0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : tptp2X_and_run_prover9 %d %s 0.02/0.23 % Computer : n132.star.cs.uiowa.edu 0.02/0.23 % Model : x86_64 x86_64 0.02/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.02/0.23 % Memory : 32218.625MB 0.02/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.02/0.23 % CPULimit : 300 0.02/0.23 % DateTime : Sat Jul 14 04:55:40 CDT 2018 0.02/0.23 % CPUTime : 0.57/0.82 ============================== Prover9 =============================== 0.57/0.82 Prover9 (32) version 2009-11A, November 2009. 0.57/0.82 Process 12378 was started by sandbox2 on n132.star.cs.uiowa.edu, 0.57/0.82 Sat Jul 14 04:55:40 2018 0.57/0.82 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_12346_n132.star.cs.uiowa.edu". 0.57/0.82 ============================== end of head =========================== 0.57/0.82 0.57/0.82 ============================== INPUT ================================= 0.57/0.82 0.57/0.82 % Reading from file /tmp/Prover9_12346_n132.star.cs.uiowa.edu 0.57/0.82 0.57/0.82 set(prolog_style_variables). 0.57/0.82 set(auto2). 0.57/0.82 % set(auto2) -> set(auto). 0.57/0.82 % set(auto) -> set(auto_inference). 0.57/0.82 % set(auto) -> set(auto_setup). 0.57/0.82 % set(auto_setup) -> set(predicate_elim). 0.57/0.82 % set(auto_setup) -> assign(eq_defs, unfold). 0.57/0.82 % set(auto) -> set(auto_limits). 0.57/0.82 % set(auto_limits) -> assign(max_weight, "100.000"). 0.57/0.82 % set(auto_limits) -> assign(sos_limit, 20000). 0.57/0.82 % set(auto) -> set(auto_denials). 0.57/0.82 % set(auto) -> set(auto_process). 0.57/0.82 % set(auto2) -> assign(new_constants, 1). 0.57/0.82 % set(auto2) -> assign(fold_denial_max, 3). 0.57/0.82 % set(auto2) -> assign(max_weight, "200.000"). 0.57/0.82 % set(auto2) -> assign(max_hours, 1). 0.57/0.82 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.57/0.82 % set(auto2) -> assign(max_seconds, 0). 0.57/0.82 % set(auto2) -> assign(max_minutes, 5). 0.57/0.82 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.57/0.82 % set(auto2) -> set(sort_initial_sos). 0.57/0.82 % set(auto2) -> assign(sos_limit, -1). 0.57/0.82 % set(auto2) -> assign(lrs_ticks, 3000). 0.57/0.82 % set(auto2) -> assign(max_megs, 400). 0.57/0.82 % set(auto2) -> assign(stats, some). 0.57/0.82 % set(auto2) -> clear(echo_input). 0.57/0.82 % set(auto2) -> set(quiet). 0.57/0.82 % set(auto2) -> clear(print_initial_clauses). 0.57/0.82 % set(auto2) -> clear(print_given). 0.57/0.82 assign(lrs_ticks,-1). 0.57/0.82 assign(sos_limit,10000). 0.57/0.82 assign(order,kbo). 0.57/0.82 set(lex_order_vars). 0.57/0.82 clear(print_given). 0.57/0.82 0.57/0.82 % formulas(sos). % not echoed (206 formulas) 0.57/0.82 0.57/0.82 ============================== end of input ========================== 0.57/0.82 0.57/0.82 % From the command line: assign(max_seconds, 300). 0.57/0.82 0.57/0.82 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.57/0.82 0.57/0.82 % Formulas that are not ordinary clauses: 0.57/0.82 1 (all X all Y all Z (-s_e(X,Y,Z,Z) | Y = X)) # label(aA3) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 2 (all X all Y all X1 all Y1 all Z all Z1 all V all V1 (-s_e(Y,Z,Y1,Z1) | -s_e(Y,V,Y1,V1) | -s_t(X,Y,Z) | -s_t(X1,Y1,Z1) | X = Y | s_e(Z,V,Z1,V1) | -s_e(X,V,X1,V1) | -s_e(X,Y,X1,Y1))) # label(aA5) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 3 (all X all Y s_e(X,Y,Y,X)) # label(aA1) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 4 (all X all Y (X = Y | -s_t(X,Y,X))) # label(aA6) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 5 (all X all Y all W all V (s_e(Y,ext(X,Y,W,V),W,V) & s_t(X,Y,ext(X,Y,W,V)))) # label(aA4) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 6 (all X all Y all Z all V all Z2 all V2 (-s_e(X,Y,Z,V) | -s_e(X,Y,Z2,V2) | s_e(Z,V,Z2,V2))) # label(aA2) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 7 (all Xa all Xp all Xc all Xb all Xq ((-s_t(Xb,Xq,Xc) | s_t(Xp,ip(Xa,Xp,Xc,Xb,Xq),Xb) | -s_t(Xa,Xp,Xc)) & (-s_t(Xa,Xp,Xc) | -s_t(Xb,Xq,Xc) | s_t(Xq,ip(Xa,Xp,Xc,Xb,Xq),Xa)))) # label(aA7) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 8 (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]. 0.57/0.82 9 (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]. 0.57/0.82 10 (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_e(Xa,Xp,Xb,Xr) | ip(Xp,Xt,Xq,Xb,Xr) != Xcx | s_m(Xp,Xcx,Xr) | -s_col(Xa,Xb,Xt))) # label(aSatz8_24b) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 11 (all Xa all Xb all Xp all Xq all Xc ((Xq = Xp | s_r(Xc,Xp,Xq) | -perp(Xa,Xb,Xc,Xp) | -s_col(Xa,Xb,Xq) | -s_col(Xa,Xb,Xp) | Xa = Xb) & (Xb = Xa | -s_col(Xa,Xb,Xq) | -s_col(Xa,Xb,Xc) | -perp(Xa,Xb,Xc,Xp) | Xp = Xq | -s_col(Xa,Xb,Xp)))) # label(aSatz8_16a) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 12 (all Xq all Xa all Xd all Xb all Xc (Xa = Xq | Xd = ext(Xq,Xa,Xb,Xc) | -s_e(Xa,Xd,Xb,Xc) | -s_t(Xq,Xa,Xd))) # label(aSatz2_12) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 13 (all Xr all Xa all Xb all Xc ((Xa = Xr | sameside(insert(Xb,Xc,Xa,Xr),Xa,Xr) | Xc = Xb) & (Xc = Xb | s_e(Xa,insert(Xb,Xc,Xa,Xr),Xb,Xc) | Xa = Xr))) # label(aSatz6_11a) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 14 (all Xp all Xq all Xc all Xa all Xb (s_col(Xc,Xa,Xb) | Xc = Xa | -perpAt(Xp,Xq,Xc,Xb,Xc) | -perpAt(Xp,Xq,Xc,Xa,Xc) | Xp = Xq)) # label(aLemma9_13g) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 15 (all Xa all Xm (Xa = Xm | -s_m(Xa,Xm,Xa))) # label(aSatz7_3a) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 16 (all Xa all Xp Xp = s(Xa,s(Xa,Xp))) # label(aSatz7_7) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 17 (all Xa all Xb all Xc all Xd all Za all Zb all Zc all Zd ((-s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_t(Xa,Xb,Xc)) & (s_e(Xa,Xc,Za,Zc) | -s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)) & (-s_t(Xa,Xb,Xc) | -s_t(Za,Zb,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_e(Xa,Xc,Za,Zc)) & (-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,Xd,Za,Zd)) & (-s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_e(Xb,Xc,Zb,Zc)) & (s_t(Za,Zb,Zc) | -s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)))) # label(d_Defn4_1) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 18 (all Xa all Xp all Xb all Xc (Xp = Xb | Xp = Xc | -s_t(Xa,Xp,Xc) | -s_t(Xb,Xp,Xc) | sameside(Xa,Xp,Xb) | Xa = Xp)) # label(aSatz6_2a) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 