TSTP Solution File: GEO597+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GEO597+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n023.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 05:57:09 EDT 2022
% Result : Theorem 17.76s 18.05s
% Output : Refutation 17.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO597+1 : TPTP v8.1.0. Released v7.5.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jun 18 07:49:34 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.79/1.11 ============================== Prover9 ===============================
% 0.79/1.11 Prover9 (32) version 2009-11A, November 2009.
% 0.79/1.11 Process 30025 was started by sandbox on n023.cluster.edu,
% 0.79/1.11 Sat Jun 18 07:49:35 2022
% 0.79/1.11 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_29872_n023.cluster.edu".
% 0.79/1.11 ============================== end of head ===========================
% 0.79/1.11
% 0.79/1.11 ============================== INPUT =================================
% 0.79/1.11
% 0.79/1.11 % Reading from file /tmp/Prover9_29872_n023.cluster.edu
% 0.79/1.11
% 0.79/1.11 set(prolog_style_variables).
% 0.79/1.11 set(auto2).
% 0.79/1.11 % set(auto2) -> set(auto).
% 0.79/1.11 % set(auto) -> set(auto_inference).
% 0.79/1.11 % set(auto) -> set(auto_setup).
% 0.79/1.11 % set(auto_setup) -> set(predicate_elim).
% 0.79/1.11 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.79/1.11 % set(auto) -> set(auto_limits).
% 0.79/1.11 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.79/1.11 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.79/1.11 % set(auto) -> set(auto_denials).
% 0.79/1.11 % set(auto) -> set(auto_process).
% 0.79/1.11 % set(auto2) -> assign(new_constants, 1).
% 0.79/1.11 % set(auto2) -> assign(fold_denial_max, 3).
% 0.79/1.11 % set(auto2) -> assign(max_weight, "200.000").
% 0.79/1.11 % set(auto2) -> assign(max_hours, 1).
% 0.79/1.11 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.79/1.11 % set(auto2) -> assign(max_seconds, 0).
% 0.79/1.11 % set(auto2) -> assign(max_minutes, 5).
% 0.79/1.11 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.79/1.11 % set(auto2) -> set(sort_initial_sos).
% 0.79/1.11 % set(auto2) -> assign(sos_limit, -1).
% 0.79/1.11 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.79/1.11 % set(auto2) -> assign(max_megs, 400).
% 0.79/1.11 % set(auto2) -> assign(stats, some).
% 0.79/1.11 % set(auto2) -> clear(echo_input).
% 0.79/1.11 % set(auto2) -> set(quiet).
% 0.79/1.11 % set(auto2) -> clear(print_initial_clauses).
% 0.79/1.11 % set(auto2) -> clear(print_given).
% 0.79/1.11 assign(lrs_ticks,-1).
% 0.79/1.11 assign(sos_limit,10000).
% 0.79/1.11 assign(order,kbo).
% 0.79/1.11 set(lex_order_vars).
% 0.79/1.11 clear(print_given).
% 0.79/1.11
% 0.79/1.11 % formulas(sos). % not echoed (95 formulas)
% 0.79/1.11
% 0.79/1.11 ============================== end of input ==========================
% 0.79/1.11
% 0.79/1.11 % From the command line: assign(max_seconds, 300).
% 0.79/1.11
% 0.79/1.11 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.79/1.11
% 0.79/1.11 % Formulas that are not ordinary clauses:
% 0.79/1.11 1 (all A all B all C (coll(A,B,C) -> coll(A,C,B))) # label(ruleD1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 2 (all A all B all C (coll(A,B,C) -> coll(B,A,C))) # label(ruleD2) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 11 (all A all B all M (midp(M,B,A) -> midp(M,A,B))) # label(ruleD11) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 67 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 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].
% 0.79/1.11 69 (all A all B all C (midp(A,B,C) -> cong(A,B,A,C))) # label(ruleD68) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 70 (all A all B all C (midp(A,B,C) -> coll(A,B,C))) # label(ruleD69) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.11 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].
% 0.79/1.12 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].
% 0.79/1.12 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].
% 0.79/1.12 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].
% 0.79/1.12 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].
% 0.79/1.12 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].
% 0.79/1.12 95 -(all A all B all C all O all M all N all NWPNT1 (circle(O,A,B,C) & midp(M,B,A) & coll(N,O,M) & circle(O,A,N,NWPNT1) -> eqangle(A,C,C,N,N,C,C,B))) # label(exemplo6GDDFULL416059) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.79/1.12
% 0.79/1.12 ============================== end of process non-clausal formulas ===
% 0.79/1.12
% 0.79/1.12 ============================== PROCESS INITIAL CLAUSES ===============
% 0.79/1.12
% 0.79/1.12 ============================== PREDICATE ELIMINATION =================
% 0.79/1.12 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)].
% 0.79/1.12 97 -cong(A,B,A,C) | -cong(A,B,A,D) | circle(A,B,C,D) # label(ruleD12) # label(axiom). [clausify(12)].
% 0.79/1.12 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)].
% 0.79/1.12 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)].
% 0.79/1.12 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)].
% 0.79/1.12 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)].
% 0.79/1.12 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)].
% 0.79/1.12 100 -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)].
% 0.79/1.12 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)].
% 0.79/1.12 101 -circle(A,B,C,D) | -coll(A,B,D) | perp(B,C,C,D) # label(ruleD53) # label(axiom). [clausify(54)].
% 0.79/1.12 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)].
% 0.79/1.12 102 -circle(A,B,C,D) | perp(f12(B,C,D,A),B,B,A) # label(ruleX11) # label(axiom). [clausify(87)].
% 0.79/1.12 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)].
% 0.79/1.12 103 -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)].
% 0.79/1.12 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)].
% 0.79/1.12 104 -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)].
% 0.79/1.12 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)].
% 0.79/1.12 105 -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)].
% 0.79/1.12 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)].
% 0.79/1.12 106 -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)].
% 0.79/1.12 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)].
% 0.79/1.12 107 -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)].
% 0.79/1.12 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)].
% 0.79/1.12 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)].
% 0.79/1.12 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)].
% 0.79/1.12 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)].
% 0.79/1.12 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)].
% 0.79/1.12 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)].
% 0.79/1.12 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)].
% 0.79/1.12 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)].
% 0.79/1.12 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)].
% 0.79/1.12 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)].
% 0.79/1.12 108 -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)].
% 0.79/1.12 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)].
% 0.79/1.12 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)].
% 0.79/1.12 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)].
% 0.79/1.12 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)].
% 0.79/1.12 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)].
% 0.79/1.12 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)].
% 0.79/1.12 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)].
% 0.79/1.12 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)].
% 0.79/1.12 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)].
% 0.79/1.12 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)].
% 0.79/1.12 109 circle(c4,c1,c2,c3) # label(exemplo6GDDFULL416059) # label(negated_conjecture). [clausify(95)].
