != Xp1) & (-s_col(Xa,Xb,midpoint(Xp,Xp1)) | -perp(Xa,Xb,Xp,Xp1) | reflect(Xa,Xb,Xp) = Xp1 | Xb = Xa))) # label(aSatz10_2b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	20 (all Xa all Xb all Xp all Xp1 (Xb = Xa | Xp1 != reflect(Xa,Xb,Xp) | reflect(Xa,Xb,Xp1) = Xp)) # label(aSatz10_4) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	21 (all Xa all Xb all Xc all Xp all Xq (Xb = Xa | -s_e(Xa,Xp,Xa,Xq) | s_e(Xc,Xp,Xc,Xq) | -s_e(Xb,Xp,Xb,Xq) | -s_col(Xa,Xb,Xc))) # label(aSatz4_17) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	22 (all Xa all Xb all Xc (s_col(Xc,Xb,Xa) | -s_col(Xa,Xb,Xc))) # label(aSatz4_11c) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	23 (all Xp all Xa all Xq all Xb (Xa = Xb | -s_m(Xp,Xb,Xq) | -s_m(Xp,Xa,Xq))) # label(aSatz7_17) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	24 (all Xa all Xb all Xc (-s_col(Xa,Xb,Xc) | s_col(Xb,Xc,Xa))) # label(aSatz4_11a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	25 (all Xa all Xb all Xc all Xd (-s_t(Xa,Xb,Xc) | s_t(Xa,Xc,Xd) | s_t(Xa,Xd,Xc) | -s_t(Xa,Xb,Xd) | Xa = Xb)) # label(aSatz5_1) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	26 (all Xa all Xb all Xc (-s_r(Xa,Xc,Xb) | Xb = Xc | -s_r(Xa,Xb,Xc))) # label(aSatz8_7) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	27 (all Xa all Xb s_m(Xa,midpoint(Xa,Xb),Xb)) # label(aSatz8_22) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	28 (all Xa all Xb all Xp all Xq all Xc ((-s_col(Xa,Xb,Xp) | Xp = Xq | -perp(Xa,Xb,Xc,Xp) | -s_col(Xa,Xb,Xc) | -s_col(Xa,Xb,Xq) | Xa = Xb) & (Xb = Xa | s_r(Xc,Xp,Xq) | -perp(Xa,Xb,Xc,Xp) | Xp = Xq | -s_col(Xa,Xb,Xq) | -s_col(Xa,Xb,Xp)))) # label(aSatz8_16a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	29 (all Xa all Xp all Xb (-sameside(Xa,Xp,Xb) | -s_t(Xp,Xa,Xb) | le(Xp,Xa,Xp,Xb))) # label(aSatz6_13b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	30 (all Xa all Xb all Xp all Xq all Xr (-s_col(Xp,Xq,Xa) | -s_col(Xp,Xq,Xb) | s_col(Xa,Xb,Xr) | -s_col(Xp,Xq,Xr) | Xp = Xq | Xb = Xa)) # label(aSatz6_18) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	31 (all Xa all Xb all Xp all Xq (-perp(Xa,Xb,Xp,Xq) | -s_col(Xa,Xb,Xq) | -s_col(Xa,Xb,Xp))) # label(aSatz8_14a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	32 (all Xa all Xb s_t(Xa,Xb,Xb)) # label(aSatz3_1) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	33 (all Xa all Xb all Xc all Xa1 (Xb = Xa | -s_col(Xb,Xa,Xa1) | s_r(Xa1,Xb,Xc) | -s_r(Xa,Xb,Xc))) # label(aSatz8_3) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	34 (all Xa all Xb all Xc all Xd all Xa1 all Xb1 all Xc1 all Xd1 (s_e(Xb,Xd,Xb1,Xd1) | -s_ifs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1))) # label(aSatz4_2) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	35 (all Xp all Xq all Xr all Xcs all Xa (-s_e(Xp,Xq,Xr,Xcs) | s_e(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr),s(Xa,Xcs)))) # label(aSatz7_16a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	36 (all Xp all Xq all Xr all Xa (Xp = Xq | -s_t(Xq,Xp,Xr) | s_col(Xa,Xp,Xq) | -sameside(Xa,Xp,Xq) | Xr = Xp)) # label(aSatz6_15b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	37 (all Xa all Xb all Xc all Xd all Xe (-s_e(Xa,Xe,Xc,Xd) | -s_t(Xa,Xb,Xe) | le(Xa,Xb,Xc,Xd))) # label(aSatz5_5b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	38 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_t(Xa,Xb,Xc) | -s_t(Xa1,Xb1,Xc1) | -s_e(Xa,Xb,Xa1,Xb1) | -s_e(Xb,Xc,Xb1,Xc1) | s_e(Xa,Xc,Xa1,Xc1))) # label(aSatz2_11) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	39 (all Xa all Xb all Xc all Xd all Xa1 all Xb1 all Xc1 all Xd1 (Xa = Xb | s_e(Xc,Xd,Xc1,Xd1) | -s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1))) # label(aSatz4_16) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	40 (all Xc all Xd all Xp all Xa all Xb (Xc = Xd | -s_col(Xc,Xd,Xp) | -s_col(Xa,Xb,Xp) | s_col(Xc,Xd,Xa) | samesideline(Xa,Xb,Xc,Xd) | -sameside(Xa,Xp,Xb))) # label(aSatz9_19b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	41 (all Xa all Xb all Xp all Xq all Xc all Xd (-s_col(Xa,Xb,Xp) | -perp(Xa,Xb,Xc,Xd) | perp(Xp,Xq,Xc,Xd) | Xb = Xa | Xq = Xp | -s_col(Xa,Xb,Xq))) # label(aExtPerp5) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	42 (all Xp all Xq all Xr all Xa (-s_t(Xp,Xq,Xr) | s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr)))) # label(aSatz7_15a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	43 (all Xa all Xb all Xp (Xa = Xb | s(Xb,s(Xa,Xp)) != s(Xa,s(Xb,Xp)))) # label(aSatz7_19) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	44 (all Xa all Xp (Xa = Xp | s(Xa,Xp) != Xp)) # label(aSatz7_10a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	45 (all Xa all Xc all Xp all Xb all Xq ((-s_t(Xa,Xc,Xp) | s_t(Xa,op(Xq,Xb,Xp,Xc,Xa),Xb) | -s_t(Xb,Xq,Xc)) & (-s_t(Xa,Xc,Xp) | -s_t(Xb,Xq,Xc) | s_t(Xp,Xq,op(Xq,Xb,Xp,Xc,Xa))))) # label(aSatz9_6) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	46 (all Xa all Xb all Xa1 all Xc1 ext(ext(Xc1,Xa1,alpha,gamma),Xa1,Xa,Xb) = insert(Xa,Xb,Xa1,Xc1)) # label(d_insert) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	47 (all Xa all Xb all Xp ((Xb = Xa | reflect(Xa,Xb,Xp) = Xp | perp(Xa,Xb,Xp,reflect(Xa,Xb,Xp))) & (Xb = Xa | s_col(Xa,Xb,midpoint(Xp,reflect(Xa,Xb,Xp)))))) # label(aSatz10_2a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	48 (all Xd all Xe all Xd1 all Xa all Xb (-samesideline(Xa,Xb,Xd1,Xe) | samesideline(Xa,Xb,Xd,Xe) | -s_t(Xe,Xd,Xd1) | Xe = Xd)) # label(aLemma9_13c) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	49 (all Xa all Xp all Xq all Xc all Xcs all Xr all Xm all U (-perp(Xp,Xq,Xa,Xr) | -s_m(Xr,Xm,Xcs) | -sameside(U,Xr,Xa) | Xcs = Xr | sameside(s(Xm,U),Xcs,Xc) | -le(Xcs,Xc,Xr,Xa) | -perp(Xp,Xq,Xc,Xcs) | -s_col(Xp,Xq,Xr) | -s_col(Xp,Xq,Xcs) | Xq = Xp | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_4a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	50 (all Xa all Xb all Xc ((s_e(Xa,Xc,Xa,s(Xb,Xc)) | -s_r(Xa,Xb,Xc)) & (s_r(Xa,Xb,Xc) | -s_e(Xa,Xc,Xa,s(Xb,Xc))))) # label(d_Defn8_1) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	51 (all Xa all Xp all Xb all Xc (Xp = Xb | Xp = Xc | -s_t(Xa,Xp,Xc) | -sameside(Xa,Xp,Xb) | s_t(Xb,Xp,Xc) | Xp = Xa)) # label(aSatz6_2b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	52 (all Xp all Xq all Xr all Xcs (Xq = Xp | Xp != foot(Xp,Xq,Xr) | opposite(Xr,Xp,Xq,Xcs) | samesideline(Xr,Xcs,Xp,Xq) | s_col(Xp,Xq,Xcs) | s_col(Xp,Xq,Xr))) # label(aLemma9_13f_case1) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	53 (all Xa all Xm (Xa = Xm | -s_m(Xa,Xm,Xa))) # label(aSatz7_3a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	54 (all Xa all Xb all Xp all Xq all Xr (samesideline(Xr,Xb,Xp,Xq) | -sameside(Xa,Xq,Xr) | -samesideline(Xa,Xb,Xp,Xq))) # label(aSatz9_16) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	55 (all Xa all Xp all Xb ((-s_t(Xa,Xp,Xb) | -sameside(Xa,Xp,Xb)) & (-sameside(Xa,Xp,Xb) | s_col(Xa,Xp,Xb)))) # label(aSatz6_4a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	56 (all Xa all Xb all Xc (-s_col(Xa,Xb,Xc) | le(Xa,Xb,Xa,Xc) | -s_t(Xa,Xb,Xc))) # label(aSatz5_12a1) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	57 (all Xa all Xp all Xr all