TSTP Solution File: GEO557+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GEO557+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n003.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 05:56:56 EDT 2022
% Result : Theorem 5.08s 5.36s
% Output : Refutation 5.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEO557+1 : TPTP v8.1.0. Released v7.5.0.
% 0.10/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sat Jun 18 11:05:58 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.85/1.10 ============================== Prover9 ===============================
% 0.85/1.10 Prover9 (32) version 2009-11A, November 2009.
% 0.85/1.10 Process 21886 was started by sandbox2 on n003.cluster.edu,
% 0.85/1.10 Sat Jun 18 11:05:58 2022
% 0.85/1.10 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_21730_n003.cluster.edu".
% 0.85/1.10 ============================== end of head ===========================
% 0.85/1.10
% 0.85/1.10 ============================== INPUT =================================
% 0.85/1.10
% 0.85/1.10 % Reading from file /tmp/Prover9_21730_n003.cluster.edu
% 0.85/1.10
% 0.85/1.10 set(prolog_style_variables).
% 0.85/1.10 set(auto2).
% 0.85/1.10 % set(auto2) -> set(auto).
% 0.85/1.10 % set(auto) -> set(auto_inference).
% 0.85/1.10 % set(auto) -> set(auto_setup).
% 0.85/1.10 % set(auto_setup) -> set(predicate_elim).
% 0.85/1.10 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.85/1.10 % set(auto) -> set(auto_limits).
% 0.85/1.10 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.85/1.10 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.85/1.10 % set(auto) -> set(auto_denials).
% 0.85/1.10 % set(auto) -> set(auto_process).
% 0.85/1.10 % set(auto2) -> assign(new_constants, 1).
% 0.85/1.10 % set(auto2) -> assign(fold_denial_max, 3).
% 0.85/1.10 % set(auto2) -> assign(max_weight, "200.000").
% 0.85/1.10 % set(auto2) -> assign(max_hours, 1).
% 0.85/1.10 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.85/1.10 % set(auto2) -> assign(max_seconds, 0).
% 0.85/1.10 % set(auto2) -> assign(max_minutes, 5).
% 0.85/1.10 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.85/1.10 % set(auto2) -> set(sort_initial_sos).
% 0.85/1.10 % set(auto2) -> assign(sos_limit, -1).
% 0.85/1.10 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.85/1.10 % set(auto2) -> assign(max_megs, 400).
% 0.85/1.10 % set(auto2) -> assign(stats, some).
% 0.85/1.10 % set(auto2) -> clear(echo_input).
% 0.85/1.10 % set(auto2) -> set(quiet).
% 0.85/1.10 % set(auto2) -> clear(print_initial_clauses).
% 0.85/1.10 % set(auto2) -> clear(print_given).
% 0.85/1.10 assign(lrs_ticks,-1).
% 0.85/1.10 assign(sos_limit,10000).
% 0.85/1.10 assign(order,kbo).
% 0.85/1.10 set(lex_order_vars).
% 0.85/1.10 clear(print_given).
% 0.85/1.10
% 0.85/1.10 % formulas(sos). % not echoed (95 formulas)
% 0.85/1.10
% 0.85/1.10 ============================== end of input ==========================
% 0.85/1.10
% 0.85/1.10 % From the command line: assign(max_seconds, 300).
% 0.85/1.10
% 0.85/1.10 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.85/1.10
% 0.85/1.10 % Formulas that are not ordinary clauses:
% 0.85/1.10 1 (all A all B all C (coll(A,B,C) -> coll(A,C,B))) # label(ruleD1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.10 2 (all A all B all C (coll(A,B,C) -> coll(B,A,C))) # label(ruleD2) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 11 (all A all B all M (midp(M,B,A) -> midp(M,A,B))) # label(ruleD11) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.10 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].
% 0.85/1.11 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].
% 0.85/1.11 67 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.11 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].
% 0.85/1.11 69 (all A all B all C (midp(A,B,C) -> cong(A,B,A,C))) # label(ruleD68) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.11 70 (all A all B all C (midp(A,B,C) -> coll(A,B,C))) # label(ruleD69) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.11 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].
