0.07/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.13	% Command    : tptp2X_and_run_prover9 %d %s
0.13/0.34	% Computer   : n015.cluster.edu
0.13/0.34	% Model      : x86_64 x86_64
0.13/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory     : 8042.1875MB
0.13/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit   : 180
0.13/0.34	% DateTime   : Thu Aug 29 11:51:22 EDT 2019
0.13/0.34	% CPUTime    : 
1.07/1.36	============================== Prover9 ===============================
1.07/1.36	Prover9 (32) version 2009-11A, November 2009.
1.07/1.36	Process 10656 was started by sandbox on n015.cluster.edu,
1.07/1.36	Thu Aug 29 11:51:23 2019
1.07/1.36	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 180 -f /tmp/Prover9_10501_n015.cluster.edu".
1.07/1.36	============================== end of head ===========================
1.07/1.36	
1.07/1.36	============================== INPUT =================================
1.07/1.36	
1.07/1.36	% Reading from file /tmp/Prover9_10501_n015.cluster.edu
1.07/1.36	
1.07/1.36	set(prolog_style_variables).
1.07/1.36	set(auto2).
1.07/1.36	    % set(auto2) -> set(auto).
1.07/1.36	    % set(auto) -> set(auto_inference).
1.07/1.36	    % set(auto) -> set(auto_setup).
1.07/1.36	    % set(auto_setup) -> set(predicate_elim).
1.07/1.36	    % set(auto_setup) -> assign(eq_defs, unfold).
1.07/1.36	    % set(auto) -> set(auto_limits).
1.07/1.36	    % set(auto_limits) -> assign(max_weight, "100.000").
1.07/1.36	    % set(auto_limits) -> assign(sos_limit, 20000).
1.07/1.36	    % set(auto) -> set(auto_denials).
1.07/1.36	    % set(auto) -> set(auto_process).
1.07/1.36	    % set(auto2) -> assign(new_constants, 1).
1.07/1.36	    % set(auto2) -> assign(fold_denial_max, 3).
1.07/1.36	    % set(auto2) -> assign(max_weight, "200.000").
1.07/1.36	    % set(auto2) -> assign(max_hours, 1).
1.07/1.36	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
1.07/1.36	    % set(auto2) -> assign(max_seconds, 0).
1.07/1.36	    % set(auto2) -> assign(max_minutes, 5).
1.07/1.36	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
1.07/1.36	    % set(auto2) -> set(sort_initial_sos).
1.07/1.36	    % set(auto2) -> assign(sos_limit, -1).
1.07/1.36	    % set(auto2) -> assign(lrs_ticks, 3000).
1.07/1.36	    % set(auto2) -> assign(max_megs, 400).
1.07/1.36	    % set(auto2) -> assign(stats, some).
1.07/1.36	    % set(auto2) -> clear(echo_input).
1.07/1.36	    % set(auto2) -> set(quiet).
1.07/1.36	    % set(auto2) -> clear(print_initial_clauses).
1.07/1.36	    % set(auto2) -> clear(print_given).
1.07/1.36	assign(lrs_ticks,-1).
1.07/1.36	assign(sos_limit,10000).
1.07/1.36	assign(order,kbo).
1.07/1.36	set(lex_order_vars).
1.07/1.36	clear(print_given).
1.07/1.36	
1.07/1.36	% formulas(sos).  % not echoed (212 formulas)
1.07/1.36	
1.07/1.36	============================== end of input ==========================
1.07/1.36	
1.07/1.36	% From the command line: assign(max_seconds, 180).
1.07/1.36	
1.07/1.36	============================== PROCESS NON-CLAUSAL FORMULAS ==========
1.07/1.36	
1.07/1.36	% Formulas that are not ordinary clauses:
1.07/1.36	1 (all X all Y all W all V (s_t(X,Y,ext(X,Y,W,V)) & s_e(Y,ext(X,Y,W,V),W,V))) # label(aA4) # label(axiom) # label(non_clause).  [assumption].
1.07/1.36	2 (all X all Y all X1 all Y1 all Z all Z1 all V all V1 (-s_e(X,V,X1,V1) | -s_e(Y,V,Y1,V1) | Y = X | s_e(Z,V,Z1,V1) | -s_t(X1,Y1,Z1) | -s_t(X,Y,Z) | -s_e(Y,Z,Y1,Z1) | -s_e(X,Y,X1,Y1))) # label(aA5) # label(axiom) # label(non_clause).  [assumption].
1.07/1.36	3 (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(Xb,Xq,Xc) | s_t(Xq,ip(Xa,Xp,Xc,Xb,Xq),Xa) | -s_t(Xa,Xp,Xc)))) # label(aA7) # label(axiom) # label(non_clause).  [assumption].
1.07/1.36	4 (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].
1.07/1.36	5 (all X all Y (X = Y | -s_t(X,Y,X))) # label(aA6) # label(axiom) # label(non_clause).  [assumption].
1.07/1.36	6 (all X all Y all Z (X = Y | -s_e(X,Y,Z,Z))) # label(aA3) # label(axiom) # label(non_clause).  [assumption].
1.07/1.36	7 (all X all Y s_e(X,Y,Y,X)) # label(aA1) # label(axiom) # label(non_clause).  [assumption].
1.07/1.36	8 (all Xa all Xp all Xb (-sameside(Xa,Xp,Xb) | s_t(Xp,Xa,Xb) | -le(Xp,Xa,Xp,Xb))) # label(aSatz6_13a) # label(axiom) # label(non_clause).  [assumption].
1.07/1.36	9 (all Xp all Xq all Xr all Xa (Xp = Xq | -s_t(Xq,Xp,Xr) | -sameside(Xa,Xp,Xq) | s_col(Xa,Xp,Xq) | Xp = Xr)) # label(aSatz6_15b) # label(axiom) # label(non_clause).  [assumption].
1.07/1.36	10 (all Xa all Xb all Xp all Xq all Xc ((Xa = Xb | -s_col(Xa,Xb,Xp) | -s_col(Xa,Xb,Xq) | -perp(Xa,Xb,Xc,Xp) | s_r(Xc,Xp,Xq) | Xq = Xp) & (-s_col(Xa,Xb,Xp) | Xq = Xp | -s_col(Xa,Xb,Xc) | -perp(Xa,Xb,Xc,Xp) | -s_col(Xa,Xb,Xq) | Xa = Xb))) # label(aSatz8_16a) # label(axiom) # label(non_clause).  [assumption].
1.07/1.36	11 (all Xa all Xb s_t(Xa,Xb,ext(Xa,Xb,alpha,gamma))) # label(aSatz3_14a) # label(axiom) # label(non_clause).  [assumption].
1.07/1.36	12 (all Xa all Xc all Xp all Xb all Xq ((-s_t(Xb,Xq,Xc) | s_t(Xa,op(Xq,Xb,Xp,Xc,Xa),Xb) | -s_t(Xa,Xc,Xp)) & (s_t(Xp,Xq,op(Xq,Xb,Xp,Xc,Xa)) | -s_t(Xb,Xq,Xc) | -s_t(Xa,Xc,Xp)))) # label(aSatz9_6) # label(axiom) # label(non_clause).  [assumption].
1.07/1.36	13 (all Xp all Xq all Xcs all Xr (Xp = Xq | Xp = Xcs | -s_col(Xp,Xq,Xr) | s_col(Xp,Xcs,Xr) | -s_col(Xp,Xq,Xcs))) # label(aSatz6_16b) # label(axiom) # label(non_clause).  [assumption].
1.07/1.36	14 (all Xa all Xb all Xc all Xd (-s_col(Xa,Xb,Xd) | Xa = Xb | s_col(Xa,Xc,Xd) | -s_col(Xa,Xb,Xc))) # label(aext1) # label(axiom) # label(non_clause).  [assumption].
1.07/1.36	15 (all Xa all Xb all Xp (Xa = Xb | reflect(Xa,Xb,Xp) = Xp | -s_col(Xa,Xb,Xp))) # label(aSatz10_8b) # label(axiom) # label(non_clause).  [assumption].
1.07/1.36	16 (all Xa all Xm (s_m(Xa,Xm,Xa) | Xm != Xa)) # label(aSatz7_3b) # label(axiom) # label(non_clause).  [assumption].
1.07/1.36	17 (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].
1.07/1.36	18 (all Xa all Xb all Xc all Xd (-s_t(Xa,Xb,Xc) | -s_t(Xa,Xb,Xd) | s_t(Xa,Xd,Xc) | s_t(Xa,Xc,Xd) | Xa = Xb)) # label(aSatz5_1) # label(axiom) # label(non_clause).  [assumption].
1.07/1.36	19 (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_t(Xa,ss1(Xa,Xb,Xp,Xq),ss3(Xa,Xb,Xp,Xq))) & (-samesideline(Xa,Xb,Xp,Xq) | Xb != ss2(Xa,Xb,Xp,Xq)) & (-samesideline(Xa,Xb,Xp,Xq) | Xp != Xq) & (-s_col(Xp,Xq,Xa) | -samesideline(Xa,Xb,Xp,Xq)) & (-s_t(Xb,Xv,Xc) | -s_col(Xp,Xq,Xv) | Xc = Xv | Xa = Xu | s_col(Xp,Xq,Xa) | s_col(Xp,Xq,Xb) | samesideline(Xa,Xb,Xp,Xq) | Xv = Xb | Xc = Xu | Xp = Xq | -s_col(Xp,Xq,Xu) | -s_t(Xa,Xu,Xc)) & (-samesideline(Xa,Xb,Xp,Xq) | -s_col(Xp,Xq,Xb)) & (ss3(Xa,Xb,Xp,Xq) != ss2(Xa,Xb,Xp,Xq) | -samesideline(Xa,Xb,Xp,Xq)) & (-samesideline(Xa,Xb,Xp,Xq) | ss1(Xa,Xb,Xp,Xq) != ss3(Xa,Xb,Xp,Xq)) & (ss1(Xa,Xb,Xp,Xq) != Xa | -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].