Xq (Xq = Xp | s(Xa,Xq) != Xr | s(Xa,Xp) != Xr)) # label(aSatz7_8) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	58 (all Xa all Xp all Xq all Xc all Xm all Xr all Xb (-opposite(Xa,Xp,Xq,Xc) | -s_col(Xp,Xq,Xr) | -sameside(Xa,Xr,Xb) | opposite(Xb,Xp,Xq,Xc) | -s_t(Xr,Xb,Xa) | -s_m(Xa,Xm,Xc) | -s_col(Xp,Xq,Xm))) # label(aSatz9_3a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	59 (all Xa all Xb all Xc all Xd (s_t(Xa,Xb,Xd) | -s_t(Xa,Xc,Xd) | -s_t(Xa,Xb,Xc))) # label(aSatz3_6b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	60 (all Xp all Xa all Xq (-s_m(Xp,Xa,Xq) | Xq = s(Xa,Xp))) # label(aSatz7_6) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	61 (all Xa all Xb all Xp (Xa = Xb | reflect(Xa,Xb,reflect(Xa,Xb,Xp)) = Xp)) # label(aSatz10_5) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	62 (all Xa1 all Xm1 all Xb1 all Xc all Xb2 all Xm2 all Xa2 (s_t(Xm1,Xc,Xm2) | -s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2))) # label(aSatz7_22b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	63 (all Xa all Xb all Xc all Xd all Xp (s_col(Xa,Xb,Xc) | Xd = Xb | -s_e(Xb,Xc,Xd,Xa) | -s_col(Xa,Xp,Xc) | -s_col(Xb,Xp,Xd) | s_m(Xa,Xp,Xc) | -s_e(Xa,Xb,Xc,Xd))) # label(aSatz7_21) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	64 (all Xa all Xb all Xc all Xd (s_e(Xa,Xb,Xc,Xd) | -le(Xc,Xd,Xa,Xb) | -le(Xa,Xb,Xc,Xd))) # label(aSatz5_9) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	65 (all Xp all Xq all Xr (Xq = Xp | s_col(Xq,Xp,Xr) | -s_col(Xp,Xq,Xr))) # label(aSatz6_17b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	66 (all Xa all Xb all Xc all Xd all Y ((-le(Xa,Xb,Xc,Xd) | s_e(Xa,Xb,Xc,insert(Xa,Xb,Xc,Xd))) & (le(Xa,Xb,Xc,Xd) | -s_e(Xa,Xb,Xc,Y) | -s_t(Xc,Y,Xd)) & (-le(Xa,Xb,Xc,Xd) | s_t(Xc,insert(Xa,Xb,Xc,Xd),Xd)))) # label(d_Defn5_4) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	67 (all Xp all Xq all Xa all Xb (-samesideline(Xp,Xq,Xa,Xb) | samesideline(Xp,Xq,Xb,Xa))) # label(aLemma9_13a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	68 (all Xa all Xb all Xc all Xd all Xa1 all Xb1 all Xc1 all Xd1 (-le(Xa,Xb,Xc,Xd) | -s_e(Xa,Xb,Xa1,Xb1) | le(Xa1,Xb1,Xc1,Xd1) | -s_e(Xc,Xd,Xc1,Xd1))) # label(aSatz5_6) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	69 (all Xa all Xb (-s_col(Xa,Xb,pointOffLine(Xa,Xb)) | Xa = Xb)) # label(aSatz6_25) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	70 (all Xa all Xc all Xb all Xc1 (-s_t(Xa,Xc,Xb) | -s_e(Xa,Xc,Xa,Xc1) | Xc = Xc1 | -s_e(Xb,Xc,Xb,Xc1))) # label(aSatz4_19) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	71 (all Xa all Xb all Xp all Xp1 (Xp1 != reflect(Xa,Xb,Xp) | reflect(Xa,Xb,Xp1) = Xp | Xb = Xa)) # label(aSatz10_6) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	72 (all Xa all Xp all Xb (-le(Xp,Xa,Xp,Xb) | s_t(Xp,Xa,Xb) | -sameside(Xa,Xp,Xb))) # label(aSatz6_13a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	73 (all Xp all Xa all Xr all Xq (-s_m(Xp,Xa,Xq) | Xq = Xr | -s_m(Xp,Xa,Xr))) # label(aSatz7_4b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	74 (all Xa all Xb all Xc all Xd (-s_e(Xa,Xb,Xc,Xd) | s_e(Xa,Xb,Xd,Xc))) # label(aSatz2_5) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	75 (all Xa1 all Xc all Xa2 all Xb1 all Xb2 all Xm1 all Xm2 (s_t(Xm1,Xc,Xm2) | -s_m(Xa2,Xm2,Xb2) | -s_m(Xa1,Xm1,Xb1) | -s_e(Xc,Xa2,Xc,Xb2) | -s_e(Xc,Xa1,Xc,Xb1) | -s_t(Xb1,Xc,Xb2) | -s_t(Xa1,Xc,Xa2))) # label(aSatz7_22) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	76 (all Xa all Xp all Xq all Xc all Xcs all Xr all Xm all U (Xq = Xp | -s_col(Xp,Xq,Xcs) | -s_col(Xp,Xq,Xr) | -perp(Xp,Xq,Xa,Xr) | sameside(U,Xr,Xa) | -le(Xcs,Xc,Xr,Xa) | Xr = Xcs | -sameside(s(Xm,U),Xcs,Xc) | -s_m(Xr,Xm,Xcs) | -perp(Xp,Xq,Xc,Xcs) | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_4a2) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	77 (all Xb all Xc all Xa (-s_e(Xb,Xc,Xa,Xa) | Xb = Xc)) # label(aSatz2_13) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	78 (all Xp all Xa all Xb all Xq all Xt all Xr all Xcx (-perp(Xp,Xa,Xa,Xb) | -s_col(Xa,Xb,Xt) | -s_t(Xb,Xr,Xq) | -s_e(Xa,Xp,Xb,Xr) | Xcx != ip(Xp,Xt,Xq,Xb,Xr) | s_m(Xa,Xcx,Xb) | -s_t(Xp,Xt,Xq) | -perp(Xq,Xb,Xa,Xb))) # label(aSatz8_24a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	79 (all Xa all Xb all Xc (-s_t(Xa,Xb,Xc) | s_t(Xc,Xb,Xa))) # label(aSatz3_2) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	80 (all Xp all Xq all Xr all Xcs (samesideline(Xr,Xcs,Xp,Xq) | Xp = foot(Xp,Xq,Xr) | opposite(Xr,Xp,Xq,Xcs) | s_col(Xp,Xq,Xcs) | s_col(Xp,Xq,Xr) | Xq = Xp)) # label(aLemma9_13f_case2) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	81 (all Xa all Xb s_col(Xa,Xb,Xa)) # label(aSatz4_12b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	82 (all Xa all Xb all Xc all Xd (Xc = Xb | s_t(Xa,Xb,Xd) | -s_t(Xb,Xc,Xd) | -s_t(Xa,Xb,Xc))) # label(aSatz3_7b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	83 (all Xp all Xq all Xp1 all Xq1 all X ((-perp(Xp,Xq,Xp1,Xq1) | perpAt(Xp,Xq,il(Xp,Xq,Xp1,Xq1),Xp1,Xq1)) & (perp(Xp,Xq,Xp1,Xq1) | -perpAt(Xp,Xq,X,Xp1,Xq1)))) # label(d_Defn8_11b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	84 (all Xa all Xb all Xc all Xd all Za all Zb all Zc all Zd ((s_t(Xa,Xb,Xc) | -s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)) & (-s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_e(Xa,Xb,Za,Zb)) & (s_e(Xb,Xd,Zb,Zd) | -s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)) & (-s_t(Xa,Xb,Xc) | -s_e(Xa,Xb,Za,Zb) | -s_e(Xb,Xd,Zb,Zd) | s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | -s_e(Xa,Xd,Za,Zd) | -s_e(Xb,Xc,Zb,Zc) | -s_t(Za,Zb,Zc)) & (s_e(Xa,Xd,Za,Zd) | -s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)) & (-s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_e(Xb,Xc,Zb,Zc)) & (-s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_t(Za,Zb,Zc)))) # label(d_Defn2_10) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	85 (all Xa all Xb all Xc all Xd (s_e(Xb,Xa,Xd,Xc) | -s_e(Xa,Xb,Xc,Xd))) # label(aSatz2_14) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	86 (all Xa all Xm (s_m(Xa,Xm,Xa) | Xa != Xm)) # label(aSatz7_3b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	87 (all Xa all Xb all Xd all Xc (-s_t(Xa,Xb,Xd) | -s_t(Xb,Xc,Xd) | s_t(Xa,Xb,Xc))) # label(aSatz3_5a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	88 (all Xa all Xb all Xp all Xq (Xb = Xa | s_e(Xp,Xq,reflect(Xa,Xb,Xp),reflect(Xa,Xb,Xq)) | -s_col(Xa,Xb,Xp))) # label(aSatz10_10a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	89 (all Xa all Xb all Xp all Xq all Xc (-s_col(Xa,Xb,Xq) | s_col(Xa,Xb,Xc) | -s_r(Xc,Xp,Xq) | perp(Xa,Xb,Xc,Xp) | Xq = Xp | -s_col(Xa,Xb,Xp) | Xb = Xa)) # label(aSatz8_16b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	90 (all Xa all Xb all Xc all Xp (-s_r(Xa,Xb,Xc) | -s_m(s(Xa,Xc),Xp,s(Xb,Xc)) | s_r(Xb,Xa,Xp))) # label(aSatz8_20a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	91 (all Xa all Xb all Xp all Xq (perp(Xa,Xb,Xq,Xp) | -perp(Xa,Xb,Xp,Xq))) # label(aExtPerp4) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	92 (all Xa all Xp s(Xa,s(Xa,Xp)) = Xp) # label(aSatz7_7) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	93 (all Xa all Xb all Xc (-s_col(Xa,Xb,Xc) | s_col(Xa,Xc,Xb))) # label(aSatz4_11e) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	94 (all Xa all Xb all Xc (Xa = Xb | -s_t(Xb,Xa,Xc) | -s_t(Xa,Xb,Xc))) # label(aSatz3_4) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	95 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1) | s_t(Xa1,Xb1,Xc1) | -s_t(Xa,Xb,Xc))) # label(aSatz4_6) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	96 (all Xa all Xb all Xp all Xq (Xb = Xa | reflect(Xa,Xb,Xp) != reflect(Xa,Xb,Xq) | Xq = Xp)) # label(aSatz10_7) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	97 (all Xa all Xb all Xc all Xd all Xp (Xa = Xb | Xd = Xc | s_col(Xa,Xb,Xp) | -s_col(Xc,Xd,Xp) | -s_col(Xa,Xb,Xd) | -s_col(Xa,Xb,Xc))) # label(aExtCol2) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	98 (all Xa all Xb all Xc ((perp(Xa,Xb,erect(Xa,Xb,Xc),Xa) | Xb = Xa) & (Xb = Xa | s_col(Xa,Xb,erectAux(Xa,Xb,Xc))) & (Xa = Xb | s_t(Xc,erectAux(Xa,Xb,Xc),erect(Xa,Xb,Xc))))) # label(aSatz8_21) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	99 (all Xp all Xq all Xa all Xb all Xc (Xq = Xp | -samesideline(Xa,Xb,Xp,Xq) | -samesideline(Xb,Xc,Xp,Xq) | samesideline(Xa,Xc,Xp,Xq))) # label(aSatz9_13) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	100 (all Xa all Xb all Xc all Xp all Xq (-perpAt(Xa,Xb,Xc,Xp,Xq) | Xc = il(Xa,Xb,Xp,Xq))) # label(aSatz8_14c) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	101 (all Xa all Xb all Xp all Xq (s_e(Xp,Xq,reflect(Xa,Xb,Xp),reflect(Xa,Xb,Xq)) | Xb = Xa)) # label(aSatz10_10) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	102 (all Xa all Xp all Xb (s(Xa,Xp) != s(Xb,Xp) | Xb = Xa)) # label(aSatz7_18) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	103 (all Y all Z all X all Y1 all Z1 all U all V ((-perpAt(Y,Z,X,Y1,Z1) | Y1 != Z1) & (perpAt(Y,Z,X,Y1,Z1) | Z = Y | Z1 = Y1 | -s_col(Y1,Z1,X) | s_col(Y1,Z1,g811(Y,Z,Y1,Z1,X)) | -s_col(Y,Z,X)) & (Z = Y | Y1 = Z1 | -s_col(Y,Z,X) | -s_col(Y1,Z1,X) | -s_r(f811(Y,Z,Y1,Z1,X),X,g811(Y,Z,Y1,Z1,X)) | perpAt(Y,Z,X,Y1,Z1)) & (perpAt(Y,Z,X,Y1,Z1) | -s_col(Y,Z,X) | -s_col(Y1,Z1,X) | s_col(Y,Z,f811(Y,Z,Y1,Z1,X)) | Z1 = Y1 | Y = Z) & (s_r(U,X,V) | -s_col(Y1,Z1,V) | -s_col(Y,Z,U) | -perpAt(Y,Z,X,Y1,Z1)) & (Y != Z | -perpAt(Y,Z,X,Y1,Z1)) & (s_col(Y1,Z1,X) | -perpAt(Y,Z,X,Y1,Z1)) & (s_col(Y,Z,X) | -perpAt(Y,Z,X,Y1,Z1)))) # label(d_Defn8_11a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	104 (all Xa all Xb all Xc all Xa1 (-s_r(Xa,Xb,Xc) | -s_r(Xa1,Xb,Xc) | -s_t(Xa,Xc,Xa1) | Xb = Xc)) # label(aSatz8_6) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	105 (all Xa all Xb all Xp all Xq all Xr all Xc all Xd (-s_col(Xa,Xb,Xp) | -s_col(Xa,Xb,Xq) | Xa = Xb | -perpAt(Xp,Xq,Xr,Xc,Xd) | perpAt(Xa,Xb,Xr,Xc,Xd) | Xq = Xp)) # label(aExtPerp) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	106 (all Xa all Xb all Xc all XA all XB all XC (-s_e(Xa,Xb,XB,XC) | -s_e(Xb,Xc,XA,XB) | s_e(Xa,Xc,XA,XC) | -s_t(XA,XB,XC) | -s_t(Xa,Xb,Xc))) # label(aSatz2_15) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	107 (all Xa all Xb s_r(Xa,Xb,Xb)) # label(aSatz8_5) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	108 (all Xa all Xb s_t(Xa,Xb,ext(Xa,Xb,alpha,gamma))) # label(aSatz3_14a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	109 (all Xp all Xa s_m(Xp,Xa,s(Xa,Xp))) # label(aSatz7_4a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	110 (all Xa all Xb all Xc ((s_col(Xa,Xb,Xc) | s_col(Xa,Xb,foot(Xa,Xb,Xc))) & (perp(Xa,Xb,Xc,foot(Xa,Xb,Xc)) | s_col(Xa,Xb,Xc)))) # label(aSatz8_18) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	111 (all Xa all Xb all Xp all Xq (Xb = Xa | -samesideline(Xp,Xq,Xa,Xb) | samesideline(Xp,Xq,Xb,Xa))) # label(aExtSameSide2) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	112 (all Xa all Xb all Xc (-s_r(Xa,Xb,Xc) | Xc = Xb | Xb = Xa | -s_col(Xa,Xb,Xc))) # label(aSatz8_9) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	113 (all Xa all Xm all Xb (-s_m(Xa,Xm,Xb) | s_m(Xb,Xm,Xa))) # label(aSatz7_2) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	114 (all Xa all Xb all Xp all Xq (samesideline(Xq,Xp,Xa,Xb) | -samesideline(Xp,Xq,Xa,Xb) | Xa = Xb)) # label(aLemma9_13d) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	115 (all Xa all Xb all Xc all Xd ((ext(Xa,Xb,insert(Xa,Xb,Xc,Xd),Xd) = ins(Xc,Xd,Xa,Xb) | -le(Xa,Xb,Xc,Xd)) & (s_e(Xa,ins(Xc,Xd,Xa,Xb),Xc,Xd) | -le(Xa,Xb,Xc,Xd)) & (s_t(Xa,Xb,ins(Xc,Xd,Xa,Xb)) | -le(Xa,Xb,Xc,Xd)))) # label(aSatz5_5a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	116 (all Xa all Xb all Xc all Xd (-s_t(Xa,Xb,Xc) | -s_t(Xa,Xc,Xd) | s_t(Xb,Xc,Xd))) # label(aSatz3_6a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	117 (all Xa all Xb s_e(Xa,Xb,Xa,Xb)) # label(aSatz2_1) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	118 (all Xb all Xa ext(Xa,Xb,alpha,gamma) != Xb) # label(aSatz3_14b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	119 (all Xp all Xq all Xr all Xa (Xq = Xp | sameside(Xa,Xp,Xq) | sameside(Xa,Xp,Xr) | Xp = Xa | -s_col(Xa,Xp,Xq) | -s_t(Xq,Xp,Xr) | Xp = Xr)) # label(aSatz6_15a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	120 (all Xp all Xq all Xc all Xa all Xb (Xa = Xc | s_col(Xc,Xa,Xb) | -perpAt(Xp,Xq,Xc,Xb,Xc) | -perpAt(Xp,Xq,Xc,Xa,Xc) | Xq = Xp)) # label(aLemma9_13g) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	121 (all Xa all Xp all Xq all Xc all Xcs all Xr all Xm all U (Xp = Xq | -s_col(Xp,Xq,Xr) | -perp(Xp,Xq,Xa,Xr) | -perp(Xp,Xq,Xc,Xcs) | sameside(s(Xm,U),Xcs,Xc) | Xcs != Xr | -sameside(U,Xr,Xa) | -s_m(Xr,Xm,Xcs) | -s_col(Xp,Xq,Xcs) | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_4b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	122 (all Xa all Xb all Xc (-s_r(Xa,Xb,Xc) | s_r(Xc,Xb,Xa))) # label(aSatz8_2) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	123 (all Xa all Xb all Xp (Xb = Xa | Xp != reflect(Xa,Xb,Xp) | s_col(Xa,Xb,Xp))) # label(aSatz10_8a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	124 (all Xa all Xb all Xd all Xc (s_t(Xa,Xc,Xd) | -s_t(Xb,Xc,Xd) | -s_t(Xa,Xb,Xd))) # label(aSatz3_5b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	125 (all Xa all Xb (Xa = Xb | -s_r(Xa,Xb,Xa))) # label(aSatz8_8) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	126 (all Xp all Xq all Xr all Xcs (s_col(Xp,Xq,Xcs) | opposite(Xr,Xp,Xq,Xcs) | samesideline(Xr,Xcs,Xp,Xq) | s_col(Xp,Xq,Xr) | Xp = Xq)) # label(aLemma9_13f) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	127 (all Xa all Xb all Xc (-s_col(Xa,Xb,Xc) | s_t(Xa,Xb,Xc) | -le(Xb,Xc,Xa,Xc) | -le(Xa,Xb,Xa,Xc))) # label(aSatz5_12b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	128 (all Xa all Xb all Xc (-s_col(Xa,Xb,Xc) | s_col(Xb,Xa,Xc))) # label(aSatz4_11d) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	129 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_t(Xa,Xb,Xc) | -s_t(Xa1,Xb1,Xc1) | s_e(Xa,Xb,Xa1,Xb1) | -s_e(Xb,Xc,Xb1,Xc1) | -s_e(Xa,Xc,Xa1,Xc1))) # label(aSatz4_3) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	130 (all Xa all Xb all Xp all Xq all Xcx all U all V (Xa = Xb | Xq = Xp | -s_col(Xp,Xq,V) | -s_r(U,Xcx,V) | perpAt(Xa,Xb,Xcx,Xp,Xq) | Xcx = V | U = Xcx | -s_col(Xa,Xb,U) | -s_col(Xa,Xb,Xcx) | -s_col(Xp,Xq,Xcx))) # label(aSatz8_13b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	131 (all Xa all Xb all Xc all Xd all Xe all Xf (s_e(Xa,Xb,Xe,Xf) | -s_e(Xc,Xd,Xe,Xf) | -s_e(Xa,Xb,Xc,Xd))) # label(aSatz2_3) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	132 (all Xa all Xp all Xb all Xq all Xt (-le(Xa,Xp,Xb,Xq) | -perp(Xa,Xb,Xb,Xq) | s_m(Xa,midpointAux(Xa,Xb,Xp,Xq,Xt),Xb) | -s_col(Xa,Xb,Xt) | -s_t(Xp,Xt,Xq) | -perp(Xa,Xb,Xa,Xp))) # label(aSatz8_22b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	133 (all Xa all Xp all Xq all Xb (-opposite(Xa,Xp,Xq,Xb) | -samesideline(Xa,Xb,Xp,Xq))) # label(aSatz9_9) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	134 (all Xa all Xb all Xc all Xp all Xq (-s_col(Xa,Xb,Xp) | -s_col(Xa,Xb,Xq) | -perp(Xa,Xb,Xc,Xq) | Xp = Xq | -perp(Xa,Xb,Xc,Xp) | s_col(Xa,Xb,Xc))) # label(aSatz8_18a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	135 (all Xp all Xq all Xr all Xa (-s_t(Xq,Xp,Xr) | -sameside(Xa,Xp,Xr) | s_col(Xa,Xp,Xq) | Xr = Xp | Xp = Xq)) # label(aSatz6_15c) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	136 (all Xr all Xa all Xb all Xc ((sameside(insert(Xb,Xc,Xa,Xr),Xa,Xr) | Xc = Xb | Xr = Xa) & (Xc = Xb | s_e(Xa,insert(Xb,Xc,Xa,Xr),Xb,Xc) | Xr = Xa))) # label(aSatz6_11a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	137 (all Xa all Xb all Xp all Xq all Xc all Xd (Xa = Xb | -perp(Xp,Xq,Xc,Xd) | perp(Xa,Xb,Xc,Xd) | Xq = Xp | -s_col(Xa,Xb,Xq) | -s_col(Xa,Xb,Xp))) # label(aExtPerp2) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	138 (all Xa all Xb all Xc all Xd all Xa1 all Xb1 all Xc1 all Xd1 ((s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1) | -s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1)) & (-s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1) | s_e(Xb,Xd,Xb1,Xd1)) & (-s_col(Xa,Xb,Xc) | -s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1) | -s_e(Xa,Xd,Xa1,Xd1) | s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1) | -s_e(Xb,Xd,Xb1,Xd1)) & (-s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1) | s_e(Xa,Xd,Xa1,Xd1)) & (-s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1) | s_col(Xa,Xb,Xc)))) # label(d_Defn4_15) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	139 (all Xa all Xp all Xb (sameside(Xa,Xp,Xb) | -s_col(Xa,Xp,Xb) | s_t(Xa,Xp,Xb))) # label(aSatz6_4b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	140 (all Xa all Xb all Xc ((s_col(Xa,Xb,Xc) | perp(Xa,Xb,erect21a(Xa,Xb,Xc),Xa) | Xb = Xa) & (s_col(Xa,Xb,Xc) | s_col(Xa,Xb,erectAux21a(Xa,Xb,Xc)) | Xa = Xb) & (s_t(Xc,erectAux21a(Xa,Xb,Xc),erect21a(Xa,Xb,Xc)) | s_col(Xa,Xb,Xc) | Xb = Xa))) # label(aSatz8_21a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	141 (all Xa all Xb all Xd all Xc (-s_t(Xa,Xb,Xd) | -s_t(Xa,Xc,Xd) | s_t(Xa,Xc,Xb) | s_t(Xa,Xb,Xc))) # label(aSatz5_3) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	142 (all Xp all Xa all Xb all Xq all Xt all Xr (-perp(Xp,Xa,Xa,Xb) | -s_t(Xp,Xt,Xq) | s_m(Xp,midpoint(Xa,Xb),Xr) | -s_e(Xa,Xp,Xb,Xr) | -s_t(Xb,Xr,Xq) | -s_col(Xa,Xb,Xt) | -perp(Xq,Xb,Xa,Xb))) # label(aSatz8_24) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	143 (all Xa all Xb all Xp all Xq all Xc (-perp(Xa,Xb,Xp,Xq) | -s_col(Xa,Xb,Xc) | perpAt(Xa,Xb,Xc,Xp,Xq) | -s_col(Xp,Xq,Xc))) # label(aSatz8_14b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	144 (all Xa all Xb all Xc all Xa1 all Xb1 (-s_col(Xa,Xb,Xc) | s_e3(Xa,Xb,Xc,Xa1,Xb1,insert5(Xa,Xb,Xc,Xa1,Xb1)) | -s_e(Xa,Xb,Xa1,Xb1))) # label(aSatz4_14) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	145 (all Xp all Xq (Xq = Xp | s_col(Xp,Xq,Xp))) # label(aSatz6_17a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	146 (all Xa all Xb all Xc ((-s_col(Xa,Xb,Xc) | s_t(Xa,Xb,Xc) | s_t(Xc,Xa,Xb) | s_t(Xb,Xc,Xa)) & (-s_t(Xb,Xc,Xa) | s_col(Xa,Xb,Xc)) & (-s_t(Xc,Xa,Xb) | s_col(Xa,Xb,Xc)) & (-s_t(Xa,Xb,Xc) | s_col(Xa,Xb,Xc)))) # label(d_Defn4_10) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	147 (all Xa all Xb all Xc all Xp all Xq (perpAt(Xp,Xq,Xc,Xa,Xb) | -perpAt(Xa,Xb,Xc,Xp,Xq))) # label(aSatz8_12a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	148 (all Xa all Xb all Xc (-s_col(Xa,Xb,Xc) | -s_t(Xa,Xb,Xc) | le(Xb,Xc,Xa,Xc))) # label(aSatz5_12a2) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	149 (all Xa all Xp all Xb (sameside(Xb,Xp,Xa) | -sameside(Xa,Xp,Xb))) # label(aSatz6_6) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	150 (all Xa all Xp (s(Xa,Xp) = Xp | Xp != Xa)) # label(aSatz7_10b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	151 (all Xa all Xp all Xb all Xc (sameside(Xa,Xp,Xc) | -sameside(Xb,Xp,Xc) | -sameside(Xa,Xp,Xb))) # label(aSatz6_7) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	152 (all Xa all Xb all Xc all Xd (-s_t(Xc,Xa,Xb) | s_t(Xd,Xc,Xb) | s_t(Xc,Xd,Xb) | -s_t(Xd,Xa,Xb) | Xb = Xa)) # label(aSatz6_16a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	153 (all Xa all Xp all Xq all Xc all Xm all Xr all Xb (-opposite(Xa,Xp,Xq,Xc) | opposite(Xb,Xp,Xq,Xc) | -sameside(Xa,Xr,Xb) | -s_col(Xp,Xq,Xr) | -s_m(Xa,Xm,Xc) | -s_col(Xp,Xq,Xm))) # label(aSatz9_3) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	154 (all Xa all Xp all Xq all Xc all Xcs all Xr all Xm all U all V (-opposite(Xa,Xp,Xq,Xc) | -s_col(Xp,Xq,Xr) | -perp(Xp,Xq,Xa,Xr) | -perp(Xp,Xq,Xc,Xcs) | -sameside(U,Xr,Xa) | -sameside(V,Xcs,Xc) | opposite(U,Xp,Xq,V) | -s_m(Xr,Xm,Xcs) | -s_col(Xp,Xq,Xcs) | Xp = Xq)) # label(aSatz9_4c) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	155 (all Xa all Xb all Xc all Xd (-s_t(Xb,Xc,Xd) | s_t(Xa,Xc,Xd) | Xc = Xb | -s_t(Xa,Xb,Xc))) # label(aSatz3_7a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	156 (all Xa all Xb all Xc all Xa1 (-s_r(Xa,Xb,Xc) | -s_e(Xa,Xb,Xa1,Xb) | s_e(Xa,Xc,Xa1,Xc) | -s_r(Xa1,Xb,Xc))) # label(aSatz10_12b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	157 (all Xa all Xb all Xp (Xp = reflect(Xa,Xb,Xp) | -s_col(Xa,Xb,Xp) | Xa = Xb)) # label(aSatz10_8b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	158 (all Xa1 all Xm1 all Xb1 all Xc all Xb2 all Xm2 all Xa2 ((-s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) | s_e(Xc,Xa1,Xc,Xb1)) & (s_e(Xc,Xa2,Xc,Xb2) | -s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2)) & (s_m(Xa2,Xm2,Xb2) | -s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2)) & (-s_t(Xb1,Xc,Xb2) | -s_m(Xa1,Xm1,Xb1) | s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) | -s_m(Xa2,Xm2,Xb2) | -s_e(Xc,Xa2,Xc,Xb2) | -s_e(Xc,Xa1,Xc,Xb1) | -s_t(Xa1,Xc,Xa2)) & (s_m(Xa1,Xm1,Xb1) | -s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2)) & (s_t(Xb1,Xc,Xb2) | -s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2)) & (s_t(Xa1,Xc,Xa2) | -s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2)))) # label(d_Defn7_23) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	159 (all Xa all Xp all Xb all Xc (Xc = Xp | -s_t(Xa,Xp,Xc) | sameside(Xa,Xp,Xb) | -s_t(Xb,Xp,Xc) | Xb = Xp | Xa = Xp)) # label(aSatz6_2a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	160 (all Xa all Xb all Xc all Xp all Xq (-samesideline(Xp,Xq,Xa,Xb) | samesideline(Xp,Xq,Xa,Xc) | Xa = Xc | Xa = Xb | -s_col(Xa,Xb,Xc))) # label(aExtSameSide1) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	