TSTP Solution File: GEO615+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GEO615+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n006.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 05:57:14 EDT 2022
% Result : Theorem 17.80s 18.08s
% Output : Refutation 17.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GEO615+1 : TPTP v8.1.0. Released v7.5.0.
% 0.03/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.15/0.36 % Computer : n006.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Fri Jun 17 17:36:56 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.81/1.14 ============================== Prover9 ===============================
% 0.81/1.14 Prover9 (32) version 2009-11A, November 2009.
% 0.81/1.14 Process 6259 was started by sandbox on n006.cluster.edu,
% 0.81/1.14 Fri Jun 17 17:36:56 2022
% 0.81/1.14 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_6106_n006.cluster.edu".
% 0.81/1.14 ============================== end of head ===========================
% 0.81/1.14
% 0.81/1.14 ============================== INPUT =================================
% 0.81/1.14
% 0.81/1.14 % Reading from file /tmp/Prover9_6106_n006.cluster.edu
% 0.81/1.14
% 0.81/1.14 set(prolog_style_variables).
% 0.81/1.14 set(auto2).
% 0.81/1.14 % set(auto2) -> set(auto).
% 0.81/1.14 % set(auto) -> set(auto_inference).
% 0.81/1.14 % set(auto) -> set(auto_setup).
% 0.81/1.14 % set(auto_setup) -> set(predicate_elim).
% 0.81/1.14 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.81/1.14 % set(auto) -> set(auto_limits).
% 0.81/1.14 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.81/1.14 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.81/1.14 % set(auto) -> set(auto_denials).
% 0.81/1.14 % set(auto) -> set(auto_process).
% 0.81/1.14 % set(auto2) -> assign(new_constants, 1).
% 0.81/1.14 % set(auto2) -> assign(fold_denial_max, 3).
% 0.81/1.14 % set(auto2) -> assign(max_weight, "200.000").
% 0.81/1.14 % set(auto2) -> assign(max_hours, 1).
% 0.81/1.14 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.81/1.14 % set(auto2) -> assign(max_seconds, 0).
% 0.81/1.14 % set(auto2) -> assign(max_minutes, 5).
% 0.81/1.14 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.81/1.14 % set(auto2) -> set(sort_initial_sos).
% 0.81/1.14 % set(auto2) -> assign(sos_limit, -1).
% 0.81/1.14 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.81/1.14 % set(auto2) -> assign(max_megs, 400).
% 0.81/1.14 % set(auto2) -> assign(stats, some).
% 0.81/1.14 % set(auto2) -> clear(echo_input).
% 0.81/1.14 % set(auto2) -> set(quiet).
% 0.81/1.14 % set(auto2) -> clear(print_initial_clauses).
% 0.81/1.14 % set(auto2) -> clear(print_given).
% 0.81/1.14 assign(lrs_ticks,-1).
% 0.81/1.14 assign(sos_limit,10000).
% 0.81/1.14 assign(order,kbo).
% 0.81/1.14 set(lex_order_vars).
% 0.81/1.14 clear(print_given).
% 0.81/1.14
% 0.81/1.14 % formulas(sos). % not echoed (95 formulas)
% 0.81/1.14
% 0.81/1.14 ============================== end of input ==========================
% 0.81/1.14
% 0.81/1.14 % From the command line: assign(max_seconds, 300).
% 0.81/1.14
% 0.81/1.14 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.81/1.14
% 0.81/1.14 % Formulas that are not ordinary clauses:
% 0.81/1.14 1 (all A all B all C (coll(A,B,C) -> coll(A,C,B))) # label(ruleD1) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 2 (all A all B all C (coll(A,B,C) -> coll(B,A,C))) # label(ruleD2) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 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].
% 0.81/1.14 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].
% 0.81/1.14 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].
% 0.81/1.14 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].
% 0.81/1.14 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].
% 0.81/1.14 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].
% 0.81/1.14 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].
% 0.81/1.14 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].
% 0.81/1.14 11 (all A all B all M (midp(M,B,A) -> midp(M,A,B))) # label(ruleD11) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 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].
% 0.81/1.14 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].
% 0.81/1.14 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].
% 0.81/1.14 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].
% 0.81/1.14 16 (all A all B all C all D (cyclic(A,B,C,D) -> cyclic(B,A,C,D))) # label(ruleD16) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 17 (all A all B all C all D all E (cyclic(A,B,C,D) & cyclic(A,B,C,E) -> cyclic(B,C,D,E))) # label(ruleD17) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 18 (all A all B all C all D all P all Q all U all V (eqangle(A,B,C,D,P,Q,U,V) -> eqangle(B,A,C,D,P,Q,U,V))) # label(ruleD18) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 19 (all A all B all C all D all P all Q all U all V (eqangle(A,B,C,D,P,Q,U,V) -> eqangle(C,D,A,B,U,V,P,Q))) # label(ruleD19) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 20 (all A all B all C all D all P all Q all U all V (eqangle(A,B,C,D,P,Q,U,V) -> eqangle(P,Q,U,V,A,B,C,D))) # label(ruleD20) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 21 (all A all B all C all D all P all Q all U all V (eqangle(A,B,C,D,P,Q,U,V) -> eqangle(A,B,P,Q,C,D,U,V))) # label(ruleD21) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 22 (all A all B all C all D all P all Q all U all V all E all F all G all H (eqangle(A,B,C,D,P,Q,U,V) & eqangle(P,Q,U,V,E,F,G,H) -> eqangle(A,B,C,D,E,F,G,H))) # label(ruleD22) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 23 (all A all B all C all D (cong(A,B,C,D) -> cong(A,B,D,C))) # label(ruleD23) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 24 (all A all B all C all D (cong(A,B,C,D) -> cong(C,D,A,B))) # label(ruleD24) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 25 (all A all B all C all D all E all F (cong(A,B,C,D) & cong(C,D,E,F) -> cong(A,B,E,F))) # label(ruleD25) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 26 (all A all B all C all D all P all Q all U all V (eqratio(A,B,C,D,P,Q,U,V) -> eqratio(B,A,C,D,P,Q,U,V))) # label(ruleD26) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 27 (all A all B all C all D all P all Q all U all V (eqratio(A,B,C,D,P,Q,U,V) -> eqratio(C,D,A,B,U,V,P,Q))) # label(ruleD27) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 28 (all A all B all C all D all P all Q all U all V (eqratio(A,B,C,D,P,Q,U,V) -> eqratio(P,Q,U,V,A,B,C,D))) # label(ruleD28) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 29 (all A all B all C all D all P all Q all U all V (eqratio(A,B,C,D,P,Q,U,V) -> eqratio(A,B,P,Q,C,D,U,V))) # label(ruleD29) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 30 (all A all B all C all D all E all F all G all H all P all Q all U all V (eqratio(A,B,C,D,P,Q,U,V) & eqratio(P,Q,U,V,E,F,G,H) -> eqratio(A,B,C,D,E,F,G,H))) # label(ruleD30) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 