TSTP Solution File: GEO567+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GEO567+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 05:56:59 EDT 2022
% Result : Theorem 2.33s 2.61s
% Output : Refutation 2.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO567+1 : TPTP v8.1.0. Released v7.5.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sat Jun 18 02:27:29 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.80/1.13 ============================== Prover9 ===============================
% 0.80/1.13 Prover9 (32) version 2009-11A, November 2009.
% 0.80/1.13 Process 4940 was started by sandbox on n013.cluster.edu,
% 0.80/1.13 Sat Jun 18 02:27:29 2022
% 0.80/1.13 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_4787_n013.cluster.edu".
% 0.80/1.13 ============================== end of head ===========================
% 0.80/1.13
% 0.80/1.13 ============================== INPUT =================================
% 0.80/1.13
% 0.80/1.13 % Reading from file /tmp/Prover9_4787_n013.cluster.edu
% 0.80/1.13
% 0.80/1.13 set(prolog_style_variables).
% 0.80/1.13 set(auto2).
% 0.80/1.13 % set(auto2) -> set(auto).
% 0.80/1.13 % set(auto) -> set(auto_inference).
% 0.80/1.13 % set(auto) -> set(auto_setup).
% 0.80/1.13 % set(auto_setup) -> set(predicate_elim).
% 0.80/1.13 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.80/1.13 % set(auto) -> set(auto_limits).
% 0.80/1.13 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.80/1.13 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.80/1.13 % set(auto) -> set(auto_denials).
% 0.80/1.13 % set(auto) -> set(auto_process).
% 0.80/1.13 % set(auto2) -> assign(new_constants, 1).
% 0.80/1.13 % set(auto2) -> assign(fold_denial_max, 3).
% 0.80/1.13 % set(auto2) -> assign(max_weight, "200.000").
% 0.80/1.13 % set(auto2) -> assign(max_hours, 1).
% 0.80/1.13 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.80/1.13 % set(auto2) -> assign(max_seconds, 0).
% 0.80/1.13 % set(auto2) -> assign(max_minutes, 5).
% 0.80/1.13 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.80/1.13 % set(auto2) -> set(sort_initial_sos).
% 0.80/1.13 % set(auto2) -> assign(sos_limit, -1).
% 0.80/1.13 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.80/1.13 % set(auto2) -> assign(max_megs, 400).
% 0.80/1.13 % set(auto2) -> assign(stats, some).
% 0.80/1.13 % set(auto2) -> clear(echo_input).
% 0.80/1.13 % set(auto2) -> set(quiet).
% 0.80/1.13 % set(auto2) -> clear(print_initial_clauses).
% 0.80/1.13 % set(auto2) -> clear(print_given).
% 0.80/1.13 assign(lrs_ticks,-1).
% 0.80/1.13 assign(sos_limit,10000).
% 0.80/1.13 assign(order,kbo).
% 0.80/1.13 set(lex_order_vars).
% 0.80/1.13 clear(print_given).
% 0.80/1.13
% 0.80/1.13 % formulas(sos). % not echoed (95 formulas)
% 0.80/1.13
% 0.80/1.13 ============================== end of input ==========================
% 0.80/1.13
% 0.80/1.13 % From the command line: assign(max_seconds, 300).
% 0.80/1.13
% 0.80/1.13 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.80/1.13
% 0.80/1.13 % Formulas that are not ordinary clauses:
% 0.80/1.13 1 (all A all B all C (coll(A,B,C) -> coll(A,C,B))) # label(ruleD1) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 2 (all A all B all C (coll(A,B,C) -> coll(B,A,C))) # label(ruleD2) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 3 (all A all B all C all D (coll(A,B,C) & coll(A,B,D) -> coll(C,D,A))) # label(ruleD3) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 4 (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].
% 0.80/1.13 5 (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].
% 0.80/1.13 6 (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].
% 0.80/1.13 7 (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].
% 0.80/1.13 8 (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].
% 0.80/1.13 9 (all A all B all C all D all E all F (perp(A,B,C,D) & perp(C,D,E,F) -> para(A,B,E,F))) # label(ruleD9) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 10 (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].
% 0.80/1.13 11 (all A all B all M (midp(M,B,A) -> midp(M,A,B))) # label(ruleD11) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 12 (all A all B all C all O (cong(O,A,O,B) & cong(O,A,O,C) -> circle(O,A,B,C))) # label(ruleD12) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 13 (all A all B all C all D all O (cong(O,A,O,B) & cong(O,A,O,C) & cong(O,A,O,D) -> cyclic(A,B,C,D))) # label(ruleD13) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 14 (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].
% 0.80/1.13 15 (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].
% 0.80/1.14 16 (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].
% 0.80/1.14 17 (all A all B all C all D all E (cyclic(A,B,C,D) & cyclic(A,B,C,E) -> cyclic(B,C,D,E))) # label(ruleD17) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 18 (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].
% 0.80/1.14 19 (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].
% 0.80/1.14 20 (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].
% 0.80/1.14 21 (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].
% 0.80/1.14 22 (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(A,B,C,D,P,Q,U,V) & eqangle(P,Q,U,V,E,F,G,H) -> eqangle(A,B,C,D,E,F,G,H))) # label(ruleD22) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 23 (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].
% 0.80/1.14 24 (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].
% 0.80/1.14 25 (all A all B all C all D all E all F (cong(A,B,C,D) & cong(C,D,E,F) -> cong(A,B,E,F))) # label(ruleD25) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 26 (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].
% 0.80/1.14 27 (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].
% 0.80/1.14 28 (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].
% 0.80/1.14 29 (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].
% 0.80/1.14 30 (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(A,B,C,D,P,Q,U,V) & eqratio(P,Q,U,V,E,F,G,H) -> eqratio(A,B,C,D,E,F,G,H))) # label(ruleD30) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 31 (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].
% 0.80/1.14 32 (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].
% 0.80/1.14 33 (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].
% 0.80/1.14 34 (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].
% 0.80/1.14 35 (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].
% 0.80/1.14 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].
% 0.80/1.14 37 (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].
% 0.80/1.14 38 (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].
% 0.80/1.14 39 (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].
% 0.80/1.14 40 (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].
% 0.80/1.14 41 (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].
% 0.80/1.14 42 (all A all B all P all Q (eqangle(P,A,P,B,Q,A,Q,B) & -coll(P,Q,A) -> cyclic(A,B,P,Q))) # label(ruleD42a) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 43 (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].