% 0.85/1.11 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].
% 0.85/1.11 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].
% 0.85/1.11 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].
% 0.85/1.11 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].
% 0.85/1.11 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].
% 0.85/1.11 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].
% 0.85/1.11 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].
% 0.85/1.11 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].
% 0.85/1.11 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].
% 0.85/1.11 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].
% 0.85/1.11 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].
% 0.85/1.11 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].
% 0.85/1.11 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].
% 0.85/1.11 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].
% 0.85/1.11 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].
% 0.85/1.11 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].
% 0.85/1.11 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].
% 0.85/1.11 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].
% 0.85/1.11 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].
% 0.85/1.11 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].
% 0.85/1.11 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].
% 0.85/1.11 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].
% 0.85/1.11 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].
% 0.85/1.11 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(O,A,N,NWPNT1) & coll(B,A,K) & coll(B,C,N) & circle(G,A,C,B) & circle(O1,K,N,B) & circle(G,A,M,NWPNT2) & circle(O1,K,M,NWPNT3) -> cyclic(M,K,O,C))) # label(exemplo6GDDFULL012017) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.85/1.11
% 0.85/1.11 ============================== end of process non-clausal formulas ===
% 0.85/1.11
% 0.85/1.11 ============================== PROCESS INITIAL CLAUSES ===============
% 0.85/1.11
% 0.85/1.11 ============================== PREDICATE ELIMINATION =================
% 0.85/1.11 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)].
% 0.85/1.11 97 -cong(A,B,A,C) | -cong(A,B,A,D) | circle(A,B,C,D) # label(ruleD12) # label(axiom). [clausify(12)].
% 0.85/1.11 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)].
% 0.85/1.11 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)].
% 0.85/1.11 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)].
% 0.85/1.11 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)].
% 0.85/1.11 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)].
% 0.85/1.11 100 -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)].
% 0.85/1.11 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)].
% 0.85/1.11 101 -circle(A,B,C,D) | -coll(A,B,D) | perp(B,C,C,D) # label(ruleD53) # label(axiom). [clausify(54)].
% 0.85/1.11 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)].
% 0.85/1.11 102 -circle(A,B,C,D) | perp(f12(B,C,D,A),B,B,A) # label(ruleX11) # label(axiom). [clausify(87)].
% 0.85/1.11 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)].
% 0.85/1.11 103 -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)].
% 0.85/1.11 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)].
% 0.85/1.11 104 -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)].
% 0.85/1.11 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)].
% 0.85/1.11 105 -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)].
% 0.85/1.11 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)].
% 0.85/1.11 106 -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)].
% 0.85/1.11 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)].
% 0.85/1.11 107 -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)].
% 0.85/1.11 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)].
% 0.85/1.11 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)].
% 0.85/1.11 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)].
% 0.85/1.11 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)].
% 0.85/1.11 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)].
% 0.85/1.11 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)].
% 0.85/1.11 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)].
% 0.85/1.11 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)].
% 0.85/1.11 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)].
% 0.85/1.11 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)].
% 0.85/1.11 108 -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)].
% 0.85/1.11 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)].
% 0.85/1.11 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)].
% 0.85/1.11 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)].
% 0.85/1.11 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)].
% 0.85/1.11 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)].
% 0.85/1.11 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)].
% 0.85/1.11 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)].
% 0.85/1.11 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)].
% 0.85/1.11 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)].
% 0.85/1.11 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)].
% 0.85/1.11 109 circle(c4,c1,c2,c3) # label(exemplo6GDDFULL012017) # label(negated_conjecture). [clausify(95)].
% 0.85/1.11 Derived: -perp(c4,c1,c1,A) | eqangle(c1,A,c1,c2,c3,c1,c3,c2). [resolve(109,a,96,a)].
% 0.85/1.11 Derived: -eqangle(c1,A,c1,c2,c3,c1,c3,c2) | perp(c4,c1,c1,A). [resolve(109,a,98,a)].
