0.09/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.09/0.11 % Command : tptp2X_and_run_prover9 %d %s 0.10/0.31 % Computer : n009.cluster.edu 0.10/0.31 % Model : x86_64 x86_64 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.31 % Memory : 8042.1875MB 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.31 % CPULimit : 960 0.10/0.31 % WCLimit : 120 0.10/0.31 % DateTime : Tue Aug 9 03:44:35 EDT 2022 0.10/0.31 % CPUTime : 0.81/1.13 ============================== Prover9 =============================== 0.81/1.13 Prover9 (32) version 2009-11A, November 2009. 0.81/1.13 Process 23531 was started by sandbox2 on n009.cluster.edu, 0.81/1.13 Tue Aug 9 03:44:36 2022 0.81/1.13 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_23369_n009.cluster.edu". 0.81/1.13 ============================== end of head =========================== 0.81/1.13 0.81/1.13 ============================== INPUT ================================= 0.81/1.13 0.81/1.13 % Reading from file /tmp/Prover9_23369_n009.cluster.edu 0.81/1.13 0.81/1.13 set(prolog_style_variables). 0.81/1.13 set(auto2). 0.81/1.13 % set(auto2) -> set(auto). 0.81/1.13 % set(auto) -> set(auto_inference). 0.81/1.13 % set(auto) -> set(auto_setup). 0.81/1.13 % set(auto_setup) -> set(predicate_elim). 0.81/1.13 % set(auto_setup) -> assign(eq_defs, unfold). 0.81/1.13 % set(auto) -> set(auto_limits). 0.81/1.13 % set(auto_limits) -> assign(max_weight, "100.000"). 0.81/1.13 % set(auto_limits) -> assign(sos_limit, 20000). 0.81/1.13 % set(auto) -> set(auto_denials). 0.81/1.13 % set(auto) -> set(auto_process). 0.81/1.13 % set(auto2) -> assign(new_constants, 1). 0.81/1.13 % set(auto2) -> assign(fold_denial_max, 3). 0.81/1.13 % set(auto2) -> assign(max_weight, "200.000"). 0.81/1.13 % set(auto2) -> assign(max_hours, 1). 0.81/1.13 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.81/1.13 % set(auto2) -> assign(max_seconds, 0). 0.81/1.13 % set(auto2) -> assign(max_minutes, 5). 0.81/1.13 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.81/1.13 % set(auto2) -> set(sort_initial_sos). 0.81/1.13 % set(auto2) -> assign(sos_limit, -1). 0.81/1.13 % set(auto2) -> assign(lrs_ticks, 3000). 0.81/1.13 % set(auto2) -> assign(max_megs, 400). 0.81/1.13 % set(auto2) -> assign(stats, some). 0.81/1.13 % set(auto2) -> clear(echo_input). 0.81/1.13 % set(auto2) -> set(quiet). 0.81/1.13 % set(auto2) -> clear(print_initial_clauses). 0.81/1.13 % set(auto2) -> clear(print_given). 0.81/1.13 assign(lrs_ticks,-1). 0.81/1.13 assign(sos_limit,10000). 0.81/1.13 assign(order,kbo). 0.81/1.13 set(lex_order_vars). 0.81/1.13 clear(print_given). 0.81/1.13 0.81/1.13 % formulas(sos). % not echoed (95 formulas) 0.81/1.13 0.81/1.13 ============================== end of input ========================== 0.81/1.13 0.81/1.13 % From the command line: assign(max_seconds, 960). 0.81/1.13 0.81/1.13 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.81/1.13 0.81/1.13 % Formulas that are not ordinary clauses: 0.81/1.13 1 (all A all B all P all Q (-coll(P,Q,A) & eqangle(P,A,P,B,Q,A,Q,B) -> cyclic(A,B,P,Q))) # label(ruleD42a) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 2 (all A all B all C all D all P all Q all U all V (perp(P,Q,U,V) & eqangle(A,B,C,D,P,Q,U,V) -> perp(A,B,C,D))) # label(ruleD74) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 3 (all A all B all C all D all M all N exists P exists Q (cong(M,A,M,D) & N != M & cong(N,A,N,B) & circle(M,A,B,C) -> coll(Q,B,D) & cong(Q,N,N,A) & cong(P,N,N,A) & coll(P,A,C))) # label(ruleX12) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 4 (all A all B all C all E all F all G all P all Q all R (simtri(A,B,C,E,F,G) & simtri(E,F,G,P,Q,R) -> simtri(A,B,C,P,Q,R))) # label(ruleD34) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 5 (all A all B all C all D all P all Q all U all V (eqratio(A,B,C,D,P,Q,U,V) -> eqratio(B,A,C,D,P,Q,U,V))) # label(ruleD26) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 6 (all A all B all P all Q (cong(A,Q,B,Q) & cong(A,P,B,P) -> perp(A,B,P,Q))) # label(ruleD56) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 7 (all A all B all C all P all Q all R (simtri(B,A,C,Q,P,R) -> simtri(A,B,C,P,Q,R))) # label(ruleD32) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 8 (all A all B all P all Q (cyclic(A,B,P,Q) -> eqangle(P,A,P,B,Q,A,Q,B))) # label(ruleD41) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 9 (all A all B all C all D all P all Q (para(A,B,C,D) -> eqangle(A,B,P,Q,C,D,P,Q))) # label(ruleD40) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 10 (all A all B all C all D (cyclic(A,B,C,D) -> cyclic(B,A,C,D))) # label(ruleD16) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 11 (all A all B all O all X exists M (cong(O,A,O,B) & eqangle(A,O,O,X,O,X,O,B) -> coll(M,O,X) & coll(B,A,M))) # label(ruleX2) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 12 (all A all B all C all P all Q all R (simtri(P,Q,R,A,B,C) -> simtri(A,B,C,P,Q,R))) # label(ruleD33) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 13 (all A all B all P all Q (eqangle(P,A,P,B,Q,A,Q,B) & coll(P,Q,B) -> cyclic(A,B,P,Q))) # label(ruleD42b) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 