% 0.80/1.14 44 (all A all B all C all P all Q all R (cyclic(A,B,C,P) & cyclic(A,B,C,Q) & cyclic(A,B,C,R) & eqangle(C,A,C,B,R,P,R,Q) -> cong(A,B,P,Q))) # label(ruleD43) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 45 (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].
% 0.80/1.14 46 (all A all B all C all E all F (midp(E,A,B) & para(E,F,B,C) & coll(F,A,C) -> midp(F,A,C))) # label(ruleD45) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 47 (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].
% 0.80/1.14 48 (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].
% 0.80/1.14 49 (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].
% 0.80/1.14 50 (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].
% 0.80/1.14 51 (all A all B all C all O all M (circle(O,A,B,C) & midp(M,B,C) -> eqangle(A,B,A,C,O,B,O,M))) # label(ruleD50) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 52 (all A all B all C all O all M (circle(O,A,B,C) & coll(M,B,C) & eqangle(A,B,A,C,O,B,O,M) -> midp(M,B,C))) # label(ruleD51) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 53 (all A all B all C all M (perp(A,B,B,C) & midp(M,A,C) -> cong(A,M,B,M))) # label(ruleD52) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 54 (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].
% 0.80/1.14 55 (all A all B all C all D (cyclic(A,B,C,D) & para(A,B,C,D) -> eqangle(A,D,C,D,C,D,C,B))) # label(ruleD54) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 56 (all A all B all M all O (midp(M,A,B) & perp(O,M,A,B) -> cong(O,A,O,B))) # label(ruleD55) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 57 (all A all B all P all Q (cong(A,P,B,P) & cong(A,Q,B,Q) -> perp(A,B,P,Q))) # label(ruleD56) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 58 (all A all B all P all Q (cong(A,P,B,P) & cong(A,Q,B,Q) & cyclic(A,B,P,Q) -> perp(P,A,A,Q))) # label(ruleD57) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 59 (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].
% 0.80/1.14 60 (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].
% 0.80/1.14 61 (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].
% 0.80/1.14 62 (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].
% 0.80/1.14 63 (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].
% 0.80/1.14 64 (all A all B all C all D all M (midp(M,A,B) & midp(M,C,D) -> para(A,C,B,D))) # label(ruleD63) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 65 (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].
% 0.80/1.14 66 (all A all B all C all D all O (para(A,B,C,D) & coll(O,A,C) & coll(O,B,D) -> eqratio(O,A,A,C,O,B,B,D))) # label(ruleD65) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 67 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 68 (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].
% 0.80/1.14 69 (all A all B all C (midp(A,B,C) -> cong(A,B,A,C))) # label(ruleD68) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 70 (all A all B all C (midp(A,B,C) -> coll(A,B,C))) # label(ruleD69) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 71 (all A all B all C all D all M all N (midp(M,A,B) & midp(N,C,D) -> eqratio(M,A,A,B,N,C,C,D))) # label(ruleD70) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 72 (all A all B all C all D (eqangle(A,B,C,D,C,D,A,B) & -para(A,B,C,D) -> perp(A,B,C,D))) # label(ruleD71) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 73 (all A all B all C all D (eqangle(A,B,C,D,C,D,A,B) & -perp(A,B,C,D) -> para(A,B,C,D))) # label(ruleD72) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 74 (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) & para(P,Q,U,V) -> para(A,B,C,D))) # label(ruleD73) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 75 (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) & perp(P,Q,U,V) -> perp(A,B,C,D))) # label(ruleD74) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 76 (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) & cong(P,Q,U,V) -> cong(A,B,C,D))) # label(ruleD75) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 77 (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,A,M) & coll(B,O,X))) # label(ruleX1) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 78 (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(B,A,M) & coll(M,O,X))) # label(ruleX2) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 79 (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(B,A,M) & coll(M,O,X))) # label(ruleX3) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 80 (all A all B all O all X exists M (perp(O,X,A,B) & cong(O,A,O,B) -> coll(B,A,M) & coll(M,O,X))) # label(ruleX4) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 81 (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) -> eqangle(A,P,B,P,A,Q,B,Q) & cyclic(X,B,P,Q))) # label(ruleX5) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 82 (all A all B all C all D all M all N exists P (midp(M,A,B) & midp(N,C,D) -> midp(P,A,D) & para(P,M,B,D) & para(P,N,A,C))) # label(ruleX6) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 83 (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(C,A,B) & coll(D,A,B) -> midp(P,A,Q))) # label(ruleX7) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 84 (all A all B all M all P all Q all R all M exists X (midp(M,A,B) & para(A,P,R,M) & para(A,P,B,Q) & coll(P,Q,R) -> coll(X,A,Q) & coll(X,M,R))) # label(ruleX8) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 85 (all A all B all C all D all O exists P (cong(O,C,O,D) & perp(A,B,B,O) -> cong(O,C,O,P) & para(P,C,A,B) & cong(B,C,B,P))) # label(ruleX9) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 86 (all A all B all C all H exists P exists Q (perp(A,H,B,C) & perp(B,H,A,C) -> coll(P,C,B) & perp(A,P,C,B) & coll(Q,C,A) & perp(B,Q,C,A))) # label(ruleX10) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 87 (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].
% 0.80/1.14 88 (all A all B all C all D all M all N exists P exists Q (circle(M,A,B,C) & cong(M,A,M,D) & cong(N,A,N,B) & M != N -> coll(P,A,C) & cong(P,N,N,A) & coll(Q,B,D) & cong(Q,N,N,A))) # label(ruleX12) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 89 (all A all B all C all D all M exists O (cyclic(A,B,C,D) & para(A,B,C,D) & midp(M,A,B) -> circle(O,A,B,C))) # label(ruleX13) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 90 (all A all B all C all D exists O (perp(A,C,C,B) & cyclic(A,B,C,D) -> circle(O,A,B,C))) # label(ruleX14) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 91 (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].