% 0.85/1.11 Derived: -midp(A,c2,c3) | eqangle(c1,c2,c1,c3,c4,c2,c4,A). [resolve(109,a,99,a)].
% 0.85/1.11 Derived: -coll(A,c2,c3) | -eqangle(c1,c2,c1,c3,c4,c2,c4,A) | midp(A,c2,c3). [resolve(109,a,100,a)].
% 0.85/1.11 Derived: -coll(c4,c1,c3) | perp(c1,c2,c2,c3). [resolve(109,a,101,a)].
% 0.85/1.11 Derived: perp(f12(c1,c2,c3,c4),c1,c1,c4). [resolve(109,a,102,a)].
% 0.85/1.11 Derived: -cong(c4,c1,c4,A) | -cong(B,c1,B,c2) | B = c4 | coll(f13(c1,c2,c3,A,c4,B),c1,c3). [resolve(109,a,103,a)].
% 0.85/1.11 Derived: -cong(c4,c1,c4,A) | -cong(B,c1,B,c2) | B = c4 | cong(f13(c1,c2,c3,A,c4,B),B,B,c1). [resolve(109,a,104,a)].
% 0.85/1.11 Derived: -cong(c4,c1,c4,A) | -cong(B,c1,B,c2) | B = c4 | coll(f14(c1,c2,c3,A,c4,B),c2,A). [resolve(109,a,105,a)].
% 0.85/1.11 Derived: -cong(c4,c1,c4,A) | -cong(B,c1,B,c2) | B = c4 | cong(f14(c1,c2,c3,A,c4,B),B,B,c1). [resolve(109,a,106,a)].
% 0.85/1.11 110 circle(c4,c1,c5,c10) # label(exemplo6GDDFULL012017) # label(negated_conjecture). [clausify(95)].
% 0.85/1.11 Derived: -perp(c4,c1,c1,A) | eqangle(c1,A,c1,c5,c10,c1,c10,c5). [resolve(110,a,96,a)].
% 0.85/1.11 Derived: -eqangle(c1,A,c1,c5,c10,c1,c10,c5) | perp(c4,c1,c1,A). [resolve(110,a,98,a)].
% 0.85/1.11 Derived: -midp(A,c5,c10) | eqangle(c1,c5,c1,c10,c4,c5,c4,A). [resolve(110,a,99,a)].
% 0.85/1.11 Derived: -coll(A,c5,c10) | -eqangle(c1,c5,c1,c10,c4,c5,c4,A) | midp(A,c5,c10). [resolve(110,a,100,a)].
% 0.85/1.11 Derived: -coll(c4,c1,c10) | perp(c1,c5,c5,c10). [resolve(110,a,101,a)].
% 0.85/1.11 Derived: perp(f12(c1,c5,c10,c4),c1,c1,c4). [resolve(110,a,102,a)].
% 0.85/1.11 Derived: -cong(c4,c1,c4,A) | -cong(B,c1,B,c5) | B = c4 | coll(f13(c1,c5,c10,A,c4,B),c1,c10). [resolve(110,a,103,a)].
% 0.85/1.11 Derived: -cong(c4,c1,c4,A) | -cong(B,c1,B,c5) | B = c4 | cong(f13(c1,c5,c10,A,c4,B),B,B,c1). [resolve(110,a,104,a)].
% 0.85/1.11 Derived: -cong(c4,c1,c4,A) | -cong(B,c1,B,c5) | B = c4 | coll(f14(c1,c5,c10,A,c4,B),c5,A). [resolve(110,a,105,a)].
% 0.85/1.11 Derived: -cong(c4,c1,c4,A) | -cong(B,c1,B,c5) | B = c4 | cong(f14(c1,c5,c10,A,c4,B),B,B,c1). [resolve(110,a,106,a)].
% 0.85/1.11 111 circle(c7,c1,c2,c6) # label(exemplo6GDDFULL012017) # label(negated_conjecture). [clausify(95)].
