0.04/0.14 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.13/0.15 % Command : tptp2X_and_run_prover9 %d %s 0.14/0.36 % Computer : n020.cluster.edu 0.14/0.36 % Model : x86_64 x86_64 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.36 % Memory : 8042.1875MB 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.37 % CPULimit : 1440 0.14/0.37 % WCLimit : 180 0.14/0.37 % DateTime : Mon Jul 3 07:36:31 EDT 2023 0.14/0.37 % CPUTime : 1.26/1.70 ============================== Prover9 =============================== 1.26/1.70 Prover9 (32) version 2009-11A, November 2009. 1.26/1.70 Process 31369 was started by sandbox2 on n020.cluster.edu, 1.26/1.70 Mon Jul 3 07:36:32 2023 1.26/1.70 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1440 -f /tmp/Prover9_31136_n020.cluster.edu". 1.26/1.70 ============================== end of head =========================== 1.26/1.70 1.26/1.70 ============================== INPUT ================================= 1.26/1.70 1.26/1.70 % Reading from file /tmp/Prover9_31136_n020.cluster.edu 1.26/1.70 1.26/1.70 set(prolog_style_variables). 1.26/1.70 set(auto2). 1.26/1.70 % set(auto2) -> set(auto). 1.26/1.70 % set(auto) -> set(auto_inference). 1.26/1.70 % set(auto) -> set(auto_setup). 1.26/1.70 % set(auto_setup) -> set(predicate_elim). 1.26/1.70 % set(auto_setup) -> assign(eq_defs, unfold). 1.26/1.70 % set(auto) -> set(auto_limits). 1.26/1.70 % set(auto_limits) -> assign(max_weight, "100.000"). 1.26/1.70 % set(auto_limits) -> assign(sos_limit, 20000). 1.26/1.70 % set(auto) -> set(auto_denials). 1.26/1.70 % set(auto) -> set(auto_process). 1.26/1.70 % set(auto2) -> assign(new_constants, 1). 1.26/1.70 % set(auto2) -> assign(fold_denial_max, 3). 1.26/1.70 % set(auto2) -> assign(max_weight, "200.000"). 1.26/1.70 % set(auto2) -> assign(max_hours, 1). 1.26/1.70 % assign(max_hours, 1) -> assign(max_seconds, 3600). 1.26/1.70 % set(auto2) -> assign(max_seconds, 0). 1.26/1.70 % set(auto2) -> assign(max_minutes, 5). 1.26/1.70 % assign(max_minutes, 5) -> assign(max_seconds, 300). 1.26/1.70 % set(auto2) -> set(sort_initial_sos). 1.26/1.70 % set(auto2) -> assign(sos_limit, -1). 1.26/1.70 % set(auto2) -> assign(lrs_ticks, 3000). 1.26/1.70 % set(auto2) -> assign(max_megs, 400). 1.26/1.70 % set(auto2) -> assign(stats, some). 1.26/1.70 % set(auto2) -> clear(echo_input). 1.26/1.70 % set(auto2) -> set(quiet). 1.26/1.70 % set(auto2) -> clear(print_initial_clauses). 1.26/1.70 % set(auto2) -> clear(print_given). 1.26/1.70 assign(lrs_ticks,-1). 1.26/1.70 assign(sos_limit,10000). 1.26/1.70 assign(order,kbo). 1.26/1.70 set(lex_order_vars). 1.26/1.70 clear(print_given). 1.26/1.70 1.26/1.70 % formulas(sos). % not echoed (212 formulas) 1.26/1.70 1.26/1.70 ============================== end of input ========================== 1.26/1.70 1.26/1.70 % From the command line: assign(max_seconds, 1440). 1.26/1.70 1.26/1.70 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 1.26/1.70 1.26/1.70 % Formulas that are not ordinary clauses: 1.26/1.70 1 (all X all Y (Y = X | -s_t(X,Y,X))) # label(aA6) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 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]. 1.26/1.70 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]. 1.26/1.70 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]. 1.26/1.70 5 (all X all Y s_e(X,Y,Y,X)) # label(aA1) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 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]. 1.26/1.70 7 (all X all Y all Z (Y = X | -s_e(X,Y,Z,Z))) # label(aA3) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 8 (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]. 1.26/1.70 9 (all Xa all Xb all Xd all Xc (-s_t(Xa,Xc,Xd) | s_t(Xa,Xc,Xb) | s_t(Xa,Xb,Xc) | -s_t(Xa,Xb,Xd))) # label(aSatz5_3) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 10 (all Xr all Xa all Xb all Xc ((Xr = Xa | Xb = Xc | sameside(insert(Xb,Xc,Xa,Xr),Xa,Xr)) & (s_e(Xa,insert(Xb,Xc,Xa,Xr),Xb,Xc) | Xc = Xb | Xr = Xa))) # label(aSatz6_11a) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 11 (all Xa all Xb all Xc all Xp all Xq (perpAt(Xp,Xq,Xc,Xa,Xb) | -perpAt(Xa,Xb,Xc,Xp,Xq))) # label(aSatz8_12a) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 12 (all Xa all Xb all Xc all Xd all Xa1 all Xb1 all Xc1 all Xd1 (s_e(Xb,Xd,Xb1,Xd1) | -s_ifs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1))) # label(aSatz4_2) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 13 (all Xa all Xb all Xc all Xd all Xp (Xa = Xb | Xd = Xc | -s_col(Xa,Xb,Xd) | s_col(Xa,Xb,Xp) | -s_col(Xc,Xd,Xp) | -s_col(Xa,Xb,Xc))) # label(aExtCol2) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 14 (all Xa all Xp all Xb (s_t(Xp,Xa,Xb) | -le(Xp,Xa,Xp,Xb) | -sameside(Xa,Xp,Xb))) # label(aSatz6_13a) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 15 (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]. 1.26/1.70 16 (all Xa all Xm all Xb ((-s_t(Xa,Xm,Xb) | -s_e(Xm,Xa,Xm,Xb) | s_m(Xa,Xm,Xb)) & (-s_m(Xa,Xm,Xb) | s_e(Xm,Xa,Xm,Xb)) & (s_t(Xa,Xm,Xb) | -s_m(Xa,Xm,Xb)))) # label(d_Defn7_1) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 17 (all Xa all Xb all Xp all Xq (s_e(Xp,Xq,reflect(Xa,Xb,Xp),reflect(Xa,Xb,Xq)) | Xa = Xb)) # label(aSatz10_10) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 18 (all Xa all Xb all Xp (s_col(Xa,Xb,Xp) | reflect(Xa,Xb,Xp) != Xp | Xa = Xb)) # label(aSatz10_8a) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 19 (all Xa all Xb all Xc all Xd (-s_t(Xa,Xc,Xd) | s_t(Xb,Xc,Xd) | -s_t(Xa,Xb,Xc))) # label(aSatz3_6a) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 20 (all Xp all Xq all Xr all Xcs (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) | Xp = Xq)) # label(aLemma9_13f_case2) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 21 (all Xa all Xb all Xc all Xd (le(Xa,Xb,Xc,Xd) | le(Xc,Xd,Xa,Xb))) # label(aSatz5_10) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 22 (all Xa all Xp all Xb (Xb = Xa | s(Xa,Xp) != s(Xb,Xp))) # label(aSatz7_18) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 23 (all Xa all Xc all Xd le(Xa,Xa,Xc,Xd)) # label(aSatz5_11) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 24 (all Xa all Xb all Xc all Xd all Xe all Xf (-s_e(Xa,Xb,Xc,Xd) | s_e(Xa,Xb,Xe,Xf) | -s_e(Xc,Xd,Xe,Xf))) # label(aSatz2_3) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 25 (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]. 1.26/1.70 26 (all Xa all Xp all Xb (le(Xp,Xa,Xp,Xb) | -s_t(Xp,Xa,Xb) | -sameside(Xa,Xp,Xb))) # label(aSatz6_13b) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 27 (all Xa all Xb all Xc (-s_r(Xa,Xc,Xb) | Xc = Xb | -s_r(Xa,Xb,Xc))) # label(aSatz8_7) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 28 (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]. 