% 0.80/1.14 92 (all A all B all C all D all M exists P (perp(A,B,A,C) & perp(C,A,C,D) & midp(M,B,D) -> midp(P,A,C))) # label(ruleX16) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 93 (all A all B all O exists C (cong(O,A,O,B) & perp(A,O,O,B) -> coll(A,O,C) & cong(O,A,O,C))) # label(ruleX17) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 94 (all A all B all C all D all P all Q exists R (para(A,B,C,D) & coll(P,A,C) & coll(P,B,D) & coll(Q,A,B) -> coll(P,Q,R) & coll(R,C,D))) # label(ruleX18) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 95 -(all A all B all C all D all Q all P (perp(D,A,B,C) & coll(D,B,C) & perp(Q,D,A,B) & coll(Q,A,B) & perp(P,D,A,C) & coll(P,A,C) -> cyclic(B,Q,P,C))) # label(exemplo6GDDFULL214029) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.80/1.14
% 0.80/1.14 ============================== end of process non-clausal formulas ===
% 0.80/1.14
% 0.80/1.14 ============================== PROCESS INITIAL CLAUSES ===============
% 0.80/1.14
% 0.80/1.14 ============================== PREDICATE ELIMINATION =================
% 0.80/1.14 96 -circle(A,B,C,D) | -perp(A,B,B,E) | eqangle(B,E,B,C,D,B,D,C) # label(ruleD48) # label(axiom). [clausify(49)].
% 0.80/1.14 97 -cong(A,B,A,C) | -cong(A,B,A,D) | circle(A,B,C,D) # label(ruleD12) # label(axiom). [clausify(12)].
% 0.80/1.14 Derived: -perp(A,B,B,C) | eqangle(B,C,B,D,E,B,E,D) | -cong(A,B,A,D) | -cong(A,B,A,E). [resolve(96,a,97,c)].
% 0.80/1.14 98 -circle(A,B,C,D) | -eqangle(B,E,B,C,D,B,D,C) | perp(A,B,B,E) # label(ruleD49) # label(axiom). [clausify(50)].
% 0.80/1.14 Derived: -eqangle(A,B,A,C,D,A,D,C) | perp(E,A,A,B) | -cong(E,A,E,C) | -cong(E,A,E,D). [resolve(98,a,97,c)].
% 0.80/1.14 99 -circle(A,B,C,D) | -midp(E,C,D) | eqangle(B,C,B,D,A,C,A,E) # label(ruleD50) # label(axiom). [clausify(51)].
% 0.80/1.14 Derived: -midp(A,B,C) | eqangle(D,B,D,C,E,B,E,A) | -cong(E,D,E,B) | -cong(E,D,E,C). [resolve(99,a,97,c)].
% 0.80/1.14 100 -circle(A,B,C,D) | -coll(E,C,D) | -eqangle(B,C,B,D,A,C,A,E) | midp(E,C,D) # label(ruleD51) # label(axiom). [clausify(52)].
% 0.80/1.14 Derived: -coll(A,B,C) | -eqangle(D,B,D,C,E,B,E,A) | midp(A,B,C) | -cong(E,D,E,B) | -cong(E,D,E,C). [resolve(100,a,97,c)].
% 0.80/1.14 101 -circle(A,B,C,D) | -coll(A,B,D) | perp(B,C,C,D) # label(ruleD53) # label(axiom). [clausify(54)].
% 0.80/1.14 Derived: -coll(A,B,C) | perp(B,D,D,C) | -cong(A,B,A,D) | -cong(A,B,A,C). [resolve(101,a,97,c)].
% 0.80/1.14 102 -circle(A,B,C,D) | perp(f12(B,C,D,A),B,B,A) # label(ruleX11) # label(axiom). [clausify(87)].
% 0.80/1.14 Derived: perp(f12(A,B,C,D),A,A,D) | -cong(D,A,D,B) | -cong(D,A,D,C). [resolve(102,a,97,c)].
% 0.80/1.14 103 -circle(A,B,C,D) | -cong(A,B,A,E) | -cong(F,B,F,C) | F = A | coll(f13(B,C,D,E,A,F),B,D) # label(ruleX12) # label(axiom). [clausify(88)].
% 0.80/1.14 Derived: -cong(A,B,A,C) | -cong(D,B,D,E) | D = A | coll(f13(B,E,F,C,A,D),B,F) | -cong(A,B,A,E) | -cong(A,B,A,F). [resolve(103,a,97,c)].
% 0.80/1.14 104 -circle(A,B,C,D) | -cong(A,B,A,E) | -cong(F,B,F,C) | F = A | cong(f13(B,C,D,E,A,F),F,F,B) # label(ruleX12) # label(axiom). [clausify(88)].
% 0.80/1.14 Derived: -cong(A,B,A,C) | -cong(D,B,D,E) | D = A | cong(f13(B,E,F,C,A,D),D,D,B) | -cong(A,B,A,E) | -cong(A,B,A,F). [resolve(104,a,97,c)].
% 0.80/1.14 105 -circle(A,B,C,D) | -cong(A,B,A,E) | -cong(F,B,F,C) | F = A | coll(f14(B,C,D,E,A,F),C,E) # label(ruleX12) # label(axiom). [clausify(88)].
% 0.80/1.14 Derived: -cong(A,B,A,C) | -cong(D,B,D,E) | D = A | coll(f14(B,E,F,C,A,D),E,C) | -cong(A,B,A,E) | -cong(A,B,A,F). [resolve(105,a,97,c)].
% 0.80/1.14 106 -circle(A,B,C,D) | -cong(A,B,A,E) | -cong(F,B,F,C) | F = A | cong(f14(B,C,D,E,A,F),F,F,B) # label(ruleX12) # label(axiom). [clausify(88)].
% 0.80/1.14 Derived: -cong(A,B,A,C) | -cong(D,B,D,E) | D = A | cong(f14(B,E,F,C,A,D),D,D,B) | -cong(A,B,A,E) | -cong(A,B,A,F). [resolve(106,a,97,c)].
% 0.80/1.14 107 -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | circle(f15(A,B,C,D,E),A,B,C) # label(ruleX13) # label(axiom). [clausify(89)].
% 0.86/1.27 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -perp(f15(A,B,C,D,E),A,A,F) | eqangle(A,F,A,B,C,A,C,B). [resolve(107,d,96,a)].
% 0.86/1.27 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -eqangle(A,F,A,B,C,A,C,B) | perp(f15(A,B,C,D,E),A,A,F). [resolve(107,d,98,a)].
% 0.86/1.27 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -midp(F,B,C) | eqangle(A,B,A,C,f15(A,B,C,D,E),B,f15(A,B,C,D,E),F). [resolve(107,d,99,a)].
% 0.86/1.27 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -coll(F,B,C) | -eqangle(A,B,A,C,f15(A,B,C,D,E),B,f15(A,B,C,D,E),F) | midp(F,B,C). [resolve(107,d,100,a)].
