0.02/0.10	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.02/0.10	% Command    : tptp2X_and_run_prover9 %d %s
0.09/0.31	% Computer   : n012.cluster.edu
0.09/0.31	% Model      : x86_64 x86_64
0.09/0.31	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.09/0.31	% Memory     : 8042.1875MB
0.09/0.31	% OS         : Linux 3.10.0-693.el7.x86_64
0.09/0.31	% CPULimit   : 960
0.09/0.31	% DateTime   : Thu Jul  2 13:01:27 EDT 2020
0.09/0.31	% CPUTime    : 
1.21/1.50	============================== Prover9 ===============================
1.21/1.50	Prover9 (32) version 2009-11A, November 2009.
1.21/1.50	Process 25644 was started by sandbox2 on n012.cluster.edu,
1.21/1.50	Thu Jul  2 13:01:28 2020
1.21/1.50	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_25475_n012.cluster.edu".
1.21/1.50	============================== end of head ===========================
1.21/1.50	
1.21/1.50	============================== INPUT =================================
1.21/1.50	
1.21/1.50	% Reading from file /tmp/Prover9_25475_n012.cluster.edu
1.21/1.50	
1.21/1.50	set(prolog_style_variables).
1.21/1.50	set(auto2).
1.21/1.50	    % set(auto2) -> set(auto).
1.21/1.50	    % set(auto) -> set(auto_inference).
1.21/1.50	    % set(auto) -> set(auto_setup).
1.21/1.50	    % set(auto_setup) -> set(predicate_elim).
1.21/1.50	    % set(auto_setup) -> assign(eq_defs, unfold).
1.21/1.50	    % set(auto) -> set(auto_limits).
1.21/1.50	    % set(auto_limits) -> assign(max_weight, "100.000").
1.21/1.50	    % set(auto_limits) -> assign(sos_limit, 20000).
1.21/1.50	    % set(auto) -> set(auto_denials).
1.21/1.50	    % set(auto) -> set(auto_process).
1.21/1.50	    % set(auto2) -> assign(new_constants, 1).
1.21/1.50	    % set(auto2) -> assign(fold_denial_max, 3).
1.21/1.50	    % set(auto2) -> assign(max_weight, "200.000").
1.21/1.50	    % set(auto2) -> assign(max_hours, 1).
1.21/1.50	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
1.21/1.50	    % set(auto2) -> assign(max_seconds, 0).
1.21/1.50	    % set(auto2) -> assign(max_minutes, 5).
1.21/1.50	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
1.21/1.50	    % set(auto2) -> set(sort_initial_sos).
1.21/1.50	    % set(auto2) -> assign(sos_limit, -1).
1.21/1.50	    % set(auto2) -> assign(lrs_ticks, 3000).
1.21/1.50	    % set(auto2) -> assign(max_megs, 400).
1.21/1.50	    % set(auto2) -> assign(stats, some).
1.21/1.50	    % set(auto2) -> clear(echo_input).
1.21/1.50	    % set(auto2) -> set(quiet).
1.21/1.50	    % set(auto2) -> clear(print_initial_clauses).
1.21/1.50	    % set(auto2) -> clear(print_given).
1.21/1.50	assign(lrs_ticks,-1).
1.21/1.50	assign(sos_limit,10000).
1.21/1.50	assign(order,kbo).
1.21/1.50	set(lex_order_vars).
1.21/1.50	clear(print_given).
1.21/1.50	
1.21/1.50	% formulas(sos).  % not echoed (224 formulas)
1.21/1.50	
1.21/1.50	============================== end of input ==========================
1.21/1.50	
1.21/1.50	% From the command line: assign(max_seconds, 960).
1.21/1.50	
1.21/1.50	============================== PROCESS NON-CLAUSAL FORMULAS ==========
1.21/1.50	
1.21/1.50	% Formulas that are not ordinary clauses:
1.21/1.50	1 (all X all Y (X = Y | -s_t(X,Y,X))) # label(aA6) # label(axiom) # label(non_clause).  [assumption].
1.21/1.50	2 (all X all Y all Z (X = Y | -s_e(X,Y,Z,Z))) # label(aA3) # label(axiom) # label(non_clause).  [assumption].
1.21/1.50	3 (all Xa all Xp all Xc all Xb all Xq ((s_t(Xp,ip(Xa,Xp,Xc,Xb,Xq),Xb) | -s_t(Xb,Xq,Xc) | -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].
1.21/1.50	4 (all X all Y all X1 all Y1 all Z all Z1 all V all V1 (-s_e(X,Y,X1,Y1) | -s_t(X1,Y1,Z1) | s_e(Z,V,Z1,V1) | X = Y | -s_e(Y,V,Y1,V1) | -s_e(X,V,X1,V1) | -s_e(Y,Z,Y1,Z1) | -s_t(X,Y,Z))) # label(aA5) # label(axiom) # label(non_clause).  [assumption].
1.21/1.50	5 (all X all Y s_e(X,Y,Y,X)) # label(aA1) # label(axiom) # label(non_clause).  [assumption].
1.21/1.50	6 (all X all Y all Z all V all Z2 all V2 (-s_e(X,Y,Z2,V2) | s_e(Z,V,Z2,V2) | -s_e(X,Y,Z,V))) # label(aA2) # label(axiom) # label(non_clause).  [assumption].
1.21/1.50	7 (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].
1.21/1.50	8 (all Xa all Xb (-s_r(Xa,Xb,Xa) | Xa = Xb)) # label(aSatz8_8) # label(axiom) # label(non_clause).  [assumption].
1.21/1.50	9 (all Xq all Xa all Xd all Xb all Xc (-s_t(Xq,Xa,Xd) | -s_e(Xa,Xd,Xb,Xc) | Xd = ext(Xq,Xa,Xb,Xc) | Xa = Xq)) # label(aSatz2_12) # label(axiom) # label(non_clause).  [assumption].
1.21/1.50	10 (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].
1.21/1.50	11 (all Xa all Xb all Xc (s_r(Xc,Xb,Xa) | -s_r(Xa,Xb,Xc))) # label(aSatz8_2) # label(axiom) # label(non_clause).  [assumption].
1.21/1.50	12 (all Xa1 all Xb all Xa2 all Xc1 all Xc2 all Xd1 all Xe all Xd2 all Xf1 all Xf2 all Xa all Xc all Xd all Xf (-sameside(Xa1,Xb,Xa2) | -sameside(Xc1,Xb,Xc2) | -sameside(Xd1,Xe,Xd2) | Xd = Xe | Xe = Xf | -sameside(Xa2,Xb,Xa) | -sameside(Xc2,Xb,Xc) | s_e(Xa2,Xc2,Xd2,Xf2) | -s_e(Xb,Xc2,Xe,Xf2) | -s_e(Xb,Xa2,Xe,Xd2) | -sameside(Xf2,Xe,Xf) | -sameside(Xd2,Xe,Xd) | Xc = Xb | Xa = Xb | -s_e3(Xa1,Xb,Xc1,Xd1,Xe,Xf1) | -sameside(Xf1,Xe,Xf2))) # label(aSatz11_4d) # label(axiom) # label(non_clause).  [assumption].
1.21/1.50	13 (all Xa all Xb all Xc all Xa1 (Xb = Xc | -s_t(Xa,Xc,Xa1) | -s_r(Xa1,Xb,Xc) | -s_r(Xa,Xb,Xc))) # label(aSatz8_6) # label(axiom) # label(non_clause).  [assumption].
1.21/1.50	14 (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].
1.21/1.50	15 (all Xa all Xb all Xc (-s_r(Xa,Xc,Xb) | Xc = Xb | -s_r(Xa,Xb,Xc))) # label(aSatz8_7) # label(axiom) # label(non_clause).  [assumption].
1.21/1.50	16 (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].
1.21/1.50	17 (all Xa all Xb all Xc all Xd all Xp (Xc = Xd | -s_col(Xa,Xb,Xd) | -s_col(Xc,Xd,Xp) | s_col(Xa,Xb,Xp) | -s_col(Xa,Xb,Xc) | Xb = Xa)) # label(aExtCol2) # label(axiom) # label(non_clause).  [assumption].
1.21/1.50	18 (all Xa all Xb all Xp all Xq (perp(Xp,Xq,Xa,Xb) | -perp(Xa,Xb,Xp,Xq))) # label(aSatz8_12b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.50	19 (all Xp all Xq all Xc all Xa all Xb (-perpAt(Xp,Xq,Xc,Xa,Xc) | s_col(Xc,Xa,Xb) | Xa = Xc | -perpAt(Xp,Xq,Xc,Xb,Xc) | Xp = Xq)) # label(aLemma9_13g) # label(axiom) # label(non_clause).  [assumption].