1.26/1.70 29 (all Xa all Xp (Xa = Xp | sameside(Xa,Xp,Xa))) # label(aSatz6_5) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 30 (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]. 1.26/1.70 31 (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(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_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_t(Xb1,Xc,Xb2) | -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_e(Xc,Xa1,Xc,Xb1)) & (s_e(Xc,Xa2,Xc,Xb2) | -s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2)))) # label(d_Defn7_23) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 32 (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]. 1.26/1.70 33 (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]. 1.26/1.70 34 (all Xa all Xp all Xq all Xc all Xcs all Xr all Xm all U (-opposite(Xa,Xp,Xq,Xc) | -perp(Xp,Xq,Xc,Xcs) | sameside(s(Xm,U),Xcs,Xc) | Xcs != Xr | -sameside(U,Xr,Xa) | -s_m(Xr,Xm,Xcs) | -perp(Xp,Xq,Xa,Xr) | -s_col(Xp,Xq,Xr) | -s_col(Xp,Xq,Xcs) | Xq = Xp)) # label(aSatz9_4b) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 35 (all Xa all Xb all Xp all Xq all Xcx all U all V (Xa = Xb | Xq = Xp | -s_col(Xp,Xq,Xcx) | -s_col(Xa,Xb,Xcx) | -s_col(Xp,Xq,V) | V = Xcx | -s_r(U,Xcx,V) | perpAt(Xa,Xb,Xcx,Xp,Xq) | Xcx = U | -s_col(Xa,Xb,U))) # label(aSatz8_13b) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 36 (all Xa all Xb all Xc all Xa1 all Xb1 all Xp ((-s_t(Xa,Xb,Xc) | -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(Xb,crossbar(Xa,Xb,Xc,Xa1,Xb1,Xp),Xb1) | -s_t(Xa,Xp,Xa1) | -s_t(Xa1,Xb1,Xc)))) # label(aSatz3_17) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 37 (all Xa all Xp all Xb all Xc (Xa = Xp | Xp = Xb | sameside(Xa,Xp,Xb) | -s_t(Xb,Xp,Xc) | -s_t(Xa,Xp,Xc) | Xp = Xc)) # label(aSatz6_2a) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 38 (all Xa all Xp all Xq all Xc all Xm all Xr all Xb (-opposite(Xa,Xp,Xq,Xc) | -s_m(Xa,Xm,Xc) | opposite(Xb,Xp,Xq,Xc) | -sameside(Xa,Xr,Xb) | -s_col(Xp,Xq,Xr) | -s_col(Xp,Xq,Xm))) # label(aSatz9_3) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 39 (all Xa all Xb all Xc all Xd (Xb = Xa | Xa = Xc | Xb = Xc | Xd = Xa | -perp(Xb,Xa,Xa,Xc) | perp(Xb,Xa,Xa,Xd) | -s_col(Xa,Xc,Xd) | Xc = Xd)) # label(aExtPerp3) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 40 (all Xa all Xm all Xb (-s_col(Xa,Xm,Xb) | s_m(Xa,Xm,Xb) | Xb = Xa | -s_e(Xm,Xa,Xm,Xb))) # label(aSatz7_20) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 41 (all Xa all Xp all Xq all Xb all Xc (opposite(Xa,Xp,Xq,Xc) | -samesideline(Xb,Xc,Xp,Xq) | -opposite(Xa,Xp,Xq,Xb))) # label(aLemma9_13e) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 42 (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]. 1.26/1.70 43 (all Xa all Xb all Xc all Xd all Xp (s_col(Xa,Xb,Xc) | Xb = Xd | -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))) # label(aSatz7_21) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 44 (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]. 1.26/1.70 45 (all Xa all Xb all Xc (-s_e(Xa,Xc,Xa,Xb) | Xb = Xc | -s_t(Xa,Xb,Xc))) # label(aNarbouxLemma1) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 46 (all Xp all Xq all Xr all Xcs (s_col(Xp,Xq,Xcs) | samesideline(Xr,Xcs,Xp,Xq) | opposite(Xr,Xp,Xq,Xcs) | s_col(Xp,Xq,Xr) | Xq = Xp)) # label(aLemma9_13f) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 47 (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]. 1.26/1.70 48 (all Xp all Xq all Xcs all Xr (Xq = Xp | s_col(Xp,Xcs,Xr) | -s_col(Xp,Xq,Xr) | -s_col(Xp,Xq,Xcs) | Xp = Xcs)) # label(aSatz6_16b) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 49 (all Xa all Xp all Xb all Xc (-sameside(Xb,Xp,Xc) | sameside(Xa,Xp,Xc) | -sameside(Xa,Xp,Xb))) # label(aSatz6_7) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 50 (all Xa all Xb (Xb = Xa | -s_r(Xa,Xb,Xa))) # label(aSatz8_8) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 51 (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]. 1.26/1.70 52 (all Xa all Xb all Xp all Xq all Xr all Xc all Xd (Xp = Xq | perpAt(Xa,Xb,Xr,Xc,Xd) | -perpAt(Xp,Xq,Xr,Xc,Xd) | Xb = Xa | -s_col(Xa,Xb,Xq) | -s_col(Xa,Xb,Xp))) # label(aExtPerp) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 53 (all Xa all Xp all Xq all Xc all Xm all Xr all Xb (-s_m(Xa,Xm,Xc) | -s_col(Xp,Xq,Xr) | -s_t(Xr,Xb,Xa) | opposite(Xb,Xp,Xq,Xc) | -sameside(Xa,Xr,Xb) | -s_col(Xp,Xq,Xm) | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_3a) # label(axiom) # label(non_clause). [assumption]. 1.26/1.70 54 (all Xa all Xb all Xc all Xp all Xq (-perp(Xa,Xb,Xc,Xp) | Xp = Xq | -perp(Xa,Xb,Xc,Xq) | -s_col(Xa,Xb,Xq) | -s_col(Xa,Xb,Xp) | s_col(Xa,Xb,Xc))) # label(aSatz8_18a) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 55 (all Xa all Xb s_t(Xa,Xb,ext(Xa,Xb,alpha,gamma))) # label(aSatz3_14a) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 56 (all Xb all Xc all Xa (-s_e(Xb,Xc,Xa,Xa) | Xb = Xc)) # label(aSatz2_13) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 57 (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]. 1.26/1.71 58 (all Xp all Xq all Xa all Xb (-samesideline(Xp,Xq,Xa,Xb) | samesideline(Xp,Xq,Xb,Xa))) # label(aLemma9_13a) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 59 (all Xa1 all Xc all Xa2 all Xb1 all Xb2 all Xm1 all Xm2 (-s_e(Xc,Xa1,Xc,Xb1) | s_t(Xm1,Xc,Xm2) | -s_m(Xa2,Xm2,Xb2) | -s_m(Xa1,Xm1,Xb1) | -s_e(Xc,Xa2,Xc,Xb2) | -s_t(Xb1,Xc,Xb2) | -s_t(Xa1,Xc,Xa2))) # label(aSatz7_22) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 60 (all Xa all Xb all Xp all Xq all Xc (-s_col(Xa,Xb,Xc) | perpAt(Xa,Xb,Xc,Xp,Xq) | -s_col(Xp,Xq,Xc) | -perp(Xa,Xb,Xp,Xq))) # label(aSatz8_14b) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 61 (all Xa all Xb all Xc all Xd (-s_t(Xa,Xb,Xc) | s_t(Xa,Xb,Xd) | -s_t(Xa,Xc,Xd))) # label(aSatz3_6b) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 62 (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]. 