% 0.86/1.27 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -coll(f15(A,B,C,D,E),A,C) | perp(A,B,B,C). [resolve(107,d,101,a)].
% 0.86/1.27 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | perp(f12(A,B,C,f15(A,B,C,D,E)),A,A,f15(A,B,C,D,E)). [resolve(107,d,102,a)].
% 0.86/1.27 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -cong(f15(A,B,C,D,E),A,f15(A,B,C,D,E),F) | -cong(V6,A,V6,B) | V6 = f15(A,B,C,D,E) | coll(f13(A,B,C,F,f15(A,B,C,D,E),V6),A,C). [resolve(107,d,103,a)].
% 0.86/1.27 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -cong(f15(A,B,C,D,E),A,f15(A,B,C,D,E),F) | -cong(V6,A,V6,B) | V6 = f15(A,B,C,D,E) | cong(f13(A,B,C,F,f15(A,B,C,D,E),V6),V6,V6,A). [resolve(107,d,104,a)].
% 0.86/1.27 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -cong(f15(A,B,C,D,E),A,f15(A,B,C,D,E),F) | -cong(V6,A,V6,B) | V6 = f15(A,B,C,D,E) | coll(f14(A,B,C,F,f15(A,B,C,D,E),V6),B,F). [resolve(107,d,105,a)].
% 0.86/1.27 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -cong(f15(A,B,C,D,E),A,f15(A,B,C,D,E),F) | -cong(V6,A,V6,B) | V6 = f15(A,B,C,D,E) | cong(f14(A,B,C,F,f15(A,B,C,D,E),V6),V6,V6,A). [resolve(107,d,106,a)].
% 0.86/1.27 108 -perp(A,B,B,C) | -cyclic(A,C,B,D) | circle(f16(A,C,B,D),A,C,B) # label(ruleX14) # label(axiom). [clausify(90)].
% 0.86/1.27 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -perp(f16(A,C,B,D),A,A,E) | eqangle(A,E,A,C,B,A,B,C). [resolve(108,c,96,a)].
% 0.86/1.27 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -eqangle(A,E,A,C,B,A,B,C) | perp(f16(A,C,B,D),A,A,E). [resolve(108,c,98,a)].
% 0.86/1.27 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -midp(E,C,B) | eqangle(A,C,A,B,f16(A,C,B,D),C,f16(A,C,B,D),E). [resolve(108,c,99,a)].
% 0.86/1.27 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -coll(E,C,B) | -eqangle(A,C,A,B,f16(A,C,B,D),C,f16(A,C,B,D),E) | midp(E,C,B). [resolve(108,c,100,a)].
% 0.86/1.27 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -coll(f16(A,C,B,D),A,B) | perp(A,C,C,B). [resolve(108,c,101,a)].
% 0.86/1.27 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | perp(f12(A,C,B,f16(A,C,B,D)),A,A,f16(A,C,B,D)). [resolve(108,c,102,a)].
% 0.86/1.27 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -cong(f16(A,C,B,D),A,f16(A,C,B,D),E) | -cong(F,A,F,C) | F = f16(A,C,B,D) | coll(f13(A,C,B,E,f16(A,C,B,D),F),A,B). [resolve(108,c,103,a)].
% 0.86/1.27 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -cong(f16(A,C,B,D),A,f16(A,C,B,D),E) | -cong(F,A,F,C) | F = f16(A,C,B,D) | cong(f13(A,C,B,E,f16(A,C,B,D),F),F,F,A). [resolve(108,c,104,a)].
% 0.86/1.27 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -cong(f16(A,C,B,D),A,f16(A,C,B,D),E) | -cong(F,A,F,C) | F = f16(A,C,B,D) | coll(f14(A,C,B,E,f16(A,C,B,D),F),C,E). [resolve(108,c,105,a)].
% 0.86/1.27 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -cong(f16(A,C,B,D),A,f16(A,C,B,D),E) | -cong(F,A,F,C) | F = f16(A,C,B,D) | cong(f14(A,C,B,E,f16(A,C,B,D),F),F,F,A). [resolve(108,c,106,a)].
% 0.86/1.27
% 0.86/1.27 ============================== end predicate elimination =============
% 0.86/1.27
% 0.86/1.27 Auto_denials: (non-Horn, no changes).
% 0.86/1.27
% 0.86/1.27 Term ordering decisions:
% 0.86/1.27 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. f19=1. f1=1. f2=1. f3=1. f4=1. f10=1. f11=1. f12=1. f16=1. f5=1. f9=1. f15=1. f17=1. f18=1. f6=1. f13=1. f14=1. f20=1. f7=1. f8=1.
% 0.86/1.27
% 0.86/1.27 ============================== end of process initial clauses ========
% 0.86/1.27
% 0.86/1.27 ============================== CLAUSES FOR SEARCH ====================
% 0.86/1.27
% 0.86/1.27 ============================== end of clauses for search =============
% 0.86/1.27
% 0.86/1.27 ============================== SEARCH ================================
% 0.86/1.27
% 0.86/1.27 % Starting search at 0.04 seconds.
% 0.86/1.27
% 0.86/1.27 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 2147483647 (0.00 of 0.15 sec).