% 0.79/1.12 Derived: -perp(c4,c1,c1,A) | eqangle(c1,A,c1,c2,c3,c1,c3,c2). [resolve(109,a,96,a)].
% 0.79/1.12 Derived: -eqangle(c1,A,c1,c2,c3,c1,c3,c2) | perp(c4,c1,c1,A). [resolve(109,a,98,a)].
% 0.79/1.12 Derived: -midp(A,c2,c3) | eqangle(c1,c2,c1,c3,c4,c2,c4,A). [resolve(109,a,99,a)].
% 0.79/1.12 Derived: -coll(A,c2,c3) | -eqangle(c1,c2,c1,c3,c4,c2,c4,A) | midp(A,c2,c3). [resolve(109,a,100,a)].
% 0.79/1.12 Derived: -coll(c4,c1,c3) | perp(c1,c2,c2,c3). [resolve(109,a,101,a)].
% 0.79/1.12 Derived: perp(f12(c1,c2,c3,c4),c1,c1,c4). [resolve(109,a,102,a)].
% 0.79/1.12 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)].
% 0.79/1.12 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)].
% 17.76/18.05 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)].
% 17.76/18.05 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)].
% 17.76/18.05 110 circle(c4,c1,c6,c7) # label(exemplo6GDDFULL416059) # label(negated_conjecture). [clausify(95)].
% 17.76/18.05 Derived: -perp(c4,c1,c1,A) | eqangle(c1,A,c1,c6,c7,c1,c7,c6). [resolve(110,a,96,a)].
% 17.76/18.05 Derived: -eqangle(c1,A,c1,c6,c7,c1,c7,c6) | perp(c4,c1,c1,A). [resolve(110,a,98,a)].
% 17.76/18.05 Derived: -midp(A,c6,c7) | eqangle(c1,c6,c1,c7,c4,c6,c4,A). [resolve(110,a,99,a)].
% 17.76/18.05 Derived: -coll(A,c6,c7) | -eqangle(c1,c6,c1,c7,c4,c6,c4,A) | midp(A,c6,c7). [resolve(110,a,100,a)].
% 17.76/18.05 Derived: -coll(c4,c1,c7) | perp(c1,c6,c6,c7). [resolve(110,a,101,a)].
% 17.76/18.05 Derived: perp(f12(c1,c6,c7,c4),c1,c1,c4). [resolve(110,a,102,a)].
% 17.76/18.05 Derived: -cong(c4,c1,c4,A) | -cong(B,c1,B,c6) | B = c4 | coll(f13(c1,c6,c7,A,c4,B),c1,c7). [resolve(110,a,103,a)].
% 17.76/18.05 Derived: -cong(c4,c1,c4,A) | -cong(B,c1,B,c6) | B = c4 | cong(f13(c1,c6,c7,A,c4,B),B,B,c1). [resolve(110,a,104,a)].
% 17.76/18.05 Derived: -cong(c4,c1,c4,A) | -cong(B,c1,B,c6) | B = c4 | coll(f14(c1,c6,c7,A,c4,B),c6,A). [resolve(110,a,105,a)].
% 17.76/18.05 Derived: -cong(c4,c1,c4,A) | -cong(B,c1,B,c6) | B = c4 | cong(f14(c1,c6,c7,A,c4,B),B,B,c1). [resolve(110,a,106,a)].
% 17.76/18.05
% 17.76/18.05 ============================== end predicate elimination =============
% 17.76/18.05
% 17.76/18.05 Auto_denials: (non-Horn, no changes).
% 17.76/18.05
% 17.76/18.05 Term ordering decisions:
% 17.76/18.05 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=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.
% 17.76/18.05
% 17.76/18.05 ============================== end of process initial clauses ========
% 17.76/18.05
% 17.76/18.05 ============================== CLAUSES FOR SEARCH ====================
% 17.76/18.05
% 17.76/18.05 ============================== end of clauses for search =============
% 17.76/18.05
% 17.76/18.05 ============================== SEARCH ================================
% 17.76/18.05
% 17.76/18.05 % Starting search at 0.05 seconds.
% 17.76/18.05
% 17.76/18.05 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 866 (0.00 of 0.17 sec).
% 17.76/18.05
% 17.76/18.05 Low Water (keep): wt=35.000, iters=3450
% 17.76/18.05
% 17.76/18.05 Low Water (keep): wt=29.000, iters=3426
% 17.76/18.05
% 17.76/18.05 Low Water (keep): wt=26.000, iters=3335
% 17.76/18.05
% 17.76/18.05 Low Water (keep): wt=24.000, iters=3426
% 17.76/18.05
% 17.76/18.05 Low Water (keep): wt=22.000, iters=3338
% 17.76/18.05
% 17.76/18.05 Low Water (keep): wt=21.000, iters=3335
% 17.76/18.05
% 17.76/18.05 Low Water (keep): wt=19.000, iters=3402
% 17.76/18.05
% 17.76/18.05 Low Water (keep): wt=18.000, iters=3338
% 17.76/18.05
% 17.76/18.05 Low Water (keep): wt=17.000, iters=3436
% 17.76/18.05
% 17.76/18.05 Low Water (keep): wt=15.000, iters=3345
% 17.76/18.05
% 17.76/18.05 Low Water (keep): wt=14.000, iters=3334
% 17.76/18.05
% 17.76/18.05 Low Water (displace): id=5116, wt=48.000
% 17.76/18.05
% 17.76/18.05 Low Water (displace): id=13250, wt=11.000
% 17.76/18.05
% 17.76/18.05 Low Water (displace): id=13264, wt=10.000
% 17.76/18.05
% 17.76/18.05 Low Water (displace): id=13307, wt=9.000
% 17.76/18.05
% 17.76/18.05 Low Water (displace): id=13341, wt=8.000
% 17.76/18.05
% 17.76/18.05 Low Water (keep): wt=13.000, iters=3333
% 17.76/18.05
% 17.76/18.05 Low Water (keep): wt=12.000, iters=3342
% 17.76/18.05
% 17.76/18.05 Low Water (displace): id=19324, wt=7.000
% 17.76/18.05
% 17.76/18.05 Low Water (keep): wt=11.000, iters=3333
% 17.76/18.05
% 17.76/18.05 Low Water (keep): wt=10.000, iters=3349
% 17.76/18.05
% 17.76/18.05 Low Water (keep): wt=9.000, iters=3333
% 17.76/18.05
% 17.76/18.05 ============================== PROOF =================================
% 17.76/18.05 % SZS status Theorem
% 17.76/18.05 % SZS output start Refutation
% 17.76/18.05
% 17.76/18.05 % Proof 1 at 16.82 (+ 0.14) seconds.
% 17.76/18.05 % Length of proof is 343.
% 17.76/18.05 % Level of proof is 39.
% 17.76/18.05 % Maximum clause weight is 29.000.
% 17.76/18.05 % Given clauses 20007.
% 17.76/18.05
% 17.76/18.05 1 (all A all B all C (coll(A,B,C) -> coll(A,C,B))) # label(ruleD1) # label(axiom) # label(non_clause). [assumption].
