TSTP Solution File: GEO554+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GEO554+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n007.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 05:56:55 EDT 2022
% Result : Theorem 7.32s 7.69s
% Output : Refutation 7.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEO554+1 : TPTP v8.1.0. Released v7.5.0.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.33 % Computer : n007.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sat Jun 18 02:02:43 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.82/1.09 ============================== Prover9 ===============================
% 0.82/1.09 Prover9 (32) version 2009-11A, November 2009.
% 0.82/1.09 Process 8531 was started by sandbox2 on n007.cluster.edu,
% 0.82/1.09 Sat Jun 18 02:02:43 2022
% 0.82/1.09 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_8368_n007.cluster.edu".
% 0.82/1.09 ============================== end of head ===========================
% 0.82/1.09
% 0.82/1.09 ============================== INPUT =================================
% 0.82/1.09
% 0.82/1.09 % Reading from file /tmp/Prover9_8368_n007.cluster.edu
% 0.82/1.09
% 0.82/1.09 set(prolog_style_variables).
% 0.82/1.09 set(auto2).
% 0.82/1.09 % set(auto2) -> set(auto).
% 0.82/1.09 % set(auto) -> set(auto_inference).
% 0.82/1.09 % set(auto) -> set(auto_setup).
% 0.82/1.09 % set(auto_setup) -> set(predicate_elim).
% 0.82/1.09 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.82/1.09 % set(auto) -> set(auto_limits).
% 0.82/1.09 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.82/1.09 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.82/1.09 % set(auto) -> set(auto_denials).
% 0.82/1.09 % set(auto) -> set(auto_process).
% 0.82/1.09 % set(auto2) -> assign(new_constants, 1).
% 0.82/1.09 % set(auto2) -> assign(fold_denial_max, 3).
% 0.82/1.09 % set(auto2) -> assign(max_weight, "200.000").
% 0.82/1.09 % set(auto2) -> assign(max_hours, 1).
% 0.82/1.09 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.82/1.09 % set(auto2) -> assign(max_seconds, 0).
% 0.82/1.09 % set(auto2) -> assign(max_minutes, 5).
% 0.82/1.09 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.82/1.09 % set(auto2) -> set(sort_initial_sos).
% 0.82/1.09 % set(auto2) -> assign(sos_limit, -1).
% 0.82/1.09 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.82/1.09 % set(auto2) -> assign(max_megs, 400).
% 0.82/1.09 % set(auto2) -> assign(stats, some).
% 0.82/1.09 % set(auto2) -> clear(echo_input).
% 0.82/1.09 % set(auto2) -> set(quiet).
% 0.82/1.09 % set(auto2) -> clear(print_initial_clauses).
% 0.82/1.09 % set(auto2) -> clear(print_given).
% 0.82/1.09 assign(lrs_ticks,-1).
% 0.82/1.09 assign(sos_limit,10000).
% 0.82/1.09 assign(order,kbo).
% 0.82/1.09 set(lex_order_vars).
% 0.82/1.09 clear(print_given).
% 0.82/1.09
% 0.82/1.09 % formulas(sos). % not echoed (95 formulas)
% 0.82/1.09
% 0.82/1.09 ============================== end of input ==========================
% 0.82/1.09
% 0.82/1.09 % From the command line: assign(max_seconds, 300).
% 0.82/1.09
% 0.82/1.09 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.82/1.09
% 0.82/1.09 % Formulas that are not ordinary clauses:
% 0.82/1.09 1 (all A all B all C (coll(A,B,C) -> coll(A,C,B))) # label(ruleD1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 2 (all A all B all C (coll(A,B,C) -> coll(B,A,C))) # label(ruleD2) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 11 (all A all B all M (midp(M,B,A) -> midp(M,A,B))) # label(ruleD11) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 67 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 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].