% 2.33/2.61
% 2.33/2.61 Low Water (keep): wt=45.000, iters=3366
% 2.33/2.61
% 2.33/2.61 Low Water (keep): wt=44.000, iters=3343
% 2.33/2.61
% 2.33/2.61 Low Water (keep): wt=40.000, iters=3373
% 2.33/2.61
% 2.33/2.61 Low Water (keep): wt=32.000, iters=3431
% 2.33/2.61
% 2.33/2.61 Low Water (keep): wt=28.000, iters=3348
% 2.33/2.61
% 2.33/2.61 Low Water (keep): wt=26.000, iters=3334
% 2.33/2.61
% 2.33/2.61 Low Water (keep): wt=24.000, iters=3374
% 2.33/2.61
% 2.33/2.61 Low Water (keep): wt=23.000, iters=3339
% 2.33/2.61
% 2.33/2.61 Low Water (keep): wt=22.000, iters=3368
% 2.33/2.61
% 2.33/2.61 Low Water (keep): wt=21.000, iters=3347
% 2.33/2.61
% 2.33/2.61 Low Water (keep): wt=19.000, iters=3337
% 2.33/2.61
% 2.33/2.61 Low Water (keep): wt=18.000, iters=3367
% 2.33/2.61
% 2.33/2.61 Low Water (keep): wt=17.000, iters=3335
% 2.33/2.61
% 2.33/2.61 Low Water (keep): wt=15.000, iters=3363
% 2.33/2.61
% 2.33/2.61 Low Water (displace): id=6970, wt=53.000
% 2.33/2.61
% 2.33/2.61 Low Water (keep): wt=14.000, iters=3339
% 2.33/2.61
% 2.33/2.61 Low Water (displace): id=13190, wt=13.000
% 2.33/2.61
% 2.33/2.61 Low Water (displace): id=13205, wt=12.000
% 2.33/2.61
% 2.33/2.61 Low Water (displace): id=13207, wt=10.000
% 2.33/2.61
% 2.33/2.61 Low Water (displace): id=13664, wt=9.000
% 2.33/2.61
% 2.33/2.61 Low Water (keep): wt=13.000, iters=3335
% 2.33/2.61
% 2.33/2.61 Low Water (keep): wt=12.000, iters=3339
% 2.33/2.61
% 2.33/2.61 Low Water (keep): wt=11.000, iters=3333
% 2.33/2.61
% 2.33/2.61 Low Water (displace): id=16069, wt=7.000
% 2.33/2.61
% 2.33/2.61 Low Water (keep): wt=10.000, iters=3336
% 2.33/2.61
% 2.33/2.61 Low Water (displace): id=17229, wt=5.000
% 2.33/2.61
% 2.33/2.61 ============================== PROOF =================================
% 2.33/2.61 % SZS status Theorem
% 2.33/2.61 % SZS output start Refutation
% 2.33/2.61
% 2.33/2.61 % Proof 1 at 1.45 (+ 0.04) seconds.
% 2.33/2.61 % Length of proof is 168.
% 2.33/2.61 % Level of proof is 34.
% 2.33/2.61 % Maximum clause weight is 29.000.
% 2.33/2.61 % Given clauses 3352.
% 2.33/2.61
% 2.33/2.61 1 (all A all B all C (coll(A,B,C) -> coll(A,C,B))) # label(ruleD1) # label(axiom) # label(non_clause). [assumption].
% 2.33/2.61 2 (all A all B all C (coll(A,B,C) -> coll(B,A,C))) # label(ruleD2) # label(axiom) # label(non_clause). [assumption].
% 2.33/2.61 3 (all A all B all C all D (coll(A,B,C) & coll(A,B,D) -> coll(C,D,A))) # label(ruleD3) # label(axiom) # label(non_clause). [assumption].
% 2.33/2.61 8 (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].
% 2.33/2.61 9 (all A all B all C all D all E all F (perp(A,B,C,D) & perp(C,D,E,F) -> para(A,B,E,F))) # label(ruleD9) # label(axiom) # label(non_clause). [assumption].
% 2.33/2.61 11 (all A all B all M (midp(M,B,A) -> midp(M,A,B))) # label(ruleD11) # label(axiom) # label(non_clause). [assumption].
% 2.33/2.61 13 (all A all B all C all D all O (cong(O,A,O,B) & cong(O,A,O,C) & cong(O,A,O,D) -> cyclic(A,B,C,D))) # label(ruleD13) # label(axiom) # label(non_clause). [assumption].
% 2.33/2.61 14 (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].
% 2.33/2.61 15 (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].
% 2.33/2.61 16 (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].
% 2.33/2.61 17 (all A all B all C all D all E (cyclic(A,B,C,D) & cyclic(A,B,C,E) -> cyclic(B,C,D,E))) # label(ruleD17) # label(axiom) # label(non_clause). [assumption].
% 2.33/2.61 19 (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].
% 2.33/2.61 21 (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].
% 2.33/2.61 39 (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].
% 2.33/2.61 40 (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].
% 2.33/2.61 43 (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].
% 2.33/2.61 44 (all A all B all C all P all Q all R (cyclic(A,B,C,P) & cyclic(A,B,C,Q) & cyclic(A,B,C,R) & eqangle(C,A,C,B,R,P,R,Q) -> cong(A,B,P,Q))) # label(ruleD43) # label(axiom) # label(non_clause). [assumption].
% 2.33/2.61 46 (all A all B all C all E all F (midp(E,A,B) & para(E,F,B,C) & coll(F,A,C) -> midp(F,A,C))) # label(ruleD45) # label(axiom) # label(non_clause). [assumption].
% 2.33/2.61 56 (all A all B all M all O (midp(M,A,B) & perp(O,M,A,B) -> cong(O,A,O,B))) # label(ruleD55) # label(axiom) # label(non_clause). [assumption].
% 2.33/2.61 58 (all A all B all P all Q (cong(A,P,B,P) & cong(A,Q,B,Q) & cyclic(A,B,P,Q) -> perp(P,A,A,Q))) # label(ruleD57) # label(axiom) # label(non_clause). [assumption].
% 2.33/2.61 65 (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].
% 2.33/2.61 67 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption].
% 2.33/2.61 68 (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].
% 2.33/2.61 69 (all A all B all C (midp(A,B,C) -> cong(A,B,A,C))) # label(ruleD68) # label(axiom) # label(non_clause). [assumption].
% 2.33/2.61 95 -(all A all B all C all D all Q all P (perp(D,A,B,C) & coll(D,B,C) & perp(Q,D,A,B) & coll(Q,A,B) & perp(P,D,A,C) & coll(P,A,C) -> cyclic(B,Q,P,C))) # label(exemplo6GDDFULL214029) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.33/2.61 109 -coll(A,B,C) | coll(A,C,B) # label(ruleD1) # label(axiom). [clausify(1)].
% 2.33/2.61 110 -coll(A,B,C) | coll(B,A,C) # label(ruleD2) # label(axiom). [clausify(2)].
% 2.33/2.61 111 -coll(A,B,C) | -coll(A,B,D) | coll(C,D,A) # label(ruleD3) # label(axiom). [clausify(3)].
% 2.33/2.61 116 -perp(A,B,C,D) | perp(C,D,A,B) # label(ruleD8) # label(axiom). [clausify(8)].
% 2.33/2.61 117 -perp(A,B,C,D) | -perp(C,D,E,F) | para(A,B,E,F) # label(ruleD9) # label(axiom). [clausify(9)].
% 2.33/2.61 119 -midp(A,B,C) | midp(A,C,B) # label(ruleD11) # label(axiom). [clausify(11)].
