0.06/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.11/0.32 % Computer : n024.cluster.edu 0.11/0.32 % Model : x86_64 x86_64 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.32 % Memory : 8042.1875MB 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.32 % CPULimit : 960 0.11/0.32 % DateTime : Thu Jul 2 14:07:35 EDT 2020 0.11/0.33 % CPUTime : 1.14/1.54 ============================== Prover9 =============================== 1.14/1.54 Prover9 (32) version 2009-11A, November 2009. 1.14/1.54 Process 21102 was started by sandbox2 on n024.cluster.edu, 1.14/1.54 Thu Jul 2 14:07:37 2020 1.14/1.54 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_20946_n024.cluster.edu". 1.14/1.54 ============================== end of head =========================== 1.14/1.54 1.14/1.54 ============================== INPUT ================================= 1.14/1.54 1.14/1.54 % Reading from file /tmp/Prover9_20946_n024.cluster.edu 1.14/1.54 1.14/1.54 set(prolog_style_variables). 1.14/1.54 set(auto2). 1.14/1.54 % set(auto2) -> set(auto). 1.14/1.54 % set(auto) -> set(auto_inference). 1.14/1.54 % set(auto) -> set(auto_setup). 1.14/1.54 % set(auto_setup) -> set(predicate_elim). 1.14/1.54 % set(auto_setup) -> assign(eq_defs, unfold). 1.14/1.54 % set(auto) -> set(auto_limits). 1.14/1.54 % set(auto_limits) -> assign(max_weight, "100.000"). 1.14/1.54 % set(auto_limits) -> assign(sos_limit, 20000). 1.14/1.54 % set(auto) -> set(auto_denials). 1.14/1.54 % set(auto) -> set(auto_process). 1.14/1.54 % set(auto2) -> assign(new_constants, 1). 1.14/1.54 % set(auto2) -> assign(fold_denial_max, 3). 1.14/1.54 % set(auto2) -> assign(max_weight, "200.000"). 1.14/1.54 % set(auto2) -> assign(max_hours, 1). 1.14/1.54 % assign(max_hours, 1) -> assign(max_seconds, 3600). 1.14/1.54 % set(auto2) -> assign(max_seconds, 0). 1.14/1.54 % set(auto2) -> assign(max_minutes, 5). 1.14/1.54 % assign(max_minutes, 5) -> assign(max_seconds, 300). 1.14/1.54 % set(auto2) -> set(sort_initial_sos). 1.14/1.54 % set(auto2) -> assign(sos_limit, -1). 1.14/1.54 % set(auto2) -> assign(lrs_ticks, 3000). 1.14/1.54 % set(auto2) -> assign(max_megs, 400). 1.14/1.54 % set(auto2) -> assign(stats, some). 1.14/1.54 % set(auto2) -> clear(echo_input). 1.14/1.54 % set(auto2) -> set(quiet). 1.14/1.54 % set(auto2) -> clear(print_initial_clauses). 1.14/1.54 % set(auto2) -> clear(print_given). 1.14/1.54 assign(lrs_ticks,-1). 1.14/1.54 assign(sos_limit,10000). 1.14/1.54 assign(order,kbo). 1.14/1.54 set(lex_order_vars). 1.14/1.54 clear(print_given). 1.14/1.54 1.14/1.54 % formulas(sos). % not echoed (175 formulas) 1.14/1.54 1.14/1.54 ============================== end of input ========================== 1.14/1.54 1.14/1.54 % From the command line: assign(max_seconds, 960). 1.14/1.54 1.14/1.54 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 1.14/1.54 1.14/1.54 % Formulas that are not ordinary clauses: 1.14/1.54 1 (all X all Y (X = Y | -s_t(X,Y,X))) # label(aA6) # label(axiom) # label(non_clause). [assumption]. 1.14/1.54 2 (all X all Y all Z (X = Y | -s_e(X,Y,Z,Z))) # label(aA3) # label(axiom) # label(non_clause). [assumption]. 1.14/1.54 3 (all Xa all Xp all Xc all Xb all Xq ((s_t(Xp,ip(Xa,Xp,Xc,Xb,Xq),Xb) | -s_t(Xb,Xq,Xc) | -s_t(Xa,Xp,Xc)) & (-s_t(Xa,Xp,Xc) | -s_t(Xb,Xq,Xc) | s_t(Xq,ip(Xa,Xp,Xc,Xb,Xq),Xa)))) # label(aA7) # label(axiom) # label(non_clause). [assumption]. 1.14/1.54 4 (all X all Y all X1 all Y1 all Z all Z1 all V all V1 (-s_e(X,Y,X1,Y1) | -s_t(X1,Y1,Z1) | s_e(Z,V,Z1,V1) | X = Y | -s_e(Y,V,Y1,V1) | -s_e(X,V,X1,V1) | -s_e(Y,Z,Y1,Z1) | -s_t(X,Y,Z))) # label(aA5) # label(axiom) # label(non_clause). [assumption]. 1.14/1.54 5 (all X all Y s_e(X,Y,Y,X)) # label(aA1) # label(axiom) # label(non_clause). [assumption]. 1.14/1.54 6 (all X all Y all Z all V all Z2 all V2 (-s_e(X,Y,Z2,V2) | s_e(Z,V,Z2,V2) | -s_e(X,Y,Z,V))) # label(aA2) # label(axiom) # label(non_clause). [assumption]. 1.14/1.54 7 (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]. 1.14/1.54 8 (all Xa all Xb all Xc all Xd (le(Xc,Xd,Xa,Xb) | le(Xa,Xb,Xc,Xd))) # label(aSatz5_10) # label(axiom) # label(non_clause). [assumption]. 1.14/1.54 9 (all Xa all Xb all Xc ((Xb = Xa | s_t(Xc,erectAux(Xa,Xb,Xc),erect(Xa,Xb,Xc))) & (s_col(Xa,Xb,erectAux(Xa,Xb,Xc)) | Xb = Xa) & (perp(Xa,Xb,erect(Xa,Xb,Xc),Xa) | Xb = Xa))) # label(aSatz8_21) # label(axiom) # label(non_clause). [assumption]. 1.14/1.54 10 (all Xp all Xa all Xq (Xq = s(Xa,Xp) | -s_m(Xp,Xa,Xq))) # label(aSatz7_6) # label(axiom) # label(non_clause). [assumption]. 1.14/1.54 11 (all Xa all Xb all Xc all Xd (-s_t(Xb,Xc,Xd) | s_t(Xa,Xb,Xd) | Xb = Xc | -s_t(Xa,Xb,Xc))) # label(aSatz3_7b) # label(axiom) # label(non_clause). [assumption]. 1.14/1.54 12 (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]. 1.14/1.54 13 (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]. 1.14/1.54 14 (all Xa all Xb all Xp all Xq all Xc all Xd (-s_col(Xa,Xb,Xq) | Xb = Xa | -perp(Xa,Xb,Xc,Xd) | perp(Xp,Xq,Xc,Xd) | Xq = Xp | -s_col(Xa,Xb,Xp))) # label(aExtPerp5) # label(axiom) # label(non_clause). [assumption]. 1.14/1.54 15 (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]. 1.14/1.54 16 (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]. 1.14/1.54 17 (all Xa1 all Xm1 all Xb1 all Xc all Xb2 all Xm2 all Xa2 (s_t(Xm1,Xc,Xm2) | -le(Xc,Xa1,Xc,Xa2) | -s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2))) # label(aSatz7_22a) # label(axiom) # label(non_clause). [assumption]. 