% 0.85/1.11 Derived: -perp(c7,c1,c1,A) | eqangle(c1,A,c1,c2,c6,c1,c6,c2). [resolve(111,a,96,a)].
% 0.85/1.11 Derived: -eqangle(c1,A,c1,c2,c6,c1,c6,c2) | perp(c7,c1,c1,A). [resolve(111,a,98,a)].
% 0.85/1.11 Derived: -midp(A,c2,c6) | eqangle(c1,c2,c1,c6,c7,c2,c7,A). [resolve(111,a,99,a)].
% 0.85/1.11 Derived: -coll(A,c2,c6) | -eqangle(c1,c2,c1,c6,c7,c2,c7,A) | midp(A,c2,c6). [resolve(111,a,100,a)].
% 0.85/1.11 Derived: -coll(c7,c1,c6) | perp(c1,c2,c2,c6). [resolve(111,a,101,a)].
% 0.85/1.11 Derived: perp(f12(c1,c2,c6,c7),c1,c1,c7). [resolve(111,a,102,a)].
% 0.85/1.11 Derived: -cong(c7,c1,c7,A) | -cong(B,c1,B,c2) | B = c7 | coll(f13(c1,c2,c6,A,c7,B),c1,c6). [resolve(111,a,103,a)].
% 0.85/1.11 Derived: -cong(c7,c1,c7,A) | -cong(B,c1,B,c2) | B = c7 | cong(f13(c1,c2,c6,A,c7,B),B,B,c1). [resolve(111,a,104,a)].
% 0.85/1.11 Derived: -cong(c7,c1,c7,A) | -cong(B,c1,B,c2) | B = c7 | coll(f14(c1,c2,c6,A,c7,B),c2,A). [resolve(111,a,105,a)].
% 0.85/1.11 Derived: -cong(c7,c1,c7,A) | -cong(B,c1,B,c2) | B = c7 | cong(f14(c1,c2,c6,A,c7,B),B,B,c1). [resolve(111,a,106,a)].
% 0.85/1.11 112 circle(c8,c3,c5,c6) # label(exemplo6GDDFULL012017) # label(negated_conjecture). [clausify(95)].
% 0.85/1.11 Derived: -perp(c8,c3,c3,A) | eqangle(c3,A,c3,c5,c6,c3,c6,c5). [resolve(112,a,96,a)].
% 0.85/1.11 Derived: -eqangle(c3,A,c3,c5,c6,c3,c6,c5) | perp(c8,c3,c3,A). [resolve(112,a,98,a)].
% 0.85/1.11 Derived: -midp(A,c5,c6) | eqangle(c3,c5,c3,c6,c8,c5,c8,A). [resolve(112,a,99,a)].
% 0.85/1.11 Derived: -coll(A,c5,c6) | -eqangle(c3,c5,c3,c6,c8,c5,c8,A) | midp(A,c5,c6). [resolve(112,a,100,a)].
% 0.85/1.11 Derived: -coll(c8,c3,c6) | perp(c3,c5,c5,c6). [resolve(112,a,101,a)].
% 0.85/1.11 Derived: perp(f12(c3,c5,c6,c8),c3,c3,c8). [resolve(112,a,102,a)].
% 0.85/1.11 Derived: -cong(c8,c3,c8,A) | -cong(B,c3,B,c5) | B = c8 | coll(f13(c3,c5,c6,A,c8,B),c3,c6). [resolve(112,a,103,a)].
% 0.85/1.11 Derived: -cong(c8,c3,c8,A) | -cong(B,c3,B,c5) | B = c8 | cong(f13(c3,c5,c6,A,c8,B),B,B,c3). [resolve(112,a,104,a)].
% 0.85/1.11 Derived: -cong(c8,c3,c8,A) | -cong(B,c3,B,c5) | B = c8 | coll(f14(c3,c5,c6,A,c8,B),c5,A). [resolve(112,a,105,a)].