19 (all Xa all Xm all Xb (-s_m(Xa,Xm,Xb) | s_m(Xb,Xm,Xa))) # label(aSatz7_2) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 20 (all Xa all Xp all Xq all Xc all Xcs all Xr all Xm all U all V (-opposite(Xa,Xp,Xq,Xc) | Xq = Xp | -s_col(Xp,Xq,Xr) | -perp(Xp,Xq,Xa,Xr) | -s_m(Xr,Xm,Xcs) | opposite(U,Xp,Xq,V) | -sameside(V,Xcs,Xc) | -sameside(U,Xr,Xa) | -perp(Xp,Xq,Xc,Xcs) | -s_col(Xp,Xq,Xcs))) # label(aSatz9_4c) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 21 (all Xa all Xb le(Xa,Xb,Xa,Xb)) # label(aSatz5_7) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 22 (all Xa all Xb all Xc all Xp all Xq (-s_e(Xa,Xp,Xa,Xq) | s_e(Xc,Xp,Xc,Xq) | -s_e(Xb,Xp,Xb,Xq) | -s_col(Xa,Xb,Xc) | Xa = Xb)) # label(aSatz4_17) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 23 (all Xa all Xp all Xb all Xc (sameside(Xa,Xp,Xb) | Xa = Xp | Xc = Xp | -s_t(Xa,Xp,Xc) | -s_t(Xb,Xp,Xc) | Xb = Xp)) # label(aSatz6_3b) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 24 (all Xa all Xb (Xa = Xb | -s_col(Xa,Xb,pointOffLine(Xa,Xb)))) # label(aSatz6_25) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 25 (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]. 0.57/0.82 26 (all Xa all Xb all Xc all Xd (le(Xa,Xb,Xc,Xd) | le(Xc,Xd,Xa,Xb))) # label(aSatz5_10) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 27 (all Xp all Xa all Xb all Xq all Xt all Xr all Xcx (-perp(Xp,Xa,Xa,Xb) | -s_t(Xp,Xt,Xq) | -s_t(Xb,Xr,Xq) | -s_e(Xa,Xp,Xb,Xr) | s_m(Xa,Xcx,Xb) | Xcx != ip(Xp,Xt,Xq,Xb,Xr) | -s_col(Xa,Xb,Xt) | -perp(Xq,Xb,Xa,Xb))) # label(aSatz8_24a) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 28 (all Xa all Xb all Xc (-s_col(Xa,Xb,Xc) | -le(Xa,Xb,Xa,Xc) | -le(Xb,Xc,Xa,Xc) | s_t(Xa,Xb,Xc))) # label(aSatz5_12b) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 29 (all Xa all Xb all Xp all Xp1 (Xb = Xa | Xp = reflect(Xa,Xb,Xp1) | Xp1 != reflect(Xa,Xb,Xp))) # label(aSatz10_4) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 30 (all Xa all Xb s_m(Xa,midpoint(Xa,Xb),Xb)) # label(aSatz8_22) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 31 (all Xa all Xb all Xc all Xd all Xp (Xa = Xb | -s_col(Xa,Xb,Xd) | s_col(Xa,Xb,Xp) | -s_col(Xc,Xd,Xp) | -s_col(Xa,Xb,Xc) | Xd = Xc)) # label(aExtCol2) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 32 (all Xa all Xb all Xc all Xd ((-le(Xa,Xb,Xc,Xd) | s_t(Xa,Xb,ins(Xc,Xd,Xa,Xb))) & (-le(Xa,Xb,Xc,Xd) | s_e(Xa,ins(Xc,Xd,Xa,Xb),Xc,Xd)) & (ext(Xa,Xb,insert(Xa,Xb,Xc,Xd),Xd) = ins(Xc,Xd,Xa,Xb) | -le(Xa,Xb,Xc,Xd)))) # label(aSatz5_5a) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 33 (all Xa all Xb all Xc ((Xb = Xa | perp(Xa,Xb,erect(Xa,Xb,Xc),Xa)) & (s_col(Xa,Xb,erectAux(Xa,Xb,Xc)) | Xb = Xa) & (s_t(Xc,erectAux(Xa,Xb,Xc),erect(Xa,Xb,Xc)) | Xb = Xa))) # label(aSatz8_21) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 34 (all Xa all Xb all Xc all Xd (-s_t(Xa,Xb,Xc) | s_t(Xb,Xc,Xd) | -s_t(Xa,Xc,Xd))) # label(aSatz3_6a) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 35 (all Xa all Xm (s_m(Xa,Xm,Xa) | Xm != Xa)) # label(aSatz7_3b) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 36 (all Xa all Xb all Xc all Xd (-s_t(Xa,Xb,Xc) | s_t(Xa,Xc,Xd) | Xc = Xb | -s_t(Xb,Xc,Xd))) # label(aSatz3_7a) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 37 (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]. 0.57/0.82 38 (all Xb all Xa ext(Xa,Xb,alpha,gamma) != Xb) # label(aSatz3_14b) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 39 (all Xa all Xp all Xb all Xc (Xp = Xa | -sameside(Xa,Xp,Xb) | s_t(Xb,Xp,Xc) | -s_t(Xa,Xp,Xc) | Xp = Xc | Xb = Xp)) # label(aSatz6_2b) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 40 (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]. 0.57/0.82 41 (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]. 0.57/0.82 42 (all Xp all Xq all Xa all Xb all Xt ((Xp = Xq | -s_t(Xa,Xt,Xb) | -s_col(Xp,Xq,Xt) | opposite(Xa,Xp,Xq,Xb) | s_col(Xp,Xq,Xb) | s_col(Xp,Xq,Xa)) & (-s_col(Xp,Xq,Xa) | -opposite(Xa,Xp,Xq,Xb)) & (-s_col(Xp,Xq,Xb) | -opposite(Xa,Xp,Xq,Xb)) & (-opposite(Xa,Xp,Xq,Xb) | s_t(Xa,il(Xa,Xb,Xp,Xq),Xb)) & (-opposite(Xa,Xp,Xq,Xb) | s_col(Xp,Xq,il(Xa,Xb,Xp,Xq))))) # label(d_Defn9_1) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 43 (all Xc all Xd all Xp all Xa all Xb (-sameside(Xa,Xp,Xb) | s_col(Xc,Xd,Xa) | samesideline(Xa,Xb,Xc,Xd) | -s_col(Xa,Xb,Xp) | -s_col(Xc,Xd,Xp) | Xd = Xc)) # label(aSatz9_19b) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 44 (all Xa all Xp all Xr all Xq (s(Xa,Xq) != Xr | Xp = Xq | s(Xa,Xp) != Xr)) # label(aSatz7_8) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 45 (all Xa all Xp all Xb ((-sameside(Xa,Xp,Xb) | Xp != c63(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)) & (-sameside(Xa,Xp,Xb) | Xp != Xb) & (-sameside(Xa,Xp,Xb) | Xp != Xa))) # label(aSatz6_3a) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 46 (all Xp all Xa all Xq (-s_m(Xp,Xa,Xq) | s(Xa,Xp) = Xq)) # label(aSatz7_6) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 47 (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_e(Xa,Xd,Xa1,Xd1) | -s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1)) & (-s_col(Xa,Xb,Xc) | -s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1) | -s_e(Xb,Xd,Xb1,Xd1) | s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1) | -s_e(Xa,Xd,Xa1,Xd1)) & (s_e(Xb,Xd,Xb1,Xd1) | -s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1)) & (s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1) | -s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1)))) # label(d_Defn4_15) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 48 (all Xa all Xb all Xc all Xd (-s_col(Xa,Xb,Xd) | s_col(Xa,Xc,Xd) | Xa = Xb | -s_col(Xa,Xb,Xc))) # label(aext1) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 49 (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]. 