0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.12/0.34 % Computer : n012.cluster.edu 0.12/0.34 % Model : x86_64 x86_64 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.34 % Memory : 8042.1875MB 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.34 % CPULimit : 1440 0.12/0.34 % WCLimit : 180 0.12/0.34 % DateTime : Mon Jul 3 10:53:22 EDT 2023 0.12/0.34 % CPUTime : 1.11/1.42 ============================== Prover9 =============================== 1.11/1.42 Prover9 (32) version 2009-11A, November 2009. 1.11/1.42 Process 7885 was started by sandbox on n012.cluster.edu, 1.11/1.42 Mon Jul 3 10:53:23 2023 1.11/1.42 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1440 -f /tmp/Prover9_7705_n012.cluster.edu". 1.11/1.42 ============================== end of head =========================== 1.11/1.42 1.11/1.42 ============================== INPUT ================================= 1.11/1.42 1.11/1.42 % Reading from file /tmp/Prover9_7705_n012.cluster.edu 1.11/1.42 1.11/1.42 set(prolog_style_variables). 1.11/1.42 set(auto2). 1.11/1.42 % set(auto2) -> set(auto). 1.11/1.42 % set(auto) -> set(auto_inference). 1.11/1.42 % set(auto) -> set(auto_setup). 1.11/1.42 % set(auto_setup) -> set(predicate_elim). 1.11/1.42 % set(auto_setup) -> assign(eq_defs, unfold). 1.11/1.42 % set(auto) -> set(auto_limits). 1.11/1.42 % set(auto_limits) -> assign(max_weight, "100.000"). 1.11/1.42 % set(auto_limits) -> assign(sos_limit, 20000). 1.11/1.42 % set(auto) -> set(auto_denials). 1.11/1.42 % set(auto) -> set(auto_process). 1.11/1.42 % set(auto2) -> assign(new_constants, 1). 1.11/1.42 % set(auto2) -> assign(fold_denial_max, 3). 1.11/1.42 % set(auto2) -> assign(max_weight, "200.000"). 1.11/1.42 % set(auto2) -> assign(max_hours, 1). 1.11/1.42 % assign(max_hours, 1) -> assign(max_seconds, 3600). 1.11/1.42 % set(auto2) -> assign(max_seconds, 0). 1.11/1.42 % set(auto2) -> assign(max_minutes, 5). 1.11/1.42 % assign(max_minutes, 5) -> assign(max_seconds, 300). 1.11/1.42 % set(auto2) -> set(sort_initial_sos). 1.11/1.42 % set(auto2) -> assign(sos_limit, -1). 1.11/1.42 % set(auto2) -> assign(lrs_ticks, 3000). 1.11/1.42 % set(auto2) -> assign(max_megs, 400). 1.11/1.42 % set(auto2) -> assign(stats, some). 1.11/1.42 % set(auto2) -> clear(echo_input). 1.11/1.42 % set(auto2) -> set(quiet). 1.11/1.42 % set(auto2) -> clear(print_initial_clauses). 1.11/1.42 % set(auto2) -> clear(print_given). 1.11/1.42 assign(lrs_ticks,-1). 1.11/1.42 assign(sos_limit,10000). 1.11/1.42 assign(order,kbo). 1.11/1.42 set(lex_order_vars). 1.11/1.42 clear(print_given). 1.11/1.42 1.11/1.42 % formulas(sos). % not echoed (225 formulas) 1.11/1.42 1.11/1.42 ============================== end of input ========================== 1.11/1.42 1.11/1.42 % From the command line: assign(max_seconds, 1440). 1.11/1.42 1.11/1.42 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 1.11/1.42 1.11/1.42 % Formulas that are not ordinary clauses: 1.11/1.42 1 (all X all Y (Y = X | -s_t(X,Y,X))) # label(aA6) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 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]. 1.11/1.42 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]. 1.11/1.42 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]. 1.11/1.42 5 (all X all Y s_e(X,Y,Y,X)) # label(aA1) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 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]. 1.11/1.42 7 (all X all Y all Z (Y = X | -s_e(X,Y,Z,Z))) # label(aA3) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 8 (all Xa all Xb all Xp all Xq (Xa = Xb | Xp = Xq | reflect(Xa,Xb,Xp) != reflect(Xa,Xb,Xq))) # label(aSatz10_7) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 9 (all Xa all Xb all Xc (-s_t(Xa,Xb,Xc) | s_t(Xc,Xb,Xa))) # label(aSatz3_2) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 10 (all Xa all Xb all Xc all Xa1 (-s_r(Xa,Xb,Xc) | -s_r(Xa1,Xb,Xc) | -s_e(Xa,Xb,Xa1,Xb) | s_e(Xa,Xc,Xa1,Xc))) # label(aSatz10_12b) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 11 (all Xa all Xb all Xc (-s_col(Xa,Xb,Xc) | -le(Xa,Xb,Xa,Xc) | -le(Xb,Xc,Xa,Xc) | s_t(Xa,Xb,Xc))) # label(aSatz5_12b) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 12 (all Xa1 all Xb all Xa2 all Xc1 all Xc2 all Xd1 all Xe all Xd2 all Xf1 all Xf2 all Xa all Xc all Xd all Xf (-sameside(Xc1,Xb,Xc2) | -sameside(Xd1,Xe,Xd2) | -sameside(Xf1,Xe,Xf2) | -s_e3(Xa1,Xb,Xc1,Xd1,Xe,Xf1) | Xb = Xc | Xd = Xe | -sameside(Xa2,Xb,Xa) | -sameside(Xc2,Xb,Xc) | -sameside(Xd2,Xe,Xd) | -sameside(Xf2,Xe,Xf) | -s_e(Xb,Xa2,Xe,Xd2) | s_e(Xa2,Xc2,Xd2,Xf2) | -s_e(Xb,Xc2,Xe,Xf2) | Xe = Xf | Xb = Xa | -sameside(Xa1,Xb,Xa2))) # label(aSatz11_4d) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 13 (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]. 1.16/1.42 14 (all Xa all Xb all Xc ((s_t(Xc,Xa,Xb) | s_t(Xb,Xc,Xa) | s_t(Xa,Xb,Xc) | -s_col(Xa,Xb,Xc)) & (s_col(Xa,Xb,Xc) | -s_t(Xa,Xb,Xc)) & (-s_t(Xb,Xc,Xa) | s_col(Xa,Xb,Xc)) & (-s_t(Xc,Xa,Xb) | s_col(Xa,Xb,Xc)))) # label(d_Defn4_10) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 15 (all Xa all Xb all Xp (Xp = reflect(Xa,Xb,reflect(Xa,Xb,Xp)) | Xb = Xa)) # label(aSatz10_5) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 16 (all Xa all Xb all Xc all Xd ((-le(Xa,Xb,Xc,Xd) | s_e(Xa,ins(Xc,Xd,Xa,Xb),Xc,Xd)) & (ins(Xc,Xd,Xa,Xb) = ext(Xa,Xb,insert(Xa,Xb,Xc,Xd),Xd) | -le(Xa,Xb,Xc,Xd)) & (s_t(Xa,Xb,ins(Xc,Xd,Xa,Xb)) | -le(Xa,Xb,Xc,Xd)))) # label(aSatz5_5a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 17 (all Xa all Xb all Xc all Xp all Xq ((Xp != Xq | -perpAt(Xa,Xb,Xc,Xp,Xq)) & (s_col(Xp,Xq,Xc) | -perpAt(Xa,Xb,Xc,Xp,Xq)) & (-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) | Xc != g813(Xa,Xb,Xp,Xq,Xc)) & (-perpAt(Xa,Xb,Xc,Xp,Xq) | f813(Xa,Xb,Xp,Xq,Xc) != Xc) & (s_col(Xp,Xq,g813(Xa,Xb,Xp,Xq,Xc)) | -perpAt(Xa,Xb,Xc,Xp,Xq)) & (s_col(Xa,Xb,f813(Xa,Xb,Xp,Xq,Xc)) | -perpAt(Xa,Xb,Xc,Xp,Xq)) & (s_col(Xa,Xb,Xc) | -perpAt(Xa,Xb,Xc,Xp,Xq)) & (Xb != Xa | -perpAt(Xa,Xb,Xc,Xp,Xq)))) # label(aSatz8_13a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 18 (all Xa all Xb all Xc all Xd all Xe all Xf ((-congruent(Xa,Xb,Xc,Xd,Xe,Xf) | sameside(ext(Xe,Xd,Xb,Xa),Xe,Xd)) & (sameside(ext(Xe,Xf,Xb,Xc),Xe,Xf) | -congruent(Xa,Xb,Xc,Xd,Xe,Xf)) & (-congruent(Xa,Xb,Xc,Xd,Xe,Xf) | s_e3(ext(Xb,Xa,Xe,Xd),Xb,ext(Xb,Xc,Xe,Xf),ext(Xe,Xd,Xb,Xa),Xe,ext(Xe,Xf,Xb,Xc))) & (sameside(ext(Xb,Xc,Xe,Xf),Xb,Xc) | -congruent(Xa,Xb,Xc,Xd,Xe,Xf)) & (-congruent(Xa,Xb,Xc,Xd,Xe,Xf) | sameside(ext(Xb,Xa,Xe,Xd),Xb,Xa)))) # label(aSatz11_3a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 19 (all Xa all Xb all Xc all Xd (Xb = Xa | Xb = Xc | Xc = Xd | perp(Xb,Xa,Xa,Xd) | -s_col(Xa,Xc,Xd) | -perp(Xb,Xa,Xa,Xc) | Xa = Xd | Xa = Xc)) # label(aExtPerp3) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 20 (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]. 1.16/1.42 21 (all Xa all Xb all Xp (-s_col(Xa,Xb,Xp) | Xp = reflect(Xa,Xb,Xp) | Xa = Xb)) # label(aSatz10_8b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 22 (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]. 1.16/1.42 23 (all Xa1 all Xc all Xa2 all Xb1 all Xb2 all Xm1 all Xm2 (-s_t(Xa1,Xc,Xa2) | -s_t(Xb1,Xc,Xb2) | -s_e(Xc,Xa1,Xc,Xb1) | -s_m(Xa1,Xm1,Xb1) | s_t(Xm1,Xc,Xm2) | -s_m(Xa2,Xm2,Xb2) | -s_e(Xc,Xa2,Xc,Xb2))) # label(aSatz7_22) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 24 (all Xa all Xb all Xc ((Xa = Xb | perp(Xa,Xb,erect21a(Xa,Xb,Xc),Xa) | s_col(Xa,Xb,Xc)) & (s_col(Xa,Xb,Xc) | s_t(Xc,erectAux21a(Xa,Xb,Xc),erect21a(Xa,Xb,Xc)) | Xb = Xa) & (s_col(Xa,Xb,erectAux21a(Xa,Xb,Xc)) | s_col(Xa,Xb,Xc) | Xa = Xb))) # label(aSatz8_21a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 25 (all Xa all Xb all Xc all Xa1 all Xc1 (-s_e(Xa,Xb,Xa1,Xb) | s_e(Xa,Xc,Xa1,Xc1) | -s_e(Xb,Xc,Xb,Xc1) | -s_r(Xa1,Xb,Xc1) | -s_r(Xa,Xb,Xc))) # label(aSatz10_12a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 26 (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]. 1.16/1.42 27 (all Xa all Xp all Xq all Xc all Xm all Xr all Xb (-opposite(Xa,Xp,Xq,Xc) | -s_col(Xp,Xq,Xm) | -s_m(Xa,Xm,Xc) | -s_col(Xp,Xq,Xr) | -sameside(Xa,Xr,Xb) | opposite(Xb,Xp,Xq,Xc))) # label(aSatz9_3) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 28 (all Xa all Xc all Xp all Xb all Xq ((-s_t(Xa,Xc,Xp) | -s_t(Xb,Xq,Xc) | s_t(Xa,op(Xq,Xb,Xp,Xc,Xa),Xb)) & (s_t(Xp,Xq,op(Xq,Xb,Xp,Xc,Xa)) | -s_t(Xb,Xq,Xc) | -s_t(Xa,Xc,Xp)))) # label(aSatz9_6) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 29 (all Xa all Xp all Xb all Xc (sameside(Xa,Xp,Xb) | Xa = Xp | Xp = Xb | -s_t(Xa,Xp,Xc) | -s_t(Xb,Xp,Xc) | Xc = Xp)) # label(aSatz6_3b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 30 (all Xa all Xb all Xc all Xa1 all Xb1 (-s_e(Xa,Xb,Xa1,Xb1) | s_e3(Xa,Xb,Xc,Xa1,Xb1,insert5(Xa,Xb,Xc,Xa1,Xb1)) | -s_col(Xa,Xb,Xc))) # label(aSatz4_14) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 31 (all Xa all Xb s_t(Xa,Xb,Xb)) # label(aSatz3_1) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 32 (all Xa all Xb all Xc all Xd (s_e(Xa,Xb,Xc,Xd) | -le(Xc,Xd,Xa,Xb) | -le(Xa,Xb,Xc,Xd))) # label(aSatz5_9) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 33 (all Xa all Xp all Xq (s(Xa,Xp) != s(Xa,Xq) | Xq = Xp)) # label(aSatz7_9) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 34 (all Xa all Xb (Xa = Xb | -s_r(Xa,Xb,Xa))) # label(aSatz8_8) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 35 (all Xa all Xp all Xq all Xb all Xc (-opposite(Xa,Xp,Xq,Xb) | opposite(Xa,Xp,Xq,Xc) | -samesideline(Xb,Xc,Xp,Xq))) # label(aLemma9_13e) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 36 (all Xp all Xa all Xr all Xq (-s_m(Xp,Xa,Xr) | Xq = Xr | -s_m(Xp,Xa,Xq))) # label(aSatz7_4b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 37 (all Xa all Xb all Xc all Xp all Xq (Xa = Xb | Xa = Xc | -samesideline(Xp,Xq,Xa,Xb) | samesideline(Xp,Xq,Xa,Xc) | -s_col(Xa,Xb,Xc))) # label(aExtSameSide1) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 38 (all Xa all Xb all Xa1 all Xc1 insert(Xa,Xb,Xa1,Xc1) = ext(ext(Xc1,Xa1,alpha,gamma),Xa1,Xa,Xb)) # label(d_insert) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 39 (all Xa all Xb all Xc all Xp all Xq (-s_col(Xa,Xb,Xq) | Xp = Xq | -perp(Xa,Xb,Xc,Xq) | -perp(Xa,Xb,Xc,Xp) | -s_col(Xa,Xb,Xp) | s_col(Xa,Xb,Xc))) # label(aSatz8_18a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 40 (all Xa all Xb all Xc all Xd all Xe all Xf (le(Xa,Xb,Xe,Xf) | -le(Xc,Xd,Xe,Xf) | -le(Xa,Xb,Xc,Xd))) # label(aSatz5_8) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 41 (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]. 1.16/1.42 42 (all Xp all Xq all Xr all Xa (-sameside(Xa,Xp,Xr) | s_col(Xa,Xp,Xq) | -s_t(Xq,Xp,Xr) | Xp = Xr | Xq = Xp)) # label(aSatz6_15c) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 43 (all Xa all Xb all Xc all Xa1 all Xc1 (-s_r(Xa1,Xb,Xc1) | -s_e(Xb,Xc,Xb,Xc1) | s_e(Xa,Xc,Xa1,Xc1) | Xc1 = Xc | midpoint(Xc,Xc1) != Xb | -s_e(Xa,Xb,Xa1,Xb) | -s_r(Xa,Xb,Xc))) # label(aSatz10_12c) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 44 (all Xp all Xa all Xq all Xb (-s_m(Xp,Xb,Xq) | Xb = Xa | -s_m(Xp,Xa,Xq))) # label(aSatz7_17) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 45 (all Xa all Xb s_m(Xa,midpoint(Xa,Xb),Xb)) # label(aSatz8_22) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 46 (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) | Xa = Xb | -s_col(Xa,Xb,Xq) | -s_col(Xa,Xb,Xp))) # label(aExtPerp) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 47 (all Xa all Xb all Xc all Xd all Xa1 all Xb1 all Xc1 all Xd1 ((-s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1) | s_e(Xa,Xd,Xa1,Xd1)) & (s_e(Xb,Xd,Xb1,Xd1) | -s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1)) & (-s_col(Xa,Xb,Xc) | -s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1) | -s_e(Xa,Xd,Xa1,Xd1) | s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1) | -s_e(Xb,Xd,Xb1,Xd1)) & (-s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1) | s_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]. 