% 0.82/1.09 69 (all A all B all C (midp(A,B,C) -> cong(A,B,A,C))) # label(ruleD68) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 70 (all A all B all C (midp(A,B,C) -> coll(A,B,C))) # label(ruleD69) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 95 -(all A all B all C all D all E all F all G all NWPNT1 all NWPNT2 all NWPNT3 all NWPNT4 all NWPNT5 all NWPNT6 all NWPNT7 all NWPNT8 all NWPNT9 (perp(C,A,C,B) & circle(A,C,NWPNT1,NWPNT2) & circle(B,C,NWPNT3,NWPNT4) & circle(A,C,D,NWPNT5) & coll(C,D,E) & circle(B,C,E,NWPNT6) & coll(B,E,F) & circle(B,C,F,NWPNT7) & circle(A,C,G,NWPNT8) & circle(B,C,G,NWPNT9) -> coll(D,F,G))) # label(exemplo6GDDFULL012014) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.82/1.10
% 0.82/1.10 ============================== end of process non-clausal formulas ===
% 0.82/1.10
% 0.82/1.10 ============================== PROCESS INITIAL CLAUSES ===============
% 0.82/1.10
% 0.82/1.10 ============================== PREDICATE ELIMINATION =================
% 0.82/1.10 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)].
% 0.82/1.10 97 -cong(A,B,A,C) | -cong(A,B,A,D) | circle(A,B,C,D) # label(ruleD12) # label(axiom). [clausify(12)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 100 -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)].
% 0.82/1.10 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)].
% 0.82/1.10 101 -circle(A,B,C,D) | -coll(A,B,D) | perp(B,C,C,D) # label(ruleD53) # label(axiom). [clausify(54)].
% 0.82/1.10 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)].
% 0.82/1.10 102 -circle(A,B,C,D) | perp(f12(B,C,D,A),B,B,A) # label(ruleX11) # label(axiom). [clausify(87)].
% 0.82/1.10 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)].
% 0.82/1.10 103 -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)].
% 0.82/1.10 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)].
% 0.82/1.10 104 -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)].
% 0.82/1.10 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)].
% 0.82/1.10 105 -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)].
% 0.82/1.10 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)].
% 0.82/1.10 106 -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)].
% 0.82/1.10 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)].
% 0.82/1.10 107 -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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 108 -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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 109 circle(c1,c3,c8,c9) # label(exemplo6GDDFULL012014) # label(negated_conjecture). [clausify(95)].
% 0.82/1.10 Derived: -perp(c1,c3,c3,A) | eqangle(c3,A,c3,c8,c9,c3,c9,c8). [resolve(109,a,96,a)].
% 0.82/1.10 Derived: -eqangle(c3,A,c3,c8,c9,c3,c9,c8) | perp(c1,c3,c3,A). [resolve(109,a,98,a)].
% 0.82/1.10 Derived: -midp(A,c8,c9) | eqangle(c3,c8,c3,c9,c1,c8,c1,A). [resolve(109,a,99,a)].
% 0.82/1.10 Derived: -coll(A,c8,c9) | -eqangle(c3,c8,c3,c9,c1,c8,c1,A) | midp(A,c8,c9). [resolve(109,a,100,a)].
% 0.82/1.10 Derived: -coll(c1,c3,c9) | perp(c3,c8,c8,c9). [resolve(109,a,101,a)].
% 0.82/1.10 Derived: perp(f12(c3,c8,c9,c1),c3,c3,c1). [resolve(109,a,102,a)].
% 0.82/1.10 Derived: -cong(c1,c3,c1,A) | -cong(B,c3,B,c8) | B = c1 | coll(f13(c3,c8,c9,A,c1,B),c3,c9). [resolve(109,a,103,a)].
% 0.82/1.10 Derived: -cong(c1,c3,c1,A) | -cong(B,c3,B,c8) | B = c1 | cong(f13(c3,c8,c9,A,c1,B),B,B,c3). [resolve(109,a,104,a)].
% 0.82/1.10 Derived: -cong(c1,c3,c1,A) | -cong(B,c3,B,c8) | B = c1 | coll(f14(c3,c8,c9,A,c1,B),c8,A). [resolve(109,a,105,a)].
% 0.82/1.10 Derived: -cong(c1,c3,c1,A) | -cong(B,c3,B,c8) | B = c1 | cong(f14(c3,c8,c9,A,c1,B),B,B,c3). [resolve(109,a,106,a)].
% 0.82/1.10 110 circle(c2,c3,c10,c11) # label(exemplo6GDDFULL012014) # label(negated_conjecture). [clausify(95)].
% 0.82/1.10 Derived: -perp(c2,c3,c3,A) | eqangle(c3,A,c3,c10,c11,c3,c11,c10). [resolve(110,a,96,a)].
% 0.82/1.10 Derived: -eqangle(c3,A,c3,c10,c11,c3,c11,c10) | perp(c2,c3,c3,A). [resolve(110,a,98,a)].