0.57/0.82 50 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-sameside(Xa,Xb,Xc) | s_e(Xa,Xc,Xa1,Xc1) | -s_e(Xb,Xc,Xb1,Xc1) | -s_e(Xb,Xa,Xb1,Xa1) | -sameside(Xa1,Xb1,Xc1))) # label(aSatz6_28) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 51 (all Xa all Xp (Xp != Xa | Xp = s(Xa,Xp))) # label(aSatz7_10b) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 52 (all Xa all Xb all Xp all Xq all Xr all Xc all Xd (-s_col(Xa,Xb,Xp) | -s_col(Xa,Xb,Xq) | perpAt(Xa,Xb,Xr,Xc,Xd) | -perpAt(Xp,Xq,Xr,Xc,Xd) | Xa = Xb | Xp = Xq)) # label(aExtPerp) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 53 (all Xp all Xq all Xcs all Xr (Xp = Xq | -s_col(Xp,Xq,Xcs) | s_col(Xp,Xcs,Xr) | -s_col(Xp,Xq,Xr) | Xp = Xcs)) # label(aSatz6_16b) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 54 (all Xa all Xb all Xc all Xp all Xq ((Xa != Xb | -perpAt(Xa,Xb,Xc,Xp,Xq)) & (-perpAt(Xa,Xb,Xc,Xp,Xq) | Xp != Xq) & (s_col(Xa,Xb,f813(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))) & (-perpAt(Xa,Xb,Xc,Xp,Xq) | f813(Xa,Xb,Xp,Xq,Xc) != Xc) & (-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(Xa,Xb,Xc)) & (-perpAt(Xa,Xb,Xc,Xp,Xq) | s_col(Xp,Xq,Xc)))) # label(aSatz8_13a) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 55 (all Xp all Xq all Xr all Xa (Xp = Xq | 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]. 0.57/0.82 56 (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]. 0.57/0.82 57 (all Xa all Xb all Xc (-s_t(Xa,Xb,Xc) | s_t(Xc,Xb,Xa))) # label(aSatz3_2) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 58 (all Xa all Xb all Xc all Xd (Xb = Xa | s_t(Xa,Xc,Xd) | s_t(Xa,Xd,Xc) | -s_t(Xa,Xb,Xd) | -s_t(Xa,Xb,Xc))) # label(aSatz5_1) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 59 (all Xa all Xb all Xp all Xp1 ((-s_col(Xa,Xb,midpoint(Xp,Xp1)) | -perp(Xa,Xb,Xp,Xp1) | reflect(Xa,Xb,Xp) = Xp1 | Xb = Xa) & (Xb = Xa | -s_col(Xa,Xb,midpoint(Xp,Xp1)) | Xp != Xp1 | Xp1 = reflect(Xa,Xb,Xp)))) # label(aSatz10_2b) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 60 (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]. 0.57/0.82 61 (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,Xc,Xcs) | -s_m(Xr,Xm,Xcs) | -sameside(U,Xr,Xa) | Xcs != Xr | sameside(s(Xm,U),Xcs,Xc) | -perp(Xp,Xq,Xa,Xr) | -s_col(Xp,Xq,Xcs) | Xp = Xq)) # label(aSatz9_4b) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 62 (all Xa all Xb all Xc all Xa1 all Xc1 ((-s_t(Xa,Xb,Xc) | -s_e(Xa,Xc,Xa1,Xc1) | s_e3(Xa,Xb,Xc,Xa1,insert(Xa,Xb,Xa1,Xc1),Xc1)) & (-s_t(Xa,Xb,Xc) | s_t(Xa1,insert(Xa,Xb,Xa1,Xc1),Xc1) | -s_e(Xa,Xc,Xa1,Xc1)))) # label(aSatz4_5) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 63 (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]. 0.57/0.82 64 (all Xa all Xb all Xp all Xq (-perp(Xa,Xb,Xp,Xq) | -s_col(Xa,Xb,Xp) | -s_col(Xa,Xb,Xq))) # label(aSatz8_14a) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 65 (all Xp all Xq all Xr all Xcs all Xa (-s_e(Xp,Xq,Xr,Xcs) | s_e(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr),s(Xa,Xcs)))) # label(aSatz7_16a) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 66 (all Xa all Xb all Xc all Xd all Y ((-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))) & (s_t(Xc,insert(Xa,Xb,Xc,Xd),Xd) | -le(Xa,Xb,Xc,Xd)))) # label(d_Defn5_4) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 67 (all Xa all Xb all Xd all Xc (s_t(Xa,Xc,Xd) | -s_t(Xb,Xc,Xd) | -s_t(Xa,Xb,Xd))) # label(aSatz3_5b) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 68 (all Xa all Xp all Xb (-le(Xp,Xa,Xp,Xb) | s_t(Xp,Xa,Xb) | -sameside(Xa,Xp,Xb))) # label(aSatz6_13a) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 69 (all Xa all Xb s_e(Xa,Xa,Xb,Xb)) # label(aSatz2_8) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 70 (all Xp all Xq all Xr all Xa (-s_t(Xq,Xp,Xr) | s_col(Xa,Xp,Xq) | -sameside(Xa,Xp,Xq) | Xr = Xp | Xp = Xq)) # label(aSatz6_15b) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 71 (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]. 0.57/0.82 72 (all Xa all Xb all Xc all Xd all Xe all Xf (s_e(Xa,Xb,Xe,Xf) | -s_e(Xc,Xd,Xe,Xf) | -s_e(Xa,Xb,Xc,Xd))) # label(aSatz2_3) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 73 (all Xp all Xq all Xr all Xa (-s_t(Xp,Xq,Xr) | s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr)))) # label(aSatz7_15a) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 74 (all Xa all Xp all Xq all Xc all Xcs all Xr all Xm all U (-s_col(Xp,Xq,Xcs) | -perp(Xp,Xq,Xa,Xr) | -perp(Xp,Xq,Xc,Xcs) | -s_m(Xr,Xm,Xcs) | sameside(s(Xm,U),Xcs,Xc) | -sameside(U,Xr,Xa) | -s_col(Xp,Xq,Xr) | Xp = Xq | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_4) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 75 (all Xa all Xm all 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)) & (-s_m(Xa,Xm,Xb) | s_t(Xa,Xm,Xb)))) # label(d_Defn7_1) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 76 (all Xa all Xb all Xp all Xq all Xcx all U all V (-s_col(Xa,Xb,Xcx) | -s_r(U,Xcx,V) | perpAt(Xa,Xb,Xcx,Xp,Xq) | Xcx = V | Xcx = U | -s_col(Xp,Xq,V) | -s_col(Xa,Xb,U) | -s_col(Xp,Xq,Xcx) | Xp = Xq | Xa = Xb)) # label(aSatz8_13b) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 77 (all Xa all Xb all Xc all Xd (Xa = Xb | Xa = Xc | Xc = Xb | -perp(Xb,Xa,Xa,Xc) | -s_col(Xa,Xc,Xd) | perp(Xb,Xa,Xa,Xd) | Xd = Xa | Xd = Xc)) # label(aExtPerp3) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 78 (all Xa all Xb all Xc all Xd all Xe (le(Xa,Xb,Xc,Xd) | -s_e(Xa,Xe,Xc,Xd) | -s_t(Xa,Xb,Xe))) # label(aSatz5_5b) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 79 (all Xa all Xb all Xc all Xd all Za all Zb all Zc all Zd ((-s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_e(Xb,Xd,Zb,Zd)) & (-s_t(Xa,Xb,Xc) | -s_e(Xb,Xc,Zb,Zc) | -s_e(Xa,Xd,Za,Zd) | -s_e(Xb,Xd,Zb,Zd) | s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | -s_e(Xa,Xb,Za,Zb) | -s_t(Za,Zb,Zc)) & (-s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_e(Xa,Xd,Za,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_e(Xa,Xb,Za,Zb)) & (-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_t(Xa,Xb,Xc)))) # label(d_Defn2_10) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 80 (all Xa all Xp all Xq all Xc all Xm all Xr all Xb (-opposite(Xa,Xp,Xq,Xc) | -s_col(Xp,Xq,Xm) | -s_m(Xa,Xm,Xc) | -s_col(Xp,Xq,Xr) | opposite(Xb,Xp,Xq,Xc) | -sameside(Xa,Xr,Xb))) # label(aSatz9_3) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 81 (all Xp all Xq all Xr all Xa (Xp = Xq | Xr = Xp | -s_t(Xq,Xp,Xr) | -s_col(Xa,Xp,Xq) | sameside(Xa,Xp,Xr) | sameside(Xa,Xp,Xq) | Xp = Xa)) # label(aSatz6_15a) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 82 (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]. 