1.14/1.54 18 (all Xa all Xb all Xp all Xq all Xr all Xc all Xd (-s_col(Xa,Xb,Xq) | Xa = Xb | -perpAt(Xp,Xq,Xr,Xc,Xd) | perpAt(Xa,Xb,Xr,Xc,Xd) | Xp = Xq | -s_col(Xa,Xb,Xp))) # label(aExtPerp) # label(axiom) # label(non_clause). [assumption]. 1.14/1.54 19 (all Xa all Xb all Xc all Xd (-le(Xa,Xb,Xc,Xd) | -le(Xc,Xd,Xa,Xb) | s_e(Xa,Xb,Xc,Xd))) # label(aSatz5_9) # label(axiom) # label(non_clause). [assumption]. 1.14/1.54 20 (all Xa all Xp (Xp = s(Xa,Xp) | Xa != Xp)) # label(aSatz7_10b) # label(axiom) # label(non_clause). [assumption]. 1.14/1.54 21 (all Xa all Xb all Xc all Xa1 all Xb1 all Xp ((-s_t(Xa1,Xb1,Xc) | -s_t(Xa,Xp,Xa1) | s_t(Xp,crossbar(Xa,Xb,Xc,Xa1,Xb1,Xp),Xc) | -s_t(Xa,Xb,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]. 1.14/1.54 22 (all Xa all Xm all Xb ((-s_m(Xa,Xm,Xb) | s_t(Xa,Xm,Xb)) & (-s_t(Xa,Xm,Xb) | s_m(Xa,Xm,Xb) | -s_e(Xm,Xa,Xm,Xb)) & (-s_m(Xa,Xm,Xb) | s_e(Xm,Xa,Xm,Xb)))) # label(d_Defn7_1) # label(axiom) # label(non_clause). [assumption]. 1.14/1.54 23 (all Xa all Xb all Xc all Xp (-s_r(Xa,Xb,Xc) | Xa != Xp | Xc = Xb | -s_m(s(Xa,Xc),Xp,s(Xb,Xc)))) # label(aSatz8_20b) # label(axiom) # label(non_clause). [assumption]. 1.14/1.54 24 (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_t(Za,Zb,Zc) | -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_t(Za,Zb,Zc) | -s_e(Xa,Xc,Za,Zc) | -s_e(Xa,Xd,Za,Zd) | -s_e(Xc,Xd,Zc,Zd) | s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | -s_e(Xb,Xc,Zb,Zc) | -s_t(Xa,Xb,Xc)) & (s_e(Xb,Xc,Zb,Zc) | -s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)) & (-s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_e(Xa,Xc,Za,Zc)))) # label(d_Defn4_1) # label(axiom) # label(non_clause). [assumption]. 1.14/1.54 25 (all Xa all Xb all Xc (-s_r(Xa,Xc,Xb) | Xb = Xc | -s_r(Xa,Xb,Xc))) # label(aSatz8_7) # label(axiom) # label(non_clause). [assumption]. 1.14/1.54 26 (all Xa all Xp all Xb ((-sameside(Xa,Xp,Xb) | Xp != Xb) & (-sameside(Xa,Xp,Xb) | Xp != c63(Xa,Xp,Xb)) & (-sameside(Xa,Xp,Xb) | s_t(Xa,Xp,c63(Xa,Xp,Xb))) & (s_t(Xb,Xp,c63(Xa,Xp,Xb)) | -sameside(Xa,Xp,Xb)) & (Xa != Xp | -sameside(Xa,Xp,Xb)))) # label(aSatz6_3a) # label(axiom) # label(non_clause). [assumption]. 1.14/1.54 27 (all Xa all Xb s_col(Xa,Xa,Xb)) # label(aSatz4_12) # label(axiom) # label(non_clause). [assumption]. 1.14/1.54 28 (all Xa all Xm (Xm = Xa | -s_m(Xa,Xm,Xa))) # label(aSatz7_3a) # label(axiom) # label(non_clause). [assumption]. 1.14/1.54 29 (all Xa all Xb all Xc all Xa1 all Xc1 ((s_t(Xa1,insert(Xa,Xb,Xa1,Xc1),Xc1) | -s_e(Xa,Xc,Xa1,Xc1) | -s_t(Xa,Xb,Xc)) & (s_e3(Xa,Xb,Xc,Xa1,insert(Xa,Xb,Xa1,Xc1),Xc1) | -s_e(Xa,Xc,Xa1,Xc1) | -s_t(Xa,Xb,Xc)))) # label(aSatz4_5) # label(axiom) # label(non_clause). [assumption]. 1.14/1.54 30 (all Xa all Xb all Xc (le(Xa,Xb,Xa,Xc) | -s_t(Xa,Xb,Xc) | -s_col(Xa,Xb,Xc))) # label(aSatz5_12a1) # label(axiom) # label(non_clause). [assumption]. 1.14/1.54 31 (all Xa all Xb all Xp all Xq all Xc (-s_col(Xa,Xb,Xq) | perp(Xa,Xb,Xc,Xp) | s_col(Xa,Xb,Xc) | -s_r(Xc,Xp,Xq) | Xp = Xq | -s_col(Xa,Xb,Xp) | Xb = Xa)) # label(aSatz8_16b) # label(axiom) # label(non_clause). [assumption]. 1.14/1.54 32 (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]. 1.14/1.55 33 (all Xa all Xb all Xp all Xq all Xr (Xq = Xp | s_col(Xa,Xb,Xr) | -s_col(Xp,Xq,Xr) | -s_col(Xp,Xq,Xb) | -s_col(Xp,Xq,Xa) | Xb = Xa)) # label(aSatz6_18) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 34 (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_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1)) & (-s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1) | s_e(Xb,Xd,Xb1,Xd1)) & (-s_col(Xa,Xb,Xc) | s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1) | -s_e(Xb,Xd,Xb1,Xd1) | -s_e(Xa,Xd,Xa1,Xd1) | -s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1)) & (s_e(Xa,Xd,Xa1,Xd1) | -s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1)) & (-s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1) | s_col(Xa,Xb,Xc)))) # label(d_Defn4_15) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 35 (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]. 1.14/1.55 36 (all Xa all Xb all Xc (Xc = Xb | Xa = Xb | -s_col(Xa,Xb,Xc) | -s_r(Xa,Xb,Xc))) # label(aSatz8_9) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 37 (all Xa all Xp all Xb all Xc (Xc = Xp | -s_t(Xb,Xp,Xc) | -s_t(Xa,Xp,Xc) | Xb = Xp | Xp = Xa | sameside(Xa,Xp,Xb))) # label(aSatz6_3b) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 38 (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]. 1.14/1.55 39 (all Xa all Xp (s(Xa,Xp) != Xp | Xa = Xp)) # label(aSatz7_10a) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 40 (all Xa all Xb all Xc all Xd (Xb = Xc | Xd = Xc | perp(Xb,Xa,Xa,Xd) | -s_col(Xa,Xc,Xd) | -perp(Xb,Xa,Xa,Xc) | Xd = Xa | Xc = Xa | Xa = Xb)) # label(aExtPerp3) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 41 (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]. 1.14/1.55 42 (all Xp all Xq all Xp1 all Xq1 all X ((perpAt(Xp,Xq,il(Xp,Xq,Xp1,Xq1),Xp1,Xq1) | -perp(Xp,Xq,Xp1,Xq1)) & (-perpAt(Xp,Xq,X,Xp1,Xq1) | perp(Xp,Xq,Xp1,Xq1)))) # label(d_Defn8_11b) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 43 (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]. 1.14/1.55 44 (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]. 1.14/1.55 45 (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]. 1.14/1.55 46 (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]. 