% 17.76/18.05 2 (all A all B all C (coll(A,B,C) -> coll(B,A,C))) # label(ruleD2) # label(axiom) # label(non_clause). [assumption].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 11 (all A all B all M (midp(M,B,A) -> midp(M,A,B))) # label(ruleD11) # label(axiom) # label(non_clause). [assumption].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 67 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption].
% 17.76/18.05 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].
% 17.76/18.05 69 (all A all B all C (midp(A,B,C) -> cong(A,B,A,C))) # label(ruleD68) # label(axiom) # label(non_clause). [assumption].
% 17.76/18.05 70 (all A all B all C (midp(A,B,C) -> coll(A,B,C))) # label(ruleD69) # label(axiom) # label(non_clause). [assumption].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 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].
% 17.76/18.05 95 -(all A all B all C all O all M all N all NWPNT1 (circle(O,A,B,C) & midp(M,B,A) & coll(N,O,M) & circle(O,A,N,NWPNT1) -> eqangle(A,C,C,N,N,C,C,B))) # label(exemplo6GDDFULL416059) # label(negated_conjecture) # label(non_clause). [assumption].
% 17.76/18.05 97 -cong(A,B,A,C) | -cong(A,B,A,D) | circle(A,B,C,D) # label(ruleD12) # label(axiom). [clausify(12)].
% 17.76/18.05 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)].
% 17.76/18.05 100 -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)].
% 17.76/18.05 101 -circle(A,B,C,D) | -coll(A,B,D) | perp(B,C,C,D) # label(ruleD53) # label(axiom). [clausify(54)].
% 17.76/18.05 102 -circle(A,B,C,D) | perp(f12(B,C,D,A),B,B,A) # label(ruleX11) # label(axiom). [clausify(87)].
% 17.76/18.05 109 circle(c4,c1,c2,c3) # label(exemplo6GDDFULL416059) # label(negated_conjecture). [clausify(95)].
% 17.76/18.05 111 -coll(A,B,C) | coll(A,C,B) # label(ruleD1) # label(axiom). [clausify(1)].
% 17.76/18.05 112 -coll(A,B,C) | coll(B,A,C) # label(ruleD2) # label(axiom). [clausify(2)].
% 17.76/18.05 113 -coll(A,B,C) | -coll(A,B,D) | coll(C,D,A) # label(ruleD3) # label(axiom). [clausify(3)].
% 17.76/18.05 114 -para(A,B,C,D) | para(A,B,D,C) # label(ruleD4) # label(axiom). [clausify(4)].
% 17.76/18.05 115 -para(A,B,C,D) | para(C,D,A,B) # label(ruleD5) # label(axiom). [clausify(5)].
% 17.76/18.05 116 -para(A,B,C,D) | -para(C,D,E,F) | para(A,B,E,F) # label(ruleD6) # label(axiom). [clausify(6)].
% 17.76/18.05 118 -perp(A,B,C,D) | perp(C,D,A,B) # label(ruleD8) # label(axiom). [clausify(8)].
% 17.76/18.05 119 -perp(A,B,C,D) | -perp(C,D,E,F) | para(A,B,E,F) # label(ruleD9) # label(axiom). [clausify(9)].
% 17.76/18.05 120 -para(A,B,C,D) | -perp(C,D,E,F) | perp(A,B,E,F) # label(ruleD10) # label(axiom). [clausify(10)].
% 17.76/18.05 121 -midp(A,B,C) | midp(A,C,B) # label(ruleD11) # label(axiom). [clausify(11)].
% 17.76/18.05 122 -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)].
% 17.76/18.05 123 -cyclic(A,B,C,D) | cyclic(A,B,D,C) # label(ruleD14) # label(axiom). [clausify(14)].
% 17.76/18.05 124 -cyclic(A,B,C,D) | cyclic(A,C,B,D) # label(ruleD15) # label(axiom). [clausify(15)].
% 17.76/18.05 125 -cyclic(A,B,C,D) | cyclic(B,A,C,D) # label(ruleD16) # label(axiom). [clausify(16)].
% 17.76/18.05 126 -cyclic(A,B,C,D) | -cyclic(A,B,C,E) | cyclic(B,C,D,E) # label(ruleD17) # label(axiom). [clausify(17)].
% 17.76/18.05 127 -eqangle(A,B,C,D,E,F,V6,V7) | eqangle(B,A,C,D,E,F,V6,V7) # label(ruleD18) # label(axiom). [clausify(18)].
% 17.76/18.05 128 -eqangle(A,B,C,D,E,F,V6,V7) | eqangle(C,D,A,B,V6,V7,E,F) # label(ruleD19) # label(axiom). [clausify(19)].
% 17.76/18.05 129 -eqangle(A,B,C,D,E,F,V6,V7) | eqangle(E,F,V6,V7,A,B,C,D) # label(ruleD20) # label(axiom). [clausify(20)].
% 17.76/18.05 130 -eqangle(A,B,C,D,E,F,V6,V7) | eqangle(A,B,E,F,C,D,V6,V7) # label(ruleD21) # label(axiom). [clausify(21)].
% 17.76/18.05 131 -eqangle(A,B,C,D,E,F,V6,V7) | -eqangle(E,F,V6,V7,V8,V9,V10,V11) | eqangle(A,B,C,D,V8,V9,V10,V11) # label(ruleD22) # label(axiom). [clausify(22)].
% 17.76/18.05 134 -cong(A,B,C,D) | -cong(C,D,E,F) | cong(A,B,E,F) # label(ruleD25) # label(axiom). [clausify(25)].
% 17.76/18.05 149 -para(A,B,C,D) | eqangle(A,B,E,F,C,D,E,F) # label(ruleD40) # label(axiom). [clausify(40)].
% 17.76/18.05 150 -cyclic(A,B,C,D) | eqangle(C,A,C,B,D,A,D,B) # label(ruleD41) # label(axiom). [clausify(41)].
% 17.76/18.05 152 -eqangle(A,B,A,C,D,B,D,C) | -coll(A,D,C) | cyclic(B,C,A,D) # label(ruleD42b) # label(axiom). [clausify(43)].
% 17.76/18.05 153 -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)].
% 17.76/18.05 154 -midp(A,B,C) | -midp(D,B,E) | para(A,D,C,E) # label(ruleD44) # label(axiom). [clausify(45)].
% 17.76/18.05 155 -midp(A,B,C) | -para(A,D,C,E) | -coll(D,B,E) | midp(D,B,E) # label(ruleD45) # label(axiom). [clausify(46)].
% 17.76/18.05 156 -cong(A,B,A,C) | eqangle(A,B,B,C,B,C,A,C) # label(ruleD46) # label(axiom). [clausify(47)].
% 17.76/18.05 159 -cyclic(A,B,C,D) | -para(A,B,C,D) | eqangle(A,D,C,D,C,D,C,B) # label(ruleD54) # label(axiom). [clausify(55)].