14 (all A all B all C all D all O (cong(O,A,O,C) & cong(O,A,O,D) & cong(O,A,O,B) -> cyclic(A,B,C,D))) # label(ruleD13) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 15 (all A all B all C all D all P all Q all U all V (cong(P,Q,U,V) & eqratio(A,B,C,D,P,Q,U,V) -> cong(A,B,C,D))) # label(ruleD75) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 16 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 17 (all A all B all O exists C (cong(O,A,O,B) & perp(A,O,O,B) -> cong(O,A,O,C) & coll(A,O,C))) # label(ruleX17) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 18 (all A all B all C all D all M exists P (midp(M,B,D) & perp(C,A,C,D) & perp(A,B,A,C) -> midp(P,A,C))) # label(ruleX16) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 19 (all A all B all C all O all M (circle(O,A,B,C) & eqangle(A,B,A,C,O,B,O,M) & coll(M,B,C) -> midp(M,B,C))) # label(ruleD51) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 20 (all A all B all O (cong(O,A,O,B) -> eqangle(O,A,A,B,A,B,O,B))) # label(ruleD46) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 21 (all A all B all C all P all Q all R (eqangle(A,B,B,C,P,Q,Q,R) & eqangle(A,C,B,C,P,R,Q,R) & -coll(A,B,C) -> simtri(A,B,C,P,Q,R))) # label(ruleD58) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 22 (all A all B all C all P all Q all R (contri(P,Q,R,A,B,C) -> contri(A,B,C,P,Q,R))) # label(ruleD37) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 23 (all A all B all C all D all P all Q all U all V (eqratio(A,B,C,D,P,Q,U,V) -> eqratio(P,Q,U,V,A,B,C,D))) # label(ruleD28) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 24 (all A all B all C all D all O exists P (perp(A,B,B,O) & cong(O,C,O,D) -> para(P,C,A,B) & cong(B,C,B,P) & cong(O,C,O,P))) # label(ruleX9) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 25 (all A all B all C all P all Q all R (simtri(A,C,B,P,R,Q) -> simtri(A,B,C,P,Q,R))) # label(ruleD31) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 26 (all A all B all C (midp(A,B,C) -> coll(A,B,C))) # label(ruleD69) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 27 (all A all B all C all D (cyclic(A,B,C,D) -> cyclic(A,B,D,C))) # label(ruleD14) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 28 (all A all B all C all D all P all Q all U all V (eqangle(A,B,C,D,P,Q,U,V) -> eqangle(A,B,P,Q,C,D,U,V))) # label(ruleD21) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 29 (all A all B all C all M (midp(M,A,C) & perp(A,B,B,C) -> cong(A,M,B,M))) # label(ruleD52) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 30 (all A all B all C all D all M (midp(M,A,B) & para(A,C,B,D) & para(A,D,B,C) -> midp(M,C,D))) # label(ruleD64) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 31 (all A all B all C all P all Q all R (contri(A,C,B,P,R,Q) -> contri(A,B,C,P,Q,R))) # label(ruleD35) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 32 (all A all B all C all D all O (coll(O,B,D) & coll(O,A,C) & para(A,B,C,D) -> eqratio(O,A,A,C,O,B,B,D))) # label(ruleD65) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 33 (all A all B all C all E all F all G all P all Q all R (contri(A,B,C,E,F,G) & contri(E,F,G,P,Q,R) -> contri(A,B,C,P,Q,R))) # label(ruleD38) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 34 (all A all B all C all O (cong(O,A,O,C) & cong(O,A,O,B) -> circle(O,A,B,C))) # label(ruleD12) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 35 (all A all B all C all D all P all Q all U all V (eqangle(A,B,C,D,P,Q,U,V) -> eqangle(B,A,C,D,P,Q,U,V))) # label(ruleD18) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 36 (all A all B all C all P all Q all R (contri(B,A,C,Q,P,R) -> contri(A,B,C,P,Q,R))) # label(ruleD36) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 37 (all A all B all M all O (perp(O,M,A,B) & midp(M,A,B) -> cong(O,A,O,B))) # label(ruleD55) # label(axiom) # label(non_clause). [assumption]. 0.81/1.13 38 (all A all B all C all O all X (circle(O,A,B,C) & perp(O,A,A,X) -> eqangle(A,X,A,B,C,A,C,B))) # label(ruleD48) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 39 (all A all B all C all H exists P exists Q (perp(A,H,B,C) & perp(B,H,A,C) -> perp(B,Q,C,A) & coll(Q,C,A) & perp(A,P,C,B) & coll(P,C,B))) # label(ruleX10) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 40 (all A all B all C all P all Q all R (simtri(A,B,C,P,Q,R) -> eqangle(A,B,B,C,P,Q,Q,R))) # label(ruleD60) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 41 (all A all B all C all D all M all N exists P (midp(M,A,B) & midp(N,C,D) -> para(P,M,B,D) & para(P,N,A,C) & midp(P,A,D))) # label(ruleX6) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 42 (all A all B all M (midp(M,B,A) -> midp(M,A,B))) # label(ruleD11) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 43 (all A all B all C all P all Q all R (cyclic(A,B,C,P) & cyclic(A,B,C,Q) & eqangle(C,A,C,B,R,P,R,Q) & cyclic(A,B,C,R) -> cong(A,B,P,Q))) # label(ruleD43) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 44 (all A all B all C all O (circle(O,A,B,C) & coll(O,A,C) -> perp(A,B,B,C))) # label(ruleD53) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 45 (all A all B all C all D all M all N