% 0.85/1.11 Derived: -cong(c8,c3,c8,A) | -cong(B,c3,B,c5) | B = c8 | cong(f14(c3,c5,c6,A,c8,B),B,B,c3). [resolve(112,a,106,a)].
% 0.85/1.11 113 circle(c7,c1,c9,c11) # label(exemplo6GDDFULL012017) # label(negated_conjecture). [clausify(95)].
% 0.85/1.11 Derived: -perp(c7,c1,c1,A) | eqangle(c1,A,c1,c9,c11,c1,c11,c9). [resolve(113,a,96,a)].
% 0.85/1.11 Derived: -eqangle(c1,A,c1,c9,c11,c1,c11,c9) | perp(c7,c1,c1,A). [resolve(113,a,98,a)].
% 0.85/1.11 Derived: -midp(A,c9,c11) | eqangle(c1,c9,c1,c11,c7,c9,c7,A). [resolve(113,a,99,a)].
% 0.85/1.11 Derived: -coll(A,c9,c11) | -eqangle(c1,c9,c1,c11,c7,c9,c7,A) | midp(A,c9,c11). [resolve(113,a,100,a)].
% 5.08/5.36 Derived: -coll(c7,c1,c11) | perp(c1,c9,c9,c11). [resolve(113,a,101,a)].
% 5.08/5.36 Derived: perp(f12(c1,c9,c11,c7),c1,c1,c7). [resolve(113,a,102,a)].
% 5.08/5.36 Derived: -cong(c7,c1,c7,A) | -cong(B,c1,B,c9) | B = c7 | coll(f13(c1,c9,c11,A,c7,B),c1,c11). [resolve(113,a,103,a)].
% 5.08/5.36 Derived: -cong(c7,c1,c7,A) | -cong(B,c1,B,c9) | B = c7 | cong(f13(c1,c9,c11,A,c7,B),B,B,c1). [resolve(113,a,104,a)].
% 5.08/5.36 Derived: -cong(c7,c1,c7,A) | -cong(B,c1,B,c9) | B = c7 | coll(f14(c1,c9,c11,A,c7,B),c9,A). [resolve(113,a,105,a)].
% 5.08/5.36 Derived: -cong(c7,c1,c7,A) | -cong(B,c1,B,c9) | B = c7 | cong(f14(c1,c9,c11,A,c7,B),B,B,c1). [resolve(113,a,106,a)].
% 5.08/5.36 114 circle(c8,c3,c9,c12) # label(exemplo6GDDFULL012017) # label(negated_conjecture). [clausify(95)].
% 5.08/5.36 Derived: -perp(c8,c3,c3,A) | eqangle(c3,A,c3,c9,c12,c3,c12,c9). [resolve(114,a,96,a)].
% 5.08/5.36 Derived: -eqangle(c3,A,c3,c9,c12,c3,c12,c9) | perp(c8,c3,c3,A). [resolve(114,a,98,a)].
% 5.08/5.36 Derived: -midp(A,c9,c12) | eqangle(c3,c9,c3,c12,c8,c9,c8,A). [resolve(114,a,99,a)].
% 5.08/5.36 Derived: -coll(A,c9,c12) | -eqangle(c3,c9,c3,c12,c8,c9,c8,A) | midp(A,c9,c12). [resolve(114,a,100,a)].
% 5.08/5.36 Derived: -coll(c8,c3,c12) | perp(c3,c9,c9,c12). [resolve(114,a,101,a)].
% 5.08/5.36 Derived: perp(f12(c3,c9,c12,c8),c3,c3,c8). [resolve(114,a,102,a)].
% 5.08/5.36 Derived: -cong(c8,c3,c8,A) | -cong(B,c3,B,c9) | B = c8 | coll(f13(c3,c9,c12,A,c8,B),c3,c12). [resolve(114,a,103,a)].
% 5.08/5.36 Derived: -cong(c8,c3,c8,A) | -cong(B,c3,B,c9) | B = c8 | cong(f13(c3,c9,c12,A,c8,B),B,B,c3). [resolve(114,a,104,a)].
