TSTP Solution File: GEO591+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GEO591+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n028.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 05:57:07 EDT 2022
% Result : Theorem 14.00s 14.29s
% Output : Refutation 14.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GEO591+1 : TPTP v8.1.0. Released v7.5.0.
% 0.08/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Fri Jun 17 23:05:58 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.80/1.11 ============================== Prover9 ===============================
% 0.80/1.11 Prover9 (32) version 2009-11A, November 2009.
% 0.80/1.11 Process 4439 was started by sandbox on n028.cluster.edu,
% 0.80/1.11 Fri Jun 17 23:05:59 2022
% 0.80/1.11 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_4286_n028.cluster.edu".
% 0.80/1.11 ============================== end of head ===========================
% 0.80/1.11
% 0.80/1.11 ============================== INPUT =================================
% 0.80/1.11
% 0.80/1.11 % Reading from file /tmp/Prover9_4286_n028.cluster.edu
% 0.80/1.11
% 0.80/1.11 set(prolog_style_variables).
% 0.80/1.11 set(auto2).
% 0.80/1.11 % set(auto2) -> set(auto).
% 0.80/1.11 % set(auto) -> set(auto_inference).
% 0.80/1.11 % set(auto) -> set(auto_setup).
% 0.80/1.11 % set(auto_setup) -> set(predicate_elim).
% 0.80/1.11 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.80/1.11 % set(auto) -> set(auto_limits).
% 0.80/1.11 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.80/1.11 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.80/1.11 % set(auto) -> set(auto_denials).
% 0.80/1.11 % set(auto) -> set(auto_process).
% 0.80/1.11 % set(auto2) -> assign(new_constants, 1).
% 0.80/1.11 % set(auto2) -> assign(fold_denial_max, 3).
% 0.80/1.11 % set(auto2) -> assign(max_weight, "200.000").
% 0.80/1.11 % set(auto2) -> assign(max_hours, 1).
% 0.80/1.11 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.80/1.11 % set(auto2) -> assign(max_seconds, 0).
% 0.80/1.11 % set(auto2) -> assign(max_minutes, 5).
% 0.80/1.11 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.80/1.11 % set(auto2) -> set(sort_initial_sos).
% 0.80/1.11 % set(auto2) -> assign(sos_limit, -1).
% 0.80/1.11 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.80/1.11 % set(auto2) -> assign(max_megs, 400).
% 0.80/1.11 % set(auto2) -> assign(stats, some).
% 0.80/1.11 % set(auto2) -> clear(echo_input).
% 0.80/1.11 % set(auto2) -> set(quiet).
% 0.80/1.11 % set(auto2) -> clear(print_initial_clauses).
% 0.80/1.11 % set(auto2) -> clear(print_given).
% 0.80/1.11 assign(lrs_ticks,-1).
% 0.80/1.11 assign(sos_limit,10000).
% 0.80/1.11 assign(order,kbo).
% 0.80/1.11 set(lex_order_vars).
% 0.80/1.11 clear(print_given).
% 0.80/1.11
% 0.80/1.11 % formulas(sos). % not echoed (95 formulas)
% 0.80/1.11
% 0.80/1.11 ============================== end of input ==========================
% 0.80/1.11
% 0.80/1.11 % From the command line: assign(max_seconds, 300).
% 0.80/1.11
% 0.80/1.11 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.80/1.11
% 0.80/1.11 % Formulas that are not ordinary clauses:
% 0.80/1.11 1 (all A all B all C (coll(A,B,C) -> coll(A,C,B))) # label(ruleD1) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.11 2 (all A all B all C (coll(A,B,C) -> coll(B,A,C))) # label(ruleD2) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 11 (all A all B all M (midp(M,B,A) -> midp(M,A,B))) # label(ruleD11) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 67 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.11 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].
% 0.80/1.11 69 (all A all B all C (midp(A,B,C) -> cong(A,B,A,C))) # label(ruleD68) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.11 70 (all A all B all C (midp(A,B,C) -> coll(A,B,C))) # label(ruleD69) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.12 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].