1.21/1.50	20 (all Xa all Xp all Xq all Xc all Xr all Xb (-opposite(Xa,Xp,Xq,Xc) | -s_col(Xp,Xq,Xr) | -sameside(Xa,Xr,Xb) | opposite(Xb,Xp,Xq,Xc))) # label(aSatz9_5) # label(axiom) # label(non_clause).  [assumption].
1.21/1.50	21 (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].
1.21/1.50	22 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_t(Xa,Xb,Xc) | s_e(Xa,Xb,Xa1,Xb1) | -s_e(Xb,Xc,Xb1,Xc1) | -s_e(Xa,Xc,Xa1,Xc1) | -s_t(Xa1,Xb1,Xc1))) # label(aSatz4_3) # label(axiom) # label(non_clause).  [assumption].
1.21/1.50	23 (all Xa all Xc all Xd le(Xa,Xa,Xc,Xd)) # label(aSatz5_11) # label(axiom) # label(non_clause).  [assumption].
1.21/1.50	24 (all Xa all Xb all Xc all Xd all Xe all Xf ((-congruent(Xa,Xb,Xc,Xd,Xe,Xf) | s_e3(ext(Xb,Xa,Xe,Xd),Xb,ext(Xb,Xc,Xe,Xf),ext(Xe,Xd,Xb,Xa),Xe,ext(Xe,Xf,Xb,Xc))) & (sameside(ext(Xe,Xf,Xb,Xc),Xe,Xf) | -congruent(Xa,Xb,Xc,Xd,Xe,Xf)) & (sameside(ext(Xe,Xd,Xb,Xa),Xe,Xd) | -congruent(Xa,Xb,Xc,Xd,Xe,Xf)) & (-congruent(Xa,Xb,Xc,Xd,Xe,Xf) | sameside(ext(Xb,Xc,Xe,Xf),Xb,Xc)) & (-congruent(Xa,Xb,Xc,Xd,Xe,Xf) | sameside(ext(Xb,Xa,Xe,Xd),Xb,Xa)))) # label(aSatz11_3a) # label(axiom) # label(non_clause).  [assumption].
1.21/1.50	25 (all Xa all Xb all Xc all Xd (Xb = Xa | -s_t(Xc,Xa,Xb) | -s_t(Xd,Xa,Xb) | s_t(Xc,Xd,Xb) | s_t(Xd,Xc,Xb))) # label(aSatz6_16a) # label(axiom) # label(non_clause).  [assumption].
1.21/1.50	26 (all Xa all Xb all Xc all Xd (-s_e(Xa,Xb,Xc,Xd) | s_e(Xb,Xa,Xd,Xc))) # label(aSatz2_14) # label(axiom) # label(non_clause).  [assumption].
1.21/1.50	27 (all Xa all Xb all Xd all Xc (-s_t(Xb,Xc,Xd) | s_t(Xa,Xb,Xc) | -s_t(Xa,Xb,Xd))) # label(aSatz3_5a) # label(axiom) # label(non_clause).  [assumption].
1.21/1.50	28 (all Xa all Xb all Xc (-s_r(Xa,Xb,Xc) | -s_col(Xa,Xb,Xc) | Xc = Xb | Xb = Xa)) # label(aSatz8_9) # label(axiom) # label(non_clause).  [assumption].
1.21/1.50	29 (all Xa all Xb all Xp all Xq (-samesideline(Xp,Xq,Xa,Xb) | samesideline(Xq,Xp,Xa,Xb) | Xb = Xa)) # label(aLemma9_13d) # label(axiom) # label(non_clause).  [assumption].
1.21/1.50	30 (all Xp all Xq all Xr all Xa (Xr = Xp | -sameside(Xa,Xp,Xq) | s_col(Xa,Xp,Xq) | -s_t(Xq,Xp,Xr) | Xq = Xp)) # label(aSatz6_15b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.50	31 (all Xa1 all Xa2 all Xa3 all Xb1 all Xb2 all Xb3 ((s_e(Xa1,Xa3,Xb1,Xb3) | -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_e(Xa1,Xa2,Xb1,Xb2) | -s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3)))) # label(d_Defn4_4) # label(axiom) # label(non_clause).  [assumption].
1.21/1.50	32 (all Xp all Xq all Xr (s_col(Xq,Xp,Xr) | -s_col(Xp,Xq,Xr) | Xq = Xp)) # label(aSatz6_17b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	33 (all Xp all Xq all Xcs all Xr (Xq = Xp | s_col(Xp,Xcs,Xr) | -s_col(Xp,Xq,Xr) | -s_col(Xp,Xq,Xcs) | Xcs = Xp)) # label(aSatz6_16b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	34 (all Xa all Xb all Xc all Xp all Xq (-s_e(Xb,Xp,Xb,Xq) | s_e(Xc,Xp,Xc,Xq) | -s_e(Xa,Xp,Xa,Xq) | -s_col(Xa,Xb,Xc) | Xb = Xa)) # label(aSatz4_17) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	35 (all Xp all Xq all Xr all Xcs (s_col(Xp,Xq,Xr) | s_col(Xp,Xq,Xcs) | samesideline(Xr,Xcs,Xp,Xq) | opposite(Xr,Xp,Xq,Xcs) | Xq = Xp)) # label(aLemma9_13f) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	36 (all Xa all Xb all Xp (Xb = Xa | Xp = reflect(Xa,Xb,reflect(Xa,Xb,Xp)))) # label(aSatz10_5) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	37 (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].
1.21/1.51	38 (all Xa all Xb all U all V all W (Xa = Xb | s_col(Xa,Xb,V) | -s_col(Xa,Xb,W) | -s_col(Xa,Xb,U) | -s_m(U,V,W))) # label(aLemma9_13b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	39 (all Xp all Xq all Xr all Xa (Xq = Xp | Xp = Xr | -s_t(Xq,Xp,Xr) | Xp != Xa | s_col(Xa,Xp,Xq))) # label(aSatz6_15d) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	40 (all Xa1 all Xc all Xa2 all Xb1 all Xb2 all Xm1 all Xm2 (-s_e(Xc,Xa1,Xc,Xb1) | -s_m(Xa1,Xm1,Xb1) | s_t(Xm1,Xc,Xm2) | -s_m(Xa2,Xm2,Xb2) | -s_e(Xc,Xa2,Xc,Xb2) | -s_t(Xb1,Xc,Xb2) | -s_t(Xa1,Xc,Xa2))) # label(aSatz7_22) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	41 (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].
1.21/1.51	42 (all Xa all Xp all Xq all Xc all Xcs all Xr all Xm all U (-opposite(Xa,Xp,Xq,Xc) | Xp = Xq | -s_col(Xp,Xq,Xcs) | -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) | Xcs = Xr | -le(Xcs,Xc,Xr,Xa) | -s_col(Xp,Xq,Xr))) # label(aSatz9_4a) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	43 (all Xa all Xb all Xp (Xa = Xb | -s_col(Xa,Xb,Xp) | reflect(Xa,Xb,Xp) = Xp)) # label(aSatz10_8b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	44 (all Xa all Xb all Xc all Xd (-s_t(Xa,Xb,Xc) | -s_t(Xa,Xb,Xd) | s_t(Xb,Xc,Xd) | s_t(Xb,Xd,Xc) | Xa = Xb)) # label(aSatz5_2) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	45 (all Xa all Xb all Xp all Xq all Xc all Xd all Xe (Xa = Xb | -s_col(Xa,Xb,Xc) | -s_col(Xp,Xq,Xd) | Xc = Xd | -s_col(Xa,Xb,Xe) | s_col(Xp,Xq,Xe) | -s_col(Xa,Xb,Xd) | -s_col(Xp,Xq,Xc) | Xp = Xq)) # label(aSatz6_21) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	46 (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].