161 (all Xq all Xa all Xd all Xb all Xc (Xd = ext(Xq,Xa,Xb,Xc) | -s_e(Xa,Xd,Xb,Xc) | -s_t(Xq,Xa,Xd) | Xq = Xa)) # label(aSatz2_12) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	162 (all Xp all Xq all Xa s_e(Xp,Xq,s(Xa,Xp),s(Xa,Xq))) # label(aSatz7_13) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	163 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-sameside(Xa1,Xb1,Xc1) | -s_e(Xb,Xa,Xb1,Xa1) | -s_e(Xb,Xc,Xb1,Xc1) | s_e(Xa,Xc,Xa1,Xc1) | -sameside(Xa,Xb,Xc))) # label(aSatz6_28) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	164 (all Xa all Xp (Xa = Xp | sameside(Xa,Xp,Xa))) # label(aSatz6_5) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	165 (all Xa all Xb all U all V all W (Xb = Xa | -s_col(Xa,Xb,W) | s_col(Xa,Xb,V) | -s_col(Xa,Xb,U) | -s_m(U,V,W))) # label(aLemma9_13b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	166 (all Xa all Xb all Xp all Xq all Xc all Xd all Xe (Xp = Xq | -s_col(Xp,Xq,Xc) | -s_col(Xa,Xb,Xd) | s_col(Xp,Xq,Xe) | -s_col(Xa,Xb,Xe) | Xc = Xd | -s_col(Xp,Xq,Xd) | -s_col(Xa,Xb,Xc) | Xb = Xa)) # label(aSatz6_21) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	167 (all Xp all Xa all Xb all Xq all Xt all Xr all Xcx (-perp(Xp,Xa,Xa,Xb) | -s_t(Xp,Xt,Xq) | ip(Xp,Xt,Xq,Xb,Xr) != Xcx | s_m(Xp,Xcx,Xr) | -s_e(Xa,Xp,Xb,Xr) | -s_t(Xb,Xr,Xq) | -s_col(Xa,Xb,Xt) | -perp(Xq,Xb,Xa,Xb))) # label(aSatz8_24b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	168 (all Xa all Xm all Xb ((-s_m(Xa,Xm,Xb) | s_t(Xa,Xm,Xb)) & (-s_t(Xa,Xm,Xb) | -s_e(Xm,Xa,Xm,Xb) | s_m(Xa,Xm,Xb)) & (s_e(Xm,Xa,Xm,Xb) | -s_m(Xa,Xm,Xb)))) # label(d_Defn7_1) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	169 (all Xa all Xb all Xp all Xq (-perp(Xa,Xb,Xp,Xq) | perp(Xp,Xq,Xa,Xb))) # label(aSatz8_12b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	170 (all Xa all Xb all Xc all Xm (-sameside(Xa,Xb,Xc) | sameside(s(Xm,Xa),s(Xm,Xb),s(Xm,Xc)))) # label(aSideReflect) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	171 (all Xa all Xc all Xd le(Xa,Xa,Xc,Xd)) # label(aSatz5_11) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	172 (all Xa all Xb all Xc all Xp all Xq ((-perpAt(Xa,Xb,Xc,Xp,Xq) | Xa != Xb) & (s_col(Xp,Xq,Xc) | -perpAt(Xa,Xb,Xc,Xp,Xq)) & (-perpAt(Xa,Xb,Xc,Xp,Xq) | s_r(f813(Xa,Xb,Xp,Xq,Xc),Xc,g813(Xa,Xb,Xp,Xq,Xc))) & (-perpAt(Xa,Xb,Xc,Xp,Xq) | Xc != g813(Xa,Xb,Xp,Xq,Xc)) & (f813(Xa,Xb,Xp,Xq,Xc) != Xc | -perpAt(Xa,Xb,Xc,Xp,Xq)) & (-perpAt(Xa,Xb,Xc,Xp,Xq) | s_col(Xp,Xq,g813(Xa,Xb,Xp,Xq,Xc))) & (-perpAt(Xa,Xb,Xc,Xp,Xq) | s_col(Xa,Xb,f813(Xa,Xb,Xp,Xq,Xc))) & (-perpAt(Xa,Xb,Xc,Xp,Xq) | s_col(Xa,Xb,Xc)) & (-perpAt(Xa,Xb,Xc,Xp,Xq) | Xp != Xq))) # label(aSatz8_13a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	173 (all Xa all Xb all Xp all Xq all Xu all Xc all Xv ((-samesideline(Xa,Xb,Xp,Xq) | s_col(Xp,Xq,ss1(Xa,Xb,Xp,Xq))) & (-samesideline(Xa,Xb,Xp,Xq) | s_col(Xp,Xq,ss2(Xa,Xb,Xp,Xq))) & (s_t(Xb,ss2(Xa,Xb,Xp,Xq),ss3(Xa,Xb,Xp,Xq)) | -samesideline(Xa,Xb,Xp,Xq)) & (-samesideline(Xa,Xb,Xp,Xq) | Xb != ss2(Xa,Xb,Xp,Xq)) & (-samesideline(Xa,Xb,Xp,Xq) | -s_col(Xp,Xq,Xa)) & (-s_col(Xp,Xq,Xb) | -samesideline(Xa,Xb,Xp,Xq)) & (-s_t(Xa,Xu,Xc) | -s_col(Xp,Xq,Xu) | -s_col(Xp,Xq,Xv) | Xu = Xa | Xv = Xb | s_col(Xp,Xq,Xa) | samesideline(Xa,Xb,Xp,Xq) | s_col(Xp,Xq,Xb) | Xv = Xc | Xc = Xu | Xp = Xq | -s_t(Xb,Xv,Xc)) & (-samesideline(Xa,Xb,Xp,Xq) | Xq != Xp) & (ss3(Xa,Xb,Xp,Xq) != ss2(Xa,Xb,Xp,Xq) | -samesideline(Xa,Xb,Xp,Xq)) & (ss1(Xa,Xb,Xp,Xq) != ss3(Xa,Xb,Xp,Xq) | -samesideline(Xa,Xb,Xp,Xq)) & (Xa != ss1(Xa,Xb,Xp,Xq) | -samesideline(Xa,Xb,Xp,Xq)) & (-samesideline(Xa,Xb,Xp,Xq) | s_t(Xa,ss1(Xa,Xb,Xp,Xq),ss3(Xa,Xb,Xp,Xq))))) # label(d_Defn9_7) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	174 (all Xp all Xq all Xr all Xcs all Xa (s_e(Xp,Xq,Xr,Xcs) | -s_e(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr),s(Xa,Xcs)))) # label(aSatz7_16b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.85	175 (all Xa all Xb all Xc all Xd (Xa = Xb | Xa = Xc | Xc = Xb | Xd = Xa | -perp(Xb,Xa,Xa,Xc) | -s_col(Xa,Xc,Xd) | perp(Xb,Xa,Xa,Xd) | Xc = Xd)) # label(aExtPerp3) # label(axiom) # label(non_clause).  [assumption].
0.56/0.86	176 (all Xa all Xb all Xc all Xd (le(Xa,Xb,Xc,Xd) | le(Xc,Xd,Xa,Xb))) # label(aSatz5_10) # label(axiom) # label(non_clause).  [assumption].
0.56/0.86	177 (all Xa all Xb all Xc (-s_t(Xa,Xb,Xc) | Xb = Xc | -s_e(Xa,Xc,Xa,Xb))) # label(aNarbouxLemma1) # label(axiom) # label(non_clause).  [assumption].
0.56/0.86	178 (all Xa all Xp all Xq all Xc all Xb (-samesideline(Xa,Xb,Xp,Xq) | opposite(Xb,Xp,Xq,Xc) | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_8) # label(axiom) # label(non_clause).  [assumption].
0.56/0.86	179 (all Xa all Xp all Xq (Xp = Xq | s(Xa,Xp) != s(Xa,Xq))) # label(aSatz7_9) # label(axiom) # label(non_clause).  [assumption].
0.56/0.86	180 (all Xa all Xb all Xc all Xd (-s_col(Xa,Xb,Xd) | s_col(Xa,Xc,Xd) | Xb = Xa | -s_col(Xa,Xb,Xc))) # label(aext1) # label(axiom) # label(non_clause).  [assumption].
0.56/0.86	181 (all Xa all Xp all Xq all Xc all Xcs all Xr all Xm all U (-opposite(Xa,Xp,Xq,Xc) | -s_col(Xp,Xq,Xr) | -perp(Xp,Xq,Xa,Xr) | -perp(Xp,Xq,Xc,Xcs) | -s_m(Xr,Xm,Xcs) | -sameside(U,Xr,Xa) | sameside(s(Xm,U),Xcs,Xc) | -s_col(Xp,Xq,Xcs) | Xp = Xq)) # label(aSatz9_4) # label(axiom) # label(non_clause).  [assumption].
0.56/0.86	182 (all Xa all Xb all Xc all Xd all Za all Zb all Zc all Zd ((-s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_t(Za,Zb,Zc)) & (-s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_e(Xb,Xc,Zb,Zc)) & (-s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_e(Xa,Xd,Za,Zd)) & (-s_e(Xb,Xc,Zb,Zc) | -s_e(Xa,Xd,Za,Zd) | s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | -s_e(Xc,Xd,Zc,Zd) | -s_e(Xa,Xc,Za,Zc) | -s_t(Za,Zb,Zc) | -s_t(Xa,Xb,Xc)) & (-s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_e(Xc,Xd,Zc,Zd)) & (-s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_e(Xa,Xc,Za,Zc)) & (-s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_t(Xa,Xb,Xc)))) # label(d_Defn4_1) # label(axiom) # label(non_clause).  [assumption].
0.56/0.86	183 (all Xc all Xa all Xb (-s_e(Xc,Xa,Xc,Xb) | s_m(Xa,isomidpoint(Xa,Xb,Xc),Xb))) # label(aSatz7_25) # label(axiom) # label(non_clause).  [assumption].
0.56/0.86	184 (all Xa all Xb all Xp all Xq (perp(Xb,Xa,Xp,Xq) | -perp(Xa,Xb,Xp,Xq))) # label(aperp1) # label(axiom) # label(non_clause).  [assumption].
0.56/0.86	185 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_r(Xa,Xb,Xc) | s_r(Xa1,Xb1,Xc1) | -s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1))) # label(aSatz8_10) # label(axiom) # label(non_clause).  [assumption].
0.56/0.86	186 (all Xa all Xb s_col(Xa,Xa,Xb)) # label(aSatz4_12) # label(axiom) # label(non_clause).  [assumption].
0.56/0.86	187 (all Xp all Xq all Xa all Xb all Xt ((-s_col(Xp,Xq,Xb) | -opposite(Xa,Xp,Xq,Xb)) & (s_col(Xp,Xq,il(Xa,Xb,Xp,Xq)) | -opposite(Xa,Xp,Xq,Xb)) & (s_t(Xa,il(Xa,Xb,Xp,Xq),Xb) | -opposite(Xa,Xp,Xq,Xb)) & (-s_col(Xp,Xq,Xa) | -opposite(Xa,Xp,Xq,Xb)) & (s_col(Xp,Xq,Xb) | -s_t(Xa,Xt,Xb) | -s_col(Xp,Xq,Xt) | opposite(Xa,Xp,Xq,Xb) | s_col(Xp,Xq,Xa) | Xp = Xq))) # label(d_Defn9_1) # label(axiom) # label(non_clause).  [assumption].