1.26/1.71 63 (all Xp all Xa all Xr all Xq (-s_m(Xp,Xa,Xq) | Xq = Xr | -s_m(Xp,Xa,Xr))) # label(aSatz7_4b) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 64 (all Xa all Xp all Xb ((-sameside(Xa,Xp,Xb) | -s_t(Xa,Xp,Xb)) & (-sameside(Xa,Xp,Xb) | s_col(Xa,Xp,Xb)))) # label(aSatz6_4a) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 65 (all Xp all Xa all Xb all Xq all Xt all Xr (-perp(Xp,Xa,Xa,Xb) | -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))) # label(aSatz8_24) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 66 (all Xa all Xb all Xp (Xp = reflect(Xa,Xb,Xp) | -s_col(Xa,Xb,Xp) | Xa = Xb)) # label(aSatz10_8b) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 67 (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(Xa1,insert(Xa,Xb,Xa1,Xc1),Xc1) | -s_e(Xa,Xc,Xa1,Xc1) | -s_t(Xa,Xb,Xc)))) # label(aSatz4_5) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 68 (all Xa all Xb s_t(Xa,Xb,Xb)) # label(aSatz3_1) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 69 (all Xa all Xb s_e(Xa,Xb,Xa,Xb)) # label(aSatz2_1) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 70 (all Xa all Xb all Xc all Xp all Xq (-samesideline(Xp,Xq,Xa,Xb) | samesideline(Xp,Xq,Xa,Xc) | Xc = Xa | Xa = Xb | -s_col(Xa,Xb,Xc))) # label(aExtSameSide1) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 71 (all Xa all Xb all Xp all Xq (perp(Xa,Xb,Xq,Xp) | -perp(Xa,Xb,Xp,Xq))) # label(aExtPerp4) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 72 (all Xb all Xa ext(Xa,Xb,alpha,gamma) != Xb) # label(aSatz3_14b) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 73 (all Xa all Xp all Xq all Xc all Xcs all Xr all Xm all U (-opposite(Xa,Xp,Xq,Xc) | -s_col(Xp,Xq,Xcs) | -s_col(Xp,Xq,Xr) | -perp(Xp,Xq,Xc,Xcs) | -s_m(Xr,Xm,Xcs) | sameside(U,Xr,Xa) | -le(Xcs,Xc,Xr,Xa) | Xcs = Xr | -sameside(s(Xm,U),Xcs,Xc) | -perp(Xp,Xq,Xa,Xr) | Xp = Xq)) # label(aSatz9_4a2) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 74 (all Xa all Xp (Xa = Xp | Xp != s(Xa,Xp))) # label(aSatz7_10a) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 75 (all Xa all Xp all Xq all Xb (opposite(Xb,Xp,Xq,Xa) | -opposite(Xa,Xp,Xq,Xb))) # label(aSatz9_2) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 76 (all Y all Z all X all Y1 all Z1 all U all V ((-perpAt(Y,Z,X,Y1,Z1) | s_col(Y1,Z1,X)) & (-perpAt(Y,Z,X,Y1,Z1) | Y != Z) & (perpAt(Y,Z,X,Y1,Z1) | Z = Y | Z1 = Y1 | -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)) & (Z = Y | -s_col(Y,Z,X) | -s_col(Y1,Z1,X) | s_col(Y1,Z1,g811(Y,Z,Y1,Z1,X)) | Y1 = Z1 | perpAt(Y,Z,X,Y1,Z1)) & (Y = Z | Z1 = Y1 | -s_col(Y1,Z1,X) | s_col(Y,Z,f811(Y,Z,Y1,Z1,X)) | -s_col(Y,Z,X) | 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)) & (-perpAt(Y,Z,X,Y1,Z1) | Z1 != Y1) & (s_col(Y,Z,X) | -perpAt(Y,Z,X,Y1,Z1)))) # label(d_Defn8_11a) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 77 (all Xc all Xd all Xp all Xa all Xb (-s_col(Xc,Xd,Xp) | -sameside(Xa,Xp,Xb) | samesideline(Xa,Xb,Xc,Xd) | s_col(Xc,Xd,Xa) | -s_col(Xa,Xb,Xp) | Xd = Xc)) # label(aSatz9_19b) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 78 (all Xa all Xb all Xp all Xq all Xc all Xd (-s_col(Xa,Xb,Xq) | Xp = Xq | perp(Xa,Xb,Xc,Xd) | -perp(Xp,Xq,Xc,Xd) | Xb = Xa | -s_col(Xa,Xb,Xp))) # label(aExtPerp2) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 79 (all Xa all Xb all Xc all Xd (-s_t(Xa,Xb,Xc) | s_t(Xa,Xb,Xd) | Xb = Xc | -s_t(Xb,Xc,Xd))) # label(aSatz3_7b) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 80 (all Xp all Xq all Xr all Xcs (Xp = Xq | s_col(Xp,Xq,Xcs) | samesideline(Xr,Xcs,Xp,Xq) | Xp != foot(Xp,Xq,Xr) | opposite(Xr,Xp,Xq,Xcs) | s_col(Xp,Xq,Xr))) # label(aLemma9_13f_case1) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 81 (all Xa1 all Xa2 all Xa3 all Xb1 all Xb2 all Xb3 ((-s_e(Xa1,Xa2,Xb1,Xb2) | -s_e(Xa1,Xa3,Xb1,Xb3) | -s_e(Xa2,Xa3,Xb2,Xb3) | s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3)) & (s_e(Xa2,Xa3,Xb2,Xb3) | -s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3)) & (s_e(Xa1,Xa3,Xb1,Xb3) | -s_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]. 1.26/1.71 82 (all Xp all Xq all Xr all Xcs all Xa (-s_e(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr),s(Xa,Xcs)) | s_e(Xp,Xq,Xr,Xcs))) # label(aSatz7_16b) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 83 (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]. 1.26/1.71 84 (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]. 1.26/1.71 85 (all Xa all Xb all Xc all Xd (-s_t(Xb,Xc,Xd) | s_t(Xa,Xc,Xd) | Xb = Xc | -s_t(Xa,Xb,Xc))) # label(aSatz3_7a) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 86 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-sameside(Xa,Xb,Xc) | -s_e(Xb,Xc,Xb1,Xc1) | s_e(Xa,Xc,Xa1,Xc1) | -s_e(Xb,Xa,Xb1,Xa1) | -sameside(Xa1,Xb1,Xc1))) # label(aSatz6_28) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 87 (all Xa all Xc all Xp all Xb all Xq ((-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) | -s_t(Xb,Xq,Xc) | s_t(Xa,op(Xq,Xb,Xp,Xc,Xa),Xb)))) # label(aSatz9_6) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 88 (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]. 1.26/1.71 89 (all Xa all Xm all Xb (s_m(Xb,Xm,Xa) | -s_m(Xa,Xm,Xb))) # label(aSatz7_2) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 90 (all Xa all Xp all Xb (-s_col(Xa,Xp,Xb) | s_t(Xa,Xp,Xb) | sameside(Xa,Xp,Xb))) # label(aSatz6_4b) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 91 (all Xa all Xp Xp = s(Xa,s(Xa,Xp))) # label(aSatz7_7) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 92 (all Xa all Xb all Xp (Xa = Xb | s(Xb,s(Xa,Xp)) != s(Xa,s(Xb,Xp)))) # label(aSatz7_19) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 93 (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]. 1.26/1.71 94 (all Xa all Xb all Xc ((s_e(Xa,Xc,Xa,s(Xb,Xc)) | -s_r(Xa,Xb,Xc)) & (s_r(Xa,Xb,Xc) | -s_e(Xa,Xc,Xa,s(Xb,Xc))))) # label(d_Defn8_1) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 95 (all Xa all Xp all Xb all Xc (sameside(Xa,Xp,Xb) | Xa = Xp | -s_t(Xa,Xp,Xc) | -s_t(Xb,Xp,Xc) | Xp = Xc | Xb = Xp)) # label(aSatz6_3b) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 96 (all Xa all Xb all Xp all Xq all Xr (Xa = Xb | Xp = Xq | -s_col(Xp,Xq,Xa) | s_col(Xa,Xb,Xr) | -s_col(Xp,Xq,Xr) | -s_col(Xp,Xq,Xb))) # label(aSatz6_18) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 97 (all Xa all Xp all Xb ((-sameside(Xa,Xp,Xb) | Xb != Xp) & (-sameside(Xa,Xp,Xb) | s_t(Xb,Xp,c63(Xa,Xp,Xb))) & (-sameside(Xa,Xp,Xb) | s_t(Xa,Xp,c63(Xa,Xp,Xb))) & (Xp != c63(Xa,Xp,Xb) | -sameside(Xa,Xp,Xb)) & (Xp != Xa | -sameside(Xa,Xp,Xb)))) # label(aSatz6_3a) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 98 (all Xa all Xp all Xb (sameside(Xb,Xp,Xa) | -sameside(Xa,Xp,Xb))) # label(aSatz6_6) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 99 (all Xa all Xp all Xb ((Xp != Xa | -sameside(Xa,Xp,Xb)) & (-sameside(Xa,Xp,Xb) | Xp != Xb) & (Xb = Xp | sameside(Xa,Xp,Xb) | Xa = Xp | -s_t(Xp,Xb,Xa)) & (Xa = Xp | Xp = xb | sameside(Xa,Xp,Xb) | -s_t(Xp,Xa,Xb)) & (s_t(Xp,Xb,Xa) | s_t(Xp,Xa,Xb) | -sameside(Xa,Xp,Xb)))) # label(d_Defn6_1) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 100 (all Xa all Xp all Xq (Xp = Xq | s(Xa,Xp) != s(Xa,Xq))) # label(aSatz7_9) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 101 (all Xa all Xb all Xc all Xd all Za all Zb all Zc all Zd ((s_t(Xa,Xb,Xc) | -s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)) & (s_e(Xa,Xd,Za,Zd) | -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_e(Xc,Xd,Zc,Zd) | s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | -s_e(Xb,Xc,Zb,Zc) | -s_e(Xa,Xc,Za,Zc) | -s_t(Za,Zb,Zc) | -s_t(Xa,Xb,Xc)) & (s_e(Xb,Xc,Zb,Zc) | -s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)) & (s_e(Xa,Xc,Za,Zc) | -s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)) & (-s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_t(Za,Zb,Zc)))) # label(d_Defn4_1) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 