0.08/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.08/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.35 % Computer : n007.cluster.edu 0.13/0.35 % Model : x86_64 x86_64 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.35 % Memory : 8042.1875MB 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.35 % CPULimit : 1440 0.13/0.35 % WCLimit : 180 0.13/0.35 % DateTime : Mon Jul 3 11:09:43 EDT 2023 0.13/0.35 % CPUTime : 1.02/1.32 ============================== Prover9 =============================== 1.02/1.32 Prover9 (32) version 2009-11A, November 2009. 1.02/1.32 Process 444 was started by sandbox2 on n007.cluster.edu, 1.02/1.32 Mon Jul 3 11:09:44 2023 1.02/1.32 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1440 -f /tmp/Prover9_32759_n007.cluster.edu". 1.02/1.32 ============================== end of head =========================== 1.02/1.32 1.02/1.32 ============================== INPUT ================================= 1.02/1.32 1.02/1.32 % Reading from file /tmp/Prover9_32759_n007.cluster.edu 1.02/1.32 1.02/1.32 set(prolog_style_variables). 1.02/1.32 set(auto2). 1.02/1.32 % set(auto2) -> set(auto). 1.02/1.32 % set(auto) -> set(auto_inference). 1.02/1.32 % set(auto) -> set(auto_setup). 1.02/1.32 % set(auto_setup) -> set(predicate_elim). 1.02/1.32 % set(auto_setup) -> assign(eq_defs, unfold). 1.02/1.32 % set(auto) -> set(auto_limits). 1.02/1.32 % set(auto_limits) -> assign(max_weight, "100.000"). 1.02/1.32 % set(auto_limits) -> assign(sos_limit, 20000). 1.02/1.32 % set(auto) -> set(auto_denials). 1.02/1.32 % set(auto) -> set(auto_process). 1.02/1.32 % set(auto2) -> assign(new_constants, 1). 1.02/1.32 % set(auto2) -> assign(fold_denial_max, 3). 1.02/1.32 % set(auto2) -> assign(max_weight, "200.000"). 1.02/1.32 % set(auto2) -> assign(max_hours, 1). 1.02/1.32 % assign(max_hours, 1) -> assign(max_seconds, 3600). 1.02/1.32 % set(auto2) -> assign(max_seconds, 0). 1.02/1.32 % set(auto2) -> assign(max_minutes, 5). 1.02/1.32 % assign(max_minutes, 5) -> assign(max_seconds, 300). 1.02/1.32 % set(auto2) -> set(sort_initial_sos). 1.02/1.32 % set(auto2) -> assign(sos_limit, -1). 1.02/1.32 % set(auto2) -> assign(lrs_ticks, 3000). 1.02/1.32 % set(auto2) -> assign(max_megs, 400). 1.02/1.32 % set(auto2) -> assign(stats, some). 1.02/1.32 % set(auto2) -> clear(echo_input). 1.02/1.32 % set(auto2) -> set(quiet). 1.02/1.32 % set(auto2) -> clear(print_initial_clauses). 1.02/1.32 % set(auto2) -> clear(print_given). 1.02/1.32 assign(lrs_ticks,-1). 1.02/1.32 assign(sos_limit,10000). 1.02/1.32 assign(order,kbo). 1.02/1.32 set(lex_order_vars). 1.02/1.32 clear(print_given). 1.02/1.32 1.02/1.32 % formulas(sos). % not echoed (197 formulas) 1.02/1.32 1.02/1.32 ============================== end of input ========================== 1.02/1.32 1.02/1.32 % From the command line: assign(max_seconds, 1440). 1.02/1.32 1.02/1.32 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 1.02/1.32 1.02/1.32 % Formulas that are not ordinary clauses: 1.02/1.32 1 (all X all Y (Y = X | -s_t(X,Y,X))) # label(aA6) # label(axiom) # label(non_clause). [assumption]. 1.02/1.32 2 (all X all Y all W all V (s_e(Y,ext(X,Y,W,V),W,V) & s_t(X,Y,ext(X,Y,W,V)))) # label(aA4) # label(axiom) # label(non_clause). [assumption]. 1.02/1.32 3 (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]. 1.02/1.32 4 (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) | s_e(Z,V,Z1,V1) | X = Y | -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]. 1.02/1.32 5 (all X all Y s_e(X,Y,Y,X)) # label(aA1) # label(axiom) # label(non_clause). [assumption]. 1.02/1.32 6 (all Xa all Xp all Xc all Xb all Xq ((-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) | -s_t(Xb,Xq,Xc) | s_t(Xp,ip(Xa,Xp,Xc,Xb,Xq),Xb)))) # label(aA7) # label(axiom) # label(non_clause). [assumption]. 1.02/1.32 7 (all X all Y all Z (Y = X | -s_e(X,Y,Z,Z))) # label(aA3) # label(axiom) # label(non_clause). [assumption]. 1.02/1.32 8 (all Xa all Xb all Xc all Xp all Xq (-s_col(Xa,Xb,Xc) | -samesideline(Xp,Xq,Xa,Xb) | samesideline(Xp,Xq,Xa,Xc) | Xa = Xc | Xb = Xa)) # label(aExtSameSide1) # label(axiom) # label(non_clause). [assumption]. 1.02/1.32 9 (all Xa all Xb all Xc all Xp all Xq (-perpAt(Xa,Xb,Xc,Xp,Xq) | Xc = il(Xa,Xb,Xp,Xq))) # label(aSatz8_14c) # label(axiom) # label(non_clause). [assumption]. 1.02/1.32 10 (all Xa all Xb s_t(Xa,Xb,Xb)) # label(aSatz3_1) # label(axiom) # label(non_clause). [assumption]. 1.02/1.32 11 (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]. 1.02/1.32 12 (all Xa all Xb all Xc all Xd (-s_t(Xb,Xc,Xd) | Xb = Xc | s_t(Xa,Xc,Xd) | -s_t(Xa,Xb,Xc))) # label(aSatz3_7a) # label(axiom) # label(non_clause). [assumption]. 1.02/1.32 13 (all Xa all Xb all Xc all Xp all Xq (-s_e(Xa,Xp,Xa,Xq) | -s_e(Xb,Xp,Xb,Xq) | s_e(Xc,Xp,Xc,Xq) | -s_col(Xa,Xb,Xc) | Xb = Xa)) # label(aSatz4_17) # label(axiom) # label(non_clause). [assumption]. 1.02/1.32 14 (all Xa all Xb all Xc all Xd (s_t(Xd,Xc,Xb) | s_t(Xc,Xd,Xb) | -s_t(Xd,Xa,Xb) | -s_t(Xc,Xa,Xb) | Xb = Xa)) # label(aSatz6_16a) # label(axiom) # label(non_clause). [assumption]. 1.02/1.32 15 (all Xa all Xp all Xq all Xc all Xr all Xb (-s_col(Xp,Xq,Xr) | opposite(Xb,Xp,Xq,Xc) | -sameside(Xa,Xr,Xb) | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_5) # label(axiom) # label(non_clause). [assumption]. 1.02/1.32 16 (all Xp all Xa all Xb all Xq all Xt all Xr (-perp(Xp,Xa,Xa,Xb) | -perp(Xq,Xb,Xa,Xb) | -s_e(Xa,Xp,Xb,Xr) | s_m(Xp,midpoint(Xa,Xb),Xr) | -s_t(Xb,Xr,Xq) | -s_t(Xp,Xt,Xq) | -s_col(Xa,Xb,Xt))) # label(aSatz8_24) # label(axiom) # label(non_clause). [assumption]. 1.02/1.32 17 (all Xa all Xb all Xc all Xd all Xe (-s_e(Xa,Xe,Xc,Xd) | -s_t(Xa,Xb,Xe) | le(Xa,Xb,Xc,Xd))) # label(aSatz5_5b) # label(axiom) # label(non_clause). [assumption]. 1.02/1.32 18 (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]. 1.02/1.32 19 (all Xa all Xb all Xc all Xd (Xb = Xa | -s_t(Xa,Xb,Xc) | -s_t(Xa,Xb,Xd) | s_t(Xa,Xc,Xd) | s_t(Xa,Xd,Xc))) # label(aSatz5_1) # label(axiom) # label(non_clause). [assumption]. 1.02/1.32 20 (all Xa all Xp all Xq all Xc all Xcs all Xr all Xm all U (-opposite(Xa,Xp,Xq,Xc) | Xp = Xq | -perp(Xp,Xq,Xa,Xr) | -sameside(U,Xr,Xa) | 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))) # label(aSatz9_4) # label(axiom) # label(non_clause). [assumption]. 