0.00/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.10 % Command : tptp2X_and_run_prover9 %d %s 0.09/0.30 % Computer : n003.cluster.edu 0.09/0.30 % Model : x86_64 x86_64 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.09/0.30 % Memory : 8042.1875MB 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64 0.09/0.30 % CPULimit : 960 0.09/0.30 % WCLimit : 120 0.09/0.30 % DateTime : Tue Aug 9 05:01:51 EDT 2022 0.15/0.30 % CPUTime : 1.16/1.36 ============================== Prover9 =============================== 1.16/1.36 Prover9 (32) version 2009-11A, November 2009. 1.16/1.36 Process 5470 was started by sandbox2 on n003.cluster.edu, 1.16/1.36 Tue Aug 9 05:01:52 2022 1.16/1.36 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_5317_n003.cluster.edu". 1.16/1.36 ============================== end of head =========================== 1.16/1.36 1.16/1.36 ============================== INPUT ================================= 1.16/1.36 1.16/1.36 % Reading from file /tmp/Prover9_5317_n003.cluster.edu 1.16/1.36 1.16/1.36 set(prolog_style_variables). 1.16/1.36 set(auto2). 1.16/1.36 % set(auto2) -> set(auto). 1.16/1.36 % set(auto) -> set(auto_inference). 1.16/1.36 % set(auto) -> set(auto_setup). 1.16/1.36 % set(auto_setup) -> set(predicate_elim). 1.16/1.36 % set(auto_setup) -> assign(eq_defs, unfold). 1.16/1.36 % set(auto) -> set(auto_limits). 1.16/1.36 % set(auto_limits) -> assign(max_weight, "100.000"). 1.16/1.36 % set(auto_limits) -> assign(sos_limit, 20000). 1.16/1.36 % set(auto) -> set(auto_denials). 1.16/1.36 % set(auto) -> set(auto_process). 1.16/1.36 % set(auto2) -> assign(new_constants, 1). 1.16/1.36 % set(auto2) -> assign(fold_denial_max, 3). 1.16/1.36 % set(auto2) -> assign(max_weight, "200.000"). 1.16/1.36 % set(auto2) -> assign(max_hours, 1). 1.16/1.36 % assign(max_hours, 1) -> assign(max_seconds, 3600). 1.16/1.36 % set(auto2) -> assign(max_seconds, 0). 1.16/1.36 % set(auto2) -> assign(max_minutes, 5). 1.16/1.36 % assign(max_minutes, 5) -> assign(max_seconds, 300). 1.16/1.36 % set(auto2) -> set(sort_initial_sos). 1.16/1.36 % set(auto2) -> assign(sos_limit, -1). 1.16/1.36 % set(auto2) -> assign(lrs_ticks, 3000). 1.16/1.36 % set(auto2) -> assign(max_megs, 400). 1.16/1.36 % set(auto2) -> assign(stats, some). 1.16/1.36 % set(auto2) -> clear(echo_input). 1.16/1.36 % set(auto2) -> set(quiet). 1.16/1.36 % set(auto2) -> clear(print_initial_clauses). 1.16/1.36 % set(auto2) -> clear(print_given). 1.16/1.36 assign(lrs_ticks,-1). 1.16/1.36 assign(sos_limit,10000). 1.16/1.36 assign(order,kbo). 1.16/1.36 set(lex_order_vars). 1.16/1.36 clear(print_given). 1.16/1.36 1.16/1.36 % formulas(sos). % not echoed (212 formulas) 1.16/1.36 1.16/1.36 ============================== end of input ========================== 1.16/1.36 1.16/1.36 % From the command line: assign(max_seconds, 960). 1.16/1.36 1.16/1.36 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 1.16/1.36 1.16/1.36 % Formulas that are not ordinary clauses: 1.16/1.36 1 (all X all Y all Z (-s_e(X,Y,Z,Z) | X = Y)) # label(aA3) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 2 (all X all Y all W all V (s_t(X,Y,ext(X,Y,W,V)) & s_e(Y,ext(X,Y,W,V),W,V))) # label(aA4) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 3 (all X all Y (X = Y | -s_t(X,Y,X))) # label(aA6) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 4 (all X all Y s_e(X,Y,Y,X)) # label(aA1) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 5 (all Xa all Xp all Xc all Xb all Xq ((s_t(Xq,ip(Xa,Xp,Xc,Xb,Xq),Xa) | -s_t(Xb,Xq,Xc) | -s_t(Xa,Xp,Xc)) & (-s_t(Xa,Xp,Xc) | -s_t(Xb,Xq,Xc) | s_t(Xp,ip(Xa,Xp,Xc,Xb,Xq),Xb)))) # label(aA7) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 6 (all X all Y all Z all V all Z2 all V2 (s_e(Z,V,Z2,V2) | -s_e(X,Y,Z2,V2) | -s_e(X,Y,Z,V))) # label(aA2) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 7 (all X all Y all X1 all Y1 all Z all Z1 all V all V1 (-s_e(X,Y,X1,Y1) | -s_e(Y,Z,Y1,Z1) | -s_e(Y,V,Y1,V1) | -s_t(X1,Y1,Z1) | s_e(Z,V,Z1,V1) | X = Y | -s_t(X,Y,Z) | -s_e(X,V,X1,V1))) # label(aA5) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 8 (all Xa all Xb all Xc (-s_col(Xa,Xb,Xc) | Xb = Xc | Xa = Xb | -s_r(Xa,Xb,Xc))) # label(aSatz8_9) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 9 (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]. 1.16/1.36 10 (all Xa all Xb all Xp all Xq all Xr (Xq = Xp | -s_col(Xp,Xq,Xr) | s_col(Xa,Xb,Xr) | -s_col(Xp,Xq,Xb) | -s_col(Xp,Xq,Xa) | Xa = Xb)) # label(aSatz6_18) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 11 (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]. 1.16/1.36 12 (all Xa all Xb all Xp all Xq (s_e(Xp,Xq,reflect(Xa,Xb,Xp),reflect(Xa,Xb,Xq)) | Xb = Xa)) # label(aSatz10_10) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 13 (all Xa all Xp (Xp != s(Xa,Xp) | Xa = Xp)) # label(aSatz7_10a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 14 (all Xa all Xb all Xp all Xq all Xc all Xd (-s_col(Xa,Xb,Xp) | Xp = Xq | Xb = Xa | -perp(Xa,Xb,Xc,Xd) | perp(Xp,Xq,Xc,Xd) | -s_col(Xa,Xb,Xq))) # label(aExtPerp5) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 15 (all Xa all Xb all Xc (s_col(Xb,Xa,Xc) | -s_col(Xa,Xb,Xc))) # label(aSatz4_11d) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 16 (all Xa all Xb all Xp all Xq (Xp = Xq | reflect(Xa,Xb,Xp) != reflect(Xa,Xb,Xq) | Xa = Xb)) # label(aSatz10_7) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 17 (all Xa all Xb all Xp all Xq all Xu all Xc all Xv ((-samesideline(Xa,Xb,Xp,Xq) | s_col(Xp,Xq,ss2(Xa,Xb,Xp,Xq))) & (s_t(Xb,ss2(Xa,Xb,Xp,Xq),ss3(Xa,Xb,Xp,Xq)) | -samesideline(Xa,Xb,Xp,Xq)) & (-samesideline(Xa,Xb,Xp,Xq) | Xq != Xp) & (-s_col(Xp,Xq,Xu) | -s_col(Xp,Xq,Xv) | Xp = Xq | Xv = Xc | s_col(Xp,Xq,Xb) | samesideline(Xa,Xb,Xp,Xq) | s_col(Xp,Xq,Xa) | Xb = Xv | Xu = Xa | Xc = Xu | -s_t(Xb,Xv,Xc) | -s_t(Xa,Xu,Xc)) & (-samesideline(Xa,Xb,Xp,Xq) | -s_col(Xp,Xq,Xb)) & (-samesideline(Xa,Xb,Xp,Xq) | -s_col(Xp,Xq,Xa)) & (-samesideline(Xa,Xb,Xp,Xq) | ss2(Xa,Xb,Xp,Xq) != ss3(Xa,Xb,Xp,Xq)) & (ss1(Xa,Xb,Xp,Xq) != ss3(Xa,Xb,Xp,Xq) | -samesideline(Xa,Xb,Xp,Xq)) & (-samesideline(Xa,Xb,Xp,Xq) | ss2(Xa,Xb,Xp,Xq) != Xb) & (-samesideline(Xa,Xb,Xp,Xq) | Xa != ss1(Xa,Xb,Xp,Xq)) & (-samesideline(Xa,Xb,Xp,Xq) | s_t(Xa,ss1(Xa,Xb,Xp,Xq),ss3(Xa,Xb,Xp,Xq))) & (s_col(Xp,Xq,ss1(Xa,Xb,Xp,Xq)) | -samesideline(Xa,Xb,Xp,Xq)))) # label(d_Defn9_7) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 18 (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) | Xb = Xd)) # label(aSatz7_21) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 19 (all Xp all Xq all Xr all Xa (-s_t(Xp,Xq,Xr) | s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr)))) # label(aSatz7_15a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 20 (all Xa all Xp all Xq all Xc all Xcs all Xr all Xm all U all V (-opposite(Xa,Xp,Xq,Xc) | Xq = Xp | -s_m(Xr,Xm,Xcs) | -sameside(V,Xcs,Xc) | opposite(U,Xp,Xq,V) | -sameside(U,Xr,Xa) | -perp(Xp,Xq,Xc,Xcs) | -perp(Xp,Xq,Xa,Xr) | -s_col(Xp,Xq,Xr) | -s_col(Xp,Xq,Xcs))) # label(aSatz9_4c) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 21 (all