1.16/1.42 48 (all Xb all Xa Xb != ext(Xa,Xb,alpha,gamma)) # label(aSatz3_14b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 49 (all Xa all Xc all Xd le(Xa,Xa,Xc,Xd)) # label(aSatz5_11) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 50 (all Xa all Xb all Xc all Xd (Xa = Xb | s_t(Xa,Xc,Xd) | s_t(Xa,Xd,Xc) | -s_t(Xa,Xb,Xd) | -s_t(Xa,Xb,Xc))) # label(aSatz5_1) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 51 (all Xa all Xb all Xc (Xb = Xa | Xb = Xc | congruent(Xa,Xb,Xc,Xa,Xb,Xc))) # label(aSatz11_6) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 52 (all Xa all Xb all Xc all Xa1 all Xb1 all Xp ((-s_t(Xa,Xb,Xc) | -s_t(Xa1,Xb1,Xc) | -s_t(Xa,Xp,Xa1) | s_t(Xp,crossbar(Xa,Xb,Xc,Xa1,Xb1,Xp),Xc)) & (-s_t(Xa,Xp,Xa1) | s_t(Xb,crossbar(Xa,Xb,Xc,Xa1,Xb1,Xp),Xb1) | -s_t(Xa1,Xb1,Xc) | -s_t(Xa,Xb,Xc)))) # label(aSatz3_17) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 53 (all Xp all Xq all Xr all Xa (Xp = Xr | -s_col(Xa,Xp,Xq) | sameside(Xa,Xp,Xr) | sameside(Xa,Xp,Xq) | Xp = Xa | -s_t(Xq,Xp,Xr) | Xq = Xp)) # label(aSatz6_15a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 54 (all Xa all Xb all Xc all Xa1 (-s_r(Xa,Xb,Xc) | Xb = Xc | -s_t(Xa,Xc,Xa1) | -s_r(Xa1,Xb,Xc))) # label(aSatz8_6) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 55 (all Xa all Xp s(Xa,s(Xa,Xp)) = Xp) # label(aSatz7_7) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 56 (all Xa all Xb all Xp all Xq all Xu all Xc all Xv ((s_t(Xa,ss1(Xa,Xb,Xp,Xq),ss3(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) | 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) | ss3(Xa,Xb,Xp,Xq) != ss2(Xa,Xb,Xp,Xq)) & (Xq != Xp | -samesideline(Xa,Xb,Xp,Xq)) & (-s_col(Xp,Xq,Xa) | -samesideline(Xa,Xb,Xp,Xq)) & (-samesideline(Xa,Xb,Xp,Xq) | -s_col(Xp,Xq,Xb)) & (-s_col(Xp,Xq,Xu) | Xc = Xu | Xc = Xv | Xa = Xu | s_col(Xp,Xq,Xb) | samesideline(Xa,Xb,Xp,Xq) | s_col(Xp,Xq,Xa) | Xb = Xv | Xq = Xp | -s_col(Xp,Xq,Xv) | -s_t(Xb,Xv,Xc) | -s_t(Xa,Xu,Xc)) & (s_t(Xb,ss2(Xa,Xb,Xp,Xq),ss3(Xa,Xb,Xp,Xq)) | -samesideline(Xa,Xb,Xp,Xq)) & (-samesideline(Xa,Xb,Xp,Xq) | s_col(Xp,Xq,ss2(Xa,Xb,Xp,Xq))) & (s_col(Xp,Xq,ss1(Xa,Xb,Xp,Xq)) | -samesideline(Xa,Xb,Xp,Xq)))) # label(d_Defn9_7) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 57 (all Xa all Xb all Xc all Xa1 all Xb1 all Xp all Xc1 all Xc2 (Xb = Xa | s_col(Xa1,Xb1,Xp) | -s_e(Xa,Xb,Xa1,Xb1) | -s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc2) | Xc1 = Xc2 | -samesideline(Xc2,Xp,Xa1,Xb1) | -samesideline(Xc1,Xp,Xa1,Xb1) | -s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1) | s_col(Xa,Xb,Xc))) # label(aSatz10_16b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 58 (all Xa all Xb all Xp ((s_col(Xa,Xb,midpoint(Xp,reflect(Xa,Xb,Xp))) | Xb = Xa) & (perp(Xa,Xb,Xp,reflect(Xa,Xb,Xp)) | reflect(Xa,Xb,Xp) = Xp | Xa = Xb))) # label(aSatz10_2a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 59 (all Xb all Xc all Xa all Xq ((-s_col(Xb,Xc,Xa) | samesideline(erectsameside(Xb,Xc,Xa,Xq),Xq,Xb,Xc) | s_col(Xb,Xc,Xq) | Xb = Xc) & (Xc = Xb | s_col(Xb,Xc,Xq) | perp(Xb,Xc,erectsameside(Xb,Xc,Xa,Xq),Xa) | -s_col(Xb,Xc,Xa)))) # label(aSatz10_15) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 60 (all Xa all Xb all Xc all Xd (-s_t(Xa,Xb,Xc) | -s_t(Xa,Xc,Xd) | s_t(Xb,Xc,Xd))) # label(aSatz3_6a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 61 (all Xa all Xb all Xc all Xc1 (Xa = Xb | Xc1 = Xc | -s_e(Xb,Xc,Xb,Xc1) | -s_e(Xa,Xc,Xa,Xc1) | -s_col(Xa,Xb,Xc))) # label(aSatz4_18) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 62 (all Xa all Xb all Xc all Xa1 all Xc1 ((-s_t(Xa,Xb,Xc) | -s_e(Xa,Xc,Xa1,Xc1) | s_e3(Xa,Xb,Xc,Xa1,insert(Xa,Xb,Xa1,Xc1),Xc1)) & (s_t(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]. 1.16/1.42 63 (all Xa all Xb all Xc (-s_t(Xa,Xb,Xc) | -s_e(Xa,Xc,Xa,Xb) | Xb = Xc)) # label(aNarbouxLemma1) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 64 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_e(Xb,Xc,Xb1,Xc1) | s_e(Xa,Xc,Xa1,Xc1) | -s_e(Xb,Xa,Xb1,Xa1) | -sameside(Xa1,Xb1,Xc1) | -sameside(Xa,Xb,Xc))) # label(aSatz6_28) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 65 (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]. 1.16/1.42 66 (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]. 1.16/1.42 67 (all Xa all Xb all Xc all Xd all Xe all Xf all Xa2 all Xc2 all Xd2 all Xf2 (-congruent(Xa,Xb,Xc,Xd,Xe,Xf) | -sameside(Xa2,Xb,Xa) | -sameside(Xd2,Xe,Xd) | s_e(Xa2,Xc2,Xd2,Xf2) | -s_e(Xb,Xc2,Xe,Xf2) | -s_e(Xb,Xa2,Xe,Xd2) | -sameside(Xf2,Xe,Xf) | -sameside(Xc2,Xb,Xc))) # label(aSatz11_4) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 68 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_col(Xa,Xb,Xc) | s_col(Xa1,Xb1,Xc1) | -s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1))) # label(aSatz4_13) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 69 (all Xa all Xb s_e(Xa,Xa,Xb,Xb)) # label(aSatz2_8) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 70 (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]. 1.16/1.42 71 (all Xa all Xb all Xd all Xc (-s_t(Xa,Xb,Xd) | s_t(Xa,Xb,Xc) | -s_t(Xb,Xc,Xd))) # label(aSatz3_5a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 72 (all Xa all Xb all Xp all Xq all Xc ((-s_col(Xa,Xb,Xp) | -s_col(Xa,Xb,Xc) | -perp(Xa,Xb,Xc,Xp) | Xq = Xp | -s_col(Xa,Xb,Xq) | Xb = Xa) & (-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]. 