% 0.82/1.10 Derived: -midp(A,c10,c11) | eqangle(c3,c10,c3,c11,c2,c10,c2,A). [resolve(110,a,99,a)].
% 0.82/1.10 Derived: -coll(A,c10,c11) | -eqangle(c3,c10,c3,c11,c2,c10,c2,A) | midp(A,c10,c11). [resolve(110,a,100,a)].
% 0.82/1.10 Derived: -coll(c2,c3,c11) | perp(c3,c10,c10,c11). [resolve(110,a,101,a)].
% 0.82/1.10 Derived: perp(f12(c3,c10,c11,c2),c3,c3,c2). [resolve(110,a,102,a)].
% 0.82/1.10 Derived: -cong(c2,c3,c2,A) | -cong(B,c3,B,c10) | B = c2 | coll(f13(c3,c10,c11,A,c2,B),c3,c11). [resolve(110,a,103,a)].
% 0.82/1.10 Derived: -cong(c2,c3,c2,A) | -cong(B,c3,B,c10) | B = c2 | cong(f13(c3,c10,c11,A,c2,B),B,B,c3). [resolve(110,a,104,a)].
% 0.82/1.10 Derived: -cong(c2,c3,c2,A) | -cong(B,c3,B,c10) | B = c2 | coll(f14(c3,c10,c11,A,c2,B),c10,A). [resolve(110,a,105,a)].
% 0.82/1.10 Derived: -cong(c2,c3,c2,A) | -cong(B,c3,B,c10) | B = c2 | cong(f14(c3,c10,c11,A,c2,B),B,B,c3). [resolve(110,a,106,a)].
% 0.82/1.10 111 circle(c1,c3,c4,c12) # label(exemplo6GDDFULL012014) # label(negated_conjecture). [clausify(95)].
% 0.82/1.10 Derived: -perp(c1,c3,c3,A) | eqangle(c3,A,c3,c4,c12,c3,c12,c4). [resolve(111,a,96,a)].
% 0.82/1.10 Derived: -eqangle(c3,A,c3,c4,c12,c3,c12,c4) | perp(c1,c3,c3,A). [resolve(111,a,98,a)].
% 0.82/1.10 Derived: -midp(A,c4,c12) | eqangle(c3,c4,c3,c12,c1,c4,c1,A). [resolve(111,a,99,a)].
% 0.82/1.10 Derived: -coll(A,c4,c12) | -eqangle(c3,c4,c3,c12,c1,c4,c1,A) | midp(A,c4,c12). [resolve(111,a,100,a)].
% 0.82/1.10 Derived: -coll(c1,c3,c12) | perp(c3,c4,c4,c12). [resolve(111,a,101,a)].
% 0.82/1.10 Derived: perp(f12(c3,c4,c12,c1),c3,c3,c1). [resolve(111,a,102,a)].
% 0.82/1.10 Derived: -cong(c1,c3,c1,A) | -cong(B,c3,B,c4) | B = c1 | coll(f13(c3,c4,c12,A,c1,B),c3,c12). [resolve(111,a,103,a)].
% 0.82/1.10 Derived: -cong(c1,c3,c1,A) | -cong(B,c3,B,c4) | B = c1 | cong(f13(c3,c4,c12,A,c1,B),B,B,c3). [resolve(111,a,104,a)].
% 0.82/1.10 Derived: -cong(c1,c3,c1,A) | -cong(B,c3,B,c4) | B = c1 | coll(f14(c3,c4,c12,A,c1,B),c4,A). [resolve(111,a,105,a)].
% 0.82/1.10 Derived: -cong(c1,c3,c1,A) | -cong(B,c3,B,c4) | B = c1 | cong(f14(c3,c4,c12,A,c1,B),B,B,c3). [resolve(111,a,106,a)].
% 0.82/1.10 112 circle(c2,c3,c5,c13) # label(exemplo6GDDFULL012014) # label(negated_conjecture). [clausify(95)].
% 0.82/1.10 Derived: -perp(c2,c3,c3,A) | eqangle(c3,A,c3,c5,c13,c3,c13,c5). [resolve(112,a,96,a)].
% 0.82/1.10 Derived: -eqangle(c3,A,c3,c5,c13,c3,c13,c5) | perp(c2,c3,c3,A). [resolve(112,a,98,a)].