all Q exists P (midp(M,A,B) & midp(N,C,D) & coll(D,A,B) & coll(C,A,B) -> midp(P,A,Q))) # label(ruleX7) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 46 (all A all B all C all O exists P (circle(O,A,B,C) -> perp(P,A,A,O))) # label(ruleX11) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 47 (all A all B all C (coll(A,B,C) -> coll(B,A,C))) # label(ruleD2) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 48 (all A all B all C all D all M all N (midp(N,C,D) & midp(M,A,B) -> eqratio(M,A,A,B,N,C,C,D))) # label(ruleD70) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 49 (all A all B all C all D (coll(A,B,D) & coll(A,B,C) -> coll(C,D,A))) # label(ruleD3) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 50 (all A all B all C all D all P all Q all U all V (eqratio(A,B,C,D,P,Q,U,V) -> eqratio(C,D,A,B,U,V,P,Q))) # label(ruleD27) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 51 (all A all B all P all Q (cong(A,P,B,P) & cyclic(A,B,P,Q) & cong(A,Q,B,Q) -> perp(P,A,A,Q))) # label(ruleD57) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 52 (all A all B all C (coll(A,B,C) -> coll(A,C,B))) # label(ruleD1) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 53 (all A all B all C all P all Q all R (simtri(A,B,C,P,Q,R) -> eqratio(A,B,A,C,P,Q,P,R))) # label(ruleD59) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 54 (all A all B all C all E all F (midp(E,A,B) & coll(F,A,C) & para(E,F,B,C) -> midp(F,A,C))) # label(ruleD45) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 55 (all A all B all C all D (para(A,B,C,D) -> para(A,B,D,C))) # label(ruleD4) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 56 (all A all B all C all D all M exists O (midp(M,A,B) & para(A,B,C,D) & cyclic(A,B,C,D) -> circle(O,A,B,C))) # label(ruleX13) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 57 (all A all B all C all D (para(A,B,C,D) -> para(C,D,A,B))) # label(ruleD5) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 58 (all A all B all C all D all M (midp(M,C,D) & midp(M,A,B) -> para(A,C,B,D))) # label(ruleD63) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 59 (all A all B all P all X all Y exists Q (eqangle(A,P,B,P,A,X,B,Y) & -coll(A,B,P) -> cyclic(X,B,P,Q) & eqangle(A,P,B,P,A,Q,B,Q))) # label(ruleX5) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 60 (all A all B all C (cong(A,B,A,C) & coll(A,B,C) -> midp(A,B,C))) # label(ruleD67) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 61 (all A all B all C all O all M (midp(M,B,C) & circle(O,A,B,C) -> eqangle(A,B,A,C,O,B,O,M))) # label(ruleD50) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 62 (all A all B all C all D all P all Q all U all V (eqratio(A,B,C,D,P,Q,U,V) -> eqratio(A,B,P,Q,C,D,U,V))) # label(ruleD29) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 63 (all A all B all C all D all E all F (para(A,B,C,D) & perp(C,D,E,F) -> perp(A,B,E,F))) # label(ruleD10) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 64 (all A all B all C all D (cong(A,B,C,D) -> cong(C,D,A,B))) # label(ruleD24) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 65 (all A all B all C all D (perp(A,B,C,D) -> perp(C,D,A,B))) # label(ruleD8) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 66 (all A all B all C all D (-para(A,B,C,D) & eqangle(A,B,C,D,C,D,A,B) -> perp(A,B,C,D))) # label(ruleD71) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 67 (all A all B all C (midp(A,B,C) -> cong(A,B,A,C))) # label(ruleD68) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 68 (all A all B all C all E all F exists P (perp(A,C,C,B) & coll(B,E,F) -> coll(P,E,F) & perp(P,A,E,F))) # label(ruleX15) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 69 (all A all M all O all X exists B (perp(O,M,M,A) & eqangle(X,O,M,O,M,O,A,O) -> coll(B,O,X) & coll(B,A,M))) # label(ruleX1) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 70 (all A all B all C all D all P all Q all U all V all E all F all G all H (eqangle(P,Q,U,V,E,F,G,H) & eqangle(A,B,C,D,P,Q,U,V) -> eqangle(A,B,C,D,E,F,G,H))) # label(ruleD22) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 71 (all A all B all C all D all E all F (perp(C,D,E,F) & perp(A,B,C,D) -> para(A,B,E,F))) # label(ruleD9) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 72 (all A all B all C all D all E all F (cong(C,D,E,F) & cong(A,B,C,D) -> cong(A,B,E,F))) # label(ruleD25) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 73 (all A all B all O all X exists M (cong(O,A,O,B) & perp(O,X,A,B) -> coll(M,O,X) & coll(B,A,M))) # label(ruleX4) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 74 (all A all B all C all D (-perp(A,B,C,D) & eqangle(A,B,C,D,C,D,A,B) -> para(A,B,C,D))) # label(ruleD72) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 75 (all A all B all C all P all Q all R (contri(A,B,C,P,Q,R) -> cong(A,B,P,Q))) # label(ruleD62) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 76 (all A all B all C all D all P all Q exists R (para(A,B,C,D) & coll(P,B,D) & coll(Q,A,B) & coll(P,A,C) -> coll(R,C,D) & coll(P,Q,R))) # label(ruleX18) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 77 (all A all B all C all D (cyclic(A,B,C,D) -> cyclic(A,C,B,D))) # label(ruleD15) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 78 (all A all B all O all X exists M (perp(O,X,A,B) & eqangle(A,O,O,X,O,X,O,B) -> coll(M,O,X) & coll(B,A,M))) # label(ruleX3) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 79 (all A all B all C all D all P all Q all U all V (eqangle(A,B,C,D,P,Q,U,V) -> eqangle(C,D,A,B,U,V,P,Q))) # label(ruleD19) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 80 (all A all B all C all E all F (midp(E,A,B) & midp(F,A,C) -> para(E,F,B,C))) # label(ruleD44) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 81 (all A all B all M all P all Q all R all M exists X (para(A,P,R,M) & coll(P,Q,R) & para(A,P,B,Q) & midp(M,A,B) -> coll(X,M,R) & coll(X,A,Q))) # label(ruleX8) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 82 (all A all B all O (eqangle(O,A,A,B,A,B,O,B) & -coll(O,A,B) -> cong(O,A,O,B))) # label(ruleD47) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 83 (all A all B all C all D all E all F all G all H all P all Q all U all V (eqratio(P,Q,U,V,E,F,G,H) & eqratio(A,B,C,D,P,Q,U,V) -> eqratio(A,B,C,D,E,F,G,H))) # label(ruleD30) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 84 (all A all B all C all D all E all F (para(A,B,C,D) & para(C,D,E,F) -> para(A,B,E,F))) # label(ruleD6) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 85 (all A all B all C all D (perp(A,B,C,D) -> perp(A,B,D,C))) # label(ruleD7) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 86 (all A all B all C all P all Q all R (simtri(A,B,C,P,Q,R) & cong(A,B,P,Q) -> contri(A,B,C,P,Q,R))) # label(ruleD61) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 87 (all A all B all C all O all X (circle(O,A,B,C) & eqangle(A,X,A,B,C,A,C,B) -> perp(O,A,A,X))) # label(ruleD49) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 88 (all A all B all C all D all P all Q all U all V (para(P,Q,U,V) & eqangle(A,B,C,D,P,Q,U,V) -> para(A,B,C,D))) # label(ruleD73) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 89 (all A all B all C all D all E (cyclic(A,B,C,E) & cyclic(A,B,C,D) -> cyclic(B,C,D,E))) # label(ruleD17) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 90 (all A all B all C all D exists O (cyclic(A,B,C,D) & perp(A,C,C,B) -> circle(O,A,B,C))) # label(ruleX14) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 91 (all A all B all C all D all P all Q (eqangle(A,B,P,Q,C,D,P,Q) -> para(A,B,C,D))) # label(ruleD39) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 92 (all A all B all C all D (para(A,B,C,D) & cyclic(A,B,C,D) -> eqangle(A,D,C,D,C,D,C,B))) # label(ruleD54) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 93 (all A all B all C all D all P all Q all U all V (eqangle(A,B,C,D,P,Q,U,V) -> eqangle(P,Q,U,V,A,B,C,D))) # label(ruleD20) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 94 (all A all B all C all D (cong(A,B,C,D) -> cong(A,B,D,C))) # label(ruleD23) # label(axiom) # label(non_clause). [assumption]. 0.81/1.14 95 -(all A all C all K all O all N all B all G all O1 all M all NWPNT1 all NWPNT2 all NWPNT3 (circle(O,A,C,K) & circle(G,A,C,B) & circle(O1,K,M,NWPNT3) & circle(G,A,M,NWPNT2) & circle(O1,K,N,B) & coll(B,C,N) & coll(B,A,K) & circle(O,A,N,NWPNT1) -> cyclic(M,K,O,C))) # label(exemplo6GDDFULL012017) # label(negated_conjecture) # label(non_clause). [assumption]. 0.81/1.14 0.81/1.14 ============================== end of process non-clausal formulas === 0.81/1.14 0.81/1.14 ============================== PROCESS INITIAL CLAUSES =============== 0.81/1.14 0.81/1.14 ============================== PREDICATE ELIMINATION ================= 0.81/1.14 96 -cong(A,B,A,C) | -cong(A,B,A,D) | circle(A,B,D,C) # label(ruleD12) # label(axiom). [clausify(34)]. 0.81/1.14 97 -cong(A,B,A,C) | D = A | -cong(D,B,D,E) | -circle(A,B,E,F) | coll(f2(B,E,F,C,A,D),E,C) # label(ruleX12) # label(axiom). [clausify(3)]. 0.81/1.14 98 -cong(A,B,A,C) | D = A | -cong(D,B,D,E) | -circle(A,B,E,F) | cong(f2(B,E,F,C,A,D),D,D,B) # label(ruleX12) # label(axiom). [clausify(3)]. 0.81/1.14 99 -cong(A,B,A,C) | D = A | -cong(D,B,D,E) | -circle(A,B,E,F) | cong(f1(B,E,F,C,A,D),D,D,B) # label(ruleX12) # label(axiom). [clausify(3)]. 0.81/1.14 100 -cong(A,B,A,C) | D = A | -cong(D,B,D,E) | -circle(A,B,E,F) | coll(f1(B,E,F,C,A,D),B,F) # label(ruleX12) # label(axiom). [clausify(3)]. 0.81/1.14 101 -circle(A,B,C,D) | -eqangle(B,C,B,D,A,C,A,E) | -coll(E,C,D) | midp(E,C,D) # label(ruleD51) # label(axiom). [clausify(19)]. 0.81/1.14 Derived: -cong(A,B,A,C) | -cong(A,B,A,D) | -cong(A,B,A,E) | F = A | -cong(F,B,F,D) | coll(f2(B,D,C,E,A,F),D,E). [resolve(96,c,97,d)]. 0.81/1.14 Derived: -cong(A,B,A,C) | -cong(A,B,A,D) | -cong(A,B,A,E) | F = A | -cong(F,B,F,D) | cong(f2(B,D,C,E,A,F),F,F,B). [resolve(96,c,98,d)]. 0.81/1.14 Derived: -cong(A,B,A,C) | -cong(A,B,A,D) | -cong(A,B,A,E) | F = A | -cong(F,B,F,D) | cong(f1(B,D,C,E,A,F),F,F,B). [resolve(96,c,99,d)]. 0.81/1.14 Derived: -cong(A,B,A,C) | -cong(A,B,A,D) | -cong(A,B,A,E) | F = A | -cong(F,B,F,D) | coll(f1(B,D,C,E,A,F),B,C). [resolve(96,c,100,d)]. 0.81/1.14 Derived: -cong(A,B,A,C) | -cong(A,B,A,D) | -eqangle(B,D,B,C,A,D,A,E) | -coll(E,D,C) | midp(E,D,C). [resolve(96,c,101,a)]. 