Xp all Xa all Xb all Xq all Xt all Xr all Xcx (-s_col(Xa,Xb,Xt) | -s_t(Xp,Xt,Xq) | -s_t(Xb,Xr,Xq) | s_m(Xp,Xcx,Xr) | Xcx != ip(Xp,Xt,Xq,Xb,Xr) | -s_e(Xa,Xp,Xb,Xr) | -perp(Xq,Xb,Xa,Xb) | -perp(Xp,Xa,Xa,Xb))) # label(aSatz8_24b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 22 (all Xa all Xp all Xb (-sameside(Xa,Xp,Xb) | le(Xp,Xa,Xp,Xb) | -s_t(Xp,Xa,Xb))) # label(aSatz6_13b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 23 (all Xp all Xq all Xr all Xa (Xp = Xq | -s_t(Xq,Xp,Xr) | s_col(Xa,Xp,Xq) | -sameside(Xa,Xp,Xr) | Xp = Xr)) # label(aSatz6_15c) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 24 (all Xa all Xb all Xc all Xp all Xq ((Xb != Xa | -perpAt(Xa,Xb,Xc,Xp,Xq)) & (s_col(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) | f813(Xa,Xb,Xp,Xq,Xc) != Xc) & (-perpAt(Xa,Xb,Xc,Xp,Xq) | Xc != g813(Xa,Xb,Xp,Xq,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,f813(Xa,Xb,Xp,Xq,Xc)) | -perpAt(Xa,Xb,Xc,Xp,Xq)) & (-perpAt(Xa,Xb,Xc,Xp,Xq) | s_col(Xa,Xb,Xc)) & (Xq != Xp | -perpAt(Xa,Xb,Xc,Xp,Xq)))) # label(aSatz8_13a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 25 (all Xa all Xp all Xb all Xc (sameside(Xa,Xp,Xb) | Xp = Xb | -s_t(Xa,Xp,Xc) | -s_t(Xb,Xp,Xc) | Xc = Xp | Xa = Xp)) # label(aSatz6_3b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 26 (all Xa all Xb all Xc ((-s_t(Xa,Xb,Xc) | s_col(Xa,Xb,Xc)) & (s_col(Xa,Xb,Xc) | -s_t(Xb,Xc,Xa)) & (s_col(Xa,Xb,Xc) | -s_t(Xc,Xa,Xb)) & (s_t(Xc,Xa,Xb) | s_t(Xb,Xc,Xa) | s_t(Xa,Xb,Xc) | -s_col(Xa,Xb,Xc)))) # label(d_Defn4_10) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 27 (all Xp all Xa all Xr all Xq (Xq = Xr | -s_m(Xp,Xa,Xq) | -s_m(Xp,Xa,Xr))) # label(aSatz7_4b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 28 (all Xa all Xb all Xc all Xp all Xq (s_col(Xa,Xb,Xc) | -s_col(Xa,Xb,Xp) | -perp(Xa,Xb,Xc,Xq) | Xq = Xp | -perp(Xa,Xb,Xc,Xp) | -s_col(Xa,Xb,Xq))) # label(aSatz8_18a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 29 (all Xa all Xb all Xp all Xq all Xc (Xa = Xb | -s_col(Xa,Xb,Xq) | Xq = Xp | perp(Xa,Xb,Xc,Xp) | s_col(Xa,Xb,Xc) | -s_r(Xc,Xp,Xq) | -s_col(Xa,Xb,Xp))) # label(aSatz8_16b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 30 (all Xa all Xb all Xc all Xd all Xp (Xa = Xb | Xc = Xd | -s_col(Xa,Xb,Xc) | -s_col(Xc,Xd,Xp) | s_col(Xa,Xb,Xp) | -s_col(Xa,Xb,Xd))) # label(aExtCol2) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 31 (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]. 1.16/1.36 32 (all Xa all Xp all Xq all Xc all Xcs all Xr all Xm all U (Xq = Xp | -s_col(Xp,Xq,Xr) | -perp(Xp,Xq,Xc,Xcs) | -s_m(Xr,Xm,Xcs) | sameside(U,Xr,Xa) | -le(Xcs,Xc,Xr,Xa) | -sameside(s(Xm,U),Xcs,Xc) | Xcs = Xr | -perp(Xp,Xq,Xa,Xr) | -s_col(Xp,Xq,Xcs) | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_4a2) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 33 (all Xa all Xb all Xd all Xc (Xb = Xa | 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]. 1.16/1.36 34 (all Xa all Xb all Xp all Xq all Xr all Xc all Xd (-s_col(Xa,Xb,Xp) | Xb = Xa | -perpAt(Xp,Xq,Xr,Xc,Xd) | perpAt(Xa,Xb,Xr,Xc,Xd) | Xq = Xp | -s_col(Xa,Xb,Xq))) # label(aExtPerp) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 35 (all Xa all Xb all Xc all Xp all Xq (-s_col(Xa,Xb,Xc) | samesideline(Xp,Xq,Xa,Xc) | -samesideline(Xp,Xq,Xa,Xb) | Xa = Xc | Xb = Xa)) # label(aExtSameSide1) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 36 (all Xa all Xp all Xq all Xc all Xr all Xb (-opposite(Xa,Xp,Xq,Xc) | -sameside(Xa,Xr,Xb) | opposite(Xb,Xp,Xq,Xc) | -s_col(Xp,Xq,Xr))) # label(aSatz9_5) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 37 (all Xa all Xb all Xc all Xd (-s_t(Xa,Xb,Xc) | -s_t(Xb,Xc,Xd) | Xb = Xc | s_t(Xa,Xb,Xd))) # label(aSatz3_7b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 38 (all Xa all Xb all Xc all Xd all Za all Zb all Zc all Zd ((s_e(Xb,Xc,Zb,Zc) | -s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)) & (-s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_e(Xa,Xd,Za,Zd)) & (-s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_e(Xb,Xd,Zb,Zd)) & (-s_t(Xa,Xb,Xc) | -s_e(Xb,Xd,Zb,Zd) | s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | -s_e(Xa,Xd,Za,Zd) | -s_e(Xb,Xc,Zb,Zc) | -s_e(Xa,Xb,Za,Zb) | -s_t(Za,Zb,Zc)) & (-s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_e(Xa,Xb,Za,Zb)) & (-s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_t(Za,Zb,Zc)) & (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]. 1.16/1.36 39 (all Xa all Xb all Xc (s_r(Xc,Xb,Xa) | -s_r(Xa,Xb,Xc))) # label(aSatz8_2) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 40 (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]. 1.16/1.36 41 (all Xb all Xa Xb != ext(Xa,Xb,alpha,gamma)) # label(aSatz3_14b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 42 (all Xq all Xa all Xd all Xb all Xc (Xq = Xa | -s_e(Xa,Xd,Xb,Xc) | Xd = ext(Xq,Xa,Xb,Xc) | -s_t(Xq,Xa,Xd))) # label(aSatz2_12) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 43 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-sameside(Xa1,Xb1,Xc1) | -s_e(Xb,Xc,Xb1,Xc1) | s_e(Xa,Xc,Xa1,Xc1) | -s_e(Xb,Xa,Xb1,Xa1) | -sameside(Xa,Xb,Xc))) # label(aSatz6_28) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 44 (all Xa all Xb all Xc all Xd (s_col(Xa,Xc,Xd) | Xb = Xa | -s_col(Xa,Xb,Xd) | -s_col(Xa,Xb,Xc))) # label(aext1) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 45 (all Xa all Xb s_m(Xa,midpoint(Xa,Xb),Xb)) # label(aSatz8_22) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 46 (all Xa all Xb all Xp all Xq all Xc all Xd all Xe (Xb = Xa | -s_col(Xa,Xb,Xc) | -s_col(Xp,Xq,Xc) | s_col(Xp,Xq,Xe) | -s_col(Xa,Xb,Xe) | Xc = Xd | -s_col(Xp,Xq,Xd) | -s_col(Xa,Xb,Xd) | Xq = Xp)) # label(aSatz6_21) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 47 (all Xa all Xp all Xq (Xq = Xp | s(Xa,Xp) != s(Xa,Xq))) # label(aSatz7_9) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 48 (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)) & (s_t(Xc,insert(Xa,Xb,Xc,Xd),Xd) | -le(Xa,Xb,Xc,Xd)))) # label(d_Defn5_4) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 49 (all Xp all Xq all Xa all Xb (-samesideline(Xp,Xq,Xa,Xb) | samesideline(Xp,Xq,Xb,Xa))) # label(aLemma9_13a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 50 (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]. 