0.56/0.86	188 (all Xa1 all Xm1 all Xb1 all Xc all Xb2 all Xm2 all Xa2 (-le(Xc,Xa1,Xc,Xa2) | s_t(Xm1,Xc,Xm2) | -s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2))) # label(aSatz7_22a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.86	189 (all Xa all Xb all Xc all Xp (Xc = Xb | Xa != Xp | -s_m(s(Xa,Xc),Xp,s(Xb,Xc)) | -s_r(Xa,Xb,Xc))) # label(aSatz8_20b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.86	190 (all Xa all Xp all Xq all Xb (opposite(Xb,Xp,Xq,Xa) | -opposite(Xa,Xp,Xq,Xb))) # label(aSatz9_2) # label(axiom) # label(non_clause).  [assumption].
0.56/0.86	191 (all Xa all Xp all Xq all Xb all Xc (-opposite(Xa,Xp,Xq,Xb) | opposite(Xa,Xp,Xq,Xc) | -samesideline(Xb,Xc,Xp,Xq))) # label(aLemma9_13e) # label(axiom) # label(non_clause).  [assumption].
0.56/0.86	192 (all Xr all Xa all Xb all Xc all Xp all Xq (Xc = Xb | -s_e(Xa,Xp,Xb,Xc) | -sameside(Xq,Xa,Xr) | Xp = Xq | -s_e(Xa,Xq,Xb,Xc) | -sameside(Xp,Xa,Xr) | Xa = Xr)) # label(aSatz6_11b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.86	193 (all Xa all Xp all Xq all Xc all Xr all Xb (-opposite(Xa,Xp,Xq,Xc) | opposite(Xb,Xp,Xq,Xc) | -sameside(Xa,Xr,Xb) | -s_col(Xp,Xq,Xr))) # label(aSatz9_5) # label(axiom) # label(non_clause).  [assumption].
0.56/0.86	194 (all Xa all Xb all Xd all Xc (Xb = Xa | -perp(Xa,Xb,Xc,Xd) | perpAt(Xa,Xb,Xd,Xc,Xd) | -s_col(Xa,Xb,Xd))) # label(aSatz8_15) # label(axiom) # label(non_clause).  [assumption].
0.56/0.86	195 (all Xa all Xp all Xb ((-sameside(Xa,Xp,Xb) | Xa != Xp) & (Xb != Xp | -sameside(Xa,Xp,Xb)) & (s_t(Xb,Xp,c63(Xa,Xp,Xb)) | -sameside(Xa,Xp,Xb)) & (s_t(Xa,Xp,c63(Xa,Xp,Xb)) | -sameside(Xa,Xp,Xb)) & (c63(Xa,Xp,Xb) != Xp | -sameside(Xa,Xp,Xb)))) # label(aSatz6_3a) # label(axiom) # label(non_clause).  [assumption].
0.56/0.86	196 (all Xa all Xb all Xc all Xd (-s_e(Xa,Xb,Xc,Xd) | s_e(Xc,Xd,Xa,Xb))) # label(aSatz2_2) # label(axiom) # label(non_clause).  [assumption].
0.56/0.86	197 (all Xa all Xp all Xb ((-sameside(Xa,Xp,Xb) | Xa != Xp) & (Xp = Xa | Xp = Xb | sameside(Xa,Xp,Xb) | -s_t(Xp,Xb,Xa)) & (-s_t(Xp,Xa,Xb) | Xp = Xa | Xp = xb | sameside(Xa,Xp,Xb)) & (s_t(Xp,Xb,Xa) | s_t(Xp,Xa,Xb) | -sameside(Xa,Xp,Xb)) & (Xb != Xp | -sameside(Xa,Xp,Xb)))) # label(d_Defn6_1) # label(axiom) # label(non_clause).  [assumption].
0.56/0.86	198 (all Xa all Xb s_e(Xa,Xa,Xb,Xb)) # label(aSatz2_8) # label(axiom) # label(non_clause).  [assumption].
0.56/0.86	199 (all Xa all Xm all Xb (-s_e(Xm,Xa,Xm,Xb) | s_m(Xa,Xm,Xb) | Xb = Xa | -s_col(Xa,Xm,Xb))) # label(aSatz7_20) # label(axiom) # label(non_clause).  [assumption].
0.56/0.86	200 (all Xa all Xb all Xc (-s_col(Xa,Xb,Xc) | s_col(Xc,Xa,Xb))) # label(aSatz4_11b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.86	201 (all Xa all Xb all Xc all Xd (-s_t(Xa,Xb,Xc) | s_t(Xb,Xc,Xd) | s_t(Xb,Xd,Xc) | -s_t(Xa,Xb,Xd) | Xb = Xa)) # label(aSatz5_2) # label(axiom) # label(non_clause).  [assumption].
0.56/0.86	202 (all Xa all Xb all Xc all Xd (-s_e(Xa,Xb,Xc,Xd) | s_e(Xb,Xa,Xc,Xd))) # label(aSatz2_4) # label(axiom) # label(non_clause).  [assumption].
0.56/0.86	203 (all Xa all Xp all Xb all Xc (sameside(Xa,Xp,Xb) | Xa = Xp | Xc = Xp | -s_t(Xb,Xp,Xc) | -s_t(Xa,Xp,Xc) | Xp = Xb)) # label(aSatz6_3b) # label(axiom) # label(non_clause).  [assumption].
0.56/0.86	204 (all Xa1 all Xa2 all Xa3 all Xb1 all Xb2 all Xb3 ((s_e(Xa1,Xa2,Xb1,Xb2) | -s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3)) & (-s_e(Xa2,Xa3,Xb2,Xb3) | s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3) | -s_e(Xa1,Xa3,Xb1,Xb3) | -s_e(Xa1,Xa2,Xb1,Xb2)) & (-s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3) | s_e(Xa2,Xa3,Xb2,Xb3)) & (-s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3) | s_e(Xa1,Xa3,Xb1,Xb3)))) # label(d_Defn4_4) # label(axiom) # label(non_clause).  [assumption].
0.56/0.86	205 -(all Xa all Xb all Xc all Xa1 all Xc1 (-s_r(Xa1,Xb,Xc1) | -s_e(Xa,Xb,Xa1,Xb) | -s_e(Xb,Xc,Xb,Xc1) | Xb != midpoint(Xc,Xc1) | Xc = Xc1 | s_e(Xa,Xc,Xa1,Xc1) | -s_r(Xa,Xb,Xc))) # label(aSatz10_12c) # label(negated_conjecture) # label(non_clause).  [assumption].
0.56/0.86	
0.56/0.86	============================== end of process non-clausal formulas ===
0.56/0.86	
0.56/0.86	============================== PROCESS INITIAL CLAUSES ===============
0.56/0.86	
0.56/0.86	============================== PREDICATE ELIMINATION =================
0.56/0.86	206 -s_col(A,B,C) | s_col(D,E,F) | -s_e3(A,B,C,D,E,F) # label(aSatz4_13) # label(axiom).  [clausify(17)].
0.56/0.86	207 -s_t(A,B,C) | s_e3(A,B,C,D,insert(A,B,D,E),E) | -s_e(A,C,D,E) # label(aSatz4_5) # label(axiom).  [clausify(11)].
0.56/0.86	Derived: -s_col(A,B,C) | s_col(D,insert(A,B,D,E),E) | -s_t(A,B,C) | -s_e(A,C,D,E).  [resolve(206,c,207,b)].
0.56/0.86	208 -s_e3(A,B,C,D,E,F) | s_t(D,E,F) | -s_t(A,B,C) # label(aSatz4_6) # label(axiom).  [clausify(95)].
0.56/0.86	Derived: s_t(A,insert(B,C,A,D),D) | -s_t(B,C,E) | -s_t(B,C,E) | -s_e(B,E,A,D).  [resolve(208,a,207,b)].
0.56/0.86	209 s_e3(A,B,C,D,E,F) | -s_fs(A,B,C,V6,D,E,F,V7) # label(d_Defn4_15) # label(axiom).  [clausify(138)].
0.56/0.86	Derived: -s_fs(A,B,C,D,E,F,V6,V7) | -s_col(A,B,C) | s_col(E,F,V6).  [resolve(209,a,206,c)].
0.56/0.86	Derived: -s_fs(A,B,C,D,E,F,V6,V7) | s_t(E,F,V6) | -s_t(A,B,C).  [resolve(209,a,208,a)].
0.56/0.86	210 -s_col(A,B,C) | -s_e3(A,B,C,D,E,F) | -s_e(A,V6,D,V7) | s_fs(A,B,C,V6,D,E,F,V7) | -s_e(B,V6,E,V7) # label(d_Defn4_15) # label(axiom).  [clausify(138)].
0.56/0.86	Derived: -s_col(A,B,C) | -s_e(A,D,E,F) | s_fs(A,B,C,D,E,insert(A,B,E,V6),V6,F) | -s_e(B,D,insert(A,B,E,V6),F) | -s_t(A,B,C) | -s_e(A,C,E,V6).  [resolve(210,b,207,b)].
0.56/0.86	Derived: -s_col(A,B,C) | -s_e(A,D,E,F) | s_fs(A,B,C,D,E,V6,V7,F) | -s_e(B,D,V6,F) | -s_fs(A,B,C,V8,E,V6,V7,V9).  [resolve(210,b,209,a)].
0.56/0.86	211 -s_col(A,B,C) | s_e3(A,B,C,D,E,insert5(A,B,C,D,E)) | -s_e(A,B,D,E) # label(aSatz4_14) # label(axiom).  [clausify(144)].
0.56/0.86	Derived: -s_col(A,B,C) | -s_e(A,B,D,E) | -s_col(A,B,C) | s_col(D,E,insert5(A,B,C,D,E)).  [resolve(211,b,206,c)].
0.65/0.87	Derived: -s_col(A,B,C) | -s_e(A,B,D,E) | s_t(D,E,insert5(A,B,C,D,E)) | -s_t(A,B,C).  [resolve(211,b,208,a)].