1.21/1.51	47 (all Xa all Xm all 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)) & (s_t(Xa,Xm,Xb) | -s_m(Xa,Xm,Xb)))) # label(d_Defn7_1) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	48 (all Xa all Xb all Xd all Xc (s_t(Xa,Xb,Xc) | s_t(Xa,Xc,Xb) | -s_t(Xa,Xc,Xd) | -s_t(Xa,Xb,Xd))) # label(aSatz5_3) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	49 (all Xa all Xb all Xc ((Xa = Xb | s_col(Xa,Xb,Xc) | perp(Xa,Xb,erect21a(Xa,Xb,Xc),Xa)) & (s_t(Xc,erectAux21a(Xa,Xb,Xc),erect21a(Xa,Xb,Xc)) | s_col(Xa,Xb,Xc) | Xb = Xa) & (s_col(Xa,Xb,erectAux21a(Xa,Xb,Xc)) | s_col(Xa,Xb,Xc) | Xb = Xa))) # label(aSatz8_21a) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	50 (all Xa all Xb all Xc all Xd ((s_t(Xa,Xb,ins(Xc,Xd,Xa,Xb)) | -le(Xa,Xb,Xc,Xd)) & (-le(Xa,Xb,Xc,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)))) # label(aSatz5_5a) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	51 (all Xa all Xb s_t(Xa,Xb,Xb)) # label(aSatz3_1) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	52 (all Xa all Xb all Xc (s_t(Xa,Xb,Xc) | -le(Xb,Xc,Xa,Xc) | -le(Xa,Xb,Xa,Xc) | -s_col(Xa,Xb,Xc))) # label(aSatz5_12b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	53 (all Xd all Xe all Xd1 all Xa all Xb (Xe = Xd | -s_t(Xe,Xd,Xd1) | -samesideline(Xa,Xb,Xd1,Xe) | samesideline(Xa,Xb,Xd,Xe))) # label(aLemma9_13c) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	54 (all Xa all Xb all Xc all Xd (-s_t(Xa,Xb,Xc) | Xc = Xb | s_t(Xa,Xc,Xd) | -s_t(Xb,Xc,Xd))) # label(aSatz3_7a) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	55 (all Xp all Xq all Xr all Xa (Xr = Xp | -s_t(Xq,Xp,Xr) | -s_col(Xa,Xp,Xq) | Xa = Xp | sameside(Xa,Xp,Xr) | sameside(Xa,Xp,Xq) | Xp = Xq)) # label(aSatz6_15a) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	56 (all Xa all Xb all Xp all Xq all Xc (-s_col(Xa,Xb,Xp) | -s_col(Xa,Xb,Xq) | perp(Xa,Xb,Xc,Xp) | s_col(Xa,Xb,Xc) | -s_r(Xc,Xp,Xq) | Xp = Xq | Xb = Xa)) # label(aSatz8_16b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	57 (all Xa all Xp all Xq all Xb (-opposite(Xa,Xp,Xq,Xb) | opposite(Xb,Xp,Xq,Xa))) # label(aSatz9_2) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	58 (all Xa all Xb s_t(Xa,Xb,ext(Xa,Xb,alpha,gamma))) # label(aSatz3_14a) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	59 (all Xa all Xp all Xq all Xc all Xcs all Xr all Xm all U (-s_col(Xp,Xq,Xr) | -perp(Xp,Xq,Xa,Xr) | -s_m(Xr,Xm,Xcs) | sameside(s(Xm,U),Xcs,Xc) | Xcs != Xr | -sameside(U,Xr,Xa) | -perp(Xp,Xq,Xc,Xcs) | -s_col(Xp,Xq,Xcs) | Xq = Xp | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_4b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	60 (all Xa all Xb all Xc all Xp all Xq (-s_col(Xa,Xb,Xc) | Xc = Xa | samesideline(Xp,Xq,Xa,Xc) | -samesideline(Xp,Xq,Xa,Xb) | Xb = Xa)) # label(aExtSameSide1) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	61 (all Xa1 all Xm1 all Xb1 all Xc all Xb2 all Xm2 all Xa2 (s_t(Xm1,Xc,Xm2) | -le(Xc,Xa1,Xc,Xa2) | -s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2))) # label(aSatz7_22a) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	62 (all Xa all Xb all Xc all Xd all Xa1 all Xb1 all Xc1 all Xd1 (-s_ifs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1) | s_e(Xb,Xd,Xb1,Xd1))) # label(aSatz4_2) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	63 (all Xa all Xb all Xc all Xd all Za all Zb all Zc all Zd ((s_t(Xa,Xb,Xc) | -s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)) & (-s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,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(Xa,Xc,Za,Zc) | s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | -s_e(Xc,Xd,Zc,Zd) | -s_e(Xa,Xd,Za,Zd) | -s_e(Xb,Xc,Zb,Zc) | -s_t(Za,Zb,Zc) | -s_t(Xa,Xb,Xc)) & (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_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_t(Za,Zb,Zc)))) # label(d_Defn4_1) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	64 (all Xa all Xp all Xb all Xq all Xt (-le(Xa,Xp,Xb,Xq) | -s_col(Xa,Xb,Xt) | s_m(Xa,midpointAux(Xa,Xb,Xp,Xq,Xt),Xb) | -s_t(Xp,Xt,Xq) | -perp(Xa,Xb,Xb,Xq) | -perp(Xa,Xb,Xa,Xp))) # label(aSatz8_22b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	65 (all Xa all Xb all Xp all Xq all Xc all Xd (-s_col(Xa,Xb,Xp) | -s_col(Xa,Xb,Xq) | Xa = Xb | -perp(Xp,Xq,Xc,Xd) | perp(Xa,Xb,Xc,Xd) | Xq = Xp)) # label(aExtPerp2) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	66 (all Xa all Xm (Xa != Xm | s_m(Xa,Xm,Xa))) # label(aSatz7_3b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	67 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_e(Xb,Xc,Xb1,Xc1) | s_e(Xa,Xc,Xa1,Xc1) | -s_e(Xa,Xb,Xa1,Xb1) | -s_r(Xa1,Xb1,Xc1) | -s_r(Xa,Xb,Xc))) # label(aSatz10_12) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	68 (all Xa all Xb all Xd all Xc (-s_t(Xb,Xc,Xd) | s_t(Xa,Xc,Xd) | -s_t(Xa,Xb,Xd))) # label(aSatz3_5b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	69 (all Xa all Xb all Xa1 all Xc1 insert(Xa,Xb,Xa1,Xc1) = ext(ext(Xc1,Xa1,alpha,gamma),Xa1,Xa,Xb)) # label(d_insert) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	70 (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].
1.21/1.51	71 (all Xa all Xb all Xc all Xa1 all Xc1 (-s_r(Xa1,Xb,Xc1) | s_e(Xa,Xc,Xa1,Xc1) | -s_e(Xb,Xc,Xb,Xc1) | -s_e(Xa,Xb,Xa1,Xb) | -s_r(Xa,Xb,Xc))) # label(aSatz10_12a) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	72 (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)) & (-perpAt(Xp,Xq,X,Xp1,Xq1) | perp(Xp,Xq,Xp1,Xq1)))) # label(d_Defn8_11b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	73 (all Xa all Xb all Xc all Xa1 all Xc1 (-s_r(Xa,Xb,Xc) | -s_r(Xa1,Xb,Xc1) | -s_e(Xa,Xb,Xa1,Xb) | -s_e(Xb,Xc,Xb,Xc1) | Xc = Xc1 | Xb != midpoint(Xc,Xc1) | s_e(Xa,Xc,Xa1,Xc1))) # label(aSatz10_12c) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	74 (all Xa all Xm all Xb (s_m(Xa,Xm,Xb) | Xb = Xa | -s_e(Xm,Xa,Xm,Xb) | -s_col(Xa,Xm,Xb))) # label(aSatz7_20) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	75 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_e(Xb,Xa,Xb1,Xa1) | -s_e(Xb,Xc,Xb1,Xc1) | s_e(Xa,Xc,Xa1,Xc1) | -sameside(Xa1,Xb1,Xc1) | -sameside(Xa,Xb,Xc))) # label(aSatz6_28) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	76 (all Xp all Xq all Xr all Xcs (Xp = Xq | s_col(Xp,Xq,Xr) | opposite(Xr,Xp,Xq,Xcs) | foot(Xp,Xq,Xr) = Xp | samesideline(Xr,Xcs,Xp,Xq) | s_col(Xp,Xq,Xcs))) # label(aLemma9_13f_case2) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	77 (all Xa all Xb s_col(Xa,Xb,Xa)) # label(aSatz4_12b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	78 (all Xa all Xp all Xb all Xc (Xp = Xa | Xp = Xb | Xp = Xc | -s_t(Xa,Xp,Xc) | sameside(Xa,Xp,Xb) | -s_t(Xb,Xp,Xc))) # label(aSatz6_2a) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	79 (all Xa all Xb all Xp all Xp1 (Xp1 != reflect(Xa,Xb,Xp) | s_col(Xa,Xb,Xp) | opposite(Xp,Xa,Xb,Xp1) | Xa = Xb)) # label(aSatz10_14) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	80 (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].