0.57/0.82 83 (all Xa all Xb s_col(Xa,Xb,Xa)) # label(aSatz4_12b) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 84 (all Xr all Xa all Xb all Xc all Xp all Xq (-s_e(Xa,Xp,Xb,Xc) | -sameside(Xq,Xa,Xr) | -s_e(Xa,Xq,Xb,Xc) | Xp = Xq | -sameside(Xp,Xa,Xr) | Xb = Xc | Xr = Xa)) # label(aSatz6_11b) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 85 (all Xa all Xc all Xb all Xc1 (-s_t(Xa,Xc,Xb) | -s_e(Xa,Xc,Xa,Xc1) | Xc1 = Xc | -s_e(Xb,Xc,Xb,Xc1))) # label(aSatz4_19) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 86 (all Xp all Xq all Xr (s_col(Xq,Xp,Xr) | -s_col(Xp,Xq,Xr) | Xp = Xq)) # label(aSatz6_17b) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 87 (all Xa all Xb s_t(Xa,Xb,Xb)) # label(aSatz3_1) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 88 (all Xa all Xm all Xb (-s_col(Xa,Xm,Xb) | Xa = Xb | s_m(Xa,Xm,Xb) | -s_e(Xm,Xa,Xm,Xb))) # label(aSatz7_20) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 89 (all Xa all Xb all Xp all Xq all Xc (-s_col(Xa,Xb,Xp) | perp(Xa,Xb,Xc,Xp) | s_col(Xa,Xb,Xc) | -s_r(Xc,Xp,Xq) | Xq = Xp | -s_col(Xa,Xb,Xq) | Xa = Xb)) # label(aSatz8_16b) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 90 (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) | -perp(Xp,Xq,Xc,Xcs) | sameside(U,Xr,Xa) | -sameside(s(Xm,U),Xcs,Xc) | Xr = Xcs | -le(Xcs,Xc,Xr,Xa) | -s_m(Xr,Xm,Xcs) | -s_col(Xp,Xq,Xr) | -s_col(Xp,Xq,Xcs) | Xq = Xp)) # label(aSatz9_4a2) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 91 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_col(Xa,Xb,Xc) | -s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1) | s_col(Xa1,Xb1,Xc1))) # label(aSatz4_13) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 92 (all Xa all Xb all Xd all Xc (-s_t(Xa,Xc,Xd) | s_t(Xa,Xb,Xc) | s_t(Xa,Xc,Xb) | -s_t(Xa,Xb,Xd))) # label(aSatz5_3) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 93 (all Xa all Xb all Xp all Xp1 (Xp1 != reflect(Xa,Xb,Xp) | reflect(Xa,Xb,Xp1) = Xp | Xa = Xb)) # label(aSatz10_6) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 94 (all Xa all Xb all Xc ((Xb = Xa | s_col(Xa,Xb,erectAux21a(Xa,Xb,Xc)) | s_col(Xa,Xb,Xc)) & (s_t(Xc,erectAux21a(Xa,Xb,Xc),erect21a(Xa,Xb,Xc)) | s_col(Xa,Xb,Xc) | Xb = Xa) & (perp(Xa,Xb,erect21a(Xa,Xb,Xc),Xa) | s_col(Xa,Xb,Xc) | Xb = Xa))) # label(aSatz8_21a) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 95 (all Xp all Xq all Xr all Xa (s_t(Xp,Xq,Xr) | -s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr)))) # label(aSatz7_15b) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 96 (all Xp all Xq all Xr all Xcs all Xa (s_e(Xp,Xq,Xr,Xcs) | -s_e(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr),s(Xa,Xcs)))) # label(aSatz7_16b) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 97 (all Xa all Xb all Xc all Xa1 all Xb1 all Xp ((-s_t(Xa1,Xb1,Xc) | -s_t(Xa,Xp,Xa1) | s_t(Xb,crossbar(Xa,Xb,Xc,Xa1,Xb1,Xp),Xb1) | -s_t(Xa,Xb,Xc)) & (-s_t(Xa,Xb,Xc) | s_t(Xp,crossbar(Xa,Xb,Xc,Xa1,Xb1,Xp),Xc) | -s_t(Xa,Xp,Xa1) | -s_t(Xa1,Xb1,Xc)))) # label(aSatz3_17) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 98 (all Xa all Xb all Xp ((s_col(Xa,Xb,midpoint(Xp,reflect(Xa,Xb,Xp))) | Xa = Xb) & (perp(Xa,Xb,Xp,reflect(Xa,Xb,Xp)) | Xp = reflect(Xa,Xb,Xp) | Xa = Xb))) # label(aSatz10_2a) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 99 (all Xp all Xq all Xr all Xcs (Xp = Xq | opposite(Xr,Xp,Xq,Xcs) | Xp = foot(Xp,Xq,Xr) | samesideline(Xr,Xcs,Xp,Xq) | s_col(Xp,Xq,Xcs) | s_col(Xp,Xq,Xr))) # label(aLemma9_13f_case2) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 100 (all Xa all Xp all Xq all Xc all Xm all Xr all Xb (-s_col(Xp,Xq,Xm) | -s_m(Xa,Xm,Xc) | -s_col(Xp,Xq,Xr) | -s_t(Xr,Xb,Xa) | opposite(Xb,Xp,Xq,Xc) | -sameside(Xa,Xr,Xb) | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_3a) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 101 (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,Xc,Xa1,Xc1) | -s_e(Xa,Xb,Xa1,Xb1) | -s_t(Xa1,Xb1,Xc1))) # label(aSatz2_11) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 102 (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) | -le(Xc,Xa1,Xc,Xa2))) # label(aSatz7_22a) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 103 (all Xa all Xb all Xc (Xa = Xb | Xc = Xb | -s_col(Xa,Xb,Xc) | -s_r(Xa,Xb,Xc))) # label(aSatz8_9) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 104 (all Xa all Xb all Xc all Xa1 (-s_r(Xa1,Xb,Xc) | Xc = Xb | -s_t(Xa,Xc,Xa1) | -s_r(Xa,Xb,Xc))) # label(aSatz8_6) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 105 (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)) & (s_col(Y1,Z1,X) | -perpAt(Y,Z,X,Y1,Z1)) & (Y != Z | -perpAt(Y,Z,X,Y1,Z1)) & (-s_col(Y,Z,U) | -s_col(Y1,Z1,V) | s_r(U,X,V) | -perpAt(Y,Z,X,Y1,Z1)) & (Y = Z | Z1 = Y1 | -s_col(Y,Z,X) | -s_col(Y1,Z1,X) | s_col(Y1,Z1,g811(Y,Z,Y1,Z1,X)) | perpAt(Y,Z,X,Y1,Z1)) & (perpAt(Y,Z,X,Y1,Z1) | -s_col(Y,Z,X) | -s_col(Y1,Z1,X) | -s_r(f811(Y,Z,Y1,Z1,X),X,g811(Y,Z,Y1,Z1,X)) | Y1 = Z1 | Z = Y) & (perpAt(Y,Z,X,Y1,Z1) | Y = Z | -s_col(Y1,Z1,X) | s_col(Y,Z,f811(Y,Z,Y1,Z1,X)) | -s_col(Y,Z,X) | Y1 = Z1) & (Y1 != Z1 | -perpAt(Y,Z,X,Y1,Z1)))) # label(d_Defn8_11a) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 106 (all Xa all Xp all Xb (s(Xb,Xp) != s(Xa,Xp) | Xa = Xb)) # label(aSatz7_18) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 107 (all Xa all Xb all Xc ((-s_t(Xa,Xb,Xc) | s_col(Xa,Xb,Xc)) & (s_col(Xa,Xb,Xc) | -s_t(Xc,Xa,Xb)) & (s_col(Xa,Xb,Xc) | -s_t(Xb,Xc,Xa)) & (-s_col(Xa,Xb,Xc) | s_t(Xa,Xb,Xc) | s_t(Xc,Xa,Xb) | s_t(Xb,Xc,Xa)))) # label(d_Defn4_10) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 108 (all Xp all Xa all Xb all Xq all Xt all Xr (-s_col(Xa,Xb,Xt) | -s_t(Xp,Xt,Xq) | -s_t(Xb,Xr,Xq) | s_m(Xp,midpoint(Xa,Xb),Xr) | -s_e(Xa,Xp,Xb,Xr) | -perp(Xq,Xb,Xa,Xb) | -perp(Xp,Xa,Xa,Xb))) # label(aSatz8_24) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 109 (all Xa all Xb all Xc (-s_col(Xa,Xb,Xc) | s_col(Xb,Xc,Xa))) # label(aSatz4_11a) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 110 (all Xa all Xb all Xc (le(Xb,Xc,Xa,Xc) | -s_t(Xa,Xb,Xc) | -s_col(Xa,Xb,Xc))) # label(aSatz5_12a2) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 111 (all Xp all Xq all Xa all Xb (-samesideline(Xp,Xq,Xa,Xb) | samesideline(Xp,Xq,Xb,Xa))) # label(aLemma9_13a) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 112 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_t(Xa,Xb,Xc) | s_t(Xa1,Xb1,Xc1) | -s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1))) # label(aSatz4_6) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 113 (all Xa all Xb all Xd all Xc (-s_t(Xa,Xb,Xd) | -s_t(Xb,Xc,Xd) | s_t(Xa,Xb,Xc))) # label(aSatz3_5a) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 114 (all Xa all Xb all Xc all Xm (-sameside(Xa,Xb,Xc) | sameside(s(Xm,Xa),s(Xm,Xb),s(Xm,Xc)))) # label(aSideReflect) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 115 (all Xa all Xb all Xc all Xd (s_t(Xa,Xb,Xd) | -s_t(Xa,Xc,Xd) | -s_t(Xa,Xb,Xc))) # label(aSatz3_6b) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 116 (all Xa all Xb all Xc all Xd (-s_e(Xa,Xb,Xc,Xd) | s_e(Xa,Xb,Xd,Xc))) # label(aSatz2_5) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 117 (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]. 