1.14/1.55 47 (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]. 1.14/1.55 48 (all Xa all Xb all Xc all Xp all Xq (-perpAt(Xa,Xb,Xc,Xp,Xq) | Xc = il(Xa,Xb,Xp,Xq))) # label(aSatz8_14c) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 49 (all Xa all Xp all Xb all Xc (Xa = Xp | Xp = Xb | s_t(Xb,Xp,Xc) | -sameside(Xa,Xp,Xb) | -s_t(Xa,Xp,Xc) | Xp = Xc)) # label(aSatz6_2b) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 50 (all Xa all Xb all Xc all Xp all Xq ((-perpAt(Xa,Xb,Xc,Xp,Xq) | Xa != Xb) & (-perpAt(Xa,Xb,Xc,Xp,Xq) | Xq != Xp) & (-perpAt(Xa,Xb,Xc,Xp,Xq) | s_col(Xp,Xq,Xc)) & (s_col(Xa,Xb,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(Xp,Xq,g813(Xa,Xb,Xp,Xq,Xc)) | -perpAt(Xa,Xb,Xc,Xp,Xq)) & (Xc != f813(Xa,Xb,Xp,Xq,Xc) | -perpAt(Xa,Xb,Xc,Xp,Xq)) & (-perpAt(Xa,Xb,Xc,Xp,Xq) | Xc != g813(Xa,Xb,Xp,Xq,Xc)) & (s_r(f813(Xa,Xb,Xp,Xq,Xc),Xc,g813(Xa,Xb,Xp,Xq,Xc)) | -perpAt(Xa,Xb,Xc,Xp,Xq)))) # label(aSatz8_13a) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 51 (all Xa all Xb all Xc all Xd (-s_col(Xa,Xb,Xc) | Xa = Xb | s_col(Xa,Xc,Xd) | -s_col(Xa,Xb,Xd))) # label(aext1) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 52 (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]. 1.14/1.55 53 (all Xa all Xb s_m(Xa,midpoint(Xa,Xb),Xb)) # label(aSatz8_22) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 54 (all Xa all Xb all Xc all Xd (-s_t(Xc,Xa,Xb) | -s_t(Xd,Xa,Xb) | s_t(Xc,Xd,Xb) | s_t(Xd,Xc,Xb) | Xb = Xa)) # label(aSatz6_16a) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 55 (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]. 1.14/1.55 56 (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]. 1.14/1.55 57 (all Xa all Xb all Xd all Xc (Xa = Xb | perpAt(Xa,Xb,Xd,Xc,Xd) | -perp(Xa,Xb,Xc,Xd) | -s_col(Xa,Xb,Xd))) # label(aSatz8_15) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 58 (all Xa all Xb all Xc all Xd all Za all Zb all Zc all Zd ((-s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_e(Xa,Xb,Za,Zb)) & (s_e(Xa,Xd,Za,Zd) | -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_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_e(Xb,Xc,Zb,Zc)) & (s_t(Za,Zb,Zc) | -s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)) & (s_t(Xa,Xb,Xc) | -s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)))) # label(d_Defn2_10) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 59 (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]. 1.14/1.55 60 (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]. 1.14/1.55 61 (all Xa all Xb all Xc (-s_r(Xa,Xb,Xc) | s_r(Xc,Xb,Xa))) # label(aSatz8_2) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 62 (all Xq all Xa all Xd all Xb all Xc (-s_t(Xq,Xa,Xd) | -s_e(Xa,Xd,Xb,Xc) | ext(Xq,Xa,Xb,Xc) = Xd | Xq = Xa)) # label(aSatz2_12) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 63 (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]. 1.14/1.55 64 (all Xa all Xp all Xb all Xq all Xt (-le(Xa,Xp,Xb,Xq) | -s_t(Xp,Xt,Xq) | -s_col(Xa,Xb,Xt) | s_m(Xa,midpointAux(Xa,Xb,Xp,Xq,Xt),Xb) | -perp(Xa,Xb,Xb,Xq) | -perp(Xa,Xb,Xa,Xp))) # label(aSatz8_22b) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 65 (all Xa all Xb all Xc all Xd all Xa1 all Xb1 all Xc1 all Xd1 (Xa = Xb | s_e(Xc,Xd,Xc1,Xd1) | -s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1))) # label(aSatz4_16) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 66 (all Xa all Xb all Xc all Xd all Xp (Xa = Xb | -s_col(Xa,Xb,Xd) | s_col(Xa,Xb,Xp) | -s_col(Xc,Xd,Xp) | -s_col(Xa,Xb,Xc) | Xc = Xd)) # label(aExtCol2) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 67 (all Xp all Xa all Xb all Xq all Xt all Xr all Xcx (-perp(Xq,Xb,Xa,Xb) | -s_t(Xp,Xt,Xq) | -s_t(Xb,Xr,Xq) | s_m(Xa,Xcx,Xb) | ip(Xp,Xt,Xq,Xb,Xr) != Xcx | -s_e(Xa,Xp,Xb,Xr) | -s_col(Xa,Xb,Xt) | -perp(Xp,Xa,Xa,Xb))) # label(aSatz8_24a) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 68 (all Xa all Xb s_col(Xa,Xb,Xa)) # label(aSatz4_12b) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 69 (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) | s_t(Xb,ss2(Xa,Xb,Xp,Xq),ss3(Xa,Xb,Xp,Xq))) & (ss1(Xa,Xb,Xp,Xq) != Xa | -samesideline(Xa,Xb,Xp,Xq)) & (-samesideline(Xa,Xb,Xp,Xq) | ss2(Xa,Xb,Xp,Xq) != Xb) & (-samesideline(Xa,Xb,Xp,Xq) | Xp != Xq) & (-samesideline(Xa,Xb,Xp,Xq) | -s_col(Xp,Xq,Xa)) & (-s_col(Xp,Xq,Xb) | -samesideline(Xa,Xb,Xp,Xq)) & (-s_t(Xa,Xu,Xc) | -s_col(Xp,Xq,Xu) | Xp = Xq | s_col(Xp,Xq,Xa) | s_col(Xp,Xq,Xb) | samesideline(Xa,Xb,Xp,Xq) | Xb = Xv | Xa = Xu | Xv = Xc | Xc = Xu | -s_col(Xp,Xq,Xv) | -s_t(Xb,Xv,Xc)) & (-samesideline(Xa,Xb,Xp,Xq) | ss2(Xa,Xb,Xp,Xq) != ss3(Xa,Xb,Xp,Xq)) & (-samesideline(Xa,Xb,Xp,Xq) | ss1(Xa,Xb,Xp,Xq) != ss3(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]. 1.14/1.55 70 (all Xp all Xq all Xr all Xa (Xp = Xq | Xr = Xp | -s_col(Xa,Xp,Xq) | Xp = Xa | sameside(Xa,Xp,Xq) | sameside(Xa,Xp,Xr) | -s_t(Xq,Xp,Xr))) # label(aSatz6_15a) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 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]. 1.14/1.55 72 (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]. 1.14/1.55 73 (all Xa all Xp all Xb (sameside(Xb,Xp,Xa) | -sameside(Xa,Xp,Xb))) # label(aSatz6_6) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 74 (all Xa1 all Xc all Xa2 all Xb1 all Xb2 all Xm1 all Xm2 (-s_t(Xa1,Xc,Xa2) | -s_e(Xc,Xa1,Xc,Xb1) | -s_e(Xc,Xa2,Xc,Xb2) | -s_m(Xa1,Xm1,Xb1) | -s_m(Xa2,Xm2,Xb2) | s_t(Xm1,Xc,Xm2) | -s_t(Xb1,Xc,Xb2))) # label(aSatz7_22) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 75 (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]. 