% 0.82/1.10 Derived: -midp(A,c5,c13) | eqangle(c3,c5,c3,c13,c2,c5,c2,A). [resolve(112,a,99,a)].
% 0.82/1.10 Derived: -coll(A,c5,c13) | -eqangle(c3,c5,c3,c13,c2,c5,c2,A) | midp(A,c5,c13). [resolve(112,a,100,a)].
% 0.82/1.10 Derived: -coll(c2,c3,c13) | perp(c3,c5,c5,c13). [resolve(112,a,101,a)].
% 0.82/1.10 Derived: perp(f12(c3,c5,c13,c2),c3,c3,c2). [resolve(112,a,102,a)].
% 0.82/1.10 Derived: -cong(c2,c3,c2,A) | -cong(B,c3,B,c5) | B = c2 | coll(f13(c3,c5,c13,A,c2,B),c3,c13). [resolve(112,a,103,a)].
% 0.82/1.10 Derived: -cong(c2,c3,c2,A) | -cong(B,c3,B,c5) | B = c2 | cong(f13(c3,c5,c13,A,c2,B),B,B,c3). [resolve(112,a,104,a)].
% 0.82/1.10 Derived: -cong(c2,c3,c2,A) | -cong(B,c3,B,c5) | B = c2 | coll(f14(c3,c5,c13,A,c2,B),c5,A). [resolve(112,a,105,a)].
% 0.82/1.10 Derived: -cong(c2,c3,c2,A) | -cong(B,c3,B,c5) | B = c2 | cong(f14(c3,c5,c13,A,c2,B),B,B,c3). [resolve(112,a,106,a)].
% 0.82/1.10 113 circle(c2,c3,c6,c14) # label(exemplo6GDDFULL012014) # label(negated_conjecture). [clausify(95)].
% 0.82/1.10 Derived: -perp(c2,c3,c3,A) | eqangle(c3,A,c3,c6,c14,c3,c14,c6). [resolve(113,a,96,a)].
% 0.82/1.10 Derived: -eqangle(c3,A,c3,c6,c14,c3,c14,c6) | perp(c2,c3,c3,A). [resolve(113,a,98,a)].
% 1.43/1.71 Derived: -midp(A,c6,c14) | eqangle(c3,c6,c3,c14,c2,c6,c2,A). [resolve(113,a,99,a)].
% 1.43/1.71 Derived: -coll(A,c6,c14) | -eqangle(c3,c6,c3,c14,c2,c6,c2,A) | midp(A,c6,c14). [resolve(113,a,100,a)].
% 1.43/1.71 Derived: -coll(c2,c3,c14) | perp(c3,c6,c6,c14). [resolve(113,a,101,a)].
% 1.43/1.71 Derived: perp(f12(c3,c6,c14,c2),c3,c3,c2). [resolve(113,a,102,a)].
% 1.43/1.71 Derived: -cong(c2,c3,c2,A) | -cong(B,c3,B,c6) | B = c2 | coll(f13(c3,c6,c14,A,c2,B),c3,c14). [resolve(113,a,103,a)].
% 1.43/1.71 Derived: -cong(c2,c3,c2,A) | -cong(B,c3,B,c6) | B = c2 | cong(f13(c3,c6,c14,A,c2,B),B,B,c3). [resolve(113,a,104,a)].
% 1.43/1.71 Derived: -cong(c2,c3,c2,A) | -cong(B,c3,B,c6) | B = c2 | coll(f14(c3,c6,c14,A,c2,B),c6,A). [resolve(113,a,105,a)].
% 1.43/1.71 Derived: -cong(c2,c3,c2,A) | -cong(B,c3,B,c6) | B = c2 | cong(f14(c3,c6,c14,A,c2,B),B,B,c3). [resolve(113,a,106,a)].
% 1.43/1.71 114 circle(c1,c3,c7,c15) # label(exemplo6GDDFULL012014) # label(negated_conjecture). [clausify(95)].
% 1.43/1.71 Derived: -perp(c1,c3,c3,A) | eqangle(c3,A,c3,c7,c15,c3,c15,c7). [resolve(114,a,96,a)].
% 1.43/1.71 Derived: -eqangle(c3,A,c3,c7,c15,c3,c15,c7) | perp(c1,c3,c3,A). [resolve(114,a,98,a)].
% 1.43/1.71 Derived: -midp(A,c7,c15) | eqangle(c3,c7,c3,c15,c1,c7,c1,A). [resolve(114,a,99,a)].
