0.12/0.14 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.14 % Command : tptp2X_and_run_prover9 %d %s 0.14/0.36 % Computer : n004.cluster.edu 0.14/0.36 % Model : x86_64 x86_64 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.36 % Memory : 8042.1875MB 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.36 % CPULimit : 1200 0.14/0.36 % DateTime : Tue Jul 13 14:01:54 EDT 2021 0.14/0.36 % CPUTime : 1.01/1.32 ============================== Prover9 =============================== 1.01/1.32 Prover9 (32) version 2009-11A, November 2009. 1.01/1.32 Process 7815 was started by sandbox2 on n004.cluster.edu, 1.01/1.32 Tue Jul 13 14:01:55 2021 1.01/1.32 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1200 -f /tmp/Prover9_7659_n004.cluster.edu". 1.01/1.32 ============================== end of head =========================== 1.01/1.32 1.01/1.32 ============================== INPUT ================================= 1.01/1.32 1.01/1.32 % Reading from file /tmp/Prover9_7659_n004.cluster.edu 1.01/1.32 1.01/1.32 set(prolog_style_variables). 1.01/1.32 set(auto2). 1.01/1.32 % set(auto2) -> set(auto). 1.01/1.32 % set(auto) -> set(auto_inference). 1.01/1.32 % set(auto) -> set(auto_setup). 1.01/1.32 % set(auto_setup) -> set(predicate_elim). 1.01/1.32 % set(auto_setup) -> assign(eq_defs, unfold). 1.01/1.32 % set(auto) -> set(auto_limits). 1.01/1.32 % set(auto_limits) -> assign(max_weight, "100.000"). 1.01/1.32 % set(auto_limits) -> assign(sos_limit, 20000). 1.01/1.32 % set(auto) -> set(auto_denials). 1.01/1.32 % set(auto) -> set(auto_process). 1.01/1.32 % set(auto2) -> assign(new_constants, 1). 1.01/1.32 % set(auto2) -> assign(fold_denial_max, 3). 1.01/1.32 % set(auto2) -> assign(max_weight, "200.000"). 1.01/1.32 % set(auto2) -> assign(max_hours, 1). 1.01/1.32 % assign(max_hours, 1) -> assign(max_seconds, 3600). 1.01/1.32 % set(auto2) -> assign(max_seconds, 0). 1.01/1.32 % set(auto2) -> assign(max_minutes, 5). 1.01/1.32 % assign(max_minutes, 5) -> assign(max_seconds, 300). 1.01/1.32 % set(auto2) -> set(sort_initial_sos). 1.01/1.32 % set(auto2) -> assign(sos_limit, -1). 1.01/1.32 % set(auto2) -> assign(lrs_ticks, 3000). 1.01/1.32 % set(auto2) -> assign(max_megs, 400). 1.01/1.32 % set(auto2) -> assign(stats, some). 1.01/1.32 % set(auto2) -> clear(echo_input). 1.01/1.32 % set(auto2) -> set(quiet). 1.01/1.32 % set(auto2) -> clear(print_initial_clauses). 1.01/1.32 % set(auto2) -> clear(print_given). 1.01/1.32 assign(lrs_ticks,-1). 1.01/1.32 assign(sos_limit,10000). 1.01/1.32 assign(order,kbo). 1.01/1.32 set(lex_order_vars). 1.01/1.32 clear(print_given). 1.01/1.32 1.01/1.32 % formulas(sos). % not echoed (175 formulas) 1.01/1.32 1.01/1.32 ============================== end of input ========================== 1.01/1.32 1.01/1.32 % From the command line: assign(max_seconds, 1200). 1.01/1.32 1.01/1.32 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 1.01/1.32 1.01/1.32 % Formulas that are not ordinary clauses: 1.01/1.32 1 (all X all Y all Z all V all Z2 all V2 (-s_e(X,Y,Z,V) | s_e(Z,V,Z2,V2) | -s_e(X,Y,Z2,V2))) # label(aA2) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 2 (all X all Y all Z (X = Y | -s_e(X,Y,Z,Z))) # label(aA3) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 3 (all X all Y s_e(X,Y,Y,X)) # label(aA1) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 4 (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]. 1.01/1.32 5 (all X all Y (Y = X | -s_t(X,Y,X))) # label(aA6) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 6 (all Xa all Xp all Xc all Xb all Xq ((-s_t(Xa,Xp,Xc) | s_t(Xp,ip(Xa,Xp,Xc,Xb,Xq),Xb) | -s_t(Xb,Xq,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]. 1.01/1.32 7 (all X all Y all X1 all Y1 all Z all Z1 all V all V1 (-s_e(Y,V,Y1,V1) | -s_t(X1,Y1,Z1) | s_e(Z,V,Z1,V1) | Y = X | -s_t(X,Y,Z) | -s_e(X,V,X1,V1) | -s_e(Y,Z,Y1,Z1) | -s_e(X,Y,X1,Y1))) # label(aA5) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 8 (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]. 1.01/1.32 9 (all Xa all Xb all Xc (-s_r(Xa,Xb,Xc) | Xb = Xc | Xa = Xb | -s_col(Xa,Xb,Xc))) # label(aSatz8_9) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 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]. 1.01/1.32 11 (all Xp all Xq (s_col(Xp,Xq,Xp) | Xq = Xp)) # label(aSatz6_17a) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 12 (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]. 1.01/1.32 13 (all Xp all Xa all Xb all Xq all Xt all Xr all Xcx (-perp(Xp,Xa,Xa,Xb) | -perp(Xq,Xb,Xa,Xb) | -s_t(Xb,Xr,Xq) | -s_e(Xa,Xp,Xb,Xr) | s_m(Xp,Xcx,Xr) | ip(Xp,Xt,Xq,Xb,Xr) != Xcx | -s_t(Xp,Xt,Xq) | -s_col(Xa,Xb,Xt))) # label(aSatz8_24b) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 14 (all Xa all Xb s_r(Xa,Xb,Xb)) # label(aSatz8_5) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 15 (all Xa all Xb all Xc all Xd (-s_t(Xa,Xb,Xc) | s_t(Xa,Xb,Xd) | Xc = Xb | -s_t(Xb,Xc,Xd))) # label(aSatz3_7b) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 16 (all Xa all Xb all Xc all Xd (s_t(Xa,Xb,Xd) | -s_t(Xa,Xc,Xd) | -s_t(Xa,Xb,Xc))) # label(aSatz3_6b) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 17 (all Xa all Xb all Xp all Xq all Xc (Xa = Xb | -s_col(Xa,Xb,Xp) | perp(Xa,Xb,Xc,Xp) | s_col(Xa,Xb,Xc) | -s_r(Xc,Xp,Xq) | Xq = Xp | -s_col(Xa,Xb,Xq))) # label(aSatz8_16b) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 18 (all Xa1 all Xc all Xa2 all Xb1 all Xb2 all Xm1 all Xm2 (-s_t(Xb1,Xc,Xb2) | -s_e(Xc,Xa2,Xc,Xb2) | s_t(Xm1,Xc,Xm2) | -s_m(Xa2,Xm2,Xb2) | -s_m(Xa1,Xm1,Xb1) | -s_e(Xc,Xa1,Xc,Xb1) | -s_t(Xa1,Xc,Xa2))) # label(aSatz7_22) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 19 (all Xa all Xp all Xb all Xc (Xp = Xb | Xp = Xc | -s_t(Xa,Xp,Xc) | -s_t(Xb,Xp,Xc) | sameside(Xa,Xp,Xb) | Xa = Xp)) # label(aSatz6_2a) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 20 (all Xa all Xb all Xc all Xc1 (-s_col(Xa,Xb,Xc) | -s_e(Xa,Xc,Xa,Xc1) | Xc = Xc1 | -s_e(Xb,Xc,Xb,Xc1) | Xb = Xa)) # label(aSatz4_18) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 21 (all Xa1 all Xb1 s_t(Xa1,Xa1,Xb1)) # label(aSatz3_3) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 22 (all Xa all Xb all Xp all Xq all Xr all Xc all Xd (-s_col(Xa,Xb,Xq) | -perpAt(Xp,Xq,Xr,Xc,Xd) | perpAt(Xa,Xb,Xr,Xc,Xd) | Xb = Xa | Xq = Xp | -s_col(Xa,Xb,Xp))) # label(aExtPerp) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 23 (all Xa all Xb all Xc ((Xa = Xb | s_t(Xc,erectAux(Xa,Xb,Xc),erect(Xa,Xb,Xc))) & (Xb = Xa | s_col(Xa,Xb,erectAux(Xa,Xb,Xc))) & (perp(Xa,Xb,erect(Xa,Xb,Xc),Xa) | Xa = Xb))) # label(aSatz8_21) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 24 (all Xb all Xc all Xa (-s_e(Xb,Xc,Xa,Xa) | Xb = Xc)) # label(aSatz2_13) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 25 (all Xa all Xb all Xc all Xd (-s_e(Xa,Xb,Xc,Xd) | s_e(Xb,Xa,Xd,Xc))) # label(aSatz2_14) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 26 (all Xp all Xq all Xr all Xa (Xq = Xp | Xp = Xr | -sameside(Xa,Xp,Xr) | s_col(Xa,Xp,Xq) | -s_t(Xq,Xp,Xr))) # label(aSatz6_15c) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 27 (all Xa all Xm all Xb (s_m(Xb,Xm,Xa) | -s_m(Xa,Xm,Xb))) # label(aSatz7_2) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 28 (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]. 1.01/1.32 29 (all Xa all Xm (-s_m(Xa,Xm,Xa) | Xm = Xa)) # label(aSatz7_3a) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 30 (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]. 1.01/1.32 31 (all Xa all Xb all Xc all Xd (-s_t(Xa,Xb,Xc) | s_t(Xa,Xd,Xc) | s_t(Xa,Xc,Xd) | -s_t(Xa,Xb,Xd) | Xa = Xb)) # label(aSatz5_1) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 32 (all Xa all Xb all Xc ((s_col(Xa,Xb,erectAux21a(Xa,Xb,Xc)) | s_col(Xa,Xb,Xc) | Xb = Xa) & (s_t(Xc,erectAux21a(Xa,Xb,Xc),erect21a(Xa,Xb,Xc)) | s_col(Xa,Xb,Xc) | Xa = Xb) & (s_col(Xa,Xb,Xc) | perp(Xa,Xb,erect21a(Xa,Xb,Xc),Xa) | Xa = Xb))) # label(aSatz8_21a) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 33 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_t(Xa,Xb,Xc) | s_t(Xa1,Xb1,Xc1) | -s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1))) # label(aSatz4_6) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 34 (all Xa all Xb s_e(Xa,Xa,Xb,Xb)) # label(aSatz2_8) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 35 (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]. 1.01/1.32 36 (all Xa all Xc all Xb all Xc1 (-s_t(Xa,Xc,Xb) | -s_e(Xb,Xc,Xb,Xc1) | Xc1 = Xc | -s_e(Xa,Xc,Xa,Xc1))) # label(aSatz4_19) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 37 (all Xa all Xp all Xb ((Xp != Xb | -sameside(Xa,Xp,Xb)) & (Xp = Xb | sameside(Xa,Xp,Xb) | Xa = Xp | -s_t(Xp,Xb,Xa)) & (Xa = Xp | Xp = xb | sameside(Xa,Xp,Xb) | -s_t(Xp,Xa,Xb)) & (s_t(Xp,Xa,Xb) | s_t(Xp,Xb,Xa) | -sameside(Xa,Xp,Xb)) & (Xp != Xa | -sameside(Xa,Xp,Xb)))) # label(d_Defn6_1) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 38 (all Xa all Xp all Xb (s(Xb,Xp) != s(Xa,Xp) | Xb = Xa)) # label(aSatz7_18) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 39 (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(aExtPerp2) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 40 (all Xa all Xb all Xc all Xa1 (Xb = Xa | s_r(Xa1,Xb,Xc) | -s_col(Xb,Xa,Xa1) | -s_r(Xa,Xb,Xc))) # label(aSatz8_3) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 41 (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]. 1.01/1.32 42 (all Xa all Xb all Xc (-s_col(Xa,Xb,Xc) | -s_t(Xa,Xb,Xc) | le(Xb,Xc,Xa,Xc))) # label(aSatz5_12a2) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 43 (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]. 1.01/1.32 44 (all Xa all Xp all Xb ((-sameside(Xa,Xp,Xb) | Xp != Xa) & (c63(Xa,Xp,Xb) != Xp | -sameside(Xa,Xp,Xb)) & (s_t(Xb,Xp,c63(Xa,Xp,Xb)) | -sameside(Xa,Xp,Xb)) & (s_t(Xa,Xp,c63(Xa,Xp,Xb)) | -sameside(Xa,Xp,Xb)) & (Xp != Xb | -sameside(Xa,Xp,Xb)))) # label(aSatz6_3a) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 45 (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]. 1.01/1.32 46 (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]. 1.01/1.32 47 (all Xb all Xa ext(Xa,Xb,alpha,gamma) != Xb) # label(aSatz3_14b) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 48 (all Xa all Xb all Xc all Xd all Xp (-s_e(Xb,Xc,Xd,Xa) | -s_col(Xa,Xp,Xc) | s_m(Xa,Xp,Xc) | -s_col(Xb,Xp,Xd) | -s_e(Xa,Xb,Xc,Xd) | Xb = Xd | s_col(Xa,Xb,Xc))) # label(aSatz7_21) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 49 (all Xp all Xq all Xp1 all Xq1 all X ((-perp(Xp,Xq,Xp1,Xq1) | perpAt(Xp,Xq,il(Xp,Xq,Xp1,Xq1),Xp1,Xq1)) & (-perpAt(Xp,Xq,X,Xp1,Xq1) | perp(Xp,Xq,Xp1,Xq1)))) # label(d_Defn8_11b) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 50 (all Xp all Xq all Xcs all Xr (Xp = Xq | Xcs = Xp | s_col(Xp,Xcs,Xr) | -s_col(Xp,Xq,Xr) | -s_col(Xp,Xq,Xcs))) # label(aSatz6_16b) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 51 (all Xa all Xp all Xr all Xq (Xr != s(Xa,Xp) | Xq = Xp | Xr != s(Xa,Xq))) # label(aSatz7_8) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 52 (all Xa all Xb all Xc all Xd ((s_e(Xa,ins(Xc,Xd,Xa,Xb),Xc,Xd) | -le(Xa,Xb,Xc,Xd)) & (ext(Xa,Xb,insert(Xa,Xb,Xc,Xd),Xd) = ins(Xc,Xd,Xa,Xb) | -le(Xa,Xb,Xc,Xd)) & (-le(Xa,Xb,Xc,Xd) | s_t(Xa,Xb,ins(Xc,Xd,Xa,Xb))))) # label(aSatz5_5a) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 53 (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]. 