1.02/1.32 21 (all Xa all Xb all Xc all Xp (s_r(Xb,Xa,Xp) | -s_m(s(Xa,Xc),Xp,s(Xb,Xc)) | -s_r(Xa,Xb,Xc))) # label(aSatz8_20a) # label(axiom) # label(non_clause). [assumption]. 1.02/1.32 22 (all Xa all Xb all Xc all Xp all Xq ((-perpAt(Xa,Xb,Xc,Xp,Xq) | Xa != Xb) & (s_col(Xp,Xq,Xc) | -perpAt(Xa,Xb,Xc,Xp,Xq)) & (-perpAt(Xa,Xb,Xc,Xp,Xq) | s_col(Xa,Xb,Xc)) & (-perpAt(Xa,Xb,Xc,Xp,Xq) | f813(Xa,Xb,Xp,Xq,Xc) != Xc) & (-perpAt(Xa,Xb,Xc,Xp,Xq) | s_r(f813(Xa,Xb,Xp,Xq,Xc),Xc,g813(Xa,Xb,Xp,Xq,Xc))) & (g813(Xa,Xb,Xp,Xq,Xc) != Xc | -perpAt(Xa,Xb,Xc,Xp,Xq)) & (-perpAt(Xa,Xb,Xc,Xp,Xq) | s_col(Xp,Xq,g813(Xa,Xb,Xp,Xq,Xc))) & (s_col(Xa,Xb,f813(Xa,Xb,Xp,Xq,Xc)) | -perpAt(Xa,Xb,Xc,Xp,Xq)) & (-perpAt(Xa,Xb,Xc,Xp,Xq) | Xp != Xq))) # label(aSatz8_13a) # label(axiom) # label(non_clause). [assumption]. 1.02/1.32 23 (all Xa all Xb all Xc all Xd all Xe all Xf (-le(Xa,Xb,Xc,Xd) | -le(Xc,Xd,Xe,Xf) | le(Xa,Xb,Xe,Xf))) # label(aSatz5_8) # label(axiom) # label(non_clause). [assumption]. 1.02/1.32 24 (all Xb all Xc all Xa (-s_e(Xb,Xc,Xa,Xa) | Xb = Xc)) # label(aSatz2_13) # label(axiom) # label(non_clause). [assumption]. 1.02/1.32 25 (all Xa all Xm (Xa = Xm | -s_m(Xa,Xm,Xa))) # label(aSatz7_3a) # label(axiom) # label(non_clause). [assumption]. 1.02/1.32 26 (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]. 1.02/1.32 27 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-sameside(Xa,Xb,Xc) | -sameside(Xa1,Xb1,Xc1) | -s_e(Xb,Xc,Xb1,Xc1) | s_e(Xa,Xc,Xa1,Xc1) | -s_e(Xb,Xa,Xb1,Xa1))) # label(aSatz6_28) # label(axiom) # label(non_clause). [assumption]. 1.02/1.32 28 (all Xp all Xq all Xr all Xa (Xp = Xr | s_col(Xa,Xp,Xq) | -sameside(Xa,Xp,Xq) | -s_t(Xq,Xp,Xr) | Xq = Xp)) # label(aSatz6_15b) # label(axiom) # label(non_clause). [assumption]. 1.02/1.32 29 (all Xa all Xb le(Xa,Xb,Xa,Xb)) # label(aSatz5_7) # label(axiom) # label(non_clause). [assumption]. 1.02/1.32 30 (all Xp all Xq all Xp1 all Xq1 all X ((perp(Xp,Xq,Xp1,Xq1) | -perpAt(Xp,Xq,X,Xp1,Xq1)) & (perpAt(Xp,Xq,il(Xp,Xq,Xp1,Xq1),Xp1,Xq1) | -perp(Xp,Xq,Xp1,Xq1)))) # label(d_Defn8_11b) # label(axiom) # label(non_clause). [assumption]. 1.02/1.32 31 (all Xa all Xb all Xd all Xc (-s_t(Xa,Xb,Xd) | -s_t(Xa,Xc,Xd) | s_t(Xa,Xb,Xc) | s_t(Xa,Xc,Xb))) # label(aSatz5_3) # label(axiom) # label(non_clause). [assumption]. 1.02/1.32 32 (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_t(Xa,Xb,Xc) | s_e3(Xa,Xb,Xc,Xa1,insert(Xa,Xb,Xa1,Xc1),Xc1) | -s_e(Xa,Xc,Xa1,Xc1)))) # label(aSatz4_5) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 33 (all Xa all Xb all Xp all Xq all Xr (Xa = Xb | Xq = Xp | -s_col(Xp,Xq,Xb) | -s_col(Xp,Xq,Xr) | s_col(Xa,Xb,Xr) | -s_col(Xp,Xq,Xa))) # label(aSatz6_18) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 34 (all Xa all Xb all Xc ((Xa = Xb | 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) | Xa = Xb) & (Xa = Xb | s_col(Xa,Xb,Xc) | perp(Xa,Xb,erect21a(Xa,Xb,Xc),Xa)))) # label(aSatz8_21a) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 35 (all Xa all Xb all Xc all Xd (-s_t(Xb,Xc,Xd) | s_t(Xa,Xb,Xd) | Xc = Xb | -s_t(Xa,Xb,Xc))) # label(aSatz3_7b) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 36 (all Xp all Xq all Xa all Xb all Xc (Xp = Xq | -samesideline(Xa,Xb,Xp,Xq) | samesideline(Xa,Xc,Xp,Xq) | -samesideline(Xb,Xc,Xp,Xq))) # label(aSatz9_13) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 37 (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]. 1.02/1.33 38 (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]. 1.02/1.33 39 (all Xa all Xb all Xp all Xq all Xu all Xc all Xv ((s_col(Xp,Xq,ss1(Xa,Xb,Xp,Xq)) | -samesideline(Xa,Xb,Xp,Xq)) & (-samesideline(Xa,Xb,Xp,Xq) | s_t(Xa,ss1(Xa,Xb,Xp,Xq),ss3(Xa,Xb,Xp,Xq))) & (s_t(Xb,ss2(Xa,Xb,Xp,Xq),ss3(Xa,Xb,Xp,Xq)) | -samesideline(Xa,Xb,Xp,Xq)) & (-samesideline(Xa,Xb,Xp,Xq) | Xb != ss2(Xa,Xb,Xp,Xq)) & (-samesideline(Xa,Xb,Xp,Xq) | ss3(Xa,Xb,Xp,Xq) != ss1(Xa,Xb,Xp,Xq)) & (-samesideline(Xa,Xb,Xp,Xq) | Xp != Xq) & (-samesideline(Xa,Xb,Xp,Xq) | -s_col(Xp,Xq,Xa)) & (-samesideline(Xa,Xb,Xp,Xq) | -s_col(Xp,Xq,Xb)) & (-s_t(Xa,Xu,Xc) | -s_t(Xb,Xv,Xc) | -s_col(Xp,Xq,Xu) | Xp = Xq | Xv = Xc | Xa = Xu | Xv = Xb | s_col(Xp,Xq,Xa) | s_col(Xp,Xq,Xb) | samesideline(Xa,Xb,Xp,Xq) | Xc = Xu | -s_col(Xp,Xq,Xv)) & (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) != Xa) & (-samesideline(Xa,Xb,Xp,Xq) | s_col(Xp,Xq,ss2(Xa,Xb,Xp,Xq))))) # label(d_Defn9_7) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 40 (all Xp all Xq all Xr all Xcs all Xa (s_e(Xp,Xq,Xr,Xcs) | -s_e(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr),s(Xa,Xcs)))) # label(aSatz7_16b) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 41 (all Xa all Xb all Xa1 all Xc1 ext(ext(Xc1,Xa1,alpha,gamma),Xa1,Xa,Xb) = insert(Xa,Xb,Xa1,Xc1)) # label(d_insert) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 42 (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_t(Xa,Xb,Xc)) & (-s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_t(Za,Zb,Zc)) & (-s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_e(Xb,Xc,Zb,Zc)) & (-s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_e(Xa,Xd,Za,Zd)) & (-s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_e(Xb,Xd,Zb,Zd)) & (-s_t(Za,Zb,Zc) | -s_e(Xb,Xc,Zb,Zc) | -s_e(Xa,Xd,Za,Zd) | s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | -s_e(Xb,Xd,Zb,Zd) | -s_e(Xa,Xb,Za,Zb) | -s_t(Xa,Xb,Xc)) & (-s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_e(Xa,Xb,Za,Zb)))) # label(d_Defn2_10) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 43 (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]. 