% 0.80/1.12 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].
% 0.80/1.12 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].
% 0.80/1.12 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].
% 0.80/1.12 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].
% 0.80/1.12 95 -(all O all A all B all C all E all D all NWPNT1 all NWPNT2 all NWPNT3 (circle(O,A,NWPNT1,NWPNT2) & circle(O,A,B,NWPNT3) & perp(O,B,B,E) & perp(O,A,A,D) & coll(C,A,B) & perp(O,C,C,E) & coll(D,C,E) -> cong(O,E,O,D))) # label(exemplo6GDDFULL416053) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.80/1.12
% 0.80/1.12 ============================== end of process non-clausal formulas ===
% 0.80/1.12
% 0.80/1.12 ============================== PROCESS INITIAL CLAUSES ===============
% 0.80/1.12
% 0.80/1.12 ============================== PREDICATE ELIMINATION =================
% 0.80/1.12 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)].
% 0.80/1.12 97 -cong(A,B,A,C) | -cong(A,B,A,D) | circle(A,B,C,D) # label(ruleD12) # label(axiom). [clausify(12)].
% 0.80/1.12 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)].
% 0.80/1.12 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)].
% 0.80/1.12 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)].
% 0.80/1.12 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)].
% 0.80/1.12 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)].
% 0.80/1.12 100 -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)].
% 0.80/1.12 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)].
% 0.80/1.12 101 -circle(A,B,C,D) | -coll(A,B,D) | perp(B,C,C,D) # label(ruleD53) # label(axiom). [clausify(54)].
% 0.80/1.12 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)].
% 0.80/1.12 102 -circle(A,B,C,D) | perp(f12(B,C,D,A),B,B,A) # label(ruleX11) # label(axiom). [clausify(87)].
% 0.80/1.12 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)].
% 0.80/1.12 103 -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)].
% 0.80/1.12 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)].
% 0.80/1.12 104 -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)].
% 0.80/1.12 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)].
% 0.80/1.12 105 -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)].
% 0.80/1.12 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)].
% 0.80/1.12 106 -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)].
% 0.80/1.12 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)].
% 0.80/1.12 107 -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)].
% 0.80/1.12 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)].
% 0.80/1.12 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)].
% 0.80/1.12 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)].
% 0.80/1.12 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)].
% 0.80/1.12 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)].
% 0.80/1.12 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)].
% 0.80/1.12 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)].
% 0.80/1.12 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)].
% 0.80/1.12 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)].
% 0.80/1.12 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)].
% 0.80/1.12 108 -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)].
% 0.80/1.12 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)].
% 0.80/1.12 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)].
% 0.80/1.12 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)].
% 0.80/1.12 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)].
% 0.80/1.12 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)].
% 0.80/1.12 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)].
% 0.80/1.12 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)].
% 0.80/1.12 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)].
% 0.80/1.12 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)].
% 0.80/1.12 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)].
% 0.80/1.12 109 circle(c1,c2,c7,c8) # label(exemplo6GDDFULL416053) # label(negated_conjecture). [clausify(95)].
% 0.80/1.12 Derived: -perp(c1,c2,c2,A) | eqangle(c2,A,c2,c7,c8,c2,c8,c7). [resolve(109,a,96,a)].
% 0.80/1.12 Derived: -eqangle(c2,A,c2,c7,c8,c2,c8,c7) | perp(c1,c2,c2,A). [resolve(109,a,98,a)].
% 0.80/1.12 Derived: -midp(A,c7,c8) | eqangle(c2,c7,c2,c8,c1,c7,c1,A). [resolve(109,a,99,a)].
% 0.80/1.12 Derived: -coll(A,c7,c8) | -eqangle(c2,c7,c2,c8,c1,c7,c1,A) | midp(A,c7,c8). [resolve(109,a,100,a)].