1.01/1.32 54 (all Xa all Xb all Xc (s_t(Xc,Xb,Xa) | -s_t(Xa,Xb,Xc))) # label(aSatz3_2) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 55 (all Xp all Xa all Xr all Xq (-s_m(Xp,Xa,Xr) | -s_m(Xp,Xa,Xq) | Xq = Xr)) # label(aSatz7_4b) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 56 (all Xa all Xb all Xc all Xd all Xe (le(Xa,Xb,Xc,Xd) | -s_t(Xa,Xb,Xe) | -s_e(Xa,Xe,Xc,Xd))) # label(aSatz5_5b) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 57 (all Xa all Xb all Xc (-le(Xa,Xb,Xa,Xc) | -le(Xb,Xc,Xa,Xc) | s_t(Xa,Xb,Xc) | -s_col(Xa,Xb,Xc))) # label(aSatz5_12b) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 58 (all Xa all Xb s_t(Xa,Xb,ext(Xa,Xb,alpha,gamma))) # label(aSatz3_14a) # label(axiom) # label(non_clause). [assumption]. 1.01/1.32 59 (all Xa all Xb all Xc all XA all XB all XC (-s_t(Xa,Xb,Xc) | s_e(Xa,Xc,XA,XC) | -s_e(Xb,Xc,XA,XB) | -s_e(Xa,Xb,XB,XC) | -s_t(XA,XB,XC))) # label(aSatz2_15) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 60 (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)) & (-le(Xa,Xb,Xc,Xd) | s_t(Xc,insert(Xa,Xb,Xc,Xd),Xd)))) # label(d_Defn5_4) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 61 (all Xa all Xb all Xc all Xd all Xa1 all Xb1 all Xc1 all Xd1 (-le(Xa,Xb,Xc,Xd) | -s_e(Xa,Xb,Xa1,Xb1) | -s_e(Xc,Xd,Xc1,Xd1) | le(Xa1,Xb1,Xc1,Xd1))) # label(aSatz5_6) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 62 (all Xa all Xb all Xc all Xd (Xa = Xb | s_col(Xa,Xc,Xd) | -s_col(Xa,Xb,Xd) | -s_col(Xa,Xb,Xc))) # label(aext1) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 63 (all Xa all Xb all Xc all Xd (Xb = Xc | s_t(Xa,Xc,Xd) | -s_t(Xb,Xc,Xd) | -s_t(Xa,Xb,Xc))) # label(aSatz3_7a) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 64 (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]. 1.01/1.33 65 (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]. 1.01/1.33 66 (all Xp all Xq all Xr (s_col(Xq,Xp,Xr) | -s_col(Xp,Xq,Xr) | Xq = Xp)) # label(aSatz6_17b) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 67 (all Xa all Xm all Xb ((-s_m(Xa,Xm,Xb) | s_t(Xa,Xm,Xb)) & (s_e(Xm,Xa,Xm,Xb) | -s_m(Xa,Xm,Xb)) & (s_m(Xa,Xm,Xb) | -s_e(Xm,Xa,Xm,Xb) | -s_t(Xa,Xm,Xb)))) # label(d_Defn7_1) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 68 (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]. 1.01/1.33 69 (all Xa all Xp all Xb all Xc (Xa = Xp | Xb = Xp | -sameside(Xa,Xp,Xb) | s_t(Xb,Xp,Xc) | -s_t(Xa,Xp,Xc) | Xc = Xp)) # label(aSatz6_2b) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 70 (all Xa all Xb all Xc ((s_t(Xa,Xb,Xc) | s_t(Xb,Xc,Xa) | s_t(Xc,Xa,Xb) | -s_col(Xa,Xb,Xc)) & (s_col(Xa,Xb,Xc) | -s_t(Xc,Xa,Xb)) & (-s_t(Xb,Xc,Xa) | s_col(Xa,Xb,Xc)) & (s_col(Xa,Xb,Xc) | -s_t(Xa,Xb,Xc)))) # label(d_Defn4_10) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 71 (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]. 1.01/1.33 72 (all Xa all Xp all Xb all Xc (Xp = Xa | Xp = Xc | -s_t(Xa,Xp,Xc) | -s_t(Xb,Xp,Xc) | Xp = Xb | sameside(Xa,Xp,Xb))) # label(aSatz6_3b) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 73 (all Xr all Xa all Xb all Xc ((Xr = Xa | Xb = Xc | sameside(insert(Xb,Xc,Xa,Xr),Xa,Xr)) & (Xr = Xa | s_e(Xa,insert(Xb,Xc,Xa,Xr),Xb,Xc) | Xb = Xc))) # label(aSatz6_11a) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 74 (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,Xa2,Xc,Xb2)) & (s_m(Xa2,Xm2,Xb2) | -s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2)) & (-s_m(Xa1,Xm1,Xb1) | -s_m(Xa2,Xm2,Xb2) | s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) | -s_e(Xc,Xa2,Xc,Xb2) | -s_e(Xc,Xa1,Xc,Xb1) | -s_t(Xb1,Xc,Xb2) | -s_t(Xa1,Xc,Xa2)) & (s_m(Xa1,Xm1,Xb1) | -s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,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_t(Xb1,Xc,Xb2)) & (-s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) | s_t(Xa1,Xc,Xa2)))) # label(d_Defn7_23) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 75 (all Xa all Xb all Xc all Xp all Xq ((-perpAt(Xa,Xb,Xc,Xp,Xq) | s_col(Xp,Xq,Xc)) & (s_col(Xa,Xb,f813(Xa,Xb,Xp,Xq,Xc)) | -perpAt(Xa,Xb,Xc,Xp,Xq)) & (-perpAt(Xa,Xb,Xc,Xp,Xq) | 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) | g813(Xa,Xb,Xp,Xq,Xc) != Xc) & (-perpAt(Xa,Xb,Xc,Xp,Xq) | s_r(f813(Xa,Xb,Xp,Xq,Xc),Xc,g813(Xa,Xb,Xp,Xq,Xc))) & (s_col(Xa,Xb,Xc) | -perpAt(Xa,Xb,Xc,Xp,Xq)) & (Xq != Xp | -perpAt(Xa,Xb,Xc,Xp,Xq)) & (-perpAt(Xa,Xb,Xc,Xp,Xq) | Xa != Xb))) # label(aSatz8_13a) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 76 (all Xa all Xb s_m(Xa,midpoint(Xa,Xb),Xb)) # label(aSatz8_22) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 77 (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]. 1.01/1.33 78 (all Xa all Xp (Xp = Xa | s(Xa,Xp) != Xp)) # label(aSatz7_10a) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 79 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_r(Xa,Xb,Xc) | -s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1) | s_r(Xa1,Xb1,Xc1))) # label(aSatz8_10) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 80 (all Xa all Xb all Xc (-s_r(Xa,Xc,Xb) | Xc = Xb | -s_r(Xa,Xb,Xc))) # label(aSatz8_7) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 81 (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]. 