1.16/1.36 51 (all Xc all Xa all Xb (-s_e(Xc,Xa,Xc,Xb) | s_m(Xa,isomidpoint(Xa,Xb,Xc),Xb))) # label(aSatz7_25) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 52 (all Xa all Xb all Xc all Xa1 all Xb1 all Xp ((-s_t(Xa,Xb,Xc) | -s_t(Xa,Xp,Xa1) | s_t(Xp,crossbar(Xa,Xb,Xc,Xa1,Xb1,Xp),Xc) | -s_t(Xa1,Xb1,Xc)) & (s_t(Xb,crossbar(Xa,Xb,Xc,Xa1,Xb1,Xp),Xb1) | -s_t(Xa,Xp,Xa1) | -s_t(Xa1,Xb1,Xc) | -s_t(Xa,Xb,Xc)))) # label(aSatz3_17) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 53 (all Xa all Xb all Xp all Xq (Xa = Xb | samesideline(Xq,Xp,Xa,Xb) | -samesideline(Xp,Xq,Xa,Xb))) # label(aLemma9_13d) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 54 (all Xa all Xb all Xc all Xd all Xa1 all Xb1 all Xc1 all Xd1 (s_e(Xb,Xd,Xb1,Xd1) | -s_ifs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1))) # label(aSatz4_2) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 55 (all Xa all Xp (sameside(Xa,Xp,Xa) | Xp = Xa)) # label(aSatz6_5) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 56 (all Xa all Xb all Xp all Xp1 ((-s_col(Xa,Xb,midpoint(Xp,Xp1)) | -perp(Xa,Xb,Xp,Xp1) | reflect(Xa,Xb,Xp) = Xp1 | Xa = Xb) & (Xb = Xa | reflect(Xa,Xb,Xp) = Xp1 | Xp != Xp1 | -s_col(Xa,Xb,midpoint(Xp,Xp1))))) # label(aSatz10_2b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 57 (all Xa all Xb all Xd all Xc (-s_t(Xa,Xc,Xd) | s_t(Xa,Xb,Xc) | s_t(Xa,Xc,Xb) | -s_t(Xa,Xb,Xd))) # label(aSatz5_3) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 58 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1) | s_col(Xa1,Xb1,Xc1) | -s_col(Xa,Xb,Xc))) # label(aSatz4_13) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 59 (all Xb all Xc all Xa (-s_e(Xb,Xc,Xa,Xa) | Xb = Xc)) # label(aSatz2_13) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 60 (all Xp all Xa all Xb all Xq all Xt all Xr all Xcx (-perp(Xq,Xb,Xa,Xb) | -s_col(Xa,Xb,Xt) | Xcx != ip(Xp,Xt,Xq,Xb,Xr) | s_m(Xa,Xcx,Xb) | -s_e(Xa,Xp,Xb,Xr) | -s_t(Xb,Xr,Xq) | -s_t(Xp,Xt,Xq) | -perp(Xp,Xa,Xa,Xb))) # label(aSatz8_24a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 61 (all Xp all Xq all Xr all Xcs (s_col(Xp,Xq,Xcs) | opposite(Xr,Xp,Xq,Xcs) | samesideline(Xr,Xcs,Xp,Xq) | s_col(Xp,Xq,Xr) | Xp = Xq)) # label(aLemma9_13f) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 62 (all Xa all Xb all Xc (s_col(Xc,Xa,Xb) | -s_col(Xa,Xb,Xc))) # label(aSatz4_11b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 63 (all Xa all Xb (Xb = Xa | -s_col(Xa,Xb,pointOffLine(Xa,Xb)))) # label(aSatz6_25) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 64 (all Xa all Xb all Xp (-s_col(Xa,Xb,Xp) | Xp = reflect(Xa,Xb,Xp) | Xa = Xb)) # label(aSatz10_8b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 65 (all Xa all Xb all Xc (-s_col(Xa,Xb,Xc) | -le(Xa,Xb,Xa,Xc) | -le(Xb,Xc,Xa,Xc) | s_t(Xa,Xb,Xc))) # label(aSatz5_12b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 66 (all Xa all Xb all Xc all Xd all Xa1 all Xb1 all Xc1 all Xd1 ((-s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1) | s_e(Xa,Xd,Xa1,Xd1)) & (-s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1) | s_e(Xb,Xd,Xb1,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_e(Xa,Xd,Xa1,Xd1) | -s_col(Xa,Xb,Xc)) & (s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1) | -s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1)) & (-s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1) | s_col(Xa,Xb,Xc)))) # label(d_Defn4_15) # label(axiom) # label(non_clause). [assumption]. 1.16/1.36 67 (all Xa all Xm all Xb (-s_col(Xa,Xm,Xb) | s_m(Xa,Xm,Xb) | Xb = Xa | -s_e(Xm,Xa,Xm,Xb))) # label(aSatz7_20) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 68 (all Xa all Xp all Xb (s_t(Xa,Xp,Xb) | -s_col(Xa,Xp,Xb) | sameside(Xa,Xp,Xb))) # label(aSatz6_4b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 69 (all Xa all Xp all Xb ((-sameside(Xa,Xp,Xb) | s_t(Xa,Xp,c63(Xa,Xp,Xb))) & (-sameside(Xa,Xp,Xb) | s_t(Xb,Xp,c63(Xa,Xp,Xb))) & (-sameside(Xa,Xp,Xb) | Xp != c63(Xa,Xp,Xb)) & (Xb != Xp | -sameside(Xa,Xp,Xb)) & (-sameside(Xa,Xp,Xb) | Xa != Xp))) # label(aSatz6_3a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 70 (all Xa all Xm (Xa = Xm | -s_m(Xa,Xm,Xa))) # label(aSatz7_3a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 71 (all Xa all Xb all Xc all Xd all Xe all Xf (-s_e(Xa,Xb,Xc,Xd) | s_e(Xa,Xb,Xe,Xf) | -s_e(Xc,Xd,Xe,Xf))) # label(aSatz2_3) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 72 (all Xa all Xp all Xq all Xc all Xm all Xr all Xb (-s_col(Xp,Xq,Xm) | -sameside(Xa,Xr,Xb) | -s_t(Xr,Xb,Xa) | opposite(Xb,Xp,Xq,Xc) | -s_col(Xp,Xq,Xr) | -s_m(Xa,Xm,Xc) | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_3a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 73 (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]. 1.16/1.37 74 (all Xa all Xb all Xc all Xd all Xa1 all Xb1 all Xc1 all Xd1 (s_e(Xc,Xd,Xc1,Xd1) | Xb = Xa | -s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1))) # label(aSatz4_16) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 75 (all Xa all Xb all Xc (-s_col(Xa,Xb,Xc) | s_col(Xc,Xb,Xa))) # label(aSatz4_11c) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 76 (all Xa all Xb all Xp all Xq all Xc all Xd (-s_col(Xa,Xb,Xp) | Xp = Xq | perp(Xa,Xb,Xc,Xd) | -perp(Xp,Xq,Xc,Xd) | Xb = Xa | -s_col(Xa,Xb,Xq))) # label(aExtPerp2) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 77 (all Xp all Xa all Xq (-s_m(Xp,Xa,Xq) | s(Xa,Xp) = Xq)) # label(aSatz7_6) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 78 (all Xd all Xe all Xd1 all Xa all Xb (samesideline(Xa,Xb,Xd,Xe) | -samesideline(Xa,Xb,Xd1,Xe) | -s_t(Xe,Xd,Xd1) | Xd = Xe)) # label(aLemma9_13c) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 79 (all Xa all Xb all Xc all Xd (Xb = Xa | Xa = Xc | Xb = Xc | Xd = Xc | -perp(Xb,Xa,Xa,Xc) | perp(Xb,Xa,Xa,Xd) | -s_col(Xa,Xc,Xd) | Xd = Xa)) # label(aExtPerp3) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 80 (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(Xa,Xb,Xc) | s_t(Xa1,insert(Xa,Xb,Xa1,Xc1),Xc1) | -s_e(Xa,Xc,Xa1,Xc1)))) # label(aSatz4_5) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 81 (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]. 1.16/1.37 82 (all Xa all Xb all Xc all Xa1 (-s_r(Xa,Xb,Xc) | Xa = Xb | -s_col(Xb,Xa,Xa1) | s_r(Xa1,Xb,Xc))) # label(aSatz8_3) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 83 (all Xa all Xb all Xc all Xd (-s_t(Xa,Xb,Xc) | s_t(Xb,Xc,Xd) | -s_t(Xa,Xc,Xd))) # label(aSatz3_6a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 84 (all Xa all Xb all Xc all Xp all Xq (Xa = Xb | s_e(Xc,Xp,Xc,Xq) | -s_e(Xb,Xp,Xb,Xq) | -s_e(Xa,Xp,Xa,Xq) | -s_col(Xa,Xb,Xc))) # label(aSatz4_17) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 85 (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]. 1.16/1.37 86 (all Xa all Xb all Xp all Xq all Xc (-perp(Xa,Xb,Xp,Xq) | -s_col(Xa,Xb,Xc) | -s_col(Xp,Xq,Xc) | perpAt(Xa,Xb,Xc,Xp,Xq))) # label(aSatz8_14b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 87 (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]. 1.16/1.37 88 (all Xa all Xb all Xc all Xd (-s_t(Xa,Xb,Xc) | s_t(Xa,Xc,Xd) | Xb = Xc | -s_t(Xb,Xc,Xd))) # label(aSatz3_7a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 89 (all Xa all Xb all Xc all Xd ((ins(Xc,Xd,Xa,Xb) = ext(Xa,Xb,insert(Xa,Xb,Xc,Xd),Xd) | -le(Xa,Xb,Xc,Xd)) & (s_e(Xa,ins(Xc,Xd,Xa,Xb),Xc,Xd) | -le(Xa,Xb,Xc,Xd)) & (s_t(Xa,Xb,ins(Xc,Xd,Xa,Xb)) | -le(Xa,Xb,Xc,Xd)))) # label(aSatz5_5a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 90 (all Xa all Xb all Xc ((s_col(Xa,Xb,foot(Xa,Xb,Xc)) | s_col(Xa,Xb,Xc)) & (s_col(Xa,Xb,Xc) | perp(Xa,Xb,Xc,foot(Xa,Xb,Xc))))) # label(aSatz8_18) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 91 (all Xa all Xb all Xp all Xq (Xa = Xb | samesideline(Xp,Xq,Xb,Xa) | -samesideline(Xp,Xq,Xa,Xb))) # label(aExtSameSide2) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 92 (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]. 