0.81/1.14 102 -circle(A,B,C,D) | -perp(A,B,B,E) | eqangle(B,E,B,C,D,B,D,C) # label(ruleD48) # label(axiom). [clausify(38)]. 0.81/1.14 Derived: -perp(A,B,B,C) | eqangle(B,C,B,D,E,B,E,D) | -cong(A,B,A,E) | -cong(A,B,A,D). [resolve(102,a,96,c)]. 0.81/1.14 103 -circle(A,B,C,D) | -coll(A,B,D) | perp(B,C,C,D) # label(ruleD53) # label(axiom). [clausify(44)]. 0.81/1.14 Derived: -coll(A,B,C) | perp(B,D,D,C) | -cong(A,B,A,C) | -cong(A,B,A,D). [resolve(103,a,96,c)]. 0.81/1.14 104 -circle(A,B,C,D) | perp(f11(B,C,D,A),B,B,A) # label(ruleX11) # label(axiom). [clausify(46)]. 0.81/1.14 Derived: perp(f11(A,B,C,D),A,A,D) | -cong(D,A,D,C) | -cong(D,A,D,B). [resolve(104,a,96,c)]. 0.81/1.14 105 -midp(A,B,C) | -para(B,C,D,E) | -cyclic(B,C,D,E) | circle(f12(B,C,D,E,A),B,C,D) # label(ruleX13) # label(axiom). [clausify(56)]. 0.81/1.14 Derived: -midp(A,B,C) | -para(B,C,D,E) | -cyclic(B,C,D,E) | -cong(f12(B,C,D,E,A),B,f12(B,C,D,E,A),F) | V6 = f12(B,C,D,E,A) | -cong(V6,B,V6,C) | coll(f2(B,C,D,F,f12(B,C,D,E,A),V6),C,F). [resolve(105,d,97,d)]. 0.81/1.14 Derived: -midp(A,B,C) | -para(B,C,D,E) | -cyclic(B,C,D,E) | -cong(f12(B,C,D,E,A),B,f12(B,C,D,E,A),F) | V6 = f12(B,C,D,E,A) | -cong(V6,B,V6,C) | cong(f2(B,C,D,F,f12(B,C,D,E,A),V6),V6,V6,B). [resolve(105,d,98,d)]. 0.81/1.14 Derived: -midp(A,B,C) | -para(B,C,D,E) | -cyclic(B,C,D,E) | -cong(f12(B,C,D,E,A),B,f12(B,C,D,E,A),F) | V6 = f12(B,C,D,E,A) | -cong(V6,B,V6,C) | cong(f1(B,C,D,F,f12(B,C,D,E,A),V6),V6,V6,B). [resolve(105,d,99,d)]. 0.81/1.14 Derived: -midp(A,B,C) | -para(B,C,D,E) | -cyclic(B,C,D,E) | -cong(f12(B,C,D,E,A),B,f12(B,C,D,E,A),F) | V6 = f12(B,C,D,E,A) | -cong(V6,B,V6,C) | coll(f1(B,C,D,F,f12(B,C,D,E,A),V6),B,D). [resolve(105,d,100,d)]. 0.81/1.14 Derived: -midp(A,B,C) | -para(B,C,D,E) | -cyclic(B,C,D,E) | -eqangle(B,C,B,D,f12(B,C,D,E,A),C,f12(B,C,D,E,A),F) | -coll(F,C,D) | midp(F,C,D). [resolve(105,d,101,a)]. 0.81/1.14 Derived: -midp(A,B,C) | -para(B,C,D,E) | -cyclic(B,C,D,E) | -perp(f12(B,C,D,E,A),B,B,F) | eqangle(B,F,B,C,D,B,D,C). [resolve(105,d,102,a)]. 0.81/1.14 Derived: -midp(A,B,C) | -para(B,C,D,E) | -cyclic(B,C,D,E) | -coll(f12(B,C,D,E,A),B,D) | perp(B,C,C,D). [resolve(105,d,103,a)]. 0.81/1.14 Derived: -midp(A,B,C) | -para(B,C,D,E) | -cyclic(B,C,D,E) | perp(f11(B,C,D,f12(B,C,D,E,A)),B,B,f12(B,C,D,E,A)). [resolve(105,d,104,a)]. 0.81/1.14 106 -midp(A,B,C) | -circle(D,E,B,C) | eqangle(E,B,E,C,D,B,D,A) # label(ruleD50) # label(axiom). [clausify(61)]. 0.81/1.14 Derived: -midp(A,B,C) | eqangle(D,B,D,C,E,B,E,A) | -cong(E,D,E,C) | -cong(E,D,E,B). [resolve(106,b,96,c)]. 0.81/1.14 Derived: -midp(A,B,C) | eqangle(D,B,D,C,f12(D,B,C,E,F),B,f12(D,B,C,E,F),A) | -midp(F,D,B) | -para(D,B,C,E) | -cyclic(D,B,C,E). [resolve(106,b,105,d)]. 0.81/1.14 107 -circle(A,B,C,D) | -eqangle(B,E,B,C,D,B,D,C) | perp(A,B,B,E) # label(ruleD49) # label(axiom). [clausify(87)]. 0.81/1.14 Derived: -eqangle(A,B,A,C,D,A,D,C) | perp(E,A,A,B) | -cong(E,A,E,D) | -cong(E,A,E,C). [resolve(107,a,96,c)]. 0.81/1.14 Derived: -eqangle(A,B,A,C,D,A,D,C) | perp(f12(A,C,D,E,F),A,A,B) | -midp(F,A,C) | -para(A,C,D,E) | -cyclic(A,C,D,E). [resolve(107,a,105,d)]. 0.81/1.14 108 -cyclic(A,B,C,D) | -perp(A,C,C,B) | circle(f20(A,B,C,D),A,B,C) # label(ruleX14) # label(axiom). [clausify(90)]. 0.81/1.14 Derived: -cyclic(A,B,C,D) | -perp(A,C,C,B) | -cong(f20(A,B,C,D),A,f20(A,B,C,D),E) | F = f20(A,B,C,D) | -cong(F,A,F,B) | coll(f2(A,B,C,E,f20(A,B,C,D),F),B,E). [resolve(108,c,97,d)]. 0.81/1.14 Derived: -cyclic(A,B,C,D) | -perp(A,C,C,B) | -cong(f20(A,B,C,D),A,f20(A,B,C,D),E) | F = f20(A,B,C,D) | -cong(F,A,F,B) | cong(f2(A,B,C,E,f20(A,B,C,D),F),F,F,A). [resolve(108,c,98,d)]. 0.81/1.14 Derived: -cyclic(A,B,C,D) | -perp(A,C,C,B) | -cong(f20(A,B,C,D),A,f20(A,B,C,D),E) | F = f20(A,B,C,D) | -cong(F,A,F,B) | cong(f1(A,B,C,E,f20(A,B,C,D),F),F,F,A). [resolve(108,c,99,d)]. 0.81/1.14 Derived: -cyclic(A,B,C,D) | -perp(A,C,C,B) | -cong(f20(A,B,C,D),A,f20(A,B,C,D),E) | F = f20(A,B,C,D) | -cong(F,A,F,B) | coll(f1(A,B,C,E,f20(A,B,C,D),F),A,C). [resolve(108,c,100,d)]. 0.81/1.14 Derived: -cyclic(A,B,C,D) | -perp(A,C,C,B) | -eqangle(A,B,A,C,f20(A,B,C,D),B,f20(A,B,C,D),E) | -coll(E,B,C) | midp(E,B,C). [resolve(108,c,101,a)]. 0.81/1.14 Derived: -cyclic(A,B,C,D) | -perp(A,C,C,B) | -perp(f20(A,B,C,D),A,A,E) | eqangle(A,E,A,B,C,A,C,B). [resolve(108,c,102,a)]. 0.81/1.14 Derived: -cyclic(A,B,C,D) | -perp(A,C,C,B) | -coll(f20(A,B,C,D),A,C) | perp(A,B,B,C). [resolve(108,c,103,a)]. 0.81/1.14 Derived: -cyclic(A,B,C,D) | -perp(A,C,C,B) | perp(f11(A,B,C,f20(A,B,C,D)),A,A,f20(A,B,C,D)). [resolve(108,c,104,a)]. 0.81/1.14 Derived: -cyclic(A,B,C,D) | -perp(A,C,C,B) | -midp(E,B,C) | eqangle(A,B,A,C,f20(A,B,C,D),B,f20(A,B,C,D),E). [resolve(108,c,106,b)]. 0.81/1.14 Derived: -cyclic(A,B,C,D) | -perp(A,C,C,B) | -eqangle(A,E,A,B,C,A,C,B) | perp(f20(A,B,C,D),A,A,E). [resolve(108,c,107,a)]. 0.81/1.14 109 circle(c4,c1,c2,c3) # label(exemplo6GDDFULL012017) # label(negated_conjecture). [clausify(95)]. 0.81/1.14 Derived: -cong(c4,c1,c4,A) | B = c4 | -cong(B,c1,B,c2) | coll(f2(c1,c2,c3,A,c4,B),c2,A). [resolve(109,a,97,d)]. 0.81/1.14 Derived: -cong(c4,c1,c4,A) | B = c4 | -cong(B,c1,B,c2) | cong(f2(c1,c2,c3,A,c4,B),B,B,c1). [resolve(109,a,98,d)]. 