1.01/1.33 82 (all Xa all Xb all Xc all Xd all Xe all Xf (-le(Xc,Xd,Xe,Xf) | le(Xa,Xb,Xe,Xf) | -le(Xa,Xb,Xc,Xd))) # label(aSatz5_8) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 83 (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]. 1.01/1.33 84 (all Xa all Xb s_col(Xa,Xa,Xb)) # label(aSatz4_12) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 85 (all Xp all Xa all Xb all Xq all Xt all Xr all Xcx (s_m(Xa,Xcx,Xb) | ip(Xp,Xt,Xq,Xb,Xr) != Xcx | -s_e(Xa,Xp,Xb,Xr) | -s_t(Xb,Xr,Xq) | -s_t(Xp,Xt,Xq) | -s_col(Xa,Xb,Xt) | -perp(Xq,Xb,Xa,Xb) | -perp(Xp,Xa,Xa,Xb))) # label(aSatz8_24a) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 86 (all Xa all Xb all Xc all Xd (Xb = Xa | -perp(Xb,Xa,Xa,Xc) | perp(Xb,Xa,Xa,Xd) | -s_col(Xa,Xc,Xd) | Xd = Xa | Xc = Xd | Xc = Xb | Xa = Xc)) # label(aExtPerp3) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 87 (all Xa all Xp (Xa != Xp | Xp = s(Xa,Xp))) # label(aSatz7_10b) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 88 (all Xa all Xp all Xb (-sameside(Xa,Xp,Xb) | -s_t(Xp,Xa,Xb) | le(Xp,Xa,Xp,Xb))) # label(aSatz6_13b) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 89 (all Xp all Xa all Xq all Xb (Xa = Xb | -s_m(Xp,Xb,Xq) | -s_m(Xp,Xa,Xq))) # label(aSatz7_17) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 90 (all Xa all Xc all Xd le(Xa,Xa,Xc,Xd)) # label(aSatz5_11) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 91 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_t(Xa,Xb,Xc) | -s_t(Xa1,Xb1,Xc1) | s_e(Xa,Xc,Xa1,Xc1) | -s_e(Xb,Xc,Xb1,Xc1) | -s_e(Xa,Xb,Xa1,Xb1))) # label(aSatz2_11) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 92 (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_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_e(Xa,Xd,Za,Zd)) & (s_e(Xb,Xd,Zb,Zd) | -s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)) & (-s_t(Xa,Xb,Xc) | -s_t(Za,Zb,Zc) | -s_e(Xb,Xc,Zb,Zc) | -s_e(Xb,Xd,Zb,Zd) | s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | -s_e(Xa,Xd,Za,Zd) | -s_e(Xa,Xb,Za,Zb)) & (s_e(Xb,Xc,Zb,Zc) | -s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)) & (-s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_t(Xa,Xb,Xc)))) # label(d_Defn2_10) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 93 (all Xp all Xq all Xr all Xcs all Xa (-s_e(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr),s(Xa,Xcs)) | s_e(Xp,Xq,Xr,Xcs))) # label(aSatz7_16b) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 94 (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]. 1.01/1.33 95 (all Xa all Xp all Xb all Xq all Xt (-le(Xa,Xp,Xb,Xq) | -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) | -perp(Xa,Xb,Xa,Xp))) # label(aSatz8_22b) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 96 (all Xa all Xb all Xc (-s_t(Xb,Xa,Xc) | Xa = Xb | -s_t(Xa,Xb,Xc))) # label(aSatz3_4) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 97 (all Xa all Xb all Xp all Xq all Xc all Xd (-perp(Xa,Xb,Xc,Xd) | perp(Xp,Xq,Xc,Xd) | Xa = Xb | Xq = Xp | -s_col(Xa,Xb,Xq) | -s_col(Xa,Xb,Xp))) # label(aExtPerp5) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 98 (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]. 1.01/1.33 99 (all Xa all Xb all Xp all Xq all Xcx all U all V (-s_col(Xp,Xq,Xcx) | -s_col(Xa,Xb,U) | -s_col(Xp,Xq,V) | Xcx = U | Xcx = V | -s_r(U,Xcx,V) | perpAt(Xa,Xb,Xcx,Xp,Xq) | -s_col(Xa,Xb,Xcx) | Xq = Xp | Xa = Xb)) # label(aSatz8_13b) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 100 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-sameside(Xa,Xb,Xc) | -sameside(Xa1,Xb1,Xc1) | -s_e(Xb,Xc,Xb1,Xc1) | s_e(Xa,Xc,Xa1,Xc1) | -s_e(Xb,Xa,Xb1,Xa1))) # label(aSatz6_28) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 101 (all Xp all Xq all Xa all Xb all Xt ((Xq = Xp | s_col(Xp,Xq,Xb) | opposite(Xa,Xp,Xq,Xb) | -s_col(Xp,Xq,Xt) | -s_t(Xa,Xt,Xb) | s_col(Xp,Xq,Xa)) & (-s_col(Xp,Xq,Xa) | -opposite(Xa,Xp,Xq,Xb)) & (s_col(Xp,Xq,il(Xa,Xb,Xp,Xq)) | -opposite(Xa,Xp,Xq,Xb)) & (-opposite(Xa,Xp,Xq,Xb) | s_t(Xa,il(Xa,Xb,Xp,Xq),Xb)) & (-opposite(Xa,Xp,Xq,Xb) | -s_col(Xp,Xq,Xb)))) # label(d_Defn9_1) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 102 (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]. 1.01/1.33 103 (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]. 1.01/1.33 104 (all Xa all Xb all Xp all Xq (-perp(Xa,Xb,Xp,Xq) | perp(Xb,Xa,Xp,Xq))) # label(aperp1) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 105 (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]. 1.01/1.33 106 (all Xa all Xm (Xa != Xm | s_m(Xa,Xm,Xa))) # label(aSatz7_3b) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 107 (all Xa all Xb all Xc all Xd (-le(Xa,Xb,Xc,Xd) | s_e(Xa,Xb,Xc,Xd) | -le(Xc,Xd,Xa,Xb))) # label(aSatz5_9) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 108 (all Xa all Xm all Xb (-s_col(Xa,Xm,Xb) | Xa = Xb | s_m(Xa,Xm,Xb) | -s_e(Xm,Xa,Xm,Xb))) # label(aSatz7_20) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 109 (all Xa all Xb (-s_r(Xa,Xb,Xa) | Xb = Xa)) # label(aSatz8_8) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 110 (all Xa all Xb all Xc all Xd all Za all Zb all Zc all Zd ((-s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_t(Xa,Xb,Xc)) & (-s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_t(Za,Zb,Zc)) & (s_e(Xa,Xc,Za,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_t(Xa,Xb,Xc) | -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(Za,Zb,Zc)) & (s_e(Xc,Xd,Zc,Zd) | -s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)) & (-s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_e(Xa,Xd,Za,Zd)))) # label(d_Defn4_1) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 111 (all Xa all Xb le(Xa,Xb,Xa,Xb)) # label(aSatz5_7) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 112 (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]. 