% 5.08/5.36 Derived: -cong(c8,c3,c8,A) | -cong(B,c3,B,c9) | B = c8 | coll(f14(c3,c9,c12,A,c8,B),c9,A). [resolve(114,a,105,a)].
% 5.08/5.36 Derived: -cong(c8,c3,c8,A) | -cong(B,c3,B,c9) | B = c8 | cong(f14(c3,c9,c12,A,c8,B),B,B,c3). [resolve(114,a,106,a)].
% 5.08/5.36
% 5.08/5.36 ============================== end predicate elimination =============
% 5.08/5.36
% 5.08/5.36 Auto_denials: (non-Horn, no changes).
% 5.08/5.36
% 5.08/5.36 Term ordering decisions:
% 5.08/5.36 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. 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.
% 5.08/5.36
% 5.08/5.36 ============================== end of process initial clauses ========
% 5.08/5.36
% 5.08/5.36 ============================== CLAUSES FOR SEARCH ====================
% 5.08/5.36
% 5.08/5.36 ============================== end of clauses for search =============
% 5.08/5.36
% 5.08/5.36 ============================== SEARCH ================================
% 5.08/5.36
% 5.08/5.36 % Starting search at 0.05 seconds.
% 5.08/5.36
% 5.08/5.36 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 2147483647 (0.00 of 0.14 sec).
% 5.08/5.36
% 5.08/5.36 Low Water (keep): wt=49.000, iters=3383
% 5.08/5.36
% 5.08/5.36 Low Water (keep): wt=45.000, iters=3355
% 5.08/5.36
% 5.08/5.36 Low Water (keep): wt=44.000, iters=3385
% 5.08/5.36
% 5.08/5.36 Low Water (keep): wt=39.000, iters=3387
% 5.08/5.36
% 5.08/5.36 Low Water (keep): wt=31.000, iters=3378
% 5.08/5.36
% 5.08/5.36 Low Water (keep): wt=26.000, iters=3334
% 5.08/5.36
% 5.08/5.36 Low Water (keep): wt=23.000, iters=3337
% 5.08/5.36
% 5.08/5.36 Low Water (keep): wt=22.000, iters=3381
% 5.08/5.36
% 5.08/5.36 Low Water (keep): wt=21.000, iters=3333
% 5.08/5.36
% 5.08/5.36 Low Water (keep): wt=18.000, iters=3368
% 5.08/5.36
% 5.08/5.36 Low Water (keep): wt=17.000, iters=3336
% 5.08/5.36
% 5.08/5.36 Low Water (keep): wt=16.000, iters=3334
% 5.08/5.36
% 5.08/5.36 Low Water (keep): wt=14.000, iters=3436
% 5.08/5.36
% 5.08/5.36 Low Water (keep): wt=13.000, iters=3635
% 5.08/5.36
% 5.08/5.36 Low Water (keep): wt=12.000, iters=3333
% 5.08/5.36
% 5.08/5.36 ============================== PROOF =================================
% 5.08/5.36 % SZS status Theorem
% 5.08/5.36 % SZS output start Refutation
% 5.08/5.36
% 5.08/5.36 % Proof 1 at 4.22 (+ 0.06) seconds.
% 5.08/5.36 % Length of proof is 60.
% 5.08/5.36 % Level of proof is 16.
% 5.08/5.36 % Maximum clause weight is 18.000.
% 5.08/5.36 % Given clauses 8410.
% 5.08/5.36
% 5.08/5.36 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].
% 5.08/5.36 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].
% 5.08/5.36 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].
% 5.08/5.36 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].
% 5.08/5.36 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].
% 5.08/5.36 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].
% 5.08/5.36 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].
% 5.08/5.36 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].
% 5.08/5.36 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].
% 5.08/5.36 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].
% 5.08/5.36 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].
% 5.08/5.36 67 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption].
% 5.08/5.36 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].