102 (all Xa all Xb all Xp all Xq (Xb = Xa | samesideline(Xq,Xp,Xa,Xb) | -samesideline(Xp,Xq,Xa,Xb))) # label(aLemma9_13d) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 103 (all Xa all Xb all Xc all Xd all Xa1 all Xb1 all Xc1 all Xd1 (le(Xa1,Xb1,Xc1,Xd1) | -s_e(Xc,Xd,Xc1,Xd1) | -s_e(Xa,Xb,Xa1,Xb1) | -le(Xa,Xb,Xc,Xd))) # label(aSatz5_6) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 104 (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) | Xcx != ip(Xp,Xt,Xq,Xb,Xr) | s_m(Xp,Xcx,Xr) | -s_e(Xa,Xp,Xb,Xr) | -s_t(Xb,Xr,Xq) | -s_col(Xa,Xb,Xt))) # label(aSatz8_24b) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 105 (all Xa all Xb all Xc (-s_t(Xb,Xa,Xc) | Xb = Xa | -s_t(Xa,Xb,Xc))) # label(aSatz3_4) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 106 (all Xa1 all Xb1 s_t(Xa1,Xa1,Xb1)) # label(aSatz3_3) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 107 (all Xa all Xb all Xc (s_r(Xc,Xb,Xa) | -s_r(Xa,Xb,Xc))) # label(aSatz8_2) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 108 (all Xa all Xb all Xp all Xq (Xb = Xa | -s_col(Xa,Xb,Xp) | s_e(Xp,Xq,reflect(Xa,Xb,Xp),reflect(Xa,Xb,Xq)))) # label(aSatz10_10a) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 109 (all Xa all Xb s_r(Xa,Xb,Xb)) # label(aSatz8_5) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 110 (all Xa all Xb all Xc (-s_col(Xa,Xb,Xc) | s_col(Xb,Xa,Xc))) # label(aSatz4_11d) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 111 (all Xp all Xq all Xp1 all Xq1 all X ((-perp(Xp,Xq,Xp1,Xq1) | perpAt(Xp,Xq,il(Xp,Xq,Xp1,Xq1),Xp1,Xq1)) & (-perpAt(Xp,Xq,X,Xp1,Xq1) | perp(Xp,Xq,Xp1,Xq1)))) # label(d_Defn8_11b) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 112 (all Xa all Xp (s(Xa,Xp) = Xp | Xa != Xp)) # label(aSatz7_10b) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 113 (all Xa all Xp all Xr all Xq (Xq = Xp | Xr != s(Xa,Xq) | Xr != s(Xa,Xp))) # label(aSatz7_8) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 114 (all Xa all Xb s_e(Xa,Xa,Xb,Xb)) # label(aSatz2_8) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 115 (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_e(Xa,Xb,Za,Zb) | -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_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_e(Xa,Xb,Za,Zb) | -s_e(Xb,Xc,Zb,Zc) | -s_e(Xb,Xd,Zb,Zd) | s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | -s_e(Xa,Xd,Za,Zd) | -s_t(Za,Zb,Zc) | -s_t(Xa,Xb,Xc)) & (-s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_t(Za,Zb,Zc)))) # label(d_Defn2_10) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 116 (all Xa all Xb all Xp all Xq all Xr (-sameside(Xa,Xq,Xr) | samesideline(Xr,Xb,Xp,Xq) | -samesideline(Xa,Xb,Xp,Xq))) # label(aSatz9_16) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 117 (all Xp all Xq all Xr all Xa (s_col(Xa,Xp,Xq) | -sameside(Xa,Xp,Xq) | -s_t(Xq,Xp,Xr) | Xp = Xr | Xp = Xq)) # label(aSatz6_15b) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 118 (all Xa all Xb all Xp all Xq all Xc all Xd all Xe (Xp = Xq | -s_col(Xa,Xb,Xc) | -s_col(Xp,Xq,Xc) | s_col(Xp,Xq,Xe) | -s_col(Xa,Xb,Xe) | Xc = Xd | -s_col(Xp,Xq,Xd) | -s_col(Xa,Xb,Xd) | Xa = Xb)) # label(aSatz6_21) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 119 (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]. 1.26/1.71 120 (all Xa all Xb all Xp all Xp1 ((Xp1 = reflect(Xa,Xb,Xp) | Xp != Xp1 | -s_col(Xa,Xb,midpoint(Xp,Xp1)) | Xb = Xa) & (Xb = Xa | -s_col(Xa,Xb,midpoint(Xp,Xp1)) | -perp(Xa,Xb,Xp,Xp1) | reflect(Xa,Xb,Xp) = Xp1))) # label(aSatz10_2b) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 121 (all Xa all Xb all Xc all Xd (Xa = Xb | s_t(Xa,Xd,Xc) | s_t(Xa,Xc,Xd) | -s_t(Xa,Xb,Xd) | -s_t(Xa,Xb,Xc))) # label(aSatz5_1) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 122 (all Xa all Xb all Xc all Xp all Xq (-s_col(Xa,Xb,Xc) | s_e(Xc,Xp,Xc,Xq) | -s_e(Xb,Xp,Xb,Xq) | -s_e(Xa,Xp,Xa,Xq) | Xa = Xb)) # label(aSatz4_17) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 123 (all Xp all Xq (Xp = Xq | s_col(Xp,Xq,Xp))) # label(aSatz6_17a) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 124 (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]. 1.26/1.71 125 (all Xp all Xa all Xq all Xb (-s_m(Xp,Xa,Xq) | -s_m(Xp,Xb,Xq) | Xa = Xb)) # label(aSatz7_17) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 126 (all Xp all Xq all Xr all Xa (Xp = Xr | sameside(Xa,Xp,Xq) | sameside(Xa,Xp,Xr) | Xp = Xa | -s_col(Xa,Xp,Xq) | -s_t(Xq,Xp,Xr) | Xq = Xp)) # label(aSatz6_15a) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 127 (all Xa all Xb all Xc ((s_col(Xa,Xb,foot(Xa,Xb,Xc)) | s_col(Xa,Xb,Xc)) & (perp(Xa,Xb,Xc,foot(Xa,Xb,Xc)) | s_col(Xa,Xb,Xc)))) # label(aSatz8_18) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 128 (all Xa all Xm (s_m(Xa,Xm,Xa) | Xm != Xa)) # label(aSatz7_3b) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 129 (all Xq all Xa all Xd all Xb all Xc (Xq = Xa | -s_e(Xa,Xd,Xb,Xc) | Xd = ext(Xq,Xa,Xb,Xc) | -s_t(Xq,Xa,Xd))) # label(aSatz2_12) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 130 (all Xa all Xb all U all V all W (Xa = Xb | -s_col(Xa,Xb,W) | s_col(Xa,Xb,V) | -s_col(Xa,Xb,U) | -s_m(U,V,W))) # label(aLemma9_13b) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 131 (all Xa all Xp all Xb all Xc (Xp = Xb | s_t(Xb,Xp,Xc) | -sameside(Xa,Xp,Xb) | -s_t(Xa,Xp,Xc) | Xc = Xp | Xa = Xp)) # label(aSatz6_2b) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 132 (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]. 1.26/1.71 133 (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]. 1.26/1.71 134 (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) | Xq = Xp | -s_col(Xa,Xb,Xp) | Xa = Xb) & (-s_col(Xa,Xb,Xp) | -s_col(Xa,Xb,Xq) | Xq = Xp | -perp(Xa,Xb,Xc,Xp) | s_r(Xc,Xp,Xq) | Xa = Xb))) # label(aSatz8_16a) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 135 (all Xa all Xb all Xc all Xd all Y ((s_t(Xc,insert(Xa,Xb,Xc,Xd),Xd) | -le(Xa,Xb,Xc,Xd)) & (-le(Xa,Xb,Xc,Xd) | s_e(Xa,Xb,Xc,insert(Xa,Xb,Xc,Xd))) & (le(Xa,Xb,Xc,Xd) | -s_e(Xa,Xb,Xc,Y) | -s_t(Xc,Y,Xd)))) # label(d_Defn5_4) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 136 (all Xa all Xb all Xc all XA all XB all XC (-s_t(Xa,Xb,Xc) | -s_t(XA,XB,XC) | -s_e(Xa,Xb,XB,XC) | s_e(Xa,Xc,XA,XC) | -s_e(Xb,Xc,XA,XB))) # label(aSatz2_15) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 137 (all Xp all Xa all Xb all Xq all Xt all Xr all Xcx (-s_col(Xa,Xb,Xt) | -s_t(Xp,Xt,Xq) | -s_e(Xa,Xp,Xb,Xr) | s_m(Xa,Xcx,Xb) | Xcx != ip(Xp,Xt,Xq,Xb,Xr) | -s_t(Xb,Xr,Xq) | -perp(Xq,Xb,Xa,Xb) | -perp(Xp,Xa,Xa,Xb))) # label(aSatz8_24a) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 138 (all Xp all Xa s_m(Xp,Xa,s(Xa,Xp))) # label(aSatz7_4a) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 139 (all Xa all Xb all Xc all Xp all Xq ((-perpAt(Xa,Xb,Xc,Xp,Xq) | Xb != Xa) & (-perpAt(Xa,Xb,Xc,Xp,Xq) | Xq != Xp) & (s_col(Xa,Xb,Xc) | -perpAt(Xa,Xb,Xc,Xp,Xq)) & (-perpAt(Xa,Xb,Xc,Xp,Xq) | s_col(Xp,Xq,g813(Xa,Xb,Xp,Xq,Xc))) & (g813(Xa,Xb,Xp,Xq,Xc) != Xc | -perpAt(Xa,Xb,Xc,Xp,Xq)) & (s_r(f813(Xa,Xb,Xp,Xq,Xc),Xc,g813(Xa,Xb,Xp,Xq,Xc)) | -perpAt(Xa,Xb,Xc,Xp,Xq)) & (-perpAt(Xa,Xb,Xc,Xp,Xq) | Xc != f813(Xa,Xb,Xp,Xq,Xc)) & (-perpAt(Xa,Xb,Xc,Xp,Xq) | s_col(Xa,Xb,f813(Xa,Xb,Xp,Xq,Xc))) & (s_col(Xp,Xq,Xc) | -perpAt(Xa,Xb,Xc,Xp,Xq)))) # label(aSatz8_13a) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 140 (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]. 