1.16/1.42 73 (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]. 1.16/1.42 74 (all Xa1 all Xb1 s_t(Xa1,Xa1,Xb1)) # label(aSatz3_3) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 75 (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]. 1.16/1.42 76 (all Xa all Xb all Xc (-s_col(Xa,Xb,Xc) | Xc = Xb | Xa = Xb | -s_r(Xa,Xb,Xc))) # label(aSatz8_9) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 77 (all Xd all Xe all Xd1 all Xa all Xb (Xd = Xe | -s_t(Xe,Xd,Xd1) | -samesideline(Xa,Xb,Xd1,Xe) | samesideline(Xa,Xb,Xd,Xe))) # label(aLemma9_13c) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 78 (all Xa all Xb all Xp all Xp1 (Xa = Xb | Xp1 != reflect(Xa,Xb,Xp) | reflect(Xa,Xb,Xp1) = Xp)) # label(aSatz10_4) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 79 (all Xp all Xq all Xa all Xb all Xt ((-s_col(Xp,Xq,Xa) | -opposite(Xa,Xp,Xq,Xb)) & (-s_col(Xp,Xq,Xb) | -opposite(Xa,Xp,Xq,Xb)) & (-opposite(Xa,Xp,Xq,Xb) | s_t(Xa,il(Xa,Xb,Xp,Xq),Xb)) & (-opposite(Xa,Xp,Xq,Xb) | s_col(Xp,Xq,il(Xa,Xb,Xp,Xq))) & (Xq = Xp | s_col(Xp,Xq,Xa) | opposite(Xa,Xp,Xq,Xb) | -s_col(Xp,Xq,Xt) | -s_t(Xa,Xt,Xb) | s_col(Xp,Xq,Xb)))) # label(d_Defn9_1) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 80 (all Xp all Xq all Xr all Xcs (opposite(Xr,Xp,Xq,Xcs) | samesideline(Xr,Xcs,Xp,Xq) | s_col(Xp,Xq,Xcs) | s_col(Xp,Xq,Xr) | Xq = Xp)) # label(aLemma9_13f) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 81 (all Xa all Xb all Xc all Xd all Xa1 all Xb1 all Xc1 all Xd1 (-s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1) | s_e(Xc,Xd,Xc1,Xd1) | Xa = Xb)) # label(aSatz4_16) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 82 (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_t(Xr,Xb,Xa) | -s_m(Xa,Xm,Xc))) # label(aSatz9_3a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 83 (all Xc all Xd all Xp all Xa all Xb (-s_col(Xa,Xb,Xp) | -sameside(Xa,Xp,Xb) | s_col(Xc,Xd,Xa) | samesideline(Xa,Xb,Xc,Xd) | -s_col(Xc,Xd,Xp) | Xd = Xc)) # label(aSatz9_19b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 84 (all Xa all Xb all Xp all Xq all Xcx all U all V (Xa = Xb | -s_col(Xp,Xq,Xcx) | -s_col(Xa,Xb,U) | V = Xcx | perpAt(Xa,Xb,Xcx,Xp,Xq) | -s_r(U,Xcx,V) | U = Xcx | -s_col(Xp,Xq,V) | -s_col(Xa,Xb,Xcx) | Xq = Xp)) # label(aSatz8_13b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 85 (all Xa all Xb s_e(Xa,Xb,Xa,Xb)) # label(aSatz2_1) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 86 (all Xa all Xp all Xq all Xc all Xcs all Xr all Xm all U (-opposite(Xa,Xp,Xq,Xc) | Xq = Xp | -s_col(Xp,Xq,Xr) | -perp(Xp,Xq,Xc,Xcs) | sameside(s(Xm,U),Xcs,Xc) | Xr = Xcs | -le(Xcs,Xc,Xr,Xa) | -sameside(U,Xr,Xa) | -s_m(Xr,Xm,Xcs) | -perp(Xp,Xq,Xa,Xr) | -s_col(Xp,Xq,Xcs))) # label(aSatz9_4a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 87 (all Xa all Xp all Xb all Xc (-s_t(Xa,Xp,Xc) | sameside(Xa,Xp,Xb) | -s_t(Xb,Xp,Xc) | Xc = Xp | Xb = Xp | Xa = Xp)) # label(aSatz6_2a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 88 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_r(Xa1,Xb1,Xc1) | -s_e(Xa,Xb,Xa1,Xb1) | s_e(Xa,Xc,Xa1,Xc1) | -s_e(Xb,Xc,Xb1,Xc1) | -s_r(Xa,Xb,Xc))) # label(aSatz10_12) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 89 (all Xa all Xb all Xc all Xd (s_col(Xa,Xc,Xd) | Xa = Xb | -s_col(Xa,Xb,Xd) | -s_col(Xa,Xb,Xc))) # label(aext1) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 90 (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]. 1.16/1.42 91 (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]. 1.16/1.42 92 (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]. 1.16/1.42 93 (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]. 1.16/1.42 94 (all Xa all Xb all Xc all Xd (-s_t(Xc,Xa,Xb) | s_t(Xc,Xd,Xb) | s_t(Xd,Xc,Xb) | -s_t(Xd,Xa,Xb) | Xa = Xb)) # label(aSatz6_16a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 95 (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]. 1.16/1.42 96 (all Xa all Xb all Xc all Xd all Y ((le(Xa,Xb,Xc,Xd) | -s_e(Xa,Xb,Xc,Y) | -s_t(Xc,Y,Xd)) & (s_e(Xa,Xb,Xc,insert(Xa,Xb,Xc,Xd)) | -le(Xa,Xb,Xc,Xd)) & (s_t(Xc,insert(Xa,Xb,Xc,Xd),Xd) | -le(Xa,Xb,Xc,Xd)))) # label(d_Defn5_4) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 97 (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]. 1.16/1.42 98 (all Xa all Xp all Xq all Xc all Xcs all Xr all Xm all U (-opposite(Xa,Xp,Xq,Xc) | Xq = Xp | -s_col(Xp,Xq,Xr) | -sameside(U,Xr,Xa) | sameside(s(Xm,U),Xcs,Xc) | -s_m(Xr,Xm,Xcs) | -perp(Xp,Xq,Xc,Xcs) | -perp(Xp,Xq,Xa,Xr) | -s_col(Xp,Xq,Xcs))) # label(aSatz9_4) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 99 (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]. 1.16/1.42 100 (all Xa all Xb all Xc (-s_r(Xa,Xb,Xc) | Xc = Xb | -s_r(Xa,Xc,Xb))) # label(aSatz8_7) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 101 (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_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3) | -s_e(Xa2,Xa3,Xb2,Xb3) | -s_e(Xa1,Xa3,Xb1,Xb3) | -s_e(Xa1,Xa2,Xb1,Xb2)) & (s_e(Xa2,Xa3,Xb2,Xb3) | -s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3)) & (s_e(Xa1,Xa2,Xb1,Xb2) | -s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3)))) # label(d_Defn4_4) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 102 (all Xa all Xp (s(Xa,Xp) != Xp | Xa = Xp)) # label(aSatz7_10a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 103 (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]. 1.16/1.42 104 (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]. 