1.21/1.51	81 (all Xa all Xb all Xc all Xa1 (-s_col(Xb,Xa,Xa1) | s_r(Xa1,Xb,Xc) | Xa = Xb | -s_r(Xa,Xb,Xc))) # label(aSatz8_3) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	82 (all Xa all Xb all Xp all Xq all Xu all Xc all Xv ((s_col(Xp,Xq,ss1(Xa,Xb,Xp,Xq)) | -samesideline(Xa,Xb,Xp,Xq)) & (s_t(Xa,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) | ss1(Xa,Xb,Xp,Xq) != ss3(Xa,Xb,Xp,Xq)) & (Xq != Xp | -samesideline(Xa,Xb,Xp,Xq)) & (-s_t(Xa,Xu,Xc) | -s_t(Xb,Xv,Xc) | s_col(Xp,Xq,Xa) | samesideline(Xa,Xb,Xp,Xq) | s_col(Xp,Xq,Xb) | Xv = Xb | Xu = Xa | Xc = Xv | Xc = Xu | Xp = Xq | -s_col(Xp,Xq,Xv) | -s_col(Xp,Xq,Xu)) & (-samesideline(Xa,Xb,Xp,Xq) | -s_col(Xp,Xq,Xb)) & (-samesideline(Xa,Xb,Xp,Xq) | -s_col(Xp,Xq,Xa)) & (ss3(Xa,Xb,Xp,Xq) != ss2(Xa,Xb,Xp,Xq) | -samesideline(Xa,Xb,Xp,Xq)) & (ss2(Xa,Xb,Xp,Xq) != Xb | -samesideline(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) | s_col(Xp,Xq,ss2(Xa,Xb,Xp,Xq))))) # label(d_Defn9_7) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	83 (all Xa all Xb all Xc all Xa1 all Xb1 all Xp ((s_col(Xa1,Xb1,Xp) | -s_e(Xa,Xb,Xa1,Xb1) | s_e3(Xa,Xb,Xc,Xa1,Xb1,triangle(Xa,Xb,Xc,Xa1,Xb1,Xp)) | s_col(Xa,Xb,Xc) | Xb = Xa) & (s_col(Xa,Xb,Xc) | s_col(Xa1,Xb1,Xp) | -s_e(Xa,Xb,Xa1,Xb1) | samesideline(triangle(Xa,Xb,Xc,Xa1,Xb1,Xp),Xp,Xa1,Xb1) | Xb = Xa))) # label(aSatz10_16a) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	84 (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].
1.21/1.51	85 (all Xa all Xp (sameside(Xa,Xp,Xa) | Xp = Xa)) # label(aSatz6_5) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	86 (all Xa all Xb all Xc all Xd all Xe all Xf all Xa2 all Xc2 all Xd2 all Xf2 (-congruent(Xa,Xb,Xc,Xd,Xe,Xf) | -sameside(Xc2,Xb,Xc) | s_e(Xa2,Xc2,Xd2,Xf2) | -s_e(Xb,Xc2,Xe,Xf2) | -s_e(Xb,Xa2,Xe,Xd2) | -sameside(Xf2,Xe,Xf) | -sameside(Xd2,Xe,Xd) | -sameside(Xa2,Xb,Xa))) # label(aSatz11_4) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	87 (all Xa all Xb all Xp all Xp1 ((Xp1 != Xp | Xp1 = reflect(Xa,Xb,Xp) | -s_col(Xa,Xb,midpoint(Xp,Xp1)) | Xa = Xb) & (-s_col(Xa,Xb,midpoint(Xp,Xp1)) | reflect(Xa,Xb,Xp) = Xp1 | -perp(Xa,Xb,Xp,Xp1) | Xb = Xa))) # label(aSatz10_2b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	88 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1) | s_col(Xa1,Xb1,Xc1) | -s_col(Xa,Xb,Xc))) # label(aSatz4_13) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	89 (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].
1.21/1.51	90 (all Xa all Xb s_col(Xa,Xa,Xb)) # label(aSatz4_12) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	91 (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_t(Za,Zb,Zc) | -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,Xc,Zb,Zc) | -s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)) & (-s_t(Za,Zb,Zc) | -s_e(Xb,Xc,Zb,Zc) | -s_e(Xb,Xd,Zb,Zd) | s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | -s_e(Xa,Xd,Za,Zd) | -s_e(Xa,Xb,Za,Zb) | -s_t(Xa,Xb,Xc)) & (s_e(Xb,Xd,Zb,Zd) | -s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)) & (-s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_e(Xa,Xd,Za,Zd)))) # label(d_Defn2_10) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	92 (all Xa all Xp all Xq all Xc all Xm all Xr all Xb (-opposite(Xa,Xp,Xq,Xc) | -s_col(Xp,Xq,Xr) | opposite(Xb,Xp,Xq,Xc) | -sameside(Xa,Xr,Xb) | -s_m(Xa,Xm,Xc) | -s_col(Xp,Xq,Xm))) # label(aSatz9_3) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	93 (all Xr all Xa all Xb all Xc all Xp all Xq (Xc = Xb | -sameside(Xp,Xa,Xr) | -sameside(Xq,Xa,Xr) | Xq = Xp | -s_e(Xa,Xq,Xb,Xc) | -s_e(Xa,Xp,Xb,Xc) | Xr = Xa)) # label(aSatz6_11b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	94 (all Xa all Xb all Xc all Xp all Xq (il(Xa,Xb,Xp,Xq) = Xc | -perpAt(Xa,Xb,Xc,Xp,Xq))) # label(aSatz8_14c) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	95 (all Xc all Xa all Xb (s_m(Xa,isomidpoint(Xa,Xb,Xc),Xb) | -s_e(Xc,Xa,Xc,Xb))) # label(aSatz7_25) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	96 (all Xb all Xc all Xa all Xq ((Xb = Xc | -s_col(Xb,Xc,Xa) | s_col(Xb,Xc,Xq) | perp(Xb,Xc,erectsameside(Xb,Xc,Xa,Xq),Xa)) & (-s_col(Xb,Xc,Xa) | s_col(Xb,Xc,Xq) | samesideline(erectsameside(Xb,Xc,Xa,Xq),Xq,Xb,Xc) | Xb = Xc))) # label(aSatz10_15) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	97 (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].
1.21/1.51	98 (all Xa all Xp all Xb (le(Xp,Xa,Xp,Xb) | -s_t(Xp,Xa,Xb) | -sameside(Xa,Xp,Xb))) # label(aSatz6_13b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	99 (all Xa all Xb s_m(Xa,midpoint(Xa,Xb),Xb)) # label(aSatz8_22) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	100 (all Xa all Xb all Xc all Xd (-s_col(Xa,Xb,Xc) | s_col(Xa,Xc,Xd) | Xb = Xa | -s_col(Xa,Xb,Xd))) # label(aext1) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	101 (all Xa all Xb all Xc all Xd all Y ((s_t(Xc,insert(Xa,Xb,Xc,Xd),Xd) | -le(Xa,Xb,Xc,Xd)) & (-s_e(Xa,Xb,Xc,Y) | le(Xa,Xb,Xc,Xd) | -s_t(Xc,Y,Xd)) & (-le(Xa,Xb,Xc,Xd) | s_e(Xa,Xb,Xc,insert(Xa,Xb,Xc,Xd))))) # label(d_Defn5_4) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	102 (all Xp all Xq all Xr all Xa (Xp = Xq | s_col(Xa,Xp,Xq) | -sameside(Xa,Xp,Xr) | -s_t(Xq,Xp,Xr) | Xr = Xp)) # label(aSatz6_15c) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	103 (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].
1.21/1.51	104 (all Xa all Xb all Xp (reflect(Xa,Xb,Xp) != Xp | s_col(Xa,Xb,Xp) | Xb = Xa)) # label(aSatz10_8a) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	105 (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].