1.14/1.55 76 (all Xa all Xb all Xc all Xc1 (Xb = Xa | -s_col(Xa,Xb,Xc) | -s_e(Xa,Xc,Xa,Xc1) | -s_e(Xb,Xc,Xb,Xc1) | Xc1 = Xc)) # label(aSatz4_18) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 77 (all Xa all Xp s(Xa,s(Xa,Xp)) = Xp) # label(aSatz7_7) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 78 (all Xa1 all Xm1 all Xb1 all Xc all Xb2 all Xm2 all Xa2 ((-s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) | s_e(Xc,Xa1,Xc,Xb1)) & (-s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) | s_m(Xa1,Xm1,Xb1)) & (-s_t(Xa1,Xc,Xa2) | -s_m(Xa1,Xm1,Xb1) | s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) | -s_m(Xa2,Xm2,Xb2) | -s_e(Xc,Xa2,Xc,Xb2) | -s_e(Xc,Xa1,Xc,Xb1) | -s_t(Xb1,Xc,Xb2)) & (s_m(Xa2,Xm2,Xb2) | -s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2)) & (-s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) | s_e(Xc,Xa2,Xc,Xb2)) & (-s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) | s_t(Xb1,Xc,Xb2)) & (s_t(Xa1,Xc,Xa2) | -s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2)))) # label(d_Defn7_23) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 79 (all Xa all Xc all Xb all Xc1 (Xc1 = Xc | -s_e(Xb,Xc,Xb,Xc1) | -s_e(Xa,Xc,Xa,Xc1) | -s_t(Xa,Xc,Xb))) # label(aSatz4_19) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 80 (all Xa all Xb all Xc (s_col(Xb,Xc,Xa) | -s_col(Xa,Xb,Xc))) # label(aSatz4_11a) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 81 (all Xa all Xp all Xb (s(Xa,Xp) != s(Xb,Xp) | Xa = Xb)) # label(aSatz7_18) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 82 (all Xa all Xp all Xb ((-sameside(Xa,Xp,Xb) | s_t(Xp,Xb,Xa) | s_t(Xp,Xa,Xb)) & (Xp = xb | sameside(Xa,Xp,Xb) | Xa = Xp | -s_t(Xp,Xa,Xb)) & (Xp = Xb | sameside(Xa,Xp,Xb) | Xp = Xa | -s_t(Xp,Xb,Xa)) & (-sameside(Xa,Xp,Xb) | Xp != Xb) & (Xa != Xp | -sameside(Xa,Xp,Xb)))) # label(d_Defn6_1) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 83 (all Xa all Xb all Xc all Xd (Xb = Xa | -s_t(Xa,Xb,Xc) | s_t(Xa,Xc,Xd) | s_t(Xa,Xd,Xc) | -s_t(Xa,Xb,Xd))) # label(aSatz5_1) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 84 (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]. 1.14/1.55 85 (all Xp all Xq all Xr all Xa (-sameside(Xa,Xp,Xq) | s_col(Xa,Xp,Xq) | -s_t(Xq,Xp,Xr) | Xp = Xr | Xq = Xp)) # label(aSatz6_15b) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 86 (all Xa all Xb s_e(Xa,Xb,Xa,Xb)) # label(aSatz2_1) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 87 (all Xa all Xb all Xd all Xc (-s_t(Xb,Xc,Xd) | s_t(Xa,Xb,Xc) | -s_t(Xa,Xb,Xd))) # label(aSatz3_5a) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 88 (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]. 1.14/1.55 89 (all Xa all Xb all Xc (-s_col(Xa,Xb,Xc) | s_t(Xa,Xb,Xc) | -le(Xa,Xb,Xa,Xc) | -le(Xb,Xc,Xa,Xc))) # label(aSatz5_12b) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 90 (all Xa all Xc all Xd le(Xa,Xa,Xc,Xd)) # label(aSatz5_11) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 91 (all Xa all Xb all Xc all Xp all Xq (-perpAt(Xa,Xb,Xc,Xp,Xq) | perpAt(Xp,Xq,Xc,Xa,Xb))) # label(aSatz8_12a) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 92 (all Xa all Xb all Xc ((s_e(Xa,Xc,Xa,s(Xb,Xc)) | -s_r(Xa,Xb,Xc)) & (-s_e(Xa,Xc,Xa,s(Xb,Xc)) | s_r(Xa,Xb,Xc)))) # label(d_Defn8_1) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 93 (all Xp all Xa all Xr all Xq (Xr = Xq | -s_m(Xp,Xa,Xq) | -s_m(Xp,Xa,Xr))) # label(aSatz7_4b) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 94 (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]. 1.14/1.55 95 (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_t(Xb,Xc,Xa) | s_col(Xa,Xb,Xc)) & (s_col(Xa,Xb,Xc) | -s_t(Xc,Xa,Xb)) & (s_col(Xa,Xb,Xc) | -s_t(Xa,Xb,Xc)))) # label(d_Defn4_10) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 96 (all Xa all Xb s_r(Xa,Xb,Xb)) # label(aSatz8_5) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 97 (all Xa all Xb all Xc all Xp (-s_r(Xa,Xb,Xc) | -s_m(s(Xa,Xc),Xp,s(Xb,Xc)) | s_r(Xb,Xa,Xp))) # label(aSatz8_20a) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 98 (all Xa all Xb all Xc all Xd (s_e(Xa,Xb,Xd,Xc) | -s_e(Xa,Xb,Xc,Xd))) # label(aSatz2_5) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 99 (all Xp all Xq all Xa all Xz all Xb all Xc (-s_e(Xb,Xp,Xb,Xq) | s_t(Xa,Xb,Xc) | s_t(Xb,Xc,Xa) | s_t(Xc,Xa,Xb) | -s_e(Xc,Xp,Xc,Xq) | -s_e(Xa,Xp,Xz,Xq) | Xp = Xq)) # label(aA9) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 100 (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]. 1.14/1.55 101 (all Xa1 all Xb1 s_t(Xa1,Xa1,Xb1)) # label(aSatz3_3) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 102 (all Xa all Xb all Xc all Xd (-s_t(Xa,Xb,Xc) | s_t(Xa,Xc,Xd) | Xc = Xb | -s_t(Xb,Xc,Xd))) # label(aSatz3_7a) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 103 (all Xa all Xb s_t(Xa,Xb,Xb)) # label(aSatz3_1) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 104 (all Xp all Xa s_m(Xp,Xa,s(Xa,Xp))) # label(aSatz7_4a) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 105 (all Xb all Xc all Xa (Xb = Xc | -s_e(Xb,Xc,Xa,Xa))) # label(aSatz2_13) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 106 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_r(Xa,Xb,Xc) | s_r(Xa1,Xb1,Xc1) | -s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1))) # label(aSatz8_10) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 