1.01/1.33 113 (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) | Xc = Xd)) # label(aExtCol2) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 114 (all Xa all Xb all Xc all Xd all Xe all Xf (-s_e(Xa,Xb,Xc,Xd) | -s_e(Xc,Xd,Xe,Xf) | s_e(Xa,Xb,Xe,Xf))) # label(aSatz2_3) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 115 (all Xp all Xa all Xb all Xq all Xt all Xr (-perp(Xq,Xb,Xa,Xb) | -s_e(Xa,Xp,Xb,Xr) | s_m(Xp,midpoint(Xa,Xb),Xr) | -s_t(Xb,Xr,Xq) | -s_t(Xp,Xt,Xq) | -s_col(Xa,Xb,Xt) | -perp(Xp,Xa,Xa,Xb))) # label(aSatz8_24) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 116 (all Xr all Xa all Xb all Xc all Xp all Xq (-s_e(Xa,Xp,Xb,Xc) | -sameside(Xq,Xa,Xr) | Xq = Xp | -s_e(Xa,Xq,Xb,Xc) | -sameside(Xp,Xa,Xr) | Xb = Xc | Xr = Xa)) # label(aSatz6_11b) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 117 (all Xa all Xb all Xc all Xp (-s_r(Xa,Xb,Xc) | Xp != Xa | Xc = Xb | -s_m(s(Xa,Xc),Xp,s(Xb,Xc)))) # label(aSatz8_20b) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 118 (all Xa all Xp (Xa = Xp | sameside(Xa,Xp,Xa))) # label(aSatz6_5) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 119 (all Xa all Xb all Xc ((perp(Xa,Xb,Xc,foot(Xa,Xb,Xc)) | s_col(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]. 1.01/1.33 120 (all Xa all Xb all Xc all Xp (s_r(Xb,Xa,Xp) | -s_m(s(Xa,Xc),Xp,s(Xb,Xc)) | -s_r(Xa,Xb,Xc))) # label(aSatz8_20a) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 121 (all Xa all Xb all Xa1 all Xc1 ext(ext(Xc1,Xa1,alpha,gamma),Xa1,Xa,Xb) = insert(Xa,Xb,Xa1,Xc1)) # label(d_insert) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 122 (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]. 1.01/1.33 123 (all Xa all Xb s_col(Xa,Xb,Xa)) # label(aSatz4_12b) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 124 (all Xa all Xb all Xd all Xc (s_t(Xa,Xc,Xb) | s_t(Xa,Xb,Xc) | -s_t(Xa,Xc,Xd) | -s_t(Xa,Xb,Xd))) # label(aSatz5_3) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 125 (all Xa1 all Xa2 all Xa3 all Xb1 all Xb2 all Xb3 ((-s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3) | s_e(Xa1,Xa2,Xb1,Xb2)) & (-s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3) | s_e(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,Xa3,Xb1,Xb3)) & (s_e(Xa2,Xa3,Xb2,Xb3) | -s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3)))) # label(d_Defn4_4) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 126 (all Xa all Xp all Xb all Xc (-sameside(Xa,Xp,Xb) | -sameside(Xb,Xp,Xc) | sameside(Xa,Xp,Xc))) # label(aSatz6_7) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 127 (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]. 1.01/1.33 128 (all Xa all Xb all Xp all Xq all Xr (Xq = Xp | -s_col(Xp,Xq,Xa) | -s_col(Xp,Xq,Xr) | s_col(Xa,Xb,Xr) | -s_col(Xp,Xq,Xb) | Xa = Xb)) # label(aSatz6_18) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 129 (all Xp all Xq all Xr all Xa (-s_t(Xq,Xp,Xr) | Xp != Xa | s_col(Xa,Xp,Xq) | Xr = Xp | Xq = Xp)) # label(aSatz6_15d) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 130 (all Xa all Xb all Xp all Xq all Xc ((-s_col(Xa,Xb,Xp) | -s_col(Xa,Xb,Xq) | s_r(Xc,Xp,Xq) | -perp(Xa,Xb,Xc,Xp) | Xp = Xq | Xa = Xb) & (-perp(Xa,Xb,Xc,Xp) | -s_col(Xa,Xb,Xc) | Xp = Xq | -s_col(Xa,Xb,Xq) | -s_col(Xa,Xb,Xp) | Xa = Xb))) # label(aSatz8_16a) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 131 (all Xa all Xb all Xc all Xa1 all 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(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]. 1.01/1.33 132 (all Xa all Xb all Xc all Xp all Xq (il(Xa,Xb,Xp,Xq) = Xc | -perpAt(Xa,Xb,Xc,Xp,Xq))) # label(aSatz8_14c) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 133 (all Xa all Xb all Xp all Xq all Xc (-perp(Xa,Xb,Xp,Xq) | -s_col(Xa,Xb,Xc) | perpAt(Xa,Xb,Xc,Xp,Xq) | -s_col(Xp,Xq,Xc))) # label(aSatz8_14b) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 134 (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]. 1.01/1.33 135 (all Xa all Xb all Xc (-s_col(Xa,Xb,Xc) | s_col(Xc,Xa,Xb))) # label(aSatz4_11b) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 136 (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]. 1.01/1.33 137 (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]. 1.01/1.33 138 (all Xa all Xb all Xc (-s_t(Xa,Xb,Xc) | Xb = Xc | -s_e(Xa,Xc,Xa,Xb))) # label(aNarbouxLemma1) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 139 (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]. 1.01/1.33 140 (all Xa all Xb (-s_col(Xa,Xb,pointOffLine(Xa,Xb)) | Xa = Xb)) # label(aSatz6_25) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 141 (all Xa all Xb all Xc all Xa1 (Xb = Xc | -s_t(Xa,Xc,Xa1) | -s_r(Xa1,Xb,Xc) | -s_r(Xa,Xb,Xc))) # label(aSatz8_6) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 142 (all Xa all Xb all Xc all Xp all Xq (Xa = Xb | -s_col(Xa,Xb,Xc) | s_e(Xc,Xp,Xc,Xq) | -s_e(Xb,Xp,Xb,Xq) | -s_e(Xa,Xp,Xa,Xq))) # label(aSatz4_17) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 143 (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]. 