31 (all A all B all C all P all Q all R (simtri(A,C,B,P,R,Q) -> simtri(A,B,C,P,Q,R))) # label(ruleD31) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 32 (all A all B all C all P all Q all R (simtri(B,A,C,Q,P,R) -> simtri(A,B,C,P,Q,R))) # label(ruleD32) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 33 (all A all B all C all P all Q all R (simtri(P,Q,R,A,B,C) -> simtri(A,B,C,P,Q,R))) # label(ruleD33) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 34 (all A all B all C all E all F all G all P all Q all R (simtri(A,B,C,E,F,G) & simtri(E,F,G,P,Q,R) -> simtri(A,B,C,P,Q,R))) # label(ruleD34) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 35 (all A all B all C all P all Q all R (contri(A,C,B,P,R,Q) -> contri(A,B,C,P,Q,R))) # label(ruleD35) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 36 (all A all B all C all P all Q all R (contri(B,A,C,Q,P,R) -> contri(A,B,C,P,Q,R))) # label(ruleD36) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 37 (all A all B all C all P all Q all R (contri(P,Q,R,A,B,C) -> contri(A,B,C,P,Q,R))) # label(ruleD37) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 38 (all A all B all C all E all F all G all P all Q all R (contri(A,B,C,E,F,G) & contri(E,F,G,P,Q,R) -> contri(A,B,C,P,Q,R))) # label(ruleD38) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 39 (all A all B all C all D all P all Q (eqangle(A,B,P,Q,C,D,P,Q) -> para(A,B,C,D))) # label(ruleD39) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 40 (all A all B all C all D all P all Q (para(A,B,C,D) -> eqangle(A,B,P,Q,C,D,P,Q))) # label(ruleD40) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 41 (all A all B all P all Q (cyclic(A,B,P,Q) -> eqangle(P,A,P,B,Q,A,Q,B))) # label(ruleD41) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 42 (all A all B all P all Q (eqangle(P,A,P,B,Q,A,Q,B) & -coll(P,Q,A) -> cyclic(A,B,P,Q))) # label(ruleD42a) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 43 (all A all B all P all Q (eqangle(P,A,P,B,Q,A,Q,B) & coll(P,Q,B) -> cyclic(A,B,P,Q))) # label(ruleD42b) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 44 (all A all B all C all P all Q all R (cyclic(A,B,C,P) & cyclic(A,B,C,Q) & cyclic(A,B,C,R) & eqangle(C,A,C,B,R,P,R,Q) -> cong(A,B,P,Q))) # label(ruleD43) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 45 (all A all B all C all E all F (midp(E,A,B) & midp(F,A,C) -> para(E,F,B,C))) # label(ruleD44) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 46 (all A all B all C all E all F (midp(E,A,B) & para(E,F,B,C) & coll(F,A,C) -> midp(F,A,C))) # label(ruleD45) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 47 (all A all B all O (cong(O,A,O,B) -> eqangle(O,A,A,B,A,B,O,B))) # label(ruleD46) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 48 (all A all B all O (eqangle(O,A,A,B,A,B,O,B) & -coll(O,A,B) -> cong(O,A,O,B))) # label(ruleD47) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 49 (all A all B all C all O all X (circle(O,A,B,C) & perp(O,A,A,X) -> eqangle(A,X,A,B,C,A,C,B))) # label(ruleD48) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 50 (all A all B all C all O all X (circle(O,A,B,C) & eqangle(A,X,A,B,C,A,C,B) -> perp(O,A,A,X))) # label(ruleD49) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 51 (all A all B all C all O all M (circle(O,A,B,C) & midp(M,B,C) -> eqangle(A,B,A,C,O,B,O,M))) # label(ruleD50) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 52 (all A all B all C all O all M (circle(O,A,B,C) & coll(M,B,C) & eqangle(A,B,A,C,O,B,O,M) -> midp(M,B,C))) # label(ruleD51) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 53 (all A all B all C all M (perp(A,B,B,C) & midp(M,A,C) -> cong(A,M,B,M))) # label(ruleD52) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 54 (all A all B all C all O (circle(O,A,B,C) & coll(O,A,C) -> perp(A,B,B,C))) # label(ruleD53) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 55 (all A all B all C all D (cyclic(A,B,C,D) & para(A,B,C,D) -> eqangle(A,D,C,D,C,D,C,B))) # label(ruleD54) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 56 (all A all B all M all O (midp(M,A,B) & perp(O,M,A,B) -> cong(O,A,O,B))) # label(ruleD55) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 57 (all A all B all P all Q (cong(A,P,B,P) & cong(A,Q,B,Q) -> perp(A,B,P,Q))) # label(ruleD56) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 58 (all A all B all P all Q (cong(A,P,B,P) & cong(A,Q,B,Q) & cyclic(A,B,P,Q) -> perp(P,A,A,Q))) # label(ruleD57) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 59 (all A all B all C all P all Q all R (eqangle(A,B,B,C,P,Q,Q,R) & eqangle(A,C,B,C,P,R,Q,R) & -coll(A,B,C) -> simtri(A,B,C,P,Q,R))) # label(ruleD58) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 60 (all A all B all C all P all Q all R (simtri(A,B,C,P,Q,R) -> eqratio(A,B,A,C,P,Q,P,R))) # label(ruleD59) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 61 (all A all B all C all P all Q all R (simtri(A,B,C,P,Q,R) -> eqangle(A,B,B,C,P,Q,Q,R))) # label(ruleD60) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 62 (all A all B all C all P all Q all R (simtri(A,B,C,P,Q,R) & cong(A,B,P,Q) -> contri(A,B,C,P,Q,R))) # label(ruleD61) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 63 (all A all B all C all P all Q all R (contri(A,B,C,P,Q,R) -> cong(A,B,P,Q))) # label(ruleD62) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 64 (all A all B all C all D all M (midp(M,A,B) & midp(M,C,D) -> para(A,C,B,D))) # label(ruleD63) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 65 (all A all B all C all D all M (midp(M,A,B) & para(A,C,B,D) & para(A,D,B,C) -> midp(M,C,D))) # label(ruleD64) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 66 (all A all B all C all D all O (para(A,B,C,D) & coll(O,A,C) & coll(O,B,D) -> eqratio(O,A,A,C,O,B,B,D))) # label(ruleD65) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 67 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 68 (all A all B all C (cong(A,B,A,C) & coll(A,B,C) -> midp(A,B,C))) # label(ruleD67) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 69 (all A all B all C (midp(A,B,C) -> cong(A,B,A,C))) # label(ruleD68) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 70 (all A all B all C (midp(A,B,C) -> coll(A,B,C))) # label(ruleD69) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 71 (all A all B all C all D all M all N (midp(M,A,B) & midp(N,C,D) -> eqratio(M,A,A,B,N,C,C,D))) # label(ruleD70) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 72 (all A all B all C all D (eqangle(A,B,C,D,C,D,A,B) & -para(A,B,C,D) -> perp(A,B,C,D))) # label(ruleD71) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 73 (all A all B all C all D (eqangle(A,B,C,D,C,D,A,B) & -perp(A,B,C,D) -> para(A,B,C,D))) # label(ruleD72) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 74 (all A all B all C all D all P all Q all U all V (eqangle(A,B,C,D,P,Q,U,V) & para(P,Q,U,V) -> para(A,B,C,D))) # label(ruleD73) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 75 (all A all B all C all D all P all Q