0.57/0.82 118 (all Xa all Xb all Xp all Xq all Xu all Xc all Xv ((-samesideline(Xa,Xb,Xp,Xq) | s_col(Xp,Xq,ss2(Xa,Xb,Xp,Xq))) & (s_t(Xa,ss1(Xa,Xb,Xp,Xq),ss3(Xa,Xb,Xp,Xq)) | -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) | Xa != ss1(Xa,Xb,Xp,Xq)) & (-samesideline(Xa,Xb,Xp,Xq) | Xq != Xp) & (-s_col(Xp,Xq,Xa) | -samesideline(Xa,Xb,Xp,Xq)) & (-s_col(Xp,Xq,Xv) | Xc = Xv | Xa = Xu | Xv = Xb | s_col(Xp,Xq,Xa) | samesideline(Xa,Xb,Xp,Xq) | s_col(Xp,Xq,Xb) | Xu = Xc | Xq = Xp | -s_col(Xp,Xq,Xu) | -s_t(Xb,Xv,Xc) | -s_t(Xa,Xu,Xc)) & (-s_col(Xp,Xq,Xb) | -samesideline(Xa,Xb,Xp,Xq)) & (ss3(Xa,Xb,Xp,Xq) != ss2(Xa,Xb,Xp,Xq) | -samesideline(Xa,Xb,Xp,Xq)) & (ss1(Xa,Xb,Xp,Xq) != ss3(Xa,Xb,Xp,Xq) | -samesideline(Xa,Xb,Xp,Xq)) & (-samesideline(Xa,Xb,Xp,Xq) | ss2(Xa,Xb,Xp,Xq) != Xb) & (-samesideline(Xa,Xb,Xp,Xq) | s_col(Xp,Xq,ss1(Xa,Xb,Xp,Xq))))) # label(d_Defn9_7) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 119 (all Xa all Xb (-s_r(Xa,Xb,Xa) | Xb = Xa)) # label(aSatz8_8) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 120 (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]. 0.57/0.82 121 (all Xa all Xp (sameside(Xa,Xp,Xa) | Xa = Xp)) # label(aSatz6_5) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 122 (all Xa all Xb all Xc all Xd (s_t(Xa,Xb,Xd) | Xb = Xc | -s_t(Xb,Xc,Xd) | -s_t(Xa,Xb,Xc))) # label(aSatz3_7b) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 123 (all Xa all Xp all Xb all Xq all Xt (-le(Xa,Xp,Xb,Xq) | -perp(Xa,Xb,Xa,Xp) | -s_t(Xp,Xt,Xq) | -s_col(Xa,Xb,Xt) | s_m(Xa,midpointAux(Xa,Xb,Xp,Xq,Xt),Xb) | -perp(Xa,Xb,Xb,Xq))) # label(aSatz8_22b) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 124 (all Xa all Xb s_r(Xa,Xb,Xb)) # label(aSatz8_5) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 125 (all Xa all Xp all Xq (Xq = Xp | s(Xa,Xq) != s(Xa,Xp))) # label(aSatz7_9) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 126 (all Xa all Xp all Xb ((-sameside(Xa,Xp,Xb) | Xa != Xp) & (-sameside(Xa,Xp,Xb) | Xb != Xp) & (-s_t(Xp,Xa,Xb) | sameside(Xa,Xp,Xb) | xb = Xp | Xp = Xa) & (Xp = Xa | Xp = Xb | sameside(Xa,Xp,Xb) | -s_t(Xp,Xb,Xa)) & (-sameside(Xa,Xp,Xb) | s_t(Xp,Xb,Xa) | s_t(Xp,Xa,Xb)))) # label(d_Defn6_1) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 127 (all Xp all Xq all Xr all Xa (-s_t(Xq,Xp,Xr) | Xa != Xp | s_col(Xa,Xp,Xq) | Xp = Xr | Xp = Xq)) # label(aSatz6_15d) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 128 (all Xa1 all Xc all Xa2 all Xb1 all Xb2 all Xm1 all Xm2 (-s_e(Xc,Xa2,Xc,Xb2) | -s_m(Xa1,Xm1,Xb1) | -s_m(Xa2,Xm2,Xb2) | s_t(Xm1,Xc,Xm2) | -s_e(Xc,Xa1,Xc,Xb1) | -s_t(Xb1,Xc,Xb2) | -s_t(Xa1,Xc,Xa2))) # label(aSatz7_22) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 129 (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]. 0.57/0.82 130 (all Xa all Xb all Xc all Xp (-s_r(Xa,Xb,Xc) | s_r(Xb,Xa,Xp) | -s_m(s(Xa,Xc),Xp,s(Xb,Xc)))) # label(aSatz8_20a) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 131 (all Xa all Xp all Xb (sameside(Xb,Xp,Xa) | -sameside(Xa,Xp,Xb))) # label(aSatz6_6) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 132 (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]. 0.57/0.82 133 (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) | -s_e(Xc,Xd,Xc1,Xd1) | le(Xa1,Xb1,Xc1,Xd1))) # label(aSatz5_6) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 134 (all Xa all Xb all Xp all Xq all Xc (-s_col(Xp,Xq,Xc) | perpAt(Xa,Xb,Xc,Xp,Xq) | -s_col(Xa,Xb,Xc) | -perp(Xa,Xb,Xp,Xq))) # label(aSatz8_14b) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 135 (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]. 0.57/0.82 136 (all Xa all Xb all Xc all Xa1 (s_r(Xa1,Xb,Xc) | -s_col(Xb,Xa,Xa1) | Xb = Xa | -s_r(Xa,Xb,Xc))) # label(aSatz8_3) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 137 (all Xa all Xb s_t(Xa,Xb,ext(Xa,Xb,alpha,gamma))) # label(aSatz3_14a) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 138 (all Xa all Xb all Xc all Xa1 all Xb1 (s_e3(Xa,Xb,Xc,Xa1,Xb1,insert5(Xa,Xb,Xc,Xa1,Xb1)) | -s_e(Xa,Xb,Xa1,Xb1) | -s_col(Xa,Xb,Xc))) # label(aSatz4_14) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 139 (all Xa all Xc all Xp all Xb all Xq ((s_t(Xa,op(Xq,Xb,Xp,Xc,Xa),Xb) | -s_t(Xb,Xq,Xc) | -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]. 0.57/0.82 140 (all Xa all Xb all Xp all Xq (samesideline(Xq,Xp,Xa,Xb) | -samesideline(Xp,Xq,Xa,Xb) | Xa = Xb)) # label(aLemma9_13d) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 141 (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]. 0.57/0.82 142 (all Xp all Xq (s_col(Xp,Xq,Xp) | Xq = Xp)) # label(aSatz6_17a) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 143 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_r(Xa,Xb,Xc) | -s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1) | s_r(Xa1,Xb1,Xc1))) # label(aSatz8_10) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 144 (all Xa all Xp all Xb (sameside(Xa,Xp,Xb) | -s_col(Xa,Xp,Xb) | s_t(Xa,Xp,Xb))) # label(aSatz6_4b) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 145 (all Xp all Xq all Xr all Xcs (Xq = Xp | samesideline(Xr,Xcs,Xp,Xq) | opposite(Xr,Xp,Xq,Xcs) | Xp != foot(Xp,Xq,Xr) | s_col(Xp,Xq,Xcs) | s_col(Xp,Xq,Xr))) # label(aLemma9_13f_case1) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 146 (all Xa all Xb all Xc all Xp all Xq (s_col(Xa,Xb,Xc) | -s_col(Xa,Xb,Xq) | -perp(Xa,Xb,Xc,Xq) | Xp = Xq | -perp(Xa,Xb,Xc,Xp) | -s_col(Xa,Xb,Xp))) # label(aSatz8_18a) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 147 (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]. 0.57/0.82 148 (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]. 