1.07/1.36	20 (all Xa all Xp all Xb all Xc (Xa = Xp | -s_t(Xa,Xp,Xc) | -s_t(Xb,Xp,Xc) | Xp = Xc | Xp = Xb | sameside(Xa,Xp,Xb))) # label(aSatz6_3b) # label(axiom) # label(non_clause).  [assumption].
1.07/1.36	21 (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].
1.07/1.36	22 (all Xa all Xb all Xc all Xd all Xp (s_col(Xa,Xb,Xc) | Xb = Xd | s_m(Xa,Xp,Xc) | -s_col(Xb,Xp,Xd) | -s_col(Xa,Xp,Xc) | -s_e(Xb,Xc,Xd,Xa) | -s_e(Xa,Xb,Xc,Xd))) # label(aSatz7_21) # label(axiom) # label(non_clause).  [assumption].
1.07/1.36	23 (all Xp all Xa all Xr all Xq (-s_m(Xp,Xa,Xq) | Xr = Xq | -s_m(Xp,Xa,Xr))) # label(aSatz7_4b) # label(axiom) # label(non_clause).  [assumption].
1.07/1.36	24 (all Xa all Xb all Xc (le(Xa,Xb,Xa,Xc) | -s_t(Xa,Xb,Xc) | -s_col(Xa,Xb,Xc))) # label(aSatz5_12a1) # label(axiom) # label(non_clause).  [assumption].
1.07/1.36	25 (all Xa all Xb all Xd all Xc (-s_col(Xa,Xb,Xd) | perpAt(Xa,Xb,Xd,Xc,Xd) | -perp(Xa,Xb,Xc,Xd) | Xb = Xa)) # label(aSatz8_15) # label(axiom) # label(non_clause).  [assumption].
1.07/1.36	26 (all Xp all Xq all Xr all Xa (-s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr)) | s_t(Xp,Xq,Xr))) # label(aSatz7_15b) # label(axiom) # label(non_clause).  [assumption].
1.07/1.36	27 (all Xa all Xp all Xb ((s_col(Xa,Xp,Xb) | -sameside(Xa,Xp,Xb)) & (-sameside(Xa,Xp,Xb) | -s_t(Xa,Xp,Xb)))) # label(aSatz6_4a) # label(axiom) # label(non_clause).  [assumption].
1.07/1.36	28 (all Xa all Xp all Xq all Xb all Xc (-opposite(Xa,Xp,Xq,Xb) | -samesideline(Xb,Xc,Xp,Xq) | opposite(Xa,Xp,Xq,Xc))) # label(aLemma9_13e) # label(axiom) # label(non_clause).  [assumption].
1.07/1.36	29 (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].
1.07/1.36	30 (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].
1.07/1.36	31 (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].
1.07/1.37	32 (all Xa all Xp all Xq all Xc all Xm all Xr all Xb (-s_col(Xp,Xq,Xr) | -sameside(Xa,Xr,Xb) | -s_t(Xr,Xb,Xa) | opposite(Xb,Xp,Xq,Xc) | -s_m(Xa,Xm,Xc) | -s_col(Xp,Xq,Xm) | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_3a) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	33 (all Xp all Xa all Xb all Xq all Xt all Xr all Xcx (-s_col(Xa,Xb,Xt) | -s_t(Xb,Xr,Xq) | s_m(Xp,Xcx,Xr) | Xcx != ip(Xp,Xt,Xq,Xb,Xr) | -s_e(Xa,Xp,Xb,Xr) | -s_t(Xp,Xt,Xq) | -perp(Xq,Xb,Xa,Xb) | -perp(Xp,Xa,Xa,Xb))) # label(aSatz8_24b) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	34 (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].
1.07/1.37	35 (all Xa all Xb all Xc (Xc = Xb | -s_e(Xa,Xc,Xa,Xb) | -s_t(Xa,Xb,Xc))) # label(aNarbouxLemma1) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	36 (all Xa all Xb all Xc all Xd (-s_t(Xa,Xc,Xd) | s_t(Xb,Xc,Xd) | -s_t(Xa,Xb,Xc))) # label(aSatz3_6a) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	37 (all Xa all Xb all Xc all Xd all Xa1 all Xb1 all Xc1 all Xd1 (Xb = Xa | 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].
1.07/1.37	38 (all Xa all Xp (Xp = Xa | Xp != s(Xa,Xp))) # label(aSatz7_10a) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	39 (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].
1.07/1.37	40 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_t(Xa1,Xb1,Xc1) | s_e(Xa,Xc,Xa1,Xc1) | -s_e(Xb,Xc,Xb1,Xc1) | -s_e(Xa,Xb,Xa1,Xb1) | -s_t(Xa,Xb,Xc))) # label(aSatz2_11) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	41 (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].
1.07/1.37	42 (all Xa all Xb all Xd all Xc (-s_t(Xa,Xb,Xd) | s_t(Xa,Xb,Xc) | s_t(Xa,Xc,Xb) | -s_t(Xa,Xc,Xd))) # label(aSatz5_3) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	43 (all Xa all Xb all Xp all Xp1 (Xa = Xb | reflect(Xa,Xb,Xp1) = Xp | reflect(Xa,Xb,Xp) != Xp1)) # label(aSatz10_6) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	44 (all Xa all Xb all Xp all Xq all Xr (-samesideline(Xa,Xb,Xp,Xq) | -sameside(Xa,Xq,Xr) | samesideline(Xr,Xb,Xp,Xq))) # label(aSatz9_16) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	45 (all Xa all Xc all Xd le(Xa,Xa,Xc,Xd)) # label(aSatz5_11) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	46 (all Xa all Xb all Xc all Xa1 all Xb1 all Xp ((-s_t(Xa,Xp,Xa1) | s_t(Xb,crossbar(Xa,Xb,Xc,Xa1,Xb1,Xp),Xb1) | -s_t(Xa1,Xb1,Xc) | -s_t(Xa,Xb,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].
1.07/1.37	47 (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].
1.07/1.37	48 (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].
1.07/1.37	49 (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].
1.07/1.37	50 (all Xa all Xb s_t(Xa,Xb,Xb)) # label(aSatz3_1) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	51 (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 | -s_col(Y,Z,X) | -s_col(Y1,Z1,X) | s_col(Y,Z,f811(Y,Z,Y1,Z1,X)) | Y1 = Z1 | perpAt(Y,Z,X,Y1,Z1)) & (perpAt(Y,Z,X,Y1,Z1) | -s_col(Y1,Z1,X) | s_col(Y1,Z1,g811(Y,Z,Y1,Z1,X)) | -s_col(Y,Z,X) | Z1 = Y1 | Y = Z) & (perpAt(Y,Z,X,Y1,Z1) | Y = Z | Z1 = Y1 | -s_col(Y1,Z1,X) | -s_r(f811(Y,Z,Y1,Z1,X),X,g811(Y,Z,Y1,Z1,X)) | -s_col(Y,Z,X)) & (-perpAt(Y,Z,X,Y1,Z1) | -s_col(Y,Z,U) | s_r(U,X,V) | -s_col(Y1,Z1,V)) & (Y1 != Z1 | -perpAt(Y,Z,X,Y1,Z1)) & (-perpAt(Y,Z,X,Y1,Z1) | Z != Y) & (s_col(Y1,Z1,X) | -perpAt(Y,Z,X,Y1,Z1)))) # label(d_Defn8_11a) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	52 (all Xp all Xq all Xr all Xa (Xp = Xq | -s_t(Xq,Xp,Xr) | Xa != Xp | s_col(Xa,Xp,Xq) | Xp = Xr)) # label(aSatz6_15d) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	53 (all Xc all Xd all Xp all Xa all Xb (Xc = Xd | -s_col(Xa,Xb,Xp) | -sameside(Xa,Xp,Xb) | samesideline(Xa,Xb,Xc,Xd) | s_col(Xc,Xd,Xa) | -s_col(Xc,Xd,Xp))) # label(aSatz9_19b) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	54 (all Xa all Xb s_e(Xa,Xa,Xb,Xb)) # label(aSatz2_8) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	55 (all Xa all Xb all Xd all Xc (-s_t(Xa,Xb,Xd) | s_t(Xa,Xb,Xc) | -s_t(Xb,Xc,Xd))) # label(aSatz3_5a) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	56 (all Xa all Xb all Xc all Xa1 all Xc1 ((-s_t(Xa,Xb,Xc) | -s_e(Xa,Xc,Xa1,Xc1) | s_t(Xa1,insert(Xa,Xb,Xa1,Xc1),Xc1)) & (s_e3(Xa,Xb,Xc,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].
1.07/1.37	57 (all Xp all Xa all Xb all Xq all Xt all Xr (-s_t(Xp,Xt,Xq) | -s_e(Xa,Xp,Xb,Xr) | s_m(Xp,midpoint(Xa,Xb),Xr) | -s_t(Xb,Xr,Xq) | -s_col(Xa,Xb,Xt) | -perp(Xq,Xb,Xa,Xb) | -perp(Xp,Xa,Xa,Xb))) # label(aSatz8_24) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	58 (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].
1.07/1.37	59 (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].