all U all V (eqangle(A,B,C,D,P,Q,U,V) & perp(P,Q,U,V) -> perp(A,B,C,D))) # label(ruleD74) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 76 (all A all B all C all D all P all Q all U all V (eqratio(A,B,C,D,P,Q,U,V) & cong(P,Q,U,V) -> cong(A,B,C,D))) # label(ruleD75) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 77 (all A all M all O all X exists B (perp(O,M,M,A) & eqangle(X,O,M,O,M,O,A,O) -> coll(B,A,M) & coll(B,O,X))) # label(ruleX1) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 78 (all A all B all O all X exists M (cong(O,A,O,B) & eqangle(A,O,O,X,O,X,O,B) -> coll(B,A,M) & coll(M,O,X))) # label(ruleX2) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 79 (all A all B all O all X exists M (perp(O,X,A,B) & eqangle(A,O,O,X,O,X,O,B) -> coll(B,A,M) & coll(M,O,X))) # label(ruleX3) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 80 (all A all B all O all X exists M (perp(O,X,A,B) & cong(O,A,O,B) -> coll(B,A,M) & coll(M,O,X))) # label(ruleX4) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 81 (all A all B all P all X all Y exists Q (eqangle(A,P,B,P,A,X,B,Y) & -coll(A,B,P) -> eqangle(A,P,B,P,A,Q,B,Q) & cyclic(X,B,P,Q))) # label(ruleX5) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 82 (all A all B all C all D all M all N exists P (midp(M,A,B) & midp(N,C,D) -> midp(P,A,D) & para(P,M,B,D) & para(P,N,A,C))) # label(ruleX6) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 83 (all A all B all C all D all M all N all Q exists P (midp(M,A,B) & midp(N,C,D) & coll(C,A,B) & coll(D,A,B) -> midp(P,A,Q))) # label(ruleX7) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 84 (all A all B all M all P all Q all R all M exists X (midp(M,A,B) & para(A,P,R,M) & para(A,P,B,Q) & coll(P,Q,R) -> coll(X,A,Q) & coll(X,M,R))) # label(ruleX8) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 85 (all A all B all C all D all O exists P (cong(O,C,O,D) & perp(A,B,B,O) -> cong(O,C,O,P) & para(P,C,A,B) & cong(B,C,B,P))) # label(ruleX9) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 86 (all A all B all C all H exists P exists Q (perp(A,H,B,C) & perp(B,H,A,C) -> coll(P,C,B) & perp(A,P,C,B) & coll(Q,C,A) & perp(B,Q,C,A))) # label(ruleX10) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 87 (all A all B all C all O exists P (circle(O,A,B,C) -> perp(P,A,A,O))) # label(ruleX11) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 88 (all A all B all C all D all M all N exists P exists Q (circle(M,A,B,C) & cong(M,A,M,D) & cong(N,A,N,B) & M != N -> coll(P,A,C) & cong(P,N,N,A) & coll(Q,B,D) & cong(Q,N,N,A))) # label(ruleX12) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 89 (all A all B all C all D all M exists O (cyclic(A,B,C,D) & para(A,B,C,D) & midp(M,A,B) -> circle(O,A,B,C))) # label(ruleX13) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 90 (all A all B all C all D exists O (perp(A,C,C,B) & cyclic(A,B,C,D) -> circle(O,A,B,C))) # label(ruleX14) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 91 (all A all B all C all E all F exists P (perp(A,C,C,B) & coll(B,E,F) -> coll(P,E,F) & perp(P,A,E,F))) # label(ruleX15) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 92 (all A all B all C all D all M exists P (perp(A,B,A,C) & perp(C,A,C,D) & midp(M,B,D) -> midp(P,A,C))) # label(ruleX16) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 93 (all A all B all O exists C (cong(O,A,O,B) & perp(A,O,O,B) -> coll(A,O,C) & cong(O,A,O,C))) # label(ruleX17) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 94 (all A all B all C all D all P all Q exists R (para(A,B,C,D) & coll(P,A,C) & coll(P,B,D) & coll(Q,A,B) -> coll(P,Q,R) & coll(R,C,D))) # label(ruleX18) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.14 95 -(all A all B all C all D all E all F all G all NWPNT1 all NWPNT2 all NWPNT3 all NWPNT4 all NWPNT5 (eqangle(D,A,A,B,D,A,A,C) & eqangle(D,B,B,C,D,B,B,A) & eqangle(D,C,C,A,D,C,C,B) & midpoint(NWPNT1,B,D) & perp(B,D,NWPNT1,E) & perp(A,B,B,E) & circle(E,B,NWPNT2,NWPNT3) & coll(F,A,C) & circle(E,B,F,NWPNT4) & circle(E,F,G,NWPNT5) & coll(G,F,A) -> eqangle(F,D,D,C,C,D,D,G))) # label(exemplo6GDDFULL618077) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.81/1.14
% 0.81/1.14 ============================== end of process non-clausal formulas ===
% 0.81/1.14
% 0.81/1.14 ============================== PROCESS INITIAL CLAUSES ===============
% 0.81/1.14
% 0.81/1.14 ============================== PREDICATE ELIMINATION =================
% 0.81/1.14 96 -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)].
% 0.81/1.14 97 -cong(A,B,A,C) | -cong(A,B,A,D) | circle(A,B,C,D) # label(ruleD12) # label(axiom). [clausify(12)].
% 0.81/1.14 Derived: -perp(A,B,B,C) | eqangle(B,C,B,D,E,B,E,D) | -cong(A,B,A,D) | -cong(A,B,A,E). [resolve(96,a,97,c)].
% 0.81/1.14 98 -circle(A,B,C,D) | -eqangle(B,E,B,C,D,B,D,C) | perp(A,B,B,E) # label(ruleD49) # label(axiom). [clausify(50)].
% 0.81/1.14 Derived: -eqangle(A,B,A,C,D,A,D,C) | perp(E,A,A,B) | -cong(E,A,E,C) | -cong(E,A,E,D). [resolve(98,a,97,c)].
% 0.81/1.14 99 -circle(A,B,C,D) | -midp(E,C,D) | eqangle(B,C,B,D,A,C,A,E) # label(ruleD50) # label(axiom). [clausify(51)].
% 0.81/1.14 Derived: -midp(A,B,C) | eqangle(D,B,D,C,E,B,E,A) | -cong(E,D,E,B) | -cong(E,D,E,C). [resolve(99,a,97,c)].
% 0.81/1.14 100 -circle(A,B,C,D) | -coll(E,C,D) | -eqangle(B,C,B,D,A,C,A,E) | midp(E,C,D) # label(ruleD51) # label(axiom). [clausify(52)].
% 0.81/1.14 Derived: -coll(A,B,C) | -eqangle(D,B,D,C,E,B,E,A) | midp(A,B,C) | -cong(E,D,E,B) | -cong(E,D,E,C). [resolve(100,a,97,c)].
% 0.81/1.14 101 -circle(A,B,C,D) | -coll(A,B,D) | perp(B,C,C,D) # label(ruleD53) # label(axiom). [clausify(54)].
% 0.81/1.14 Derived: -coll(A,B,C) | perp(B,D,D,C) | -cong(A,B,A,D) | -cong(A,B,A,C). [resolve(101,a,97,c)].
% 0.81/1.14 102 -circle(A,B,C,D) | perp(f12(B,C,D,A),B,B,A) # label(ruleX11) # label(axiom). [clausify(87)].
% 0.81/1.14 Derived: perp(f12(A,B,C,D),A,A,D) | -cong(D,A,D,B) | -cong(D,A,D,C). [resolve(102,a,97,c)].
% 0.81/1.14 103 -circle(A,B,C,D) | -cong(A,B,A,E) | -cong(F,B,F,C) | F = A | coll(f13(B,C,D,E,A,F),B,D) # label(ruleX12) # label(axiom). [clausify(88)].
% 0.81/1.14 Derived: -cong(A,B,A,C) | -cong(D,B,D,E) | D = A | coll(f13(B,E,F,C,A,D),B,F) | -cong(A,B,A,E) | -cong(A,B,A,F). [resolve(103,a,97,c)].
% 0.81/1.14 104 -circle(A,B,C,D) | -cong(A,B,A,E) | -cong(F,B,F,C) | F = A | cong(f13(B,C,D,E,A,F),F,F,B) # label(ruleX12) # label(axiom). [clausify(88)].
% 0.81/1.14 Derived: -cong(A,B,A,C) | -cong(D,B,D,E) | D = A | cong(f13(B,E,F,C,A,D),D,D,B) | -cong(A,B,A,E) | -cong(A,B,A,F). [resolve(104,a,97,c)].
% 0.81/1.14 105 -circle(A,B,C,D) | -cong(A,B,A,E) | -cong(F,B,F,C) | F = A | coll(f14(B,C,D,E,A,F),C,E) # label(ruleX12) # label(axiom). [clausify(88)].
% 0.81/1.14 Derived: -cong(A,B,A,C) | -cong(D,B,D,E) | D = A | coll(f14(B,E,F,C,A,D),E,C) | -cong(A,B,A,E) | -cong(A,B,A,F). [resolve(105,a,97,c)].
% 0.81/1.14 106 -circle(A,B,C,D) | -cong(A,B,A,E) | -cong(F,B,F,C) | F = A | cong(f14(B,C,D,E,A,F),F,F,B) # label(ruleX12) # label(axiom). [clausify(88)].