1.16/1.42 105 (all Xa all Xm (s_m(Xa,Xm,Xa) | Xa != Xm)) # label(aSatz7_3b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 106 (all Xr all Xa all Xb all Xc ((Xc = Xb | s_e(Xa,insert(Xb,Xc,Xa,Xr),Xb,Xc) | Xa = Xr) & (sameside(insert(Xb,Xc,Xa,Xr),Xa,Xr) | Xc = Xb | Xr = Xa))) # label(aSatz6_11a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 107 (all Xa all Xb all Xp all Xq (perp(Xp,Xq,Xa,Xb) | -perp(Xa,Xb,Xp,Xq))) # label(aSatz8_12b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 108 (all Xp all Xq all Xr all Xcs (Xq = Xp | s_col(Xp,Xq,Xcs) | samesideline(Xr,Xcs,Xp,Xq) | opposite(Xr,Xp,Xq,Xcs) | foot(Xp,Xq,Xr) != Xp | s_col(Xp,Xq,Xr))) # label(aLemma9_13f_case1) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 109 (all Xp all Xq (Xq = Xp | s_col(Xp,Xq,Xp))) # label(aSatz6_17a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 110 (all Xa all Xb all Xc all Xd all Za all Zb all Zc all Zd ((s_t(Za,Zb,Zc) | -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_t(Xa,Xb,Xc) | -s_e(Xa,Xc,Za,Zc) | -s_e(Xb,Xc,Zb,Zc) | -s_e(Xa,Xd,Za,Zd) | -s_e(Xc,Xd,Zc,Zd) | s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | -s_t(Za,Zb,Zc)) & (-s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_e(Xa,Xd,Za,Zd)) & (s_e(Xa,Xc,Za,Zc) | -s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)) & (s_t(Xa,Xb,Xc) | -s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)))) # label(d_Defn4_1) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 111 (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_m(Xp,Xcx,Xr) | Xcx != ip(Xp,Xt,Xq,Xb,Xr) | -s_e(Xa,Xp,Xb,Xr) | -s_t(Xb,Xr,Xq) | -perp(Xq,Xb,Xa,Xb) | -perp(Xp,Xa,Xa,Xb))) # label(aSatz8_24b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 112 (all Xa all Xb all Xc (-s_col(Xa,Xb,Xc) | s_col(Xc,Xb,Xa))) # label(aSatz4_11c) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 113 (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]. 1.16/1.42 114 (all Xp all Xq all Xcs all Xr (-s_col(Xp,Xq,Xcs) | -s_col(Xp,Xq,Xr) | s_col(Xp,Xcs,Xr) | Xcs = Xp | Xq = Xp)) # label(aSatz6_16b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 115 (all Xa all Xb all Xp all Xp1 ((-s_col(Xa,Xb,midpoint(Xp,Xp1)) | Xp1 = reflect(Xa,Xb,Xp) | Xp1 != Xp | Xb = Xa) & (Xb = Xa | -perp(Xa,Xb,Xp,Xp1) | Xp1 = reflect(Xa,Xb,Xp) | -s_col(Xa,Xb,midpoint(Xp,Xp1))))) # label(aSatz10_2b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 116 (all Xa all Xb all Xp all Xq (s_e(Xp,Xq,reflect(Xa,Xb,Xp),reflect(Xa,Xb,Xq)) | -s_col(Xa,Xb,Xp) | Xb = Xa)) # label(aSatz10_10a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 117 (all Xp all Xq all Xr (Xq = Xp | -s_col(Xp,Xq,Xr) | s_col(Xq,Xp,Xr))) # label(aSatz6_17b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 118 (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]. 1.16/1.42 119 (all Xp all Xq all Xr all Xa (Xp = Xr | -s_t(Xq,Xp,Xr) | -sameside(Xa,Xp,Xq) | s_col(Xa,Xp,Xq) | Xq = Xp)) # label(aSatz6_15b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 120 (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]. 1.16/1.42 121 (all Y all Z all X all Y1 all Z1 all U all V ((s_col(Y1,Z1,X) | -perpAt(Y,Z,X,Y1,Z1)) & (Y != Z | -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)) & (Y = Z | -s_col(Y,Z,X) | -s_r(f811(Y,Z,Y1,Z1,X),X,g811(Y,Z,Y1,Z1,X)) | -s_col(Y1,Z1,X) | Y1 = Z1 | perpAt(Y,Z,X,Y1,Z1)) & (perpAt(Y,Z,X,Y1,Z1) | Y = Z | -s_col(Y1,Z1,X) | s_col(Y1,Z1,g811(Y,Z,Y1,Z1,X)) | -s_col(Y,Z,X) | Y1 = Z1) & (Y1 = Z1 | -s_col(Y,Z,X) | -s_col(Y1,Z1,X) | s_col(Y,Z,f811(Y,Z,Y1,Z1,X)) | Y = Z | perpAt(Y,Z,X,Y1,Z1)) & (-perpAt(Y,Z,X,Y1,Z1) | Y1 != Z1) & (s_col(Y,Z,X) | -perpAt(Y,Z,X,Y1,Z1)))) # label(d_Defn8_11a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 122 (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]. 1.16/1.42 123 (all Xa all Xb all Xd all Xc (-s_t(Xa,Xb,Xd) | -s_t(Xa,Xc,Xd) | s_t(Xa,Xc,Xb) | s_t(Xa,Xb,Xc))) # label(aSatz5_3) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 124 (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,Xa2,Xc,Xb2)) & (-s_e(Xc,Xa1,Xc,Xb1) | s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) | -s_m(Xa2,Xm2,Xb2) | -s_m(Xa1,Xm1,Xb1) | -s_e(Xc,Xa2,Xc,Xb2) | -s_t(Xb1,Xc,Xb2) | -s_t(Xa1,Xc,Xa2)) & (-s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) | s_m(Xa2,Xm2,Xb2)) & (-s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) | s_m(Xa1,Xm1,Xb1)) & (-s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) | s_e(Xc,Xa1,Xc,Xb1)))) # label(d_Defn7_23) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 125 (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]. 1.16/1.42 126 (all Xp all Xq all Xr all Xa (Xr = Xp | s_col(Xa,Xp,Xq) | Xp != Xa | -s_t(Xq,Xp,Xr) | Xq = Xp)) # label(aSatz6_15d) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 127 (all Xa all Xp (Xp != Xa | Xp = s(Xa,Xp))) # label(aSatz7_10b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 128 (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)) & (perp(Xp,Xq,Xp1,Xq1) | -perpAt(Xp,Xq,X,Xp1,Xq1)))) # label(d_Defn8_11b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 129 (all Xp all Xq all Xr all Xcs (Xq = Xp | opposite(Xr,Xp,Xq,Xcs) | foot(Xp,Xq,Xr) = Xp | samesideline(Xr,Xcs,Xp,Xq) | s_col(Xp,Xq,Xcs) | s_col(Xp,Xq,Xr))) # label(aLemma9_13f_case2) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 130 (all Xa all Xb all Xc all Xp all Xq (-s_e(Xb,Xp,Xb,Xq) | s_e(Xc,Xp,Xc,Xq) | -s_e(Xa,Xp,Xa,Xq) | -s_col(Xa,Xb,Xc) | Xb = Xa)) # label(aSatz4_17) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 131 (all Xa all Xb all Xp all Xp1 (Xb = Xa | Xp1 != reflect(Xa,Xb,Xp) | s_col(Xa,Xb,Xp) | opposite(Xp,Xa,Xb,Xp1))) # label(aSatz10_14) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 132 (all Xa all Xp all Xq all Xc all Xb (-samesideline(Xa,Xb,Xp,Xq) | opposite(Xb,Xp,Xq,Xc) | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_8) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 133 (all Xa all Xb all Xc ((s_col(Xa,Xb,foot(Xa,Xb,Xc)) | s_col(Xa,Xb,Xc)) & (s_col(Xa,Xb,Xc) | perp(Xa,Xb,Xc,foot(Xa,Xb,Xc))))) # label(aSatz8_18) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 134 (all Xp all Xa all Xb all Xq all Xt all Xr all Xcx (-perp(Xq,Xb,Xa,Xb) | -s_col(Xa,Xb,Xt) | -s_t(Xp,Xt,Xq) | -s_t(Xb,Xr,Xq) | Xcx != ip(Xp,Xt,Xq,Xb,Xr) | s_m(Xa,Xcx,Xb) | -s_e(Xa,Xp,Xb,Xr) | -perp(Xp,Xa,Xa,Xb))) # label(aSatz8_24a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 135 (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]. 