0.81/1.14 Derived: -cong(c4,c1,c4,A) | B = c4 | -cong(B,c1,B,c2) | cong(f1(c1,c2,c3,A,c4,B),B,B,c1). [resolve(109,a,99,d)]. 0.81/1.14 Derived: -cong(c4,c1,c4,A) | B = c4 | -cong(B,c1,B,c2) | coll(f1(c1,c2,c3,A,c4,B),c1,c3). [resolve(109,a,100,d)]. 0.81/1.14 Derived: -eqangle(c1,c2,c1,c3,c4,c2,c4,A) | -coll(A,c2,c3) | midp(A,c2,c3). [resolve(109,a,101,a)]. 0.81/1.14 Derived: -perp(c4,c1,c1,A) | eqangle(c1,A,c1,c2,c3,c1,c3,c2). [resolve(109,a,102,a)]. 0.81/1.14 Derived: -coll(c4,c1,c3) | perp(c1,c2,c2,c3). [resolve(109,a,103,a)]. 0.81/1.14 Derived: perp(f11(c1,c2,c3,c4),c1,c1,c4). [resolve(109,a,104,a)]. 0.81/1.14 Derived: -midp(A,c2,c3) | eqangle(c1,c2,c1,c3,c4,c2,c4,A). [resolve(109,a,106,b)]. 0.81/1.14 Derived: -eqangle(c1,A,c1,c2,c3,c1,c3,c2) | perp(c4,c1,c1,A). [resolve(109,a,107,a)]. 0.81/1.14 110 circle(c7,c1,c2,c6) # label(exemplo6GDDFULL012017) # label(negated_conjecture). [clausify(95)]. 0.81/1.14 Derived: -cong(c7,c1,c7,A) | B = c7 | -cong(B,c1,B,c2) | coll(f2(c1,c2,c6,A,c7,B),c2,A). [resolve(110,a,97,d)]. 0.81/1.14 Derived: -cong(c7,c1,c7,A) | B = c7 | -cong(B,c1,B,c2) | cong(f2(c1,c2,c6,A,c7,B),B,B,c1). [resolve(110,a,98,d)]. 0.81/1.14 Derived: -cong(c7,c1,c7,A) | B = c7 | -cong(B,c1,B,c2) | cong(f1(c1,c2,c6,A,c7,B),B,B,c1). [resolve(110,a,99,d)]. 0.81/1.14 Derived: -cong(c7,c1,c7,A) | B = c7 | -cong(B,c1,B,c2) | coll(f1(c1,c2,c6,A,c7,B),c1,c6). [resolve(110,a,100,d)]. 0.81/1.14 Derived: -eqangle(c1,c2,c1,c6,c7,c2,c7,A) | -coll(A,c2,c6) | midp(A,c2,c6). [resolve(110,a,101,a)]. 0.81/1.14 Derived: -perp(c7,c1,c1,A) | eqangle(c1,A,c1,c2,c6,c1,c6,c2). [resolve(110,a,102,a)]. 0.81/1.14 Derived: -coll(c7,c1,c6) | perp(c1,c2,c2,c6). [resolve(110,a,103,a)]. 0.81/1.14 Derived: perp(f11(c1,c2,c6,c7),c1,c1,c7). [resolve(110,a,104,a)]. 0.81/1.14 Derived: -midp(A,c2,c6) | eqangle(c1,c2,c1,c6,c7,c2,c7,A). [resolve(110,a,106,b)]. 0.81/1.14 Derived: -eqangle(c1,A,c1,c2,c6,c1,c6,c2) | perp(c7,c1,c1,A). [resolve(110,a,107,a)]. 0.81/1.14 111 circle(c8,c3,c9,c12) # label(exemplo6GDDFULL012017) # label(negated_conjecture). [clausify(95)]. 0.81/1.14 Derived: -cong(c8,c3,c8,A) | B = c8 | -cong(B,c3,B,c9) | coll(f2(c3,c9,c12,A,c8,B),c9,A). [resolve(111,a,97,d)]. 0.81/1.14 Derived: -cong(c8,c3,c8,A) | B = c8 | -cong(B,c3,B,c9) | cong(f2(c3,c9,c12,A,c8,B),B,B,c3). [resolve(111,a,98,d)]. 0.81/1.14 Derived: -cong(c8,c3,c8,A) | B = c8 | -cong(B,c3,B,c9) | cong(f1(c3,c9,c12,A,c8,B),B,B,c3). [resolve(111,a,99,d)]. 0.81/1.14 Derived: -cong(c8,c3,c8,A) | B = c8 | -cong(B,c3,B,c9) | coll(f1(c3,c9,c12,A,c8,B),c3,c12). [resolve(111,a,100,d)]. 0.81/1.14 Derived: -eqangle(c3,c9,c3,c12,c8,c9,c8,A) | -coll(A,c9,c12) | midp(A,c9,c12). [resolve(111,a,101,a)]. 0.81/1.14 Derived: -perp(c8,c3,c3,A) | eqangle(c3,A,c3,c9,c12,c3,c12,c9). [resolve(111,a,102,a)]. 0.81/1.14 Derived: -coll(c8,c3,c12) | perp(c3,c9,c9,c12). [resolve(111,a,103,a)]. 0.81/1.14 Derived: perp(f11(c3,c9,c12,c8),c3,c3,c8). [resolve(111,a,104,a)]. 0.81/1.14 Derived: -midp(A,c9,c12) | eqangle(c3,c9,c3,c12,c8,c9,c8,A). [resolve(111,a,106,b)]. 0.81/1.14 Derived: -eqangle(c3,A,c3,c9,c12,c3,c12,c9) | perp(c8,c3,c3,A). [resolve(111,a,107,a)]. 0.81/1.14 112 circle(c7,c1,c9,c11) # label(exemplo6GDDFULL012017) # label(negated_conjecture). [clausify(95)]. 0.81/1.14 Derived: -cong(c7,c1,c7,A) | B = c7 | -cong(B,c1,B,c9) | coll(f2(c1,c9,c11,A,c7,B),c9,A). [resolve(112,a,97,d)]. 0.81/1.14 Derived: -cong(c7,c1,c7,A) | B = c7 | -cong(B,c1,B,c9) | cong(f2(c1,c9,c11,A,c7,B),B,B,c1). [resolve(112,a,98,d)]. 0.81/1.14 Derived: -cong(c7,c1,c7,A) | B = c7 | -cong(B,c1,B,c9) | cong(f1(c1,c9,c11,A,c7,B),B,B,c1). [resolve(112,a,99,d)]. 0.81/1.14 Derived: -cong(c7,c1,c7,A) | B = c7 | -cong(B,c1,B,c9) | coll(f1(c1,c9,c11,A,c7,B),c1,c11). [resolve(112,a,100,d)]. 0.81/1.14 Derived: -eqangle(c1,c9,c1,c11,c7,c9,c7,A) | -coll(A,c9,c11) | midp(A,c9,c11). [resolve(112,a,101,a)]. 0.81/1.14 Derived: -perp(c7,c1,c1,A) | eqangle(c1,A,c1,c9,c11,c1,c11,c9). [resolve(112,a,102,a)]. 0.81/1.14 Derived: -coll(c7,c1,c11) | perp(c1,c9,c9,c11). [resolve(112,a,103,a)]. 0.81/1.14 Derived: perp(f11(c1,c9,c11,c7),c1,c1,c7). [resolve(112,a,104,a)]. 0.81/1.14 Derived: -midp(A,c9,c11) | eqangle(c1,c9,c1,c11,c7,c9,c7,A). [resolve(112,a,106,b)]. 0.81/1.14 Derived: -eqangle(c1,A,c1,c9,c11,c1,c11,c9) | perp(c7,c1,c1,A). [resolve(112,a,107,a)]. 0.81/1.14 113 circle(c8,c3,c5,c6) # label(exemplo6GDDFULL012017) # label(negated_conjecture). [clausify(95)]. 0.81/1.14 Derived: -cong(c8,c3,c8,A) | B = c8 | -cong(B,c3,B,c5) | coll(f2(c3,c5,c6,A,c8,B),c5,A). [resolve(113,a,97,d)]. 0.81/1.14 Derived: -cong(c8,c3,c8,A) | B = c8 | -cong(B,c3,B,c5) | cong(f2(c3,c5,c6,A,c8,B),B,B,c3). [resolve(113,a,98,d)]. 0.81/1.14 Derived: -cong(c8,c3,c8,A) | B = c8 | -cong(B,c3,B,c5) | cong(f1(c3,c5,c6,A,c8,B),B,B,c3). [resolve(113,a,99,d)]. 0.81/1.14 Derived: -cong(c8,c3,c8,A) | B = c8 | -cong(B,c3,B,c5) | coll(f1(c3,c5,c6,A,c8,B),c3,c6). [resolve(113,a,100,d)]. 7.96/8.31 Derived: -eqangle(c3,c5,c3,c6,c8,c5,c8,A) | -coll(A,c5,c6) | midp(A,c5,c6). [resolve(113,a,101,a)]. 7.96/8.31 Derived: -perp(c8,c3,c3,A) | eqangle(c3,A,c3,c5,c6,c3,c6,c5). [resolve(113,a,102,a)]. 