1.02/1.33 44 (all Xa all Xb all Xc all Xd (-le(Xa,Xb,Xc,Xd) | -le(Xc,Xd,Xa,Xb) | s_e(Xa,Xb,Xc,Xd))) # label(aSatz5_9) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 45 (all Xa all Xb s_r(Xa,Xb,Xb)) # label(aSatz8_5) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 46 (all Xa all Xc all Xb all Xc1 (-s_t(Xa,Xc,Xb) | -s_e(Xa,Xc,Xa,Xc1) | -s_e(Xb,Xc,Xb,Xc1) | Xc1 = Xc)) # label(aSatz4_19) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 47 (all Xa all Xb all Xc all Xd (le(Xc,Xd,Xa,Xb) | le(Xa,Xb,Xc,Xd))) # label(aSatz5_10) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 48 (all Xa all Xp all Xq all Xc all Xb (-opposite(Xa,Xp,Xq,Xc) | opposite(Xb,Xp,Xq,Xc) | -samesideline(Xa,Xb,Xp,Xq))) # label(aSatz9_8) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 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(Xb1,Xc,Xb2)) & (s_e(Xc,Xa1,Xc,Xb1) | -s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2)) & (s_m(Xa1,Xm1,Xb1) | -s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2)) & (s_m(Xa2,Xm2,Xb2) | -s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2)) & (-s_t(Xa1,Xc,Xa2) | -s_e(Xc,Xa1,Xc,Xb1) | -s_e(Xc,Xa2,Xc,Xb2) | s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) | -s_m(Xa2,Xm2,Xb2) | -s_m(Xa1,Xm1,Xb1) | -s_t(Xb1,Xc,Xb2)) & (s_e(Xc,Xa2,Xc,Xb2) | -s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2)) & (s_t(Xa1,Xc,Xa2) | -s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2)))) # label(d_Defn7_23) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 50 (all Xa all Xb s_col(Xa,Xa,Xb)) # label(aSatz4_12) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 51 (all Xa all Xb all Xc all Xd (Xb = Xc | Xd = Xa | -perp(Xb,Xa,Xa,Xc) | -s_col(Xa,Xc,Xd) | perp(Xb,Xa,Xa,Xd) | Xc = Xd | Xc = Xa | Xb = Xa)) # label(aExtPerp3) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 52 (all Xa all Xb all U all V all W (-s_m(U,V,W) | -s_col(Xa,Xb,U) | -s_col(Xa,Xb,W) | s_col(Xa,Xb,V) | Xa = Xb)) # label(aLemma9_13b) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 53 (all Xa all Xb all Xc all Xm (sameside(s(Xm,Xa),s(Xm,Xb),s(Xm,Xc)) | -sameside(Xa,Xb,Xc))) # label(aSideReflect) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 54 (all Xa all Xp all Xb all Xc (Xp = Xa | Xb = Xp | -s_t(Xa,Xp,Xc) | sameside(Xa,Xp,Xb) | -s_t(Xb,Xp,Xc) | Xc = Xp)) # label(aSatz6_2a) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 55 (all Xc all Xa all Xb (s_m(Xa,isomidpoint(Xa,Xb,Xc),Xb) | -s_e(Xc,Xa,Xc,Xb))) # label(aSatz7_25) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 56 (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]. 1.02/1.33 57 (all Xa all Xp all Xb (-le(Xp,Xa,Xp,Xb) | s_t(Xp,Xa,Xb) | -sameside(Xa,Xp,Xb))) # label(aSatz6_13a) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 58 (all Xa all Xb all Xp all Xq all Xc all Xd all Xe (Xq = Xp | -s_col(Xa,Xb,Xc) | -s_col(Xp,Xq,Xc) | Xd = Xc | s_col(Xp,Xq,Xe) | -s_col(Xa,Xb,Xe) | -s_col(Xp,Xq,Xd) | -s_col(Xa,Xb,Xd) | Xa = Xb)) # label(aSatz6_21) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 59 (all Xd all Xe all Xd1 all Xa all Xb (Xd = Xe | -samesideline(Xa,Xb,Xd1,Xe) | samesideline(Xa,Xb,Xd,Xe) | -s_t(Xe,Xd,Xd1))) # label(aLemma9_13c) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 60 (all Xa all Xb all Xc all Xd all Xa1 all Xb1 all Xc1 all Xd1 (-s_ifs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1) | s_e(Xb,Xd,Xb1,Xd1))) # label(aSatz4_2) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 61 (all Xa all Xp all Xq all Xb (-opposite(Xa,Xp,Xq,Xb) | opposite(Xb,Xp,Xq,Xa))) # label(aSatz9_2) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 62 (all Xa all Xp all Xb ((-sameside(Xa,Xp,Xb) | Xp != Xa) & (s_t(Xp,Xb,Xa) | s_t(Xp,Xa,Xb) | -sameside(Xa,Xp,Xb)) & (Xb = Xp | sameside(Xa,Xp,Xb) | Xa = Xp | -s_t(Xp,Xb,Xa)) & (Xa = Xp | sameside(Xa,Xp,Xb) | Xp = xb | -s_t(Xp,Xa,Xb)) & (Xb != Xp | -sameside(Xa,Xp,Xb)))) # label(d_Defn6_1) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 63 (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]. 1.02/1.33 64 (all Xa all Xb all Xd all Xc (-s_t(Xb,Xc,Xd) | s_t(Xa,Xb,Xc) | -s_t(Xa,Xb,Xd))) # label(aSatz3_5a) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 65 (all Xa all Xb all Xc all Xa1 (-s_r(Xa,Xb,Xc) | s_r(Xa1,Xb,Xc) | -s_col(Xb,Xa,Xa1) | Xa = Xb)) # label(aSatz8_3) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 66 (all Xa all Xb s_m(Xa,midpoint(Xa,Xb),Xb)) # label(aSatz8_22) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 67 (all Xa all Xp all Xq all Xc all Xm all Xr all Xb (-s_col(Xp,Xq,Xm) | -s_t(Xr,Xb,Xa) | opposite(Xb,Xp,Xq,Xc) | -sameside(Xa,Xr,Xb) | -s_col(Xp,Xq,Xr) | -s_m(Xa,Xm,Xc) | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_3a) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 68 (all Xa all Xb all Xc all Xd all Xa1 all Xb1 all Xc1 all Xd1 ((-s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1) | -s_e(Xa,Xd,Xa1,Xd1) | s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1) | -s_e(Xb,Xd,Xb1,Xd1) | -s_col(Xa,Xb,Xc)) & (s_e(Xb,Xd,Xb1,Xd1) | -s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1)) & (-s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1) | s_e(Xa,Xd,Xa1,Xd1)) & (s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1) | -s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1)) & (-s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1) | s_col(Xa,Xb,Xc)))) # label(d_Defn4_15) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 69 (all Xa all Xb s_e(Xa,Xa,Xb,Xb)) # label(aSatz2_8) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 70 (all Xa all Xp (s(Xa,Xp) = Xp | Xp != Xa)) # label(aSatz7_10b) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 71 (all Xp all Xq all Xr all Xa (s_t(Xp,Xq,Xr) | -s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr)))) # label(aSatz7_15b) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 72 (all Xa all Xb all Xp all Xq all Xc (-perp(Xa,Xb,Xp,Xq) | -s_col(Xa,Xb,Xc) | -s_col(Xp,Xq,Xc) | perpAt(Xa,Xb,Xc,Xp,Xq))) # label(aSatz8_14b) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 73 (all Xa all Xb all Xc (-s_r(Xa,Xb,Xc) | Xa = Xb | Xb = Xc | -s_col(Xa,Xb,Xc))) # label(aSatz8_9) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 74 (all Xa all Xb all Xc all Xd all Xa1 all Xb1 all Xc1 all Xd1 (-s_e(Xa,Xb,Xa1,Xb1) | le(Xa1,Xb1,Xc1,Xd1) | -s_e(Xc,Xd,Xc1,Xd1) | -le(Xa,Xb,Xc,Xd))) # label(aSatz5_6) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 75 (all Xa all Xb all Xc all Xd (-s_t(Xa,Xb,Xc) | -s_t(Xa,Xc,Xd) | s_t(Xa,Xb,Xd))) # label(aSatz3_6b) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 76 (all Xa all Xb all Xc all Xd all Xp (Xb = Xa | -s_col(Xa,Xb,Xd) | -s_col(Xc,Xd,Xp) | s_col(Xa,Xb,Xp) | -s_col(Xa,Xb,Xc) | Xd = Xc)) # label(aExtCol2) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 77 (all Xa all Xb all Xc all Xd ((s_e(Xa,ins(Xc,Xd,Xa,Xb),Xc,Xd) | -le(Xa,Xb,Xc,Xd)) & (-le(Xa,Xb,Xc,Xd) | ext(Xa,Xb,insert(Xa,Xb,Xc,Xd),Xd) = ins(Xc,Xd,Xa,Xb)) & (s_t(Xa,Xb,ins(Xc,Xd,Xa,Xb)) | -le(Xa,Xb,Xc,Xd)))) # label(aSatz5_5a) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 78 (all Xp all Xq all Xr (-s_col(Xp,Xq,Xr) | s_col(Xq,Xp,Xr) | Xq = Xp)) # label(aSatz6_17b) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 79 (all Xa all Xp all Xb (sameside(Xb,Xp,Xa) | -sameside(Xa,Xp,Xb))) # label(aSatz6_6) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 80 (all Xa1 all Xm1 all Xb1 all Xc all Xb2 all Xm2 all Xa2 (-le(Xc,Xa1,Xc,Xa2) | s_t(Xm1,Xc,Xm2) | -s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2))) # label(aSatz7_22a) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 81 (all Xa all Xb all Xp all Xq all Xc all Xd (-s_col(Xa,Xb,Xp) | Xp = Xq | -perp(Xa,Xb,Xc,Xd) | perp(Xp,Xq,Xc,Xd) | Xb = Xa | -s_col(Xa,Xb,Xq))) # label(aExtPerp5) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 82 (all Xa all Xb all Xc all Xp all Xq (Xq = Xp | -perp(Xa,Xb,Xc,Xq) | -perp(Xa,Xb,Xc,Xp) | -s_col(Xa,Xb,Xq) | -s_col(Xa,Xb,Xp) | s_col(Xa,Xb,Xc))) # label(aSatz8_18a) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 83 (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]. 1.02/1.33 84 (all Xa all Xb all Xp all Xq all Xcx all U all V (Xb = Xa | -s_col(Xa,Xb,U) | -s_col(Xp,Xq,V) | -s_r(U,Xcx,V) | perpAt(Xa,Xb,Xcx,Xp,Xq) | V = Xcx | U = Xcx | -s_col(Xa,Xb,Xcx) | -s_col(Xp,Xq,Xcx) | Xp = Xq)) # label(aSatz8_13b) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 85 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1) | s_col(Xa1,Xb1,Xc1) | -s_col(Xa,Xb,Xc))) # label(aSatz4_13) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 86 (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]. 1.02/1.33 87 (all Xa all Xp all Xb (-s_t(Xp,Xa,Xb) | le(Xp,Xa,Xp,Xb) | -sameside(Xa,Xp,Xb))) # label(aSatz6_13b) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 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]. 1.02/1.33 89 (all Xa all Xp all Xq all Xb (-opposite(Xa,Xp,Xq,Xb) | -samesideline(Xa,Xb,Xp,Xq))) # label(aSatz9_9) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 90 (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]. 1.02/1.33 91 (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]. 1.02/1.33 92 (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]. 1.02/1.33 93 (all Xa all Xb all Xc (s_col(Xc,Xb,Xa) | -s_col(Xa,Xb,Xc))) # label(aSatz4_11c) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 94 (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]. 1.02/1.33 95 (all Xa all Xb all Xc all XA all XB all XC (-s_t(XA,XB,XC) | -s_e(Xb,Xc,XA,XB) | s_e(Xa,Xc,XA,XC) | -s_e(Xa,Xb,XB,XC) | -s_t(Xa,Xb,Xc))) # label(aSatz2_15) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 96 (all Xa all Xm all Xb ((s_m(Xa,Xm,Xb) | -s_e(Xm,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)))) # label(d_Defn7_1) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 97 (all Xa all Xp all Xb ((s_col(Xa,Xp,Xb) | -sameside(Xa,Xp,Xb)) & (-s_t(Xa,Xp,Xb) | -sameside(Xa,Xp,Xb)))) # label(aSatz6_4a) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 98 (all Xa all Xm (Xa != Xm | s_m(Xa,Xm,Xa))) # label(aSatz7_3b) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 99 (all Xr all Xa all Xb all Xc all Xp all Xq (-s_e(Xa,Xq,Xb,Xc) | Xp = Xq | -sameside(Xq,Xa,Xr) | -s_e(Xa,Xp,Xb,Xc) | -sameside(Xp,Xa,Xr) | Xc = Xb | Xr = Xa)) # label(aSatz6_11b) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 100 (all Xb all Xa ext(Xa,Xb,alpha,gamma) != Xb) # label(aSatz3_14b) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 101 (all Xp all Xq all Xa all Xb (samesideline(Xp,Xq,Xb,Xa) | -samesideline(Xp,Xq,Xa,Xb))) # label(aLemma9_13a) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 102 (all Xa1 all Xm1 all Xb1 all Xc all Xb2 all Xm2 all Xa2 (s_t(Xm1,Xc,Xm2) | -s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2))) # label(aSatz7_22b) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 103 (all Xa all Xb all Xc all Xc1 (Xa = Xb | -s_col(Xa,Xb,Xc) | -s_e(Xa,Xc,Xa,Xc1) | Xc = Xc1 | -s_e(Xb,Xc,Xb,Xc1))) # label(aSatz4_18) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 104 (all Xa all Xp all Xq all Xb all Xc (-samesideline(Xb,Xc,Xp,Xq) | opposite(Xa,Xp,Xq,Xc) | -opposite(Xa,Xp,Xq,Xb))) # label(aLemma9_13e) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 105 (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]. 1.02/1.33 106 (all Xa all Xp all Xq all Xc all Xcs all Xr all Xm all U (Xq = Xp | -s_col(Xp,Xq,Xcs) | -perp(Xp,Xq,Xa,Xr) | -s_m(Xr,Xm,Xcs) | -le(Xcs,Xc,Xr,Xa) | -sameside(s(Xm,U),Xcs,Xc) | Xcs = Xr | sameside(U,Xr,Xa) | -perp(Xp,Xq,Xc,Xcs) | -s_col(Xp,Xq,Xr) | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_4a2) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 107 (all Xa all Xb (-s_col(Xa,Xb,pointOffLine(Xa,Xb)) | Xb = Xa)) # label(aSatz6_25) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 108 (all Xa all Xb all Xc all Xa1 (Xb = Xc | -s_t(Xa,Xc,Xa1) | -s_r(Xa1,Xb,Xc) | -s_r(Xa,Xb,Xc))) # label(aSatz8_6) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 109 (all Xp all Xa all Xq all Xb (Xa = Xb | -s_m(Xp,Xb,Xq) | -s_m(Xp,Xa,Xq))) # label(aSatz7_17) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 110 (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_col(Xa,Xb,Xt) | -s_t(Xp,Xt,Xq) | -s_t(Xb,Xr,Xq) | ip(Xp,Xt,Xq,Xb,Xr) != Xcx | s_m(Xp,Xcx,Xr) | -s_e(Xa,Xp,Xb,Xr))) # label(aSatz8_24b) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 111 (all Xa all Xb all Xc ((perp(Xa,Xb,erect(Xa,Xb,Xc),Xa) | Xb = Xa) & (Xb = Xa | s_col(Xa,Xb,erectAux(Xa,Xb,Xc))) & (Xa = Xb | s_t(Xc,erectAux(Xa,Xb,Xc),erect(Xa,Xb,Xc))))) # label(aSatz8_21) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 112 (all Xa all Xp all Xb (s(Xb,Xp) != s(Xa,Xp) | Xa = Xb)) # label(aSatz7_18) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 113 (all Xa all Xb all Xc all Xd (s_e(Xb,Xa,Xd,Xc) | -s_e(Xa,Xb,Xc,Xd))) # label(aSatz2_14) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 114 (all Xa all Xb s_col(Xa,Xb,Xa)) # label(aSatz4_12b) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 115 (all Xa all Xp all Xb all Xc (sameside(Xa,Xp,Xb) | Xp = Xb | -s_t(Xa,Xp,Xc) | -s_t(Xb,Xp,Xc) | Xp = Xc | Xa = Xp)) # label(aSatz6_3b) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 116 (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]. 