1.16/1.42 136 (all Xa all Xb s_col(Xa,Xb,Xa)) # label(aSatz4_12b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 137 (all Xp all Xa all Xb all Xq all Xt all Xr (-s_t(Xb,Xr,Xq) | s_m(Xp,midpoint(Xa,Xb),Xr) | -s_e(Xa,Xp,Xb,Xr) | -s_t(Xp,Xt,Xq) | -s_col(Xa,Xb,Xt) | -perp(Xq,Xb,Xa,Xb) | -perp(Xp,Xa,Xa,Xb))) # label(aSatz8_24) # label(axiom) # label(non_clause). [assumption]. 1.16/1.42 138 (all Xa all Xb all Xc all Xd all Xe all Xf ((Xd = Xe | congruent(Xa,Xb,Xc,Xd,Xe,Xf) | sameside(f113a(Xa,Xb,Xc,Xd,Xe,Xf),Xb,Xa) | Xf = Xe | Xc = Xb | Xb = Xa) & (Xd = Xe | congruent(Xa,Xb,Xc,Xd,Xe,Xf) | sameside(f113c(Xa,Xb,Xc,Xd,Xe,Xf),Xb,Xc) | Xf = Xe | Xb = Xc | Xb = Xa) & (Xa = Xb | Xb = Xc | congruent(Xa,Xb,Xc,Xd,Xe,Xf) | -s_e(f113a(Xa,Xb,Xc,Xd,Xe,Xf),f113c(Xa,Xb,Xc,Xd,Xe,Xf),f113d(Xa,Xb,Xc,Xd,Xe,Xf),f113f(Xa,Xb,Xc,Xd,Xe,Xf)) | Xe = Xf | Xd = Xe) & (Xa = Xb | Xb = Xc | Xd = Xe | Xe = Xf | s_e(Xb,f113c(Xa,Xb,Xc,Xd,Xe,Xf),Xe,f113f(Xa,Xb,Xc,Xd,Xe,Xf)) | congruent(Xa,Xb,Xc,Xd,Xe,Xf)) & (Xf = Xe | congruent(Xa,Xb,Xc,Xd,Xe,Xf) | s_e(Xb,f113a(Xa,Xb,Xc,Xd,Xe,Xf),Xe,f113d(Xa,Xb,Xc,Xd,Xe,Xf)) | Xe = Xd | Xb = Xc | Xb = Xa) & (Xe = Xf | sameside(f113f(Xa,Xb,Xc,Xd,Xe,Xf),Xe,Xf) | congruent(Xa,Xb,Xc,Xd,Xe,Xf) | Xd = Xe | Xb = Xc | Xa = Xb) & (Xb = Xc | Xe = Xd | Xf = Xe | sameside(f113d(Xa,Xb,Xc,Xd,Xe,Xf),Xe,Xd) | congruent(Xa,Xb,Xc,Xd,Xe,Xf) | Xb = Xa))) # label(aSatz11_4b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 139 (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]. 1.16/1.43 140 (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]. 1.16/1.43 141 (all Xa all Xp all Xb all Xq all Xt (-perp(Xa,Xb,Xa,Xp) | -perp(Xa,Xb,Xb,Xq) | -s_t(Xp,Xt,Xq) | s_m(Xa,midpointAux(Xa,Xb,Xp,Xq,Xt),Xb) | -s_col(Xa,Xb,Xt) | -le(Xa,Xp,Xb,Xq))) # label(aSatz8_22b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 142 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_t(Xa1,Xb1,Xc1) | -s_e(Xa,Xb,Xa1,Xb1) | -s_e(Xb,Xc,Xb1,Xc1) | s_e(Xa,Xc,Xa1,Xc1) | -s_t(Xa,Xb,Xc))) # label(aSatz2_11) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 143 (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]. 1.16/1.43 144 (all Xa all Xb all Xp all Xq all Xc all Xd all Xe (Xa = Xb | Xq = Xp | -s_col(Xp,Xq,Xc) | -s_col(Xa,Xb,Xd) | s_col(Xp,Xq,Xe) | -s_col(Xa,Xb,Xe) | Xc = Xd | -s_col(Xp,Xq,Xd) | -s_col(Xa,Xb,Xc))) # label(aSatz6_21) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 145 (all Xa all Xb all Xc all Xp all Xq (Xc = il(Xa,Xb,Xp,Xq) | -perpAt(Xa,Xb,Xc,Xp,Xq))) # label(aSatz8_14c) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 146 (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]. 1.16/1.43 147 (all Xa all Xm all Xb (-s_col(Xa,Xm,Xb) | Xb = Xa | s_m(Xa,Xm,Xb) | -s_e(Xm,Xa,Xm,Xb))) # label(aSatz7_20) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 148 (all Xa all Xb all Xp all Xq (s_e(Xp,Xq,reflect(Xa,Xb,Xp),reflect(Xa,Xb,Xq)) | Xb = Xa)) # label(aSatz10_10) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 149 (all Xp all Xq all Xc all Xa all Xb (Xp = Xq | -perpAt(Xp,Xq,Xc,Xa,Xc) | -perpAt(Xp,Xq,Xc,Xb,Xc) | Xa = Xc | s_col(Xc,Xa,Xb))) # label(aLemma9_13g) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 150 (all Xp all Xa all Xq (-s_m(Xp,Xa,Xq) | s(Xa,Xp) = Xq)) # label(aSatz7_6) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 151 (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(Za,Zb,Zc)) & (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_e(Xa,Xb,Za,Zb) | -s_e(Xb,Xc,Zb,Zc) | -s_e(Xa,Xd,Za,Zd) | -s_e(Xb,Xd,Zb,Zd) | s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | -s_t(Za,Zb,Zc) | -s_t(Xa,Xb,Xc)) & (s_e(Xb,Xd,Zb,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_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_t(Xa,Xb,Xc)))) # label(d_Defn2_10) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 152 (all Xa all Xb all Xc all Xd all Xp (Xa = Xb | -s_col(Xa,Xb,Xc) | -s_col(Xa,Xb,Xd) | s_col(Xa,Xb,Xp) | -s_col(Xc,Xd,Xp) | Xd = Xc)) # label(aExtCol2) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 153 (all Xa all Xp all Xb all Xc (Xa = Xp | Xc = Xp | -s_t(Xa,Xp,Xc) | -sameside(Xa,Xp,Xb) | s_t(Xb,Xp,Xc) | Xp = Xb)) # label(aSatz6_2b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 154 (all Xa all Xb all Xc all Xm (-sameside(Xa,Xb,Xc) | sameside(s(Xm,Xa),s(Xm,Xb),s(Xm,Xc)))) # label(aSideReflect) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 155 (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]. 1.16/1.43 156 (all Xa all Xb all Xp all Xq all Xc (Xb = Xa | perp(Xa,Xb,Xc,Xp) | s_col(Xa,Xb,Xc) | -s_r(Xc,Xp,Xq) | Xq = Xp | -s_col(Xa,Xb,Xq) | -s_col(Xa,Xb,Xp))) # label(aSatz8_16b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 157 (all Xa all Xp all Xr all Xq (s(Xa,Xp) != Xr | Xr != s(Xa,Xq) | Xp = Xq)) # label(aSatz7_8) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 158 (all Xa all Xp all Xb all Xc (sameside(Xa,Xp,Xc) | -sameside(Xb,Xp,Xc) | -sameside(Xa,Xp,Xb))) # label(aSatz6_7) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 159 (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]. 