7.96/8.31 Derived: -coll(c8,c3,c6) | perp(c3,c5,c5,c6). [resolve(113,a,103,a)]. 7.96/8.31 Derived: perp(f11(c3,c5,c6,c8),c3,c3,c8). [resolve(113,a,104,a)]. 7.96/8.31 Derived: -midp(A,c5,c6) | eqangle(c3,c5,c3,c6,c8,c5,c8,A). [resolve(113,a,106,b)]. 7.96/8.31 Derived: -eqangle(c3,A,c3,c5,c6,c3,c6,c5) | perp(c8,c3,c3,A). [resolve(113,a,107,a)]. 7.96/8.31 114 circle(c4,c1,c5,c10) # label(exemplo6GDDFULL012017) # label(negated_conjecture). [clausify(95)]. 7.96/8.31 Derived: -cong(c4,c1,c4,A) | B = c4 | -cong(B,c1,B,c5) | coll(f2(c1,c5,c10,A,c4,B),c5,A). [resolve(114,a,97,d)]. 7.96/8.31 Derived: -cong(c4,c1,c4,A) | B = c4 | -cong(B,c1,B,c5) | cong(f2(c1,c5,c10,A,c4,B),B,B,c1). [resolve(114,a,98,d)]. 7.96/8.31 Derived: -cong(c4,c1,c4,A) | B = c4 | -cong(B,c1,B,c5) | cong(f1(c1,c5,c10,A,c4,B),B,B,c1). [resolve(114,a,99,d)]. 7.96/8.31 Derived: -cong(c4,c1,c4,A) | B = c4 | -cong(B,c1,B,c5) | coll(f1(c1,c5,c10,A,c4,B),c1,c10). [resolve(114,a,100,d)]. 7.96/8.31 Derived: -eqangle(c1,c5,c1,c10,c4,c5,c4,A) | -coll(A,c5,c10) | midp(A,c5,c10). [resolve(114,a,101,a)]. 7.96/8.31 Derived: -perp(c4,c1,c1,A) | eqangle(c1,A,c1,c5,c10,c1,c10,c5). [resolve(114,a,102,a)]. 7.96/8.31 Derived: -coll(c4,c1,c10) | perp(c1,c5,c5,c10). [resolve(114,a,103,a)]. 7.96/8.31 Derived: perp(f11(c1,c5,c10,c4),c1,c1,c4). [resolve(114,a,104,a)]. 7.96/8.31 Derived: -midp(A,c5,c10) | eqangle(c1,c5,c1,c10,c4,c5,c4,A). [resolve(114,a,106,b)]. 7.96/8.31 Derived: -eqangle(c1,A,c1,c5,c10,c1,c10,c5) | perp(c4,c1,c1,A). [resolve(114,a,107,a)]. 7.96/8.31 7.96/8.31 ============================== end predicate elimination ============= 7.96/8.31 7.96/8.31 Auto_denials: (non-Horn, no changes). 7.96/8.31 7.96/8.31 Term ordering decisions: 7.96/8.31 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. c10=1. c11=1. c12=1. f4=1. f3=1. f7=1. f8=1. f11=1. f15=1. f16=1. f18=1. f20=1. f5=1. f6=1. f12=1. f13=1. f14=1. f1=1. f2=1. f9=1. f17=1. f10=1. f19=1. 7.96/8.31 7.96/8.31 ============================== end of process initial clauses ======== 7.96/8.31 7.96/8.31 ============================== CLAUSES FOR SEARCH ==================== 7.96/8.31 7.96/8.31 ============================== end of clauses for search ============= 7.96/8.31 7.96/8.31 ============================== SEARCH ================================ 7.96/8.31 7.96/8.31 % Starting search at 0.04 seconds. 7.96/8.31 7.96/8.31 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 2147483647 (0.00 of 0.12 sec). 7.96/8.31 7.96/8.31 Low Water (keep): wt=26.000, iters=3333 7.96/8.31 7.96/8.31 Low Water (keep): wt=22.000, iters=3344 7.96/8.31 7.96/8.31 Low Water (keep): wt=21.000, iters=3355 7.96/8.31 7.96/8.31 Low Water (keep): wt=18.000, iters=3343 7.96/8.31 7.96/8.31 Low Water (keep): wt=17.000, iters=3346 7.96/8.31 7.96/8.31 Low Water (keep): wt=16.000, iters=3338 7.96/8.31 7.96/8.31 Low Water (keep): wt=15.000, iters=3424 7.96/8.31 7.96/8.31 Low Water (keep): wt=14.000, iters=3413 7.96/8.31 7.96/8.31 Low Water (keep): wt=13.000, iters=3346 7.96/8.31 7.96/8.31 Low Water (keep): wt=12.000, iters=3333 7.96/8.31 7.96/8.31 ============================== PROOF ================================= 7.96/8.31 % SZS status Theorem 7.96/8.31 % SZS output start Refutation 7.96/8.31 7.96/8.31 % Proof 1 at 7.09 (+ 0.10) seconds. 7.96/8.31 % Length of proof is 58. 7.96/8.31 % Level of proof is 16. 7.96/8.31 % Maximum clause weight is 18.000. 7.96/8.31 % Given clauses 8380. 7.96/8.31 7.96/8.31 9 (all A all B all C all D all P all Q (para(A,B,C,D) -> eqangle(A,B,P,Q,C,D,P,Q))) # label(ruleD40) # label(axiom) # label(non_clause). [assumption]. 7.96/8.31 13 (all A all B all P all Q (eqangle(P,A,P,B,Q,A,Q,B) & coll(P,Q,B) -> cyclic(A,B,P,Q))) # label(ruleD42b) # label(axiom) # label(non_clause). [assumption]. 7.96/8.31 16 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption]. 7.96/8.31 27 (all A all B all C all D (cyclic(A,B,C,D) -> cyclic(A,B,D,C))) # label(ruleD14) # label(axiom) # label(non_clause). [assumption]. 7.96/8.31 46 (all A all B all C all O exists P (circle(O,A,B,C) -> perp(P,A,A,O))) # label(ruleX11) # label(axiom) # label(non_clause). [assumption]. 7.96/8.31 49 (all A all B all C all D (coll(A,B,D) & coll(A,B,C) -> coll(C,D,A))) # label(ruleD3) # label(axiom) # label(non_clause). [assumption]. 7.96/8.31 55 (all A all B all C all D (para(A,B,C,D) -> para(A,B,D,C))) # label(ruleD4) # label(axiom) # label(non_clause). [assumption]. 7.96/8.31 57 (all A all B all C all D (para(A,B,C,D) -> para(C,D,A,B))) # label(ruleD5) # label(axiom) # label(non_clause). [assumption]. 7.96/8.31 65 (all A all B all C all D (perp(A,B,C,D) -> perp(C,D,A,B))) # label(ruleD8) # label(axiom) # label(non_clause). [assumption]. 7.96/8.31 71 (all A all B all C all D all E all F (perp(C,D,E,F) & perp(A,B,C,D) -> para(A,B,E,F))) # label(ruleD9) # label(axiom) # label(non_clause). [assumption]. 7.96/8.31 77 (all A all B all C all D (cyclic(A,B,C,D) -> cyclic(A,C,B,D))) # label(ruleD15) # label(axiom) # label(non_clause). [assumption]. 7.96/8.31 79 (all A all B all C all D all P all Q all U all V (eqangle(A,B,C,D,P,Q,U,V) -> eqangle(C,D,A,B,U,V,P,Q))) # label(ruleD19) # label(axiom) # label(non_clause). [assumption]. 