% 17.76/18.05 160 -midp(A,B,C) | -perp(D,A,B,C) | cong(D,B,D,C) # label(ruleD55) # label(axiom). [clausify(56)].
% 17.76/18.05 161 -cong(A,B,C,B) | -cong(A,D,C,D) | perp(A,C,B,D) # label(ruleD56) # label(axiom). [clausify(57)].
% 17.76/18.05 162 -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)].
% 17.76/18.05 168 -midp(A,B,C) | -midp(A,D,E) | para(B,D,C,E) # label(ruleD63) # label(axiom). [clausify(64)].
% 17.76/18.05 169 -midp(A,B,C) | -para(B,D,C,E) | -para(B,E,C,D) | midp(A,D,E) # label(ruleD64) # label(axiom). [clausify(65)].
% 17.76/18.05 171 -para(A,B,A,C) | coll(A,B,C) # label(ruleD66) # label(axiom). [clausify(67)].
% 17.76/18.05 172 -cong(A,B,A,C) | -coll(A,B,C) | midp(A,B,C) # label(ruleD67) # label(axiom). [clausify(68)].
% 17.76/18.05 173 -midp(A,B,C) | cong(A,B,A,C) # label(ruleD68) # label(axiom). [clausify(69)].
% 17.76/18.05 174 -midp(A,B,C) | coll(A,B,C) # label(ruleD69) # label(axiom). [clausify(70)].
% 17.76/18.05 190 -midp(A,B,C) | -midp(D,E,F) | midp(f6(B,C,E,F,A,D),B,F) # label(ruleX6) # label(axiom). [clausify(82)].
% 17.76/18.05 193 -midp(A,B,C) | -midp(D,E,F) | -coll(E,B,C) | -coll(F,B,C) | midp(f7(B,C,E,F,A,D,V6),B,V6) # label(ruleX7) # label(axiom). [clausify(83)].
% 17.76/18.05 210 midp(c5,c2,c1) # label(exemplo6GDDFULL416059) # label(negated_conjecture). [clausify(95)].
% 17.76/18.05 211 coll(c6,c4,c5) # label(exemplo6GDDFULL416059) # label(negated_conjecture). [clausify(95)].
% 17.76/18.05 212 -eqangle(c1,c3,c3,c6,c6,c3,c3,c2) # label(exemplo6GDDFULL416059) # label(negated_conjecture). [clausify(95)].
% 17.76/18.05 215 -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)].
% 17.76/18.05 216 -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)].
% 17.76/18.05 217 -coll(A,B,C) | perp(B,D,D,C) | -cong(A,B,A,D) | -cong(A,B,A,C). [resolve(101,a,97,c)].
% 17.76/18.05 256 perp(f12(c1,c2,c3,c4),c1,c1,c4). [resolve(109,a,102,a)].
% 17.76/18.05 279 -coll(A,B,C) | coll(C,C,A). [factor(113,a,b)].
% 17.76/18.05 281 -cong(A,B,A,C) | -cong(A,B,A,D) | cyclic(B,C,C,D). [factor(122,a,b)].
% 17.76/18.05 284 -cyclic(A,B,C,D) | cyclic(B,C,D,D). [factor(126,a,b)].
% 17.76/18.05 285 -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(153,a,b)].
% 17.76/18.05 286 -cyclic(A,B,C,D) | -cyclic(A,B,C,E) | -eqangle(C,A,C,B,D,D,D,E) | cong(A,B,D,E). [factor(153,a,c)].
% 17.76/18.05 288 -midp(A,B,C) | para(A,A,C,C). [factor(154,a,b)].
% 17.76/18.05 289 -cong(A,B,C,B) | perp(A,C,B,B). [factor(161,a,b)].
% 17.76/18.05 292 -midp(A,B,C) | para(B,B,C,C). [factor(168,a,b)].
% 17.76/18.05 293 -midp(A,B,C) | -para(B,D,C,D) | midp(A,D,D). [factor(169,b,c)].
% 17.76/18.05 316 -midp(A,B,B) | eqangle(C,B,C,B,D,B,D,A) | -cong(D,C,D,B). [factor(215,c,d)].
% 17.76/18.05 317 -coll(A,B,B) | -eqangle(C,B,C,B,D,B,D,A) | midp(A,B,B) | -cong(D,C,D,B). [factor(216,d,e)].
% 17.76/18.05 318 -coll(A,B,C) | perp(B,C,C,C) | -cong(A,B,A,C). [factor(217,c,d)].
% 17.76/18.05 333 -cong(A,B,A,C) | cyclic(B,C,C,C). [factor(281,a,b)].
% 17.76/18.05 334 -cyclic(A,B,C,D) | -eqangle(C,A,C,B,D,D,D,D) | cong(A,B,D,D). [factor(285,a,b)].
% 17.76/18.05 343 -midp(A,B,C) | -coll(B,c2,c1) | -coll(C,c2,c1) | midp(f7(c2,c1,B,C,c5,A,D),c2,D). [resolve(210,a,193,a)].
% 17.76/18.05 348 -midp(A,B,C) | midp(f6(B,C,c2,c1,A,c5),B,c1). [resolve(210,a,190,b)].
% 17.76/18.05 352 coll(c5,c2,c1). [resolve(210,a,174,a)].
% 17.76/18.05 353 cong(c5,c2,c5,c1). [resolve(210,a,173,a)].
% 17.76/18.05 354 -midp(c5,A,B) | para(A,c2,B,c1). [resolve(210,a,168,b)].
% 17.76/18.05 355 -midp(c5,A,B) | para(c2,A,c1,B). [resolve(210,a,168,a)].
% 17.76/18.05 358 midp(c5,c1,c2). [resolve(210,a,121,a)].
% 17.76/18.05 363 coll(c6,c5,c4). [resolve(211,a,111,a)].
% 17.76/18.05 384 -perp(A,B,f12(c1,c2,c3,c4),c1) | para(A,B,c1,c4). [resolve(256,a,119,b)].
% 17.76/18.05 386 perp(c1,c4,f12(c1,c2,c3,c4),c1). [resolve(256,a,118,a)].
% 17.76/18.05 414 coll(c5,c5,c6). [resolve(279,a,211,a)].
% 17.76/18.05 415 para(c5,c5,c1,c1). [resolve(288,a,210,a)].
% 17.76/18.05 422 coll(c1,c1,c5). [resolve(352,a,279,a)].
% 17.76/18.05 425 coll(c2,c5,c1). [resolve(352,a,112,a)].
% 17.76/18.05 446 cong(c5,c1,c5,c2). [resolve(358,a,173,a)].
% 17.76/18.05 447 -midp(c5,A,B) | para(A,c1,B,c2). [resolve(358,a,168,b)].
% 17.76/18.05 456 -coll(c6,c5,A) | coll(A,c4,c6). [resolve(363,a,113,b)].