1.02/1.33 117 (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]. 1.02/1.33 118 (all Xa all Xb all Xc (-s_t(Xa,Xb,Xc) | le(Xa,Xb,Xa,Xc) | -s_col(Xa,Xb,Xc))) # label(aSatz5_12a1) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 119 (all Xa1 all Xa2 all Xa3 all Xb1 all Xb2 all Xb3 ((-s_e(Xa1,Xa3,Xb1,Xb3) | s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3) | -s_e(Xa2,Xa3,Xb2,Xb3) | -s_e(Xa1,Xa2,Xb1,Xb2)) & (s_e(Xa2,Xa3,Xb2,Xb3) | -s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3)) & (s_e(Xa1,Xa3,Xb1,Xb3) | -s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,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]. 1.02/1.33 120 (all Xa all Xc all Xp all Xb all Xq ((s_t(Xp,Xq,op(Xq,Xb,Xp,Xc,Xa)) | -s_t(Xb,Xq,Xc) | -s_t(Xa,Xc,Xp)) & (s_t(Xa,op(Xq,Xb,Xp,Xc,Xa),Xb) | -s_t(Xb,Xq,Xc) | -s_t(Xa,Xc,Xp)))) # label(aSatz9_6) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 121 (all Xa all Xb all Xc all Xd all Xa1 all Xb1 all Xc1 all Xd1 (Xa = Xb | s_e(Xc,Xd,Xc1,Xd1) | -s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1))) # label(aSatz4_16) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 122 (all Xa all Xb all Xc all Xp (Xb = Xc | Xa != Xp | -s_m(s(Xa,Xc),Xp,s(Xb,Xc)) | -s_r(Xa,Xb,Xc))) # label(aSatz8_20b) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 123 (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]. 1.02/1.33 124 (all Xa all Xc all Xd le(Xa,Xa,Xc,Xd)) # label(aSatz5_11) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 125 (all Xa all Xp all Xb all Xq all Xt (-perp(Xa,Xb,Xa,Xp) | -s_col(Xa,Xb,Xt) | s_m(Xa,midpointAux(Xa,Xb,Xp,Xq,Xt),Xb) | -s_t(Xp,Xt,Xq) | -perp(Xa,Xb,Xb,Xq) | -le(Xa,Xp,Xb,Xq))) # label(aSatz8_22b) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 126 (all Xp all Xa s_m(Xp,Xa,s(Xa,Xp))) # label(aSatz7_4a) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 127 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_r(Xa,Xb,Xc) | s_r(Xa1,Xb1,Xc1) | -s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1))) # label(aSatz8_10) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 128 (all Xa all Xb all Xc all Xd all Xp (Xb = Xd | -s_e(Xb,Xc,Xd,Xa) | -s_col(Xa,Xp,Xc) | -s_col(Xb,Xp,Xd) | s_m(Xa,Xp,Xc) | -s_e(Xa,Xb,Xc,Xd) | s_col(Xa,Xb,Xc))) # label(aSatz7_21) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 129 (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]. 1.02/1.33 130 (all Xp all Xq all Xc all Xa all Xb (Xq = Xp | -perpAt(Xp,Xq,Xc,Xa,Xc) | -perpAt(Xp,Xq,Xc,Xb,Xc) | s_col(Xc,Xa,Xb) | Xa = Xc)) # label(aLemma9_13g) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 131 (all Xa all Xb all Xp all Xq (-samesideline(Xp,Xq,Xa,Xb) | samesideline(Xq,Xp,Xa,Xb) | Xa = Xb)) # label(aLemma9_13d) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 132 (all Xa all Xb all Xd all Xc (-s_t(Xa,Xb,Xd) | s_t(Xa,Xc,Xd) | -s_t(Xb,Xc,Xd))) # label(aSatz3_5b) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 133 (all Xa all Xb all Xp all Xq (samesideline(Xp,Xq,Xb,Xa) | -samesideline(Xp,Xq,Xa,Xb) | Xb = Xa)) # label(aExtSameSide2) # label(axiom) # label(non_clause). [assumption]. 1.02/1.33 134 (all Xa all Xb all Xc all Xa1 all Xb1 all Xp ((-s_t(Xa,Xp,Xa1) | s_t(Xp,crossbar(Xa,Xb,Xc,Xa1,Xb1,Xp),Xc) | -s_t(Xa1,Xb1,Xc) | -s_t(Xa,Xb,Xc)) & (-s_t(Xa1,Xb1,Xc) | s_t(Xb,crossbar(Xa,Xb,Xc,Xa1,Xb1,Xp),Xb1) | -s_t(Xa,Xp,Xa1) | -s_t(Xa,Xb,Xc)))) # label(aSatz3_17) # label(axiom) # label(non_clause). [assumption]. 1.06/1.33 135 (all Xp all Xq all Xa all Xb all Xt ((-opposite(Xa,Xp,Xq,Xb) | -s_col(Xp,Xq,Xb)) & (s_col(Xp,Xq,il(Xa,Xb,Xp,Xq)) | -opposite(Xa,Xp,Xq,Xb)) & (-opposite(Xa,Xp,Xq,Xb) | s_t(Xa,il(Xa,Xb,Xp,Xq),Xb)) & (-s_col(Xp,Xq,Xa) | -opposite(Xa,Xp,Xq,Xb)) & (Xp = Xq | s_col(Xp,Xq,Xa) | s_col(Xp,Xq,Xb) | -s_t(Xa,Xt,Xb) | -s_col(Xp,Xq,Xt) | opposite(Xa,Xp,Xq,Xb)))) # label(d_Defn9_1) # label(axiom) # label(non_clause). [assumption]. 1.06/1.33 136 (all Xp all Xa all Xb all Xq all Xt all Xr all Xcx (-perp(Xq,Xb,Xa,Xb) | -s_t(Xp,Xt,Xq) | -s_t(Xb,Xr,Xq) | s_m(Xa,Xcx,Xb) | Xcx != ip(Xp,Xt,Xq,Xb,Xr) | -s_e(Xa,Xp,Xb,Xr) | -s_col(Xa,Xb,Xt) | -perp(Xp,Xa,Xa,Xb))) # label(aSatz8_24a) # label(axiom) # label(non_clause). [assumption]. 1.06/1.33 137 (all Xp all Xa all Xq (Xq = s(Xa,Xp) | -s_m(Xp,Xa,Xq))) # label(aSatz7_6) # label(axiom) # label(non_clause). [assumption]. 1.06/1.33 138 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_t(Xa,Xb,Xc) | -s_t(Xa1,Xb1,Xc1) | -s_e(Xa,Xb,Xa1,Xb1) | s_e(Xa,Xc,Xa1,Xc1) | -s_e(Xb,Xc,Xb1,Xc1))) # label(aSatz2_11) # label(axiom) # label(non_clause). [assumption]. 1.06/1.33 139 (all Xa all Xp all Xq all Xc all Xcs all Xr all Xm all U (Xp = Xq | -perp(Xp,Xq,Xa,Xr) | -perp(Xp,Xq,Xc,Xcs) | -sameside(U,Xr,Xa) | -le(Xcs,Xc,Xr,Xa) | Xr = Xcs | sameside(s(Xm,U),Xcs,Xc) | -s_m(Xr,Xm,Xcs) | -s_col(Xp,Xq,Xr) | -s_col(Xp,Xq,Xcs) | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_4a) # label(axiom) # label(non_clause). [assumption]. 1.06/1.33 140 (all Xa all Xb s_t(Xa,Xb,ext(Xa,Xb,alpha,gamma))) # label(aSatz3_14a) # label(axiom) # label(non_clause). [assumption]. 1.06/1.33 141 (all Xa1 all Xb1 s_t(Xa1,Xa1,Xb1)) # label(aSatz3_3) # label(axiom) # label(non_clause). [assumption]. 1.06/1.33 142 (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]. 1.06/1.33 143 (all Xp all Xq all Xr all Xa (Xq = Xp | -s_t(Xq,Xp,Xr) | Xa = Xp | sameside(Xa,Xp,Xq) | sameside(Xa,Xp,Xr) | -s_col(Xa,Xp,Xq) | Xp = Xr)) # label(aSatz6_15a) # label(axiom) # label(non_clause). [assumption]. 1.06/1.33 144 (all Xa all Xb all Xc (s_col(Xb,Xa,Xc) | -s_col(Xa,Xb,Xc))) # label(aSatz4_11d) # label(axiom) # label(non_clause). [assumption]. 