7.96/8.31 89 (all A all B all C all D all E (cyclic(A,B,C,E) & cyclic(A,B,C,D) -> cyclic(B,C,D,E))) # label(ruleD17) # label(axiom) # label(non_clause). [assumption]. 7.96/8.31 91 (all A all B all C all D all P all Q (eqangle(A,B,P,Q,C,D,P,Q) -> para(A,B,C,D))) # label(ruleD39) # label(axiom) # label(non_clause). [assumption]. 7.96/8.31 95 -(all A all C all K all O all N all B all G all O1 all M all NWPNT1 all NWPNT2 all NWPNT3 (circle(O,A,C,K) & circle(G,A,C,B) & circle(O1,K,M,NWPNT3) & circle(G,A,M,NWPNT2) & circle(O1,K,N,B) & coll(B,C,N) & coll(B,A,K) & circle(O,A,N,NWPNT1) -> cyclic(M,K,O,C))) # label(exemplo6GDDFULL012017) # label(negated_conjecture) # label(non_clause). [assumption]. 7.96/8.31 104 -circle(A,B,C,D) | perp(f11(B,C,D,A),B,B,A) # label(ruleX11) # label(axiom). [clausify(46)]. 7.96/8.31 109 circle(c4,c1,c2,c3) # label(exemplo6GDDFULL012017) # label(negated_conjecture). [clausify(95)]. 7.96/8.31 111 circle(c8,c3,c9,c12) # label(exemplo6GDDFULL012017) # label(negated_conjecture). [clausify(95)]. 7.96/8.31 122 -para(A,B,C,D) | eqangle(A,B,E,F,C,D,E,F) # label(ruleD40) # label(axiom). [clausify(9)]. 7.96/8.31 127 -eqangle(A,B,A,C,D,B,D,C) | -coll(A,D,C) | cyclic(B,C,A,D) # label(ruleD42b) # label(axiom). [clausify(13)]. 7.96/8.31 130 -para(A,B,A,C) | coll(A,B,C) # label(ruleD66) # label(axiom). [clausify(16)]. 7.96/8.31 143 -cyclic(A,B,C,D) | cyclic(A,B,D,C) # label(ruleD14) # label(axiom). [clausify(27)]. 7.96/8.31 166 -coll(A,B,C) | -coll(A,B,D) | coll(D,C,A) # label(ruleD3) # label(axiom). [clausify(49)]. 7.96/8.31 172 -para(A,B,C,D) | para(A,B,D,C) # label(ruleD4) # label(axiom). [clausify(55)]. 7.96/8.31 173 -para(A,B,C,D) | para(C,D,A,B) # label(ruleD5) # label(axiom). [clausify(57)]. 7.96/8.31 181 -perp(A,B,C,D) | perp(C,D,A,B) # label(ruleD8) # label(axiom). [clausify(65)]. 7.96/8.31 189 -perp(A,B,C,D) | -perp(E,F,A,B) | para(E,F,C,D) # label(ruleD9) # label(axiom). [clausify(71)]. 7.96/8.31 196 -cyclic(A,B,C,D) | cyclic(A,C,B,D) # label(ruleD15) # label(axiom). [clausify(77)]. 7.96/8.31 199 -eqangle(A,B,C,D,E,F,V6,V7) | eqangle(C,D,A,B,V6,V7,E,F) # label(ruleD19) # label(axiom). [clausify(79)]. 7.96/8.31 209 -cyclic(A,B,C,D) | -cyclic(A,B,C,E) | cyclic(B,C,E,D) # label(ruleD17) # label(axiom). [clausify(89)]. 7.96/8.31 210 -eqangle(A,B,C,D,E,F,C,D) | para(A,B,E,F) # label(ruleD39) # label(axiom). [clausify(91)]. 7.96/8.31 216 -cyclic(c9,c3,c4,c2) # label(exemplo6GDDFULL012017) # label(negated_conjecture). [clausify(95)]. 7.96/8.31 266 perp(f11(c1,c2,c3,c4),c1,c1,c4). [resolve(109,a,104,a)]. 7.96/8.31 294 perp(f11(c3,c9,c12,c8),c3,c3,c8). [resolve(111,a,104,a)]. 7.96/8.31 360 -coll(A,B,C) | coll(C,C,A). [factor(166,a,b)]. 7.96/8.31 415 -perp(A,B,f11(c1,c2,c3,c4),c1) | para(A,B,c1,c4). [resolve(266,a,189,a)]. 7.96/8.31 418 perp(c1,c4,f11(c1,c2,c3,c4),c1). [resolve(266,a,181,a)]. 7.96/8.31 465 -perp(A,B,f11(c3,c9,c12,c8),c3) | para(A,B,c3,c8). [resolve(294,a,189,a)]. 7.96/8.31 468 perp(c3,c8,f11(c3,c9,c12,c8),c3). [resolve(294,a,181,a)]. 7.96/8.31 718 para(c1,c4,c1,c4). [resolve(418,a,415,a)]. 7.96/8.31 747 eqangle(c1,c4,A,B,c1,c4,A,B). [resolve(718,a,122,a)]. 7.96/8.31 1636 para(c3,c8,c3,c8). [resolve(468,a,465,a)]. 7.96/8.31 1661 para(c3,c8,c8,c3). [resolve(1636,a,172,a)]. 7.96/8.31 1822 para(c8,c3,c3,c8). [resolve(1661,a,173,a)]. 7.96/8.31 1863 para(c8,c3,c8,c3). [resolve(1822,a,172,a)]. 7.96/8.31 1906 eqangle(c8,c3,A,B,c8,c3,A,B). [resolve(1863,a,122,a)]. 7.96/8.31 3382 eqangle(A,B,c1,c4,A,B,c1,c4). [resolve(747,a,199,a)]. 7.96/8.31 13766 -coll(c8,c8,A) | cyclic(c3,A,c8,c8). [resolve(1906,a,127,a)]. 7.96/8.31 17078 para(A,B,A,B). [resolve(3382,a,210,a)]. 7.96/8.31 17086 coll(A,B,B). [resolve(17078,a,130,a)]. 7.96/8.31 17178 coll(A,A,B). [resolve(17086,a,360,a)]. 7.96/8.31 17306 cyclic(c3,A,c8,c8). [back_unit_del(13766),unit_del(a,17178)]. 7.96/8.31 17841 cyclic(c3,c8,A,c8). [resolve(17306,a,196,a)]. 7.96/8.31 18078 cyclic(c3,c8,c8,A). [resolve(17841,a,143,a)]. 7.96/8.31 18538 cyclic(c8,c8,A,B). [resolve(18078,a,209,b),unit_del(a,18078)]. 7.96/8.31 19214 cyclic(c8,A,B,C). [resolve(18538,a,209,b),unit_del(a,18538)]. 7.96/8.31 19898 cyclic(A,B,C,D). [resolve(19214,a,209,b),unit_del(a,19214)]. 7.96/8.31 19899 $F. [resolve(19898,a,216,a)]. 7.96/8.31 7.96/8.31 % SZS output end Refutation 7.96/8.31 ============================== end of proof ========================== 7.96/8.31 7.96/8.31 ============================== STATISTICS ============================ 7.96/8.31 7.96/8.31 Given=8380. Generated=93700. Kept=19752. proofs=1. 7.96/8.31 Usable=7106. Sos=6437. Demods=0. Limbo=4, Disabled=6416. Hints=0. 7.96/8.31 Megabytes=14.49. 7.96/8.31 User_CPU=7.09, System_CPU=0.10, Wall_clock=7. 7.96/8.31 7.96/8.31 ============================== end of statistics ===================== 7.96/8.31 7.96/8.31 ============================== end of search ========================= 7.96/8.31 7.96/8.31 THEOREM PROVED 7.96/8.31 % SZS status Theorem 7.96/8.31 7.96/8.31 Exiting with 1 proof. 7.96/8.31 7.96/8.31 Process 23531 exit (max_proofs) Tue Aug 9 03:44:43 2022 7.96/8.31 Prover9 interrupted 7.96/8.31 EOF