% 17.76/18.05 459 -coll(c1,c2,c1) | -coll(c2,c2,c1) | midp(f7(c2,c1,c1,c2,c5,c5,A),c2,A). [resolve(343,a,358,a)].
% 17.76/18.05 461 -coll(c5,c5,A) | coll(A,c6,c5). [resolve(414,a,113,b)].
% 17.76/18.05 467 coll(c1,c5,c1). [resolve(422,a,111,a)].
% 17.76/18.05 468 coll(c1,c1,c2). [resolve(425,a,279,a)].
% 17.76/18.05 469 -coll(c2,c5,A) | coll(A,c1,c2). [resolve(425,a,113,b)].
% 17.76/18.05 471 coll(c2,c1,c5). [resolve(425,a,111,a)].
% 17.76/18.05 503 coll(c1,c1,c1). [resolve(467,a,279,a)].
% 17.76/18.05 506 coll(c5,c1,c1). [resolve(467,a,112,a)].
% 17.76/18.05 508 coll(c2,c2,c1). [resolve(468,a,279,a)].
% 17.76/18.05 511 coll(c1,c2,c1). [resolve(468,a,111,a)].
% 17.76/18.05 512 midp(f7(c2,c1,c1,c2,c5,c5,A),c2,A). [back_unit_del(459),unit_del(a,511),unit_del(b,508)].
% 17.76/18.05 514 coll(c5,c5,c2). [resolve(471,a,279,a)].
% 17.76/18.05 535 midp(f6(c1,c2,c2,c1,c5,c5),c1,c1). [resolve(348,a,358,a)].
% 17.76/18.05 555 -coll(c2,c2,A) | coll(c1,A,c2). [resolve(508,a,113,a)].
% 17.76/18.05 590 cyclic(c2,c1,c1,c1). [resolve(353,a,333,a)].
% 17.76/18.05 628 perp(c2,c1,c1,c1). [resolve(353,a,318,c),unit_del(a,352)].
% 17.76/18.05 659 -cong(A,B,c5,c2) | cong(A,B,c5,c1). [resolve(353,a,134,b)].
% 17.76/18.05 672 para(c1,c2,c2,c1). [resolve(354,a,358,a)].
% 17.76/18.05 682 para(c2,c1,c1,c2). [resolve(355,a,358,a)].
% 17.76/18.05 706 para(c1,c1,c5,c5). [resolve(415,a,115,a)].
% 17.76/18.05 755 cyclic(c1,c2,c2,c2). [resolve(446,a,333,a)].
% 17.76/18.05 835 cyclic(c1,c1,c1,c1). [resolve(590,a,284,a)].
% 17.76/18.05 853 cyclic(c1,c2,c1,c1). [resolve(590,a,125,a)].
% 17.76/18.05 872 -midp(c1,c1,c1) | cong(c2,c1,c2,c1). [resolve(628,a,160,b)].
% 17.76/18.05 875 -perp(c1,c1,A,B) | para(c2,c1,A,B). [resolve(628,a,119,a)].
% 17.76/18.05 903 para(c1,c2,c1,c2). [resolve(672,a,114,a)].
% 17.76/18.05 919 para(c2,c1,c2,c1). [resolve(682,a,114,a)].
% 17.76/18.05 930 -perp(c5,c5,A,B) | perp(c1,c1,A,B). [resolve(706,a,120,a)].
% 17.76/18.05 965 cyclic(c2,c1,c2,c2). [resolve(755,a,125,a)].
% 17.76/18.05 1016 eqangle(c1,c1,c1,c1,c1,c1,c1,c1). [resolve(835,a,150,a)].
% 17.76/18.05 1035 eqangle(c1,c1,c1,c2,c1,c1,c1,c2). [resolve(853,a,150,a)].
% 17.76/18.05 1037 cyclic(c1,c1,c2,c1). [resolve(853,a,124,a)].
% 17.76/18.05 1056 -midp(A,c1,c1) | midp(A,c2,c2). [resolve(903,a,293,b)].
% 17.76/18.05 1065 eqangle(c1,c2,A,B,c1,c2,A,B). [resolve(903,a,149,a)].
% 17.76/18.05 1077 eqangle(c2,c1,A,B,c2,c1,A,B). [resolve(919,a,149,a)].
% 17.76/18.05 1115 cyclic(c2,c2,c1,c2). [resolve(965,a,124,a)].
% 17.76/18.05 1148 cyclic(c1,c1,c1,c2). [resolve(1037,a,123,a)].
% 17.76/18.05 1190 -cyclic(c2,c2,c1,A) | cyclic(c2,c1,A,c2). [resolve(1115,a,126,b)].
% 17.76/18.05 1191 cyclic(c2,c2,c2,c1). [resolve(1115,a,123,a)].
% 17.76/18.05 1228 cyclic(c1,c1,c2,c2). [resolve(1148,a,284,a)].
% 17.76/18.05 1247 -cyclic(c1,c1,c1,A) | cyclic(c1,c1,c2,A). [resolve(1148,a,126,a)].
% 17.76/18.05 1274 cyclic(c2,c2,c1,c1). [resolve(1191,a,284,a)].
% 17.76/18.05 1292 -cyclic(c2,c2,c2,A) | cyclic(c2,c2,A,c1). [resolve(1191,a,126,b)].
% 17.76/18.05 1293 -cyclic(c2,c2,c2,A) | cyclic(c2,c2,c1,A). [resolve(1191,a,126,a)].
% 17.76/18.05 1345 -cyclic(c1,c1,c2,A) | cyclic(c1,c2,c2,A). [resolve(1228,a,126,a)].
% 17.76/18.05 1346 cyclic(c1,c2,c1,c2). [resolve(1228,a,124,a)].
% 17.76/18.05 1376 -cyclic(c2,c2,c1,A) | cyclic(c2,c1,c1,A). [resolve(1274,a,126,a)].
% 17.76/18.05 1409 cyclic(c2,c1,c1,c2). [resolve(1346,a,125,a)].
% 17.76/18.05 1410 cyclic(c1,c2,c2,c1). [resolve(1346,a,123,a)].
% 17.76/18.05 1446 -cyclic(c2,c1,c1,A) | cyclic(c1,c1,A,c2). [resolve(1409,a,126,b)].
% 17.76/18.05 1464 -cyclic(c1,c2,c2,A) | cyclic(c2,c2,A,c1). [resolve(1410,a,126,b)].
% 17.76/18.05 1465 -cyclic(c1,c2,c2,A) | cyclic(c2,c2,c1,A). [resolve(1410,a,126,a)].
% 17.76/18.05 1466 coll(c2,c6,c5). [resolve(461,a,514,a)].
% 17.76/18.05 1470 coll(c6,c2,c5). [resolve(1466,a,112,a)].
% 17.76/18.05 1471 coll(c2,c5,c6). [resolve(1466,a,111,a)].
% 17.76/18.05 1478 coll(c6,c5,c2). [resolve(1470,a,111,a)].
% 17.76/18.05 1491 coll(c2,c4,c6). [resolve(1478,a,456,a)].