1.16/1.43 160 (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]. 1.16/1.43 161 (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]. 1.16/1.43 162 (all Xa1 all Xb all Xa all Xc1 all Xc all Xd1 all Xe all Xd all Xf1 all Xf (-sameside(Xa1,Xb,Xa) | congruent(Xa,Xb,Xc,Xd,Xe,Xf) | -s_e3(Xa1,Xb,Xc1,Xd1,Xe,Xf1) | -sameside(Xf1,Xe,Xf) | -sameside(Xd1,Xe,Xd) | -sameside(Xc1,Xb,Xc))) # label(aSatz11_3d) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 163 (all Xa all Xp all Xb (sameside(Xb,Xp,Xa) | -sameside(Xa,Xp,Xb))) # label(aSatz6_6) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 164 (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]. 1.16/1.43 165 (all Xb all Xc all Xa (-s_e(Xb,Xc,Xa,Xa) | Xc = Xb)) # label(aSatz2_13) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 166 (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]. 1.16/1.43 167 (all Xa all Xb all Xd all Xc (perpAt(Xa,Xb,Xd,Xc,Xd) | -perp(Xa,Xb,Xc,Xd) | -s_col(Xa,Xb,Xd) | Xb = Xa)) # label(aSatz8_15) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 168 (all Xa all Xb le(Xa,Xb,Xa,Xb)) # label(aSatz5_7) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 169 (all Xa all Xb all Xp all Xp1 (Xa = Xb | reflect(Xa,Xb,Xp) != Xp1 | Xp = reflect(Xa,Xb,Xp1))) # label(aSatz10_6) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 170 (all Xa all Xb all Xc all Xp (-s_m(s(Xa,Xc),Xp,s(Xb,Xc)) | Xb = Xc | Xa != Xp | -s_r(Xa,Xb,Xc))) # label(aSatz8_20b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 171 (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]. 1.16/1.43 172 (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]. 1.16/1.43 173 (all Xa all Xb all Xp all Xq all Xc all Xd (-s_col(Xa,Xb,Xp) | -s_col(Xa,Xb,Xq) | Xp = Xq | -perp(Xa,Xb,Xc,Xd) | perp(Xp,Xq,Xc,Xd) | Xa = Xb)) # label(aExtPerp5) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 174 (all Xa1 all Xm1 all Xb1 all Xc all Xb2 all Xm2 all Xa2 (-s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) | -le(Xc,Xa1,Xc,Xa2) | s_t(Xm1,Xc,Xm2))) # label(aSatz7_22a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 175 (all Xa all Xb all Xp all Xq all Xc (-s_col(Xp,Xq,Xc) | perpAt(Xa,Xb,Xc,Xp,Xq) | -s_col(Xa,Xb,Xc) | -perp(Xa,Xb,Xp,Xq))) # label(aSatz8_14b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 176 (all Xa all Xb all Xc all XA all XB all XC (-s_t(XA,XB,XC) | -s_e(Xa,Xb,XB,XC) | -s_e(Xb,Xc,XA,XB) | s_e(Xa,Xc,XA,XC) | -s_t(Xa,Xb,Xc))) # label(aSatz2_15) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 177 (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]. 1.16/1.43 178 (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))) & (s_t(Xc,erectAux(Xa,Xb,Xc),erect(Xa,Xb,Xc)) | Xb = Xa))) # label(aSatz8_21) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 179 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_t(Xa,Xb,Xc) | -s_e(Xa,Xc,Xa1,Xc1) | s_e(Xa,Xb,Xa1,Xb1) | -s_e(Xb,Xc,Xb1,Xc1) | -s_t(Xa1,Xb1,Xc1))) # label(aSatz4_3) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 180 (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]. 1.16/1.43 181 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1) | s_r(Xa1,Xb1,Xc1) | -s_r(Xa,Xb,Xc))) # label(aSatz8_10) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 182 (all Xa all Xb all Xp (Xb = Xa | s_col(Xa,Xb,Xp) | Xp != reflect(Xa,Xb,Xp))) # label(aSatz10_8a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 183 (all Xa all Xp all Xq all Xc all Xcs all Xr all Xm all U (-opposite(Xa,Xp,Xq,Xc) | -s_col(Xp,Xq,Xcs) | -perp(Xp,Xq,Xa,Xr) | Xr != Xcs | sameside(s(Xm,U),Xcs,Xc) | -sameside(U,Xr,Xa) | -s_m(Xr,Xm,Xcs) | -perp(Xp,Xq,Xc,Xcs) | -s_col(Xp,Xq,Xr) | Xq = Xp)) # label(aSatz9_4b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 184 (all Xa all Xb s_col(Xa,Xa,Xb)) # label(aSatz4_12) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 185 (all Xr all Xa all Xb all Xc all Xp all Xq (Xc = Xb | -s_e(Xa,Xp,Xb,Xc) | -sameside(Xq,Xa,Xr) | Xq = Xp | -s_e(Xa,Xq,Xb,Xc) | -sameside(Xp,Xa,Xr) | Xa = Xr)) # label(aSatz6_11b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 186 (all Xa all Xb all Xc all Xd all Xp (-s_e(Xa,Xb,Xc,Xd) | -s_e(Xb,Xc,Xd,Xa) | -s_col(Xb,Xp,Xd) | s_m(Xa,Xp,Xc) | -s_col(Xa,Xp,Xc) | Xb = Xd | s_col(Xa,Xb,Xc))) # label(aSatz7_21) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 187 (all Xa all Xb all Xp (s(Xb,s(Xa,Xp)) != s(Xa,s(Xb,Xp)) | Xb = Xa)) # label(aSatz7_19) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 188 (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) | -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,Xr) | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_4c) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 189 (all Xa all Xb all Xc all Xd (-s_t(Xa,Xb,Xc) | -s_t(Xb,Xc,Xd) | Xc = Xb | s_t(Xa,Xb,Xd))) # label(aSatz3_7b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 190 (all Xa all Xb all Xp all Xq (-samesideline(Xp,Xq,Xa,Xb) | samesideline(Xp,Xq,Xb,Xa) | Xa = Xb)) # label(aExtSameSide2) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 191 (all Xq all Xa all Xd all Xb all Xc (-s_t(Xq,Xa,Xd) | ext(Xq,Xa,Xb,Xc) = Xd | -s_e(Xa,Xd,Xb,Xc) | Xq = Xa)) # label(aSatz2_12) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 192 (all Xa all Xp all Xb ((Xp != Xa | -sameside(Xa,Xp,Xb)) & (Xb != Xp | -sameside(Xa,Xp,Xb)) & (-s_t(Xp,Xa,Xb) | Xp = Xa | xb = Xp | sameside(Xa,Xp,Xb)) & (Xb = Xp | sameside(Xa,Xp,Xb) | Xp = Xa | -s_t(Xp,Xb,Xa)) & (s_t(Xp,Xb,Xa) | s_t(Xp,Xa,Xb) | -sameside(Xa,Xp,Xb)))) # label(d_Defn6_1) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 193 (all Xp all Xa s_m(Xp,Xa,s(Xa,Xp))) # label(aSatz7_4a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 194 (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]. 