% 5.08/5.36 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(O,A,N,NWPNT1) & coll(B,A,K) & coll(B,C,N) & circle(G,A,C,B) & circle(O1,K,N,B) & circle(G,A,M,NWPNT2) & circle(O1,K,M,NWPNT3) -> cyclic(M,K,O,C))) # label(exemplo6GDDFULL012017) # label(negated_conjecture) # label(non_clause). [assumption].
% 5.08/5.36 102 -circle(A,B,C,D) | perp(f12(B,C,D,A),B,B,A) # label(ruleX11) # label(axiom). [clausify(87)].
% 5.08/5.36 109 circle(c4,c1,c2,c3) # label(exemplo6GDDFULL012017) # label(negated_conjecture). [clausify(95)].
% 5.08/5.36 117 -coll(A,B,C) | -coll(A,B,D) | coll(C,D,A) # label(ruleD3) # label(axiom). [clausify(3)].
% 5.08/5.36 122 -perp(A,B,C,D) | perp(C,D,A,B) # label(ruleD8) # label(axiom). [clausify(8)].
% 5.08/5.36 123 -perp(A,B,C,D) | -perp(C,D,E,F) | para(A,B,E,F) # label(ruleD9) # label(axiom). [clausify(9)].
% 5.08/5.36 127 -cyclic(A,B,C,D) | cyclic(A,B,D,C) # label(ruleD14) # label(axiom). [clausify(14)].
% 5.08/5.36 128 -cyclic(A,B,C,D) | cyclic(A,C,B,D) # label(ruleD15) # label(axiom). [clausify(15)].
% 5.08/5.36 130 -cyclic(A,B,C,D) | -cyclic(A,B,C,E) | cyclic(B,C,D,E) # label(ruleD17) # label(axiom). [clausify(17)].
% 5.08/5.36 132 -eqangle(A,B,C,D,E,F,V6,V7) | eqangle(C,D,A,B,V6,V7,E,F) # label(ruleD19) # label(axiom). [clausify(19)].
% 5.08/5.36 134 -eqangle(A,B,C,D,E,F,V6,V7) | eqangle(A,B,E,F,C,D,V6,V7) # label(ruleD21) # label(axiom). [clausify(21)].
% 5.08/5.36 152 -eqangle(A,B,C,D,E,F,C,D) | para(A,B,E,F) # label(ruleD39) # label(axiom). [clausify(39)].
% 5.08/5.36 153 -para(A,B,C,D) | eqangle(A,B,E,F,C,D,E,F) # label(ruleD40) # label(axiom). [clausify(40)].
% 5.08/5.36 156 -eqangle(A,B,A,C,D,B,D,C) | -coll(A,D,C) | cyclic(B,C,A,D) # label(ruleD42b) # label(axiom). [clausify(43)].
% 5.08/5.36 175 -para(A,B,A,C) | coll(A,B,C) # label(ruleD66) # label(axiom). [clausify(67)].
% 5.08/5.36 216 -cyclic(c9,c3,c4,c2) # label(exemplo6GDDFULL012017) # label(negated_conjecture). [clausify(95)].
% 5.08/5.36 260 perp(f12(c1,c2,c3,c4),c1,c1,c4). [resolve(109,a,102,a)].
% 5.08/5.36 339 -coll(A,B,C) | coll(C,C,A). [factor(117,a,b)].
% 5.08/5.36 430 -perp(A,B,f12(c1,c2,c3,c4),c1) | para(A,B,c1,c4). [resolve(260,a,123,b)].
% 5.08/5.36 432 perp(c1,c4,f12(c1,c2,c3,c4),c1). [resolve(260,a,122,a)].
% 5.08/5.36 789 para(c1,c4,c1,c4). [resolve(432,a,430,a)].
% 5.08/5.36 967 coll(c1,c4,c4). [resolve(789,a,175,a)].
% 5.08/5.36 970 eqangle(c1,c4,A,B,c1,c4,A,B). [resolve(789,a,153,a)].
% 5.08/5.36 972 coll(c4,c4,c1). [resolve(967,a,339,a)].
% 5.08/5.36 982 coll(c1,c1,c4). [resolve(972,a,339,a)].