% 0.81/1.14 Derived: -cong(A,B,A,C) | -cong(D,B,D,E) | D = A | cong(f14(B,E,F,C,A,D),D,D,B) | -cong(A,B,A,E) | -cong(A,B,A,F). [resolve(106,a,97,c)].
% 0.87/1.14 107 -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | circle(f15(A,B,C,D,E),A,B,C) # label(ruleX13) # label(axiom). [clausify(89)].
% 0.87/1.14 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)].
% 0.87/1.14 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)].
% 0.87/1.14 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)].
% 0.87/1.14 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)].
% 0.87/1.14 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)].
% 0.87/1.14 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)].
% 0.87/1.14 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)].
% 0.87/1.14 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)].
% 0.87/1.14 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)].
% 0.87/1.14 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)].
% 0.87/1.14 108 -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)].
% 0.87/1.14 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)].
% 0.87/1.14 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)].
% 0.87/1.14 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)].
% 0.87/1.14 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)].
% 0.87/1.14 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)].
% 0.87/1.14 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)].
% 0.87/1.14 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)].
% 0.87/1.14 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)].
% 0.87/1.14 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)].
% 0.87/1.14 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)].
% 0.87/1.14 109 circle(c5,c2,c9,c10) # label(exemplo6GDDFULL618077) # label(negated_conjecture). [clausify(95)].
% 0.87/1.14 Derived: -perp(c5,c2,c2,A) | eqangle(c2,A,c2,c9,c10,c2,c10,c9). [resolve(109,a,96,a)].
% 0.87/1.14 Derived: -eqangle(c2,A,c2,c9,c10,c2,c10,c9) | perp(c5,c2,c2,A). [resolve(109,a,98,a)].
% 0.87/1.14 Derived: -midp(A,c9,c10) | eqangle(c2,c9,c2,c10,c5,c9,c5,A). [resolve(109,a,99,a)].
% 0.87/1.14 Derived: -coll(A,c9,c10) | -eqangle(c2,c9,c2,c10,c5,c9,c5,A) | midp(A,c9,c10). [resolve(109,a,100,a)].
% 0.87/1.14 Derived: -coll(c5,c2,c10) | perp(c2,c9,c9,c10). [resolve(109,a,101,a)].
% 3.51/3.83 Derived: perp(f12(c2,c9,c10,c5),c2,c2,c5). [resolve(109,a,102,a)].
% 3.51/3.83 Derived: -cong(c5,c2,c5,A) | -cong(B,c2,B,c9) | B = c5 | coll(f13(c2,c9,c10,A,c5,B),c2,c10). [resolve(109,a,103,a)].
% 3.51/3.83 Derived: -cong(c5,c2,c5,A) | -cong(B,c2,B,c9) | B = c5 | cong(f13(c2,c9,c10,A,c5,B),B,B,c2). [resolve(109,a,104,a)].
% 3.51/3.83 Derived: -cong(c5,c2,c5,A) | -cong(B,c2,B,c9) | B = c5 | coll(f14(c2,c9,c10,A,c5,B),c9,A). [resolve(109,a,105,a)].
% 3.51/3.83 Derived: -cong(c5,c2,c5,A) | -cong(B,c2,B,c9) | B = c5 | cong(f14(c2,c9,c10,A,c5,B),B,B,c2). [resolve(109,a,106,a)].
% 3.51/3.83 110 circle(c5,c2,c6,c11) # label(exemplo6GDDFULL618077) # label(negated_conjecture). [clausify(95)].
% 3.51/3.83 Derived: -perp(c5,c2,c2,A) | eqangle(c2,A,c2,c6,c11,c2,c11,c6). [resolve(110,a,96,a)].
% 3.51/3.83 Derived: -eqangle(c2,A,c2,c6,c11,c2,c11,c6) | perp(c5,c2,c2,A). [resolve(110,a,98,a)].
% 3.51/3.83 Derived: -midp(A,c6,c11) | eqangle(c2,c6,c2,c11,c5,c6,c5,A). [resolve(110,a,99,a)].
% 3.51/3.83 Derived: -coll(A,c6,c11) | -eqangle(c2,c6,c2,c11,c5,c6,c5,A) | midp(A,c6,c11). [resolve(110,a,100,a)].
% 3.51/3.83 Derived: -coll(c5,c2,c11) | perp(c2,c6,c6,c11). [resolve(110,a,101,a)].
% 3.51/3.83 Derived: perp(f12(c2,c6,c11,c5),c2,c2,c5). [resolve(110,a,102,a)].
% 3.51/3.83 Derived: -cong(c5,c2,c5,A) | -cong(B,c2,B,c6) | B = c5 | coll(f13(c2,c6,c11,A,c5,B),c2,c11). [resolve(110,a,103,a)].
% 3.51/3.83 Derived: -cong(c5,c2,c5,A) | -cong(B,c2,B,c6) | B = c5 | cong(f13(c2,c6,c11,A,c5,B),B,B,c2). [resolve(110,a,104,a)].
% 3.51/3.83 Derived: -cong(c5,c2,c5,A) | -cong(B,c2,B,c6) | B = c5 | coll(f14(c2,c6,c11,A,c5,B),c6,A). [resolve(110,a,105,a)].
% 3.51/3.83 Derived: -cong(c5,c2,c5,A) | -cong(B,c2,B,c6) | B = c5 | cong(f14(c2,c6,c11,A,c5,B),B,B,c2). [resolve(110,a,106,a)].
% 3.51/3.83 111 circle(c5,c6,c7,c12) # label(exemplo6GDDFULL618077) # label(negated_conjecture). [clausify(95)].
% 3.51/3.83 Derived: -perp(c5,c6,c6,A) | eqangle(c6,A,c6,c7,c12,c6,c12,c7). [resolve(111,a,96,a)].
% 3.51/3.83 Derived: -eqangle(c6,A,c6,c7,c12,c6,c12,c7) | perp(c5,c6,c6,A). [resolve(111,a,98,a)].
% 3.51/3.83 Derived: -midp(A,c7,c12) | eqangle(c6,c7,c6,c12,c5,c7,c5,A). [resolve(111,a,99,a)].
% 3.51/3.83 Derived: -coll(A,c7,c12) | -eqangle(c6,c7,c6,c12,c5,c7,c5,A) | midp(A,c7,c12). [resolve(111,a,100,a)].
% 3.51/3.83 Derived: -coll(c5,c6,c12) | perp(c6,c7,c7,c12). [resolve(111,a,101,a)].
% 3.51/3.83 Derived: perp(f12(c6,c7,c12,c5),c6,c6,c5). [resolve(111,a,102,a)].
% 3.51/3.83 Derived: -cong(c5,c6,c5,A) | -cong(B,c6,B,c7) | B = c5 | coll(f13(c6,c7,c12,A,c5,B),c6,c12). [resolve(111,a,103,a)].
% 3.51/3.83 Derived: -cong(c5,c6,c5,A) | -cong(B,c6,B,c7) | B = c5 | cong(f13(c6,c7,c12,A,c5,B),B,B,c6). [resolve(111,a,104,a)].
% 3.51/3.83 Derived: -cong(c5,c6,c5,A) | -cong(B,c6,B,c7) | B = c5 | coll(f14(c6,c7,c12,A,c5,B),c7,A). [resolve(111,a,105,a)].
% 3.51/3.83 Derived: -cong(c5,c6,c5,A) | -cong(B,c6,B,c7) | B = c5 | cong(f14(c6,c7,c12,A,c5,B),B,B,c6). [resolve(111,a,106,a)].
% 3.51/3.83
% 3.51/3.83 ============================== end predicate elimination =============
% 3.51/3.83
% 3.51/3.83 Auto_denials: (non-Horn, no changes).
% 3.51/3.83
% 3.51/3.83 Term ordering decisions:
% 3.51/3.83 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.