1.07/1.37	60 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_t(Xa,Xb,Xc) | -s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1) | s_t(Xa1,Xb1,Xc1))) # label(aSatz4_6) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	61 (all Xa all Xp all Xb (-sameside(Xa,Xp,Xb) | le(Xp,Xa,Xp,Xb) | -s_t(Xp,Xa,Xb))) # label(aSatz6_13b) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	62 (all Xa all Xb all Xc all Xd all Xe all Xf (-s_e(Xa,Xb,Xc,Xd) | -s_e(Xc,Xd,Xe,Xf) | s_e(Xa,Xb,Xe,Xf))) # label(aSatz2_3) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	63 (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].
1.07/1.37	64 (all Xa all Xb all Xp all Xq all Xc all Xd all Xe (Xa = Xb | Xq = Xp | -s_col(Xp,Xq,Xc) | -s_col(Xa,Xb,Xd) | -s_col(Xp,Xq,Xd) | -s_col(Xa,Xb,Xe) | s_col(Xp,Xq,Xe) | Xc = Xd | -s_col(Xa,Xb,Xc))) # label(aSatz6_21) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	65 (all Xa all Xp (Xp = Xa | sameside(Xa,Xp,Xa))) # label(aSatz6_5) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	66 (all Xp all Xa all Xb all Xq all Xt all Xr all Xcx (-perp(Xp,Xa,Xa,Xb) | -s_t(Xb,Xr,Xq) | -s_e(Xa,Xp,Xb,Xr) | ip(Xp,Xt,Xq,Xb,Xr) != Xcx | s_m(Xa,Xcx,Xb) | -s_t(Xp,Xt,Xq) | -s_col(Xa,Xb,Xt) | -perp(Xq,Xb,Xa,Xb))) # label(aSatz8_24a) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	67 (all Xp all Xq all Xr all Xcs (s_col(Xp,Xq,Xr) | s_col(Xp,Xq,Xcs) | opposite(Xr,Xp,Xq,Xcs) | samesideline(Xr,Xcs,Xp,Xq) | Xp = Xq)) # label(aLemma9_13f) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	68 (all Xa all Xb all Xp ((Xa = Xb | s_col(Xa,Xb,midpoint(Xp,reflect(Xa,Xb,Xp)))) & (Xb = Xa | Xp = reflect(Xa,Xb,Xp) | perp(Xa,Xb,Xp,reflect(Xa,Xb,Xp))))) # label(aSatz10_2a) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	69 (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].
1.07/1.37	70 (all Xd all Xe all Xd1 all Xa all Xb (samesideline(Xa,Xb,Xd,Xe) | -samesideline(Xa,Xb,Xd1,Xe) | -s_t(Xe,Xd,Xd1) | Xe = Xd)) # label(aLemma9_13c) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	71 (all Xa all Xb all Xc (Xb = Xc | Xa = Xb | -s_col(Xa,Xb,Xc) | -s_r(Xa,Xb,Xc))) # label(aSatz8_9) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	72 (all Xa all Xb all Xp all Xp1 ((Xb = Xa | reflect(Xa,Xb,Xp) = Xp1 | -perp(Xa,Xb,Xp,Xp1) | -s_col(Xa,Xb,midpoint(Xp,Xp1))) & (Xa = Xb | Xp != Xp1 | Xp1 = reflect(Xa,Xb,Xp) | -s_col(Xa,Xb,midpoint(Xp,Xp1))))) # label(aSatz10_2b) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	73 (all Xa all Xb all Xc (-s_col(Xa,Xb,Xc) | le(Xb,Xc,Xa,Xc) | -s_t(Xa,Xb,Xc))) # label(aSatz5_12a2) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	74 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-sameside(Xa,Xb,Xc) | -sameside(Xa1,Xb1,Xc1) | -s_e(Xb,Xa,Xb1,Xa1) | -s_e(Xb,Xc,Xb1,Xc1) | s_e(Xa,Xc,Xa1,Xc1))) # label(aSatz6_28) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	75 (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].
1.07/1.37	76 (all Xa all Xb all Xc (s_col(Xc,Xa,Xb) | -s_col(Xa,Xb,Xc))) # label(aSatz4_11b) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	77 (all Xa all Xb all Xc all Xa1 all Xb1 (-s_e(Xa,Xb,Xa1,Xb1) | s_e3(Xa,Xb,Xc,Xa1,Xb1,insert5(Xa,Xb,Xc,Xa1,Xb1)) | -s_col(Xa,Xb,Xc))) # label(aSatz4_14) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	78 (all Xa all Xb s_col(Xa,Xb,Xa)) # label(aSatz4_12b) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	79 (all Xa all Xb all Xc all Xd all Xe (-s_t(Xa,Xb,Xe) | -s_e(Xa,Xe,Xc,Xd) | le(Xa,Xb,Xc,Xd))) # label(aSatz5_5b) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	80 (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_e(Xb,Xc,Zb,Zc)) & (-s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_e(Xa,Xd,Za,Zd)) & (-s_t(Za,Zb,Zc) | -s_e(Xa,Xc,Za,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(Xb,Xc,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(Za,Zb,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].
1.07/1.37	81 (all Xa1 all Xb1 s_t(Xa1,Xa1,Xb1)) # label(aSatz3_3) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	82 (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].
1.07/1.37	83 (all Xa all Xb all Xc all Xp all Xq ((Xa != Xb | -perpAt(Xa,Xb,Xc,Xp,Xq)) & (Xq != Xp | -perpAt(Xa,Xb,Xc,Xp,Xq)) & (s_col(Xp,Xq,Xc) | -perpAt(Xa,Xb,Xc,Xp,Xq)) & (-perpAt(Xa,Xb,Xc,Xp,Xq) | s_col(Xa,Xb,Xc)) & (Xc != f813(Xa,Xb,Xp,Xq,Xc) | -perpAt(Xa,Xb,Xc,Xp,Xq)) & (-perpAt(Xa,Xb,Xc,Xp,Xq) | Xc != g813(Xa,Xb,Xp,Xq,Xc)) & (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) | s_col(Xp,Xq,g813(Xa,Xb,Xp,Xq,Xc))) & (s_col(Xa,Xb,f813(Xa,Xb,Xp,Xq,Xc)) | -perpAt(Xa,Xb,Xc,Xp,Xq)))) # label(aSatz8_13a) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	84 (all Xa all Xb all Xp all Xq (s_e(Xp,Xq,reflect(Xa,Xb,Xp),reflect(Xa,Xb,Xq)) | Xa = Xb)) # label(aSatz10_10) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	85 (all Xp all Xq all Xr (Xp = Xq | -s_col(Xp,Xq,Xr) | s_col(Xq,Xp,Xr))) # label(aSatz6_17b) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	86 (all Xa1 all Xm1 all Xb1 all Xc all Xb2 all Xm2 all Xa2 ((s_t(Xa1,Xc,Xa2) | -s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2)) & (s_e(Xc,Xa1,Xc,Xb1) | -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(Xa1,Xc,Xa2) | -s_e(Xc,Xa1,Xc,Xb1) | s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) | -s_m(Xa2,Xm2,Xb2) | -s_m(Xa1,Xm1,Xb1) | -s_e(Xc,Xa2,Xc,Xb2) | -s_t(Xb1,Xc,Xb2)) & (-s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) | s_m(Xa1,Xm1,Xb1)) & (-s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) | s_e(Xc,Xa2,Xc,Xb2)) & (s_t(Xb1,Xc,Xb2) | -s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2)))) # label(d_Defn7_23) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	87 (all Xp all Xq all Xr all Xcs (s_col(Xp,Xq,Xcs) | Xp = foot(Xp,Xq,Xr) | opposite(Xr,Xp,Xq,Xcs) | samesideline(Xr,Xcs,Xp,Xq) | s_col(Xp,Xq,Xr) | Xq = Xp)) # label(aLemma9_13f_case2) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	88 (all Xb all Xc all Xa (-s_e(Xb,Xc,Xa,Xa) | Xb = Xc)) # label(aSatz2_13) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	89 (all Xa all Xb all Xp all Xq all Xc (-s_col(Xa,Xb,Xq) | -s_r(Xc,Xp,Xq) | s_col(Xa,Xb,Xc) | perp(Xa,Xb,Xc,Xp) | Xq = Xp | -s_col(Xa,Xb,Xp) | Xb = Xa)) # label(aSatz8_16b) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	90 (all Xa all Xb all Xp all Xq all Xc all Xd (Xq = Xp | Xa = Xb | perp(Xp,Xq,Xc,Xd) | -perp(Xa,Xb,Xc,Xd) | -s_col(Xa,Xb,Xq) | -s_col(Xa,Xb,Xp))) # label(aExtPerp5) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	91 (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].
1.07/1.37	92 (all Xa all Xb all Xd all Xc (-s_t(Xa,Xb,Xd) | -s_t(Xb,Xc,Xd) | s_t(Xa,Xc,Xd))) # label(aSatz3_5b) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	93 (all Xa all Xp all Xb all Xc (-s_t(Xa,Xp,Xc) | -s_t(Xb,Xp,Xc) | sameside(Xa,Xp,Xb) | Xp = Xc | Xp = Xb | Xa = Xp)) # label(aSatz6_2a) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	94 (all Xa all Xb all Xc (-s_col(Xa,Xb,Xc) | -le(Xb,Xc,Xa,Xc) | -le(Xa,Xb,Xa,Xc) | s_t(Xa,Xb,Xc))) # label(aSatz5_12b) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	95 (all Xa all Xb all Xc all Xp all Xq (-perpAt(Xa,Xb,Xc,Xp,Xq) | perpAt(Xp,Xq,Xc,Xa,Xb))) # label(aSatz8_12a) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	96 (all Xa all Xp all Xr all Xq (s(Xa,Xq) != Xr | Xp = Xq | Xr != s(Xa,Xp))) # label(aSatz7_8) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	97 (all Xa all Xp all Xb ((-sameside(Xa,Xp,Xb) | Xa != Xp) & (-sameside(Xa,Xp,Xb) | s_t(Xa,Xp,c63(Xa,Xp,Xb))) & (-sameside(Xa,Xp,Xb) | s_t(Xb,Xp,c63(Xa,Xp,Xb))) & (-sameside(Xa,Xp,Xb) | c63(Xa,Xp,Xb) != Xp) & (Xb != Xp | -sameside(Xa,Xp,Xb)))) # label(aSatz6_3a) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	98 (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].