0.57/0.82 149 (all Xb all Xc all Xa (Xb = Xc | -s_e(Xb,Xc,Xa,Xa))) # label(aSatz2_13) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 150 (all Xa all Xc all Xd le(Xa,Xa,Xc,Xd)) # label(aSatz5_11) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 151 (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) | s_e(Xc,Xd,Xc1,Xd1) | Xb = Xa)) # label(aSatz4_16) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 152 (all Xa all Xb all Xc all Xd (-s_e(Xa,Xb,Xc,Xd) | s_e(Xc,Xd,Xa,Xb))) # label(aSatz2_2) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 153 (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]. 0.57/0.82 154 (all Xa all Xb all Xc (-s_t(Xa,Xb,Xc) | Xb = Xa | -s_t(Xb,Xa,Xc))) # label(aSatz3_4) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 155 (all Xa all Xp (Xa = Xp | Xp != s(Xa,Xp))) # label(aSatz7_10a) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 156 (all Xa all Xb all Xp (reflect(Xa,Xb,reflect(Xa,Xb,Xp)) = Xp | Xb = Xa)) # label(aSatz10_5) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 157 (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]. 0.57/0.82 158 (all Xa all Xb s_e(Xa,Xb,Xa,Xb)) # label(aSatz2_1) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 159 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_e(Xa,Xc,Xa1,Xc1) | s_e(Xa,Xb,Xa1,Xb1) | -s_e(Xb,Xc,Xb1,Xc1) | -s_t(Xa1,Xb1,Xc1) | -s_t(Xa,Xb,Xc))) # label(aSatz4_3) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 160 (all Xa all Xp all Xq all Xc all Xcs all Xr all Xm all U (-s_col(Xp,Xq,Xcs) | -perp(Xp,Xq,Xa,Xr) | -perp(Xp,Xq,Xc,Xcs) | -le(Xcs,Xc,Xr,Xa) | Xcs = Xr | sameside(s(Xm,U),Xcs,Xc) | -sameside(U,Xr,Xa) | -s_m(Xr,Xm,Xcs) | -s_col(Xp,Xq,Xr) | Xq = Xp | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_4a) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 161 (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]. 0.57/0.82 162 (all Xa all Xb all Xc all Xd all Xp (-s_e(Xa,Xb,Xc,Xd) | s_m(Xa,Xp,Xc) | -s_col(Xb,Xp,Xd) | -s_col(Xa,Xp,Xc) | -s_e(Xb,Xc,Xd,Xa) | Xd = Xb | s_col(Xa,Xb,Xc))) # label(aSatz7_21) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 163 (all Xp all Xa s_m(Xp,Xa,s(Xa,Xp))) # label(aSatz7_4a) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 164 (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]. 0.57/0.82 165 (all Xa all Xb all Xc all Xp (-s_r(Xa,Xb,Xc) | Xb = Xc | Xp != Xa | -s_m(s(Xa,Xc),Xp,s(Xb,Xc)))) # label(aSatz8_20b) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 166 (all Xa all Xb all Xc (-s_r(Xa,Xb,Xc) | Xc = Xb | -s_r(Xa,Xc,Xb))) # label(aSatz8_7) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 167 (all Xp all Xq all Xr all Xcs (opposite(Xr,Xp,Xq,Xcs) | samesideline(Xr,Xcs,Xp,Xq) | s_col(Xp,Xq,Xcs) | s_col(Xp,Xq,Xr) | Xp = Xq)) # label(aLemma9_13f) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 168 (all Xa all Xp all Xq all Xc all Xr all Xb (-s_col(Xp,Xq,Xr) | -sameside(Xa,Xr,Xb) | opposite(Xb,Xp,Xq,Xc) | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_5) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 169 (all Xa all Xb all Xc (-s_e(Xa,Xc,Xa,Xb) | Xc = Xb | -s_t(Xa,Xb,Xc))) # label(aNarbouxLemma1) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 170 (all Xa all Xb s_col(Xa,Xa,Xb)) # label(aSatz4_12) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 171 (all Xa all Xb all Xp all Xq (perp(Xb,Xa,Xp,Xq) | -perp(Xa,Xb,Xp,Xq))) # label(aperp1) # label(axiom) # label(non_clause). [assumption]. 0.57/0.82 172 (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_t(Xb1,Xc,Xb2) | -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_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) | s_e(Xc,Xa2,Xc,Xb2)) & (-s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) | s_m(Xa2,Xm2,Xb2)) & (-s_t(Xb1,Xc,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(Xa1,Xc,Xa2)) & (s_m(Xa1,Xm1,Xb1) | -s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2)))) # label(d_Defn7_23) # label(axiom) # label(non_clause). [assumption]. 0.57/0.83 173 (all Xa all Xp all Xb ((-s_t(Xa,Xp,Xb) | -sameside(Xa,Xp,Xb)) & (-sameside(Xa,Xp,Xb) | s_col(Xa,Xp,Xb)))) # label(aSatz6_4a) # label(axiom) # label(non_clause). [assumption]. 0.57/0.83 174 (all Xd all Xe all Xd1 all Xa all Xb (Xd = Xe | -s_t(Xe,Xd,Xd1) | -samesideline(Xa,Xb,Xd1,Xe) | samesideline(Xa,Xb,Xd,Xe))) # label(aLemma9_13c) # label(axiom) # label(non_clause). [assumption]. 0.57/0.83 175 (all Xa all Xb all Xc all Xd (-s_e(Xa,Xb,Xc,Xd) | s_e(Xb,Xa,Xc,Xd))) # label(aSatz2_4) # label(axiom) # label(non_clause). [assumption]. 0.57/0.83 176 (all Xa all Xb all Xc all Xd (Xb = Xa | -s_t(Xa,Xb,Xc) | -s_t(Xa,Xb,Xd) | s_t(Xb,Xd,Xc) | s_t(Xb,Xc,Xd))) # label(aSatz5_2) # label(axiom) # label(non_clause). [assumption]. 0.57/0.83 177 (all Xa all Xb all Xc all Xc1 (Xc = Xc1 | -s_e(Xb,Xc,Xb,Xc1) | -s_e(Xa,Xc,Xa,Xc1) | -s_col(Xa,Xb,Xc) | Xb = Xa)) # label(aSatz4_18) # label(axiom) # label(non_clause). [assumption]. 0.57/0.83 178 (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]. 0.57/0.83 179 (all Xa all Xb all Xc all XA all XB all XC (-s_e(Xa,Xb,XB,XC) | -s_e(Xb,Xc,XA,XB) | s_e(Xa,Xc,XA,XC) | -s_t(XA,XB,XC) | -s_t(Xa,Xb,Xc))) # label(aSatz2_15) # label(axiom) # label(non_clause). [assumption]. 0.57/0.83 180 (all Xa all Xb all Xp (s(Xa,s(Xb,Xp)) != s(Xb,s(Xa,Xp)) | Xa = Xb)) # label(aSatz7_19) # label(axiom) # label(non_clause). [assumption]. 0.57/0.83 181 (all Xa all Xb all Xc all Xp all Xq (Xb = Xa | -samesideline(Xp,Xq,Xa,Xb) | samesideline(Xp,Xq,Xa,Xc) | Xc = Xa | -s_col(Xa,Xb,Xc))) # label(aExtSameSide1) # label(axiom) # label(non_clause). [assumption]. 0.57/0.83 182 (all Xa all Xb all Xc all Xd (Xb = Xa | -s_t(Xc,Xa,Xb) | s_t(Xd,Xc,Xb) | s_t(Xc,Xd,Xb) | -s_t(Xd,Xa,Xb))) # label(aSatz6_16a) # label(axiom) # label(non_clause). [assumption]. 0.57/0.83 183 (all Xa all Xb all Xp all Xq all Xc all Xd (-s_col(Xa,Xb,Xp) | -s_col(Xa,Xb,Xq) | Xb = Xa | perp(Xa,Xb,Xc,Xd) | -perp(Xp,Xq,Xc,Xd) | Xp = Xq)) # label(aExtPerp2) # label(axiom) # label(non_clause). [assumption]. 0.57/0.83 184 (all Xa all Xb all U all V all W (Xb = Xa | -s_m(U,V,W) | -s_col(Xa,Xb,W) | s_col(Xa,Xb,V) | -s_col(Xa,Xb,U))) # label(aLemma9_13b) # label(axiom) # label(non_clause). [assumption]. 0.57/0.83 185 (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]. 0.57/0.83 186 (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]. 0.57/0.83 187 (all Xa all Xb all Xc (-s_col(Xa,Xb,Xc) | s_col(Xb,Xa,Xc))) # label(aSatz4_11d) # label(axiom) # label(non_clause). [assumption]. 