% 3.51/3.83
% 3.51/3.83 ============================== end of process initial clauses ========
% 3.51/3.83
% 3.51/3.83 ============================== CLAUSES FOR SEARCH ====================
% 3.51/3.83
% 3.51/3.83 ============================== end of clauses for search =============
% 3.51/3.83
% 3.51/3.83 ============================== SEARCH ================================
% 3.51/3.83
% 3.51/3.83 % Starting search at 0.02 seconds.
% 3.51/3.83
% 3.51/3.83 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 65 (0.00 of 0.09 sec).
% 3.51/3.83
% 3.51/3.83 Low Water (keep): wt=26.000, iters=3340
% 3.51/3.83
% 3.51/3.83 Low Water (keep): wt=22.000, iters=3371
% 3.51/3.83
% 3.51/3.83 Low Water (keep): wt=21.000, iters=3335
% 3.51/3.83
% 3.51/3.83 Low Water (keep): wt=18.000, iters=3335
% 3.51/3.83
% 3.51/3.83 Low Water (keep): wt=17.000, iters=3333
% 3.51/3.83
% 3.51/3.83 Low Water (keep): wt=16.000, iters=3347
% 3.51/3.83
% 3.51/3.83 Low Water (keep): wt=15.000, iters=3333
% 3.51/3.83
% 3.51/3.83 Low Water (keep): wt=14.000, iters=3365
% 3.51/3.83
% 3.51/3.83 Low Water (keep): wt=13.000, iters=3350
% 3.51/3.83
% 3.51/3.83 Low Water (keep): wt=12.000, iters=3333
% 3.51/3.83
% 3.51/3.83 Low Water (displace): id=17122, wt=11.000
% 3.51/3.83
% 3.51/3.83 Low Water (displace): id=17524, wt=9.000
% 3.51/3.83
% 3.51/3.83 Low Water (displace): id=17596, wt=8.000
% 3.51/3.83
% 3.51/3.83 Low Water (displace): id=17603, wt=5.000
% 17.80/18.08
% 17.80/18.08 Low Water (keep): wt=11.000, iters=3335
% 17.80/18.08
% 17.80/18.08 Low Water (keep): wt=10.000, iters=3418
% 17.80/18.08
% 17.80/18.08 ============================== PROOF =================================
% 17.80/18.08 % SZS status Theorem
% 17.80/18.08 % SZS output start Refutation
% 17.80/18.08
% 17.80/18.08 % Proof 1 at 16.82 (+ 0.13) seconds.
% 17.80/18.08 % Length of proof is 226.
% 17.80/18.08 % Level of proof is 31.
% 17.80/18.08 % Maximum clause weight is 29.000.
% 17.80/18.08 % Given clauses 19975.
% 17.80/18.08
% 17.80/18.08 1 (all A all B all C (coll(A,B,C) -> coll(A,C,B))) # label(ruleD1) # label(axiom) # label(non_clause). [assumption].
% 17.80/18.08 2 (all A all B all C (coll(A,B,C) -> coll(B,A,C))) # label(ruleD2) # label(axiom) # label(non_clause). [assumption].
% 17.80/18.08 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].
% 17.80/18.08 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].
% 17.80/18.08 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].
% 17.80/18.08 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].
% 17.80/18.08 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].
% 17.80/18.08 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].
% 17.80/18.08 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].
% 17.80/18.08 11 (all A all B all M (midp(M,B,A) -> midp(M,A,B))) # label(ruleD11) # label(axiom) # label(non_clause). [assumption].
% 17.80/18.08 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].
% 17.80/18.08 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].
% 17.80/18.08 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].
% 17.80/18.08 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].
% 17.80/18.08 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].
% 17.80/18.08 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].
% 17.80/18.08 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].
% 17.80/18.08 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].
% 17.80/18.08 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].
% 17.80/18.08 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].
% 17.80/18.08 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].
% 17.80/18.08 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].
% 17.80/18.08 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].
% 17.80/18.08 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].
% 17.80/18.08 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].
% 17.80/18.08 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].
% 17.80/18.08 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].
% 17.80/18.08 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].
% 17.80/18.08 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].
% 17.80/18.08 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].
% 17.80/18.08 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].
% 17.80/18.08 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].
% 17.80/18.08 67 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption].
% 17.80/18.08 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].
% 17.80/18.08 69 (all A all B all C (midp(A,B,C) -> cong(A,B,A,C))) # label(ruleD68) # label(axiom) # label(non_clause). [assumption].
% 17.80/18.08 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].
% 17.80/18.08 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].
% 17.80/18.08 95 -(all A all B all C all D all E all F all G all NWPNT1 all NWPNT2 all NWPNT3 all NWPNT4 all NWPNT5 (eqangle(D,A,A,B,D,A,A,C) & eqangle(D,B,B,C,D,B,B,A) & eqangle(D,C,C,A,D,C,C,B) & midpoint(NWPNT1,B,D) & perp(B,D,NWPNT1,E) & perp(A,B,B,E) & circle(E,B,NWPNT2,NWPNT3) & coll(F,A,C) & circle(E,B,F,NWPNT4) & circle(E,F,G,NWPNT5) & coll(G,F,A) -> eqangle(F,D,D,C,C,D,D,G))) # label(exemplo6GDDFULL618077) # label(negated_conjecture) # label(non_clause). [assumption].
% 17.80/18.08 97 -cong(A,B,A,C) | -cong(A,B,A,D) | circle(A,B,C,D) # label(ruleD12) # label(axiom). [clausify(12)].
% 17.80/18.08 101 -circle(A,B,C,D) | -coll(A,B,D) | perp(B,C,C,D) # label(ruleD53) # label(axiom). [clausify(54)].
% 17.80/18.08 112 -coll(A,B,C) | coll(A,C,B) # label(ruleD1) # label(axiom). [clausify(1)].
% 17.80/18.08 113 -coll(A,B,C) | coll(B,A,C) # label(ruleD2) # label(axiom). [clausify(2)].
% 17.80/18.08 114 -coll(A,B,C) | -coll(A,B,D) | coll(C,D,A) # label(ruleD3) # label(axiom). [clausify(3)].
% 17.80/18.08 115 -para(A,B,C,D) | para(A,B,D,C) # label(ruleD4) # label(axiom). [clausify(4)].
% 17.80/18.08 116 -para(A,B,C,D) | para(C,D,A,B) # label(ruleD5) # label(axiom). [clausify(5)].
% 17.80/18.08 117 -para(A,B,C,D) | -para(C,D,E,F) | para(A,B,E,F) # label(ruleD6) # label(axiom). [clausify(6)].
% 17.80/18.08 118 -perp(A,B,C,D) | perp(A,B,D,C) # label(ruleD7) # label(axiom). [clausify(7)].
% 17.80/18.08 119 -perp(A,B,C,D) | perp(C,D,A,B) # label(ruleD8) # label(axiom). [clausify(8)].
% 17.80/18.08 120 -perp(A,B,C,D) | -perp(C,D,E,F) | para(A,B,E,F) # label(ruleD9) # label(axiom). [clausify(9)].
% 17.80/18.08 122 -midp(A,B,C) | midp(A,C,B) # label(ruleD11) # label(axiom). [clausify(11)].
% 17.80/18.08 124 -cyclic(A,B,C,D) | cyclic(A,B,D,C) # label(ruleD14) # label(axiom). [clausify(14)].
% 17.80/18.08 125 -cyclic(A,B,C,D) | cyclic(A,C,B,D) # label(ruleD15) # label(axiom). [clausify(15)].
% 17.80/18.08 126 -cyclic(A,B,C,D) | cyclic(B,A,C,D) # label(ruleD16) # label(axiom). [clausify(16)].
% 17.80/18.08 127 -cyclic(A,B,C,D) | -cyclic(A,B,C,E) | cyclic(B,C,D,E) # label(ruleD17) # label(axiom). [clausify(17)].
% 17.80/18.08 129 -eqangle(A,B,C,D,E,F,V6,V7) | eqangle(C,D,A,B,V6,V7,E,F) # label(ruleD19) # label(axiom). [clausify(19)].