% 17.76/18.05 1492 coll(c2,c2,c6). [resolve(1478,a,279,a)].
% 17.76/18.05 1519 coll(c2,c6,c4). [resolve(1491,a,111,a)].
% 17.76/18.05 1521 -coll(c2,c2,A) | coll(c6,A,c2). [resolve(1492,a,113,a)].
% 17.76/18.05 1522 coll(c2,c6,c2). [resolve(1492,a,111,a)].
% 17.76/18.05 1552 coll(c4,c4,c2). [resolve(1519,a,279,a)].
% 17.76/18.05 1558 coll(c6,c2,c2). [resolve(1522,a,112,a)].
% 17.76/18.05 1595 coll(c4,c2,c4). [resolve(1552,a,111,a)].
% 17.76/18.05 1598 -coll(c6,c2,A) | coll(A,c2,c6). [resolve(1558,a,113,b)].
% 17.76/18.05 1659 para(c1,c4,c1,c4). [resolve(386,a,384,a)].
% 17.76/18.05 1714 -midp(A,c1,c1) | midp(A,c4,c4). [resolve(1659,a,293,b)].
% 17.76/18.05 1722 -midp(c1,A,c1) | -coll(c4,A,c4) | midp(c4,A,c4). [resolve(1659,a,155,b)].
% 17.76/18.05 1770 coll(c6,c1,c2). [resolve(469,a,1471,a)].
% 17.76/18.05 1779 coll(c1,c6,c2). [resolve(1770,a,112,a)].
% 17.76/18.05 1791 coll(c1,c2,c6). [resolve(1779,a,111,a)].
% 17.76/18.05 1800 -coll(c1,c2,A) | coll(A,c6,c1). [resolve(1791,a,113,b)].
% 17.76/18.05 2248 para(c2,c2,A,A). [resolve(512,a,292,a)].
% 17.76/18.05 2264 -midp(f7(c2,c1,c1,c2,c5,c5,A),B,C) | para(c2,B,A,C). [resolve(512,a,168,a)].
% 17.76/18.05 2267 midp(f7(c2,c1,c1,c2,c5,c5,A),A,c2). [resolve(512,a,121,a)].
% 17.76/18.05 2288 eqangle(c2,c2,A,B,C,C,A,B). [resolve(2248,a,149,a)].
% 17.76/18.05 2292 para(A,A,c2,c2). [resolve(2248,a,115,a)].
% 17.76/18.05 2302 eqangle(A,A,B,C,c2,c2,B,C). [resolve(2292,a,149,a)].
% 17.76/18.05 2403 para(c1,c1,c1,c1). [resolve(535,a,292,a)].
% 17.76/18.05 2439 eqangle(c1,c1,A,B,c1,c1,A,B). [resolve(2403,a,149,a)].
% 17.76/18.05 3774 cong(c5,c1,c5,c1). [resolve(659,a,446,a)].
% 17.76/18.05 3856 midp(c5,c1,c1). [resolve(3774,a,172,a),unit_del(a,506)].
% 17.76/18.05 3877 midp(c5,c4,c4). [resolve(3856,a,1714,a)].
% 17.76/18.05 3878 midp(c5,c2,c2). [resolve(3856,a,1056,a)].
% 17.76/18.05 3883 para(c1,c1,c1,c2). [resolve(3856,a,447,a)].
% 17.76/18.05 3896 para(c1,c2,c1,c1). [resolve(3856,a,354,a)].
% 17.76/18.05 3970 para(c2,c4,c1,c4). [resolve(3877,a,355,a)].
% 17.76/18.05 3998 cong(c5,c4,c5,c4). [resolve(3877,a,173,a)].
% 17.76/18.05 4006 para(c2,c1,c2,c2). [resolve(3878,a,447,a)].
% 17.76/18.05 4303 -midp(A,c1,c1) | midp(A,c2,c1). [resolve(3883,a,169,c),unit_del(b,3896)].
% 17.76/18.05 4304 -midp(A,c1,c1) | midp(A,c1,c2). [resolve(3883,a,169,b),unit_del(b,3896)].
% 17.76/18.05 4388 para(c2,c4,c4,c1). [resolve(3970,a,114,a)].
% 17.76/18.05 4499 perp(c5,c5,c4,c4). [resolve(3998,a,289,a)].
% 17.76/18.05 4757 -perp(c2,c2,A,B) | perp(c2,c1,A,B). [resolve(4006,a,120,a)].
% 17.76/18.05 5066 -midp(A,c2,c4) | -para(c2,c1,c4,c4) | midp(A,c4,c1). [resolve(4388,a,169,b)].
% 17.76/18.05 9597 perp(c1,c1,c4,c4). [resolve(930,a,4499,a)].
% 17.76/18.05 9598 para(c2,c1,c4,c4). [resolve(9597,a,875,a)].
% 17.76/18.05 9613 -midp(A,c2,c4) | midp(A,c4,c1). [back_unit_del(5066),unit_del(b,9598)].
% 17.76/18.05 10459 cong(c1,c1,c1,c1). [resolve(1016,a,334,b),unit_del(a,835)].
% 17.76/18.05 10460 midp(c1,c1,c1). [resolve(1016,a,317,b),unit_del(a,503),unit_del(c,10459)].
% 17.76/18.05 10479 cong(c2,c1,c2,c1). [back_unit_del(872),unit_del(a,10460)].
% 17.76/18.05 10492 midp(c1,c1,c2). [resolve(10460,a,4304,a)].
% 17.76/18.05 10493 midp(c1,c2,c1). [resolve(10460,a,4303,a)].
% 17.76/18.05 10736 cong(c1,c2,c1,c2). [resolve(1035,a,286,c),unit_del(a,853),unit_del(b,1346)].
% 17.76/18.05 12420 -coll(c1,c1,A) | cyclic(c2,A,c1,c1). [resolve(1065,a,152,a)].
% 17.76/18.05 12769 -coll(c2,c2,A) | cyclic(c1,A,c2,c2). [resolve(1077,a,152,a)].
% 17.76/18.05 15716 midp(c4,c2,c4). [resolve(1722,a,10493,a),unit_del(a,1595)].
% 17.76/18.05 15722 midp(c4,c4,c1). [resolve(15716,a,9613,a)].
% 17.76/18.05 15755 midp(c4,c4,c2). [resolve(15716,a,121,a)].
% 17.76/18.05 15819 cong(c4,c4,c4,c1). [resolve(15722,a,173,a)].
% 17.76/18.05 15849 cong(c4,c4,c4,c2). [resolve(15755,a,173,a)].
% 17.76/18.05 15920 cyclic(c4,c1,c1,c1). [resolve(15819,a,333,a)].
% 17.76/18.05 15934 cyclic(c4,c2,c2,c2). [resolve(15849,a,333,a)].
% 17.76/18.05 16035 cyclic(c1,c4,c1,c1). [resolve(15920,a,125,a)].