107 (all Xa all Xb s_e(Xa,Xa,Xb,Xb)) # label(aSatz2_8) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 108 (all Xa all Xp all Xb (sameside(Xa,Xp,Xb) | -s_col(Xa,Xp,Xb) | s_t(Xa,Xp,Xb))) # label(aSatz6_4b) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 109 (all Xp all Xq all Xa all Xb all Xt ((-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)) & (-s_col(Xp,Xq,Xb) | -opposite(Xa,Xp,Xq,Xb)) & (-opposite(Xa,Xp,Xq,Xb) | -s_col(Xp,Xq,Xa)) & (s_col(Xp,Xq,Xa) | -s_col(Xp,Xq,Xt) | opposite(Xa,Xp,Xq,Xb) | -s_t(Xa,Xt,Xb) | s_col(Xp,Xq,Xb) | Xp = Xq))) # label(d_Defn9_1) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 110 (all Xp all Xq all Xr all Xa (-s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr)) | s_t(Xp,Xq,Xr))) # label(aSatz7_15b) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 111 (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) | Xcs = Xp)) # label(aSatz6_16b) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 112 (all Xp all Xa all Xb all Xq all Xt all Xr (-s_t(Xp,Xt,Xq) | -s_e(Xa,Xp,Xb,Xr) | s_m(Xp,midpoint(Xa,Xb),Xr) | -s_t(Xb,Xr,Xq) | -s_col(Xa,Xb,Xt) | -perp(Xq,Xb,Xa,Xb) | -perp(Xp,Xa,Xa,Xb))) # label(aSatz8_24) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 113 (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(Xb,Xr,Xq) | -s_e(Xa,Xp,Xb,Xr) | s_m(Xp,Xcx,Xr) | Xcx != ip(Xp,Xt,Xq,Xb,Xr) | -s_t(Xp,Xt,Xq) | -perp(Xp,Xa,Xa,Xb))) # label(aSatz8_24b) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 114 (all Xa all Xb all Xp all Xq all Xc all Xd all Xe (-s_col(Xp,Xq,Xc) | -s_col(Xa,Xb,Xd) | s_col(Xp,Xq,Xe) | -s_col(Xa,Xb,Xe) | Xd = Xc | -s_col(Xp,Xq,Xd) | -s_col(Xa,Xb,Xc) | Xq = Xp | Xa = Xb)) # label(aSatz6_21) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 115 (all Xr all Xa all Xb all Xc ((Xa = Xr | Xc = Xb | s_e(Xa,insert(Xb,Xc,Xa,Xr),Xb,Xc)) & (sameside(insert(Xb,Xc,Xa,Xr),Xa,Xr) | Xc = Xb | Xr = Xa))) # label(aSatz6_11a) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 116 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (s_t(Xa1,Xb1,Xc1) | -s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1) | -s_t(Xa,Xb,Xc))) # label(aSatz4_6) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 117 (all Xp all Xq (s_col(Xp,Xq,Xp) | Xq = Xp)) # label(aSatz6_17a) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 118 (all Xa all Xp (sameside(Xa,Xp,Xa) | Xp = Xa)) # label(aSatz6_5) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 119 (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]. 1.14/1.55 120 (all Xa all Xb all Xc all Xd (Xb = Xa | -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]. 1.14/1.55 121 (all Xa all Xm all Xb (-s_e(Xm,Xa,Xm,Xb) | Xb = Xa | s_m(Xa,Xm,Xb) | -s_col(Xa,Xm,Xb))) # label(aSatz7_20) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 122 (all Xa all Xb all Xc all Xd ((-le(Xa,Xb,Xc,Xd) | s_t(Xa,Xb,ins(Xc,Xd,Xa,Xb))) & (-le(Xa,Xb,Xc,Xd) | ext(Xa,Xb,insert(Xa,Xb,Xc,Xd),Xd) = ins(Xc,Xd,Xa,Xb)) & (s_e(Xa,ins(Xc,Xd,Xa,Xb),Xc,Xd) | -le(Xa,Xb,Xc,Xd)))) # label(aSatz5_5a) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 123 (all Xa all Xb all Xc all Xa1 (-s_r(Xa,Xb,Xc) | Xc = Xb | -s_t(Xa,Xc,Xa1) | -s_r(Xa1,Xb,Xc))) # label(aSatz8_6) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 124 (all Xp all Xq all Xr all Xa (-s_t(Xq,Xp,Xr) | -sameside(Xa,Xp,Xr) | s_col(Xa,Xp,Xq) | Xr = Xp | Xq = Xp)) # label(aSatz6_15c) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 125 (all Xa all Xb all Xp all Xq all Xc all Xd (-s_col(Xa,Xb,Xp) | Xq = Xp | Xa = Xb | -perp(Xp,Xq,Xc,Xd) | perp(Xa,Xb,Xc,Xd) | -s_col(Xa,Xb,Xq))) # label(aExtPerp2) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 126 (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(Xb,Xc,XA,XB) | s_e(Xa,Xc,XA,XC))) # label(aSatz2_15) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 127 (all Xa all Xb (Xb = Xa | -s_col(Xa,Xb,pointOffLine(Xa,Xb)))) # label(aSatz6_25) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 128 (all Xp all Xq all Xr all Xcs all Xa (-s_e(Xp,Xq,Xr,Xcs) | s_e(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr),s(Xa,Xcs)))) # label(aSatz7_16a) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 129 (all Xa1 all Xa2 all Xa3 all Xb1 all Xb2 all Xb3 ((s_e(Xa1,Xa2,Xb1,Xb2) | -s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3)) & (s_e(Xa1,Xa3,Xb1,Xb3) | -s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3)) & (s_e(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_e(Xa1,Xa2,Xb1,Xb2)))) # label(d_Defn4_4) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 130 (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]. 1.14/1.55 131 (all Xb all Xa Xb != ext(Xa,Xb,alpha,gamma)) # label(aSatz3_14b) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 132 (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]. 1.14/1.55 133 (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]. 1.14/1.55 134 (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]. 1.14/1.55 135 (all Xa all Xb all Xc all Xd all Xp (s_col(Xa,Xb,Xc) | -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) | Xd = Xb)) # label(aSatz7_21) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 136 (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]. 1.14/1.55 137 (all Xa all Xb s_t(Xa,Xb,ext(Xa,Xb,alpha,gamma))) # label(aSatz3_14a) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 138 (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]. 