1.07/1.37	99 (all Xr all Xa all Xb all Xc all Xp all Xq (-sameside(Xp,Xa,Xr) | -s_e(Xa,Xp,Xb,Xc) | -sameside(Xq,Xa,Xr) | Xq = Xp | -s_e(Xa,Xq,Xb,Xc) | Xb = Xc | Xr = Xa)) # label(aSatz6_11b) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	100 (all Xa all Xp all Xq all Xc all Xb (-opposite(Xa,Xp,Xq,Xc) | -samesideline(Xa,Xb,Xp,Xq) | opposite(Xb,Xp,Xq,Xc))) # label(aSatz9_8) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	101 (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].
1.07/1.37	102 (all Xa all Xb all Xp (s(Xb,s(Xa,Xp)) != s(Xa,s(Xb,Xp)) | Xa = Xb)) # label(aSatz7_19) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	103 (all Xa all Xb all Xp all Xp1 (reflect(Xa,Xb,Xp) != Xp1 | Xp = reflect(Xa,Xb,Xp1) | Xa = Xb)) # label(aSatz10_4) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	104 (all Xa all Xb all Xp all Xq (Xq = Xp | reflect(Xa,Xb,Xq) != reflect(Xa,Xb,Xp) | Xb = Xa)) # label(aSatz10_7) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	105 (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_16b) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	106 (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].
1.07/1.37	107 (all Xa all Xb (-s_col(Xa,Xb,pointOffLine(Xa,Xb)) | Xb = Xa)) # label(aSatz6_25) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	108 (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].
1.07/1.37	109 (all Xa all Xb all U all V all W (-s_m(U,V,W) | -s_col(Xa,Xb,U) | s_col(Xa,Xb,V) | -s_col(Xa,Xb,W) | Xb = Xa)) # label(aLemma9_13b) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	110 (all Xa1 all Xa2 all Xa3 all Xb1 all Xb2 all Xb3 ((-s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3) | s_e(Xa2,Xa3,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(Xa1,Xa3,Xb1,Xb3)) & (-s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3) | s_e(Xa1,Xa2,Xb1,Xb2)))) # label(d_Defn4_4) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	111 (all Xa all Xb all Xc all Xp all Xq (s_e(Xc,Xp,Xc,Xq) | -s_e(Xb,Xp,Xb,Xq) | -s_e(Xa,Xp,Xa,Xq) | -s_col(Xa,Xb,Xc) | Xa = Xb)) # label(aSatz4_17) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	112 (all Xa all Xb all Xc all Xd (Xa = Xb | Xb = Xc | Xd = Xa | -s_col(Xa,Xc,Xd) | perp(Xb,Xa,Xa,Xd) | -perp(Xb,Xa,Xa,Xc) | Xc = Xd | Xa = Xc)) # label(aExtPerp3) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	113 (all Xa all Xb s_r(Xa,Xb,Xb)) # label(aSatz8_5) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	114 (all Xa all Xb all Xp all Xq all Xr (-s_col(Xp,Xq,Xr) | s_col(Xa,Xb,Xr) | -s_col(Xp,Xq,Xb) | -s_col(Xp,Xq,Xa) | Xp = Xq | Xb = Xa)) # label(aSatz6_18) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	115 (all Xa all Xb all Xc (s_t(Xc,Xb,Xa) | -s_t(Xa,Xb,Xc))) # label(aSatz3_2) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	116 (all Xa all Xb all Xc all Xd (-s_t(Xb,Xc,Xd) | Xc = Xb | s_t(Xa,Xb,Xd) | -s_t(Xa,Xb,Xc))) # label(aSatz3_7b) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	117 (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].
1.07/1.37	118 (all Xa all Xp all Xb (sameside(Xb,Xp,Xa) | -sameside(Xa,Xp,Xb))) # label(aSatz6_6) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	119 (all Xa all Xb s_col(Xa,Xa,Xb)) # label(aSatz4_12) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	120 (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].
1.07/1.37	121 (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)) | Xb = Xa)) # label(aSatz10_10a) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	122 (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(Xa,Xd,Za,Zd) | -s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)) & (-s_t(Za,Zb,Zc) | -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(Xa,Xb,Xc)) & (-s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_e(Xb,Xd,Zb,Zd)) & (s_e(Xb,Xc,Zb,Zc) | -s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)) & (-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].
1.07/1.37	123 (all Xa all Xp all Xb all Xc (Xp = Xa | Xp = Xc | -sameside(Xa,Xp,Xb) | s_t(Xb,Xp,Xc) | -s_t(Xa,Xp,Xc) | Xb = Xp)) # label(aSatz6_2b) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	124 (all Xp all Xa s_m(Xp,Xa,s(Xa,Xp))) # label(aSatz7_4a) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	125 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (s_col(Xa1,Xb1,Xc1) | -s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1) | -s_col(Xa,Xb,Xc))) # label(aSatz4_13) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	126 (all Xa all Xp all Xq all Xc all Xm all Xr all Xb (opposite(Xb,Xp,Xq,Xc) | -sameside(Xa,Xr,Xb) | -s_col(Xp,Xq,Xr) | -s_m(Xa,Xm,Xc) | -s_col(Xp,Xq,Xm) | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_3) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	127 (all Xp all Xq all Xa all Xb all Xt ((-opposite(Xa,Xp,Xq,Xb) | -s_col(Xp,Xq,Xa)) & (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)) & (-opposite(Xa,Xp,Xq,Xb) | -s_col(Xp,Xq,Xb)) & (s_col(Xp,Xq,Xa) | -s_t(Xa,Xt,Xb) | -s_col(Xp,Xq,Xt) | opposite(Xa,Xp,Xq,Xb) | s_col(Xp,Xq,Xb) | Xq = Xp))) # label(d_Defn9_1) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	128 (all Xa all Xb all Xc all Xd ((s_e(Xa,ins(Xc,Xd,Xa,Xb),Xc,Xd) | -le(Xa,Xb,Xc,Xd)) & (ins(Xc,Xd,Xa,Xb) = ext(Xa,Xb,insert(Xa,Xb,Xc,Xd),Xd) | -le(Xa,Xb,Xc,Xd)) & (-le(Xa,Xb,Xc,Xd) | s_t(Xa,Xb,ins(Xc,Xd,Xa,Xb))))) # label(aSatz5_5a) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	129 (all Xa all Xb all Xc all Xa1 (-s_r(Xa,Xb,Xc) | -s_r(Xa1,Xb,Xc) | Xb = Xc | -s_t(Xa,Xc,Xa1))) # label(aSatz8_6) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	130 (all Xa all Xp all Xq all Xc all Xcs all Xr all Xm all U (Xp = Xq | -perp(Xp,Xq,Xc,Xcs) | -s_m(Xr,Xm,Xcs) | -sameside(U,Xr,Xa) | sameside(s(Xm,U),Xcs,Xc) | -perp(Xp,Xq,Xa,Xr) | -s_col(Xp,Xq,Xr) | -s_col(Xp,Xq,Xcs) | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_4) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	131 (all Xa all Xp all Xb (-s_col(Xa,Xp,Xb) | s_t(Xa,Xp,Xb) | sameside(Xa,Xp,Xb))) # label(aSatz6_4b) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	132 (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].