% 1.43/1.71 Derived: -coll(A,c7,c15) | -eqangle(c3,c7,c3,c15,c1,c7,c1,A) | midp(A,c7,c15). [resolve(114,a,100,a)].
% 1.43/1.71 Derived: -coll(c1,c3,c15) | perp(c3,c7,c7,c15). [resolve(114,a,101,a)].
% 1.43/1.71 Derived: perp(f12(c3,c7,c15,c1),c3,c3,c1). [resolve(114,a,102,a)].
% 1.43/1.71 Derived: -cong(c1,c3,c1,A) | -cong(B,c3,B,c7) | B = c1 | coll(f13(c3,c7,c15,A,c1,B),c3,c15). [resolve(114,a,103,a)].
% 1.43/1.71 Derived: -cong(c1,c3,c1,A) | -cong(B,c3,B,c7) | B = c1 | cong(f13(c3,c7,c15,A,c1,B),B,B,c3). [resolve(114,a,104,a)].
% 1.43/1.71 Derived: -cong(c1,c3,c1,A) | -cong(B,c3,B,c7) | B = c1 | coll(f14(c3,c7,c15,A,c1,B),c7,A). [resolve(114,a,105,a)].
% 1.43/1.71 Derived: -cong(c1,c3,c1,A) | -cong(B,c3,B,c7) | B = c1 | cong(f14(c3,c7,c15,A,c1,B),B,B,c3). [resolve(114,a,106,a)].
% 1.43/1.71 115 circle(c2,c3,c7,c16) # label(exemplo6GDDFULL012014) # label(negated_conjecture). [clausify(95)].
% 1.43/1.71 Derived: -perp(c2,c3,c3,A) | eqangle(c3,A,c3,c7,c16,c3,c16,c7). [resolve(115,a,96,a)].
% 1.43/1.71 Derived: -eqangle(c3,A,c3,c7,c16,c3,c16,c7) | perp(c2,c3,c3,A). [resolve(115,a,98,a)].
% 1.43/1.71 Derived: -midp(A,c7,c16) | eqangle(c3,c7,c3,c16,c2,c7,c2,A). [resolve(115,a,99,a)].
% 1.43/1.71 Derived: -coll(A,c7,c16) | -eqangle(c3,c7,c3,c16,c2,c7,c2,A) | midp(A,c7,c16). [resolve(115,a,100,a)].
% 1.43/1.71 Derived: -coll(c2,c3,c16) | perp(c3,c7,c7,c16). [resolve(115,a,101,a)].
% 1.43/1.71 Derived: perp(f12(c3,c7,c16,c2),c3,c3,c2). [resolve(115,a,102,a)].
% 1.43/1.71 Derived: -cong(c2,c3,c2,A) | -cong(B,c3,B,c7) | B = c2 | coll(f13(c3,c7,c16,A,c2,B),c3,c16). [resolve(115,a,103,a)].
% 1.43/1.71 Derived: -cong(c2,c3,c2,A) | -cong(B,c3,B,c7) | B = c2 | cong(f13(c3,c7,c16,A,c2,B),B,B,c3). [resolve(115,a,104,a)].
% 1.43/1.71 Derived: -cong(c2,c3,c2,A) | -cong(B,c3,B,c7) | B = c2 | coll(f14(c3,c7,c16,A,c2,B),c7,A). [resolve(115,a,105,a)].
% 1.43/1.71 Derived: -cong(c2,c3,c2,A) | -cong(B,c3,B,c7) | B = c2 | cong(f14(c3,c7,c16,A,c2,B),B,B,c3). [resolve(115,a,106,a)].
% 1.43/1.71
% 1.43/1.71 ============================== end predicate elimination =============
% 1.43/1.71
% 1.43/1.71 Auto_denials: (non-Horn, no changes).
% 1.43/1.71
% 1.43/1.71 Term ordering decisions:
% 1.43/1.71 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. c13=1. c14=1. c15=1. c16=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.
% 1.43/1.71
% 1.43/1.71 ============================== end of process initial clauses ========
% 1.43/1.71
% 1.43/1.71 ============================== CLAUSES FOR SEARCH ====================
% 1.43/1.71
% 1.43/1.71 ============================== end of clauses for search =============
% 1.43/1.71
% 1.43/1.71 ============================== SEARCH ================================
% 1.43/1.71
% 1.43/1.71 % Starting search at 0.05 seconds.