0.65/0.87	Derived: -s_col(A,B,C) | -s_e(A,B,D,E) | -s_col(A,B,C) | -s_e(A,F,D,V6) | s_fs(A,B,C,F,D,E,insert5(A,B,C,D,E),V6) | -s_e(B,F,E,V6).  [resolve(211,b,210,b)].
0.65/0.87	212 -s_r(A,B,C) | s_r(D,E,F) | -s_e3(A,B,C,D,E,F) # label(aSatz8_10) # label(axiom).  [clausify(185)].
0.65/0.87	Derived: -s_r(A,B,C) | s_r(D,insert(A,B,D,E),E) | -s_t(A,B,C) | -s_e(A,C,D,E).  [resolve(212,c,207,b)].
0.65/0.87	Derived: -s_r(A,B,C) | s_r(D,E,F) | -s_fs(A,B,C,V6,D,E,F,V7).  [resolve(212,c,209,a)].
0.65/0.87	Derived: -s_r(A,B,C) | s_r(D,E,insert5(A,B,C,D,E)) | -s_col(A,B,C) | -s_e(A,B,D,E).  [resolve(212,c,211,b)].
0.65/0.87	213 s_e(A,B,C,D) | -s_e3(A,B,E,C,D,F) # label(d_Defn4_4) # label(axiom).  [clausify(204)].
0.65/0.87	Derived: s_e(A,B,C,insert(A,B,C,D)) | -s_t(A,B,E) | -s_e(A,E,C,D).  [resolve(213,b,207,b)].
0.65/0.87	Derived: s_e(A,B,C,D) | -s_fs(A,B,E,F,C,D,V6,V7).  [resolve(213,b,209,a)].
0.65/0.87	214 -s_e(A,B,C,D) | s_e3(E,A,B,F,C,D) | -s_e(E,B,F,D) | -s_e(E,A,F,C) # label(d_Defn4_4) # label(axiom).  [clausify(204)].
0.65/0.87	Derived: -s_e(A,B,C,D) | -s_e(E,B,F,D) | -s_e(E,A,F,C) | -s_col(E,A,B) | s_col(F,C,D).  [resolve(214,b,206,c)].
0.65/0.87	Derived: -s_e(A,B,C,D) | -s_e(E,B,F,D) | -s_e(E,A,F,C) | s_t(F,C,D) | -s_t(E,A,B).  [resolve(214,b,208,a)].
0.65/0.87	Derived: -s_e(A,B,C,D) | -s_e(E,B,F,D) | -s_e(E,A,F,C) | -s_col(E,A,B) | -s_e(E,V6,F,V7) | s_fs(E,A,B,V6,F,C,D,V7) | -s_e(A,V6,C,V7).  [resolve(214,b,210,b)].
0.65/0.87	Derived: -s_e(A,B,C,D) | -s_e(E,B,F,D) | -s_e(E,A,F,C) | -s_r(E,A,B) | s_r(F,C,D).  [resolve(214,b,212,c)].
0.65/0.87	215 -s_e3(A,B,C,D,E,F) | s_e(B,C,E,F) # label(d_Defn4_4) # label(axiom).  [clausify(204)].
0.65/0.87	Derived: s_e(A,B,insert(C,A,D,E),E) | -s_t(C,A,B) | -s_e(C,B,D,E).  [resolve(215,a,207,b)].
0.65/0.87	Derived: s_e(A,B,C,D) | -s_fs(E,A,B,F,V6,C,D,V7).  [resolve(215,a,209,a)].
0.65/0.87	Derived: s_e(A,B,C,insert5(D,A,B,E,C)) | -s_col(D,A,B) | -s_e(D,A,E,C).  [resolve(215,a,211,b)].
0.65/0.87	216 -s_e3(A,B,C,D,E,F) | s_e(A,C,D,F) # label(d_Defn4_4) # label(axiom).  [clausify(204)].
0.65/0.87	Derived: s_e(A,B,C,D) | -s_fs(A,E,B,F,C,V6,D,V7).  [resolve(216,a,209,a)].
0.65/0.87	Derived: s_e(A,B,C,insert5(A,D,B,C,E)) | -s_col(A,D,B) | -s_e(A,D,C,E).  [resolve(216,a,211,b)].
0.65/0.87	217 -s_e(A,B,C,D) | -s_e(E,F,V6,V7) | s_ifs(E,A,B,F,V6,C,D,V7) | -s_e(B,F,D,V7) | -s_e(E,B,V6,D) | -s_t(V6,C,D) | -s_t(E,A,B) # label(d_Defn4_1) # label(axiom).  [clausify(182)].
0.65/0.87	218 s_e(A,B,C,D) | -s_ifs(E,A,F,B,V6,C,V7,D) # label(aSatz4_2) # label(axiom).  [clausify(34)].
0.65/0.87	219 -s_ifs(A,B,C,D,E,F,V6,V7) | s_t(E,F,V6) # label(d_Defn4_1) # label(axiom).  [clausify(182)].
0.65/0.87	220 -s_ifs(A,B,C,D,E,F,V6,V7) | s_e(B,C,F,V6) # label(d_Defn4_1) # label(axiom).  [clausify(182)].
0.65/0.87	221 -s_ifs(A,B,C,D,E,F,V6,V7) | s_e(A,D,E,V7) # label(d_Defn4_1) # label(axiom).  [clausify(182)].
0.65/0.87	Derived: -s_e(A,B,C,D) | -s_e(E,F,V6,V7) | -s_e(B,F,D,V7) | -s_e(E,B,V6,D) | -s_t(V6,C,D) | -s_t(E,A,B) | s_e(A,F,C,V7).  [resolve(217,c,218,b)].
0.65/0.87	222 -s_ifs(A,B,C,D,E,F,V6,V7) | s_e(C,D,V6,V7) # label(d_Defn4_1) # label(axiom).  [clausify(182)].
0.65/0.87	223 -s_ifs(A,B,C,D,E,F,V6,V7) | s_e(A,C,E,V6) # label(d_Defn4_1) # label(axiom).  [clausify(182)].
0.65/0.87	224 -s_ifs(A,B,C,D,E,F,V6,V7) | s_t(A,B,C) # label(d_Defn4_1) # label(axiom).  [clausify(182)].
0.65/0.87	225 -s_t(A,B,C) | -s_m(D,E,A) | s_kf(D,E,A,B,C,F,V6) | -s_m(V6,F,C) | -s_e(B,V6,B,C) | -s_e(B,D,B,A) | -s_t(D,B,V6) # label(d_Defn7_23) # label(axiom).  [clausify(158)].
0.65/0.87	226 s_t(A,B,C) | -s_kf(D,A,E,B,F,C,V6) # label(aSatz7_22b) # label(axiom).  [clausify(62)].
0.65/0.87	227 -s_kf(A,B,C,D,E,F,V6) | s_e(D,A,D,C) # label(d_Defn7_23) # label(axiom).  [clausify(158)].
0.65/0.87	228 s_e(A,B,A,C) | -s_kf(D,E,F,A,C,V6,B) # label(d_Defn7_23) # label(axiom).  [clausify(158)].
0.65/0.87	229 s_m(A,B,C) | -s_kf(D,E,F,V6,C,B,A) # label(d_Defn7_23) # label(axiom).  [clausify(158)].
0.65/0.87	Derived: -s_t(A,B,C) | -s_m(D,E,A) | -s_m(F,V6,C) | -s_e(B,F,B,C) | -s_e(B,D,B,A) | -s_t(D,B,F) | s_t(E,B,V6).  [resolve(225,c,226,b)].
0.65/0.87	230 s_m(A,B,C) | -s_kf(A,B,C,D,E,F,V6) # label(d_Defn7_23) # label(axiom).  [clausify(158)].
0.65/0.87	231 s_t(A,B,C) | -s_kf(D,E,A,B,C,F,V6) # label(d_Defn7_23) # label(axiom).  [clausify(158)].
9.38/9.59	232 s_t(A,B,C) | -s_kf(A,D,E,B,F,V6,C) # label(d_Defn7_23) # label(axiom).  [clausify(158)].
9.38/9.59	233 -le(A,B,A,C) | s_t(D,A,E) | -s_kf(B,D,F,A,V6,E,C) # label(aSatz7_22a) # label(axiom).  [clausify(188)].
9.38/9.59	234 -s_t(A,B,C) | -s_e(A,B,D,E) | -s_e(B,F,E,V6) | s_afs(A,B,C,F,D,E,V7,V6) | -s_e(A,F,D,V6) | -s_e(B,C,E,V7) | -s_t(D,E,V7) # label(d_Defn2_10) # label(axiom).  [clausify(84)].
9.38/9.59	235 s_t(A,B,C) | -s_afs(A,B,C,D,E,F,V6,V7) # label(d_Defn2_10) # label(axiom).  [clausify(84)].
9.38/9.59	236 -s_afs(A,B,C,D,E,F,V6,V7) | s_e(A,B,E,F) # label(d_Defn2_10) # label(axiom).  [clausify(84)].
9.38/9.59	237 s_e(A,B,C,D) | -s_afs(E,A,F,B,V6,C,V7,D) # label(d_Defn2_10) # label(axiom).  [clausify(84)].
9.38/9.59	238 s_e(A,B,C,D) | -s_afs(A,E,F,B,C,V6,V7,D) # label(d_Defn2_10) # label(axiom).  [clausify(84)].
9.38/9.59	239 -s_afs(A,B,C,D,E,F,V6,V7) | s_e(B,C,F,V6) # label(d_Defn2_10) # label(axiom).  [clausify(84)].
9.38/9.59	240 -s_afs(A,B,C,D,E,F,V6,V7) | s_t(E,F,V6) # label(d_Defn2_10) # label(axiom).  [clausify(84)].
9.38/9.59	
9.38/9.59	============================== end predicate elimination =============
9.38/9.59	
9.38/9.59	Auto_denials:  (non-Horn, no changes).
9.38/9.59	
9.38/9.59	Term ordering decisions:
9.38/9.59	Function symbol KB weights:  xb=1. xa=1. xp=1. xq=1. alpha=1. gamma=1. xc=1. xd=1. beta=1. c1=1. c2=1. c3=1. c4=1. c5=1. s=1. midpoint=1. pointOffLine=1. reflect=1. foot=1. c63=1. erect=1. erect21a=1. erectAux=1. erectAux21a=1. isomidpoint=1. insert=1. ext=1. il=1. ins=1. ss1=1. ss2=1. ss3=1. insert5=1. ip=1. f811=1. f813=1. g811=1. g813=1. op=1. midpointAux=1. crossbar=1.