1.06/1.33 145 (all Xa all Xp all Xb all Xc (-sameside(Xa,Xp,Xb) | s_t(Xb,Xp,Xc) | -s_t(Xa,Xp,Xc) | Xp = Xc | Xp = Xb | Xp = Xa)) # label(aSatz6_2b) # label(axiom) # label(non_clause). [assumption]. 1.06/1.33 146 (all Xa all Xb all Xp (s(Xa,s(Xb,Xp)) != s(Xb,s(Xa,Xp)) | Xb = Xa)) # label(aSatz7_19) # label(axiom) # label(non_clause). [assumption]. 1.06/1.33 147 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_e(Xb,Xc,Xb1,Xc1) | s_e(Xa,Xb,Xa1,Xb1) | -s_e(Xa,Xc,Xa1,Xc1) | -s_t(Xa1,Xb1,Xc1) | -s_t(Xa,Xb,Xc))) # label(aSatz4_3) # label(axiom) # label(non_clause). [assumption]. 1.06/1.33 148 (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]. 1.06/1.33 149 (all Xa all Xp all Xq all Xc all Xcs all Xr all Xm all U (Xp = Xq | -perp(Xp,Xq,Xa,Xr) | -perp(Xp,Xq,Xc,Xcs) | -sameside(U,Xr,Xa) | sameside(s(Xm,U),Xcs,Xc) | Xr != Xcs | -s_m(Xr,Xm,Xcs) | -s_col(Xp,Xq,Xr) | -s_col(Xp,Xq,Xcs) | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_4b) # label(axiom) # label(non_clause). [assumption]. 1.06/1.33 150 (all Xa all Xb all Xc (-le(Xb,Xc,Xa,Xc) | -le(Xa,Xb,Xa,Xc) | s_t(Xa,Xb,Xc) | -s_col(Xa,Xb,Xc))) # label(aSatz5_12b) # label(axiom) # label(non_clause). [assumption]. 1.06/1.33 151 (all Xa all Xb all Xp all Xq all Xc ((-s_col(Xa,Xb,Xq) | -s_col(Xa,Xb,Xc) | -perp(Xa,Xb,Xc,Xp) | Xp = Xq | -s_col(Xa,Xb,Xp) | Xa = Xb) & (Xb = Xa | -perp(Xa,Xb,Xc,Xp) | s_r(Xc,Xp,Xq) | Xp = Xq | -s_col(Xa,Xb,Xq) | -s_col(Xa,Xb,Xp)))) # label(aSatz8_16a) # label(axiom) # label(non_clause). [assumption]. 1.06/1.33 152 (all Xa all Xp (Xa = Xp | sameside(Xa,Xp,Xa))) # label(aSatz6_5) # label(axiom) # label(non_clause). [assumption]. 1.06/1.33 153 (all Xa all Xp (Xp != s(Xa,Xp) | Xa = Xp)) # label(aSatz7_10a) # label(axiom) # label(non_clause). [assumption]. 1.06/1.33 154 (all Xr all Xa all Xb all Xc ((Xr = Xa | Xb = Xc | sameside(insert(Xb,Xc,Xa,Xr),Xa,Xr)) & (Xa = Xr | s_e(Xa,insert(Xb,Xc,Xa,Xr),Xb,Xc) | Xc = Xb))) # label(aSatz6_11a) # label(axiom) # label(non_clause). [assumption]. 1.06/1.34 155 (all Xa all Xb all Xp all Xq all Xc (Xa = Xb | -s_col(Xa,Xb,Xp) | perp(Xa,Xb,Xc,Xp) | -s_r(Xc,Xp,Xq) | s_col(Xa,Xb,Xc) | Xq = Xp | -s_col(Xa,Xb,Xq))) # label(aSatz8_16b) # label(axiom) # label(non_clause). [assumption]. 1.06/1.34 156 (all Xa all Xp all Xq (Xq = Xp | s(Xa,Xq) != s(Xa,Xp))) # label(aSatz7_9) # label(axiom) # label(non_clause). [assumption]. 1.06/1.34 157 (all Xa all Xb all Xc all Xd (Xa = Xb | -s_t(Xa,Xb,Xc) | s_t(Xb,Xc,Xd) | s_t(Xb,Xd,Xc) | -s_t(Xa,Xb,Xd))) # label(aSatz5_2) # label(axiom) # label(non_clause). [assumption]. 1.06/1.34 158 (all Xp all Xa all Xr all Xq (-s_m(Xp,Xa,Xr) | -s_m(Xp,Xa,Xq) | Xq = Xr)) # label(aSatz7_4b) # label(axiom) # label(non_clause). [assumption]. 1.06/1.34 159 (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)) & (-perpAt(Y,Z,X,Y1,Z1) | s_col(Y1,Z1,X)) & (Z != Y | -perpAt(Y,Z,X,Y1,Z1)) & (-perpAt(Y,Z,X,Y1,Z1) | s_r(U,X,V) | -s_col(Y1,Z1,V) | -s_col(Y,Z,U)) & (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) | Y1 = Z1 | Y = Z) & (perpAt(Y,Z,X,Y1,Z1) | -s_r(f811(Y,Z,Y1,Z1,X),X,g811(Y,Z,Y1,Z1,X)) | -s_col(Y1,Z1,X) | -s_col(Y,Z,X) | Z1 = Y1 | Z = Y) & (perpAt(Y,Z,X,Y1,Z1) | Y = Z | -s_col(Y,Z,X) | s_col(Y,Z,f811(Y,Z,Y1,Z1,X)) | -s_col(Y1,Z1,X) | Z1 = Y1) & (Y1 != Z1 | -perpAt(Y,Z,X,Y1,Z1)))) # label(d_Defn8_11a) # label(axiom) # label(non_clause). [assumption]. 1.06/1.34 160 (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]. 1.06/1.34 161 (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]. 1.06/1.34 162 (all Xa all Xb all Xc ((s_col(Xa,Xb,Xc) | -s_t(Xa,Xb,Xc)) & (s_col(Xa,Xb,Xc) | -s_t(Xc,Xa,Xb)) & (-s_t(Xb,Xc,Xa) | s_col(Xa,Xb,Xc)) & (-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]. 1.06/1.34 163 (all Xa all Xb all Xp all Xq all Xc all Xd (Xp = Xq | perp(Xa,Xb,Xc,Xd) | -perp(Xp,Xq,Xc,Xd) | Xa = Xb | -s_col(Xa,Xb,Xq) | -s_col(Xa,Xb,Xp))) # label(aExtPerp2) # label(axiom) # label(non_clause). [assumption]. 1.06/1.34 164 (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_col(Xp,Xq,Xr) | -sameside(Xa,Xr,Xb) | opposite(Xb,Xp,Xq,Xc) | -s_m(Xa,Xm,Xc))) # label(aSatz9_3) # label(axiom) # label(non_clause). [assumption]. 1.06/1.34 165 (all Xa all Xb all Xc (Xb = Xa | -s_t(Xb,Xa,Xc) | -s_t(Xa,Xb,Xc))) # label(aSatz3_4) # label(axiom) # label(non_clause). [assumption]. 1.06/1.34 166 (all Xa all Xb (Xa = Xb | -s_r(Xa,Xb,Xa))) # label(aSatz8_8) # label(axiom) # label(non_clause). [assumption]. 1.06/1.34 167 (all Xa all Xb s_e(Xa,Xb,Xa,Xb)) # label(aSatz2_1) # label(axiom) # label(non_clause). [assumption]. 1.06/1.34 168 (all Xp all Xq all Xa all Xz all Xb all Xc (Xp = Xq | -s_e(Xa,Xp,Xz,Xq) | -s_e(Xc,Xp,Xc,Xq) | s_t(Xa,Xb,Xc) | s_t(Xb,Xc,Xa) | s_t(Xc,Xa,Xb) | -s_e(Xb,Xp,Xb,Xq))) # label(aA9) # label(axiom) # label(non_clause). [assumption]. 1.06/1.34 169 (all Xa all Xb all Xc ((-s_r(Xa,Xb,Xc) | s_e(Xa,Xc,Xa,s(Xb,Xc))) & (s_r(Xa,Xb,Xc) | -s_e(Xa,Xc,Xa,s(Xb,Xc))))) # label(d_Defn8_1) # label(axiom) # label(non_clause). [assumption]. 1.06/1.34 170 (all Xa all Xp all Xb all Xc (-sameside(Xa,Xp,Xb) | sameside(Xa,Xp,Xc) | -sameside(Xb,Xp,Xc))) # label(aSatz6_7) # label(axiom) # label(non_clause). [assumption]. 1.06/1.34 171 (all Xa all Xp all Xb ((Xa != Xp | -sameside(Xa,Xp,Xb)) & (-sameside(Xa,Xp,Xb) | Xp != c63(Xa,Xp,Xb)) & (-sameside(Xa,Xp,Xb) | s_t(Xa,Xp,c63(Xa,Xp,Xb))) & (-sameside(Xa,Xp,Xb) | s_t(Xb,Xp,c63(Xa,Xp,Xb))) & (Xb != Xp | -sameside(Xa,Xp,Xb)))) # label(aSatz6_3a) # label(axiom) # label(non_clause). [assumption]. 1.06/1.34 172 (all Xa all Xb all Xp all Xq (-perp(Xa,Xb,Xp,Xq) | perp(Xa,Xb,Xq,Xp))) # label(aExtPerp4) # label(axiom) # label(non_clause). [assumption]. 1.06/1.34 173 (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]. 1.06/1.34 174 (all Xa all Xp all Xb (sameside(Xa,Xp,Xb) | s_t(Xa,Xp,Xb) | -s_col(Xa,Xp,Xb))) # label(aSatz6_4b) # label(axiom) # label(non_clause). [assumption]. 1.06/1.34 175 (all Xa all Xb all Xd all Xc (-perp(Xa,Xb,Xc,Xd) | perpAt(Xa,Xb,Xd,Xc,Xd) | -s_col(Xa,Xb,Xd) | Xb = Xa)) # label(aSatz8_15) # label(axiom) # label(non_clause). [assumption]. 1.06/1.34 176 (all Xp all Xq all Xr all Xa (Xr = Xp | -s_t(Xq,Xp,Xr) | s_col(Xa,Xp,Xq) | -sameside(Xa,Xp,Xr) | Xp = Xq)) # label(aSatz6_15c) # label(axiom) # label(non_clause). [assumption]. 