1.14/1.55 139 (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]. 1.14/1.55 140 (all Xa all Xb all Xc all Xd all Xa1 all Xb1 all Xc1 all Xd1 (-s_ifs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1) | s_e(Xb,Xd,Xb1,Xd1))) # label(aSatz4_2) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 141 (all Xa all Xb all Xc ((perp(Xa,Xb,erect21a(Xa,Xb,Xc),Xa) | s_col(Xa,Xb,Xc) | Xb = Xa) & (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]. 1.14/1.55 142 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_e(Xa,Xc,Xa1,Xc1) | -s_e(Xb,Xc,Xb1,Xc1) | s_e(Xa,Xb,Xa1,Xb1) | -s_t(Xa1,Xb1,Xc1) | -s_t(Xa,Xb,Xc))) # label(aSatz4_3) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 143 (all Y all Z all X all Y1 all Z1 all U all V ((-perpAt(Y,Z,X,Y1,Z1) | s_col(Y,Z,X)) & (-perpAt(Y,Z,X,Y1,Z1) | Y != Z) & (-perpAt(Y,Z,X,Y1,Z1) | Y1 != Z1) & (s_r(U,X,V) | -s_col(Y1,Z1,V) | -s_col(Y,Z,U) | -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)) & (perpAt(Y,Z,X,Y1,Z1) | Y = Z | -s_col(Y,Z,X) | s_col(Y1,Z1,g811(Y,Z,Y1,Z1,X)) | -s_col(Y1,Z1,X) | Y1 = Z1) & (perpAt(Y,Z,X,Y1,Z1) | Y1 = Z1 | -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) | Y = Z) & (-perpAt(Y,Z,X,Y1,Z1) | s_col(Y1,Z1,X)))) # label(d_Defn8_11a) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 144 (all Xr all Xa all Xb all Xc all Xp all Xq (Xa = Xr | Xb = Xc | -sameside(Xp,Xa,Xr) | -s_e(Xa,Xp,Xb,Xc) | Xp = Xq | -s_e(Xa,Xq,Xb,Xc) | -sameside(Xq,Xa,Xr))) # label(aSatz6_11b) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 145 (all Xa all Xb all Xc all Xp all Xq (Xa = Xb | -s_e(Xa,Xp,Xa,Xq) | -s_e(Xb,Xp,Xb,Xq) | s_e(Xc,Xp,Xc,Xq) | -s_col(Xa,Xb,Xc))) # label(aSatz4_17) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 146 (all Xa all Xb all Xc all Xd all Xe (-s_t(Xa,Xb,Xe) | -s_e(Xa,Xe,Xc,Xd) | le(Xa,Xb,Xc,Xd))) # label(aSatz5_5b) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 147 (all Xa all Xb all Xc all Xp all Xq (s_col(Xa,Xb,Xc) | -s_col(Xa,Xb,Xp) | -s_col(Xa,Xb,Xq) | -perp(Xa,Xb,Xc,Xp) | -perp(Xa,Xb,Xc,Xq) | Xp = Xq)) # label(aSatz8_18a) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 148 (all Xa all Xb all Xp all Xq all Xcx all U all V (Xb = Xa | -s_col(Xp,Xq,Xcx) | -s_col(Xp,Xq,V) | V = Xcx | perpAt(Xa,Xb,Xcx,Xp,Xq) | -s_r(U,Xcx,V) | Xcx = U | -s_col(Xa,Xb,U) | -s_col(Xa,Xb,Xcx) | Xp = Xq)) # label(aSatz8_13b) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 149 (all Xa all Xm (Xa != Xm | s_m(Xa,Xm,Xa))) # label(aSatz7_3b) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 150 (all Xp all Xq all Xr (Xq = Xp | s_col(Xq,Xp,Xr) | -s_col(Xp,Xq,Xr))) # label(aSatz6_17b) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 151 (all Xa all Xb all Xc (le(Xb,Xc,Xa,Xc) | -s_t(Xa,Xb,Xc) | -s_col(Xa,Xb,Xc))) # label(aSatz5_12a2) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 152 (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]. 1.14/1.55 153 (all Xa all Xb (-s_r(Xa,Xb,Xa) | Xa = Xb)) # label(aSatz8_8) # label(axiom) # label(non_clause). [assumption]. 1.14/1.55 154 (all Xa all Xp all Xr all Xq (Xr != s(Xa,Xp) | Xp = Xq | s(Xa,Xq) != Xr)) # label(aSatz7_8) # label(axiom) # label(non_clause). [assumption]. 1.14/1.56 155 (all Xa all Xb all Xp all Xq all Xc ((Xb = Xa | -s_col(Xa,Xb,Xq) | -s_col(Xa,Xb,Xc) | -perp(Xa,Xb,Xc,Xp) | Xq = Xp | -s_col(Xa,Xb,Xp)) & (-s_col(Xa,Xb,Xp) | -s_col(Xa,Xb,Xq) | Xp = Xq | s_r(Xc,Xp,Xq) | -perp(Xa,Xb,Xc,Xp) | Xb = Xa))) # label(aSatz8_16a) # label(axiom) # label(non_clause). [assumption]. 1.14/1.56 156 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_e(Xa,Xb,Xa1,Xb1) | -s_e(Xb,Xc,Xb1,Xc1) | s_e(Xa,Xc,Xa1,Xc1) | -s_t(Xa1,Xb1,Xc1) | -s_t(Xa,Xb,Xc))) # label(aSatz2_11) # label(axiom) # label(non_clause). [assumption]. 1.14/1.56 157 (all Xa all Xb all Xc all Xd all Y ((-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)) & (-le(Xa,Xb,Xc,Xd) | s_t(Xc,insert(Xa,Xb,Xc,Xd),Xd)))) # label(d_Defn5_4) # label(axiom) # label(non_clause). [assumption]. 1.14/1.56 158 (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]. 1.14/1.56 159 (all Xa all Xb all Xc ((s_col(Xa,Xb,Xc) | perp(Xa,Xb,Xc,foot(Xa,Xb,Xc))) & (s_col(Xa,Xb,foot(Xa,Xb,Xc)) | s_col(Xa,Xb,Xc)))) # label(aSatz8_18) # label(axiom) # label(non_clause). [assumption]. 1.14/1.56 160 (all Xa all Xp all Xq (s(Xa,Xp) != s(Xa,Xq) | Xq = Xp)) # label(aSatz7_9) # label(axiom) # label(non_clause). [assumption]. 1.14/1.56 161 (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]. 1.14/1.56 162 (all Xa all Xb le(Xa,Xb,Xa,Xb)) # label(aSatz5_7) # label(axiom) # label(non_clause). [assumption]. 1.14/1.56 163 (all Xa all Xp all Xb ((s_col(Xa,Xp,Xb) | -sameside(Xa,Xp,Xb)) & (-sameside(Xa,Xp,Xb) | -s_t(Xa,Xp,Xb)))) # label(aSatz6_4a) # label(axiom) # label(non_clause). [assumption]. 1.14/1.56 164 (all Xa all Xb all Xp all Xq (-s_col(Xa,Xb,Xp) | -s_col(Xa,Xb,Xq) | -perp(Xa,Xb,Xp,Xq))) # label(aSatz8_14a) # label(axiom) # label(non_clause). [assumption]. 1.14/1.56 165 (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]. 1.14/1.56 166 (all Xp all Xq all Xr all Xa (Xq = Xp | Xp = Xr | -s_t(Xq,Xp,Xr) | s_col(Xa,Xp,Xq) | Xp != Xa)) # label(aSatz6_15d) # label(axiom) # label(non_clause). [assumption]. 1.14/1.56 167 (all Xa all Xp all Xb all Xc (Xb = Xp | Xp = Xc | sameside(Xa,Xp,Xb) | -s_t(Xb,Xp,Xc) | -s_t(Xa,Xp,Xc) | Xa = Xp)) # label(aSatz6_2a) # label(axiom) # label(non_clause). [assumption]. 