1.26/1.71 141 (all Xa all Xb all Xp all Xq all Xc all Xd (-s_col(Xa,Xb,Xq) | Xq = Xp | perp(Xp,Xq,Xc,Xd) | -perp(Xa,Xb,Xc,Xd) | Xb = Xa | -s_col(Xa,Xb,Xp))) # label(aExtPerp5) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 142 (all Xa all Xb all Xc all Xa1 (-s_r(Xa,Xb,Xc) | Xa = Xb | s_r(Xa1,Xb,Xc) | -s_col(Xb,Xa,Xa1))) # label(aSatz8_3) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 143 (all Xa all Xb all Xd all Xc (-s_t(Xb,Xc,Xd) | s_t(Xa,Xc,Xd) | -s_t(Xa,Xb,Xd))) # label(aSatz3_5b) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 144 (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]. 1.26/1.71 145 (all Xa all Xb all Xd all Xc (Xb = Xa | -s_col(Xa,Xb,Xd) | -perp(Xa,Xb,Xc,Xd) | perpAt(Xa,Xb,Xd,Xc,Xd))) # label(aSatz8_15) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 146 (all Xa all Xb all Xc all Xp (-s_r(Xa,Xb,Xc) | Xp != Xa | Xc = Xb | -s_m(s(Xa,Xc),Xp,s(Xb,Xc)))) # label(aSatz8_20b) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 147 (all Xa all Xb all Xc all Xd (s_e(Xc,Xd,Xa,Xb) | -s_e(Xa,Xb,Xc,Xd))) # label(aSatz2_2) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 148 (all Xr all Xa all Xb all Xc all Xp all Xq (Xb = Xc | -sameside(Xp,Xa,Xr) | Xp = Xq | -s_e(Xa,Xq,Xb,Xc) | -sameside(Xq,Xa,Xr) | -s_e(Xa,Xp,Xb,Xc) | Xr = Xa)) # label(aSatz6_11b) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 149 (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]. 1.26/1.71 150 (all Xa all Xb all Xc ((Xa = Xb | perp(Xa,Xb,erect21a(Xa,Xb,Xc),Xa) | s_col(Xa,Xb,Xc)) & (Xb = Xa | s_t(Xc,erectAux21a(Xa,Xb,Xc),erect21a(Xa,Xb,Xc)) | s_col(Xa,Xb,Xc)) & (s_col(Xa,Xb,Xc) | s_col(Xa,Xb,erectAux21a(Xa,Xb,Xc)) | Xa = Xb))) # label(aSatz8_21a) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 151 (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]. 1.26/1.71 152 (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]. 1.26/1.71 153 (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]. 1.26/1.71 154 (all Xa all Xp all Xq all Xc all Xr all Xb (-opposite(Xa,Xp,Xq,Xc) | -sameside(Xa,Xr,Xb) | opposite(Xb,Xp,Xq,Xc) | -s_col(Xp,Xq,Xr))) # label(aSatz9_5) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 155 (all Xa all Xb all Xc (-s_col(Xa,Xb,Xc) | s_t(Xa,Xb,Xc) | -le(Xb,Xc,Xa,Xc) | -le(Xa,Xb,Xa,Xc))) # label(aSatz5_12b) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 156 (all Xa all Xm (Xm = Xa | -s_m(Xa,Xm,Xa))) # label(aSatz7_3a) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 157 (all Xp all Xq all Xr all Xa (s_col(Xa,Xp,Xq) | -sameside(Xa,Xp,Xr) | -s_t(Xq,Xp,Xr) | Xp = Xr | Xp = Xq)) # label(aSatz6_15c) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 158 (all Xa all Xp all Xb all Xq all Xt (-le(Xa,Xp,Xb,Xq) | -perp(Xa,Xb,Xb,Xq) | s_m(Xa,midpointAux(Xa,Xb,Xp,Xq,Xt),Xb) | -s_col(Xa,Xb,Xt) | -s_t(Xp,Xt,Xq) | -perp(Xa,Xb,Xa,Xp))) # label(aSatz8_22b) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 159 (all Xp all Xa all Xq (s(Xa,Xp) = Xq | -s_m(Xp,Xa,Xq))) # label(aSatz7_6) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 160 (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]. 1.26/1.71 161 (all Xp all Xq all Xr (Xp = Xq | s_col(Xq,Xp,Xr) | -s_col(Xp,Xq,Xr))) # label(aSatz6_17b) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 162 (all Xa all Xb all Xc all Xd (Xb = Xa | -s_t(Xc,Xa,Xb) | s_t(Xc,Xd,Xb) | s_t(Xd,Xc,Xb) | -s_t(Xd,Xa,Xb))) # label(aSatz6_16a) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 163 (all Xa all Xb all Xc (-s_t(Xa,Xb,Xc) | le(Xb,Xc,Xa,Xc) | -s_col(Xa,Xb,Xc))) # label(aSatz5_12a2) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 164 (all Xp all Xq all Xc all Xa all Xb (Xq = Xp | -perpAt(Xp,Xq,Xc,Xa,Xc) | Xa = Xc | s_col(Xc,Xa,Xb) | -perpAt(Xp,Xq,Xc,Xb,Xc))) # label(aLemma9_13g) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 165 (all Xa all Xb all Xc all Xd (-s_e(Xa,Xb,Xc,Xd) | s_e(Xb,Xa,Xc,Xd))) # label(aSatz2_4) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 166 (all Xa all Xp all Xq all Xc all Xcs all Xr all Xm all U (Xp = Xq | -perp(Xp,Xq,Xc,Xcs) | -sameside(U,Xr,Xa) | sameside(s(Xm,U),Xcs,Xc) | -s_m(Xr,Xm,Xcs) | -perp(Xp,Xq,Xa,Xr) | -s_col(Xp,Xq,Xr) | -s_col(Xp,Xq,Xcs) | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_4) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 167 (all Xd all Xe all Xd1 all Xa all Xb (-s_t(Xe,Xd,Xd1) | samesideline(Xa,Xb,Xd,Xe) | -samesideline(Xa,Xb,Xd1,Xe) | Xd = Xe)) # label(aLemma9_13c) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 168 (all Xa all Xb all Xc all Xd (-le(Xa,Xb,Xc,Xd) | s_e(Xa,Xb,Xc,Xd) | -le(Xc,Xd,Xa,Xb))) # label(aSatz5_9) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 169 (all Xa all Xb all Xp all Xq (-perp(Xa,Xb,Xp,Xq) | perp(Xb,Xa,Xp,Xq))) # label(aperp1) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 170 (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]. 1.26/1.71 171 (all Xa all Xb all Xc all Xd (Xb = Xa | s_t(Xb,Xd,Xc) | s_t(Xb,Xc,Xd) | -s_t(Xa,Xb,Xd) | -s_t(Xa,Xb,Xc))) # label(aSatz5_2) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 172 (all Xa all Xb all Xc all Xa1 (s_e(Xa,Xc,Xa1,Xc) | -s_e(Xa,Xb,Xa1,Xb) | -s_r(Xa1,Xb,Xc) | -s_r(Xa,Xb,Xc))) # label(aSatz10_12b) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 173 (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]. 1.26/1.71 174 (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]. 1.26/1.71 175 (all Xp all Xq all Xa all Xb all Xt ((Xq = Xp | -s_col(Xp,Xq,Xt) | opposite(Xa,Xp,Xq,Xb) | -s_t(Xa,Xt,Xb) | s_col(Xp,Xq,Xb) | s_col(Xp,Xq,Xa)) & (-s_col(Xp,Xq,Xa) | -opposite(Xa,Xp,Xq,Xb)) & (-opposite(Xa,Xp,Xq,Xb) | s_col(Xp,Xq,il(Xa,Xb,Xp,Xq))) & (-opposite(Xa,Xp,Xq,Xb) | s_t(Xa,il(Xa,Xb,Xp,Xq),Xb)) & (-opposite(Xa,Xp,Xq,Xb) | -s_col(Xp,Xq,Xb)))) # label(d_Defn9_1) # label(axiom) # label(non_clause). [assumption]. 1.26/1.71 176 (all Xa all Xb all Xc ((-s_col(Xa,Xb,Xc) | s_t(Xb,Xc,Xa) | s_t(Xc,Xa,Xb) | s_t(Xa,Xb,Xc)) & (-s_t(Xa,Xb,Xc) | s_col(Xa,Xb,Xc)) & (-s_t(Xb,Xc,Xa) | s_col(Xa,Xb,Xc)) & (s_col(Xa,Xb,Xc) | -s_t(Xc,Xa,Xb)))) # label(d_Defn4_10) # label(axiom) # label(non_clause). [assumption]. 1.26/1.72 177 (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]. 1.26/1.72 178 (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]. 