1.16/1.43 195 (all Xa all Xp (Xa = Xp | sameside(Xa,Xp,Xa))) # label(aSatz6_5) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 196 (all Xa all Xb all Xc all Xd (-s_t(Xa,Xb,Xc) | Xb = Xc | s_t(Xa,Xc,Xd) | -s_t(Xb,Xc,Xd))) # label(aSatz3_7a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 197 (all Xa all Xp all Xb (s(Xa,Xp) != s(Xb,Xp) | Xb = Xa)) # label(aSatz7_18) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 198 (all Xa all Xb all Xc (-s_col(Xa,Xb,Xc) | le(Xa,Xb,Xa,Xc) | -s_t(Xa,Xb,Xc))) # label(aSatz5_12a1) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 199 (all Xa all Xb all Xc all Xa1 all Xb1 all Xp ((s_col(Xa1,Xb1,Xp) | s_e3(Xa,Xb,Xc,Xa1,Xb1,triangle(Xa,Xb,Xc,Xa1,Xb1,Xp)) | -s_e(Xa,Xb,Xa1,Xb1) | s_col(Xa,Xb,Xc) | Xa = Xb) & (samesideline(triangle(Xa,Xb,Xc,Xa1,Xb1,Xp),Xp,Xa1,Xb1) | -s_e(Xa,Xb,Xa1,Xb1) | s_col(Xa1,Xb1,Xp) | s_col(Xa,Xb,Xc) | Xb = Xa))) # label(aSatz10_16a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 200 (all Xp all Xq all Xa all Xb all Xc (Xq = Xp | -samesideline(Xb,Xc,Xp,Xq) | samesideline(Xa,Xc,Xp,Xq) | -samesideline(Xa,Xb,Xp,Xq))) # label(aSatz9_13) # label(axiom) # label(non_clause). [assumption]. 1.16/1.43 201 (all Xa all Xb all Xc all Xd all Xa1 all Xb1 all Xc1 all Xd1 (-le(Xa,Xb,Xc,Xd) | -s_e(Xc,Xd,Xc1,Xd1) | le(Xa1,Xb1,Xc1,Xd1) | -s_e(Xa,Xb,Xa1,Xb1))) # label(aSatz5_6) # label(axiom) # label(non_clause). [assumption]. 1.16/1.44 202 (all Xa all Xm (Xm = Xa | -s_m(Xa,Xm,Xa))) # label(aSatz7_3a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.44 203 (all Xa all Xb (-s_col(Xa,Xb,pointOffLine(Xa,Xb)) | Xb = Xa)) # label(aSatz6_25) # label(axiom) # label(non_clause). [assumption]. 1.16/1.44 204 (all Xa all Xb s_t(Xa,Xb,ext(Xa,Xb,alpha,gamma))) # label(aSatz3_14a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.44 205 (all Xa all Xb all Xp all Xq all Xr (Xb = Xa | -s_col(Xp,Xq,Xr) | s_col(Xa,Xb,Xr) | -s_col(Xp,Xq,Xb) | -s_col(Xp,Xq,Xa) | Xq = Xp)) # label(aSatz6_18) # label(axiom) # label(non_clause). [assumption]. 1.16/1.44 206 (all Xa all Xb all Xc (s_r(Xa,Xb,s(Xb,Xc)) | -s_r(Xa,Xb,Xc))) # label(aSatz8_4) # label(axiom) # label(non_clause). [assumption]. 1.16/1.44 207 (all Xa all Xb all Xd all Xc (-s_t(Xa,Xb,Xd) | -s_t(Xb,Xc,Xd) | s_t(Xa,Xc,Xd))) # label(aSatz3_5b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.44 208 (all Xa all Xp all Xb (-sameside(Xa,Xp,Xb) | -le(Xp,Xa,Xp,Xb) | s_t(Xp,Xa,Xb))) # label(aSatz6_13a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.44 209 (all Xa all Xm all Xb ((s_t(Xa,Xm,Xb) | -s_m(Xa,Xm,Xb)) & (s_e(Xm,Xa,Xm,Xb) | -s_m(Xa,Xm,Xb)) & (-s_t(Xa,Xm,Xb) | s_m(Xa,Xm,Xb) | -s_e(Xm,Xa,Xm,Xb)))) # label(d_Defn7_1) # label(axiom) # label(non_clause). [assumption]. 1.16/1.44 210 (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]. 1.16/1.44 211 (all Xa all Xb all U all V all W (Xa = Xb | -s_m(U,V,W) | -s_col(Xa,Xb,W) | s_col(Xa,Xb,V) | -s_col(Xa,Xb,U))) # label(aLemma9_13b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.44 212 (all Xc all Xa all Xb (-s_e(Xc,Xa,Xc,Xb) | s_m(Xa,isomidpoint(Xa,Xb,Xc),Xb))) # label(aSatz7_25) # label(axiom) # label(non_clause). [assumption]. 1.16/1.44 213 (all Xa all Xp all Xb ((c63(Xa,Xp,Xb) != Xp | -sameside(Xa,Xp,Xb)) & (s_t(Xa,Xp,c63(Xa,Xp,Xb)) | -sameside(Xa,Xp,Xb)) & (s_t(Xb,Xp,c63(Xa,Xp,Xb)) | -sameside(Xa,Xp,Xb)) & (-sameside(Xa,Xp,Xb) | Xb != Xp) & (Xp != Xa | -sameside(Xa,Xp,Xb)))) # label(aSatz6_3a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.44 214 (all Xa all Xp all Xq all Xc all Xcs all Xr all Xm all U (Xp = Xq | -s_col(Xp,Xq,Xr) | -perp(Xp,Xq,Xa,Xr) | sameside(U,Xr,Xa) | -le(Xcs,Xc,Xr,Xa) | -sameside(s(Xm,U),Xcs,Xc) | Xr = Xcs | -s_m(Xr,Xm,Xcs) | -perp(Xp,Xq,Xc,Xcs) | -s_col(Xp,Xq,Xcs) | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_4a2) # label(axiom) # label(non_clause). [assumption]. 1.16/1.44 215 (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]. 1.16/1.44 216 (all Xa all Xb all Xc all Xd (Xa = Xb | -s_t(Xa,Xb,Xc) | s_t(Xb,Xd,Xc) | s_t(Xb,Xc,Xd) | -s_t(Xa,Xb,Xd))) # label(aSatz5_2) # label(axiom) # label(non_clause). [assumption]. 1.16/1.44 217 (all Xa all Xb s_r(Xa,Xb,Xb)) # label(aSatz8_5) # label(axiom) # label(non_clause). [assumption]. 1.16/1.44 218 -(all Xa all Xb all Xc all Xd all Xe all Xf (congruent(Xd,Xe,Xf,Xa,Xb,Xc) | -congruent(Xa,Xb,Xc,Xd,Xe,Xf))) # label(aSatz11_7) # label(negated_conjecture) # label(non_clause). [assumption]. 1.16/1.44 1.16/1.44 ============================== end of process non-clausal formulas === 1.16/1.44 1.16/1.44 ============================== PROCESS INITIAL CLAUSES =============== 1.16/1.44 1.16/1.44 ============================== PREDICATE ELIMINATION ================= 1.16/1.44 219 -s_col(A,B,C) | -s_e3(A,B,C,D,E,F) | -s_e(A,V6,D,V7) | s_fs(A,B,C,V6,D,E,F,V7) | -s_e(B,V6,E,V7) # label(d_Defn4_15) # label(axiom). [clausify(47)]. 1.16/1.44 220 -s_fs(A,B,C,D,E,F,V6,V7) | s_e(A,D,E,V7) # label(d_Defn4_15) # label(axiom). [clausify(47)]. 1.16/1.44 221 s_e(A,B,C,D) | -s_fs(E,A,F,B,V6,C,V7,D) # label(d_Defn4_15) # label(axiom). [clausify(47)]. 1.16/1.44 222 -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(47)]. 1.16/1.44 223 -s_fs(A,B,C,D,E,F,V6,V7) | s_col(A,B,C) # label(d_Defn4_15) # label(axiom). [clausify(47)]. 1.16/1.44 224 -s_fs(A,B,C,D,E,F,V6,V7) | s_e(C,D,V6,V7) | B = A # label(aSatz4_16) # label(axiom). [clausify(81)]. 1.16/1.44 Derived: s_e(A,B,C,D) | E = F | -s_col(F,E,A) | -s_e3(F,E,A,V6,V7,C) | -s_e(F,B,V6,D) | -s_e(E,B,V7,D). [resolve(224,a,219,d)]. 1.16/1.44 225 -s_e(A,B,A,C) | s_kf(B,D,C,A,E,F,V6) | -s_m(V6,F,E) | -s_m(B,D,Alarm clock 179.09/180.04 Prover9 interrupted 179.09/180.05 EOF