1.16/1.37 93 (all Xa all Xp all Xb (sameside(Xb,Xp,Xa) | -sameside(Xa,Xp,Xb))) # label(aSatz6_6) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 94 (all Xa all Xb all Xc ((perp(Xa,Xb,erect(Xa,Xb,Xc),Xa) | Xb = Xa) & (s_t(Xc,erectAux(Xa,Xb,Xc),erect(Xa,Xb,Xc)) | Xa = Xb) & (Xb = Xa | s_col(Xa,Xb,erectAux(Xa,Xb,Xc))))) # label(aSatz8_21) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 95 (all Xa all Xb all Xc (Xb = Xc | -s_e(Xa,Xc,Xa,Xb) | -s_t(Xa,Xb,Xc))) # label(aNarbouxLemma1) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 96 (all Xa all Xp all Xb all Xq all Xt (-le(Xa,Xp,Xb,Xq) | -perp(Xa,Xb,Xa,Xp) | -s_col(Xa,Xb,Xt) | s_m(Xa,midpointAux(Xa,Xb,Xp,Xq,Xt),Xb) | -s_t(Xp,Xt,Xq) | -perp(Xa,Xb,Xb,Xq))) # label(aSatz8_22b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 97 (all Xa all Xb all Xp all Xq (perp(Xa,Xb,Xq,Xp) | -perp(Xa,Xb,Xp,Xq))) # label(aExtPerp4) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 98 (all Xa all Xp all Xb ((Xa = Xp | xb = Xp | sameside(Xa,Xp,Xb) | -s_t(Xp,Xa,Xb)) & (Xp = Xb | sameside(Xa,Xp,Xb) | Xa = Xp | -s_t(Xp,Xb,Xa)) & (-sameside(Xa,Xp,Xb) | s_t(Xp,Xb,Xa) | s_t(Xp,Xa,Xb)) & (-sameside(Xa,Xp,Xb) | Xp != Xb) & (-sameside(Xa,Xp,Xb) | Xp != Xa))) # label(d_Defn6_1) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 99 (all Xp all Xq all Xc all Xa all Xb (-perpAt(Xp,Xq,Xc,Xb,Xc) | Xa = Xc | s_col(Xc,Xa,Xb) | -perpAt(Xp,Xq,Xc,Xa,Xc) | Xp = Xq)) # label(aLemma9_13g) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 100 (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(Xa1,Xa2,Xb1,Xb2) | s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3) | -s_e(Xa2,Xa3,Xb2,Xb3) | -s_e(Xa1,Xa3,Xb1,Xb3)) & (-s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3) | s_e(Xa2,Xa3,Xb2,Xb3)))) # label(d_Defn4_4) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 101 (all Xa all Xb all Xc all Xd (-s_t(Xc,Xa,Xb) | s_t(Xc,Xd,Xb) | s_t(Xd,Xc,Xb) | -s_t(Xd,Xa,Xb) | Xb = Xa)) # label(aSatz6_16a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 102 (all Xp all Xa all Xq all Xb (-s_m(Xp,Xa,Xq) | Xa = Xb | -s_m(Xp,Xb,Xq))) # label(aSatz7_17) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 103 (all Xa all Xb s_e(Xa,Xa,Xb,Xb)) # label(aSatz2_8) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 104 (all Xa all Xb all Xc (-s_r(Xa,Xb,Xc) | Xc = Xb | -s_r(Xa,Xc,Xb))) # label(aSatz8_7) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 105 (all Xa all Xb all Xp all Xp1 (Xb = Xa | reflect(Xa,Xb,Xp) != Xp1 | Xp = reflect(Xa,Xb,Xp1))) # label(aSatz10_4) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 106 (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]. 1.16/1.37 107 (all Xa all Xb all Xp (Xp = reflect(Xa,Xb,reflect(Xa,Xb,Xp)) | Xa = Xb)) # label(aSatz10_5) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 108 (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]. 1.16/1.37 109 (all Xp all Xq all Xr all Xa (s_col(Xa,Xp,Xq) | -sameside(Xa,Xp,Xq) | -s_t(Xq,Xp,Xr) | Xp = Xr | Xp = Xq)) # label(aSatz6_15b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 110 (all Xa all Xp all Xb all Xc (Xa = Xp | Xp = Xc | -sameside(Xa,Xp,Xb) | s_t(Xb,Xp,Xc) | -s_t(Xa,Xp,Xc) | Xb = Xp)) # label(aSatz6_2b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 111 (all Xr all Xa all Xb all Xc ((Xa = Xr | Xc = Xb | sameside(insert(Xb,Xc,Xa,Xr),Xa,Xr)) & (s_e(Xa,insert(Xb,Xc,Xa,Xr),Xb,Xc) | Xb = Xc | Xr = Xa))) # label(aSatz6_11a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 112 (all Xc all Xd all Xp all Xa all Xb (-s_col(Xa,Xb,Xp) | -sameside(Xa,Xp,Xb) | samesideline(Xa,Xb,Xc,Xd) | s_col(Xc,Xd,Xa) | -s_col(Xc,Xd,Xp) | Xd = Xc)) # label(aSatz9_19b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 113 (all Xa all Xp all Xb (-sameside(Xa,Xp,Xb) | -le(Xp,Xa,Xp,Xb) | s_t(Xp,Xa,Xb))) # label(aSatz6_13a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 114 (all Xa1 all Xm1 all Xb1 all Xc all Xb2 all Xm2 all Xa2 (s_t(Xm1,Xc,Xm2) | -s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2))) # label(aSatz7_22b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 115 (all Xa all Xb s_col(Xa,Xa,Xb)) # label(aSatz4_12) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 116 (all Xa all Xb s_r(Xa,Xb,Xb)) # label(aSatz8_5) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 117 (all Xa all Xp all Xq all Xb (-opposite(Xa,Xp,Xq,Xb) | -samesideline(Xa,Xb,Xp,Xq))) # label(aSatz9_9) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 118 (all Xa all Xp all Xq all Xc all Xm all Xr all Xb (-s_m(Xa,Xm,Xc) | -s_col(Xp,Xq,Xr) | -sameside(Xa,Xr,Xb) | opposite(Xb,Xp,Xq,Xc) | -s_col(Xp,Xq,Xm) | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_3) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 119 (all Xa all Xc all Xp all Xb all Xq ((-s_t(Xb,Xq,Xc) | s_t(Xp,Xq,op(Xq,Xb,Xp,Xc,Xa)) | -s_t(Xa,Xc,Xp)) & (-s_t(Xb,Xq,Xc) | s_t(Xa,op(Xq,Xb,Xp,Xc,Xa),Xb) | -s_t(Xa,Xc,Xp)))) # label(aSatz9_6) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 120 (all Xa all Xb all Xc all Xd (-s_t(Xa,Xb,Xd) | s_t(Xb,Xd,Xc) | s_t(Xb,Xc,Xd) | -s_t(Xa,Xb,Xc) | Xa = Xb)) # label(aSatz5_2) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 121 (all Xa all Xc all Xd le(Xa,Xa,Xc,Xd)) # label(aSatz5_11) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 122 (all Xa all Xb all Xc all Xd (le(Xa,Xb,Xc,Xd) | le(Xc,Xd,Xa,Xb))) # label(aSatz5_10) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 123 (all Xa all Xp all Xq all Xb (opposite(Xb,Xp,Xq,Xa) | -opposite(Xa,Xp,Xq,Xb))) # label(aSatz9_2) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 124 (all Xp all Xq all Xr all Xa (Xq = Xp | Xr = Xp | s_col(Xa,Xp,Xq) | Xa != Xp | -s_t(Xq,Xp,Xr))) # label(aSatz6_15d) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 125 (all Xa all Xb all Xc all Xa1 (s_e(Xa,Xc,Xa1,Xc) | -s_e(Xa,Xb,Xa1,Xb) | -s_r(Xa1,Xb,Xc) | -s_r(Xa,Xb,Xc))) # label(aSatz10_12b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 126 (all Xa all Xb all Xc all Xd (s_e(Xc,Xd,Xa,Xb) | -s_e(Xa,Xb,Xc,Xd))) # label(aSatz2_2) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 127 (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]. 1.16/1.37 128 (all Y all Z all X all Y1 all Z1 all U all V ((s_col(Y1,Z1,X) | -perpAt(Y,Z,X,Y1,Z1)) & (-s_col(Y1,Z1,V) | s_r(U,X,V) | -s_col(Y,Z,U) | -perpAt(Y,Z,X,Y1,Z1)) & (perpAt(Y,Z,X,Y1,Z1) | Z1 = Y1 | -s_col(Y,Z,X) | -s_col(Y1,Z1,X) | s_col(Y,Z,f811(Y,Z,Y1,Z1,X)) | Z = Y) & (perpAt(Y,Z,X,Y1,Z1) | Y = Z | -s_r(f811(Y,Z,Y1,Z1,X),X,g811(Y,Z,Y1,Z1,X)) | -s_col(Y1,Z1,X) | -s_col(Y,Z,X) | Y1 = Z1) & (perpAt(Y,Z,X,Y1,Z1) | Y1 = Z1 | -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) | Y1 != Z1) & (Y != Z | -perpAt(Y,Z,X,Y1,Z1)) & (s_col(Y,Z,X) | -perpAt(Y,Z,X,Y1,Z1)))) # label(d_Defn8_11a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 129 (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]. 1.16/1.37 130 (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]. 