0.57/0.83 188 (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]. 0.57/0.83 189 (all Xp all Xq all Xa s_e(Xp,Xq,s(Xa,Xp),s(Xa,Xq))) # label(aSatz7_13) # label(axiom) # label(non_clause). [assumption]. 0.57/0.83 190 (all Xc all Xa all Xb (-s_e(Xc,Xa,Xc,Xb) | s_m(Xa,isomidpoint(Xa,Xb,Xc),Xb))) # label(aSatz7_25) # label(axiom) # label(non_clause). [assumption]. 0.57/0.83 191 (all Xa all Xb all Xd all Xc (Xa = Xb | -perp(Xa,Xb,Xc,Xd) | perpAt(Xa,Xb,Xd,Xc,Xd) | -s_col(Xa,Xb,Xd))) # label(aSatz8_15) # label(axiom) # label(non_clause). [assumption]. 0.57/0.83 192 (all Xa1 all Xa2 all Xa3 all Xb1 all Xb2 all Xb3 ((s_e(Xa1,Xa2,Xb1,Xb2) | -s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3)) & (s_e(Xa1,Xa3,Xb1,Xb3) | -s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3)) & (-s_e(Xa1,Xa2,Xb1,Xb2) | s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3) | -s_e(Xa2,Xa3,Xb2,Xb3) | -s_e(Xa1,Xa3,Xb1,Xb3)) & (s_e(Xa2,Xa3,Xb2,Xb3) | -s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3)))) # label(d_Defn4_4) # label(axiom) # label(non_clause). [assumption]. 0.57/0.84 193 (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]. 0.57/0.84 194 (all Xa all Xp all Xq all Xc all Xb (-samesideline(Xa,Xb,Xp,Xq) | opposite(Xb,Xp,Xq,Xc) | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_8) # label(axiom) # label(non_clause). [assumption]. 0.57/0.84 195 (all Xa1 all Xb1 s_t(Xa1,Xa1,Xb1)) # label(aSatz3_3) # label(axiom) # label(non_clause). [assumption]. 0.57/0.84 196 (all Xa all Xb all Xp all Xq all Xr (-s_col(Xp,Xq,Xb) | s_col(Xa,Xb,Xr) | -s_col(Xp,Xq,Xr) | -s_col(Xp,Xq,Xa) | Xq = Xp | Xb = Xa)) # label(aSatz6_18) # label(axiom) # label(non_clause). [assumption]. 0.57/0.84 197 (all Xa all Xb all Xp all Xq all Xc all Xd all Xe (-s_col(Xp,Xq,Xc) | -s_col(Xp,Xq,Xd) | -s_col(Xa,Xb,Xe) | s_col(Xp,Xq,Xe) | Xc = Xd | -s_col(Xa,Xb,Xd) | -s_col(Xa,Xb,Xc) | Xq = Xp | Xb = Xa)) # label(aSatz6_21) # label(axiom) # label(non_clause). [assumption]. 0.57/0.84 198 (all Xa all Xb all Xp all Xq all Xc all Xd (-s_col(Xa,Xb,Xq) | -perp(Xa,Xb,Xc,Xd) | perp(Xp,Xq,Xc,Xd) | Xa = Xb | Xq = Xp | -s_col(Xa,Xb,Xp))) # label(aExtPerp5) # label(axiom) # label(non_clause). [assumption]. 0.57/0.84 199 -(all Xa all Xb all Xp all Xq (Xa = Xb | Xp = Xq | reflect(Xa,Xb,Xp) != reflect(Xa,Xb,Xq))) # label(aSatz10_7) # label(negated_conjecture) # label(non_clause). [assumption]. 0.57/0.84 0.57/0.84 ============================== end of process non-clausal formulas === 0.57/0.84 0.57/0.84 ============================== PROCESS INITIAL CLAUSES =============== 0.57/0.84 0.57/0.84 ============================== PREDICATE ELIMINATION ================= 0.57/0.84 200 -s_t(A,B,C) | -s_t(D,E,F) | s_ifs(A,B,C,V6,D,E,F,V7) | -s_e(C,V6,F,V7) | -s_e(A,V6,D,V7) | -s_e(B,C,E,F) | -s_e(A,C,D,F) # label(d_Defn4_1) # label(axiom). [clausify(17)]. 0.57/0.84 201 -s_ifs(A,B,C,D,E,F,V6,V7) | s_t(A,B,C) # label(d_Defn4_1) # label(axiom). [clausify(17)]. 0.57/0.84 202 s_e(A,B,C,D) | -s_ifs(A,E,B,F,C,V6,D,V7) # label(d_Defn4_1) # label(axiom). [clausify(17)]. 0.57/0.84 203 -s_ifs(A,B,C,D,E,F,V6,V7) | s_e(C,D,V6,V7) # label(d_Defn4_1) # label(axiom). [clausify(17)]. 0.57/0.84 204 -s_ifs(A,B,C,D,E,F,V6,V7) | s_e(A,D,E,V7) # label(d_Defn4_1) # label(axiom). [clausify(17)]. 0.57/0.84 205 -s_ifs(A,B,C,D,E,F,V6,V7) | s_e(B,C,F,V6) # label(d_Defn4_1) # label(axiom). [clausify(17)]. 0.57/0.84 206 s_t(A,B,C) | -s_ifs(D,E,F,V6,A,B,C,V7) # label(d_Defn4_1) # label(axiom). [clausify(17)]. 0.57/0.84 207 -s_ifs(A,B,C,D,E,F,V6,V7) | s_e(B,D,F,V7) # label(aSatz4_2) # label(axiom). [clausify(161)]. 0.57/0.84 Derived: s_e(A,B,C,D) | -s_t(E,A,F) | -s_t(V6,C,V7) | -s_e(F,B,V7,D) | -s_e(E,B,V6,D) | -s_e(A,F,C,V7) | -s_e(E,F,V6,V7). [resolve(207,a,200,c)]. 0.57/0.84 208 -s_col(A,B,C) | -s_e3(A,B,C,D,E,F) | -s_e(B,V6,E,V7) | s_fs(A,B,C,V6,D,E,F,V7) | -s_e(A,V6,D,V7) # label(d_Defn4_15) # label(axiom). [clausify(47)]. 0.57/0.84 209 s_col(A,B,C) | -s_fs(A,B,C,D,E,F,V6,V7) # label(d_Defn4_15) # label(axiom). [clausify(47)]. 0.57/0.84 210 s_e(A,B,C,D) | -s_fs(A,E,F,B,C,V6,V7,D) # label(d_Defn4_15) # label(axiom). [clausify(47)]. 0.57/0.84 211 s_e(A,B,C,D) | -s_fs(E,A,F,B,V6,C,V7,D) # label(d_Defn4_15) # label(axiom). [clausify(47)]. 0.57/0.84 212 s_e3(A,B,C,D,E,F) | -s_fs(A,B,C,V6,D,E,F,V7) # label(d_Defn4_15) # label(axiom). [clausify(47)]. 0.57/0.84 213 -s_fs(A,B,C,D,E,F,V6,V7) | s_e(C,D,V6,V7) | B = A # label(aSatz4_16) # label(axiom). [clausify(151)]. 0.57/0.84 Derived: s_e(A,B,C,D) | E = F | -s_col(F,E,A) | -s_e3(F,E,A,V6,V7,C) | -s_e(E,B,V7,D) | -s_e(F,B,V6,D). [resolve(213,a,208,d)]. 0.57/0.84 214 -s_t(A,B,C) | -s_e(B,D,B,A) | -s_m(D,E,A) | -s_m(F,V6,C) | s_kf(D,E,A,B,C,V6,F) | -s_e(B,F,B,C) | -s_t(D,B,F) # label(d_Defn7_23) # label(axiom). [clausify(172)]. 0.57/0.84 215 -s_kf(A,B,C,D,E,F,V6) | s_t(B,D,F) # label(aSatz7_22b) # label(axiom). [clausify(49)]. 0.57/0.84 216 -s_kf(A,B,C,D,E,F,V6) | s_t(B,D,F) | -le(D,A,D,V6) # label(aSatz7_22a) # label(axiom). [clausify(102)]. 0.57/0.84 217 s_t(A,B,C) | -s_kf(A,D,E,B,F,V6,C) # label(d_Defn7_23) # label(axiom). [clausify(172)]. 0.57/0.84 218 s_t(A,B,C) | -s_kf(D,E,A,B,C,F,V6) # label(d_Defn7_23) # label(axiom). [clausify(172)]. 0.57/0.84 219 s_e(A,B,A,C) | -s_kf(B,D,C,A,E,F,V6) # label(d_Defn7_23) # label(axiom). [clausify(172)]. 0.57/0.84 220 -s_kf(A,B,C,D,E,F,V6) | s_e(D,V6,D,E) # label(d_Defn7_23) # label(axiom). [clausify(172)]. 0.61/0.88 221 -s_kf(A,B,C,D,E,F,V6) | s_m(V6,F,E) # label(d_Defn7_23) # label(axiom). [clausify(172)]. 0.61/0.88 Derived: -s_t(A,B,C) | -s_e(B,D,B,A) | -s_m(D,E,A) | -s_m(F,V6,C) | -s_e(B,F,B,C) | -s_t(D,B,F) | s_t(E,B,V6). [resolve(214,e,215,a)]. 0.61/0.88 222 s_m(A,B,C) | -s_kf(A,B,C,D,E,F,V6) # label(d_Defn7_23) # label(axiom). [clausify(172)]. 0.61/0.88 223 -s_col(A,B,C) | -s_e3(A,B,C,D,E,F) | s_col(D,E,F) # label(aSatz4_13) # label(axiom). [clausify(91)]. 0.61/0.88 224 -s_t(A,B,C) | -s_e(A,C,D,E) | s_e3(A,B,C,D,insert(A,B,D,E),E) # label(aSatz4_5) # label(axiom). [clausify(62)]. 0.61/0.88 Derived: -s_col(A,B,C) | s_col(D,insert(A,B,D,E),E) | -s_t(A,B,C) | -s_e(A,C,D,E). [resolve(223,b,224,c)]. 0.61/0.88 225 -s_t(A,B,C) | s_t(D,E,F) | -s_e3(A,B,C,D,E,F) # label(aSatz4_6) # label(axiom). [clausify(112)]. 