% 17.80/18.08 130 -eqangle(A,B,C,D,E,F,V6,V7) | eqangle(E,F,V6,V7,A,B,C,D) # label(ruleD20) # label(axiom). [clausify(20)].
% 17.80/18.08 131 -eqangle(A,B,C,D,E,F,V6,V7) | eqangle(A,B,E,F,C,D,V6,V7) # label(ruleD21) # label(axiom). [clausify(21)].
% 17.80/18.08 132 -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)].
% 17.80/18.08 133 -cong(A,B,C,D) | cong(A,B,D,C) # label(ruleD23) # label(axiom). [clausify(23)].
% 17.80/18.08 134 -cong(A,B,C,D) | cong(C,D,A,B) # label(ruleD24) # label(axiom). [clausify(24)].
% 17.80/18.08 149 -eqangle(A,B,C,D,E,F,C,D) | para(A,B,E,F) # label(ruleD39) # label(axiom). [clausify(39)].
% 17.80/18.08 150 -para(A,B,C,D) | eqangle(A,B,E,F,C,D,E,F) # label(ruleD40) # label(axiom). [clausify(40)].
% 17.80/18.08 153 -eqangle(A,B,A,C,D,B,D,C) | -coll(A,D,C) | cyclic(B,C,A,D) # label(ruleD42b) # label(axiom). [clausify(43)].
% 17.80/18.08 154 -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)].
% 17.80/18.08 156 -midp(A,B,C) | -para(A,D,C,E) | -coll(D,B,E) | midp(D,B,E) # label(ruleD45) # label(axiom). [clausify(46)].
% 17.80/18.08 159 -perp(A,B,B,C) | -midp(D,A,C) | cong(A,D,B,D) # label(ruleD52) # label(axiom). [clausify(53)].
% 17.80/18.08 161 -midp(A,B,C) | -perp(D,A,B,C) | cong(D,B,D,C) # label(ruleD55) # label(axiom). [clausify(56)].
% 17.80/18.08 162 -cong(A,B,C,B) | -cong(A,D,C,D) | perp(A,C,B,D) # label(ruleD56) # label(axiom). [clausify(57)].
% 17.80/18.08 170 -midp(A,B,C) | -para(B,D,C,E) | -para(B,E,C,D) | midp(A,D,E) # label(ruleD64) # label(axiom). [clausify(65)].
% 17.80/18.08 171 -para(A,B,C,D) | -coll(E,A,C) | -coll(E,B,D) | eqratio(E,A,A,C,E,B,B,D) # label(ruleD65) # label(axiom). [clausify(66)].
% 17.80/18.08 172 -para(A,B,A,C) | coll(A,B,C) # label(ruleD66) # label(axiom). [clausify(67)].
% 17.80/18.08 173 -cong(A,B,A,C) | -coll(A,B,C) | midp(A,B,C) # label(ruleD67) # label(axiom). [clausify(68)].
% 17.80/18.08 174 -midp(A,B,C) | cong(A,B,A,C) # label(ruleD68) # label(axiom). [clausify(69)].
% 17.80/18.08 178 -eqangle(A,B,C,D,E,F,V6,V7) | -para(E,F,V6,V7) | para(A,B,C,D) # label(ruleD73) # label(axiom). [clausify(74)].
% 17.80/18.08 180 -eqratio(A,B,C,D,E,F,V6,V7) | -cong(E,F,V6,V7) | cong(A,B,C,D) # label(ruleD75) # label(axiom). [clausify(76)].
% 17.80/18.08 211 eqangle(c4,c1,c1,c2,c4,c1,c1,c3) # label(exemplo6GDDFULL618077) # label(negated_conjecture). [clausify(95)].
% 17.80/18.08 212 eqangle(c4,c2,c2,c3,c4,c2,c2,c1) # label(exemplo6GDDFULL618077) # label(negated_conjecture). [clausify(95)].
% 17.80/18.08 215 perp(c1,c2,c2,c5) # label(exemplo6GDDFULL618077) # label(negated_conjecture). [clausify(95)].
% 17.80/18.08 217 coll(c7,c6,c1) # label(exemplo6GDDFULL618077) # label(negated_conjecture). [clausify(95)].
% 17.80/18.08 218 -eqangle(c6,c4,c4,c3,c3,c4,c4,c7) # label(exemplo6GDDFULL618077) # label(negated_conjecture). [clausify(95)].
% 17.80/18.08 223 -coll(A,B,C) | perp(B,D,D,C) | -cong(A,B,A,D) | -cong(A,B,A,C). [resolve(101,a,97,c)].
% 17.80/18.08 299 -coll(A,B,C) | coll(C,C,A). [factor(114,a,b)].
% 17.80/18.08 304 -cyclic(A,B,C,D) | cyclic(B,C,D,D). [factor(127,a,b)].
% 17.80/18.08 307 -cyclic(A,B,C,D) | -cyclic(A,B,C,E) | -eqangle(C,A,C,B,E,D,E,E) | cong(A,B,D,E). [factor(154,b,c)].
% 17.80/18.08 309 -cong(A,B,C,B) | perp(A,C,B,B). [factor(162,a,b)].
% 17.80/18.08 338 -coll(A,B,C) | perp(B,C,C,C) | -cong(A,B,A,C). [factor(223,c,d)].
% 17.80/18.08 367 eqangle(c4,c1,c4,c1,c1,c2,c1,c3). [resolve(211,a,131,a)].
% 17.80/18.08 369 eqangle(c1,c2,c4,c1,c1,c3,c4,c1). [resolve(211,a,129,a)].
% 17.80/18.08 376 eqangle(c4,c2,c4,c2,c2,c3,c2,c1). [resolve(212,a,131,a)].
% 17.80/18.08 378 eqangle(c2,c3,c4,c2,c2,c1,c4,c2). [resolve(212,a,129,a)].
% 17.80/18.08 423 -perp(A,B,c1,c2) | para(A,B,c2,c5). [resolve(215,a,120,b)].
% 17.80/18.08 424 -perp(c2,c5,A,B) | para(c1,c2,A,B). [resolve(215,a,120,a)].
% 17.80/18.08 425 perp(c2,c5,c1,c2). [resolve(215,a,119,a)].
% 17.80/18.08 426 perp(c1,c2,c5,c2). [resolve(215,a,118,a)].
% 17.80/18.08 512 coll(c1,c1,c7). [resolve(299,a,217,a)].
% 17.80/18.08 532 coll(c1,c7,c1). [resolve(512,a,112,a)].
% 17.80/18.08 562 coll(c1,c1,c1). [resolve(532,a,299,a)].
% 17.80/18.08 583 -para(c1,c2,c1,c3) | para(c4,c1,c4,c1). [resolve(367,a,178,a)].
% 17.80/18.08 622 para(c1,c2,c1,c3). [resolve(369,a,149,a)].
% 17.80/18.08 626 para(c4,c1,c4,c1). [back_unit_del(583),unit_del(a,622)].
% 17.80/18.08 721 perp(c5,c2,c1,c2). [resolve(426,a,119,a)].
% 17.80/18.08 738 coll(c1,c2,c3). [resolve(622,a,172,a)].
% 17.80/18.08 739 -coll(A,c1,c1) | -coll(A,c2,c3) | eqratio(A,c1,c1,c1,A,c2,c2,c3). [resolve(622,a,171,a)].
% 17.80/18.08 741 -midp(A,c1,c1) | -para(c1,c3,c1,c2) | midp(A,c2,c3). [resolve(622,a,170,b)].
% 17.80/18.08 745 -para(A,B,c1,c2) | para(A,B,c1,c3). [resolve(622,a,117,b)].
% 17.80/18.08 747 para(c1,c3,c1,c2). [resolve(622,a,116,a)].
% 17.80/18.08 748 para(c1,c2,c3,c1). [resolve(622,a,115,a)].