1.21/1.51	106 (all Xa all Xb all Xp ((Xa = Xb | s_col(Xa,Xb,midpoint(Xp,reflect(Xa,Xb,Xp)))) & (perp(Xa,Xb,Xp,reflect(Xa,Xb,Xp)) | Xp = reflect(Xa,Xb,Xp) | Xb = Xa))) # label(aSatz10_2a) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	107 (all Xa all Xb all Xp all Xq (-s_col(Xa,Xb,Xp) | s_e(Xp,Xq,reflect(Xa,Xb,Xp),reflect(Xa,Xb,Xq)) | Xa = Xb)) # label(aSatz10_10a) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	108 (all Xa1 all Xb1 s_t(Xa1,Xa1,Xb1)) # label(aSatz3_3) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	109 (all Xp all Xq all Xr all Xcs all Xa (s_e(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr),s(Xa,Xcs)) | -s_e(Xp,Xq,Xr,Xcs))) # label(aSatz7_16a) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	110 (all Xa all Xb all Xc ((s_col(Xa,Xb,foot(Xa,Xb,Xc)) | s_col(Xa,Xb,Xc)) & (s_col(Xa,Xb,Xc) | perp(Xa,Xb,Xc,foot(Xa,Xb,Xc))))) # label(aSatz8_18) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	111 (all Xp all Xq (Xp = Xq | s_col(Xp,Xq,Xp))) # label(aSatz6_17a) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	112 (all Xp all Xq all Xa all Xb all Xt ((-opposite(Xa,Xp,Xq,Xb) | -s_col(Xp,Xq,Xb)) & (s_col(Xp,Xq,il(Xa,Xb,Xp,Xq)) | -opposite(Xa,Xp,Xq,Xb)) & (-opposite(Xa,Xp,Xq,Xb) | s_t(Xa,il(Xa,Xb,Xp,Xq),Xb)) & (-s_col(Xp,Xq,Xa) | -opposite(Xa,Xp,Xq,Xb)) & (Xq = Xp | s_col(Xp,Xq,Xb) | -s_t(Xa,Xt,Xb) | opposite(Xa,Xp,Xq,Xb) | -s_col(Xp,Xq,Xt) | s_col(Xp,Xq,Xa)))) # label(d_Defn9_1) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	113 (all Xa all Xb all Xc all Xd (-s_t(Xa,Xb,Xc) | s_t(Xa,Xd,Xc) | s_t(Xa,Xc,Xd) | -s_t(Xa,Xb,Xd) | Xb = Xa)) # label(aSatz5_1) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	114 (all Xa all Xb all Xc all Xp all Xq ((-perpAt(Xa,Xb,Xc,Xp,Xq) | Xp != Xq) & (-perpAt(Xa,Xb,Xc,Xp,Xq) | s_col(Xp,Xq,Xc)) & (s_col(Xa,Xb,Xc) | -perpAt(Xa,Xb,Xc,Xp,Xq)) & (s_col(Xa,Xb,f813(Xa,Xb,Xp,Xq,Xc)) | -perpAt(Xa,Xb,Xc,Xp,Xq)) & (f813(Xa,Xb,Xp,Xq,Xc) != Xc | -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)) & (-perpAt(Xa,Xb,Xc,Xp,Xq) | g813(Xa,Xb,Xp,Xq,Xc) != Xc) & (s_col(Xp,Xq,g813(Xa,Xb,Xp,Xq,Xc)) | -perpAt(Xa,Xb,Xc,Xp,Xq)) & (Xa != Xb | -perpAt(Xa,Xb,Xc,Xp,Xq)))) # label(aSatz8_13a) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	115 (all Xa all Xp (Xp != Xa | Xp = s(Xa,Xp))) # label(aSatz7_10b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	116 (all Xa all Xb all Xp all Xq all Xr (Xa = Xb | Xq = Xp | -s_col(Xp,Xq,Xa) | -s_col(Xp,Xq,Xr) | s_col(Xa,Xb,Xr) | -s_col(Xp,Xq,Xb))) # label(aSatz6_18) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	117 (all Xa all Xb all Xc (-s_t(Xa,Xb,Xc) | -s_t(Xb,Xa,Xc) | Xa = Xb)) # label(aSatz3_4) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	118 (all Xa all Xb all Xc (s_col(Xb,Xa,Xc) | -s_col(Xa,Xb,Xc))) # label(aSatz4_11d) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	119 (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].
1.21/1.51	120 (all Xa all Xp all Xq all Xc all Xcs all Xr all Xm all U (-opposite(Xa,Xp,Xq,Xc) | Xp = Xq | -s_col(Xp,Xq,Xcs) | -s_col(Xp,Xq,Xr) | -perp(Xp,Xq,Xa,Xr) | -le(Xcs,Xc,Xr,Xa) | -sameside(s(Xm,U),Xcs,Xc) | Xcs = Xr | sameside(U,Xr,Xa) | -s_m(Xr,Xm,Xcs) | -perp(Xp,Xq,Xc,Xcs))) # label(aSatz9_4a2) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	121 (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].
1.21/1.51	122 (all Xa all Xb all Xc all Xd all Xe all Xf (-s_e(Xc,Xd,Xe,Xf) | s_e(Xa,Xb,Xe,Xf) | -s_e(Xa,Xb,Xc,Xd))) # label(aSatz2_3) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	123 (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) | Xa = Xb | Xq = Xp | -s_col(Xa,Xb,Xq))) # label(aExtPerp5) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	124 (all Xa all Xb (Xb = Xa | -s_col(Xa,Xb,pointOffLine(Xa,Xb)))) # label(aSatz6_25) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	125 (all Xa all Xb all Xc all Xd (Xa = Xb | Xb = Xc | -s_col(Xa,Xc,Xd) | perp(Xb,Xa,Xa,Xd) | -perp(Xb,Xa,Xa,Xc) | Xd = Xa | Xc = Xd | Xa = Xc)) # label(aExtPerp3) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	126 (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].
1.21/1.51	127 (all Xa all Xp all Xb ((-sameside(Xa,Xp,Xb) | Xa != Xp) & (-sameside(Xa,Xp,Xb) | s_t(Xb,Xp,c63(Xa,Xp,Xb))) & (s_t(Xa,Xp,c63(Xa,Xp,Xb)) | -sameside(Xa,Xp,Xb)) & (-sameside(Xa,Xp,Xb) | c63(Xa,Xp,Xb) != Xp) & (-sameside(Xa,Xp,Xb) | Xb != Xp))) # label(aSatz6_3a) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	128 (all Xa all Xb all Xc (s_r(Xa,Xb,s(Xb,Xc)) | -s_r(Xa,Xb,Xc))) # label(aSatz8_4) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	129 (all Xa all Xp s(Xa,s(Xa,Xp)) = Xp) # label(aSatz7_7) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	130 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_t(Xa1,Xb1,Xc1) | -s_e(Xa,Xb,Xa1,Xb1) | -s_e(Xb,Xc,Xb1,Xc1) | s_e(Xa,Xc,Xa1,Xc1) | -s_t(Xa,Xb,Xc))) # label(aSatz2_11) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	131 (all Xa all Xb all Xp all Xp1 (Xa = Xb | reflect(Xa,Xb,Xp1) = Xp | reflect(Xa,Xb,Xp) != Xp1)) # label(aSatz10_4) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	132 (all Xa all Xb all Xc all Xp (-s_r(Xa,Xb,Xc) | Xc = Xb | Xp != Xa | -s_m(s(Xa,Xc),Xp,s(Xb,Xc)))) # label(aSatz8_20b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	133 (all Xc all Xd all Xp all Xa all Xb (samesideline(Xa,Xb,Xc,Xd) | s_col(Xc,Xd,Xa) | -sameside(Xa,Xp,Xb) | -s_col(Xa,Xb,Xp) | -s_col(Xc,Xd,Xp) | Xc = Xd)) # label(aSatz9_19b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	134 (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,Xcs) | -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,Xr) | Xq = Xp)) # label(aSatz9_4) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	135 (all Xa all Xb all Xc all Xa1 all Xb1 all Xp all Xc1 all Xc2 (s_col(Xa1,Xb1,Xp) | -s_e(Xa,Xb,Xa1,Xb1) | -samesideline(Xc1,Xp,Xa1,Xb1) | -samesideline(Xc2,Xp,Xa1,Xb1) | Xc2 = Xc1 | -s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc2) | -s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1) | s_col(Xa,Xb,Xc) | Xb = Xa)) # label(aSatz10_16b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	136 (all Xa all Xb s_r(Xa,Xb,Xb)) # label(aSatz8_5) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	137 (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].
1.21/1.51	138 (all Xp all Xa all Xr all Xq (-s_m(Xp,Xa,Xr) | Xr = Xq | -s_m(Xp,Xa,Xq))) # label(aSatz7_4b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	139 (all Xa all Xb all Xp all Xp1 (Xb = Xa | Xp1 != reflect(Xa,Xb,Xp) | reflect(Xa,Xb,Xp1) = Xp)) # label(aSatz10_6) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	140 (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].
1.21/1.51	141 (all Xa all Xp all Xb all Xc (Xp = Xa | -s_t(Xa,Xp,Xc) | -sameside(Xa,Xp,Xb) | s_t(Xb,Xp,Xc) | Xp = Xc | Xb = Xp)) # label(aSatz6_2b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	142 (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].
1.21/1.51	143 (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].
1.21/1.51	144 (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].
1.21/1.51	145 (all Xa all Xb all Xc ((-s_t(Xa,Xb,Xc) | s_col(Xa,Xb,Xc)) & (-s_t(Xb,Xc,Xa) | s_col(Xa,Xb,Xc)) & (s_col(Xa,Xb,Xc) | -s_t(Xc,Xa,Xb)) & (s_t(Xc,Xa,Xb) | s_t(Xb,Xc,Xa) | s_t(Xa,Xb,Xc) | -s_col(Xa,Xb,Xc)))) # label(d_Defn4_10) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	146 (all Xp all Xa all Xb all Xq all Xt all Xr (-perp(Xq,Xb,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(Xp,Xa,Xa,Xb))) # label(aSatz8_24) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	147 (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].