% 2.33/2.61 120 -cong(A,B,A,C) | -cong(A,B,A,D) | -cong(A,B,A,E) | cyclic(B,C,D,E) # label(ruleD13) # label(axiom). [clausify(13)].
% 2.33/2.61 121 -cyclic(A,B,C,D) | cyclic(A,B,D,C) # label(ruleD14) # label(axiom). [clausify(14)].
% 2.33/2.61 122 -cyclic(A,B,C,D) | cyclic(A,C,B,D) # label(ruleD15) # label(axiom). [clausify(15)].
% 2.33/2.61 123 -cyclic(A,B,C,D) | cyclic(B,A,C,D) # label(ruleD16) # label(axiom). [clausify(16)].
% 2.33/2.61 124 -cyclic(A,B,C,D) | -cyclic(A,B,C,E) | cyclic(B,C,D,E) # label(ruleD17) # label(axiom). [clausify(17)].
% 2.33/2.61 126 -eqangle(A,B,C,D,E,F,V6,V7) | eqangle(C,D,A,B,V6,V7,E,F) # label(ruleD19) # label(axiom). [clausify(19)].
% 2.33/2.61 128 -eqangle(A,B,C,D,E,F,V6,V7) | eqangle(A,B,E,F,C,D,V6,V7) # label(ruleD21) # label(axiom). [clausify(21)].
% 2.33/2.61 146 -eqangle(A,B,C,D,E,F,C,D) | para(A,B,E,F) # label(ruleD39) # label(axiom). [clausify(39)].
% 2.33/2.61 147 -para(A,B,C,D) | eqangle(A,B,E,F,C,D,E,F) # label(ruleD40) # label(axiom). [clausify(40)].
% 2.33/2.61 150 -eqangle(A,B,A,C,D,B,D,C) | -coll(A,D,C) | cyclic(B,C,A,D) # label(ruleD42b) # label(axiom). [clausify(43)].
% 2.33/2.61 151 -cyclic(A,B,C,D) | -cyclic(A,B,C,E) | -cyclic(A,B,C,F) | -eqangle(C,A,C,B,F,D,F,E) | cong(A,B,D,E) # label(ruleD43) # label(axiom). [clausify(44)].
% 2.33/2.61 153 -midp(A,B,C) | -para(A,D,C,E) | -coll(D,B,E) | midp(D,B,E) # label(ruleD45) # label(axiom). [clausify(46)].
% 2.33/2.61 158 -midp(A,B,C) | -perp(D,A,B,C) | cong(D,B,D,C) # label(ruleD55) # label(axiom). [clausify(56)].
% 2.33/2.61 160 -cong(A,B,C,B) | -cong(A,D,C,D) | -cyclic(A,C,B,D) | perp(B,A,A,D) # label(ruleD57) # label(axiom). [clausify(58)].
% 2.33/2.61 167 -midp(A,B,C) | -para(B,D,C,E) | -para(B,E,C,D) | midp(A,D,E) # label(ruleD64) # label(axiom). [clausify(65)].
% 2.33/2.61 169 -para(A,B,A,C) | coll(A,B,C) # label(ruleD66) # label(axiom). [clausify(67)].
% 2.33/2.61 170 -cong(A,B,A,C) | -coll(A,B,C) | midp(A,B,C) # label(ruleD67) # label(axiom). [clausify(68)].
% 2.33/2.61 171 -midp(A,B,C) | cong(A,B,A,C) # label(ruleD68) # label(axiom). [clausify(69)].
% 2.33/2.61 208 perp(c4,c1,c2,c3) # label(exemplo6GDDFULL214029) # label(negated_conjecture). [clausify(95)].
% 2.33/2.61 209 coll(c4,c2,c3) # label(exemplo6GDDFULL214029) # label(negated_conjecture). [clausify(95)].
% 2.33/2.61 210 perp(c5,c4,c1,c2) # label(exemplo6GDDFULL214029) # label(negated_conjecture). [clausify(95)].
% 2.33/2.61 212 perp(c6,c4,c1,c3) # label(exemplo6GDDFULL214029) # label(negated_conjecture). [clausify(95)].
% 2.33/2.61 213 coll(c6,c1,c3) # label(exemplo6GDDFULL214029) # label(negated_conjecture). [clausify(95)].
% 2.33/2.61 214 -cyclic(c2,c5,c6,c3) # label(exemplo6GDDFULL214029) # label(negated_conjecture). [clausify(95)].
% 2.33/2.61 253 -coll(A,B,C) | coll(C,C,A). [factor(111,a,b)].
% 2.33/2.61 255 -cong(A,B,A,C) | -cong(A,B,A,D) | cyclic(B,C,C,D). [factor(120,a,b)].
% 2.33/2.61 258 -cyclic(A,B,C,D) | cyclic(B,C,D,D). [factor(124,a,b)].
% 2.33/2.61 259 -cyclic(A,B,C,D) | -cyclic(A,B,C,E) | -eqangle(C,A,C,B,E,D,E,D) | cong(A,B,D,D). [factor(151,a,b)].
% 2.33/2.61 267 -midp(A,B,C) | -para(B,D,C,D) | midp(A,D,D). [factor(167,b,c)].
% 2.33/2.61 307 -cong(A,B,A,C) | cyclic(B,C,C,C). [factor(255,a,b)].
% 2.33/2.61 327 -perp(A,B,c4,c1) | para(A,B,c2,c3). [resolve(208,a,117,b)].
% 2.33/2.61 328 -perp(c2,c3,A,B) | para(c4,c1,A,B). [resolve(208,a,117,a)].
% 2.33/2.61 329 perp(c2,c3,c4,c1). [resolve(208,a,116,a)].
% 2.33/2.61 333 coll(c2,c4,c3). [resolve(209,a,110,a)].
% 2.33/2.61 346 -perp(A,B,c5,c4) | para(A,B,c1,c2). [resolve(210,a,117,b)].
% 2.33/2.61 348 perp(c1,c2,c5,c4). [resolve(210,a,116,a)].
% 2.33/2.61 366 -perp(c1,c3,A,B) | para(c6,c4,A,B). [resolve(212,a,117,a)].
% 2.33/2.61 367 perp(c1,c3,c6,c4). [resolve(212,a,116,a)].
% 2.33/2.61 373 coll(c3,c3,c6). [resolve(253,a,213,a)].