1.14/1.56 168 -(all Xa all Xb all Xc all Xp all Xq (-s_col(Xa,Xb,Xc) | -samesideline(Xp,Xq,Xa,Xb) | samesideline(Xp,Xq,Xa,Xc) | Xc = Xa | Xa = Xb)) # label(aExtSameSide1) # label(negated_conjecture) # label(non_clause). [assumption]. 1.14/1.56 1.14/1.56 ============================== end of process non-clausal formulas === 1.14/1.56 1.14/1.56 ============================== PROCESS INITIAL CLAUSES =============== 1.14/1.56 1.14/1.56 ============================== PREDICATE ELIMINATION ================= 1.14/1.56 169 -s_t(A,B,C) | -s_m(A,D,E) | s_kf(A,D,E,B,F,V6,C) | -s_m(C,V6,F) | -s_e(B,C,B,F) | -s_e(B,A,B,E) | -s_t(E,B,F) # label(d_Defn7_23) # label(axiom). [clausify(78)]. 1.14/1.56 170 s_t(A,B,C) | -le(B,D,B,E) | -s_kf(D,A,F,B,V6,C,E) # label(aSatz7_22a) # label(axiom). [clausify(17)]. 1.14/1.56 171 -s_kf(A,B,C,D,E,F,V6) | s_e(D,A,D,C) # label(d_Defn7_23) # label(axiom). [clausify(78)]. 1.14/1.56 172 -s_kf(A,B,C,D,E,F,V6) | s_m(A,B,C) # label(d_Defn7_23) # label(axiom). [clausify(78)]. 1.14/1.56 Derived: -s_t(A,B,C) | -s_m(A,D,E) | -s_m(C,F,V6) | -s_e(B,C,B,V6) | -s_e(B,A,B,E) | -s_t(E,B,V6) | s_t(D,B,F) | -le(B,A,B,C). [resolve(169,c,170,c)]. 1.14/1.56 173 s_m(A,B,C) | -s_kf(D,E,F,V6,C,B,A) # label(d_Defn7_23) # label(axiom). [clausify(78)]. 1.14/1.56 174 -s_kf(A,B,C,D,E,F,V6) | s_e(D,V6,D,E) # label(d_Defn7_23) # label(axiom). [clausify(78)]. 1.14/1.56 175 -s_kf(A,B,C,D,E,F,V6) | s_t(C,D,E) # label(d_Defn7_23) # label(axiom). [clausify(78)]. 1.14/1.56 176 s_t(A,B,C) | -s_kf(A,D,E,B,F,V6,C) # label(d_Defn7_23) # label(axiom). [clausify(78)]. 1.14/1.56 177 s_t(A,B,C) | -s_kf(D,A,E,B,F,C,V6) # label(aSatz7_22b) # label(axiom). [clausify(161)]. 1.14/1.56 Derived: s_t(A,B,C) | -s_t(D,B,E) | -s_m(D,A,F) | -s_m(E,C,V6) | -s_e(B,E,B,V6) | -s_e(B,D,B,F) | -s_t(F,B,V6). [resolve(177,b,169,c)]. 1.14/1.57 178 -s_t(A,B,C) | -s_e(D,E,A,C) | -s_e(D,F,A,V6) | -s_e(E,F,C,V6) | s_ifs(D,V7,E,F,A,B,C,V6) | -s_e(V7,E,B,C) | -s_t(D,V7,E) # label(d_Defn4_1) # label(axiom). [clausify(24)]. 1.14/1.57 179 s_t(A,B,C) | -s_ifs(A,B,C,D,E,F,V6,V7) # label(d_Defn4_1) # label(axiom). [clausify(24)]. 1.14/1.57 180 s_t(A,B,C) | -s_ifs(D,E,F,V6,A,B,C,V7) # label(d_Defn4_1) # label(axiom). [clausify(24)]. 1.14/1.57 181 s_e(A,B,C,D) | -s_ifs(A,E,F,B,C,V6,V7,D) # label(d_Defn4_1) # label(axiom). [clausify(24)]. 1.14/1.57 182 s_e(A,B,C,D) | -s_ifs(E,F,A,B,V6,V7,C,D) # label(d_Defn4_1) # label(axiom). [clausify(24)]. 1.14/1.57 183 s_e(A,B,C,D) | -s_ifs(E,A,B,F,V6,C,D,V7) # label(d_Defn4_1) # label(axiom). [clausify(24)]. 1.14/1.57 184 -s_ifs(A,B,C,D,E,F,V6,V7) | s_e(A,C,E,V6) # label(d_Defn4_1) # label(axiom). [clausify(24)]. 1.14/1.57 185 -s_ifs(A,B,C,D,E,F,V6,V7) | s_e(B,D,F,V7) # label(aSatz4_2) # label(axiom). [clausify(140)]. 1.14/1.57 Derived: s_e(A,B,C,D) | -s_t(E,C,F) | -s_e(V6,V7,E,F) | -s_e(V6,B,E,D) | -s_e(V7,B,F,D) | -s_e(A,V7,C,F) | -s_t(V6,A,V7). [resolve(185,a,178,e)]. 1.14/1.57 186 -s_col(A,B,C) | s_fs(A,B,C,D,E,F,V6,V7) | -s_e(B,D,F,V7) | -s_e(A,D,E,V7) | -s_e3(A,B,C,E,F,V6) # label(d_Defn4_15) # label(axiom). [clausify(34)]. 1.14/1.57 187 s_e3(A,B,C,D,insert(A,B,D,E),E) | -s_e(A,C,D,E) | -s_t(A,B,C) # label(aSatz4_5) # label(axiom). [clausify(29)]. 1.14/1.57 188 -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(34)]. 1.14/1.57 Derived: -s_col(A,B,C) | s_fs(A,B,C,D,E,insert(A,B,E,F),F,V6) | -s_e(B,D,insert(A,B,E,F),V6) | -s_e(A,D,E,V6) | -s_e(A,C,E,F) | -s_t(A,B,C). [resolve(186,e,187,a)]. 1.14/1.57 Derived: -s_col(A,B,C) | s_fs(A,B,C,D,E,F,V6,V7) | -s_e(B,D,F,V7) | -s_e(A,D,E,V7) | -s_fs(A,B,C,V8,E,F,V6,V9). [resolve(186,e,188,b)]. 1.14/1.57 189 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(41)]. 1.14/1.57 Derived: -s_e(A,B,C,D) | -s_col(A,B,E) | -s_col(A,B,E) | s_fs(A,B,E,F,C,D,insert5(A,B,E,C,D),V6) | -s_e(B,F,D,V6) | -s_e(A,F,C,V6). [resolve(189,a,186,e)]. 1.14/1.57 190 -s_r(A,B,C) | s_r(D,E,F) | -s_e3(A,B,C,D,E,F) # label(aSatz8_10) # label(axiom). [clausify(106)]. 1.14/1.57 Derived: -s_r(A,B,C) | s_r(D,insert(A,B,D,E),E) | -s_e(A,C,D,E) | -s_t(A,B,C). [resolve(190,c,187,a)]. 1.14/1.57 Derived: -s_r(A,B,C) | s_r(D,E,F) | -s_fs(A,B,C,V6,D,E,F,V7). [resolve(190,c,188,b)]. 1.14/1.57 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(190,c,189,a)]. 1.14/1.57 191 s_t(A,B,C) | -s_e3(D,E,F,A,B,C) | -s_t(D,E,F) # label(aSatz4_6) # label(axiom). [clausify(116)]. 1.14/1.57 Derived: s_t(A,insert(B,C,A,D),D) | -s_t(B,C,E) | -s_e(B,E,A,D) | -s_t(B,C,E). [resolve(191,b,187,a)]. 1.14/1.57 Derived: s_t(A,B,C) | -s_t(D,E,F) | -s_fs(D,E,F,V6,A,B,C,V7). [resolve(191,b,188,b)]. 1.14/1.57 Derived: s_t(A,B,insert5(C,D,E,A,B)) | -s_t(C,D,E) | -s_e(C,D,A,B) | -s_col(C,D,E). [resolve(191,b,189,a)]. 1.14/1.57 192 s_e(A,B,C,D) | -s_e3(A,B,E,C,D,F) # label(d_Defn4_4) # label(axiom). [clausify(129)]. 1.14/1.57 Derived: s_e(A,B,C,insert(A,B,C,D)) | -s_e(A,E,C,D) | -s_t(A,B,E). [resolve(192,b,187,a)]. 1.14/1.57 Derived: s_e(A,B,C,D) | -s_fs(A,B,E,F,C,D,V6,V7). [resolve(192,b,188,b)]. 1.14/1.57 193 s_e(A,B,C,D) | -s_e3(A,E,B,C,F,D) # label(d_Defn4_4) # label(axiom). [clausify(129)]. 1.14/1.57 Derived: s_e(A,B,C,D) | -s_fs(A,E,B,F,C,V6,D,V7). [resolve(193,b,188,b)]. 1.14/1.57 Derived: s_e(A,B,C,insert5(A,D,B,C,E)) | -s_e(A,D,C,E) | -s_col(A,D,B). [resolve(193,b,189,a)]. 1.14/1.57 194 s_e(A,B,C,D) | -s_e3(E,A,B,F,C,D) # label(d_Defn4_4) # label(axiom). [clausify(129)]. 1.14/1.57 Derived: s_e(A,B,insert(C,A,D,E),E) | -s_e(C,B,D,E) | -s_t(C,A,B). [resolve(194,b,187,a)]. 