1.21/1.51	148 (all Xa all Xb all Xp all Xq all Xcx all U all V (-s_col(Xp,Xq,Xcx) | -s_col(Xa,Xb,U) | Xcx = U | V = Xcx | perpAt(Xa,Xb,Xcx,Xp,Xq) | -s_r(U,Xcx,V) | -s_col(Xp,Xq,V) | -s_col(Xa,Xb,Xcx) | Xp = Xq | Xa = Xb)) # label(aSatz8_13b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	149 (all Xa all Xb all Xc all Xa1 all Xb1 all Xp ((-s_t(Xa,Xb,Xc) | -s_t(Xa,Xp,Xa1) | s_t(Xb,crossbar(Xa,Xb,Xc,Xa1,Xb1,Xp),Xb1) | -s_t(Xa1,Xb1,Xc)) & (-s_t(Xa1,Xb1,Xc) | s_t(Xp,crossbar(Xa,Xb,Xc,Xa1,Xb1,Xp),Xc) | -s_t(Xa,Xp,Xa1) | -s_t(Xa,Xb,Xc)))) # label(aSatz3_17) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	150 (all Y all Z all X all Y1 all Z1 all U all V ((-perpAt(Y,Z,X,Y1,Z1) | s_col(Y,Z,X)) & (Y != Z | -perpAt(Y,Z,X,Y1,Z1)) & (Z = Y | Z1 = Y1 | -s_col(Y,Z,X) | -s_r(f811(Y,Z,Y1,Z1,X),X,g811(Y,Z,Y1,Z1,X)) | -s_col(Y1,Z1,X) | perpAt(Y,Z,X,Y1,Z1)) & (perpAt(Y,Z,X,Y1,Z1) | Z = Y | Y1 = Z1 | -s_col(Y1,Z1,X) | s_col(Y1,Z1,g811(Y,Z,Y1,Z1,X)) | -s_col(Y,Z,X)) & (Y = Z | -s_col(Y,Z,X) | -s_col(Y1,Z1,X) | s_col(Y,Z,f811(Y,Z,Y1,Z1,X)) | Z1 = Y1 | perpAt(Y,Z,X,Y1,Z1)) & (-perpAt(Y,Z,X,Y1,Z1) | -s_col(Y1,Z1,V) | s_r(U,X,V) | -s_col(Y,Z,U)) & (Z1 != Y1 | -perpAt(Y,Z,X,Y1,Z1)) & (-perpAt(Y,Z,X,Y1,Z1) | s_col(Y1,Z1,X)))) # label(d_Defn8_11a) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	151 (all Xa all Xb all Xc all Xd all Xa1 all Xb1 all Xc1 all Xd1 (-s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1) | Xa = Xb | s_e(Xc,Xd,Xc1,Xd1))) # label(aSatz4_16) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	152 (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].
1.21/1.51	153 (all Xa all Xb s_e(Xa,Xb,Xa,Xb)) # label(aSatz2_1) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	154 (all Xp all Xa all Xb all Xq all Xt all Xr all Xcx (-s_t(Xb,Xr,Xq) | -s_e(Xa,Xp,Xb,Xr) | s_m(Xa,Xcx,Xb) | ip(Xp,Xt,Xq,Xb,Xr) != Xcx | -s_t(Xp,Xt,Xq) | -s_col(Xa,Xb,Xt) | -perp(Xq,Xb,Xa,Xb) | -perp(Xp,Xa,Xa,Xb))) # label(aSatz8_24a) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	155 (all Xa all Xb all Xc (-s_col(Xa,Xb,Xc) | s_col(Xc,Xb,Xa))) # label(aSatz4_11c) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	156 (all Xa all Xc all Xp all Xb all Xq ((-s_t(Xb,Xq,Xc) | s_t(Xp,Xq,op(Xq,Xb,Xp,Xc,Xa)) | -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)))) # label(aSatz9_6) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	157 (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].
1.21/1.51	158 (all Xa all Xp all Xb ((-sameside(Xa,Xp,Xb) | -s_t(Xa,Xp,Xb)) & (s_col(Xa,Xp,Xb) | -sameside(Xa,Xp,Xb)))) # label(aSatz6_4a) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	159 (all Xa all Xp (s(Xa,Xp) != Xp | Xa = Xp)) # label(aSatz7_10a) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	160 (all Xa all Xb all Xp all Xq (-perp(Xa,Xb,Xp,Xq) | perp(Xa,Xb,Xq,Xp))) # label(aExtPerp4) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	161 (all Xa all Xp all Xq all Xc all Xcs all Xr all Xm all U all V (-s_col(Xp,Xq,Xcs) | -s_col(Xp,Xq,Xr) | -perp(Xp,Xq,Xc,Xcs) | -sameside(V,Xcs,Xc) | opposite(U,Xp,Xq,V) | -sameside(U,Xr,Xa) | -s_m(Xr,Xm,Xcs) | -perp(Xp,Xq,Xa,Xr) | Xq = Xp | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_4c) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	162 (all Xa all Xb all Xc all Xd all Xe all Xf (-le(Xc,Xd,Xe,Xf) | le(Xa,Xb,Xe,Xf) | -le(Xa,Xb,Xc,Xd))) # label(aSatz5_8) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	163 (all Xa all Xb all Xc all Xd (-le(Xc,Xd,Xa,Xb) | s_e(Xa,Xb,Xc,Xd) | -le(Xa,Xb,Xc,Xd))) # label(aSatz5_9) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	164 (all Xa all Xb all Xc all Xa1 all Xc1 ((-s_t(Xa,Xb,Xc) | s_e3(Xa,Xb,Xc,Xa1,insert(Xa,Xb,Xa1,Xc1),Xc1) | -s_e(Xa,Xc,Xa1,Xc1)) & (s_t(Xa1,insert(Xa,Xb,Xa1,Xc1),Xc1) | -s_e(Xa,Xc,Xa1,Xc1) | -s_t(Xa,Xb,Xc)))) # label(aSatz4_5) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	165 (all Xb all Xa Xb != ext(Xa,Xb,alpha,gamma)) # label(aSatz3_14b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.51	166 (all Xa all Xb all Xc all XA all XB all XC (-s_t(Xa,Xb,Xc) | -s_t(XA,XB,XC) | -s_e(Xa,Xb,XB,XC) | s_e(Xa,Xc,XA,XC) | -s_e(Xb,Xc,XA,XB))) # label(aSatz2_15) # label(axiom) # label(non_clause).  [assumption].
1.21/1.52	167 (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].
1.21/1.52	168 (all Xa all Xb all Xc all Xp all Xq (s_col(Xa,Xb,Xc) | -s_col(Xa,Xb,Xp) | -perp(Xa,Xb,Xc,Xq) | Xq = Xp | -perp(Xa,Xb,Xc,Xp) | -s_col(Xa,Xb,Xq))) # label(aSatz8_18a) # label(axiom) # label(non_clause).  [assumption].
1.21/1.52	169 (all Xa all Xb all Xc ((Xa = Xb | s_t(Xc,erectAux(Xa,Xb,Xc),erect(Xa,Xb,Xc))) & (s_col(Xa,Xb,erectAux(Xa,Xb,Xc)) | Xa = Xb) & (perp(Xa,Xb,erect(Xa,Xb,Xc),Xa) | Xb = Xa))) # label(aSatz8_21) # label(axiom) # label(non_clause).  [assumption].
1.21/1.52	170 (all Xa all Xb all Xc all Xd (s_t(Xa,Xb,Xd) | Xc = Xb | -s_t(Xb,Xc,Xd) | -s_t(Xa,Xb,Xc))) # label(aSatz3_7b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.52	171 (all Xa all Xb all Xc all Xa1 all Xb1 (-s_col(Xa,Xb,Xc) | -s_e(Xa,Xb,Xa1,Xb1) | s_e3(Xa,Xb,Xc,Xa1,Xb1,insert5(Xa,Xb,Xc,Xa1,Xb1)))) # label(aSatz4_14) # label(axiom) # label(non_clause).  [assumption].
1.21/1.52	172 (all Xp all Xq all Xa all Xb all Xc (-samesideline(Xa,Xb,Xp,Xq) | -samesideline(Xb,Xc,Xp,Xq) | samesideline(Xa,Xc,Xp,Xq) | Xp = Xq)) # label(aSatz9_13) # label(axiom) # label(non_clause).  [assumption].
1.21/1.52	173 (all Xp all Xa s_m(Xp,Xa,s(Xa,Xp))) # label(aSatz7_4a) # label(axiom) # label(non_clause).  [assumption].
1.21/1.52	174 (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].