% 2.33/2.61 375 coll(c3,c3,c4). [resolve(253,a,209,a)].
% 2.33/2.61 376 coll(c3,c3,c2). [resolve(333,a,253,a)].
% 2.33/2.61 379 coll(c2,c3,c4). [resolve(333,a,109,a)].
% 2.33/2.61 401 -coll(c3,c3,A) | coll(A,c6,c3). [resolve(373,a,111,b)].
% 2.33/2.61 408 coll(c4,c4,c3). [resolve(375,a,253,a)].
% 2.33/2.61 415 coll(c3,c2,c3). [resolve(376,a,109,a)].
% 2.33/2.61 416 coll(c4,c4,c2). [resolve(379,a,253,a)].
% 2.33/2.61 467 coll(c4,c3,c4). [resolve(408,a,109,a)].
% 2.33/2.61 479 coll(c4,c2,c4). [resolve(416,a,109,a)].
% 2.33/2.61 528 coll(c4,c4,c4). [resolve(467,a,253,a)].
% 2.33/2.61 539 para(c4,c1,c4,c1). [resolve(329,a,328,a)].
% 2.33/2.61 540 para(c2,c3,c2,c3). [resolve(329,a,327,a)].
% 2.33/2.61 557 coll(c2,c4,c4). [resolve(479,a,110,a)].
% 2.33/2.61 674 -midp(A,c4,c4) | midp(A,c1,c1). [resolve(539,a,267,b)].
% 2.33/2.61 681 coll(c4,c1,c1). [resolve(539,a,169,a)].
% 2.33/2.61 684 eqangle(c4,c1,A,B,c4,c1,A,B). [resolve(539,a,147,a)].
% 2.33/2.61 686 coll(c1,c1,c4). [resolve(681,a,253,a)].
% 2.33/2.61 694 -coll(c1,c1,A) | coll(c4,A,c1). [resolve(686,a,111,a)].
% 2.33/2.61 715 -midp(c2,A,c2) | -coll(c3,A,c3) | midp(c3,A,c3). [resolve(540,a,153,b)].
% 2.33/2.61 1011 para(c1,c2,c1,c2). [resolve(346,a,348,a)].
% 2.33/2.61 1031 -midp(A,c1,c1) | midp(A,c2,c2). [resolve(1011,a,267,b)].
% 2.33/2.61 1149 coll(c4,c6,c3). [resolve(401,a,375,a)].
% 2.33/2.61 1156 coll(c6,c4,c3). [resolve(1149,a,110,a)].
% 2.33/2.61 1167 coll(c6,c3,c4). [resolve(1156,a,109,a)].
% 2.33/2.61 1187 coll(c4,c4,c6). [resolve(1167,a,253,a)].
% 2.33/2.61 1250 para(c6,c4,c6,c4). [resolve(366,a,367,a)].
% 2.33/2.61 1568 eqangle(c6,c4,A,B,c6,c4,A,B). [resolve(1250,a,147,a)].
% 2.33/2.61 1680 -coll(c4,c4,A) | cyclic(c1,A,c4,c4). [resolve(684,a,150,a)].
% 2.33/2.61 1681 eqangle(c4,c1,c4,c1,A,B,A,B). [resolve(684,a,128,a)].
% 2.33/2.61 1682 eqangle(A,B,c4,c1,A,B,c4,c1). [resolve(684,a,126,a)].
% 2.33/2.61 1898 -cyclic(c4,c4,c6,c4) | -cyclic(c4,c4,c6,c6) | cong(c4,c4,c4,c4). [resolve(1568,a,259,c)].
% 2.33/2.61 1953 cyclic(c1,c6,c4,c4). [resolve(1680,a,1187,a)].
% 2.33/2.61 1957 cyclic(c1,c2,c4,c4). [resolve(1680,a,416,a)].
% 2.33/2.61 1962 cyclic(c6,c4,c4,c4). [resolve(1953,a,258,a)].
% 2.33/2.61 1983 cyclic(c1,c4,c6,c4). [resolve(1953,a,122,a)].
% 2.33/2.61 2052 cyclic(c2,c4,c4,c4). [resolve(1957,a,258,a)].
% 2.33/2.61 2072 cyclic(c2,c1,c4,c4). [resolve(1957,a,123,a)].
% 2.33/2.61 2073 cyclic(c1,c4,c2,c4). [resolve(1957,a,122,a)].
% 2.33/2.61 2115 cyclic(c4,c6,c4,c4). [resolve(1962,a,123,a)].
% 2.33/2.61 2164 cyclic(c1,c4,c4,c6). [resolve(1983,a,121,a)].
% 2.33/2.61 2309 cyclic(c4,c2,c4,c4). [resolve(2052,a,123,a)].
% 2.33/2.61 2330 cyclic(c2,c4,c1,c4). [resolve(2072,a,122,a)].
% 2.33/2.61 2351 cyclic(c4,c1,c2,c4). [resolve(2073,a,123,a)].
% 2.33/2.61 2352 cyclic(c1,c4,c4,c2). [resolve(2073,a,121,a)].
% 2.33/2.61 2435 cyclic(c4,c4,c6,c4). [resolve(2115,a,122,a)].
% 2.33/2.61 2436 -cyclic(c4,c4,c6,c6) | cong(c4,c4,c4,c4). [back_unit_del(1898),unit_del(a,2435)].
% 2.33/2.61 2481 cyclic(c4,c4,c6,c6). [resolve(2164,a,258,a)].
% 2.33/2.61 2502 cong(c4,c4,c4,c4). [back_unit_del(2436),unit_del(a,2481)].
% 2.33/2.61 2955 cyclic(c4,c4,c2,c4). [resolve(2309,a,122,a)].
% 2.33/2.61 2976 cyclic(c4,c2,c1,c4). [resolve(2330,a,123,a)].
% 2.33/2.61 2999 cyclic(c4,c1,c4,c2). [resolve(2351,a,121,a)].
% 2.33/2.61 3000 cyclic(c4,c4,c2,c2). [resolve(2352,a,258,a)].
% 2.33/2.61 3285 midp(c4,c4,c4). [resolve(2502,a,170,a),unit_del(a,528)].
% 2.33/2.61 3295 midp(c4,c1,c1). [resolve(3285,a,674,a)].
% 2.33/2.61 3427 midp(c4,c2,c2). [resolve(3295,a,1031,a)].
% 2.33/2.61 3556 cong(c4,c2,c4,c2). [resolve(3427,a,171,a)].