0.61/0.88 Derived: -s_t(A,B,C) | s_t(D,insert(A,B,D,E),E) | -s_t(A,B,C) | -s_e(A,C,D,E). [resolve(225,c,224,c)]. 0.61/0.88 226 s_e3(A,B,C,D,E,insert5(A,B,C,D,E)) | -s_e(A,B,D,E) | -s_col(A,B,C) # label(aSatz4_14) # label(axiom). [clausify(138)]. 0.61/0.88 Derived: -s_e(A,B,C,D) | -s_col(A,B,E) | -s_col(A,B,E) | s_col(C,D,insert5(A,B,E,C,D)). [resolve(226,a,223,b)]. 0.61/0.88 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(226,a,225,c)]. 0.61/0.88 227 -s_r(A,B,C) | -s_e3(A,B,C,D,E,F) | s_r(D,E,F) # label(aSatz8_10) # label(axiom). [clausify(143)]. 0.61/0.88 Derived: -s_r(A,B,C) | s_r(D,insert(A,B,D,E),E) | -s_t(A,B,C) | -s_e(A,C,D,E). [resolve(227,b,224,c)]. 0.61/0.88 Derived: -s_r(A,B,C) | s_r(D,E,insert5(A,B,C,D,E)) | -s_e(A,B,D,E) | -s_col(A,B,C). [resolve(227,b,226,a)]. 0.61/0.88 228 s_e(A,B,C,D) | -s_e3(A,B,E,C,D,F) # label(d_Defn4_4) # label(axiom). [clausify(192)]. 0.61/0.88 Derived: s_e(A,B,C,insert(A,B,C,D)) | -s_t(A,B,E) | -s_e(A,E,C,D). [resolve(228,b,224,c)]. 0.61/0.88 229 s_e(A,B,C,D) | -s_e3(A,E,B,C,F,D) # label(d_Defn4_4) # label(axiom). [clausify(192)]. 0.61/0.88 Derived: s_e(A,B,C,insert5(A,D,B,C,E)) | -s_e(A,D,C,E) | -s_col(A,D,B). [resolve(229,b,226,a)]. 0.61/0.88 230 -s_e(A,B,C,D) | s_e3(A,B,E,C,D,F) | -s_e(B,E,D,F) | -s_e(A,E,C,F) # label(d_Defn4_4) # label(axiom). [clausify(192)]. 0.61/0.88 Derived: -s_e(A,B,C,D) | -s_e(B,E,D,F) | -s_e(A,E,C,F) | -s_col(A,B,E) | s_col(C,D,F). [resolve(230,b,223,b)]. 0.61/0.88 Derived: -s_e(A,B,C,D) | -s_e(B,E,D,F) | -s_e(A,E,C,F) | -s_t(A,B,E) | s_t(C,D,F). [resolve(230,b,225,c)]. 0.61/0.88 Derived: -s_e(A,B,C,D) | -s_e(B,E,D,F) | -s_e(A,E,C,F) | -s_r(A,B,E) | s_r(C,D,F). [resolve(230,b,227,b)]. 0.61/0.88 231 s_e(A,B,C,D) | -s_e3(E,A,B,F,C,D) # label(d_Defn4_4) # label(axiom). [clausify(192)]. 0.61/0.88 Derived: s_e(A,B,insert(C,A,D,E),E) | -s_t(C,A,B) | -s_e(C,B,D,E). [resolve(231,b,224,c)]. 0.61/0.88 Derived: s_e(A,B,C,insert5(D,A,B,E,C)) | -s_e(D,A,E,C) | -s_col(D,A,B). [resolve(231,b,226,a)]. 0.61/0.88 232 s_e(A,B,C,D) | E = F | -s_col(F,E,A) | -s_e3(F,E,A,V6,V7,C) | -s_e(E,B,V7,D) | -s_e(F,B,V6,D). [resolve(213,a,208,d)]. 0.61/0.88 Derived: s_e(A,B,C,D) | E = F | -s_col(F,E,A) | -s_e(E,B,insert(F,E,V6,C),D) | -s_e(F,B,V6,D) | -s_t(F,E,A) | -s_e(F,A,V6,C). [resolve(232,d,224,c)]. 0.61/0.88 Derived: s_e(A,B,insert5(C,D,A,E,F),V6) | D = C | -s_col(C,D,A) | -s_e(D,B,F,V6) | -s_e(C,B,E,V6) | -s_e(C,D,E,F) | -s_col(C,D,A). [resolve(232,d,226,a)]. 0.61/0.88 Derived: s_e(A,B,C,D) | E = F | -s_col(F,E,A) | -s_e(E,B,V6,D) | -s_e(F,B,V7,D) | -s_e(F,E,V7,V6) | -s_e(E,A,V6,C) | -s_e(F,A,V7,C). [resolve(232,d,230,b)]. 0.61/0.88 233 -s_t(A,B,C) | -s_e(B,C,D,E) | -s_e(A,F,V6,V7) | -s_e(B,F,D,V7) | s_afs(A,B,C,F,V6,D,E,V7) | -s_e(A,B,V6,D) | -s_t(V6,D,E) # label(d_Defn2_10) # label(axiom). [clausify(79)]. 0.61/0.88 234 -s_afs(A,B,C,D,E,F,V6,V7) | s_e(B,D,F,V7) # label(d_Defn2_10) # label(axiom). [clausify(79)]. 0.61/0.88 235 -s_afs(A,B,C,D,E,F,V6,V7) | s_e(A,D,E,V7) # label(d_Defn2_10) # label(axiom). [clausify(79)]. 0.61/0.88 236 s_e(A,B,C,D) | -s_afs(E,A,B,F,V6,C,D,V7) # label(d_Defn2_10) # label(axiom). [clausify(79)]. 0.61/0.88 237 -s_afs(A,B,C,D,E,F,V6,V7) | s_e(A,B,E,F) # label(d_Defn2_10) # label(axiom). [clausify(79)]. 0.61/0.88 238 -s_afs(A,B,C,D,E,F,V6,V7) | s_t(E,F,V6) # label(d_Defn2_10) # label(axiom). [clausify(79)]. 0.61/0.88 239 -s_afs(A,B,C,D,E,F,V6,V7) | s_t(A,B,C) # label(d_Defn2_10) # label(axiom). [clausify(79)]. 0.61/0.88 0.61/0.88 ============================== end predicate elimination ============= 0.61/0.88 0.61/0.88 Auto_denials: (non-Horn, no changes). 0.61/0.97 0.61/0.97 Term ordering decisions: 0.61/0.97 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. 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. 0.61/0.97 0.61/0.97 ============================== end of process initial clauses ======== 0.61/0.97 0.61/0.97 ============================== CLAUSES FOR SEARCH ==================== 0.61/0.97 0.61/0.97 ============================== end of clauses for search ============= 0.61/0.97 0.61/0.97 ============================== SEARCH ================================ 0.61/0.97 0.61/0.97 % Starting search at 0.08 seconds. 0.61/0.97 0.61/0.97 ============================== PROOF ================================= 0.61/0.97 % SZS status Theorem 0.61/0.97 % SZS output start Refutation 0.61/0.97 0.61/0.97 % Proof 1 at 0.17 (+ 0.01) seconds. 0.61/0.97 % Length of proof is 8. 0.61/0.97 % Level of proof is 3. 0.61/0.97 % Maximum clause weight is 15.000. 0.61/0.97 % Given clauses 230. 0.61/0.97 0.61/0.97 29 (all Xa all Xb all Xp all Xp1 (Xb = Xa | Xp = reflect(Xa,Xb,Xp1) | Xp1 != reflect(Xa,Xb,Xp))) # label(aSatz10_4) # label(axiom) # label(non_clause). [assumption]. 0.61/0.97 199 -(all Xa all Xb all Xp all Xq (Xa = Xb | Xp = Xq | reflect(Xa,Xb,Xp) != reflect(Xa,Xb,Xq))) # label(aSatz10_7) # label(negated_conjecture) # label(non_clause). [assumption]. 0.61/0.97 273 A = B | reflect(B,A,C) = D | reflect(B,A,D) != C # label(aSatz10_4) # label(axiom). [clausify(29)]. 0.61/0.97 485 c2 != c1 # label(aSatz10_7) # label(negated_conjecture). [clausify(199)]. 0.61/0.97 486 c4 != c3 # label(aSatz10_7) # label(negated_conjecture). [clausify(199)]. 0.61/0.97 487 reflect(c1,c2,c4) = reflect(c1,c2,c3) # label(aSatz10_7) # label(negated_conjecture). [clausify(199)]. 0.61/0.97 1239 reflect(c1,c2,reflect(c1,c2,c3)) = c4. [resolve(487,a,273,c),unit_del(a,485)]. 0.61/0.97 1240 $F. [resolve(487,a,273,c(flip)),rewrite([487(9),1239(10)]),unit_del(a,485),unit_del(b,486)]. 0.61/0.97 0.61/0.97 % SZS output end Refutation 0.61/0.97 ============================== end of proof ========================== 0.61/0.97 0.61/0.97 ============================== STATISTICS ============================ 0.61/0.97 0.61/0.97 Given=230. Generated=2276. Kept=989. proofs=1. 0.61/0.97 Usable=229. Sos=695. Demods=8. Limbo=1, Disabled=380. Hints=0. 0.61/0.97 Megabytes=2.31. 0.61/0.97 User_CPU=0.17, System_CPU=0.01, Wall_clock=0. 0.61/0.97 0.61/0.97 ============================== end of statistics ===================== 0.61/0.97 0.61/0.97 ============================== end of search ========================= 0.61/0.97 0.61/0.97 THEOREM PROVED 0.61/0.97 % SZS status Theorem 0.61/0.97 0.61/0.97 Exiting with 1 proof. 0.61/0.97 0.61/0.97 Process 12378 exit (max_proofs) Sat Jul 14 04:55:40 2018 0.61/0.97 Prover9 interrupted 0.61/0.97 EOF