1.01/1.33 144 (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 | Xa = Xq)) # label(aSatz2_12) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 145 (all Xa all Xb s_t(Xa,Xb,Xb)) # label(aSatz3_1) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 146 (all Xa all Xb all Xp all Xq all Xc all Xd all Xe (-s_col(Xa,Xb,Xc) | -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) | Xq = Xp | Xb = Xa)) # label(aSatz6_21) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 147 (all Xa all Xb all Xc all Xd (Xb = Xa | -s_t(Xc,Xa,Xb) | -s_t(Xd,Xa,Xb) | s_t(Xc,Xd,Xb) | s_t(Xd,Xc,Xb))) # label(aSatz6_16a) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 148 (all Xp all Xa s_m(Xp,Xa,s(Xa,Xp))) # label(aSatz7_4a) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 149 (all Xp all Xq all Xr all Xa (Xr = Xp | -s_t(Xq,Xp,Xr) | sameside(Xa,Xp,Xq) | sameside(Xa,Xp,Xr) | Xa = Xp | -s_col(Xa,Xp,Xq) | Xq = Xp)) # label(aSatz6_15a) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 150 (all Xp all Xq all Xr all Xa (-s_t(Xq,Xp,Xr) | -sameside(Xa,Xp,Xq) | s_col(Xa,Xp,Xq) | Xr = Xp | Xp = Xq)) # label(aSatz6_15b) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 151 (all Xa all Xb all Xc all Xp all Xq (-s_col(Xa,Xb,Xp) | -s_col(Xa,Xb,Xq) | -perp(Xa,Xb,Xc,Xp) | -perp(Xa,Xb,Xc,Xq) | Xq = Xp | s_col(Xa,Xb,Xc))) # label(aSatz8_18a) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 152 (all Xa all Xb all Xc all Xd all Xa1 all Xb1 all Xc1 all Xd1 ((s_col(Xa,Xb,Xc) | -s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1)) & (s_e(Xa,Xd,Xa1,Xd1) | -s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1)) & (-s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1) | s_e(Xb,Xd,Xb1,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)))) # label(d_Defn4_15) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 153 (all Xa all Xb all Xp all Xq all Xu all Xc all Xv ((-samesideline(Xa,Xb,Xp,Xq) | s_col(Xp,Xq,ss1(Xa,Xb,Xp,Xq))) & (s_t(Xa,ss1(Xa,Xb,Xp,Xq),ss3(Xa,Xb,Xp,Xq)) | -samesideline(Xa,Xb,Xp,Xq)) & (ss1(Xa,Xb,Xp,Xq) != Xa | -samesideline(Xa,Xb,Xp,Xq)) & (ss1(Xa,Xb,Xp,Xq) != ss3(Xa,Xb,Xp,Xq) | -samesideline(Xa,Xb,Xp,Xq)) & (-samesideline(Xa,Xb,Xp,Xq) | ss3(Xa,Xb,Xp,Xq) != ss2(Xa,Xb,Xp,Xq)) & (-samesideline(Xa,Xb,Xp,Xq) | Xp != Xq) & (-s_col(Xp,Xq,Xv) | Xu = Xc | Xv = Xc | Xv = Xb | s_col(Xp,Xq,Xa) | s_col(Xp,Xq,Xb) | samesideline(Xa,Xb,Xp,Xq) | Xu = Xa | Xp = Xq | -s_col(Xp,Xq,Xu) | -s_t(Xb,Xv,Xc) | -s_t(Xa,Xu,Xc)) & (-samesideline(Xa,Xb,Xp,Xq) | -s_col(Xp,Xq,Xb)) & (-s_col(Xp,Xq,Xa) | -samesideline(Xa,Xb,Xp,Xq)) & (-samesideline(Xa,Xb,Xp,Xq) | Xb != ss2(Xa,Xb,Xp,Xq)) & (s_t(Xb,ss2(Xa,Xb,Xp,Xq),ss3(Xa,Xb,Xp,Xq)) | -samesideline(Xa,Xb,Xp,Xq)) & (s_col(Xp,Xq,ss2(Xa,Xb,Xp,Xq)) | -samesideline(Xa,Xb,Xp,Xq)))) # label(d_Defn9_7) # label(axiom) # label(non_clause). [assumption]. 1.01/1.33 154 (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]. 1.01/1.33 155 (all Y all Z all X all Y1 all Z1 all U all V ((s_col(Y,Z,X) | -perpAt(Y,Z,X,Y1,Z1)) & (Z1 = Y1 | -s_col(Y,Z,X) | -s_col(Y1,Z1,X) | s_col(Y1,Z1,g811(Y,Z,Y1,Z1,X)) | Z = Y | perpAt(Y,Z,X,Y1,Z1)) & (perpAt(Y,Z,X,Y1,Z1) | Y = Z | 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)) & (Z1 = Y1 | -s_col(Y1,Z1,X) | s_col(Y,Z,f811(Y,Z,Y1,Z1,X)) | -s_col(Y,Z,X) | Z = Y | perpAt(Y,Z,X,Y1,Z1)) & (s_r(U,X,V) | -s_col(Y1,Z1,V) | -s_col(Y,Z,U) | -perpAt(Y,Z,X,Y1,Z1)) & (-perpAt(Y,Z,X,Y1,Z1) | Y1 != Z1) & (Z != Y | -perpAt(Y,Z,X,Y1,Z1)) & (s_col(Y1,Z1,X) | -perpAt(Y,Z,X,Y1,Z1)))) # label(d_Defn8_11a) # label(axiom) # label(non_clause). [assumption]. 1.01/1.34 156 (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]. 1.01/1.34 157 (all Xa all Xb all Xc all Xa1 all Xb1 all Xp ((-s_t(Xa,Xb,Xc) | -s_t(Xa,Xp,Xa1) | s_t(Xb,crossbar(Xa,Xb,Xc,Xa1,Xb1,Xp),Xb1) | -s_t(Xa1,Xb1,Xc)) & (s_t(Xp,crossbar(Xa,Xb,Xc,Xa1,Xb1,Xp),Xc) | -s_t(Xa,Xp,Xa1) | -s_t(Xa1,Xb1,Xc) | -s_t(Xa,Xb,Xc)))) # label(aSatz3_17) # label(axiom) # label(non_clause). [assumption]. 1.01/1.34 158 (all Xa all Xb all Xp all Xq (-s_col(Xa,Xb,Xq) | -s_col(Xa,Xb,Xp) | -perp(Xa,Xb,Xp,Xq))) # label(aSatz8_14a) # label(axiom) # label(non_clause). [assumption]. 1.01/1.34 159 (all Xa all Xb all Xd all Xc (perpAt(Xa,Xb,Xd,Xc,Xd) | -perp(Xa,Xb,Xc,Xd) | -s_col(Xa,Xb,Xd) | Xa = Xb)) # label(aSatz8_15) # label(axiom) # label(non_clause). [assumption]. 1.01/1.34 160 (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]. 1.01/1.34 161 (all Xa all Xb all Xc all Xa1 all Xb1 (-s_col(Xa,Xb,Xc) | s_e3(Xa,Xb,Xc,Xa1,Xb1,insert5(Xa,Xb,Xc,Xa1,Xb1)) | -s_e(Xa,Xb,Xa1,Xb1))) # label(aSatz4_14) # label(axiom) # label(non_clause). [assumption]. 1.01/1.34 162 (all Xp all Xq all Xa all Xz all Xb all Xc (-s_e(Xa,Xp,Xz,Xq) | -s_e(Xc,Xp,Xc,Xq) | s_t(Xa,Xb,Xc) | s_t(Xc,Xa,Xb) | s_t(Xb,Xc,Xa) | -s_e(Xb,Xp,Xb,Xq) | Xp = Xq)) # label(aA9) # label(axiom) # label(non_clause). [assumption]. 1.01/1.34 163 (all Xa all Xb s_e(Xa,Xb,Xa,Xb)) # label(aSatz2_1) # label(axiom) # label(non_clause). [assumption]. 1.01/1.34 164 (all Xa all Xp Xp = s(Xa,s(Xa,Xp))) # label(aSatz7_7) # label(axiom) # label(non_clause). [assumption]. 1.01/1.34 165 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_t(Xa,Xb,Xc) | -s_e(Xb,Xc,Xb1,Xc1) | s_e(Xa,Xb,Xa1,Xb1) | -s_e(Xa,Xc,Xa1,Xc1) | -s_t(Xa1,Xb1,Xc1))) # label(aSatz4_3) # label(axiom) # label(non_clause). [assumption]. 1.01/1.34 166 (all Xa all Xp all Xq (Xp = Xq | s(Xa,Xp) != s(Xa,Xq))) # label(aSatz7_9) # label(axiom) # label(non_clause). [assumption]. 