% 17.80/18.08 749 -midp(A,c1,c1) | midp(A,c2,c3). [back_unit_del(741),unit_del(b,747)].
% 17.80/18.08 754 coll(c1,c3,c2). [resolve(738,a,112,a)].
% 17.80/18.08 761 coll(c2,c2,c1). [resolve(754,a,299,a)].
% 17.80/18.08 773 -coll(c2,c2,A) | coll(A,c1,c2). [resolve(761,a,114,b)].
% 17.80/18.08 775 coll(c2,c1,c2). [resolve(761,a,112,a)].
% 17.80/18.08 781 -eqangle(A,B,C,D,c4,c2,c4,c2) | eqangle(A,B,C,D,c2,c3,c2,c1). [resolve(376,a,132,b)].
% 17.80/18.08 783 eqangle(c2,c3,c2,c1,c4,c2,c4,c2). [resolve(376,a,130,a)].
% 17.80/18.08 806 coll(c2,c2,c2). [resolve(775,a,299,a)].
% 17.80/18.08 820 para(c2,c3,c2,c1). [resolve(378,a,149,a)].
% 17.80/18.08 850 eqangle(c4,c1,A,B,c4,c1,A,B). [resolve(626,a,150,a)].
% 17.80/18.08 915 -midp(c2,c1,c2) | cong(c5,c1,c5,c2). [resolve(721,a,161,b)].
% 17.80/18.08 918 perp(c5,c2,c2,c1). [resolve(721,a,118,a)].
% 17.80/18.08 950 para(c3,c1,c1,c2). [resolve(748,a,116,a)].
% 17.80/18.08 966 -para(c2,c1,A,B) | para(c2,c3,A,B). [resolve(820,a,117,a)].
% 17.80/18.08 967 para(c2,c1,c2,c3). [resolve(820,a,116,a)].
% 17.80/18.08 968 para(c2,c3,c1,c2). [resolve(820,a,115,a)].
% 17.80/18.08 1089 -midp(A,c5,c1) | cong(c5,A,c2,A). [resolve(918,a,159,a)].
% 17.80/18.08 1147 eqangle(c2,c1,A,B,c2,c3,A,B). [resolve(967,a,150,a)].
% 17.80/18.08 1151 para(c2,c1,c3,c2). [resolve(967,a,115,a)].
% 17.80/18.08 1168 para(c1,c2,c2,c3). [resolve(968,a,116,a)].
% 17.80/18.08 1309 para(c1,c2,c3,c2). [resolve(1168,a,115,a)].
% 17.80/18.08 1435 -midp(c1,A,c3) | -coll(c2,A,c2) | midp(c2,A,c2). [resolve(1309,a,156,b)].
% 17.80/18.08 1964 para(c5,c2,c2,c5). [resolve(423,a,721,a)].
% 17.80/18.08 1965 para(c2,c5,c2,c5). [resolve(423,a,425,a)].
% 17.80/18.08 1978 para(c1,c2,c1,c2). [resolve(424,a,425,a)].
% 17.80/18.08 2023 -midp(c5,A,c2) | -coll(c2,A,c5) | midp(c2,A,c5). [resolve(1964,a,156,b)].
% 17.80/18.08 2038 coll(c2,c5,c5). [resolve(1965,a,172,a)].
% 17.80/18.08 2040 -midp(c2,A,c2) | -coll(c5,A,c5) | midp(c5,A,c5). [resolve(1965,a,156,b)].
% 17.80/18.08 2042 coll(c5,c5,c2). [resolve(2038,a,299,a)].
% 17.80/18.08 2045 coll(c5,c2,c5). [resolve(2038,a,113,a)].
% 17.80/18.08 2050 coll(c2,c2,c5). [resolve(2042,a,299,a)].
% 17.80/18.08 2095 -midp(c1,A,c1) | -coll(c2,A,c2) | midp(c2,A,c2). [resolve(1978,a,156,b)].
% 17.80/18.08 2294 coll(c5,c1,c2). [resolve(773,a,2050,a)].
% 17.80/18.08 2303 coll(c1,c5,c2). [resolve(2294,a,113,a)].
% 17.80/18.08 2307 coll(c1,c2,c5). [resolve(2303,a,112,a)].
% 17.80/18.08 2323 coll(c2,c1,c5). [resolve(2307,a,113,a)].
% 17.80/18.08 3924 eqratio(c1,c1,c1,c1,c1,c2,c2,c3). [resolve(739,b,738,a),unit_del(a,562)].
% 17.80/18.08 3978 para(c3,c1,c1,c3). [resolve(745,a,950,a)].
% 17.80/18.08 4007 para(c3,c1,c3,c1). [resolve(3978,a,115,a)].
% 17.80/18.08 4046 eqangle(c3,c1,A,B,c3,c1,A,B). [resolve(4007,a,150,a)].
% 17.80/18.08 4047 eqangle(c2,c3,c2,c1,c2,c3,c2,c1). [resolve(783,a,781,a)].
% 17.80/18.08 4137 eqangle(A,B,c4,c1,A,B,c4,c1). [resolve(850,a,129,a)].
% 17.80/18.08 4849 para(c2,c3,c3,c2). [resolve(966,a,1151,a)].
% 17.80/18.08 4870 para(c3,c2,c2,c3). [resolve(4849,a,116,a)].
% 17.80/18.08 4902 para(c3,c2,c3,c2). [resolve(4870,a,115,a)].
% 17.80/18.08 4914 eqangle(c3,c2,A,B,c3,c2,A,B). [resolve(4902,a,150,a)].
% 17.80/18.08 6793 -cyclic(c1,c2,c2,c3) | -cyclic(c1,c2,c2,c2) | cong(c1,c2,c3,c2). [resolve(1147,a,307,c)].
% 17.80/18.08 16522 -cong(c1,c2,c2,c3) | cong(c1,c1,c1,c1). [resolve(3924,a,180,a)].
% 17.80/18.08 16551 -coll(c3,c3,A) | cyclic(c1,A,c3,c3). [resolve(4046,a,153,a)].
% 17.80/18.08 16554 cyclic(c3,c1,c2,c2). [resolve(4047,a,153,a),unit_del(a,761)].
% 17.80/18.08 16559 cyclic(c1,c2,c2,c2). [resolve(16554,a,304,a)].
% 17.80/18.08 16562 cyclic(c1,c3,c2,c2). [resolve(16554,a,126,a)].
% 17.80/18.08 16564 -cyclic(c1,c2,c2,c3) | cong(c1,c2,c3,c2). [back_unit_del(6793),unit_del(b,16559)].
% 17.80/18.08 16576 cyclic(c1,c2,c3,c2). [resolve(16562,a,125,a)].
% 17.80/18.08 16596 cyclic(c2,c1,c3,c2). [resolve(16576,a,126,a)].
% 17.80/18.08 16597 cyclic(c1,c2,c2,c3). [resolve(16576,a,124,a)].
% 17.80/18.08 16598 cong(c1,c2,c3,c2). [back_unit_del(16564),unit_del(a,16597)].
% 17.80/18.08 16642 cyclic(c2,c1,c2,c3). [resolve(16596,a,124,a)].
% 17.80/18.08 16643 cyclic(c2,c2,c3,c3). [resolve(16597,a,304,a)].
% 17.80/18.08 16653 cong(c1,c2,c2,c3). [resolve(16598,a,133,a)].
% 17.80/18.08 16654 cong(c1,c1,c1,c1). [back_unit_del(16522),unit_del(a,16653)].
% 17.80/18.08 16782 cyclic(c1,c2,c3,c3). [resolve(16642,a,304,a)].
% 17.80/18.08 16789 cyclic(c2,c3,c3,c3). [resolve(16643,a,304,a)].
% 17.80/18.08 16792 cyclic(c2,c3,c2,c3). [resolve(16643,a,125,a)].
% 17.80/18.08 16822 midp(c1,c1,c1). [resolve(16654,a,173,a),unit_del(a,562)].