1.16/1.37 131 (all Xa all Xp all Xr all Xq (Xr != s(Xa,Xq) | Xp = Xq | Xr != s(Xa,Xp))) # label(aSatz7_8) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 132 (all Xa1 all Xm1 all Xb1 all Xc all Xb2 all Xm2 all Xa2 (-s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) | s_t(Xm1,Xc,Xm2) | -le(Xc,Xa1,Xc,Xa2))) # label(aSatz7_22a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 133 (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]. 1.16/1.37 134 (all Xa all Xb all U all V all W (s_col(Xa,Xb,V) | -s_col(Xa,Xb,W) | -s_col(Xa,Xb,U) | -s_m(U,V,W) | Xa = Xb)) # label(aLemma9_13b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 135 (all Xp all Xq all Xr all Xcs (Xp = Xq | s_col(Xp,Xq,Xr) | s_col(Xp,Xq,Xcs) | samesideline(Xr,Xcs,Xp,Xq) | foot(Xp,Xq,Xr) != Xp | opposite(Xr,Xp,Xq,Xcs))) # label(aLemma9_13f_case1) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 136 (all Xa all Xp (s(Xa,Xp) = Xp | Xa != Xp)) # label(aSatz7_10b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 137 (all Xa all Xb all Xc all Xa1 all Xb1 (-s_col(Xa,Xb,Xc) | -s_e(Xa,Xb,Xa1,Xb1) | s_e3(Xa,Xb,Xc,Xa1,Xb1,insert5(Xa,Xb,Xc,Xa1,Xb1)))) # label(aSatz4_14) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 138 (all Xa all Xm (Xm != Xa | s_m(Xa,Xm,Xa))) # label(aSatz7_3b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 139 (all Xa all Xb all Xc all Xa1 all Xb1 all Xc1 (-s_t(Xa1,Xb1,Xc1) | -s_e(Xb,Xc,Xb1,Xc1) | s_e(Xa,Xb,Xa1,Xb1) | -s_e(Xa,Xc,Xa1,Xc1) | -s_t(Xa,Xb,Xc))) # label(aSatz4_3) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 140 (all Xa all Xb all Xc all Xm (sameside(s(Xm,Xa),s(Xm,Xb),s(Xm,Xc)) | -sameside(Xa,Xb,Xc))) # label(aSideReflect) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 141 (all Xp all Xq all Xa all Xb all Xt ((-opposite(Xa,Xp,Xq,Xb) | -s_col(Xp,Xq,Xa)) & (-opposite(Xa,Xp,Xq,Xb) | s_t(Xa,il(Xa,Xb,Xp,Xq),Xb)) & (-opposite(Xa,Xp,Xq,Xb) | s_col(Xp,Xq,il(Xa,Xb,Xp,Xq))) & (-opposite(Xa,Xp,Xq,Xb) | -s_col(Xp,Xq,Xb)) & (s_col(Xp,Xq,Xa) | s_col(Xp,Xq,Xb) | -s_col(Xp,Xq,Xt) | opposite(Xa,Xp,Xq,Xb) | -s_t(Xa,Xt,Xb) | Xp = Xq))) # label(d_Defn9_1) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 142 (all Xa all Xb all Xc (s_col(Xa,Xc,Xb) | -s_col(Xa,Xb,Xc))) # label(aSatz4_11e) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 143 (all Xa all Xb all Xp (Xb = Xa | s(Xa,s(Xb,Xp)) != s(Xb,s(Xa,Xp)))) # label(aSatz7_19) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 144 (all Xa all Xp all Xq all Xc all Xcs all Xr all Xm all U (-perp(Xp,Xq,Xa,Xr) | -perp(Xp,Xq,Xc,Xcs) | sameside(s(Xm,U),Xcs,Xc) | -sameside(U,Xr,Xa) | -s_m(Xr,Xm,Xcs) | -s_col(Xp,Xq,Xr) | -s_col(Xp,Xq,Xcs) | Xp = Xq | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_4) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 145 (all Xa all Xb all Xc (-s_t(Xa,Xb,Xc) | le(Xa,Xb,Xa,Xc) | -s_col(Xa,Xb,Xc))) # label(aSatz5_12a1) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 146 (all Xa all Xp all Xb ((s_col(Xa,Xp,Xb) | -sameside(Xa,Xp,Xb)) & (-s_t(Xa,Xp,Xb) | -sameside(Xa,Xp,Xb)))) # label(aSatz6_4a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 147 (all Xa all Xb s_col(Xa,Xb,Xa)) # label(aSatz4_12b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 148 (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]. 1.16/1.37 149 (all Xa all Xb all Xp all Xp1 (Xa = Xb | reflect(Xa,Xb,Xp1) = Xp | reflect(Xa,Xb,Xp) != Xp1)) # label(aSatz10_6) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 150 (all Xa all Xb all Xd all Xc (s_t(Xa,Xb,Xc) | -s_t(Xb,Xc,Xd) | -s_t(Xa,Xb,Xd))) # label(aSatz3_5a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 151 (all Xa1 all Xm1 all Xb1 all Xc all Xb2 all Xm2 all Xa2 ((-s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) | s_t(Xb1,Xc,Xb2)) & (s_m(Xa2,Xm2,Xb2) | -s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2)) & (-s_t(Xa1,Xc,Xa2) | -s_t(Xb1,Xc,Xb2) | -s_e(Xc,Xa1,Xc,Xb1) | s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) | -s_m(Xa2,Xm2,Xb2) | -s_m(Xa1,Xm1,Xb1) | -s_e(Xc,Xa2,Xc,Xb2)) & (s_m(Xa1,Xm1,Xb1) | -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_e(Xc,Xa1,Xc,Xb1) | -s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2)) & (-s_kf(Xa1,Xm1,Xb1,Xc,Xb2,Xm2,Xa2) | s_t(Xa1,Xc,Xa2)))) # label(d_Defn7_23) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 152 (all Xa all Xb all Xc (-s_t(Xa,Xb,Xc) | Xb = Xa | -s_t(Xb,Xa,Xc))) # label(aSatz3_4) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 153 (all Xa all Xb all Xc all Xd (s_e(Xb,Xa,Xd,Xc) | -s_e(Xa,Xb,Xc,Xd))) # label(aSatz2_14) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 154 (all Xa all Xb all Xc all Xd all Za all Zb all Zc all Zd ((s_e(Xa,Xc,Za,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_t(Xa,Xb,Xc) | -s_t(Za,Zb,Zc) | -s_e(Xa,Xc,Za,Zc) | -s_e(Xa,Xd,Za,Zd) | s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | -s_e(Xc,Xd,Zc,Zd) | -s_e(Xb,Xc,Zb,Zc)) & (-s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) | s_e(Xc,Xd,Zc,Zd)) & (s_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_t(Za,Zb,Zc)) & (s_t(Xa,Xb,Xc) | -s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)))) # label(d_Defn4_1) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 155 (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]. 1.16/1.37 156 (all Xa all Xp all Xb all Xc (sameside(Xa,Xp,Xc) | -sameside(Xb,Xp,Xc) | -sameside(Xa,Xp,Xb))) # label(aSatz6_7) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 157 (all Xa all Xb all Xc all Xd (-s_e(Xa,Xb,Xc,Xd) | s_e(Xa,Xb,Xd,Xc))) # label(aSatz2_5) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 158 (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_e(Xm,Xa,Xm,Xb) | s_m(Xa,Xm,Xb) | -s_t(Xa,Xm,Xb)))) # label(d_Defn7_1) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 159 (all Xa all Xb (Xb = Xa | -s_r(Xa,Xb,Xa))) # label(aSatz8_8) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 160 (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]. 1.16/1.37 161 (all Xa all Xb all Xc all Xd (-s_e(Xa,Xb,Xc,Xd) | s_e(Xb,Xa,Xc,Xd))) # label(aSatz2_4) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 162 (all Xa all Xc all Xb all Xc1 (-s_e(Xb,Xc,Xb,Xc1) | Xc = Xc1 | -s_e(Xa,Xc,Xa,Xc1) | -s_t(Xa,Xc,Xb))) # label(aSatz4_19) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 163 (all Xa all Xb all Xp all Xq (-perp(Xa,Xb,Xp,Xq) | perp(Xp,Xq,Xa,Xb))) # label(aSatz8_12b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 164 (all Xp all Xq all Xr all Xcs (Xp = Xq | s_col(Xp,Xq,Xr) | opposite(Xr,Xp,Xq,Xcs) | foot(Xp,Xq,Xr) = Xp | samesideline(Xr,Xcs,Xp,Xq) | s_col(Xp,Xq,Xcs))) # label(aLemma9_13f_case2) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 165 (all Xa all Xb all Xc (s_r(Xa,Xb,s(Xb,Xc)) | -s_r(Xa,Xb,Xc))) # label(aSatz8_4) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 166 (all Xa all Xb all Xp ((s_col(Xa,Xb,midpoint(Xp,reflect(Xa,Xb,Xp))) | Xb = Xa) & (Xa = Xb | Xp = reflect(Xa,Xb,Xp) | perp(Xa,Xb,Xp,reflect(Xa,Xb,Xp))))) # label(aSatz10_2a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 167 (all Xa1 all Xb1 s_t(Xa1,Xa1,Xb1)) # label(aSatz3_3) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 168 (all Xa all Xb all Xp all Xq all Xcx all U all V (Xq = Xp | -s_col(Xp,Xq,Xcx) | -s_col(Xa,Xb,U) | -s_col(Xp,Xq,V) | U = Xcx | perpAt(Xa,Xb,Xcx,Xp,Xq) | -s_r(U,Xcx,V) | V = Xcx | -s_col(Xa,Xb,Xcx) | Xa = Xb)) # label(aSatz8_13b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 169 (all Xa all Xp all Xq all Xb all Xc (opposite(Xa,Xp,Xq,Xc) | -samesideline(Xb,Xc,Xp,Xq) | -opposite(Xa,Xp,Xq,Xb))) # label(aLemma9_13e) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 170 (all Xa all Xb all Xc all Xp all Xq (perpAt(Xp,Xq,Xc,Xa,Xb) | -perpAt(Xa,Xb,Xc,Xp,Xq))) # label(aSatz8_12a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 171 (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]. 