1.14/1.57 Derived: s_e(A,B,C,D) | -s_fs(E,A,B,F,V6,C,D,V7). [resolve(194,b,188,b)]. 1.14/1.57 Derived: s_e(A,B,C,insert5(D,A,B,E,C)) | -s_e(D,A,E,C) | -s_col(D,A,B). [resolve(194,b,189,a)]. 1.14/1.57 195 -s_e(A,B,C,D) | s_e3(E,A,B,F,C,D) | -s_e(E,B,F,D) | -s_e(E,A,F,C) # label(d_Defn4_4) # label(axiom). [clausify(129)]. 1.14/1.57 Derived: -s_e(A,B,C,D) | -s_e(E,B,F,D) | -s_e(E,A,F,C) | -s_col(E,A,B) | s_fs(E,A,B,V6,F,C,D,V7) | -s_e(A,V6,C,V7) | -s_e(E,V6,F,V7). [resolve(195,b,186,e)]. 1.14/1.57 Derived: -s_e(A,B,C,D) | -s_e(E,B,F,D) | -s_e(E,A,F,C) | -s_r(E,A,B) | s_r(F,C,D). [resolve(195,b,190,c)]. 1.14/1.57 Derived: -s_e(A,B,C,D) | -s_e(E,B,F,D) | -s_e(E,A,F,C) | s_t(F,C,D) | -s_t(E,A,B). [resolve(195,b,191,b)]. 3.50/3.94 196 -s_col(A,B,C) | s_col(D,E,F) | -s_e3(A,B,C,D,E,F) # label(aSatz4_13) # label(axiom). [clausify(136)]. 3.50/3.94 Derived: -s_col(A,B,C) | s_col(D,insert(A,B,D,E),E) | -s_e(A,C,D,E) | -s_t(A,B,C). [resolve(196,c,187,a)]. 3.50/3.94 Derived: -s_col(A,B,C) | s_col(D,E,F) | -s_fs(A,B,C,V6,D,E,F,V7). [resolve(196,c,188,b)]. 3.50/3.94 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(196,c,189,a)]. 3.50/3.94 Derived: -s_col(A,B,C) | s_col(D,E,F) | -s_e(B,C,E,F) | -s_e(A,C,D,F) | -s_e(A,B,D,E). [resolve(196,c,195,b)]. 3.50/3.94 197 -s_e(A,B,C,D) | -s_e(B,E,D,F) | -s_e(A,V6,C,V7) | -s_e(B,V6,D,V7) | s_afs(A,B,E,V6,C,D,F,V7) | -s_t(C,D,F) | -s_t(A,B,E) # label(d_Defn2_10) # label(axiom). [clausify(58)]. 3.50/3.94 198 -s_afs(A,B,C,D,E,F,V6,V7) | s_e(A,B,E,F) # label(d_Defn2_10) # label(axiom). [clausify(58)]. 3.50/3.94 199 s_e(A,B,C,D) | -s_afs(A,E,F,B,C,V6,V7,D) # label(d_Defn2_10) # label(axiom). [clausify(58)]. 3.50/3.94 200 s_e(A,B,C,D) | -s_afs(E,A,F,B,V6,C,V7,D) # label(d_Defn2_10) # label(axiom). [clausify(58)]. 3.50/3.94 201 -s_afs(A,B,C,D,E,F,V6,V7) | s_e(B,C,F,V6) # label(d_Defn2_10) # label(axiom). [clausify(58)]. 3.50/3.94 202 s_t(A,B,C) | -s_afs(D,E,F,V6,A,B,C,V7) # label(d_Defn2_10) # label(axiom). [clausify(58)]. 3.50/3.94 203 s_t(A,B,C) | -s_afs(A,B,C,D,E,F,V6,V7) # label(d_Defn2_10) # label(axiom). [clausify(58)]. 3.50/3.94 204 s_col(A,B,C) | -s_col(A,B,D) | opposite(C,A,B,E) | -s_t(C,D,E) | s_col(A,B,E) | B = A # label(d_Defn9_1) # label(axiom). [clausify(109)]. 3.50/3.94 205 -opposite(A,B,C,D) | s_col(B,C,il(A,D,B,C)) # label(d_Defn9_1) # label(axiom). [clausify(109)]. 3.50/3.94 206 -opposite(A,B,C,D) | s_t(A,il(A,D,B,C),D) # label(d_Defn9_1) # label(axiom). [clausify(109)]. 3.50/3.94 207 -s_col(A,B,C) | -opposite(D,A,B,C) # label(d_Defn9_1) # label(axiom). [clausify(109)]. 3.50/3.94 208 -opposite(A,B,C,D) | -s_col(B,C,A) # label(d_Defn9_1) # label(axiom). [clausify(109)]. 3.50/3.94 Derived: s_col(A,B,C) | -s_col(A,B,D) | -s_t(C,D,E) | s_col(A,B,E) | B = A | s_col(A,B,il(C,E,A,B)). [resolve(204,c,205,a)]. 3.50/3.94 Derived: s_col(A,B,C) | -s_col(A,B,D) | -s_t(C,D,E) | s_col(A,B,E) | B = A | s_t(C,il(C,E,A,B),E). [resolve(204,c,206,a)]. 3.50/3.94 3.50/3.94 ============================== end predicate elimination ============= 3.50/3.94 3.50/3.94 Auto_denials: (non-Horn, no changes). 3.50/3.94 3.50/3.94 Term ordering decisions: 3.50/3.94 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. c63=1. erect=1. erect21a=1. erectAux=1. erectAux21a=1. foot=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. midpointAux=1. crossbar=1. 3.50/3.94 3.50/3.94 ============================== end of process initial clauses ======== 3.50/3.94 3.50/3.94 ============================== CLAUSES FOR SEARCH ==================== 3.50/3.94 3.50/3.94 ============================== end of clauses for search ============= 3.50/3.94 3.50/3.94 ============================== SEARCH ================================ 3.50/3.94 3.50/3.94 % Starting search at 0.09 seconds. 3.50/3.94 3.50/3.94 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 168 (0.00 of 1.34 sec). 3.50/3.94 3.50/3.94 Low Water (keep): wt=50.000, iters=3343 3.50/3.94 3.50/3.94 Low Water (keep): wt=46.000, iters=3338 3.50/3.94 3.50/3.94 Low Water (keep): wt=43.000, iters=3351 3.50/3.94 3.50/3.94 Low Water (keep): wt=36.000, iters=3362 3.50/3.94 3.50/3.94 Low Water (keep): wt=34.000, iters=3382 3.50/3.94 3.50/3.94 Low Water (keep): wt=32.000, iters=3340 3.50/3.94 3.50/3.94 Low Water (keep): wt=31.000, iters=3336 3.50/3.94 3.50/3.94 Low Water (keep): wt=30.000, iters=3336 3.50/3.94 3.50/3.94 Low Water (keep): wt=29.000, iters=3349 3.50/3.94 3.50/3.94 Low Water (keep): wt=28.000, iters=3369 3.50/3.94 3.50/3.94 Low Water (keep): wt=27.000, iters=3385 3.50/3.94 3.50/3.94 Low Water (keep): wt=26.000, iters=3340 3.50/3.94 3.50/3.94 Low Water (keep): wt=25.000, iters=3338 3.50/3.94 3.50/3.94 Low Water (keep): wt=24.000, iters=3349 3.50/3.94 3.50/3.94 Low Water (displace): id=11201, wt=23.000 3.50/3.94 3.50/3.94 Low Water (displace): id=11204, wt=18.000 3.50/3.94 3.50/3.94 Low Water (displace): id=11278, wt=17.000 3.50/3.94 3.50/3.94 Low Water (displace): id=11285, wt=16.000 3.50/3.94 3.50/3.94 Low Water (displace): id=11331, wt=15.000 3.50/3.94 3.50/3.94 Low Water (displace): id=11495, wt=14.000 3.50/3.94 3.50/3.94 Low Water (displace): id=11528, wt=13.000 3.50/3.94 3.50/3.94 Low Water (keep): wt=23.000, iters=3344 3.50/3.94 3.50/3.94 Low Water (displace): id=12062, wt=11.000 3.50/3.94 3.50/3.94 Low Water (displace): id=13175, wt=10.000 3.50/3.94 3.50/3.94 Low Water (Alarm clock 119.48/120.09 Prover9 interrupted 119.48/120.09 EOF