1.07/1.37	133 (all Xa all Xp all Xq all Xb (-samesideline(Xa,Xb,Xp,Xq) | -opposite(Xa,Xp,Xq,Xb))) # label(aSatz9_9) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	134 (all Xa all Xb le(Xa,Xb,Xa,Xb)) # label(aSatz5_7) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	135 (all Xa all Xb all Xc all Xp all Xq (s_col(Xa,Xb,Xc) | -s_col(Xa,Xb,Xp) | -s_col(Xa,Xb,Xq) | Xq = Xp | -perp(Xa,Xb,Xc,Xq) | -perp(Xa,Xb,Xc,Xp))) # label(aSatz8_18a) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	136 (all Xp all Xq all Xa all Xb all Xc (samesideline(Xa,Xc,Xp,Xq) | -samesideline(Xb,Xc,Xp,Xq) | -samesideline(Xa,Xb,Xp,Xq) | Xp = Xq)) # label(aSatz9_13) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	137 (all Xa all Xb all Xc all Xd (s_e(Xb,Xa,Xc,Xd) | -s_e(Xa,Xb,Xc,Xd))) # label(aSatz2_4) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	138 (all Xa all Xp s(Xa,s(Xa,Xp)) = Xp) # label(aSatz7_7) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	139 (all Xa all Xm all Xb (Xa = Xb | s_m(Xa,Xm,Xb) | -s_e(Xm,Xa,Xm,Xb) | -s_col(Xa,Xm,Xb))) # label(aSatz7_20) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	140 (all Xa all Xb all Xc all Xp all Xq (Xc = il(Xa,Xb,Xp,Xq) | -perpAt(Xa,Xb,Xc,Xp,Xq))) # label(aSatz8_14c) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	141 (all Xq all Xa all Xd all Xb all Xc (-s_t(Xq,Xa,Xd) | Xd = ext(Xq,Xa,Xb,Xc) | -s_e(Xa,Xd,Xb,Xc) | Xa = Xq)) # label(aSatz2_12) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	142 (all Xa all Xb all Xc all Xd (-s_t(Xa,Xb,Xd) | s_t(Xb,Xc,Xd) | s_t(Xb,Xd,Xc) | -s_t(Xa,Xb,Xc) | Xb = Xa)) # label(aSatz5_2) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	143 (all Xa all Xp (Xp = s(Xa,Xp) | Xp != Xa)) # label(aSatz7_10b) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	144 (all Xa all Xb all Xc all Xd all Xa1 all Xb1 all Xc1 all Xd1 (-le(Xa,Xb,Xc,Xd) | -s_e(Xc,Xd,Xc1,Xd1) | le(Xa1,Xb1,Xc1,Xd1) | -s_e(Xa,Xb,Xa1,Xb1))) # label(aSatz5_6) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	145 (all Xa all Xb s_m(Xa,midpoint(Xa,Xb),Xb)) # label(aSatz8_22) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	146 (all Xa all Xm all Xb ((-s_m(Xa,Xm,Xb) | s_t(Xa,Xm,Xb)) & (-s_e(Xm,Xa,Xm,Xb) | s_m(Xa,Xm,Xb) | -s_t(Xa,Xm,Xb)) & (-s_m(Xa,Xm,Xb) | s_e(Xm,Xa,Xm,Xb)))) # label(d_Defn7_1) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	147 (all Xa all Xb all Xp (Xa = Xb | Xp = reflect(Xa,Xb,reflect(Xa,Xb,Xp)))) # label(aSatz10_5) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	148 (all Xa all Xb all Xp all Xq all Xcx all U all V (-s_col(Xa,Xb,U) | -s_col(Xp,Xq,V) | Xcx = V | perpAt(Xa,Xb,Xcx,Xp,Xq) | -s_r(U,Xcx,V) | U = Xcx | -s_col(Xa,Xb,Xcx) | -s_col(Xp,Xq,Xcx) | Xq = Xp | Xb = Xa)) # label(aSatz8_13b) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	149 (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].
1.07/1.37	150 (all Xp all Xq all Xr all Xa (Xq = Xp | Xp = Xr | -s_t(Xq,Xp,Xr) | -sameside(Xa,Xp,Xr) | s_col(Xa,Xp,Xq))) # label(aSatz6_15c) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	151 (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].
1.07/1.37	152 (all Xa all Xb all Xp all Xq (Xa = Xb | -samesideline(Xp,Xq,Xa,Xb) | samesideline(Xp,Xq,Xb,Xa))) # label(aExtSameSide2) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	153 (all Xa all Xb all Xc ((s_t(Xc,erectAux(Xa,Xb,Xc),erect(Xa,Xb,Xc)) | Xa = Xb) & (Xa = Xb | s_col(Xa,Xb,erectAux(Xa,Xb,Xc))) & (Xb = Xa | perp(Xa,Xb,erect(Xa,Xb,Xc),Xa)))) # label(aSatz8_21) # label(axiom) # label(non_clause).  [assumption].
1.07/1.37	154 (all Xa all Xb all Xp (Xb = Xa | reflect(Xa,Xb,Xp) != Xp | s_col(Xa,Xb,Xp))) # label(aSatz10_8a) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	155 (all Xa all Xb all Xc (-s_t(Xb,Xa,Xc) | Xa = Xb | -s_t(Xa,Xb,Xc))) # label(aSatz3_4) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	156 (all Xa all Xb all Xc all Xp all Xq (-s_col(Xa,Xb,Xc) | Xc = Xa | -samesideline(Xp,Xq,Xa,Xb) | samesideline(Xp,Xq,Xa,Xc) | Xa = Xb)) # label(aExtSameSide1) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	157 (all Xa all Xb all Xp all Xq (-s_col(Xa,Xb,Xq) | -s_col(Xa,Xb,Xp) | -perp(Xa,Xb,Xp,Xq))) # label(aSatz8_14a) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	158 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_t(Xa,Xb,Xc) | -s_e(Xb,Xc,Xb1,Xc1) | s_e(Xa,Xb,Xa1,Xb1) | -s_e(Xa,Xc,Xa1,Xc1) | -s_t(Xa1,Xb1,Xc1))) # label(aSatz4_3) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	159 (all Xa all Xb all Xc all Xd all Y ((s_e(Xa,Xb,Xc,insert(Xa,Xb,Xc,Xd)) | -le(Xa,Xb,Xc,Xd)) & (-s_t(Xc,Y,Xd) | le(Xa,Xb,Xc,Xd) | -s_e(Xa,Xb,Xc,Y)) & (-le(Xa,Xb,Xc,Xd) | s_t(Xc,insert(Xa,Xb,Xc,Xd),Xd)))) # label(d_Defn5_4) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	160 (all Xa1 all Xc all Xa2 all Xb1 all Xb2 all Xm1 all Xm2 (-s_e(Xc,Xa1,Xc,Xb1) | -s_e(Xc,Xa2,Xc,Xb2) | -s_m(Xa1,Xm1,Xb1) | -s_m(Xa2,Xm2,Xb2) | s_t(Xm1,Xc,Xm2) | -s_t(Xb1,Xc,Xb2) | -s_t(Xa1,Xc,Xa2))) # label(aSatz7_22) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	161 (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) | -sameside(s(Xm,U),Xcs,Xc) | Xr = Xcs | -s_m(Xr,Xm,Xcs) | -perp(Xp,Xq,Xc,Xcs) | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_4a2) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	162 (all Xa all Xb all Xc ((Xb = Xa | s_col(Xa,Xb,Xc) | s_col(Xa,Xb,erectAux21a(Xa,Xb,Xc))) & (Xb = Xa | s_col(Xa,Xb,Xc) | s_t(Xc,erectAux21a(Xa,Xb,Xc),erect21a(Xa,Xb,Xc))) & (perp(Xa,Xb,erect21a(Xa,Xb,Xc),Xa) | s_col(Xa,Xb,Xc) | Xa = Xb))) # label(aSatz8_21a) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	163 (all Xp all Xa all Xq (-s_m(Xp,Xa,Xq) | Xq = s(Xa,Xp))) # label(aSatz7_6) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	164 (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].
1.07/1.38	165 (all Xa all Xp all Xq all Xc all Xcs all Xr all Xm all U (-opposite(Xa,Xp,Xq,Xc) | -perp(Xp,Xq,Xa,Xr) | -sameside(U,Xr,Xa) | Xr != Xcs | sameside(s(Xm,U),Xcs,Xc) | -s_m(Xr,Xm,Xcs) | -perp(Xp,Xq,Xc,Xcs) | -s_col(Xp,Xq,Xr) | -s_col(Xp,Xq,Xcs) | Xq = Xp)) # label(aSatz9_4b) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	166 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (s_r(Xa1,Xb1,Xc1) | -s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1) | -s_r(Xa,Xb,Xc))) # label(aSatz8_10) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	167 (all Xa all Xb all Xp all Xq all Xc all Xd (-s_col(Xa,Xb,Xq) | Xb = Xa | -perp(Xp,Xq,Xc,Xd) | perp(Xa,Xb,Xc,Xd) | Xq = Xp | -s_col(Xa,Xb,Xp))) # label(aExtPerp2) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	168 (all Xa all Xp all Xb ((-sameside(Xa,Xp,Xb) | s_t(Xp,Xb,Xa) | s_t(Xp,Xa,Xb)) & (-s_t(Xp,Xa,Xb) | Xa = Xp | xb = Xp | sameside(Xa,Xp,Xb)) & (-s_t(Xp,Xb,Xa) | Xp = Xa | Xb = Xp | sameside(Xa,Xp,Xb)) & (-sameside(Xa,Xp,Xb) | Xb != Xp) & (Xa != Xp | -sameside(Xa,Xp,Xb)))) # label(d_Defn6_1) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	169 (all Xr all Xa all Xb all Xc ((s_e(Xa,insert(Xb,Xc,Xa,Xr),Xb,Xc) | Xc = Xb | Xr = Xa) & (Xc = Xb | sameside(insert(Xb,Xc,Xa,Xr),Xa,Xr) | Xa = Xr))) # label(aSatz6_11a) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	170 (all Xa all Xm (-s_m(Xa,Xm,Xa) | Xa = Xm)) # label(aSatz7_3a) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	171 (all Xa all Xb all Xc all Xc1 (Xb = Xa | -s_e(Xb,Xc,Xb,Xc1) | Xc = Xc1 | -s_e(Xa,Xc,Xa,Xc1) | -s_col(Xa,Xb,Xc))) # label(aSatz4_18) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	172 (all Xp all Xq all Xp1 all Xq1 all X ((perp(Xp,Xq,Xp1,Xq1) | -perpAt(Xp,Xq,X,Xp1,Xq1)) & (-perp(Xp,Xq,Xp1,Xq1) | perpAt(Xp,Xq,il(Xp,Xq,Xp1,Xq1),Xp1,Xq1)))) # label(d_Defn8_11b) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	173 (all Xa all Xp all Xb all Xc (-sameside(Xa,Xp,Xb) | -sameside(Xb,Xp,Xc) | sameside(Xa,Xp,Xc))) # label(aSatz6_7) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	174 (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].