9.38/9.59	
9.38/9.59	============================== end of process initial clauses ========
9.38/9.59	
9.38/9.59	============================== CLAUSES FOR SEARCH ====================
9.38/9.59	
9.38/9.59	============================== end of clauses for search =============
9.38/9.59	
9.38/9.59	============================== SEARCH ================================
9.38/9.59	
9.38/9.59	% Starting search at 0.09 seconds.
9.38/9.59	
9.38/9.59	Low Water (keep): wt=34.000, iters=3477
9.38/9.59	
9.38/9.59	Low Water (keep): wt=33.000, iters=3409
9.38/9.59	
9.38/9.59	Low Water (keep): wt=31.000, iters=3379
9.38/9.59	
9.38/9.59	Low Water (keep): wt=28.000, iters=3402
9.38/9.59	
9.38/9.59	Low Water (keep): wt=26.000, iters=3344
9.38/9.59	
9.38/9.59	Low Water (keep): wt=25.000, iters=3349
9.38/9.59	
9.38/9.59	Low Water (keep): wt=24.000, iters=3417
9.38/9.59	
9.38/9.59	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 77 (0.00 of 0.76 sec).
9.38/9.59	
9.38/9.59	Low Water (keep): wt=23.000, iters=3420
9.38/9.59	
9.38/9.59	Low Water (keep): wt=22.000, iters=3342
9.38/9.59	
9.38/9.59	Low Water (keep): wt=21.000, iters=3358
9.38/9.59	
9.38/9.59	Low Water (keep): wt=20.000, iters=3353
9.38/9.59	
9.38/9.59	Low Water (keep): wt=19.000, iters=3367
9.38/9.59	
9.38/9.59	Low Water (keep): wt=18.000, iters=3355
9.38/9.59	
9.38/9.59	Low Water (keep): wt=17.000, iters=3385
9.38/9.59	
9.38/9.59	Low Water (keep): wt=16.000, iters=3673
9.38/9.59	
9.38/9.59	Low Water (keep): wt=15.000, iters=3593
9.38/9.59	
9.38/9.59	Low Water (keep): wt=14.000, iters=3335
9.38/9.59	
9.38/9.59	Low Water (keep): wt=13.000, iters=3333
9.38/9.59	
9.38/9.59	Low Water (displace): id=1490, wt=90.000
9.38/9.59	
9.38/9.59	Low Water (displace): id=6671, wt=80.000
9.38/9.59	
9.38/9.59	Low Water (displace): id=12084, wt=11.000
9.38/9.59	
9.38/9.59	Low Water (displace): id=12253, wt=10.000
9.38/9.59	
9.38/9.59	Low Water (displace): id=12304, wt=9.000
9.38/9.59	
9.38/9.59	Low Water (keep): wt=12.000, iters=3341
9.38/9.59	
9.38/9.59	Low Water (keep): wt=11.000, iters=3450
9.38/9.59	
9.38/9.59	Low Water (displace): id=16428, wt=8.000
9.38/9.59	
9.38/9.59	Low Water (displace): id=19425, wt=7.000
9.38/9.59	
9.38/9.59	Low Water (keep): wt=10.000, iters=3431
9.38/9.59	
9.38/9.59	============================== PROOF =================================
9.38/9.59	% SZS status Theorem
9.38/9.59	% SZS output start Refutation
9.38/9.59	
9.38/9.59	% Proof 1 at 8.58 (+ 0.19) seconds.
9.38/9.59	% Length of proof is 28.
9.38/9.59	% Level of proof is 6.
9.38/9.59	% Maximum clause weight is 18.000.
9.38/9.59	% Given clauses 6814.
9.38/9.59	
9.38/9.59	12 (all Xa all Xb all Xc (-s_r(Xa,Xb,Xc) | s_r(Xa,Xb,s(Xb,Xc)))) # label(aSatz8_4) # label(axiom) # label(non_clause).  [assumption].
9.38/9.59	27 (all Xa all Xb s_m(Xa,midpoint(Xa,Xb),Xb)) # label(aSatz8_22) # label(axiom) # label(non_clause).  [assumption].
9.38/9.59	50 (all Xa all Xb all Xc ((s_e(Xa,Xc,Xa,s(Xb,Xc)) | -s_r(Xa,Xb,Xc)) & (s_r(Xa,Xb,Xc) | -s_e(Xa,Xc,Xa,s(Xb,Xc))))) # label(d_Defn8_1) # label(axiom) # label(non_clause).  [assumption].
9.38/9.59	60 (all Xp all Xa all Xq (-s_m(Xp,Xa,Xq) | Xq = s(Xa,Xp))) # label(aSatz7_6) # label(axiom) # label(non_clause).  [assumption].
9.38/9.59	131 (all Xa all Xb all Xc all Xd all Xe all Xf (s_e(Xa,Xb,Xe,Xf) | -s_e(Xc,Xd,Xe,Xf) | -s_e(Xa,Xb,Xc,Xd))) # label(aSatz2_3) # label(axiom) # label(non_clause).  [assumption].
9.38/9.59	156 (all Xa all Xb all Xc all Xa1 (-s_r(Xa,Xb,Xc) | -s_e(Xa,Xb,Xa1,Xb) | s_e(Xa,Xc,Xa1,Xc) | -s_r(Xa1,Xb,Xc))) # label(aSatz10_12b) # label(axiom) # label(non_clause).  [assumption].
9.38/9.59	205 -(all Xa all Xb all Xc all Xa1 all Xc1 (-s_r(Xa1,Xb,Xc1) | -s_e(Xa,Xb,Xa1,Xb) | -s_e(Xb,Xc,Xb,Xc1) | Xb != midpoint(Xc,Xc1) | Xc = Xc1 | s_e(Xa,Xc,Xa1,Xc1) | -s_r(Xa,Xb,Xc))) # label(aSatz10_12c) # label(negated_conjecture) # label(non_clause).  [assumption].
9.38/9.59	257 -s_r(A,B,C) | s_r(A,B,s(B,C)) # label(aSatz8_4) # label(axiom).  [clausify(12)].
9.38/9.59	273 s_m(A,midpoint(A,B),B) # label(aSatz8_22) # label(axiom).  [clausify(27)].
9.38/9.59	298 s_e(A,B,A,s(C,B)) | -s_r(A,C,B) # label(d_Defn8_1) # label(axiom).  [clausify(50)].
9.38/9.59	310 -s_m(A,B,C) | s(B,A) = C # label(aSatz7_6) # label(axiom).  [clausify(60)].
9.38/9.59	394 s_e(A,B,C,D) | -s_e(E,F,C,D) | -s_e(A,B,E,F) # label(aSatz2_3) # label(axiom).  [clausify(131)].
9.38/9.59	427 -s_r(A,B,C) | -s_e(A,B,D,B) | s_e(A,C,D,C) | -s_r(D,B,C) # label(aSatz10_12b) # label(axiom).  [clausify(156)].
9.38/9.59	499 s_r(c4,c2,c5) # label(aSatz10_12c) # label(negated_conjecture).  [clausify(205)].
9.38/9.59	500 s_e(c1,c2,c4,c2) # label(aSatz10_12c) # label(negated_conjecture).  [clausify(205)].
9.38/9.59	502 midpoint(c3,c5) = c2 # label(aSatz10_12c) # label(negated_conjecture).  [clausify(205)].
9.38/9.59	504 -s_e(c1,c3,c4,c5) # label(aSatz10_12c) # label(negated_conjecture).  [clausify(205)].
9.38/9.59	505 s_r(c1,c2,c3) # label(aSatz10_12c) # label(negated_conjecture).  [clausify(205)].
9.38/9.59	1386 -s_r(c1,c2,A) | s_e(c1,A,c4,A) | -s_r(c4,c2,A).  [resolve(500,a,427,b)].
9.38/9.59	1446 s_m(c3,c2,c5).  [para(502(a,1),273(a,2))].
9.38/9.59	1453 s_e(c1,c3,c1,s(c2,c3)).  [resolve(505,a,298,b)].
9.38/9.59	1456 s_r(c1,c2,s(c2,c3)).  [resolve(505,a,257,a)].
9.38/9.59	1976 s(c2,c3) = c5.  [resolve(1446,a,310,a)].
9.38/9.59	1978 s_r(c1,c2,c5).  [back_rewrite(1456),rewrite([1976(5)])].
9.38/9.59	1979 s_e(c1,c3,c1,c5).  [back_rewrite(1453),rewrite([1976(6)])].
9.38/9.59	3446 s_e(c1,c3,A,B) | -s_e(c1,c5,A,B).  [resolve(1979,a,394,c)].
9.38/9.59	20463 s_e(c1,c5,c4,c5).  [resolve(1386,c,499,a),unit_del(a,1978)].
9.38/9.59	26367 $F.  [resolve(3446,b,20463,a),unit_del(a,504)].
9.38/9.59	
9.38/9.59	% SZS output end Refutation
9.38/9.59	============================== end of proof ==========================
9.38/9.59	
9.38/9.59	============================== STATISTICS ============================
9.38/9.59	
9.38/9.59	Given=6814. Generated=297764. Kept=26113. proofs=1.
9.38/9.59	Usable=6644. Sos=9898. Demods=372. Limbo=1, Disabled=9902. Hints=0.
9.38/9.59	Megabytes=17.03.
9.38/9.59	User_CPU=8.58, System_CPU=0.19, Wall_clock=9.
9.38/9.59	
9.38/9.59	============================== end of statistics =====================
9.38/9.59	
9.38/9.59	============================== end of search =========================
9.38/9.59	
9.38/9.59	THEOREM PROVED
9.38/9.59	% SZS status Theorem
9.38/9.59	
9.38/9.59	Exiting with 1 proof.
9.38/9.59	
9.38/9.59	Process 5978 exit (max_proofs) Sat Jul 14 05:23:49 2018
9.38/9.59	Prover9 interrupted
9.38/9.60	EOF