1.21/1.52	175 (all Xa all Xb all Xc all Xc1 (Xb = Xa | -s_e(Xb,Xc,Xb,Xc1) | Xc1 = Xc | -s_e(Xa,Xc,Xa,Xc1) | -s_col(Xa,Xb,Xc))) # label(aSatz4_18) # label(axiom) # label(non_clause).  [assumption].
1.21/1.52	176 (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].
1.21/1.52	177 (all Xa1 all Xb all Xa all Xc1 all Xc all Xd1 all Xe all Xd all Xf1 all Xf (-sameside(Xa1,Xb,Xa) | congruent(Xa,Xb,Xc,Xd,Xe,Xf) | -s_e3(Xa1,Xb,Xc1,Xd1,Xe,Xf1) | -sameside(Xf1,Xe,Xf) | -sameside(Xd1,Xe,Xd) | -sameside(Xc1,Xb,Xc))) # label(aSatz11_3d) # label(axiom) # label(non_clause).  [assumption].
1.21/1.52	178 (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].
1.21/1.52	179 (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].
1.21/1.52	180 (all Xa1 all Xm1 all Xb1 all Xc all Xb2 all Xm2 all Xa2 (-s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) | s_t(Xm1,Xc,Xm2))) # label(aSatz7_22b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.52	181 (all Xa all Xp all Xb all Xc (Xc = Xp | -s_t(Xa,Xp,Xc) | -s_t(Xb,Xp,Xc) | Xb = Xp | Xp = Xa | sameside(Xa,Xp,Xb))) # label(aSatz6_3b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.52	182 (all Xa all Xb all Xc all Xa1 (-s_r(Xa1,Xb,Xc) | -s_e(Xa,Xb,Xa1,Xb) | s_e(Xa,Xc,Xa1,Xc) | -s_r(Xa,Xb,Xc))) # label(aSatz10_12b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.52	183 (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].
1.21/1.52	184 (all Xa all Xb all Xp all Xq all Xr all Xc all Xd (-s_col(Xa,Xb,Xp) | -s_col(Xa,Xb,Xq) | Xp = Xq | Xb = Xa | -perpAt(Xp,Xq,Xr,Xc,Xd) | perpAt(Xa,Xb,Xr,Xc,Xd))) # label(aExtPerp) # label(axiom) # label(non_clause).  [assumption].
1.21/1.52	185 (all Xa all Xp all Xb (s(Xb,Xp) != s(Xa,Xp) | Xb = Xa)) # label(aSatz7_18) # label(axiom) # label(non_clause).  [assumption].
1.21/1.52	186 (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].
1.21/1.52	187 (all Xp all Xa all Xq (-s_m(Xp,Xa,Xq) | s(Xa,Xp) = Xq)) # label(aSatz7_6) # label(axiom) # label(non_clause).  [assumption].
1.21/1.52	188 (all Xa all Xb all Xp all Xq all Xr (-sameside(Xa,Xq,Xr) | samesideline(Xr,Xb,Xp,Xq) | -samesideline(Xa,Xb,Xp,Xq))) # label(aSatz9_16) # label(axiom) # label(non_clause).  [assumption].
1.21/1.52	189 (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].
1.21/1.52	190 (all Xp all Xq all Xa all Xb (samesideline(Xp,Xq,Xb,Xa) | -samesideline(Xp,Xq,Xa,Xb))) # label(aLemma9_13a) # label(axiom) # label(non_clause).  [assumption].
1.21/1.52	191 (all Xa all Xb all Xc all Xd all Xa1 all Xb1 all Xc1 all Xd1 ((s_col(Xa,Xb,Xc) | -s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1)) & (-s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1) | s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1)) & (-s_col(Xa,Xb,Xc) | -s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1) | -s_e(Xa,Xd,Xa1,Xd1) | -s_e(Xb,Xd,Xb1,Xd1) | 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_e(Xa,Xd,Xa1,Xd1) | -s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1)))) # label(d_Defn4_15) # label(axiom) # label(non_clause).  [assumption].
1.21/1.52	192 (all Xa all Xp all Xr all Xq (Xr != s(Xa,Xp) | s(Xa,Xq) != Xr | Xp = Xq)) # label(aSatz7_8) # label(axiom) # label(non_clause).  [assumption].
1.21/1.52	193 (all Xp all Xq all Xr all Xcs (s_col(Xp,Xq,Xcs) | opposite(Xr,Xp,Xq,Xcs) | foot(Xp,Xq,Xr) != Xp | samesideline(Xr,Xcs,Xp,Xq) | s_col(Xp,Xq,Xr) | Xp = Xq)) # label(aLemma9_13f_case1) # label(axiom) # label(non_clause).  [assumption].
1.21/1.52	194 (all Xa all Xb all Xc all Xd all Xe all Xf ((Xb = Xa | Xb = Xc | Xe = Xd | sameside(f113a(Xa,Xb,Xc,Xd,Xe,Xf),Xb,Xa) | congruent(Xa,Xb,Xc,Xd,Xe,Xf) | Xe = Xf) & (Xb = Xa | Xc = Xb | Xd = Xe | Xe = Xf | congruent(Xa,Xb,Xc,Xd,Xe,Xf) | sameside(f113c(Xa,Xb,Xc,Xd,Xe,Xf),Xb,Xc)) & (Xe = Xf | sameside(f113f(Xa,Xb,Xc,Xd,Xe,Xf),Xe,Xf) | congruent(Xa,Xb,Xc,Xd,Xe,Xf) | Xe = Xd | Xb = Xc | Xa = Xb) & (Xd = Xe | s_e(Xb,f113c(Xa,Xb,Xc,Xd,Xe,Xf),Xe,f113f(Xa,Xb,Xc,Xd,Xe,Xf)) | congruent(Xa,Xb,Xc,Xd,Xe,Xf) | Xf = Xe | Xb = Xc | Xa = Xb) & (Xa = Xb | Xc = Xb | Xe = Xd | Xf = Xe | congruent(Xa,Xb,Xc,Xd,Xe,Xf) | -s_e(f113a(Xa,Xb,Xc,Xd,Xe,Xf),f113c(Xa,Xb,Xc,Xd,Xe,Xf),f113d(Xa,Xb,Xc,Xd,Xe,Xf),f113f(Xa,Xb,Xc,Xd,Xe,Xf))) & (Xa = Xb | Xe = Xd | congruent(Xa,Xb,Xc,Xd,Xe,Xf) | s_e(Xb,f113a(Xa,Xb,Xc,Xd,Xe,Xf),Xe,f113d(Xa,Xb,Xc,Xd,Xe,Xf)) | Xf = Xe | Xc = Xb) & (Xa = Xb | Xb = Xc | Xe = Xf | congruent(Xa,Xb,Xc,Xd,Xe,Xf) | sameside(f113d(Xa,Xb,Xc,Xd,Xe,Xf),Xe,Xd) | Xd = Xe))) # label(aSatz11_4b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.52	195 (all Xa all Xb all Xc all Xd all Xe (le(Xa,Xb,Xc,Xd) | -s_t(Xa,Xb,Xe) | -s_e(Xa,Xe,Xc,Xd))) # label(aSatz5_5b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.52	196 (all Xa all Xb all Xc ((s_r(Xa,Xb,Xc) | -s_e(Xa,Xc,Xa,s(Xb,Xc))) & (s_e(Xa,Xc,Xa,s(Xb,Xc)) | -s_r(Xa,Xb,Xc)))) # label(d_Defn8_1) # label(axiom) # label(non_clause).  [assumption].
1.21/1.52	197 (all Xa all Xb le(Xa,Xb,Xa,Xb)) # label(aSatz5_7) # label(axiom) # label(non_clause).  [assumption].
1.21/1.52	198 (all Xa all Xp all Xb ((-sameside(Xa,Xp,Xb) | Xa != Xp) & (-s_t(Xp,Xb,Xa) | sameside(Xa,Xp,Xb) | Xp = Xb | Xp = Xa) & (xb = Xp | sameside(Xa,Xp,Xb) | Xa = Xp | -s_t(Xp,Xa,Xb)) & (-sameside(Xa,Xp,Xb) | s_t(Xp,Xb,Xa) | s_t(Xp,Xa,Xb)) & (-sameside(Xa,Xp,Xb) | Xp != Xb))) # label(d_Defn6_1) # label(axiom) # label(non_clause).  [assumption].
1.21/1.52	199 (all Xa all Xp all Xq all Xc all Xb (-opposite(Xa,Xp,Xq,Xc) | opposite(Xb,Xp,Xq,Xc) | -samesideline(Xa,Xb,Xp,Xq))) # label(aSatz9_8) # label(axiom) # label(non_clause).  [assumption].