1.16/1.37 172 (all Xp all Xq all Xr all Xa (Xr = Xp | -s_col(Xa,Xp,Xq) | sameside(Xa,Xp,Xq) | sameside(Xa,Xp,Xr) | Xa = Xp | -s_t(Xq,Xp,Xr) | Xp = Xq)) # label(aSatz6_15a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 173 (all Xr all Xa all Xb all Xc all Xp all Xq (Xr = Xa | -s_e(Xa,Xp,Xb,Xc) | -sameside(Xq,Xa,Xr) | Xp = Xq | -s_e(Xa,Xq,Xb,Xc) | -sameside(Xp,Xa,Xr) | Xc = Xb)) # label(aSatz6_11b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 174 (all Xp all Xq all Xcs all Xr (Xq = Xp | Xp = Xcs | -s_col(Xp,Xq,Xcs) | -s_col(Xp,Xq,Xr) | s_col(Xp,Xcs,Xr))) # label(aSatz6_16b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 175 (all Xp all Xa s_m(Xp,Xa,s(Xa,Xp))) # label(aSatz7_4a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 176 (all Xa all Xp all Xq all Xc all Xcs all Xr all Xm all U (-s_m(Xr,Xm,Xcs) | sameside(s(Xm,U),Xcs,Xc) | Xr = Xcs | -le(Xcs,Xc,Xr,Xa) | -sameside(U,Xr,Xa) | -perp(Xp,Xq,Xc,Xcs) | -perp(Xp,Xq,Xa,Xr) | -s_col(Xp,Xq,Xr) | -s_col(Xp,Xq,Xcs) | Xq = Xp | -opposite(Xa,Xp,Xq,Xc))) # label(aSatz9_4a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 177 (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]. 1.16/1.37 178 (all Xa all Xb le(Xa,Xb,Xa,Xb)) # label(aSatz5_7) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 179 (all Xp all Xa all Xb all Xq all Xt all Xr (-perp(Xp,Xa,Xa,Xb) | -s_col(Xa,Xb,Xt) | -s_t(Xp,Xt,Xq) | -s_t(Xb,Xr,Xq) | -s_e(Xa,Xp,Xb,Xr) | s_m(Xp,midpoint(Xa,Xb),Xr) | -perp(Xq,Xb,Xa,Xb))) # label(aSatz8_24) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 180 (all Xp all Xq all Xr all Xa (s_t(Xp,Xq,Xr) | -s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr)))) # label(aSatz7_15b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 181 (all Xa all Xb all Xp all Xq all Xr (-samesideline(Xa,Xb,Xp,Xq) | -sameside(Xa,Xq,Xr) | samesideline(Xr,Xb,Xp,Xq))) # label(aSatz9_16) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 182 (all Xp all Xq (s_col(Xp,Xq,Xp) | Xp = Xq)) # label(aSatz6_17a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 183 (all Xa all Xb s_e(Xa,Xb,Xa,Xb)) # label(aSatz2_1) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 184 (all Xa all Xb all Xc ((Xb = Xa | perp(Xa,Xb,erect21a(Xa,Xb,Xc),Xa) | s_col(Xa,Xb,Xc)) & (s_col(Xa,Xb,Xc) | s_t(Xc,erectAux21a(Xa,Xb,Xc),erect21a(Xa,Xb,Xc)) | Xa = Xb) & (s_col(Xa,Xb,erectAux21a(Xa,Xb,Xc)) | s_col(Xa,Xb,Xc) | Xb = Xa))) # label(aSatz8_21a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 185 (all Xa all Xp s(Xa,s(Xa,Xp)) = Xp) # label(aSatz7_7) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 186 (all Xp all Xq all Xa s_e(Xp,Xq,s(Xa,Xp),s(Xa,Xq))) # label(aSatz7_13) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 187 (all Xa all Xb s_t(Xa,Xb,Xb)) # label(aSatz3_1) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 188 (all Xa all Xb all Xc all Xp (-s_r(Xa,Xb,Xc) | Xp != Xa | Xb = Xc | -s_m(s(Xa,Xc),Xp,s(Xb,Xc)))) # label(aSatz8_20b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 189 (all Xa all Xb all Xp (Xa = Xb | s_col(Xa,Xb,Xp) | reflect(Xa,Xb,Xp) != Xp)) # label(aSatz10_8a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 190 (all Xa all Xb all Xc all Xd (Xa = Xb | -s_t(Xa,Xb,Xc) | -s_t(Xa,Xb,Xd) | s_t(Xa,Xc,Xd) | s_t(Xa,Xd,Xc))) # label(aSatz5_1) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 191 (all Xa all Xp all Xb all Xc (Xa = Xp | -s_t(Xa,Xp,Xc) | -s_t(Xb,Xp,Xc) | sameside(Xa,Xp,Xb) | Xc = Xp | Xb = Xp)) # label(aSatz6_2a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 192 (all Xa all Xp all Xb (Xb = Xa | s(Xb,Xp) != s(Xa,Xp))) # label(aSatz7_18) # label(axiom) # label(non_clause). [assumption]. 1.16/1.37 193 (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_t(Xm1,Xc,Xm2) | -s_m(Xa2,Xm2,Xb2) | -s_m(Xa1,Xm1,Xb1) | -s_t(Xb1,Xc,Xb2))) # label(aSatz7_22) # label(axiom) # label(non_clause). [assumption]. 1.16/1.39 194 (all Xa all Xp all Xq all Xc all Xb (-opposite(Xa,Xp,Xq,Xc) | opposite(Xb,Xp,Xq,Xc) | -samesideline(Xa,Xb,Xp,Xq))) # label(aSatz9_8) # label(axiom) # label(non_clause). [assumption]. 1.16/1.39 195 (all Xa all Xb all Xc all Xd all Xe (-s_e(Xa,Xe,Xc,Xd) | -s_t(Xa,Xb,Xe) | le(Xa,Xb,Xc,Xd))) # label(aSatz5_5b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.39 196 (all Xp all Xq all Xa all Xb all Xc (Xq = Xp | samesideline(Xa,Xc,Xp,Xq) | -samesideline(Xb,Xc,Xp,Xq) | -samesideline(Xa,Xb,Xp,Xq))) # label(aSatz9_13) # label(axiom) # label(non_clause). [assumption]. 1.16/1.39 197 (all Xa all Xb all Xp all Xq all Xc ((-s_col(Xa,Xb,Xq) | -s_col(Xa,Xb,Xc) | -perp(Xa,Xb,Xc,Xp) | Xq = Xp | -s_col(Xa,Xb,Xp) | Xb = Xa) & (Xa = Xb | Xp = Xq | s_r(Xc,Xp,Xq) | -perp(Xa,Xb,Xc,Xp) | -s_col(Xa,Xb,Xq) | -s_col(Xa,Xb,Xp)))) # label(aSatz8_16a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.39 198 (all Xa all Xb all Xp all Xq (-perp(Xa,Xb,Xp,Xq) | -s_col(Xa,Xb,Xp) | -s_col(Xa,Xb,Xq))) # label(aSatz8_14a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.39 199 (all Xa all Xb all Xc all Xc1 (-s_col(Xa,Xb,Xc) | -s_e(Xb,Xc,Xb,Xc1) | Xc1 = Xc | -s_e(Xa,Xc,Xa,Xc1) | Xb = Xa)) # label(aSatz4_18) # label(axiom) # label(non_clause). [assumption]. 1.16/1.39 200 (all Xa all Xb s_t(Xa,Xb,ext(Xa,Xb,alpha,gamma))) # label(aSatz3_14a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.39 201 (all Xa all Xb all Xc all Xd (s_e(Xa,Xb,Xc,Xd) | -le(Xc,Xd,Xa,Xb) | -le(Xa,Xb,Xc,Xd))) # label(aSatz5_9) # label(axiom) # label(non_clause). [assumption]. 1.16/1.39 202 (all Xa all Xb all Xp all Xq (Xa = Xb | -s_col(Xa,Xb,Xp) | s_e(Xp,Xq,reflect(Xa,Xb,Xp),reflect(Xa,Xb,Xq)))) # label(aSatz10_10a) # label(axiom) # label(non_clause). [assumption]. 1.16/1.39 203 (all Xa all Xp all Xq all Xc all Xcs all Xr all Xm all U (-opposite(Xa,Xp,Xq,Xc) | Xp = Xq | -s_col(Xp,Xq,Xcs) | -s_col(Xp,Xq,Xr) | -s_m(Xr,Xm,Xcs) | Xr != Xcs | sameside(s(Xm,U),Xcs,Xc) | -sameside(U,Xr,Xa) | -perp(Xp,Xq,Xc,Xcs) | -perp(Xp,Xq,Xa,Xr))) # label(aSatz9_4b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.39 204 (all Xa all Xb all Xd all Xc (-s_t(Xa,Xb,Xd) | s_t(Xa,Xc,Xd) | -s_t(Xb,Xc,Xd))) # label(aSatz3_5b) # label(axiom) # label(non_clause). [assumption]. 1.16/1.39 205 -(all Xa all Xb all Xc all Xa1 all Xc1 (-s_r(Xa,Xb,Xc) | -s_r(Xa1,Xb,Xc1) | -s_e(Xa,Xb,Xa1,Xb) | s_e(Xa,Xc,Xa1,Xc1) | Xc = Xc1 | midpoint(Xc,Xc1) != Xb | -s_e(Xb,Xc,Xb,Xc1))) # label(aSatz10_12c) # label(negated_conjecture) # label(non_clause). [assumption]. 