% 17.76/18.05 16066 cyclic(c2,c4,c2,c2). [resolve(15934,a,125,a)].
% 17.76/18.05 16146 cyclic(c1,c1,c4,c1). [resolve(16035,a,124,a)].
% 17.76/18.05 16208 cyclic(c2,c2,c4,c2). [resolve(16066,a,124,a)].
% 17.76/18.05 16302 cyclic(c1,c1,c1,c4). [resolve(16146,a,123,a)].
% 17.76/18.05 16361 -cyclic(c2,c2,c4,A) | cyclic(c2,c4,A,c2). [resolve(16208,a,126,b)].
% 17.76/18.05 16362 cyclic(c2,c2,c2,c4). [resolve(16208,a,123,a)].
% 17.76/18.05 16434 cyclic(c1,c1,c2,c4). [resolve(16302,a,1247,a)].
% 17.76/18.05 16858 cyclic(c2,c2,c1,c4). [resolve(16362,a,1293,a)].
% 17.76/18.05 16859 cyclic(c2,c2,c4,c1). [resolve(16362,a,1292,a)].
% 17.76/18.05 16957 cyclic(c1,c2,c2,c4). [resolve(16434,a,1345,a)].
% 17.76/18.05 17179 cyclic(c2,c1,c4,c2). [resolve(16858,a,1190,a)].
% 17.76/18.05 17189 -cyclic(c2,c2,c4,A) | cyclic(c2,c4,c1,A). [resolve(16859,a,126,a)].
% 17.76/18.05 17240 -cyclic(c1,c2,c2,A) | cyclic(c2,c2,c4,A). [resolve(16957,a,126,a)].
% 17.76/18.05 17446 cyclic(c2,c4,c1,c2). [resolve(17179,a,124,a)].
% 17.76/18.05 17753 -cyclic(c2,c4,c1,A) | cyclic(c4,c1,c2,A). [resolve(17446,a,126,a)].
% 17.76/18.05 20577 para(c2,A,A,c2). [resolve(2267,a,2264,a)].
% 17.76/18.05 20581 -para(A,c2,B,C) | para(c2,A,B,C). [resolve(20577,a,116,a)].
% 17.76/18.05 20582 para(c2,A,c2,A). [resolve(20577,a,114,a)].
% 17.76/18.05 20587 -midp(A,c2,c2) | midp(A,B,B). [resolve(20582,a,293,b)].
% 17.76/18.05 20588 coll(c2,A,A). [resolve(20582,a,171,a)].
% 17.76/18.05 20595 coll(A,A,c2). [resolve(20588,a,279,a)].
% 17.76/18.05 20606 coll(c2,c2,A). [resolve(20595,a,279,a)].
% 17.76/18.05 20640 cyclic(c1,A,c2,c2). [back_unit_del(12769),unit_del(a,20606)].
% 17.76/18.05 20689 coll(c6,A,c2). [back_unit_del(1521),unit_del(a,20606)].
% 17.76/18.05 20692 coll(c1,A,c2). [back_unit_del(555),unit_del(a,20606)].
% 17.76/18.05 20774 coll(A,B,c2). [resolve(20606,a,113,b),unit_del(a,20606)].
% 17.76/18.05 20895 coll(c6,c2,A). [resolve(20689,a,111,a)].
% 17.76/18.05 20946 coll(A,c2,c6). [back_unit_del(1598),unit_del(a,20895)].
% 17.76/18.05 20960 cyclic(c2,A,c2,c2). [resolve(2288,a,152,a),unit_del(a,20606)].
% 17.76/18.05 20967 coll(c1,c2,A). [resolve(20692,a,111,a)].
% 17.76/18.05 21030 coll(A,c6,c1). [back_unit_del(1800),unit_del(a,20967)].
% 17.76/18.05 21229 coll(A,c2,B). [resolve(20774,a,111,a)].
% 17.76/18.05 21492 -cyclic(c2,A,c2,A) | cong(c2,A,c2,A). [resolve(2302,a,286,c),unit_del(a,20960)].
% 17.76/18.05 21514 coll(A,c6,B). [resolve(20946,a,113,b),unit_del(a,21229)].
% 17.76/18.05 21535 coll(A,c1,B). [resolve(21030,a,113,b),unit_del(a,21514)].
% 17.76/18.05 21538 cyclic(c2,A,c1,c1). [back_unit_del(12420),unit_del(a,21535)].
% 17.76/18.05 21569 coll(A,B,C). [resolve(21229,a,113,b),unit_del(a,21229)].
% 17.76/18.05 21572 -midp(A,B,C) | -para(A,D,C,E) | midp(D,B,E). [back_unit_del(155),unit_del(c,21569)].
% 17.76/18.05 21584 -cyclic(c1,A,c2,B) | cyclic(A,c2,B,c2). [resolve(20640,a,126,b)].
% 17.76/18.05 21587 cyclic(c1,c2,A,c2). [resolve(20640,a,124,a)].
% 17.76/18.05 21866 cyclic(c2,c1,A,c1). [resolve(21538,a,124,a)].
% 17.76/18.05 21875 -cyclic(c1,c2,A,B) | cyclic(c2,A,c2,B). [resolve(21587,a,126,a)].
% 17.76/18.05 21876 cyclic(c2,c1,A,c2). [resolve(21587,a,125,a)].
% 17.76/18.05 21877 cyclic(c1,c2,c2,A). [resolve(21587,a,123,a)].
% 17.76/18.05 21878 cyclic(c2,c2,c4,A). [back_unit_del(17240),unit_del(a,21877)].
% 17.76/18.05 21880 cyclic(c2,c2,c1,A). [back_unit_del(1465),unit_del(a,21877)].
% 17.76/18.05 21881 cyclic(c2,c2,A,c1). [back_unit_del(1464),unit_del(a,21877)].
% 17.76/18.05 21885 cyclic(c2,c4,c1,A). [back_unit_del(17189),unit_del(a,21878)].
% 17.76/18.05 21887 cyclic(c2,c4,A,c2). [back_unit_del(16361),unit_del(a,21878)].
% 17.76/18.05 21890 cyclic(c2,c1,c1,A). [back_unit_del(1376),unit_del(a,21880)].
% 17.76/18.05 21896 cyclic(c4,c1,c2,A). [back_unit_del(17753),unit_del(a,21885)].
% 17.76/18.05 21905 cyclic(c1,c1,A,c2). [back_unit_del(1446),unit_del(a,21890)].
% 17.76/18.05 22034 -cyclic(c2,c1,A,B) | cyclic(c1,A,B,c1). [resolve(21866,a,126,b)].
% 17.76/18.05 22035 -cyclic(c2,c1,A,B) | cyclic(c1,A,c1,B). [resolve(21866,a,126,a)].
% 17.76/18.05 22042 -cyclic(c2,c1,A,B) | cyclic(c1,A,c2,B). [resolve(21876,a,126,a)].