1.21/1.52	200 (all Xa all Xp all Xq (s(Xa,Xp) != s(Xa,Xq) | Xq = Xp)) # label(aSatz7_9) # label(axiom) # label(non_clause).  [assumption].
1.21/1.52	201 (all Xa1 all Xm1 all Xb1 all Xc all Xb2 all Xm2 all Xa2 ((s_e(Xc,Xa2,Xc,Xb2) | -s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2)) & (-s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) | s_m(Xa1,Xm1,Xb1)) & (-s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) | s_m(Xa2,Xm2,Xb2)) & (-s_e(Xc,Xa1,Xc,Xb1) | -s_m(Xa1,Xm1,Xb1) | -s_m(Xa2,Xm2,Xb2) | s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) | -s_e(Xc,Xa2,Xc,Xb2) | -s_t(Xb1,Xc,Xb2) | -s_t(Xa1,Xc,Xa2)) & (s_e(Xc,Xa1,Xc,Xb1) | -s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2)) & (-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)))) # label(d_Defn7_23) # label(axiom) # label(non_clause).  [assumption].
1.21/1.52	202 (all Xa all Xb all Xc all Xd all Xp (s_col(Xa,Xb,Xc) | Xb = Xd | -s_e(Xa,Xb,Xc,Xd) | -s_col(Xa,Xp,Xc) | -s_col(Xb,Xp,Xd) | s_m(Xa,Xp,Xc) | -s_e(Xb,Xc,Xd,Xa))) # label(aSatz7_21) # label(axiom) # label(non_clause).  [assumption].
1.21/1.53	203 (all Xa all Xp all Xq all Xc all Xm all Xr all Xb (-s_m(Xa,Xm,Xc) | -s_col(Xp,Xq,Xr) | -sameside(Xa,Xr,Xb) | opposite(Xb,Xp,Xq,Xc) | -s_t(Xr,Xb,Xa) | -s_col(Xp,Xq,Xm) | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_3a) # label(axiom) # label(non_clause).  [assumption].
1.21/1.53	204 (all Xa all Xb all Xp all Xq (-s_col(Xa,Xb,Xp) | -s_col(Xa,Xb,Xq) | -perp(Xa,Xb,Xp,Xq))) # label(aSatz8_14a) # label(axiom) # label(non_clause).  [assumption].
1.21/1.53	205 (all Xa all Xb all Xp all Xq all Xc ((Xb = Xa | -perp(Xa,Xb,Xc,Xp) | s_r(Xc,Xp,Xq) | Xp = Xq | -s_col(Xa,Xb,Xq) | -s_col(Xa,Xb,Xp)) & (-s_col(Xa,Xb,Xp) | Xp = Xq | -perp(Xa,Xb,Xc,Xp) | -s_col(Xa,Xb,Xc) | -s_col(Xa,Xb,Xq) | Xa = Xb))) # label(aSatz8_16a) # label(axiom) # label(non_clause).  [assumption].
1.21/1.53	206 (all Xp all Xa all Xb all Xq all Xt all Xr all Xcx (-perp(Xp,Xa,Xa,Xb) | -perp(Xq,Xb,Xa,Xb) | -s_t(Xp,Xt,Xq) | -s_t(Xb,Xr,Xq) | s_m(Xp,Xcx,Xr) | Xcx != ip(Xp,Xt,Xq,Xb,Xr) | -s_e(Xa,Xp,Xb,Xr) | -s_col(Xa,Xb,Xt))) # label(aSatz8_24b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.53	207 (all Xa all Xp all Xb (sameside(Xb,Xp,Xa) | -sameside(Xa,Xp,Xb))) # label(aSatz6_6) # label(axiom) # label(non_clause).  [assumption].
1.21/1.53	208 (all Xa all Xb all Xc all Xd (-s_t(Xa,Xb,Xc) | -s_t(Xa,Xc,Xd) | s_t(Xa,Xb,Xd))) # label(aSatz3_6b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.53	209 (all Xa all Xb all Xp all Xq (Xb = Xa | s_e(Xp,Xq,reflect(Xa,Xb,Xp),reflect(Xa,Xb,Xq)))) # label(aSatz10_10) # label(axiom) # label(non_clause).  [assumption].
1.21/1.53	210 (all Xa all Xm (Xa = Xm | -s_m(Xa,Xm,Xa))) # label(aSatz7_3a) # label(axiom) # label(non_clause).  [assumption].
1.21/1.53	211 (all Xa all Xb s_e(Xa,Xa,Xb,Xb)) # label(aSatz2_8) # label(axiom) # label(non_clause).  [assumption].
1.21/1.53	212 (all Xa all Xb all Xp all Xq all Xc (perpAt(Xa,Xb,Xc,Xp,Xq) | -s_col(Xp,Xq,Xc) | -s_col(Xa,Xb,Xc) | -perp(Xa,Xb,Xp,Xq))) # label(aSatz8_14b) # label(axiom) # label(non_clause).  [assumption].
1.21/1.53	213 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (s_t(Xa1,Xb1,Xc1) | -s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1) | -s_t(Xa,Xb,Xc))) # label(aSatz4_6) # label(axiom) # label(non_clause).  [assumption].
1.21/1.53	214 (all Xr all Xa all Xb all Xc ((Xr = Xa | s_e(Xa,insert(Xb,Xc,Xa,Xr),Xb,Xc) | Xb = Xc) & (Xr = Xa | sameside(insert(Xb,Xc,Xa,Xr),Xa,Xr) | Xc = Xb))) # label(aSatz6_11a) # label(axiom) # label(non_clause).  [assumption].
1.21/1.53	215 (all Xb all Xc all Xa (Xb = Xc | -s_e(Xb,Xc,Xa,Xa))) # label(aSatz2_13) # label(axiom) # label(non_clause).  [assumption].
1.21/1.53	216 (all Xa all Xb all Xp all Xq (Xb = Xa | samesideline(Xp,Xq,Xb,Xa) | -samesideline(Xp,Xq,Xa,Xb))) # label(aExtSameSide2) # label(axiom) # label(non_clause).  [assumption].
1.21/1.53	217 -(all Xa all Xb all Xc (Xa = Xb | Xb = Xc | congruent(Xa,Xb,Xc,Xa,Xb,Xc))) # label(aSatz11_6) # label(negated_conjecture) # label(non_clause).  [assumption].
1.21/1.53	
1.21/1.53	============================== end of process non-clausal formulas ===
1.21/1.53	
1.21/1.53	============================== PROCESS INITIAL CLAUSES ===============
1.21/1.53	
1.21/1.53	============================== PREDICATE ELIMINATION =================
1.21/1.53	218 -s_e(A,B,A,C) | -s_m(B,D,C) | -s_m(E,F,V6) | s_kf(B,D,C,A,V6,F,E) | -s_e(A,E,A,V6) | -s_t(C,A,V6) | -s_t(B,A,E) # label(d_Defn7_23) # label(axiom).  [clausify(201)].
1.21/1.53	219 s_t(A,B,C) | -le(B,D,B,E) | -s_kf(D,A,F,B,V6,C,E) # label(aSatz7_22a) # label(axiom).  [clausify(61)].
1.21/1.53	220 -s_kf(A,B,C,D,E,F,V6) | s_t(B,D,F) # label(aSatz7_22b) # label(axiom).  [clausify(180)].
1.21/1.53	221 s_e(A,B,A,C) | -s_kf(D,E,F,A,C,V6,B) # label(d_Defn7_23) # label(axiom).  [clausify(201)].
1.21/1.53	222 -s_kf(A,B,C,D,E,F,V6) | s_m(A,B,C) # label(d_Defn7_23) # label(axiom).  [clausify(201)].
1.21/1.53	223 -s_kf(A,B,C,D,E,F,V6) | s_m(V6,F,E) # label(d_Defn7_23) # label(axiom).  [clausify(201)].
1.21/1.53	Derived: -s_e(A,B,A,C) | -s_m(B,D,C) | -s_m(E,F,V6) | -s_e(A,E,A,V6) | -s_t(C,A,V6) | -s_t(B,A,E) | s_t(D,A,F) | -le(A,B,A,E).  [resolve(218,d,219,c)].
1.21/1.53	Derived: -s_e(A,B,A,C) | -s_m(B,D,C) | -s_m(E,F,V6) | -s_e(A,E,A,V6) | -s_t(C,A,V6) | -s_t(B,A,E) | s_t(D,A,F).  [resolve(218,d,220,a)].
1.21/1.53	224 s_e(A,B,A,C) | -s_kf(B,D,C,A,E,F,V6) # label(d_Defn7_23) # label(axiom).  [clausify(Alarm clock 
119.65/120.06	Prover9 interrupted
119.65/120.06	EOF