1.26/1.72 179 (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]. 1.26/1.72 180 (all Xa all Xb s_m(Xa,midpoint(Xa,Xb),Xb)) # label(aSatz8_22) # label(axiom) # label(non_clause). [assumption]. 1.26/1.72 181 (all Xa all Xc all Xb all Xc1 (-s_e(Xb,Xc,Xb,Xc1) | Xc = Xc1 | -s_e(Xa,Xc,Xa,Xc1) | -s_t(Xa,Xc,Xb))) # label(aSatz4_19) # label(axiom) # label(non_clause). [assumption]. 1.26/1.72 182 (all Xa all Xb s_col(Xa,Xa,Xb)) # label(aSatz4_12) # label(axiom) # label(non_clause). [assumption]. 1.26/1.72 183 (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]. 1.26/1.72 184 (all Xp all Xq all Xr all Xa (-s_t(Xp,Xq,Xr) | s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr)))) # label(aSatz7_15a) # label(axiom) # label(non_clause). [assumption]. 1.26/1.72 185 (all Xa all Xb all Xc all Xd all Xa1 all Xb1 all Xc1 all Xd1 ((-s_col(Xa,Xb,Xc) | -s_e(Xb,Xd,Xb1,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_e(Xb,Xd,Xb1,Xd1)) & (-s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1) | s_e(Xa,Xd,Xa1,Xd1)) & (-s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1) | s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1)) & (-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]. 1.26/1.72 186 (all Xa all Xb all Xp all Xp1 (Xb = Xa | reflect(Xa,Xb,Xp) != Xp1 | reflect(Xa,Xb,Xp1) = Xp)) # label(aSatz10_6) # label(axiom) # label(non_clause). [assumption]. 1.26/1.72 187 (all Xa all Xb s_col(Xa,Xb,Xa)) # label(aSatz4_12b) # label(axiom) # label(non_clause). [assumption]. 1.26/1.72 188 (all Xa all Xb all Xc all Xp all Xq (-perpAt(Xa,Xb,Xc,Xp,Xq) | il(Xa,Xb,Xp,Xq) = Xc)) # label(aSatz8_14c) # label(axiom) # label(non_clause). [assumption]. 1.26/1.72 189 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_t(Xa,Xb,Xc) | -s_e(Xa,Xb,Xa1,Xb1) | s_e(Xa,Xc,Xa1,Xc1) | -s_e(Xb,Xc,Xb1,Xc1) | -s_t(Xa1,Xb1,Xc1))) # label(aSatz2_11) # label(axiom) # label(non_clause). [assumption]. 1.26/1.72 190 (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) | -le(Xcs,Xc,Xr,Xa) | Xcs = Xr | sameside(s(Xm,U),Xcs,Xc) | -sameside(U,Xr,Xa) | -perp(Xp,Xq,Xa,Xr) | -s_col(Xp,Xq,Xcs) | Xq = Xp)) # label(aSatz9_4a) # label(axiom) # label(non_clause). [assumption]. 1.26/1.72 191 (all Xa all Xb le(Xa,Xb,Xa,Xb)) # label(aSatz5_7) # label(axiom) # label(non_clause). [assumption]. 1.26/1.72 192 (all Xa all Xp all Xq all Xc all Xcs all Xr all Xm all U all V (-s_col(Xp,Xq,Xr) | -perp(Xp,Xq,Xa,Xr) | -perp(Xp,Xq,Xc,Xcs) | -sameside(V,Xcs,Xc) | opposite(U,Xp,Xq,V) | -sameside(U,Xr,Xa) | -s_m(Xr,Xm,Xcs) | -s_col(Xp,Xq,Xcs) | Xq = Xp | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_4c) # label(axiom) # label(non_clause). [assumption]. 1.26/1.72 193 (all Xa all Xb all Xp all Xq all Xc (Xa = Xb | -s_col(Xa,Xb,Xq) | -s_r(Xc,Xp,Xq) | s_col(Xa,Xb,Xc) | perp(Xa,Xb,Xc,Xp) | Xp = Xq | -s_col(Xa,Xb,Xp))) # label(aSatz8_16b) # label(axiom) # label(non_clause). [assumption]. 1.26/1.72 194 (all Xa all Xb all Xp all Xp1 (Xb = Xa | Xp = reflect(Xa,Xb,Xp1) | reflect(Xa,Xb,Xp) != Xp1)) # label(aSatz10_4) # label(axiom) # label(non_clause). [assumption]. 1.26/1.72 195 (all Xa all Xb all Xc all Xc1 (Xa = Xb | -s_e(Xa,Xc,Xa,Xc1) | Xc1 = Xc | -s_e(Xb,Xc,Xb,Xc1) | -s_col(Xa,Xb,Xc))) # label(aSatz4_18) # label(axiom) # label(non_clause). [assumption]. 1.26/1.72 196 (all Xa all Xb all Xp all Xq (reflect(Xa,Xb,Xp) != reflect(Xa,Xb,Xq) | Xq = Xp | Xb = Xa)) # label(aSatz10_7) # label(axiom) # label(non_clause). [assumption]. 1.26/1.72 197 (all Xa all Xb all Xc all Xd all Xa1 all Xb1 all Xc1 all Xd1 (-s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1) | Xa = Xb | s_e(Xc,Xd,Xc1,Xd1))) # label(aSatz4_16) # label(axiom) # label(non_clause). [assumption]. 1.26/1.72 198 (all Xp all Xq all Xr all Xa (s_col(Xa,Xp,Xq) | Xp != Xa | -s_t(Xq,Xp,Xr) | Xr = Xp | Xp = Xq)) # label(aSatz6_15d) # label(axiom) # label(non_clause). [assumption]. 1.26/1.72 199 (all Xa all Xb all Xc ((Xb = Xa | perp(Xa,Xb,erect(Xa,Xb,Xc),Xa)) & (Xb = Xa | s_t(Xc,erectAux(Xa,Xb,Xc),erect(Xa,Xb,Xc))) & (Xb = Xa | s_col(Xa,Xb,erectAux(Xa,Xb,Xc))))) # label(aSatz8_21) # label(axiom) # label(non_clause). [assumption]. 1.26/1.72 200 (all Xa all Xp all Xq all Xc all Xb (opposite(Xb,Xp,Xq,Xc) | -samesideline(Xa,Xb,Xp,Xq) | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_8) # label(axiom) # label(non_clause). [assumption]. 1.26/1.72 201 (all Xa all Xb all Xp all Xq all Xu all Xc all Xv ((s_col(Xp,Xq,ss2(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))) & (-samesideline(Xa,Xb,Xp,Xq) | ss1(Xa,Xb,Xp,Xq) != Xa) & (-samesideline(Xa,Xb,Xp,Xq) | ss1(Xa,Xb,Xp,Xq) != ss3(Xa,Xb,Xp,Xq)) & (-s_col(Xp,Xq,Xb) | -samesideline(Xa,Xb,Xp,Xq)) & (-s_t(Xa,Xu,Xc) | -s_col(Xp,Xq,Xu) | Xu = Xc | Xv = Xc | Xu = Xa | Xb = Xv | s_col(Xp,Xq,Xb) | samesideline(Xa,Xb,Xp,Xq) | s_col(Xp,Xq,Xa) | Xp = Xq | -s_col(Xp,Xq,Xv) | -s_t(Xb,Xv,Xc)) & (-samesideline(Xa,Xb,Xp,Xq) | -s_col(Xp,Xq,Xa)) & (-samesideline(Xa,Xb,Xp,Xq) | Xp != Xq) & (ss3(Xa,Xb,Xp,Xq) != ss2(Xa,Xb,Xp,Xq) | -samesideline(Xa,Xb,Xp,Xq)) & (Xb != ss2(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)) & (s_col(Xp,Xq,ss1(Xa,Xb,Xp,Xq)) | -samesideline(Xa,Xb,Xp,Xq)))) # label(d_Defn9_7) # label(axiom) # label(non_clause). [assumption]. 1.26/1.72 202 (all Xa all Xb all Xp (Xp = reflect(Xa,Xb,reflect(Xa,Xb,Xp)) | Xa = Xb)) # label(aSatz10_5) # label(axiom) # label(non_clause). [assumption]. 1.26/1.72 203 (all Xp all Xq all Xa all Xb all Xc (-samesideline(Xa,Xb,Xp,Xq) | samesideline(Xa,Xc,Xp,Xq) | -samesideline(Xb,Xc,Xp,Xq) | Xp = Xq)) # label(aSatz9_13) # label(axiom) # label(non_clause). [assumption]. 1.26/1.72 204 (all Xa all Xb (-s_col(Xa,Xb,pointOffLine(Xa,Xb)) | Xa = Xb)) # label(aSatz6_25) # label(axiom) # label(non_clause). [assumption]. 1.26/1.72 205 -(all Xa all Xb all Xc all Xa1 all Xc1 (-s_r(Xa,Xb,Xc) | -s_r(Xa1,Xb,Xc1) | -s_e(Xb,Xc,Xb,Xc1) | s_e(Xa,Xc,Xa1,Xc1) | Xc = Xc1 | midpoint(Xc,Xc1) != Xb | -s_e(Xa,Xb,Xa1,Xb))) # label(aSatz10_12c) # label(negated_conjecture) # label(non_clause). [assumption]. 1.26/1.72 1.26/1.72 ============================== end of process non-clausal formulas === 1.26/1.72 1.26/1.72 ============================== PROCESS INITIAL CLAUSES =============== 1.26/1.72 1.26/1.72 ============================== PREDICATE ELIMINATION ================= 1.26/1.72 206 -s_r(A,B,C) | -s_e3(A,B,C,D,E,F) | s_r(D,E,F) # label(aSatz8_10) # label(axiom). [clausify(15)]. 1.26/1.72 207 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(8)]. 1.26/1.72 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(206,b,207,a)]. 1.26/1.72 208 -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(67)]. 1.26/1.72 Derived: -s_t(A,B,C) | -s_e(A,C,D,E) | -s_r(A,B,C) | s_r(D,insert(A,B,D,E),E). [resolve(208,c,206,b)]. 1.26/1.72 209 -s_e(A,B,C,D) | -s_e(A,E,C,F) | -s_e(B,E,D,F) | s_e3(A,B,E,C,D,F) # label(d_Defn4_4) # label(axiom). [clausify(81)]. 