% 17.80/18.08 16838 midp(c2,c1,c2). [resolve(16822,a,2095,a),unit_del(a,775)].
% 17.80/18.08 16844 midp(c1,c2,c3). [resolve(16822,a,749,a)].
% 17.80/18.08 16884 cong(c5,c1,c5,c2). [back_unit_del(915),unit_del(a,16838)].
% 17.80/18.08 17329 midp(c2,c2,c2). [resolve(16844,a,1435,a),unit_del(a,806)].
% 17.80/18.08 17617 midp(c5,c2,c5). [resolve(17329,a,2040,a),unit_del(a,2045)].
% 17.80/18.08 17767 midp(c5,c5,c2). [resolve(17617,a,122,a)].
% 17.80/18.08 17880 cong(c5,c5,c5,c2). [resolve(17767,a,174,a)].
% 17.80/18.08 18710 cyclic(c1,c3,c2,c3). [resolve(16782,a,125,a)].
% 17.80/18.08 18722 cyclic(c3,c2,c3,c3). [resolve(16789,a,126,a)].
% 17.80/18.08 18727 cyclic(c2,c3,c3,c2). [resolve(16792,a,124,a)].
% 17.80/18.08 18758 midp(c5,c1,c2). [resolve(16884,a,173,a),unit_del(a,2294)].
% 17.80/18.08 18763 midp(c2,c1,c5). [resolve(18758,a,2023,a),unit_del(a,2323)].
% 17.80/18.08 18785 midp(c2,c5,c1). [resolve(18763,a,122,a)].
% 17.80/18.08 18816 cong(c5,c2,c2,c2). [resolve(18785,a,1089,a)].
% 17.80/18.08 20063 perp(c5,c2,c2,c2). [resolve(17880,a,338,c),unit_del(a,2042)].
% 17.80/18.08 21280 cyclic(c1,c3,c3,c2). [resolve(18710,a,124,a)].
% 17.80/18.08 21290 cyclic(c3,c3,c2,c3). [resolve(18722,a,125,a)].
% 17.80/18.08 21296 cyclic(c3,c3,c2,c2). [resolve(18727,a,304,a)].
% 17.80/18.08 21342 cong(c2,c2,c5,c2). [resolve(18816,a,134,a)].
% 17.80/18.08 22335 perp(c2,c2,c5,c2). [resolve(20063,a,119,a)].
% 17.80/18.08 22676 -cyclic(c1,c3,c3,A) | cyclic(c3,c3,c2,A). [resolve(21280,a,127,a)].
% 17.80/18.08 22678 -cyclic(c3,c3,c2,A) | cyclic(c3,c2,A,c3). [resolve(21290,a,127,b)].
% 17.80/18.08 22685 -cyclic(c3,c3,c2,A) | cyclic(c3,c2,A,c2). [resolve(21296,a,127,b)].
% 17.80/18.08 22693 perp(c2,c5,c2,c2). [resolve(21342,a,309,a)].
% 17.80/18.08 23279 perp(c2,c2,c2,c5). [resolve(22335,a,118,a)].
% 17.80/18.08 24133 -perp(c2,c2,A,B) | para(c2,c5,A,B). [resolve(22693,a,120,a)].
% 17.80/18.08 25212 -perp(A,B,c2,c2) | para(A,B,c2,c5). [resolve(23279,a,120,b)].
% 17.80/18.08 28964 para(A,B,A,B). [resolve(4137,a,149,a)].
% 17.80/18.08 29648 coll(A,B,B). [resolve(28964,a,172,a)].
% 17.80/18.08 29654 coll(A,A,B). [resolve(29648,a,299,a)].
% 17.80/18.08 29658 cyclic(c1,A,c3,c3). [back_unit_del(16551),unit_del(a,29654)].
% 17.80/18.08 30352 cyclic(c1,c3,A,c3). [resolve(29658,a,125,a)].
% 17.80/18.08 30583 cyclic(c1,c3,c3,A). [resolve(30352,a,124,a)].
% 17.80/18.08 30585 cyclic(c3,c3,c2,A). [back_unit_del(22676),unit_del(a,30583)].
% 17.80/18.08 30590 cyclic(c3,c2,A,c2). [back_unit_del(22685),unit_del(a,30585)].
% 17.80/18.08 30591 cyclic(c3,c2,A,c3). [back_unit_del(22678),unit_del(a,30585)].
% 17.80/18.08 30935 cyclic(c3,c3,A,B). [resolve(30583,a,127,b),unit_del(a,30583)].
% 17.80/18.08 30939 cyclic(c3,c2,A,B). [resolve(30585,a,127,b),unit_del(a,30935)].
% 17.80/18.08 30956 cyclic(c2,A,B,c2). [resolve(30590,a,127,b),unit_del(a,30939)].
% 17.80/18.08 30962 cyclic(c2,A,B,c3). [resolve(30591,a,127,b),unit_del(a,30939)].
% 17.80/18.08 30963 cyclic(c2,A,c3,B). [resolve(30591,a,127,a),unit_del(a,30939)].
% 17.80/18.08 30980 cong(c2,A,c2,A). [resolve(4914,a,154,d),unit_del(a,30956),unit_del(b,30963),unit_del(c,30962)].
% 17.80/18.08 31396 perp(c2,c2,A,B). [resolve(30980,a,162,b),unit_del(a,30980)].
% 17.80/18.08 31403 para(c2,c5,A,B). [back_unit_del(24133),unit_del(a,31396)].
% 17.80/18.08 31748 perp(A,B,c2,c2). [resolve(31396,a,119,a)].
% 17.80/18.08 31749 para(A,B,c2,c5). [back_unit_del(25212),unit_del(a,31748)].
% 17.80/18.08 31777 para(A,B,C,D). [resolve(31403,a,117,b),unit_del(a,31749)].
% 17.80/18.08 31780 eqangle(A,B,C,D,E,F,C,D). [back_unit_del(150),unit_del(a,31777)].
% 17.80/18.08 37181 eqangle(A,B,C,D,E,F,E,F). [resolve(31780,a,131,a)].
% 17.80/18.08 37185 eqangle(A,B,C,D,c2,c3,c2,c1). [back_unit_del(781),unit_del(a,37181)].
% 17.80/18.08 42378 -eqangle(c2,c3,c2,c1,A,B,C,D) | eqangle(E,F,V6,V7,A,B,C,D). [resolve(37185,a,132,a)].
% 17.80/18.08 42379 eqangle(c2,c3,c2,c1,A,B,C,D). [resolve(37185,a,130,a)].
% 17.80/18.08 42380 eqangle(A,B,C,D,E,F,V6,V7). [back_unit_del(42378),unit_del(a,42379)].
% 17.80/18.08 42381 $F. [resolve(42380,a,218,a)].
% 17.80/18.08
% 17.80/18.08 % SZS output end Refutation
% 17.80/18.08 ============================== end of proof ==========================
% 17.80/18.08
% 17.80/18.08 ============================== STATISTICS ============================
% 17.80/18.08
% 17.80/18.08 Given=19975. Generated=237453. Kept=42249. proofs=1.
% 17.80/18.08 Usable=17495. Sos=5320. Demods=0. Limbo=1, Disabled=19617. Hints=0.
% 17.80/18.08 Megabytes=20.25.
% 17.80/18.08 User_CPU=16.83, System_CPU=0.13, Wall_clock=17.
% 17.80/18.08
% 17.80/18.08 ============================== end of statistics =====================
% 17.80/18.08
% 17.80/18.08 ============================== end of search =========================
% 17.80/18.08
% 17.80/18.08 THEOREM PROVED
% 17.80/18.08 % SZS status Theorem
% 17.80/18.08
% 17.80/18.08 Exiting with 1 proof.
% 17.80/18.08
% 17.80/18.08 Process 6259 exit (max_proofs) Fri Jun 17 17:37:13 2022
% 17.80/18.08 Prover9 interrupted
%------------------------------------------------------------------------------