1.07/1.38	175 (all Xa all Xb all Xc all Xd all Xp (Xb = Xa | -s_col(Xc,Xd,Xp) | s_col(Xa,Xb,Xp) | -s_col(Xa,Xb,Xd) | -s_col(Xa,Xb,Xc) | Xd = Xc)) # label(aExtCol2) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	176 (all Xa all Xc all Xb all Xc1 (-s_e(Xb,Xc,Xb,Xc1) | Xc = Xc1 | -s_e(Xa,Xc,Xa,Xc1) | -s_t(Xa,Xc,Xb))) # label(aSatz4_19) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	177 (all Xa all Xb all Xc all Xd (-s_t(Xc,Xa,Xb) | -s_t(Xd,Xa,Xb) | s_t(Xd,Xc,Xb) | s_t(Xc,Xd,Xb) | Xb = Xa)) # label(aSatz6_16a) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	178 (all Xa all Xb all Xc all Xd (s_e(Xc,Xd,Xa,Xb) | -s_e(Xa,Xb,Xc,Xd))) # label(aSatz2_2) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	179 (all Xp all Xq all Xr all Xa (Xq = Xp | Xr = Xp | -s_col(Xa,Xp,Xq) | Xp = Xa | sameside(Xa,Xp,Xq) | sameside(Xa,Xp,Xr) | -s_t(Xq,Xp,Xr))) # label(aSatz6_15a) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	180 (all Xa all Xp all Xb (Xb = Xa | s(Xb,Xp) != s(Xa,Xp))) # label(aSatz7_18) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	181 (all Xa all Xb all Xc ((s_col(Xa,Xb,Xc) | s_col(Xa,Xb,foot(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].
1.07/1.38	182 (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) | -le(Xcs,Xc,Xr,Xa) | sameside(s(Xm,U),Xcs,Xc) | Xr = Xcs | -sameside(U,Xr,Xa) | -s_m(Xr,Xm,Xcs) | -s_col(Xp,Xq,Xcs) | Xq = Xp)) # label(aSatz9_4a) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	183 (all Xa all Xb s_e(Xa,Xb,Xa,Xb)) # label(aSatz2_1) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	184 (all Xa all Xb all Xc ((-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)) & (s_t(Xa,Xb,Xc) | s_t(Xb,Xc,Xa) | s_t(Xc,Xa,Xb) | -s_col(Xa,Xb,Xc)))) # label(d_Defn4_10) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	185 (all Xa all Xp all Xq (Xq = Xp | s(Xa,Xq) != s(Xa,Xp))) # label(aSatz7_9) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	186 (all Xb all Xa ext(Xa,Xb,alpha,gamma) != Xb) # label(aSatz3_14b) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	187 (all Xa all Xb all Xc all XA all XB all XC (-s_t(Xa,Xb,Xc) | -s_t(XA,XB,XC) | -s_e(Xb,Xc,XA,XB) | s_e(Xa,Xc,XA,XC) | -s_e(Xa,Xb,XB,XC))) # label(aSatz2_15) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	188 (all Xa all Xb all Xc all Xp (Xa != Xp | Xc = Xb | -s_m(s(Xa,Xc),Xp,s(Xb,Xc)) | -s_r(Xa,Xb,Xc))) # label(aSatz8_20b) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	189 (all Xa all Xb all Xc all Xd (-s_t(Xa,Xb,Xc) | -s_t(Xb,Xc,Xd) | s_t(Xa,Xc,Xd) | Xc = Xb)) # label(aSatz3_7a) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	190 (all Xa all Xb all Xp all Xq all Xr all Xc all Xd (-s_col(Xa,Xb,Xp) | Xb = Xa | perpAt(Xa,Xb,Xr,Xc,Xd) | -perpAt(Xp,Xq,Xr,Xc,Xd) | Xq = Xp | -s_col(Xa,Xb,Xq))) # label(aExtPerp) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	191 (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].
1.07/1.38	192 (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].
1.07/1.38	193 (all Xp all Xq (Xq = Xp | s_col(Xp,Xq,Xp))) # label(aSatz6_17a) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	194 (all Xa all Xb (Xa = Xb | -s_r(Xa,Xb,Xa))) # label(aSatz8_8) # label(axiom) # label(non_clause).  [assumption].
1.07/1.38	195 (all Xa all Xb all Xc ((s_e(Xa,Xc,Xa,s(Xb,Xc)) | -s_r(Xa,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].
1.07/1.40	196 (all Xp all Xq all Xr all Xcs (s_col(Xp,Xq,Xr) | opposite(Xr,Xp,Xq,Xcs) | Xp != foot(Xp,Xq,Xr) | samesideline(Xr,Xcs,Xp,Xq) | s_col(Xp,Xq,Xcs) | Xp = Xq)) # label(aLemma9_13f_case1) # label(axiom) # label(non_clause).  [assumption].
1.07/1.40	197 (all Xa all Xp all Xq all Xc all Xcs all Xr all Xm all U all V (-opposite(Xa,Xp,Xq,Xc) | Xp = Xq | -perp(Xp,Xq,Xa,Xr) | -perp(Xp,Xq,Xc,Xcs) | -s_m(Xr,Xm,Xcs) | opposite(U,Xp,Xq,V) | -sameside(V,Xcs,Xc) | -sameside(U,Xr,Xa) | -s_col(Xp,Xq,Xr) | -s_col(Xp,Xq,Xcs))) # label(aSatz9_4c) # label(axiom) # label(non_clause).  [assumption].
1.07/1.40	198 (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) | Xp = Xq)) # label(aLemma9_13g) # label(axiom) # label(non_clause).  [assumption].
1.07/1.40	199 (all Xp all Xa all Xq all Xb (-s_m(Xp,Xb,Xq) | Xa = Xb | -s_m(Xp,Xa,Xq))) # label(aSatz7_17) # label(axiom) # label(non_clause).  [assumption].
1.07/1.40	200 (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].
1.07/1.40	201 (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) | s_col(Xa,Xb,Xc)) & (-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(Xb,Xd,Xb1,Xd1)) & (s_e(Xa,Xd,Xa1,Xd1) | -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)))) # label(d_Defn4_15) # label(axiom) # label(non_clause).  [assumption].
1.07/1.40	202 (all Xa all Xp all Xb all Xq all Xt (-perp(Xa,Xb,Xa,Xp) | -perp(Xa,Xb,Xb,Xq) | -s_t(Xp,Xt,Xq) | -s_col(Xa,Xb,Xt) | s_m(Xa,midpointAux(Xa,Xb,Xp,Xq,Xt),Xb) | -le(Xa,Xp,Xb,Xq))) # label(aSatz8_22b) # label(axiom) # label(non_clause).  [assumption].
1.07/1.40	203 (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].
1.07/1.40	204 (all Xa all Xb all Xp all Xq (samesideline(Xq,Xp,Xa,Xb) | -samesideline(Xp,Xq,Xa,Xb) | Xb = Xa)) # label(aLemma9_13d) # label(axiom) # label(non_clause).  [assumption].
1.07/1.40	205 -(all Xa all Xb all Xc all Xa1 all Xc1 (s_e(Xa,Xc,Xa1,Xc1) | Xc1 = Xc | midpoint(Xc,Xc1) != Xb | -s_e(Xb,Xc,Xb,Xc1) | -s_e(Xa,Xb,Xa1,Xb) | -s_r(Xa1,Xb,Xc1) | -s_r(Xa,Xb,Xc))) # label(aSatz10_12c) # label(negated_conjecture) # label(non_clause).  [assumption].
1.07/1.40	
1.07/1.40	============================== end of process non-clausal formulas ===
1.07/1.40	
1.07/1.40	============================== PROCESS INITIAL CLAUSES ===============
1.07/1.40	
1.07/1.40	============================== PREDICATE ELIMINATION =================
1.07/1.40	206 -s_t(A,B,C) | -s_e(B,A,B,D) | s_kf(A,E,D,B,F,V6,C) | -s_m(C,V6,F) | -s_m(A,E,D) | -s_e(B,C,B,F) | -s_t(D,B,F) # label(d_Defn7_23) # label(axiom).  [clausify(86)].
1.07/1.40	207 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(17)].
1.07/1.40	208 s_t(A,B,C) | -s_kf(A,D,E,B,F,V6,C) # label(d_Defn7_23) # label(axiom).  [clausify(86)].
1.07/1.40	209 s_e(A,B,A,C) | -s_kf(B,D,C,A,E,F,V6) # label(d_Defn7_23) # label(axiom).  [clausify(86)].
1.07/1.40	210 s_m(A,B,C) | -s_kf(D,E,F,V6,C,B,A) # label(d_Defn7_23) # label(axiom).  [clausify(86)].
1.07/1.40	211 -s_kf(A,B,C,D,E,F,V6) | s_m(A,B,C) # label(d_Defn7_23) # label(axiom).  [clausify(86)].
1.07/1.40	212 -s_kf(A,B,C,D,E,F,V6) | s_e(D,V6,D,E) # label(d_Defn7_23) # label(axiom).  [clausify(86)].
1.07/1.40	213 s_t(A,B,C) | -s_kf(D,E,A,B,C,F,V6) # label(d_Defn7_23) # label(axiom).  [clausify(86)].
1.07/1.40	214 -s_kf(A,B,C,D,E,F,V6) | s_t(B,D,F) # label(aSatz7_22b) # label(axiom).  [clausify(98)].
1.07/1.40	215 -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(201)].
1.07/1.40	216 A = B | s_e(C,D,E,F) | -s_fs(B,A,C,D,V6,V7,E,F) # label(aSatz4_16) # label(axiom).  [clausify(37)].
1.07/1.40	217 -s_fs(A,B,C,D,E,F,V6,V7) | s_col(A,B,C) # label(d_Defn4_15) # label(axiom).  [clausify(201)].
1.07/1.40	Derived: -s_col(A,B,C) | -s_e3(A,B,C,D,E,F) | -s_e(A,V6,D,V7) | -s_e(B,V6,E,V7) | B = A | s_e(C,V6,F,V7).  [resolve(215,d,216,c)].