1.01/1.34 167 (all Xa all Xp all Xb (sameside(Xb,Xp,Xa) | -sameside(Xa,Xp,Xb))) # label(aSatz6_6) # label(axiom) # label(non_clause). [assumption]. 1.01/1.34 168 -(all Xa all Xb all Xc all Xp all Xq (samesideline(Xp,Xq,Xa,Xc) | -samesideline(Xp,Xq,Xa,Xb) | Xc = Xa | Xa = Xb | -s_col(Xa,Xb,Xc))) # label(aExtSameSide1) # label(negated_conjecture) # label(non_clause). [assumption]. 1.01/1.34 1.01/1.34 ============================== end of process non-clausal formulas === 1.01/1.34 1.01/1.34 ============================== PROCESS INITIAL CLAUSES =============== 1.01/1.34 1.01/1.34 ============================== PREDICATE ELIMINATION ================= 1.01/1.34 169 -s_e(A,B,C,D) | -s_e(B,E,D,F) | s_e3(A,B,E,C,D,F) | -s_e(A,E,C,F) # label(d_Defn4_4) # label(axiom). [clausify(125)]. 1.01/1.34 170 -s_col(A,B,C) | s_col(D,E,F) | -s_e3(A,B,C,D,E,F) # label(aSatz4_13) # label(axiom). [clausify(12)]. 1.01/1.34 171 -s_t(A,B,C) | s_t(D,E,F) | -s_e3(A,B,C,D,E,F) # label(aSatz4_6) # label(axiom). [clausify(33)]. 1.01/1.34 172 -s_r(A,B,C) | -s_e3(A,B,C,D,E,F) | s_r(D,E,F) # label(aSatz8_10) # label(axiom). [clausify(79)]. 1.01/1.34 173 -s_e3(A,B,C,D,E,F) | s_e(A,B,D,E) # label(d_Defn4_4) # label(axiom). [clausify(125)]. 1.01/1.34 174 -s_e3(A,B,C,D,E,F) | s_e(A,C,D,F) # label(d_Defn4_4) # label(axiom). [clausify(125)]. 1.01/1.34 Derived: -s_e(A,B,C,D) | -s_e(B,E,D,F) | -s_e(A,E,C,F) | -s_col(A,B,E) | s_col(C,D,F). [resolve(169,c,170,c)]. 1.01/1.34 Derived: -s_e(A,B,C,D) | -s_e(B,E,D,F) | -s_e(A,E,C,F) | -s_t(A,B,E) | s_t(C,D,F). [resolve(169,c,171,c)]. 1.01/1.34 Derived: -s_e(A,B,C,D) | -s_e(B,E,D,F) | -s_e(A,E,C,F) | -s_r(A,B,E) | s_r(C,D,F). [resolve(169,c,172,b)]. 1.01/1.34 175 s_e(A,B,C,D) | -s_e3(E,A,B,F,C,D) # label(d_Defn4_4) # label(axiom). [clausify(125)]. 1.01/1.34 176 -s_t(A,B,C) | s_e3(A,B,C,D,insert(A,B,D,E),E) | -s_e(A,C,D,E) # label(aSatz4_5) # label(axiom). [clausify(131)]. 1.01/1.34 Derived: -s_t(A,B,C) | -s_e(A,C,D,E) | -s_col(A,B,C) | s_col(D,insert(A,B,D,E),E). [resolve(176,b,170,c)]. 1.01/1.36 Derived: -s_t(A,B,C) | -s_e(A,C,D,E) | -s_r(A,B,C) | s_r(D,insert(A,B,D,E),E). [resolve(176,b,172,b)]. 1.01/1.36 Derived: -s_t(A,B,C) | -s_e(A,C,D,E) | s_e(A,B,D,insert(A,B,D,E)). [resolve(176,b,173,a)]. 1.01/1.36 Derived: -s_t(A,B,C) | -s_e(A,C,D,E) | s_e(B,C,insert(A,B,D,E),E). [resolve(176,b,175,b)]. 1.01/1.36 177 -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(152)]. 1.01/1.36 Derived: -s_col(A,B,C) | -s_e(A,D,E,F) | s_fs(A,B,C,D,E,V6,V7,F) | -s_e(B,D,V6,F) | -s_e(A,B,E,V6) | -s_e(B,C,V6,V7) | -s_e(A,C,E,V7). [resolve(177,b,169,c)]. 1.01/1.36 Derived: -s_col(A,B,C) | -s_e(A,D,E,F) | s_fs(A,B,C,D,E,insert(A,B,E,V6),V6,F) | -s_e(B,D,insert(A,B,E,V6),F) | -s_t(A,B,C) | -s_e(A,C,E,V6). [resolve(177,b,176,b)]. 1.01/1.36 178 -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(152)]. 1.01/1.36 Derived: -s_fs(A,B,C,D,E,F,V6,V7) | -s_col(A,B,C) | s_col(E,F,V6). [resolve(178,b,170,c)]. 1.01/1.36 Derived: -s_fs(A,B,C,D,E,F,V6,V7) | -s_t(A,B,C) | s_t(E,F,V6). [resolve(178,b,171,c)]. 1.01/1.36 Derived: -s_fs(A,B,C,D,E,F,V6,V7) | -s_r(A,B,C) | s_r(E,F,V6). [resolve(178,b,172,b)]. 1.01/1.36 Derived: -s_fs(A,B,C,D,E,F,V6,V7) | s_e(A,B,E,F). [resolve(178,b,173,a)]. 1.01/1.36 Derived: -s_fs(A,B,C,D,E,F,V6,V7) | s_e(A,C,E,V6). [resolve(178,b,174,a)]. 1.01/1.36 Derived: -s_fs(A,B,C,D,E,F,V6,V7) | s_e(B,C,F,V6). [resolve(178,b,175,b)]. 1.01/1.36 Derived: -s_fs(A,B,C,D,E,F,V6,V7) | -s_col(A,B,C) | -s_e(A,V8,E,V9) | s_fs(A,B,C,V8,E,F,V6,V9) | -s_e(B,V8,F,V9). [resolve(178,b,177,b)]. 1.01/1.36 179 -s_col(A,B,C) | s_e3(A,B,C,D,E,insert5(A,B,C,D,E)) | -s_e(A,B,D,E) # label(aSatz4_14) # label(axiom). [clausify(161)]. 1.01/1.36 Derived: -s_col(A,B,C) | -s_e(A,B,D,E) | -s_col(A,B,C) | s_col(D,E,insert5(A,B,C,D,E)). [resolve(179,b,170,c)]. 1.01/1.36 Derived: -s_col(A,B,C) | -s_e(A,B,D,E) | -s_t(A,B,C) | s_t(D,E,insert5(A,B,C,D,E)). [resolve(179,b,171,c)]. 1.01/1.36 Derived: -s_col(A,B,C) | -s_e(A,B,D,E) | -s_r(A,B,C) | s_r(D,E,insert5(A,B,C,D,E)). [resolve(179,b,172,b)]. 1.01/1.36 Derived: -s_col(A,B,C) | -s_e(A,B,D,E) | s_e(A,C,D,insert5(A,B,C,D,E)). [resolve(179,b,174,a)]. 1.01/1.36 Derived: -s_col(A,B,C) | -s_e(A,B,D,E) | s_e(B,C,E,insert5(A,B,C,D,E)). [resolve(179,b,175,b)]. 1.01/1.36 Derived: -s_col(A,B,C) | -s_e(A,B,D,E) | -s_col(A,B,C) | -s_e(A,F,D,V6) | s_fs(A,B,C,F,D,E,insert5(A,B,C,D,E),V6) | -s_e(B,F,E,V6). [resolve(179,b,177,b)]. 1.01/1.36 180 -s_m(A,B,C) | -s_m(D,E,F) | s_kf(A,B,C,V6,F,E,D) | -s_e(V6,D,V6,F) | -s_e(V6,A,V6,C) | -s_t(C,V6,F) | -s_t(A,V6,D) # label(d_Defn7_23) # label(axiom). [clausify(74)]. 1.01/1.36 181 -s_kf(A,B,C,D,E,F,V6) | -le(D,A,D,V6) | s_t(B,D,F) # label(aSatz7_22a) # label(axiom). [clausify(46)]. 1.01/1.36 182 -s_kf(A,B,C,D,E,F,V6) | s_e(D,V6,D,E) # label(d_Defn7_23) # label(axiom). [clausify(74)]. 1.01/1.36 183 s_m(A,B,C) | -s_kf(D,E,F,V6,C,B,A) # label(d_Defn7_23) # label(axiom). [clausify(74)]. 1.01/1.36 Derived: -s_m(A,B,C) | -s_m(D,E,F) | -s_e(V6,D,V6,F) | -s_e(V6,A,V6,C) | -s_t(C,V6,F) | -s_t(A,V6,D) | -le(V6,A,V6,D) | s_t(B,V6,E). [resolve(180,c,181,a)]. 1.01/1.36 184 s_m(A,B,C) | -s_kf(A,B,C,D,E,F,V6) # label(d_Defn7_23) # label(axiom). [clausify(74)]. 1.01/1.36 185 -s_kf(A,B,C,D,E,F,V6) | s_e(D,A,D,C) # label(d_Defn7_23) # label(axiom). [clausify(74)]. 1.01/1.36 186 -s_kf(A,B,C,D,E,F,V6) | s_t(C,D,E) # label(d_Defn7_23) # label(axiom). [clausify(74)]. 1.01/1.36 187 -s_kf(A,B,C,D,E,F,V6) | s_t(A,D,V6) # label(d_Defn7_23) # label(axiom). [clausify(74)]. 