% 1.43/1.71
% 1.43/1.71 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 2147483647 (0.00 of 0.14 sec).
% 1.43/1.71
% 1.43/1.71 Low Water (keep): wt=40.000, iters=3337
% 1.43/1.71
% 1.43/1.71 Low Water (keep): wt=39.000, iters=3340
% 1.43/1.71
% 1.43/1.71 Low Water (keep): wt=35.000, iters=3333
% 1.43/1.71
% 1.43/1.71 Low Water (keep): wt=34.000, iters=3345
% 1.43/1.71
% 1.43/1.71 Low Water (keep): wt=27.000, iters=3336
% 1.43/1.71
% 1.43/1.71 Low Water (keep): wt=26.000, iters=3348
% 1.43/1.71
% 1.43/1.71 Low Water (keep): wt=23.000, iters=3346
% 1.43/1.71
% 1.43/1.71 Low Water (keep): wt=22.000, iters=3348
% 7.32/7.69
% 7.32/7.69 Low Water (keep): wt=21.000, iters=3445
% 7.32/7.69
% 7.32/7.69 Low Water (keep): wt=19.000, iters=3350
% 7.32/7.69
% 7.32/7.69 Low Water (keep): wt=18.000, iters=3351
% 7.32/7.69
% 7.32/7.69 Low Water (keep): wt=17.000, iters=3422
% 7.32/7.69
% 7.32/7.69 Low Water (keep): wt=16.000, iters=3428
% 7.32/7.69
% 7.32/7.69 Low Water (keep): wt=15.000, iters=3370
% 7.32/7.69
% 7.32/7.69 Low Water (keep): wt=14.000, iters=3389
% 7.32/7.69
% 7.32/7.69 Low Water (displace): id=7723, wt=40.000
% 7.32/7.69
% 7.32/7.69 Low Water (displace): id=7737, wt=36.000
% 7.32/7.69
% 7.32/7.69 Low Water (displace): id=3618, wt=35.000
% 7.32/7.69
% 7.32/7.69 Low Water (displace): id=7754, wt=34.000
% 7.32/7.69
% 7.32/7.69 Low Water (displace): id=7758, wt=32.000
% 7.32/7.69
% 7.32/7.69 Low Water (displace): id=7755, wt=30.000
% 7.32/7.69
% 7.32/7.69 Low Water (displace): id=7738, wt=29.000
% 7.32/7.69
% 7.32/7.69 Low Water (displace): id=7733, wt=27.000
% 7.32/7.69
% 7.32/7.69 Low Water (displace): id=7808, wt=26.000
% 7.32/7.69
% 7.32/7.69 Low Water (keep): wt=13.000, iters=3340
% 7.32/7.69
% 7.32/7.69 Low Water (displace): id=14331, wt=11.000
% 7.32/7.69
% 7.32/7.69 Low Water (displace): id=14441, wt=10.000
% 7.32/7.69
% 7.32/7.69 Low Water (keep): wt=12.000, iters=3373
% 7.32/7.69
% 7.32/7.69 Low Water (displace): id=14842, wt=7.000
% 7.32/7.69
% 7.32/7.69 Low Water (keep): wt=11.000, iters=3338
% 7.32/7.69
% 7.32/7.69 ============================== PROOF =================================
% 7.32/7.69 % SZS status Theorem
% 7.32/7.69 % SZS output start Refutation
% 7.32/7.69
% 7.32/7.69 % Proof 1 at 6.53 (+ 0.09) seconds.
% 7.32/7.69 % Length of proof is 28.
% 7.32/7.69 % Level of proof is 10.
% 7.32/7.69 % Maximum clause weight is 18.000.
% 7.32/7.69 % Given clauses 10771.
% 7.32/7.69
% 7.32/7.69 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].
% 7.32/7.69 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].
% 7.32/7.69 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].
% 7.32/7.69 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].
% 7.32/7.69 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].
% 7.32/7.69 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].
% 7.32/7.69 67 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption].