1.07/1.40	218 -s_fs(A,B,C,D,E,F,V6,V7) | s_e(B,D,F,V7) # label(d_Defn4_15) # label(axiom).  [clausify(201)].
1.07/1.42	219 s_e(A,B,C,D) | -s_fs(A,E,F,B,C,V6,V7,D) # label(d_Defn4_15) # label(axiom).  [clausify(201)].
1.07/1.42	220 -s_fs(A,B,C,D,E,F,V6,V7) | s_e3(A,B,C,E,F,V6) # label(d_Defn4_15) # label(axiom).  [clausify(201)].
1.07/1.42	221 -s_t(A,B,C) | -s_e3(A,B,C,D,E,F) | s_t(D,E,F) # label(aSatz4_6) # label(axiom).  [clausify(60)].
1.07/1.42	222 s_e3(A,B,C,D,insert(A,B,D,E),E) | -s_e(A,C,D,E) | -s_t(A,B,C) # label(aSatz4_5) # label(axiom).  [clausify(56)].
1.07/1.42	Derived: -s_t(A,B,C) | s_t(D,insert(A,B,D,E),E) | -s_e(A,C,D,E) | -s_t(A,B,C).  [resolve(221,b,222,a)].
1.07/1.42	223 -s_e(A,B,C,D) | s_e3(A,B,E,C,D,insert5(A,B,E,C,D)) | -s_col(A,B,E) # label(aSatz4_14) # label(axiom).  [clausify(77)].
1.07/1.42	Derived: -s_e(A,B,C,D) | -s_col(A,B,E) | -s_t(A,B,E) | s_t(C,D,insert5(A,B,E,C,D)).  [resolve(223,b,221,b)].
1.07/1.42	224 -s_e3(A,B,C,D,E,F) | s_e(B,C,E,F) # label(d_Defn4_4) # label(axiom).  [clausify(110)].
1.07/1.42	Derived: s_e(A,B,insert(C,A,D,E),E) | -s_e(C,B,D,E) | -s_t(C,A,B).  [resolve(224,a,222,a)].
1.07/1.42	Derived: s_e(A,B,C,insert5(D,A,B,E,C)) | -s_e(D,A,E,C) | -s_col(D,A,B).  [resolve(224,a,223,b)].
1.07/1.42	225 -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(110)].
1.07/1.42	Derived: -s_e(A,B,C,D) | -s_e(E,B,F,D) | -s_e(E,A,F,C) | -s_t(E,A,B) | s_t(F,C,D).  [resolve(225,b,221,b)].
1.07/1.42	226 -s_e3(A,B,C,D,E,F) | s_e(A,C,D,F) # label(d_Defn4_4) # label(axiom).  [clausify(110)].
1.07/1.42	Derived: s_e(A,B,C,insert5(A,D,B,C,E)) | -s_e(A,D,C,E) | -s_col(A,D,B).  [resolve(226,a,223,b)].
1.07/1.42	227 -s_e3(A,B,C,D,E,F) | s_e(A,B,D,E) # label(d_Defn4_4) # label(axiom).  [clausify(110)].
1.07/1.42	Derived: s_e(A,B,C,insert(A,B,C,D)) | -s_e(A,E,C,D) | -s_t(A,B,E).  [resolve(227,a,222,a)].
1.07/1.42	228 s_col(A,B,C) | -s_e3(D,E,F,A,B,C) | -s_col(D,E,F) # label(aSatz4_13) # label(axiom).  [clausify(125)].
1.07/1.42	Derived: s_col(A,insert(B,C,A,D),D) | -s_col(B,C,E) | -s_e(B,E,A,D) | -s_t(B,C,E).  [resolve(228,b,222,a)].
1.07/1.42	Derived: s_col(A,B,insert5(C,D,E,A,B)) | -s_col(C,D,E) | -s_e(C,D,A,B) | -s_col(C,D,E).  [resolve(228,b,223,b)].
1.07/1.42	Derived: s_col(A,B,C) | -s_col(D,E,F) | -s_e(E,F,B,C) | -s_e(D,F,A,C) | -s_e(D,E,A,B).  [resolve(228,b,225,b)].
1.07/1.42	229 s_r(A,B,C) | -s_e3(D,E,F,A,B,C) | -s_r(D,E,F) # label(aSatz8_10) # label(axiom).  [clausify(166)].
1.07/1.42	Derived: s_r(A,insert(B,C,A,D),D) | -s_r(B,C,E) | -s_e(B,E,A,D) | -s_t(B,C,E).  [resolve(229,b,222,a)].
1.07/1.42	Derived: s_r(A,B,insert5(C,D,E,A,B)) | -s_r(C,D,E) | -s_e(C,D,A,B) | -s_col(C,D,E).  [resolve(229,b,223,b)].
1.07/1.42	Derived: s_r(A,B,C) | -s_r(D,E,F) | -s_e(E,F,B,C) | -s_e(D,F,A,C) | -s_e(D,E,A,B).  [resolve(229,b,225,b)].
1.07/1.42	230 -s_col(A,B,C) | -s_e3(A,B,C,D,E,F) | -s_e(A,V6,D,V7) | -s_e(B,V6,E,V7) | B = A | s_e(C,V6,F,V7).  [resolve(215,d,216,c)].
1.07/1.42	Derived: -s_col(A,B,C) | -s_e(A,D,E,F) | -s_e(B,D,insert(A,B,E,V6),F) | B = A | s_e(C,D,V6,F) | -s_e(A,C,E,V6) | -s_t(A,B,C).  [resolve(230,b,222,a)].
1.07/1.42	Derived: -s_col(A,B,C) | -s_e(A,D,E,F) | -s_e(B,D,V6,F) | B = A | s_e(C,D,insert5(A,B,C,E,V6),F) | -s_e(A,B,E,V6) | -s_col(A,B,C).  [resolve(230,b,223,b)].
1.07/1.42	Derived: -s_col(A,B,C) | -s_e(A,D,E,F) | -s_e(B,D,V6,F) | B = A | s_e(C,D,V7,F) | -s_e(B,C,V6,V7) | -s_e(A,C,E,V7) | -s_e(A,B,E,V6).  [resolve(230,b,225,b)].
1.07/1.42	231 -s_t(A,B,C) | -s_e(D,E,A,C) | -s_e(D,F,A,V6) | s_ifs(D,V7,E,F,A,B,C,V6) | -s_e(E,F,C,V6) | -s_e(V7,E,B,C) | -s_t(D,V7,E) # label(d_Defn4_1) # label(axiom).  [clausify(80)].
1.07/1.42	232 -s_ifs(A,B,C,D,E,F,V6,V7) | s_e(B,C,F,V6) # label(d_Defn4_1) # label(axiom).  [clausify(80)].
1.07/1.42	233 -s_ifs(A,B,C,D,E,F,V6,V7) | s_e(A,D,E,V7) # label(d_Defn4_1) # label(axiom).  [clausify(80)].
1.07/1.42	234 -s_ifs(A,B,C,D,E,F,V6,V7) | s_e(C,D,V6,V7) # label(d_Defn4_1) # label(axiom).  [clausify(80)].
1.07/1.42	235 -s_ifs(A,B,C,D,E,F,V6,V7) | s_e(A,C,E,V6) # label(d_Defn4_1) # label(axiom).  [clausify(80)].
1.07/1.42	236 -s_ifs(A,B,C,D,E,F,V6,V7) | s_t(E,F,V6) # label(d_Defn4_1) # label(axiom).  [clausify(80)].
1.07/1.42	237 -s_ifs(A,B,C,D,E,F,V6,V7) | s_t(A,B,C) # label(d_Defn4_1) # label(axiom).  [clausify(80)].
1.07/1.42	238 s_e(A,B,C,D) | -s_ifs(E,A,F,B,V6,C,V7,D) # label(aSatz4_2) # label(axiom).  [clausify(132)].
1.07/1.42	Derived: s_e(A,B,C,D) | -s_t(E,C,F) | -s_e(V6,V7,E,F) | -s_e(V6,B,E,D) | -s_e(V7,B,F,D) | -s_e(A,V7,C,F) | -s_t(V6,A,V7).  [resolve(238,b,231,d)].
8.61/8.91	239 -s_t(A,B,C) | -s_e(D,E,A,B) | -s_e(E,F,B,V6) | s_afs(D,E,V7,F,A,B,C,V6) | -s_e(D,F,A,V6) | -s_e(E,V7,B,C) | -s_t(D,E,V7) # label(d_Defn2_10) # label(axiom).  [clausify(122)].
8.61/8.91	240 s_t(A,B,C) | -s_afs(A,B,C,D,E,F,V6,V7) # label(d_Defn2_10) # label(axiom).  [clausify(122)].
8.61/8.91	241 -s_afs(A,B,C,D,E,F,V6,V7) | s_e(A,B,E,F) # label(d_Defn2_10) # label(axiom).  [clausify(122)].
8.61/8.91	242 s_e(A,B,C,D) | -s_afs(A,E,F,B,C,V6,V7,D) # label(d_Defn2_10) # label(axiom).  [clausify(122)].
8.61/8.91	243 -s_afs(A,B,C,D,E,F,V6,V7) | s_e(B,D,F,V7) # label(d_Defn2_10) # label(axiom).  [clausify(122)].
8.61/8.91	244 s_e(A,B,C,D) | -s_afs(E,A,B,F,V6,C,D,V7) # label(d_Defn2_10) # label(axiom).  [clausify(122)].
8.61/8.91	245 -s_afs(A,B,C,D,E,F,V6,V7) | s_t(E,F,V6) # label(d_Defn2_10) # label(axiom).  [clausify(122)].