1.26/1.72 Derived: -s_e(A,B,C,D) | -s_e(A,E,C,F) | -s_e(B,E,D,F) | -s_r(A,B,E) | s_r(C,D,F). [resolve(209,d,206,b)]. 1.26/1.72 210 s_e(A,B,C,D) | -s_e3(E,A,B,F,C,D) # label(d_Defn4_4) # label(axiom). [clausify(81)]. 1.26/1.72 Derived: s_e(A,B,C,insert5(D,A,B,E,C)) | -s_e(D,A,E,C) | -s_col(D,A,B). [resolve(210,b,207,a)]. 1.26/1.72 Derived: s_e(A,B,insert(C,A,D,E),E) | -s_t(C,A,B) | -s_e(C,B,D,E). [resolve(210,b,208,c)]. 1.26/1.72 211 s_e(A,B,C,D) | -s_e3(A,E,B,C,F,D) # label(d_Defn4_4) # label(axiom). [clausify(81)]. 1.26/1.72 Derived: s_e(A,B,C,insert5(A,D,B,C,E)) | -s_e(A,D,C,E) | -s_col(A,D,B). [resolve(211,b,207,a)]. 1.26/1.72 212 -s_e3(A,B,C,D,E,F) | s_e(A,B,D,E) # label(d_Defn4_4) # label(axiom). [clausify(81)]. 1.26/1.72 Derived: s_e(A,B,C,insert(A,B,C,D)) | -s_t(A,B,E) | -s_e(A,E,C,D). [resolve(212,a,208,c)]. 1.26/1.74 213 -s_t(A,B,C) | s_t(D,E,F) | -s_e3(A,B,C,D,E,F) # label(aSatz4_6) # label(axiom). [clausify(88)]. 1.26/1.74 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(213,c,207,a)]. 1.26/1.74 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(213,c,208,c)]. 1.26/1.74 Derived: -s_t(A,B,C) | s_t(D,E,F) | -s_e(A,B,D,E) | -s_e(A,C,D,F) | -s_e(B,C,E,F). [resolve(213,c,209,d)]. 1.26/1.74 214 -s_col(A,B,C) | -s_e3(A,B,C,D,E,F) | s_col(D,E,F) # label(aSatz4_13) # label(axiom). [clausify(124)]. 1.26/1.74 Derived: -s_col(A,B,C) | s_col(D,E,insert5(A,B,C,D,E)) | -s_e(A,B,D,E) | -s_col(A,B,C). [resolve(214,b,207,a)]. 1.26/1.74 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(214,b,208,c)]. 1.26/1.74 Derived: -s_col(A,B,C) | s_col(D,E,F) | -s_e(A,B,D,E) | -s_e(A,C,D,F) | -s_e(B,C,E,F). [resolve(214,b,209,d)]. 1.26/1.74 215 -s_col(A,B,C) | -s_e(B,D,E,F) | s_fs(A,B,C,D,V6,E,V7,F) | -s_e(A,D,V6,F) | -s_e3(A,B,C,V6,E,V7) # label(d_Defn4_15) # label(axiom). [clausify(185)]. 1.26/1.74 Derived: -s_col(A,B,C) | -s_e(B,D,E,F) | s_fs(A,B,C,D,V6,E,insert5(A,B,C,V6,E),F) | -s_e(A,D,V6,F) | -s_e(A,B,V6,E) | -s_col(A,B,C). [resolve(215,e,207,a)]. 1.26/1.74 Derived: -s_col(A,B,C) | -s_e(B,D,insert(A,B,E,F),V6) | s_fs(A,B,C,D,E,insert(A,B,E,F),F,V6) | -s_e(A,D,E,V6) | -s_t(A,B,C) | -s_e(A,C,E,F). [resolve(215,e,208,c)]. 1.26/1.74 Derived: -s_col(A,B,C) | -s_e(B,D,E,F) | s_fs(A,B,C,D,V6,E,V7,F) | -s_e(A,D,V6,F) | -s_e(A,B,V6,E) | -s_e(A,C,V6,V7) | -s_e(B,C,E,V7). [resolve(215,e,209,d)]. 1.26/1.74 216 -s_fs(A,B,C,D,E,F,V6,V7) | s_e3(A,B,C,E,F,V6) # label(d_Defn4_15) # label(axiom). [clausify(185)]. 1.26/1.74 Derived: -s_fs(A,B,C,D,E,F,V6,V7) | -s_r(A,B,C) | s_r(E,F,V6). [resolve(216,b,206,b)]. 1.26/1.74 Derived: -s_fs(A,B,C,D,E,F,V6,V7) | s_e(B,C,F,V6). [resolve(216,b,210,b)]. 1.26/1.74 Derived: -s_fs(A,B,C,D,E,F,V6,V7) | s_e(A,C,E,V6). [resolve(216,b,211,b)]. 1.26/1.74 Derived: -s_fs(A,B,C,D,E,F,V6,V7) | s_e(A,B,E,F). [resolve(216,b,212,a)]. 1.26/1.74 Derived: -s_fs(A,B,C,D,E,F,V6,V7) | -s_t(A,B,C) | s_t(E,F,V6). [resolve(216,b,213,c)]. 1.26/1.74 Derived: -s_fs(A,B,C,D,E,F,V6,V7) | -s_col(A,B,C) | s_col(E,F,V6). [resolve(216,b,214,b)]. 1.26/1.74 Derived: -s_fs(A,B,C,D,E,F,V6,V7) | -s_col(A,B,C) | -s_e(B,V8,F,V9) | s_fs(A,B,C,V8,E,F,V6,V9) | -s_e(A,V8,E,V9). [resolve(216,b,215,e)]. 1.26/1.74 217 -s_e(A,B,C,D) | -s_e(E,B,F,D) | s_ifs(A,V6,E,B,C,V7,F,D) | -s_e(V6,E,V7,F) | -s_e(A,E,C,F) | -s_t(C,V7,F) | -s_t(A,V6,E) # label(d_Defn4_1) # label(axiom). [clausify(101)]. 1.26/1.74 218 s_e(A,B,C,D) | -s_ifs(E,A,F,B,V6,C,V7,D) # label(aSatz4_2) # label(axiom). [clausify(12)]. 1.26/1.74 219 s_t(A,B,C) | -s_ifs(A,B,C,D,E,F,V6,V7) # label(d_Defn4_1) # label(axiom). [clausify(101)]. 1.26/1.74 220 s_e(A,B,C,D) | -s_ifs(A,E,F,B,C,V6,V7,D) # label(d_Defn4_1) # label(axiom). [clausify(101)]. 1.26/1.74 221 s_e(A,B,C,D) | -s_ifs(E,F,A,B,V6,V7,C,D) # label(d_Defn4_1) # label(axiom). [clausify(101)]. 1.26/1.74 Derived: -s_e(A,B,C,D) | -s_e(E,B,F,D) | -s_e(V6,E,V7,F) | -s_e(A,E,C,F) | -s_t(C,V7,F) | -s_t(A,V6,E) | s_e(V6,B,V7,D). [resolve(217,c,218,b)]. 1.26/1.74 222 s_e(A,B,C,D) | -s_ifs(E,A,B,F,V6,C,D,V7) # label(d_Defn4_1) # label(axiom). [clausify(101)]. 1.26/1.74 223 s_e(A,B,C,D) | -s_ifs(A,E,B,F,C,V6,D,V7) # label(d_Defn4_1) # label(axiom). [clausify(101)]. 1.26/1.74 224 -s_ifs(A,B,C,D,E,F,V6,V7) | s_t(E,F,V6) # label(d_Defn4_1) # label(axiom). [clausify(101)]. 1.26/1.74 225 -s_t(A,B,C) | -s_t(D,B,E) | -s_m(A,F,D) | -s_m(C,V6,E) | s_kf(A,F,D,B,E,V6,C) | -s_e(B,C,B,E) | -s_e(B,A,B,D) # label(d_Defn7_23) # label(axiom). [clausify(31)]. 1.26/1.74 226 -s_kf(A,B,C,D,E,F,V6) | s_t(A,D,V6) # label(d_Defn7_23) # label(axiom). [clausify(31)]. 1.26/1.74 227 -s_kf(A,B,C,D,E,F,V6) | s_t(C,D,E) # label(d_Defn7_23) # label(axiom). [clausify(31)]. 1.26/1.74 228 -s_kf(A,B,C,D,E,F,V6) | s_e(D,A,D,C) # label(d_Defn7_23) # label(axiom). [clausify(31)]. 1.26/1.74 229 s_m(A,B,C) | -s_kf(A,B,C,D,E,F,V6) # label(d_Defn7_23) # label(axiom). [clausify(31)]. 1.26/1.74 230 s_m(A,B,C) | -s_kf(D,E,F,V6,C,B,A) # label(d_Defn7_23) # label(axiom). [clausify(31)]. 1.26/1.74 231 s_e(A,B,A,C) | -s_kf(D,E,F,A,C,V6,B) # label(d_Defn7_23) # label(axiom). [clausify(31)]. 1.26/1.74 232 -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(62)]. 1.26/1.74 Derived: s_t(A,B,C) | -le(B,D,B,E) | -s_t(D,B,E) | -s_t(F,B,V6) | -s_m(D,A,F) | -s_m(E,C,V6) | -s_e(B,E,B,V6) | -s_e(B,D,B,F). [resolve(232,a,225,e)]. 19.74/20.32 233 s_t(A,B,C) | -s_kf(D,A,E,B,F,C,V6) # label(aSatz7_22b) # label(axiom). [clausify(140)]. 19.74/20.32 Derived: s_t(A,B,C) | -s_t(D,B,E) | -s_t(F,B,V6) | -s_m(D,A,F) | -s_m(E,C,V6) | -s_e(B,E,B,V6) | -s_e(B,D,B,F). [resolve(233,b,225,e)]. 19.74/20.32 234 -s_e(A,B,C,D) | -s_e(B,E,D,F) | -s_e(B,V6,D,V7) | s_afs(A,B,E,V6,C,D,F,V7) | -s_e(A,V6,C,V7) | -s_t(C,D,F) | -s_t(A,B,E) # label(d_Defn2_10) # label(axiom). [clausify(115)]. 19.74/20.32 235 -s_afs(A,B,C,D,E,F,V6,V7) | s_t(A,B,C) # label(d_Defn2_10) # label(axiom). [clausify(115)]. 19.74/20.32 236 s_e(A,B,C,D) | -s_afs(A,B,E,F,C,D,V6,V7) # label(d_Defn2_10) # label(axiom). [clausify(115)]. 19.74/20.32 237 s_e(A,B,C,D) | -s_afs(E,A,B,F,V6,C,D,V7) # label(d_Defn2_10) # label(axiom). [clausify(115)]. 19.74/20.32 238 -s_afs(A,B,C,D,E,F,V6,V7) | s_e(A,D,E,V7) # label(d_Defn2_10) # label(axiom). [clausify(115)]. 19.74/20.32 239 -s_afs(A,B,C,D,E,F,V6,V7) | s_e(B,D,F,V7) # label(d_Defn2_10) # label(axiom). [clausify(115)]. 19.74/20.32 240 -s_afs(A,B,C,D,E,F,V6,V7) | s_t(E,F,V6) # label(d_Defn2_10) # label(axiom). [clausify(115)]. 19.74/20.32 19.74/20.32 ============================== end predicate elimination ============= 19.74/20.32 19.74/20.32 Auto_denials: (non-Horn, no changes). 19.74/20.32 19.74/20.32 Term ordering decisions: 19.74/20.32 Function symbol KB weights: xb=1. xa=1. xp=1. xq=1. alpha=1. gamma=1. xc=1. xd=1. beta=1. c1=1. c2=1. c3=1. c4=1. c5=1. s=1. midpoint=1. pointOffLine=1. reflect=1. foot=1. c63=1. erect=1. erect21a=1. erectAux=1. erectAux21a=1. isomidpoint=1. insert=1. ext=1. il=1. ins=1. ss1=1. ss2=1. ss3=1. insert5=1. ip=1. f811=1. f813=1. g811=1. g813=1. op=1. midpointAux=1. crossbar=1. 