1.16/1.39 1.16/1.39 ============================== end of process non-clausal formulas === 1.16/1.39 1.16/1.39 ============================== PROCESS INITIAL CLAUSES =============== 1.16/1.39 1.16/1.39 ============================== PREDICATE ELIMINATION ================= 1.16/1.39 206 -s_t(A,B,C) | -s_e(B,D,E,F) | s_afs(A,B,C,D,V6,E,V7,F) | -s_e(A,D,V6,F) | -s_e(B,C,E,V7) | -s_e(A,B,V6,E) | -s_t(V6,E,V7) # label(d_Defn2_10) # label(axiom). [clausify(38)]. 1.16/1.39 207 s_e(A,B,C,D) | -s_afs(E,A,B,F,V6,C,D,V7) # label(d_Defn2_10) # label(axiom). [clausify(38)]. 1.16/1.39 208 -s_afs(A,B,C,D,E,F,V6,V7) | s_e(A,D,E,V7) # label(d_Defn2_10) # label(axiom). [clausify(38)]. 1.16/1.39 209 -s_afs(A,B,C,D,E,F,V6,V7) | s_e(B,D,F,V7) # label(d_Defn2_10) # label(axiom). [clausify(38)]. 1.16/1.39 210 -s_afs(A,B,C,D,E,F,V6,V7) | s_e(A,B,E,F) # label(d_Defn2_10) # label(axiom). [clausify(38)]. 1.16/1.39 211 -s_afs(A,B,C,D,E,F,V6,V7) | s_t(E,F,V6) # label(d_Defn2_10) # label(axiom). [clausify(38)]. 1.16/1.39 212 s_t(A,B,C) | -s_afs(A,B,C,D,E,F,V6,V7) # label(d_Defn2_10) # label(axiom). [clausify(38)]. 1.16/1.39 213 -s_t(A,B,C) | -s_t(D,E,F) | -s_e(A,C,D,F) | -s_e(A,V6,D,V7) | s_ifs(A,B,C,V6,D,E,F,V7) | -s_e(C,V6,F,V7) | -s_e(B,C,E,F) # label(d_Defn4_1) # label(axiom). [clausify(154)]. 1.16/1.39 214 s_e(A,B,C,D) | -s_ifs(E,A,F,B,V6,C,V7,D) # label(aSatz4_2) # label(axiom). [clausify(54)]. 1.16/1.39 215 s_e(A,B,C,D) | -s_ifs(A,E,B,F,C,V6,D,V7) # label(d_Defn4_1) # label(axiom). [clausify(154)]. 1.16/1.39 216 s_e(A,B,C,D) | -s_ifs(A,E,F,B,C,V6,V7,D) # label(d_Defn4_1) # label(axiom). [clausify(154)]. 1.16/1.39 Derived: -s_t(A,B,C) | -s_t(D,E,F) | -s_e(A,C,D,F) | -s_e(A,V6,D,V7) | -s_e(C,V6,F,V7) | -s_e(B,C,E,F) | s_e(B,V6,E,V7). [resolve(213,e,214,b)]. 1.16/1.39 217 -s_ifs(A,B,C,D,E,F,V6,V7) | s_e(C,D,V6,V7) # label(d_Defn4_1) # label(axiom). [clausify(154)]. 1.16/1.40 218 s_e(A,B,C,D) | -s_ifs(E,A,B,F,V6,C,D,V7) # label(d_Defn4_1) # label(axiom). [clausify(154)]. 1.16/1.40 219 -s_ifs(A,B,C,D,E,F,V6,V7) | s_t(E,F,V6) # label(d_Defn4_1) # label(axiom). [clausify(154)]. 1.16/1.40 220 s_t(A,B,C) | -s_ifs(A,B,C,D,E,F,V6,V7) # label(d_Defn4_1) # label(axiom). [clausify(154)]. 1.16/1.40 221 s_e3(A,B,C,D,E,F) | -s_fs(A,B,C,V6,D,E,F,V7) # label(d_Defn4_15) # label(axiom). [clausify(66)]. 1.16/1.40 222 -s_e3(A,B,C,D,E,F) | s_col(D,E,F) | -s_col(A,B,C) # label(aSatz4_13) # label(axiom). [clausify(58)]. 1.16/1.40 223 -s_e3(A,B,C,D,E,F) | s_fs(A,B,C,V6,D,E,F,V7) | -s_e(B,V6,E,V7) | -s_e(A,V6,D,V7) | -s_col(A,B,C) # label(d_Defn4_15) # label(axiom). [clausify(66)]. 1.16/1.40 Derived: -s_fs(A,B,C,D,E,F,V6,V7) | s_col(E,F,V6) | -s_col(A,B,C). [resolve(221,a,222,a)]. 1.16/1.40 Derived: -s_fs(A,B,C,D,E,F,V6,V7) | s_fs(A,B,C,V8,E,F,V6,V9) | -s_e(B,V8,F,V9) | -s_e(A,V8,E,V9) | -s_col(A,B,C). [resolve(221,a,223,a)]. 1.16/1.40 224 -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(80)]. 1.16/1.40 Derived: -s_t(A,B,C) | -s_e(A,C,D,E) | s_col(D,insert(A,B,D,E),E) | -s_col(A,B,C). [resolve(224,b,222,a)]. 1.16/1.40 Derived: -s_t(A,B,C) | -s_e(A,C,D,E) | s_fs(A,B,C,F,D,insert(A,B,D,E),E,V6) | -s_e(B,F,insert(A,B,D,E),V6) | -s_e(A,F,D,V6) | -s_col(A,B,C). [resolve(224,b,223,a)]. 1.16/1.40 225 -s_r(A,B,C) | s_r(D,E,F) | -s_e3(A,B,C,D,E,F) # label(aSatz8_10) # label(axiom). [clausify(87)]. 1.16/1.40 Derived: -s_r(A,B,C) | s_r(D,E,F) | -s_fs(A,B,C,V6,D,E,F,V7). [resolve(225,c,221,a)]. 1.16/1.40 Derived: -s_r(A,B,C) | s_r(D,insert(A,B,D,E),E) | -s_t(A,B,C) | -s_e(A,C,D,E). [resolve(225,c,224,b)]. 1.16/1.40 226 s_e(A,B,C,D) | -s_e3(A,B,E,C,D,F) # label(d_Defn4_4) # label(axiom). [clausify(100)]. 1.16/1.40 Derived: s_e(A,B,C,D) | -s_fs(A,B,E,F,C,D,V6,V7). [resolve(226,b,221,a)]. 1.16/1.40 Derived: s_e(A,B,C,insert(A,B,C,D)) | -s_t(A,B,E) | -s_e(A,E,C,D). [resolve(226,b,224,b)]. 1.16/1.40 227 s_e(A,B,C,D) | -s_e3(A,E,B,C,F,D) # label(d_Defn4_4) # label(axiom). [clausify(100)]. 1.16/1.40 Derived: s_e(A,B,C,D) | -s_fs(A,E,B,F,C,V6,D,V7). [resolve(227,b,221,a)]. 1.16/1.40 228 -s_e(A,B,C,D) | s_e3(A,B,E,C,D,F) | -s_e(B,E,D,F) | -s_e(A,E,C,F) # label(d_Defn4_4) # label(axiom). [clausify(100)]. 1.16/1.40 Derived: -s_e(A,B,C,D) | -s_e(B,E,D,F) | -s_e(A,E,C,F) | s_col(C,D,F) | -s_col(A,B,E). [resolve(228,b,222,a)]. 1.16/1.40 Derived: -s_e(A,B,C,D) | -s_e(B,E,D,F) | -s_e(A,E,C,F) | s_fs(A,B,E,V6,C,D,F,V7) | -s_e(B,V6,D,V7) | -s_e(A,V6,C,V7) | -s_col(A,B,E). [resolve(228,b,223,a)]. 1.16/1.40 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(228,b,225,c)]. 1.16/1.40 229 -s_e3(A,B,C,D,E,F) | s_e(B,C,E,F) # label(d_Defn4_4) # label(axiom). [clausify(100)]. 1.16/1.40 Derived: s_e(A,B,C,D) | -s_fs(E,A,B,F,V6,C,D,V7). [resolve(229,a,221,a)]. 1.16/1.40 Derived: s_e(A,B,insert(C,A,D,E),E) | -s_t(C,A,B) | -s_e(C,B,D,E). [resolve(229,a,224,b)]. 1.16/1.40 230 -s_col(A,B,C) | -s_e(A,B,D,E) | s_e3(A,B,C,D,E,insert5(A,B,C,D,E)) # label(aSatz4_14) # label(axiom). [clausify(137)]. 1.16/1.40 Derived: -s_col(A,B,C) | -s_e(A,B,D,E) | s_col(D,E,insert5(A,B,C,D,E)) | -s_col(A,B,C). [resolve(230,c,222,a)]. 1.16/1.40 Derived: -s_col(A,B,C) | -s_e(A,B,D,E) | s_fs(A,B,C,F,D,E,insert5(A,B,C,D,E),V6) | -s_e(B,F,E,V6) | -s_e(A,F,D,V6) | -s_col(A,B,C). [resolve(230,c,223,a)]. 1.16/1.40 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(230,c,225,c)]. 1.16/1.40 Derived: -s_col(A,B,C) | -s_e(A,B,D,E) | s_e(A,C,D,insert5(A,B,C,D,E)). [resolve(230,c,227,b)]. 1.16/1.40 Derived: -s_col(A,B,C) | -s_e(A,B,D,E) | s_e(B,C,E,insert5(A,B,C,D,E)). [resolve(230,c,229,a)]. 1.16/1.40 231 -s_t(A,B,C) | s_t(D,E,F) | -s_e3(A,B,C,D,E,F) # label(aSatz4_6) # label(axiom). [clausify(177)]. 1.16/1.40 Derived: -s_t(A,B,C) | s_t(D,E,F) | -s_fs(A,B,C,V6,D,E,F,V7). [resolve(231,c,221,a)]. 1.16/1.40 Derived: -s_t(A,B,C) | s_t(D,insert(A,B,D,E),E) | -s_t(A,B,C) | -s_e(A,C,D,E). [resolve(231,c,224,b)]. 1.16/1.40 Derived: -s_t(A,B,C) | s_t(D,E,F) | -s_e(A,B,D,E) | -s_e(B,C,E,F) | -s_e(A,C,D,F). [resolve(231,c,228,b)]. 1.16/1.40 Derived: -s_t(A,B,C) | s_t(D,E,insert5(A,B,C,D,E)) | -s_col(A,B,C) | -s_e(A,B,D,E). [resolve(231,c,230,c)]. 1.16/1.40 232 -s_t(A,B,C) | -s_t(D,B,E) | -s_e(B,A,B,D) | s_kf(A,F,D,B,E,V6,C) | -s_m(C,V6,E) | -s_m(A,F,D) | -s_e(B,C,B,E) # label(d_Defn7_23) # label(axiom). [clausify(151)]. 15.09/15.32 233 s_t(A,B,C) | -s_kf(D,A,E,B,F,C,V6) # label(aSatz7_22b) # label(axiom). [clausify(114)]. 15.09/15.32 234 -s_kf(A,B,C,D,E,F,V6) | s_t(B,D,F) | -le(D,A,D,V6) # label(aSatz7_22a) # label(axiom). [clausify(132)]. 15.09/15.32 235 -s_kf(A,B,C,D,E,F,V6) | s_t(C,D,E) # label(d_Defn7_23) # label(axiom). [clausify(151)]. 15.09/15.32 236 s_m(A,B,C) | -s_kf(D,E,F,V6,C,B,A) # label(d_Defn7_23) # label(axiom). [clausify(151)]. 15.09/15.32 237 s_m(A,B,C) | -s_kf(A,B,C,D,E,F,V6) # label(d_Defn7_23) # label(axiom). [clausify(151)]. 15.09/15.32 238 s_e(A,B,A,C) | -s_kf(D,E,F,A,C,V6,B) # label(d_Defn7_23) # label(axiom). [clausify(151)]. 15.09/15.32 239 s_e(A,B,A,C) | -s_kf(B,D,C,A,E,F,V6) # label(d_Defn7_23) # label(axiom). [clausify(151)]. 15.09/15.32 240 -s_kf(A,B,C,D,E,F,V6) | s_t(A,D,V6) # label(d_Defn7_23) # label(axiom). [clausify(151)]. 