8.61/8.91	
8.61/8.91	============================== end predicate elimination =============
8.61/8.91	
8.61/8.91	Auto_denials:  (non-Horn, no changes).
8.61/8.91	
8.61/8.91	Term ordering decisions:
8.61/8.91	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.
8.61/8.91	
8.61/8.91	============================== end of process initial clauses ========
8.61/8.91	
8.61/8.91	============================== CLAUSES FOR SEARCH ====================
8.61/8.91	
8.61/8.91	============================== end of clauses for search =============
8.61/8.91	
8.61/8.91	============================== SEARCH ================================
8.61/8.91	
8.61/8.91	% Starting search at 0.15 seconds.
8.61/8.91	
8.61/8.91	Low Water (keep): wt=50.000, iters=3673
8.61/8.91	
8.61/8.91	Low Water (keep): wt=34.000, iters=3504
8.61/8.91	
8.61/8.91	Low Water (keep): wt=32.000, iters=3350
8.61/8.91	
8.61/8.91	Low Water (keep): wt=31.000, iters=3450
8.61/8.91	
8.61/8.91	Low Water (keep): wt=29.000, iters=3363
8.61/8.91	
8.61/8.91	Low Water (keep): wt=28.000, iters=3405
8.61/8.91	
8.61/8.91	Low Water (keep): wt=27.000, iters=3453
8.61/8.91	
8.61/8.91	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 104 (0.00 of 0.67 sec).
8.61/8.91	
8.61/8.91	Low Water (keep): wt=26.000, iters=3363
8.61/8.91	
8.61/8.91	Low Water (keep): wt=25.000, iters=3378
8.61/8.91	
8.61/8.91	Low Water (keep): wt=24.000, iters=3376
8.61/8.91	
8.61/8.91	Low Water (keep): wt=23.000, iters=3415
8.61/8.91	
8.61/8.91	Low Water (keep): wt=22.000, iters=3362
8.61/8.91	
8.61/8.91	Low Water (keep): wt=21.000, iters=3367
8.61/8.91	
8.61/8.91	Low Water (keep): wt=20.000, iters=3340
8.61/8.91	
8.61/8.91	Low Water (keep): wt=19.000, iters=3505
8.61/8.91	
8.61/8.91	Low Water (keep): wt=18.000, iters=3405
8.61/8.91	
8.61/8.91	Low Water (keep): wt=17.000, iters=3413
8.61/8.91	
8.61/8.91	Low Water (keep): wt=16.000, iters=3377
8.61/8.91	
8.61/8.91	Low Water (keep): wt=15.000, iters=3361
8.61/8.91	
8.61/8.91	Low Water (keep): wt=14.000, iters=3360
8.61/8.91	
8.61/8.91	Low Water (displace): id=1108, wt=79.000
8.61/8.91	
8.61/8.91	Low Water (displace): id=1112, wt=76.000
8.61/8.91	
8.61/8.91	Low Water (displace): id=12068, wt=12.000
8.61/8.91	
8.61/8.91	Low Water (displace): id=12069, wt=11.000
8.61/8.91	
8.61/8.91	Low Water (displace): id=12081, wt=10.000
8.61/8.91	
8.61/8.91	Low Water (keep): wt=13.000, iters=3334
8.61/8.91	
8.61/8.91	Low Water (displace): id=12340, wt=9.000
8.61/8.91	
8.61/8.91	Low Water (displace): id=14229, wt=7.000
8.61/8.91	
8.61/8.91	Low Water (keep): wt=12.000, iters=3354
8.61/8.91	
8.61/8.91	Low Water (keep): wt=11.000, iters=3336
8.61/8.91	
8.61/8.91	Low Water (keep): wt=10.000, iters=3534
8.61/8.91	
8.61/8.91	============================== PROOF =================================
8.61/8.91	% SZS status Theorem
8.61/8.91	% SZS output start Refutation
8.61/8.91	
8.61/8.91	% Proof 1 at 7.38 (+ 0.21) seconds.
8.61/8.91	% Length of proof is 28.
8.61/8.91	% Level of proof is 6.
8.61/8.91	% Maximum clause weight is 18.000.
8.61/8.91	% Given clauses 7030.
8.61/8.91	
8.61/8.91	31 (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].
8.61/8.91	34 (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].
8.61/8.91	62 (all Xa all Xb all Xc all Xd all Xe all Xf (-s_e(Xa,Xb,Xc,Xd) | -s_e(Xc,Xd,Xe,Xf) | s_e(Xa,Xb,Xe,Xf))) # label(aSatz2_3) # label(axiom) # label(non_clause).  [assumption].
8.61/8.91	145 (all Xa all Xb s_m(Xa,midpoint(Xa,Xb),Xb)) # label(aSatz8_22) # label(axiom) # label(non_clause).  [assumption].
8.61/8.91	163 (all Xp all Xa all Xq (-s_m(Xp,Xa,Xq) | Xq = s(Xa,Xp))) # label(aSatz7_6) # label(axiom) # label(non_clause).  [assumption].
8.61/8.91	195 (all Xa all Xb all Xc ((s_e(Xa,Xc,Xa,s(Xb,Xc)) | -s_r(Xa,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].
8.61/8.91	205 -(all Xa all Xb all Xc all Xa1 all Xc1 (s_e(Xa,Xc,Xa1,Xc1) | Xc1 = Xc | midpoint(Xc,Xc1) != Xb | -s_e(Xb,Xc,Xb,Xc1) | -s_e(Xa,Xb,Xa1,Xb) | -s_r(Xa1,Xb,Xc1) | -s_r(Xa,Xb,Xc))) # label(aSatz10_12c) # label(negated_conjecture) # label(non_clause).  [assumption].
8.61/8.91	294 -s_r(A,B,C) | -s_e(D,B,A,B) | s_e(D,C,A,C) | -s_r(D,B,C) # label(aSatz10_12b) # label(axiom).  [clausify(31)].
8.61/8.91	297 -s_r(A,B,C) | s_r(A,B,s(B,C)) # label(aSatz8_4) # label(axiom).  [clausify(34)].
8.61/8.91	333 -s_e(A,B,C,D) | -s_e(C,D,E,F) | s_e(A,B,E,F) # label(aSatz2_3) # label(axiom).  [clausify(62)].
8.61/8.91	426 s_m(A,midpoint(A,B),B) # label(aSatz8_22) # label(axiom).  [clausify(145)].
8.61/8.91	451 -s_m(A,B,C) | s(B,A) = C # label(aSatz7_6) # label(axiom).  [clausify(163)].
8.61/8.91	487 s_e(A,B,A,s(C,B)) | -s_r(A,C,B) # label(d_Defn8_1) # label(axiom).  [clausify(195)].
8.61/8.91	496 -s_e(c1,c3,c4,c5) # label(aSatz10_12c) # label(negated_conjecture).  [clausify(205)].
8.61/8.91	498 midpoint(c3,c5) = c2 # label(aSatz10_12c) # label(negated_conjecture).  [clausify(205)].
8.61/8.91	500 s_e(c1,c2,c4,c2) # label(aSatz10_12c) # label(negated_conjecture).  [clausify(205)].
8.61/8.91	501 s_r(c4,c2,c5) # label(aSatz10_12c) # label(negated_conjecture).  [clausify(205)].
8.61/8.91	502 s_r(c1,c2,c3) # label(aSatz10_12c) # label(negated_conjecture).  [clausify(205)].
8.61/8.91	1312 s_m(c3,c2,c5).  [para(498(a,1),426(a,2))].
8.61/8.91	1369 -s_r(c4,c2,A) | s_e(c1,A,c4,A) | -s_r(c1,c2,A).  [resolve(500,a,294,b)].
8.61/8.91	1397 s_e(c1,c3,c1,s(c2,c3)).  [resolve(502,a,487,b)].
8.61/8.91	1406 s_r(c1,c2,s(c2,c3)).  [resolve(502,a,297,a)].
8.61/8.91	1805 s(c2,c3) = c5.  [resolve(1312,a,451,a)].
8.61/8.91	1810 s_r(c1,c2,c5).  [back_rewrite(1406),rewrite([1805(5)])].
8.61/8.91	1811 s_e(c1,c3,c1,c5).  [back_rewrite(1397),rewrite([1805(6)])].
8.61/8.91	3098 -s_e(c1,c5,A,B) | s_e(c1,c3,A,B).  [resolve(1811,a,333,a)].
8.61/8.91	21066 s_e(c1,c5,c4,c5).  [resolve(1369,a,501,a),unit_del(b,1810)].
8.61/8.91	27082 $F.  [resolve(3098,a,21066,a),unit_del(a,496)].
8.61/8.91	
8.61/8.91	% SZS output end Refutation
8.61/8.91	============================== end of proof ==========================
8.61/8.91	
8.61/8.91	============================== STATISTICS ============================
8.61/8.91	
8.61/8.91	Given=7030. Generated=348100. Kept=26823. proofs=1.
8.61/8.91	Usable=6863. Sos=9999. Demods=290. Limbo=1, Disabled=10285. Hints=0.
8.61/8.91	Megabytes=17.54.
8.61/8.91	User_CPU=7.38, System_CPU=0.21, Wall_clock=7.
8.61/8.91	
8.61/8.91	============================== end of statistics =====================
8.61/8.91	
8.61/8.91	============================== end of search =========================
8.61/8.91	
8.61/8.91	THEOREM PROVED
8.61/8.91	% SZS status Theorem
8.61/8.91	
8.61/8.91	Exiting with 1 proof.
8.61/8.91	
8.61/8.91	Process 10656 exit (max_proofs) Thu Aug 29 11:51:30 2019
8.61/8.91	Prover9 interrupted
8.61/8.91	EOF