% 5.08/5.36 984 -coll(c4,c4,A) | coll(c1,A,c4). [resolve(972,a,117,a)].
% 5.08/5.36 3421 -coll(c1,c1,A) | cyclic(c4,A,c1,c1). [resolve(970,a,156,a)].
% 5.08/5.36 3422 eqangle(c1,c4,c1,c4,A,B,A,B). [resolve(970,a,134,a)].
% 5.08/5.36 3423 eqangle(A,B,c1,c4,A,B,c1,c4). [resolve(970,a,132,a)].
% 5.08/5.36 17572 cyclic(c4,c4,c1,c1). [resolve(3421,a,982,a)].
% 5.08/5.36 17595 -cyclic(c4,c4,c1,A) | cyclic(c4,c1,c1,A). [resolve(17572,a,130,a)].
% 5.08/5.36 17596 cyclic(c4,c1,c4,c1). [resolve(17572,a,128,a)].
% 5.08/5.36 17606 -coll(c1,A,c4) | cyclic(c4,c4,c1,A). [resolve(3422,a,156,a)].
% 5.08/5.36 17635 para(A,B,A,B). [resolve(3423,a,152,a)].
% 5.08/5.36 17668 cyclic(c4,c1,c1,c4). [resolve(17596,a,127,a)].
% 5.08/5.36 17740 coll(A,B,B). [resolve(17635,a,175,a)].
% 5.08/5.36 17804 coll(A,A,B). [resolve(17740,a,339,a)].
% 5.08/5.36 18131 coll(c1,A,c4). [back_unit_del(984),unit_del(a,17804)].
% 5.08/5.36 18265 cyclic(c4,c4,c1,A). [back_unit_del(17606),unit_del(a,18131)].
% 5.08/5.36 18304 cyclic(c4,c1,c1,A). [back_unit_del(17595),unit_del(a,18265)].
% 5.08/5.36 18544 cyclic(c1,c1,A,c4). [resolve(17668,a,130,b),unit_del(a,18304)].
% 5.08/5.36 19111 cyclic(c4,c1,A,B). [resolve(18265,a,130,b),unit_del(a,18265)].
% 5.08/5.36 19200 cyclic(c1,c1,A,B). [resolve(18304,a,130,b),unit_del(a,19111)].
% 5.08/5.36 19448 cyclic(c1,A,B,c4). [resolve(18544,a,130,b),unit_del(a,19200)].
% 5.08/5.36 19924 cyclic(c1,A,B,C). [resolve(19111,a,130,b),unit_del(a,19111)].
% 5.08/5.36 20560 cyclic(A,B,c4,C). [resolve(19448,a,130,a),unit_del(a,19924)].
% 5.08/5.36 20561 $F. [resolve(20560,a,216,a)].
% 5.08/5.36
% 5.08/5.36 % SZS output end Refutation
% 5.08/5.36 ============================== end of proof ==========================
% 5.08/5.36
% 5.08/5.36 ============================== STATISTICS ============================
% 5.08/5.36
% 5.08/5.36 Given=8410. Generated=93126. Kept=20414. proofs=1.
% 5.08/5.36 Usable=7147. Sos=6919. Demods=0. Limbo=6, Disabled=6553. Hints=0.
% 5.08/5.36 Megabytes=15.64.
% 5.08/5.36 User_CPU=4.22, System_CPU=0.06, Wall_clock=5.
% 5.08/5.36
% 5.08/5.36 ============================== end of statistics =====================
% 5.08/5.36
% 5.08/5.36 ============================== end of search =========================
% 5.08/5.36
% 5.08/5.36 THEOREM PROVED
% 5.08/5.36 % SZS status Theorem
% 5.08/5.36
% 5.08/5.36 Exiting with 1 proof.
% 5.08/5.36
% 5.08/5.36 Process 21886 exit (max_proofs) Sat Jun 18 11:06:03 2022
% 5.08/5.36 Prover9 interrupted
%------------------------------------------------------------------------------