15.09/15.32 15.09/15.32 ============================== end predicate elimination ============= 15.09/15.32 15.09/15.32 Auto_denials: (non-Horn, no changes). 15.09/15.32 15.09/15.32 Term ordering decisions: 15.09/15.32 Function symbol KB weights: xb=1. xa=1. xp=1. xq=1. alpha=1. gamma=1. xc=1. xd=1. beta=1. c1=1. c2=1. c3=1. c4=1. c5=1. s=1. midpoint=1. pointOffLine=1. reflect=1. foot=1. c63=1. erect=1. erect21a=1. erectAux=1. erectAux21a=1. isomidpoint=1. insert=1. ext=1. il=1. ins=1. ss1=1. ss2=1. ss3=1. insert5=1. ip=1. f811=1. f813=1. g811=1. g813=1. op=1. midpointAux=1. crossbar=1. 15.09/15.32 15.09/15.32 ============================== end of process initial clauses ======== 15.09/15.32 15.09/15.32 ============================== CLAUSES FOR SEARCH ==================== 15.09/15.32 15.09/15.32 ============================== end of clauses for search ============= 15.09/15.32 15.09/15.32 ============================== SEARCH ================================ 15.09/15.32 15.09/15.32 % Starting search at 0.11 seconds. 15.09/15.32 15.09/15.32 Low Water (keep): wt=34.000, iters=3461 15.09/15.32 15.09/15.32 Low Water (keep): wt=33.000, iters=3358 15.09/15.32 15.09/15.32 Low Water (keep): wt=31.000, iters=3395 15.09/15.32 15.09/15.32 Low Water (keep): wt=28.000, iters=3337 15.09/15.32 15.09/15.32 Low Water (keep): wt=26.000, iters=3358 15.09/15.32 15.09/15.32 Low Water (keep): wt=25.000, iters=3342 15.09/15.32 15.09/15.32 Low Water (keep): wt=24.000, iters=3333 15.09/15.32 15.09/15.32 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 74 (0.00 of 0.97 sec). 15.09/15.32 15.09/15.32 Low Water (keep): wt=23.000, iters=3385 15.09/15.32 15.09/15.32 Low Water (keep): wt=22.000, iters=3361 15.09/15.32 15.09/15.32 Low Water (keep): wt=21.000, iters=3336 15.09/15.32 15.09/15.32 Low Water (keep): wt=20.000, iters=3368 15.09/15.32 15.09/15.32 Low Water (keep): wt=19.000, iters=3336 15.09/15.32 15.09/15.32 Low Water (keep): wt=18.000, iters=3334 15.09/15.32 15.09/15.32 Low Water (keep): wt=17.000, iters=3809 15.09/15.32 15.09/15.32 Low Water (keep): wt=16.000, iters=3424 15.09/15.32 15.09/15.32 Low Water (keep): wt=15.000, iters=3368 15.09/15.32 15.09/15.32 Low Water (keep): wt=14.000, iters=3369 15.09/15.32 15.09/15.32 Low Water (keep): wt=13.000, iters=3367 15.09/15.32 15.09/15.32 Low Water (displace): id=1550, wt=90.000 15.09/15.32 15.09/15.32 Low Water (displace): id=6541, wt=80.000 15.09/15.32 15.09/15.32 Low Water (displace): id=12389, wt=12.000 15.09/15.32 15.09/15.32 Low Water (displace): id=12391, wt=11.000 15.09/15.32 15.09/15.32 Low Water (displace): id=12408, wt=9.000 15.09/15.32 15.09/15.32 Low Water (keep): wt=12.000, iters=3342 15.09/15.32 15.09/15.32 Low Water (displace): id=14265, wt=7.000 15.09/15.32 15.09/15.32 Low Water (displace): id=14287, wt=6.000 15.09/15.32 15.09/15.32 Low Water (keep): wt=11.000, iters=3335 15.09/15.32 15.09/15.32 Low Water (keep): wt=10.000, iters=3413 15.09/15.32 15.09/15.32 ============================== PROOF ================================= 15.09/15.32 % SZS status Theorem 15.09/15.32 % SZS output start Refutation 15.09/15.32 15.09/15.32 % Proof 1 at 13.64 (+ 0.35) seconds. 15.09/15.32 % Length of proof is 28. 15.09/15.32 % Level of proof is 6. 15.09/15.32 % Maximum clause weight is 18.000. 15.09/15.32 % Given clauses 7386. 15.09/15.32 15.09/15.32 31 (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]. 15.09/15.32 45 (all Xa all Xb s_m(Xa,midpoint(Xa,Xb),Xb)) # label(aSatz8_22) # label(axiom) # label(non_clause). [assumption]. 15.09/15.32 71 (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]. 15.09/15.32 77 (all Xp all Xa all Xq (-s_m(Xp,Xa,Xq) | s(Xa,Xp) = Xq)) # label(aSatz7_6) # label(axiom) # label(non_clause). [assumption]. 15.09/15.32 125 (all Xa all Xb all Xc all Xa1 (s_e(Xa,Xc,Xa1,Xc) | -s_e(Xa,Xb,Xa1,Xb) | -s_r(Xa1,Xb,Xc) | -s_r(Xa,Xb,Xc))) # label(aSatz10_12b) # label(axiom) # label(non_clause). [assumption]. 15.09/15.32 165 (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]. 15.09/15.33 205 -(all Xa all Xb all Xc all Xa1 all Xc1 (-s_r(Xa,Xb,Xc) | -s_r(Xa1,Xb,Xc1) | -s_e(Xa,Xb,Xa1,Xb) | s_e(Xa,Xc,Xa1,Xc1) | Xc = Xc1 | midpoint(Xc,Xc1) != Xb | -s_e(Xb,Xc,Xb,Xc1))) # label(aSatz10_12c) # label(negated_conjecture) # label(non_clause). [assumption]. 15.09/15.33 301 s_e(A,B,A,s(C,B)) | -s_r(A,C,B) # label(d_Defn8_1) # label(axiom). [clausify(31)]. 15.09/15.33 315 s_m(A,midpoint(A,B),B) # label(aSatz8_22) # label(axiom). [clausify(45)]. 15.09/15.33 350 -s_e(A,B,C,D) | s_e(A,B,E,F) | -s_e(C,D,E,F) # label(aSatz2_3) # label(axiom). [clausify(71)]. 15.09/15.33 355 -s_m(A,B,C) | s(B,A) = C # label(aSatz7_6) # label(axiom). [clausify(77)]. 15.09/15.33 410 s_e(A,B,C,B) | -s_e(A,D,C,D) | -s_r(C,D,B) | -s_r(A,D,B) # label(aSatz10_12b) # label(axiom). [clausify(125)]. 15.09/15.33 454 s_r(A,B,s(B,C)) | -s_r(A,B,C) # label(aSatz8_4) # label(axiom). [clausify(165)]. 15.09/15.33 492 s_r(c1,c2,c3) # label(aSatz10_12c) # label(negated_conjecture). [clausify(205)]. 15.09/15.33 493 s_r(c4,c2,c5) # label(aSatz10_12c) # label(negated_conjecture). [clausify(205)]. 15.09/15.33 494 s_e(c1,c2,c4,c2) # label(aSatz10_12c) # label(negated_conjecture). [clausify(205)]. 15.09/15.33 495 -s_e(c1,c3,c4,c5) # label(aSatz10_12c) # label(negated_conjecture). [clausify(205)]. 15.09/15.33 497 midpoint(c3,c5) = c2 # label(aSatz10_12c) # label(negated_conjecture). [clausify(205)]. 15.09/15.33 1389 s_r(c1,c2,s(c2,c3)). [resolve(492,a,454,b)]. 15.09/15.33 1393 s_e(c1,c3,c1,s(c2,c3)). [resolve(492,a,301,b)]. 15.09/15.33 1437 s_e(c1,A,c4,A) | -s_r(c4,c2,A) | -s_r(c1,c2,A). [resolve(494,a,410,b)]. 15.09/15.33 1452 s_m(c3,c2,c5). [para(497(a,1),315(a,2))]. 15.09/15.33 1973 s(c2,c3) = c5. [resolve(1452,a,355,a)]. 15.09/15.33 1976 s_e(c1,c3,c1,c5). [back_rewrite(1393),rewrite([1973(6)])]. 15.09/15.33 1977 s_r(c1,c2,c5). [back_rewrite(1389),rewrite([1973(5)])]. 15.09/15.33 3306 s_e(c1,c3,A,B) | -s_e(c1,c5,A,B). [resolve(1976,a,350,a)]. 15.09/15.33 21375 s_e(c1,c5,c4,c5). [resolve(1437,b,493,a),unit_del(b,1977)]. 15.09/15.33 27478 $F. [resolve(3306,b,21375,a),unit_del(a,495)]. 15.09/15.33 15.09/15.33 % SZS output end Refutation 15.09/15.33 ============================== end of proof ========================== 15.09/15.33 15.09/15.33 ============================== STATISTICS ============================ 15.09/15.33 15.09/15.33 Given=7386. Generated=366629. Kept=27222. proofs=1. 15.09/15.33 Usable=7175. Sos=9999. Demods=372. Limbo=1, Disabled=10378. Hints=0. 15.09/15.33 Megabytes=17.93. 15.09/15.33 User_CPU=13.64, System_CPU=0.35, Wall_clock=14. 15.09/15.33 15.09/15.33 ============================== end of statistics ===================== 15.09/15.33 15.09/15.33 ============================== end of search ========================= 15.09/15.33 15.09/15.33 THEOREM PROVED 15.09/15.33 % SZS status Theorem 15.09/15.33 15.09/15.33 Exiting with 1 proof. 15.09/15.33 15.09/15.33 Process 5470 exit (max_proofs) Tue Aug 9 05:02:06 2022 15.09/15.33 Prover9 interrupted 15.09/15.33 EOF