1.06/1.34 177 (all Xa all Xp s(Xa,s(Xa,Xp)) = Xp) # label(aSatz7_7) # label(axiom) # label(non_clause). [assumption]. 1.06/1.34 178 (all Xp all Xq (Xp = Xq | s_col(Xp,Xq,Xp))) # label(aSatz6_17a) # label(axiom) # label(non_clause). [assumption]. 1.06/1.34 179 (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_15a) # label(axiom) # label(non_clause). [assumption]. 1.06/1.34 180 (all Xa all Xb all Xc all Xd (-s_e(Xa,Xb,Xc,Xd) | s_e(Xc,Xd,Xa,Xb))) # label(aSatz2_2) # label(axiom) # label(non_clause). [assumption]. 1.06/1.34 181 (all Xa1 all Xc all Xa2 all Xb1 all Xb2 all Xm1 all Xm2 (-s_m(Xa1,Xm1,Xb1) | -s_m(Xa2,Xm2,Xb2) | s_t(Xm1,Xc,Xm2) | -s_e(Xc,Xa2,Xc,Xb2) | -s_e(Xc,Xa1,Xc,Xb1) | -s_t(Xb1,Xc,Xb2) | -s_t(Xa1,Xc,Xa2))) # label(aSatz7_22) # label(axiom) # label(non_clause). [assumption]. 1.06/1.34 182 (all Xa all Xp all Xr all Xq (Xp = Xq | Xr != s(Xa,Xq) | Xr != s(Xa,Xp))) # label(aSatz7_8) # label(axiom) # label(non_clause). [assumption]. 1.06/1.34 183 (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]. 1.06/1.34 184 (all Xq all Xa all Xd all Xb all Xc (Xq = Xa | ext(Xq,Xa,Xb,Xc) = Xd | -s_e(Xa,Xd,Xb,Xc) | -s_t(Xq,Xa,Xd))) # label(aSatz2_12) # label(axiom) # label(non_clause). [assumption]. 1.06/1.34 185 (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(Xa,Xc,Za,Zc)) & (s_e(Xa,Xd,Za,Zd) | -s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)) & (-s_t(Xa,Xb,Xc) | -s_t(Za,Zb,Zc) | -s_e(Xa,Xc,Za,Zc) | -s_e(Xa,Xd,Za,Zd) | -s_e(Xc,Xd,Zc,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(Xc,Xd,Zc,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)) & (-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]. 1.06/1.34 186 (all Xa all Xp all Xq all Xc all Xcs all Xr all Xm all U all V (Xq = Xp | -s_col(Xp,Xq,Xcs) | -s_col(Xp,Xq,Xr) | -perp(Xp,Xq,Xa,Xr) | -perp(Xp,Xq,Xc,Xcs) | -s_m(Xr,Xm,Xcs) | -sameside(U,Xr,Xa) | -sameside(V,Xcs,Xc) | opposite(U,Xp,Xq,V) | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_4c) # label(axiom) # label(non_clause). [assumption]. 1.06/1.34 187 (all Xa all Xb all Xc all Xd all Y ((-le(Xa,Xb,Xc,Xd) | s_t(Xc,insert(Xa,Xb,Xc,Xd),Xd)) & (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)))) # label(d_Defn5_4) # label(axiom) # label(non_clause). [assumption]. 1.06/1.34 188 (all Xp all Xq all Xr all Xa (Xp = Xq | Xa != Xp | s_col(Xa,Xp,Xq) | -s_t(Xq,Xp,Xr) | Xr = Xp)) # label(aSatz6_15d) # label(axiom) # label(non_clause). [assumption]. 1.06/1.34 189 (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]. 1.06/1.34 190 -(all Xp all Xq all Xr all Xcs (s_col(Xp,Xq,Xr) | s_col(Xp,Xq,Xcs) | foot(Xp,Xq,Xr) != Xp | opposite(Xr,Xp,Xq,Xcs) | samesideline(Xr,Xcs,Xp,Xq) | Xq = Xp)) # label(aLemma9_13f_case1) # label(negated_conjecture) # label(non_clause). [assumption]. 1.06/1.34 1.06/1.34 ============================== end of process non-clausal formulas === 1.06/1.34 1.06/1.34 ============================== PROCESS INITIAL CLAUSES =============== 1.06/1.34 1.06/1.34 ============================== PREDICATE ELIMINATION ================= 1.06/1.34 191 -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) | -s_col(A,B,C) # label(d_Defn4_15) # label(axiom). [clausify(68)]. 1.06/1.34 192 -s_t(A,B,C) | s_e3(A,B,C,D,insert(A,B,D,E),E) | -s_e(A,C,D,E) # label(aSatz4_5) # label(axiom). [clausify(32)]. 1.06/1.35 193 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(56)]. 1.06/1.35 Derived: -s_e(A,B,C,D) | s_fs(A,E,F,B,C,insert(A,E,C,V6),V6,D) | -s_e(E,B,insert(A,E,C,V6),D) | -s_col(A,E,F) | -s_t(A,E,F) | -s_e(A,F,C,V6). [resolve(191,a,192,b)]. 1.06/1.35 Derived: -s_e(A,B,C,D) | s_fs(A,E,F,B,C,V6,insert5(A,E,F,C,V6),D) | -s_e(E,B,V6,D) | -s_col(A,E,F) | -s_e(A,E,C,V6) | -s_col(A,E,F). [resolve(191,a,193,a)]. 1.06/1.35 194 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(68)]. 1.06/1.35 Derived: -s_fs(A,B,C,D,E,F,V6,V7) | -s_e(A,V8,E,V9) | s_fs(A,B,C,V8,E,F,V6,V9) | -s_e(B,V8,F,V9) | -s_col(A,B,C). [resolve(194,a,191,a)]. 1.06/1.35 195 -s_e3(A,B,C,D,E,F) | s_col(D,E,F) | -s_col(A,B,C) # label(aSatz4_13) # label(axiom). [clausify(85)]. 1.06/1.35 Derived: s_col(A,insert(B,C,A,D),D) | -s_col(B,C,E) | -s_t(B,C,E) | -s_e(B,E,A,D). [resolve(195,a,192,b)]. 1.06/1.35 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(195,a,193,a)]. 1.06/1.35 Derived: s_col(A,B,C) | -s_col(D,E,F) | -s_fs(D,E,F,V6,A,B,C,V7). [resolve(195,a,194,a)]. 1.06/1.35 196 -s_e(A,B,C,D) | s_e3(A,E,B,C,F,D) | -s_e(E,B,F,D) | -s_e(A,E,C,F) # label(d_Defn4_4) # label(axiom). [clausify(119)]. 1.06/1.35 Derived: -s_e(A,B,C,D) | -s_e(E,B,F,D) | -s_e(A,E,C,F) | -s_e(A,V6,C,V7) | s_fs(A,E,B,V6,C,F,D,V7) | -s_e(E,V6,F,V7) | -s_col(A,E,B). [resolve(196,b,191,a)]. 1.06/1.35 Derived: -s_e(A,B,C,D) | -s_e(E,B,F,D) | -s_e(A,E,C,F) | s_col(C,F,D) | -s_col(A,E,B). [resolve(196,b,195,a)]. 1.06/1.35 197 s_e(A,B,C,D) | -s_e3(E,A,B,F,C,D) # label(d_Defn4_4) # label(axiom). [clausify(119)]. 1.06/1.35 Derived: s_e(A,B,insert(C,A,D,E),E) | -s_t(C,A,B) | -s_e(C,B,D,E). [resolve(197,b,192,b)]. 1.06/1.35 Derived: s_e(A,B,C,insert5(D,A,B,E,C)) | -s_e(D,A,E,C) | -s_col(D,A,B). [resolve(197,b,193,a)]. 1.06/1.35 Derived: s_e(A,B,C,D) | -s_fs(E,A,B,F,V6,C,D,V7). [resolve(197,b,194,a)]. 1.06/1.35 198 s_e(A,B,C,D) | -s_e3(A,E,B,C,F,D) # label(d_Defn4_4) # label(axiom). [clausify(119)]. 1.06/1.35 Derived: s_e(A,B,C,insert5(A,D,B,C,E)) | -s_e(A,D,C,E) | -s_col(A,D,B). [resolve(198,b,193,a)]. 1.06/1.35 Derived: s_e(A,B,C,D) | -s_fs(A,E,B,F,C,V6,D,V7). [resolve(198,b,194,a)]. 1.06/1.35 199 -s_e3(A,B,C,D,E,F) | s_e(A,B,D,E) # label(d_Defn4_4) # label(axiom). [clausify(119)]. 1.06/1.35 Derived: s_e(A,B,C,insert(A,B,C,D)) | -s_t(A,B,E) | -s_e(A,E,C,D). [resolve(199,a,192,b)]. 1.06/1.35 Derived: s_e(A,B,C,D) | -s_fs(A,B,E,F,C,D,V6,V7). [resolve(199,a,194,a)]. 1.06/1.35 200 -s_r(A,B,C) | s_r(D,E,F) | -s_e3(A,B,C,D,E,F) # label(aSatz8_10) # label(axiom). [clausify(127)]. 1.06/1.35 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(200,c,192,b)]. 1.06/1.35 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(200,c,193,a)]. 1.06/1.35 Derived: -s_r(A,B,C) | s_r(D,E,F) | -s_fs(A,B,C,V6,D,E,F,V7). [resolve(200,c,194,a)]. 