19.74/20.32 19.74/20.32 ============================== end of process initial clauses ======== 19.74/20.32 19.74/20.32 ============================== CLAUSES FOR SEARCH ==================== 19.74/20.32 19.74/20.32 ============================== end of clauses for search ============= 19.74/20.32 19.74/20.32 ============================== SEARCH ================================ 19.74/20.32 19.74/20.32 % Starting search at 0.11 seconds. 19.74/20.32 19.74/20.32 Low Water (keep): wt=34.000, iters=3475 19.74/20.32 19.74/20.32 Low Water (keep): wt=33.000, iters=3412 19.74/20.32 19.74/20.32 Low Water (keep): wt=31.000, iters=3377 19.74/20.32 19.74/20.32 Low Water (keep): wt=28.000, iters=3399 19.74/20.32 19.74/20.32 Low Water (keep): wt=26.000, iters=3350 19.74/20.32 19.74/20.32 Low Water (keep): wt=25.000, iters=3344 19.74/20.32 19.74/20.32 Low Water (keep): wt=24.000, iters=3340 19.74/20.32 19.74/20.32 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 84 (0.00 of 0.88 sec). 19.74/20.32 19.74/20.32 Low Water (keep): wt=23.000, iters=3414 19.74/20.32 19.74/20.32 Low Water (keep): wt=22.000, iters=3366 19.74/20.32 19.74/20.32 Low Water (keep): wt=21.000, iters=3360 19.74/20.32 19.74/20.32 Low Water (keep): wt=20.000, iters=3344 19.74/20.32 19.74/20.32 Low Water (keep): wt=19.000, iters=3400 19.74/20.32 19.74/20.32 Low Water (keep): wt=18.000, iters=3951 19.74/20.32 19.74/20.32 Low Water (keep): wt=17.000, iters=3660 19.74/20.32 19.74/20.32 Low Water (keep): wt=16.000, iters=3368 19.74/20.32 19.74/20.32 Low Water (keep): wt=15.000, iters=3359 19.74/20.32 19.74/20.32 Low Water (keep): wt=14.000, iters=3372 19.74/20.32 19.74/20.32 Low Water (displace): id=1597, wt=90.000 19.74/20.32 19.74/20.32 Low Water (displace): id=1297, wt=79.000 19.74/20.32 19.74/20.32 Low Water (keep): wt=13.000, iters=3337 19.74/20.32 19.74/20.32 Low Water (displace): id=12084, wt=12.000 19.74/20.32 19.74/20.32 Low Water (displace): id=12175, wt=11.000 19.74/20.32 19.74/20.32 Low Water (displace): id=12435, wt=10.000 19.74/20.32 19.74/20.32 Low Water (displace): id=12725, wt=9.000 19.74/20.32 19.74/20.32 Low Water (displace): id=13606, wt=8.000 19.74/20.32 19.74/20.32 Low Water (keep): wt=12.000, iters=3336 19.74/20.32 19.74/20.32 Low Water (keep): wt=11.000, iters=3333 19.74/20.32 19.74/20.32 Low Water (keep): wt=10.000, iters=3333 19.74/20.32 19.74/20.32 ============================== PROOF ================================= 19.74/20.32 % SZS status Theorem 19.74/20.32 % SZS output start Refutation 19.74/20.32 19.74/20.32 % Proof 1 at 18.20 (+ 0.29) seconds. 19.74/20.32 % Length of proof is 28. 19.74/20.32 % Level of proof is 6. 19.74/20.32 % Maximum clause weight is 18.000. 19.74/20.32 % Given clauses 7576. 19.74/20.32 19.74/20.32 24 (all Xa all Xb all Xc all Xd all Xe all Xf (-s_e(Xa,Xb,Xc,Xd) | s_e(Xa,Xb,Xe,Xf) | -s_e(Xc,Xd,Xe,Xf))) # label(aSatz2_3) # label(axiom) # label(non_clause). [assumption]. 19.74/20.32 94 (all Xa all Xb all Xc ((s_e(Xa,Xc,Xa,s(Xb,Xc)) | -s_r(Xa,Xb,Xc)) & (s_r(Xa,Xb,Xc) | -s_e(Xa,Xc,Xa,s(Xb,Xc))))) # label(d_Defn8_1) # label(axiom) # label(non_clause). [assumption]. 19.74/20.32 119 (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]. 19.74/20.32 159 (all Xp all Xa all Xq (s(Xa,Xp) = Xq | -s_m(Xp,Xa,Xq))) # label(aSatz7_6) # label(axiom) # label(non_clause). [assumption]. 19.74/20.32 172 (all Xa all Xb all Xc all Xa1 (s_e(Xa,Xc,Xa1,Xc) | -s_e(Xa,Xb,Xa1,Xb) | -s_r(Xa1,Xb,Xc) | -s_r(Xa,Xb,Xc))) # label(aSatz10_12b) # label(axiom) # label(non_clause). [assumption]. 19.74/20.32 180 (all Xa all Xb s_m(Xa,midpoint(Xa,Xb),Xb)) # label(aSatz8_22) # label(axiom) # label(non_clause). [assumption]. 19.74/20.32 205 -(all Xa all Xb all Xc all Xa1 all Xc1 (-s_r(Xa,Xb,Xc) | -s_r(Xa1,Xb,Xc1) | -s_e(Xb,Xc,Xb,Xc1) | s_e(Xa,Xc,Xa1,Xc1) | Xc = Xc1 | midpoint(Xc,Xc1) != Xb | -s_e(Xa,Xb,Xa1,Xb))) # label(aSatz10_12c) # label(negated_conjecture) # label(non_clause). [assumption]. 19.74/20.32 269 -s_e(A,B,C,D) | s_e(A,B,E,F) | -s_e(C,D,E,F) # label(aSatz2_3) # label(axiom). [clausify(24)]. 19.74/20.32 348 s_e(A,B,A,s(C,B)) | -s_r(A,C,B) # label(d_Defn8_1) # label(axiom). [clausify(94)]. 19.74/20.32 378 -s_r(A,B,C) | s_r(A,B,s(B,C)) # label(aSatz8_4) # label(axiom). [clausify(119)]. 19.74/20.32 427 s(A,B) = C | -s_m(B,A,C) # label(aSatz7_6) # label(axiom). [clausify(159)]. 19.74/20.32 439 s_e(A,B,C,B) | -s_e(A,D,C,D) | -s_r(C,D,B) | -s_r(A,D,B) # label(aSatz10_12b) # label(axiom). [clausify(172)]. 19.74/20.32 456 s_m(A,midpoint(A,B),B) # label(aSatz8_22) # label(axiom). [clausify(180)]. 19.74/20.32 496 s_r(c1,c2,c3) # label(aSatz10_12c) # label(negated_conjecture). [clausify(205)]. 19.74/20.32 497 s_r(c4,c2,c5) # label(aSatz10_12c) # label(negated_conjecture). [clausify(205)]. 19.74/20.32 499 -s_e(c1,c3,c4,c5) # label(aSatz10_12c) # label(negated_conjecture). [clausify(205)]. 19.74/20.32 501 midpoint(c3,c5) = c2 # label(aSatz10_12c) # label(negated_conjecture). [clausify(205)]. 19.74/20.32 502 s_e(c1,c2,c4,c2) # label(aSatz10_12c) # label(negated_conjecture). [clausify(205)]. 19.74/20.32 1334 s_r(c1,c2,s(c2,c3)). [resolve(496,a,378,a)]. 19.74/20.32 1336 s_e(c1,c3,c1,s(c2,c3)). [resolve(496,a,348,b)]. 19.74/20.32 1411 s_m(c3,c2,c5). [para(501(a,1),456(a,2))]. 19.74/20.32 1415 s_e(c1,A,c4,A) | -s_r(c4,c2,A) | -s_r(c1,c2,A). [resolve(502,a,439,b)]. 19.74/20.32 1961 s(c2,c3) = c5. [resolve(1411,a,427,b)]. 19.74/20.32 1968 s_e(c1,c3,c1,c5). [back_rewrite(1336),rewrite([1961(6)])]. 19.74/20.32 1969 s_r(c1,c2,c5). [back_rewrite(1334),rewrite([1961(5)])]. 19.74/20.32 3383 s_e(c1,c3,A,B) | -s_e(c1,c5,A,B). [resolve(1968,a,269,a)]. 19.74/20.32 22355 s_e(c1,c5,c4,c5). [resolve(1415,b,497,a),unit_del(b,1969)]. 19.74/20.32 29170 $F. [resolve(3383,b,22355,a),unit_del(a,499)]. 19.74/20.32 19.74/20.32 % SZS output end Refutation 19.74/20.32 ============================== end of proof ========================== 19.74/20.32 19.74/20.32 ============================== STATISTICS ============================ 19.74/20.32 19.74/20.32 Given=7576. Generated=331263. Kept=28914. proofs=1. 19.74/20.32 Usable=7447. Sos=9999. Demods=337. Limbo=8, Disabled=11793. Hints=0. 19.74/20.32 Megabytes=18.49. 19.74/20.32 User_CPU=18.20, System_CPU=0.29, Wall_clock=19. 19.74/20.32 19.74/20.32 ============================== end of statistics ===================== 19.74/20.32 19.74/20.32 ============================== end of search ========================= 19.74/20.32 19.74/20.32 THEOREM PROVED 19.74/20.32 % SZS status Theorem 19.74/20.32 19.74/20.32 Exiting with 1 proof. 19.74/20.32 19.74/20.32 Process 31369 exit (max_proofs) Mon Jul 3 07:36:51 2023 19.74/20.33 Prover9 interrupted 19.74/20.33 EOF