% 7.32/7.69 95 -(all A all B all C all D all E all F all G all NWPNT1 all NWPNT2 all NWPNT3 all NWPNT4 all NWPNT5 all NWPNT6 all NWPNT7 all NWPNT8 all NWPNT9 (perp(C,A,C,B) & circle(A,C,NWPNT1,NWPNT2) & circle(B,C,NWPNT3,NWPNT4) & circle(A,C,D,NWPNT5) & coll(C,D,E) & circle(B,C,E,NWPNT6) & coll(B,E,F) & circle(B,C,F,NWPNT7) & circle(A,C,G,NWPNT8) & circle(B,C,G,NWPNT9) -> coll(D,F,G))) # label(exemplo6GDDFULL012014) # label(negated_conjecture) # label(non_clause). [assumption].
% 7.32/7.69 118 -coll(A,B,C) | -coll(A,B,D) | coll(C,D,A) # label(ruleD3) # label(axiom). [clausify(3)].
% 7.32/7.69 123 -perp(A,B,C,D) | perp(C,D,A,B) # label(ruleD8) # label(axiom). [clausify(8)].
% 7.32/7.69 124 -perp(A,B,C,D) | -perp(C,D,E,F) | para(A,B,E,F) # label(ruleD9) # label(axiom). [clausify(9)].
% 7.32/7.69 133 -eqangle(A,B,C,D,E,F,V6,V7) | eqangle(C,D,A,B,V6,V7,E,F) # label(ruleD19) # label(axiom). [clausify(19)].
% 7.32/7.69 153 -eqangle(A,B,C,D,E,F,C,D) | para(A,B,E,F) # label(ruleD39) # label(axiom). [clausify(39)].
% 7.32/7.69 154 -para(A,B,C,D) | eqangle(A,B,E,F,C,D,E,F) # label(ruleD40) # label(axiom). [clausify(40)].
% 7.32/7.69 176 -para(A,B,A,C) | coll(A,B,C) # label(ruleD66) # label(axiom). [clausify(67)].
% 7.32/7.69 215 perp(c3,c1,c3,c2) # label(exemplo6GDDFULL012014) # label(negated_conjecture). [clausify(95)].
% 7.32/7.69 218 -coll(c4,c6,c7) # label(exemplo6GDDFULL012014) # label(negated_conjecture). [clausify(95)].
% 7.32/7.69 355 -coll(A,B,C) | coll(C,C,A). [factor(118,a,b)].
% 7.32/7.69 428 -perp(c3,c2,A,B) | para(c3,c1,A,B). [resolve(215,a,124,a)].
% 7.32/7.69 429 perp(c3,c2,c3,c1). [resolve(215,a,123,a)].
% 7.32/7.69 788 para(c3,c1,c3,c1). [resolve(429,a,428,a)].
% 7.32/7.69 841 eqangle(c3,c1,A,B,c3,c1,A,B). [resolve(788,a,154,a)].
% 7.32/7.69 4647 eqangle(A,B,c3,c1,A,B,c3,c1). [resolve(841,a,133,a)].
% 7.32/7.69 31275 para(A,B,A,B). [resolve(4647,a,153,a)].
% 7.32/7.69 31283 coll(A,B,B). [resolve(31275,a,176,a)].
% 7.32/7.69 31322 coll(A,A,B). [resolve(31283,a,355,a)].
% 7.32/7.69 31936 coll(A,B,C). [resolve(31322,a,118,b),unit_del(a,31322)].
% 7.32/7.69 31937 $F. [resolve(31936,a,218,a)].
% 7.32/7.69
% 7.32/7.69 % SZS output end Refutation
% 7.32/7.69 ============================== end of proof ==========================
% 7.32/7.69
% 7.32/7.69 ============================== STATISTICS ============================
% 7.32/7.69
% 7.32/7.69 Given=10771. Generated=149569. Kept=31785. proofs=1.
% 7.32/7.69 Usable=10448. Sos=9491. Demods=0. Limbo=4, Disabled=12065. Hints=0.
% 7.32/7.69 Megabytes=18.48.
% 7.32/7.69 User_CPU=6.53, System_CPU=0.09, Wall_clock=7.
% 7.32/7.69
% 7.32/7.69 ============================== end of statistics =====================
% 7.32/7.69
% 7.32/7.69 ============================== end of search =========================
% 7.32/7.69
% 7.32/7.69 THEOREM PROVED
% 7.32/7.69 % SZS status Theorem
% 7.32/7.69
% 7.32/7.69 Exiting with 1 proof.
% 7.32/7.69
% 7.32/7.69 Process 8531 exit (max_proofs) Sat Jun 18 02:02:50 2022
% 7.32/7.69 Prover9 interrupted
%------------------------------------------------------------------------------