% 2.33/2.61 4418 perp(c2,c4,c4,c4). [resolve(2955,a,160,c),unit_del(a,3556),unit_del(b,2502)].
% 2.33/2.61 4449 cyclic(c4,c2,c4,c1). [resolve(2976,a,121,a)].
% 2.33/2.61 4469 cyclic(c1,c4,c2,c2). [resolve(2999,a,258,a)].
% 2.33/2.61 4491 cyclic(c4,c2,c2,c2). [resolve(3000,a,258,a)].
% 2.33/2.61 6425 cong(c2,c4,c2,c4). [resolve(4418,a,158,b),unit_del(a,3285)].
% 2.33/2.61 6468 cyclic(c2,c4,c1,c1). [resolve(4449,a,258,a)].
% 2.33/2.61 6509 -cyclic(c1,c4,c2,A) | cyclic(c4,c2,c2,A). [resolve(4469,a,124,a)].
% 2.33/2.61 6594 -cyclic(c4,c2,c2,A) | cyclic(c2,c2,c2,A). [resolve(4491,a,124,a)].
% 2.33/2.61 8173 midp(c2,c4,c4). [resolve(6425,a,170,a),unit_del(a,557)].
% 2.33/2.61 8184 midp(c2,c1,c1). [resolve(8173,a,674,a)].
% 2.33/2.61 8249 midp(c2,c2,c2). [resolve(8184,a,1031,a)].
% 2.33/2.61 8296 midp(c3,c2,c3). [resolve(8249,a,715,a),unit_del(a,415)].
% 2.33/2.61 8344 midp(c3,c3,c2). [resolve(8296,a,119,a)].
% 2.33/2.61 8364 cong(c3,c3,c3,c2). [resolve(8344,a,171,a)].
% 2.33/2.61 8406 cyclic(c4,c2,c1,c1). [resolve(6468,a,123,a)].
% 2.33/2.61 10381 cyclic(c3,c2,c2,c2). [resolve(8364,a,307,a)].
% 2.33/2.61 10423 cyclic(c4,c1,c2,c1). [resolve(8406,a,122,a)].
% 2.33/2.61 11767 cyclic(c2,c3,c2,c2). [resolve(10381,a,123,a)].
% 2.33/2.61 11822 cyclic(c1,c4,c2,c1). [resolve(10423,a,123,a)].
% 2.33/2.61 12656 cyclic(c2,c2,c3,c2). [resolve(11767,a,122,a)].
% 2.33/2.61 12718 cyclic(c1,c4,c1,c2). [resolve(11822,a,121,a)].
% 2.33/2.61 13211 cyclic(c2,c2,c2,c3). [resolve(12656,a,121,a)].
% 2.33/2.61 13282 cyclic(c1,c1,c4,c2). [resolve(12718,a,122,a)].
% 2.33/2.61 13905 -cyclic(c2,c2,c2,A) | cyclic(c2,c2,A,c3). [resolve(13211,a,124,b)].
% 2.33/2.61 13938 -cyclic(c1,c1,c4,A) | cyclic(c1,c4,A,c2). [resolve(13282,a,124,b)].
% 2.33/2.61 13939 -cyclic(c1,c1,c4,A) | cyclic(c1,c4,c2,A). [resolve(13282,a,124,a)].
% 2.33/2.61 18828 -coll(c4,A,c1) | cyclic(c1,c1,c4,A). [resolve(1681,a,150,a)].
% 2.33/2.61 18845 para(A,B,A,B). [resolve(1682,a,146,a)].
% 2.33/2.61 18850 coll(A,B,B). [resolve(18845,a,169,a)].
% 2.33/2.61 18854 coll(A,A,B). [resolve(18850,a,253,a)].
% 2.33/2.61 18891 coll(c4,A,c1). [back_unit_del(694),unit_del(a,18854)].
% 2.33/2.61 19019 cyclic(c1,c1,c4,A). [back_unit_del(18828),unit_del(a,18891)].
% 2.33/2.61 19206 cyclic(c1,c4,c2,A). [back_unit_del(13939),unit_del(a,19019)].
% 2.33/2.61 19207 cyclic(c1,c4,A,c2). [back_unit_del(13938),unit_del(a,19019)].
% 2.33/2.61 19223 cyclic(c4,c2,c2,A). [back_unit_del(6509),unit_del(a,19206)].
% 2.33/2.61 19278 cyclic(c2,c2,c2,A). [back_unit_del(6594),unit_del(a,19223)].
% 2.33/2.61 19352 cyclic(c2,c2,A,c3). [back_unit_del(13905),unit_del(a,19278)].
% 2.33/2.61 19440 cyclic(c1,c4,A,B). [resolve(19019,a,124,b),unit_del(a,19019)].
% 2.33/2.61 19458 cyclic(c4,A,c2,B). [resolve(19207,a,124,a),unit_del(a,19440)].
% 2.33/2.61 19520 cyclic(c2,c2,A,B). [resolve(19223,a,124,b),unit_del(a,19458)].
% 2.33/2.61 19795 cyclic(c2,A,B,c3). [resolve(19352,a,124,b),unit_del(a,19520)].
% 2.33/2.61 19796 $F. [resolve(19795,a,214,a)].
% 2.33/2.61
% 2.33/2.61 % SZS output end Refutation
% 2.33/2.61 ============================== end of proof ==========================
% 2.33/2.61
% 2.33/2.61 ============================== STATISTICS ============================
% 2.33/2.61
% 2.33/2.61 Given=3352. Generated=60577. Kept=19679. proofs=1.
% 2.33/2.61 Usable=2619. Sos=9256. Demods=0. Limbo=0, Disabled=7953. Hints=0.
% 2.33/2.61 Megabytes=13.19.
% 2.33/2.61 User_CPU=1.46, System_CPU=0.04, Wall_clock=2.
% 2.33/2.61
% 2.33/2.61 ============================== end of statistics =====================
% 2.33/2.61
% 2.33/2.61 ============================== end of search =========================
% 2.33/2.61
% 2.33/2.61 THEOREM PROVED
% 2.33/2.61 % SZS status Theorem
% 2.33/2.61
% 2.33/2.61 Exiting with 1 proof.
% 2.33/2.61
% 2.33/2.61 Process 4940 exit (max_proofs) Sat Jun 18 02:27:31 2022
% 2.33/2.61 Prover9 interrupted
%------------------------------------------------------------------------------