1.06/1.35 Derived: -s_r(A,B,C) | s_r(D,E,F) | -s_e(A,C,D,F) | -s_e(B,C,E,F) | -s_e(A,B,D,E). [resolve(200,c,196,b)]. 1.06/1.35 201 -s_t(A,B,C) | -s_e3(A,B,C,D,E,F) | s_t(D,E,F) # label(aSatz4_6) # label(axiom). [clausify(161)]. 1.06/1.35 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(201,b,192,b)]. 1.06/1.35 Derived: -s_t(A,B,C) | s_t(D,E,insert5(A,B,C,D,E)) | -s_e(A,B,D,E) | -s_col(A,B,C). [resolve(201,b,193,a)]. 1.06/1.35 Derived: -s_t(A,B,C) | s_t(D,E,F) | -s_fs(A,B,C,V6,D,E,F,V7). [resolve(201,b,194,a)]. 1.06/1.35 Derived: -s_t(A,B,C) | s_t(D,E,F) | -s_e(A,C,D,F) | -s_e(B,C,E,F) | -s_e(A,B,D,E). [resolve(201,b,196,b)]. 1.06/1.35 202 -s_t(A,B,C) | -s_e(D,E,B,C) | -s_e(F,V6,A,V7) | s_afs(F,D,E,V6,A,B,C,V7) | -s_e(D,V6,B,V7) | -s_e(F,D,A,B) | -s_t(F,D,E) # label(d_Defn2_10) # label(axiom). [clausify(42)]. 1.06/1.35 203 -s_afs(A,B,C,D,E,F,V6,V7) | s_t(A,B,C) # label(d_Defn2_10) # label(axiom). [clausify(42)]. 1.06/1.35 204 -s_afs(A,B,C,D,E,F,V6,V7) | s_t(E,F,V6) # label(d_Defn2_10) # label(axiom). [clausify(42)]. 1.06/1.35 205 -s_afs(A,B,C,D,E,F,V6,V7) | s_e(B,C,F,V6) # label(d_Defn2_10) # label(axiom). [clausify(42)]. 1.06/1.35 206 -s_afs(A,B,C,D,E,F,V6,V7) | s_e(A,D,E,V7) # label(d_Defn2_10) # label(axiom). [clausify(42)]. 1.06/1.35 207 -s_afs(A,B,C,D,E,F,V6,V7) | s_e(B,D,F,V7) # label(d_Defn2_10) # label(axiom). [clausify(42)]. 2.49/2.73 208 -s_afs(A,B,C,D,E,F,V6,V7) | s_e(A,B,E,F) # label(d_Defn2_10) # label(axiom). [clausify(42)]. 2.49/2.73 209 -s_t(A,B,C) | -s_e(B,A,B,D) | -s_e(B,C,B,E) | s_kf(A,F,D,B,E,V6,C) | -s_m(C,V6,E) | -s_m(A,F,D) | -s_t(D,B,E) # label(d_Defn7_23) # label(axiom). [clausify(49)]. 2.49/2.73 210 -s_kf(A,B,C,D,E,F,V6) | s_t(C,D,E) # label(d_Defn7_23) # label(axiom). [clausify(49)]. 2.49/2.73 211 s_e(A,B,A,C) | -s_kf(B,D,C,A,E,F,V6) # label(d_Defn7_23) # label(axiom). [clausify(49)]. 2.49/2.73 212 s_m(A,B,C) | -s_kf(A,B,C,D,E,F,V6) # label(d_Defn7_23) # label(axiom). [clausify(49)]. 2.49/2.73 213 s_m(A,B,C) | -s_kf(D,E,F,V6,C,B,A) # label(d_Defn7_23) # label(axiom). [clausify(49)]. 2.49/2.73 214 s_e(A,B,A,C) | -s_kf(D,E,F,A,C,V6,B) # label(d_Defn7_23) # label(axiom). [clausify(49)]. 2.49/2.73 215 s_t(A,B,C) | -s_kf(A,D,E,B,F,V6,C) # label(d_Defn7_23) # label(axiom). [clausify(49)]. 2.49/2.73 216 -le(A,B,A,C) | s_t(D,A,E) | -s_kf(B,D,F,A,V6,E,C) # label(aSatz7_22a) # label(axiom). [clausify(80)]. 2.49/2.73 217 s_t(A,B,C) | -s_kf(D,A,E,B,F,C,V6) # label(aSatz7_22b) # label(axiom). [clausify(102)]. 2.49/2.73 218 -s_t(A,B,C) | -s_t(D,E,F) | -s_e(A,C,D,F) | -s_e(A,V6,D,V7) | -s_e(C,V6,F,V7) | s_ifs(A,B,C,V6,D,E,F,V7) | -s_e(B,C,E,F) # label(d_Defn4_1) # label(axiom). [clausify(185)]. 2.49/2.73 219 -s_ifs(A,B,C,D,E,F,V6,V7) | s_e(B,D,F,V7) # label(aSatz4_2) # label(axiom). [clausify(60)]. 2.49/2.73 220 -s_ifs(A,B,C,D,E,F,V6,V7) | s_e(A,C,E,V6) # label(d_Defn4_1) # label(axiom). [clausify(185)]. 2.49/2.73 221 s_e(A,B,C,D) | -s_ifs(A,E,F,B,C,V6,V7,D) # label(d_Defn4_1) # label(axiom). [clausify(185)]. 2.49/2.73 Derived: -s_t(A,B,C) | -s_t(D,E,F) | -s_e(A,C,D,F) | -s_e(A,V6,D,V7) | -s_e(C,V6,F,V7) | -s_e(B,C,E,F) | s_e(B,V6,E,V7). [resolve(218,f,219,a)]. 2.49/2.73 222 -s_ifs(A,B,C,D,E,F,V6,V7) | s_e(C,D,V6,V7) # label(d_Defn4_1) # label(axiom). [clausify(185)]. 2.49/2.73 223 -s_ifs(A,B,C,D,E,F,V6,V7) | s_e(B,C,F,V6) # label(d_Defn4_1) # label(axiom). [clausify(185)]. 2.49/2.73 224 s_t(A,B,C) | -s_ifs(D,E,F,V6,A,B,C,V7) # label(d_Defn4_1) # label(axiom). [clausify(185)]. 2.49/2.73 225 -s_ifs(A,B,C,D,E,F,V6,V7) | s_t(A,B,C) # label(d_Defn4_1) # label(axiom). [clausify(185)]. 2.49/2.73 2.49/2.73 ============================== end predicate elimination ============= 2.49/2.73 2.49/2.73 Auto_denials: (non-Horn, no changes). 2.49/2.73 2.49/2.73 Term ordering decisions: 2.49/2.73 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. 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. 2.49/2.73 2.49/2.73 ============================== end of process initial clauses ======== 2.49/2.73 2.49/2.73 ============================== CLAUSES FOR SEARCH ==================== 2.49/2.73 2.49/2.73 ============================== end of clauses for search ============= 2.49/2.73 2.49/2.73 ============================== SEARCH ================================ 2.49/2.73 2.49/2.73 % Starting search at 0.13 seconds. 2.49/2.73 2.49/2.73 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 30 (0.00 of 0.68 sec). 2.49/2.73 2.49/2.73 Low Water (keep): wt=61.000, iters=3346 2.49/2.73 2.49/2.73 Low Water (keep): wt=58.000, iters=3351 2.49/2.73 2.49/2.73 Low Water (keep): wt=54.000, iters=3355 2.49/2.73 2.49/2.73 Low Water (keep): wt=51.000, iters=3392 2.49/2.73 2.49/2.73 Low Water (keep): wt=48.000, iters=3380 2.49/2.73 2.49/2.73 Low Water (keep): wt=46.000, iters=3350 2.49/2.73 2.49/2.73 Low Water (keep): wt=45.000, iters=3388 2.49/2.73 2.49/2.73 Low Water (keep): wt=44.000, iters=3400 2.49/2.73 2.49/2.73 Low Water (keep): wt=43.000, iters=3359 2.49/2.73 2.49/2.73 Low Water (keep): wt=42.000, iters=3375 2.49/2.73 2.49/2.73 Low Water (keep): wt=41.000, iters=3351 2.49/2.73 2.49/2.73 Low Water (keep): wt=40.000, iters=3387 2.49/2.73 2.49/2.73 Low Water (keep): wt=39.000, iters=3350 2.49/2.73 2.49/2.73 Low Water (keep): wt=37.000, iters=3333 2.49/2.73 2.49/2.73 Low Water (keep): wt=36.000, iters=3338 2.49/2.73 2.49/2.73 Low Water (keep): wt=34.000, iters=3358 2.49/2.73 2.49/2.73 Low Water (keep): wt=33.000, iters=3333 2.49/2.73 2.49/2.73 Low Water (keep): wt=31.000, iters=3363 2.49/2.73 2.49/2.73 Low Water (keep): wt=28.000, iters=5292 2.49/2.73 2.49/2.73 Low Water (keep): wt=27.000, iters=4964 2.49/2.73 2.49/2.73 Low Water (keep): wt=24.000, iters=3345 2.49/2.73 2.49/2.73 Low Water (keep): wt=23.000, iters=3376 2.49/2.73 2.49/2.73 Low Water (keep): wt=22.000, iters=3333 2.49/2.73 2.49/2.73 Low Water (keep): wt=21.000, iters=3470 2.49/2.73 2.49/2.73 Low Water (keep): wt=20.000, iters=3402 2.49/2.73 2.49/2.73 Low Water (keep): wt=19.000, iters=3670 2.49/2.73 2.49/2.73 Low Water (keep): wt=18.000, iters=3430 2.49/2.73 2.49/2.73 Low Water (dAlarm clock 179.78/180.02 Prover9 interrupted 179.78/180.03 EOF