% 17.76/18.05 22046 cyclic(c2,c2,A,B). [resolve(21877,a,126,b),unit_del(a,21877)].
% 17.76/18.05 22051 cyclic(c2,c4,A,B). [resolve(21878,a,126,b),unit_del(a,22046)].
% 17.76/18.05 22059 cyclic(c2,c1,A,B). [resolve(21880,a,126,b),unit_del(a,22046)].
% 17.76/18.05 22060 cyclic(c1,A,c2,B). [back_unit_del(22042),unit_del(a,22059)].
% 17.76/18.05 22062 cyclic(c1,A,c1,B). [back_unit_del(22035),unit_del(a,22059)].
% 17.76/18.05 22063 cyclic(c1,A,B,c1). [back_unit_del(22034),unit_del(a,22059)].
% 17.76/18.05 22065 cyclic(A,c2,B,c2). [back_unit_del(21584),unit_del(a,22060)].
% 17.76/18.05 22066 -cong(c2,A,c2,A) | perp(A,c2,c2,c1). [resolve(21881,a,162,c),unit_del(b,10479)].
% 17.76/18.05 22092 cyclic(c4,A,c2,B). [resolve(21887,a,126,a),unit_del(a,22051)].
% 17.76/18.05 22118 cyclic(c1,c2,A,B). [resolve(21896,a,126,b),unit_del(a,22092)].
% 17.76/18.05 22119 cyclic(c2,A,c2,B). [back_unit_del(21875),unit_del(a,22118)].
% 17.76/18.05 22120 cong(c2,A,c2,A). [back_unit_del(21492),unit_del(a,22119)].
% 17.76/18.05 22121 perp(A,c2,c2,c1). [back_unit_del(22066),unit_del(a,22120)].
% 17.76/18.05 22148 -cong(c1,A,c1,A) | perp(A,c1,c1,c2). [resolve(21905,a,162,c),unit_del(b,10736)].
% 17.76/18.05 22281 cyclic(c2,A,B,B). [resolve(22046,a,284,a)].
% 17.76/18.05 22298 cong(c1,A,c1,A). [resolve(2439,a,286,c),unit_del(a,22063),unit_del(b,22062)].
% 17.76/18.05 22302 perp(A,c1,c1,c2). [back_unit_del(22148),unit_del(a,22298)].
% 17.76/18.05 22344 eqangle(A,B,A,c2,c2,B,c2,c2). [resolve(22065,a,150,a)].
% 17.76/18.05 22405 perp(c2,c2,A,B). [resolve(22120,a,161,b),unit_del(a,22120)].
% 17.76/18.05 22406 eqangle(c2,A,A,A,A,A,c2,A). [resolve(22120,a,156,a)].
% 17.76/18.05 22422 perp(c2,c1,A,B). [back_unit_del(4757),unit_del(a,22405)].
% 17.76/18.05 22507 para(A,c2,B,C). [resolve(22121,a,119,a),unit_del(a,22422)].
% 17.76/18.05 22509 para(c2,A,B,C). [back_unit_del(20581),unit_del(a,22507)].
% 17.76/18.05 22630 eqangle(c2,A,A,A,A,A,A,B). [resolve(22281,a,159,a),unit_del(a,22509)].
% 17.76/18.05 22670 cong(A,c1,A,c2). [resolve(22302,a,160,b),unit_del(a,10492)].
% 17.76/18.05 22757 -perp(A,B,c2,c2) | para(A,B,C,D). [resolve(22405,a,119,b)].
% 17.76/18.05 22758 perp(A,B,c2,c2). [resolve(22405,a,118,a)].
% 17.76/18.05 22759 para(A,B,C,D). [back_unit_del(22757),unit_del(a,22758)].
% 17.76/18.05 22768 -midp(A,B,C) | midp(D,B,E). [back_unit_del(21572),unit_del(b,22759)].
% 17.76/18.05 22771 eqangle(A,B,C,D,E,F,C,D). [back_unit_del(149),unit_del(a,22759)].
% 17.76/18.05 22908 -midp(A,c2,c2) | eqangle(c1,c2,c1,c2,B,c2,B,A). [resolve(22670,a,316,c)].
% 17.76/18.05 25396 midp(c5,A,A). [resolve(20587,a,3878,a)].
% 17.76/18.05 26898 midp(A,B,C). [resolve(22768,a,25396,a)].
% 17.76/18.05 26943 eqangle(c1,c2,c1,c2,A,c2,A,B). [back_unit_del(22908),unit_del(a,26898)].
% 17.76/18.05 28366 eqangle(A,B,B,c2,c2,A,c2,c2). [resolve(22344,a,127,a)].
% 17.76/18.05 28440 eqangle(A,c2,A,A,A,A,c2,A). [resolve(22406,a,127,a)].
% 17.76/18.05 28468 eqangle(A,A,c2,A,A,B,A,A). [resolve(22630,a,128,a)].
% 17.76/18.05 28479 eqangle(A,B,C,D,E,F,E,F). [resolve(22771,a,130,a)].
% 17.76/18.05 32321 eqangle(A,B,C,D,E,c2,E,F). [resolve(26943,a,131,b),unit_del(a,28479)].
% 17.76/18.05 33649 eqangle(c2,A,c2,c2,A,B,B,c2). [resolve(28366,a,129,a)].
% 17.76/18.05 33706 eqangle(A,B,C,D,E,E,c2,E). [resolve(28440,a,131,b),unit_del(a,32321)].
% 17.76/18.05 33736 eqangle(A,B,C,D,E,F,E,E). [resolve(28468,a,131,b),unit_del(a,33706)].
% 17.76/18.05 39121 eqangle(A,B,C,D,E,F,F,c2). [resolve(33649,a,131,b),unit_del(a,33736)].
% 17.76/18.05 39122 $F. [resolve(39121,a,212,a)].
% 17.76/18.05
% 17.76/18.05 % SZS output end Refutation
% 17.76/18.05 ============================== end of proof ==========================
% 17.76/18.05
% 17.76/18.05 ============================== STATISTICS ============================
% 17.76/18.05
% 17.76/18.05 Given=20007. Generated=214604. Kept=38995. proofs=1.
% 17.76/18.05 Usable=18428. Sos=7069. Demods=0. Limbo=0, Disabled=13665. Hints=0.
% 17.76/18.05 Megabytes=19.81.
% 17.76/18.05 User_CPU=16.82, System_CPU=0.14, Wall_clock=17.
% 17.76/18.05
% 17.76/18.05 ============================== end of statistics =====================
% 17.76/18.05
% 17.76/18.05 ============================== end of search =========================
% 17.76/18.05
% 17.76/18.05 THEOREM PROVED
% 17.76/18.05 % SZS status Theorem
% 17.76/18.05
% 17.76/18.05 Exiting with 1 proof.
% 17.76/18.05
% 17.76/18.05 Process 30025 exit (max_proofs) Sat Jun 18 07:49:52 2022
% 17.76/18.05 Prover9 interrupted
%------------------------------------------------------------------------------