1.01/1.36 188 s_t(A,B,C) | -s_kf(D,A,E,B,F,C,V6) # label(aSatz7_22b) # label(axiom). [clausify(137)]. 1.01/1.36 Derived: s_t(A,B,C) | -s_m(D,A,E) | -s_m(F,C,V6) | -s_e(B,F,B,V6) | -s_e(B,D,B,E) | -s_t(E,B,V6) | -s_t(D,B,F). [resolve(188,b,180,c)]. 1.01/1.36 189 -s_t(A,B,C) | -s_e(A,C,D,E) | -s_e(A,F,D,V6) | -s_e(C,F,E,V6) | s_ifs(A,B,C,F,D,V7,E,V6) | -s_e(B,C,V7,E) | -s_t(D,V7,E) # label(d_Defn4_1) # label(axiom). [clausify(110)]. 1.01/1.36 190 s_e(A,B,C,D) | -s_ifs(E,A,F,B,V6,C,V7,D) # label(aSatz4_2) # label(axiom). [clausify(53)]. 1.01/1.36 191 -s_ifs(A,B,C,D,E,F,V6,V7) | s_t(A,B,C) # label(d_Defn4_1) # label(axiom). [clausify(110)]. 1.01/1.36 192 -s_ifs(A,B,C,D,E,F,V6,V7) | s_t(E,F,V6) # label(d_Defn4_1) # label(axiom). [clausify(110)]. 2.30/2.63 193 s_e(A,B,C,D) | -s_ifs(A,E,B,F,C,V6,D,V7) # label(d_Defn4_1) # label(axiom). [clausify(110)]. 2.30/2.63 194 s_e(A,B,C,D) | -s_ifs(E,A,B,F,V6,C,D,V7) # label(d_Defn4_1) # label(axiom). [clausify(110)]. 2.30/2.63 Derived: -s_t(A,B,C) | -s_e(A,C,D,E) | -s_e(A,F,D,V6) | -s_e(C,F,E,V6) | -s_e(B,C,V7,E) | -s_t(D,V7,E) | s_e(B,F,V7,V6). [resolve(189,e,190,b)]. 2.30/2.63 195 s_e(A,B,C,D) | -s_ifs(E,F,A,B,V6,V7,C,D) # label(d_Defn4_1) # label(axiom). [clausify(110)]. 2.30/2.63 196 -s_ifs(A,B,C,D,E,F,V6,V7) | s_e(A,D,E,V7) # label(d_Defn4_1) # label(axiom). [clausify(110)]. 2.30/2.63 197 -s_t(A,B,C) | -s_t(D,E,F) | -s_e(B,C,E,F) | -s_e(B,V6,E,V7) | s_afs(A,B,C,V6,D,E,F,V7) | -s_e(A,V6,D,V7) | -s_e(A,B,D,E) # label(d_Defn2_10) # label(axiom). [clausify(92)]. 2.30/2.63 198 -s_afs(A,B,C,D,E,F,V6,V7) | s_t(E,F,V6) # label(d_Defn2_10) # label(axiom). [clausify(92)]. 2.30/2.63 199 s_e(A,B,C,D) | -s_afs(A,B,E,F,C,D,V6,V7) # label(d_Defn2_10) # label(axiom). [clausify(92)]. 2.30/2.63 200 -s_afs(A,B,C,D,E,F,V6,V7) | s_e(A,D,E,V7) # label(d_Defn2_10) # label(axiom). [clausify(92)]. 2.30/2.63 201 s_e(A,B,C,D) | -s_afs(E,A,F,B,V6,C,V7,D) # label(d_Defn2_10) # label(axiom). [clausify(92)]. 2.30/2.63 202 s_e(A,B,C,D) | -s_afs(E,A,B,F,V6,C,D,V7) # label(d_Defn2_10) # label(axiom). [clausify(92)]. 2.30/2.63 203 -s_afs(A,B,C,D,E,F,V6,V7) | s_t(A,B,C) # label(d_Defn2_10) # label(axiom). [clausify(92)]. 2.30/2.63 204 -s_col(A,B,C) | -opposite(C,A,B,D) # label(d_Defn9_1) # label(axiom). [clausify(101)]. 2.30/2.63 205 A = B | s_col(B,A,C) | opposite(D,B,A,C) | -s_col(B,A,E) | -s_t(D,E,C) | s_col(B,A,D) # label(d_Defn9_1) # label(axiom). [clausify(101)]. 2.30/2.63 206 s_col(A,B,il(C,D,A,B)) | -opposite(C,A,B,D) # label(d_Defn9_1) # label(axiom). [clausify(101)]. 2.30/2.63 Derived: s_col(A,B,il(C,D,A,B)) | B = A | s_col(A,B,D) | -s_col(A,B,E) | -s_t(C,E,D) | s_col(A,B,C). [resolve(206,b,205,c)]. 2.30/2.63 207 -opposite(A,B,C,D) | s_t(A,il(A,D,B,C),D) # label(d_Defn9_1) # label(axiom). [clausify(101)]. 2.30/2.63 Derived: s_t(A,il(A,B,C,D),B) | D = C | s_col(C,D,B) | -s_col(C,D,E) | -s_t(A,E,B) | s_col(C,D,A). [resolve(207,a,205,c)]. 2.30/2.63 208 -opposite(A,B,C,D) | -s_col(B,C,D) # label(d_Defn9_1) # label(axiom). [clausify(101)]. 2.30/2.63 2.30/2.63 ============================== end predicate elimination ============= 2.30/2.63 2.30/2.63 Auto_denials: (non-Horn, no changes). 2.30/2.63 2.30/2.63 Term ordering decisions: 2.30/2.63 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. 2.30/2.63 2.30/2.63 ============================== end of process initial clauses ======== 2.30/2.63 2.30/2.63 ============================== CLAUSES FOR SEARCH ==================== 2.30/2.63 2.30/2.63 ============================== end of clauses for search ============= 2.30/2.63 2.30/2.63 ============================== SEARCH ================================ 2.30/2.63 2.30/2.63 % Starting search at 0.13 seconds. 2.30/2.63 2.30/2.63 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 209 (0.00 of 0.93 sec). 2.30/2.63 2.30/2.63 Low Water (keep): wt=50.000, iters=3333 2.30/2.63 2.30/2.63 Low Water (keep): wt=46.000, iters=3345 2.30/2.63 2.30/2.63 Low Water (keep): wt=45.000, iters=3391 2.30/2.63 2.30/2.63 Low Water (keep): wt=44.000, iters=3380 2.30/2.63 2.30/2.63 Low Water (keep): wt=42.000, iters=3450 2.30/2.63 2.30/2.63 Low Water (keep): wt=39.000, iters=3341 2.30/2.63 2.30/2.63 Low Water (keep): wt=38.000, iters=3337 2.30/2.63 2.30/2.63 Low Water (keep): wt=37.000, iters=3334 2.30/2.63 2.30/2.63 Low Water (keep): wt=36.000, iters=3341 2.30/2.63 2.30/2.63 Low Water (keep): wt=35.000, iters=3370 2.30/2.63 2.30/2.63 Low Water (keep): wt=34.000, iters=3336 2.30/2.63 2.30/2.63 Low Water (keep): wt=33.000, iters=3371 2.30/2.63 2.30/2.63 Low Water (keep): wt=32.000, iters=3355 2.30/2.63 2.30/2.63 Low Water (keep): wt=31.000, iters=3335 2.30/2.63 2.30/2.63 Low Water (keep): wt=30.000, iters=3563 2.30/2.63 2.30/2.63 Low Water (keep): wt=29.000, iters=3543 2.30/2.63 2.30/2.63 Low Water (keep): wt=28.000, iters=3502 2.30/2.63 2.30/2.63 Low Water (keep): wt=27.000, iters=3350 2.30/2.63 2.30/2.63 Low Water (keep): wt=26.000, iters=3341 2.30/2.63 2.30/2.63 Low Water (displace): id=1252, wt=90.000 2.30/2.63 2.30/2.63 Low Water (displace): id=2628, wt=80.000 2.30/2.63 2.30/2.63 Low Water (displace): id=2738, wt=71.000 2.30/2.63 2.30/2.63 Low Water (displace): id=1253, wt=70.000 2.30/2.63 2.30/2.63 Low Water (displace): id=2897, wt=66.000 2.30/2.63 2.30/2.63 Low Water (displace): id=1248, wt=61.000 2.30/2.63 2.30/2.63 Low Water (displace): id=3162, wt=60.000 2.30/2.63 2.30/2.63 Low Water (dispAlarm clock 119.86/120.12 Prover9 interrupted 119.86/120.12 EOF