% 0.80/1.12 Derived: -coll(c1,c2,c8) | perp(c2,c7,c7,c8). [resolve(109,a,101,a)].
% 0.80/1.12 Derived: perp(f12(c2,c7,c8,c1),c2,c2,c1). [resolve(109,a,102,a)].
% 0.80/1.12 Derived: -cong(c1,c2,c1,A) | -cong(B,c2,B,c7) | B = c1 | coll(f13(c2,c7,c8,A,c1,B),c2,c8). [resolve(109,a,103,a)].
% 14.00/14.29 Derived: -cong(c1,c2,c1,A) | -cong(B,c2,B,c7) | B = c1 | cong(f13(c2,c7,c8,A,c1,B),B,B,c2). [resolve(109,a,104,a)].
% 14.00/14.29 Derived: -cong(c1,c2,c1,A) | -cong(B,c2,B,c7) | B = c1 | coll(f14(c2,c7,c8,A,c1,B),c7,A). [resolve(109,a,105,a)].
% 14.00/14.29 Derived: -cong(c1,c2,c1,A) | -cong(B,c2,B,c7) | B = c1 | cong(f14(c2,c7,c8,A,c1,B),B,B,c2). [resolve(109,a,106,a)].
% 14.00/14.29 110 circle(c1,c2,c3,c9) # label(exemplo6GDDFULL416053) # label(negated_conjecture). [clausify(95)].
% 14.00/14.29 Derived: -perp(c1,c2,c2,A) | eqangle(c2,A,c2,c3,c9,c2,c9,c3). [resolve(110,a,96,a)].
% 14.00/14.29 Derived: -eqangle(c2,A,c2,c3,c9,c2,c9,c3) | perp(c1,c2,c2,A). [resolve(110,a,98,a)].
% 14.00/14.29 Derived: -midp(A,c3,c9) | eqangle(c2,c3,c2,c9,c1,c3,c1,A). [resolve(110,a,99,a)].
% 14.00/14.29 Derived: -coll(A,c3,c9) | -eqangle(c2,c3,c2,c9,c1,c3,c1,A) | midp(A,c3,c9). [resolve(110,a,100,a)].
% 14.00/14.29 Derived: -coll(c1,c2,c9) | perp(c2,c3,c3,c9). [resolve(110,a,101,a)].
% 14.00/14.29 Derived: perp(f12(c2,c3,c9,c1),c2,c2,c1). [resolve(110,a,102,a)].
% 14.00/14.29 Derived: -cong(c1,c2,c1,A) | -cong(B,c2,B,c3) | B = c1 | coll(f13(c2,c3,c9,A,c1,B),c2,c9). [resolve(110,a,103,a)].
% 14.00/14.29 Derived: -cong(c1,c2,c1,A) | -cong(B,c2,B,c3) | B = c1 | cong(f13(c2,c3,c9,A,c1,B),B,B,c2). [resolve(110,a,104,a)].
% 14.00/14.29 Derived: -cong(c1,c2,c1,A) | -cong(B,c2,B,c3) | B = c1 | coll(f14(c2,c3,c9,A,c1,B),c3,A). [resolve(110,a,105,a)].
% 14.00/14.29 Derived: -cong(c1,c2,c1,A) | -cong(B,c2,B,c3) | B = c1 | cong(f14(c2,c3,c9,A,c1,B),B,B,c2). [resolve(110,a,106,a)].
% 14.00/14.29
% 14.00/14.29 ============================== end predicate elimination =============
% 14.00/14.29
% 14.00/14.29 Auto_denials: (non-Horn, no changes).
% 14.00/14.29
% 14.00/14.29 Term ordering decisions:
% 14.00/14.29 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=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.
% 14.00/14.29
% 14.00/14.29 ============================== end of process initial clauses ========
% 14.00/14.29
% 14.00/14.29 ============================== CLAUSES FOR SEARCH ====================
% 14.00/14.29
% 14.00/14.29 ============================== end of clauses for search =============
% 14.00/14.29
% 14.00/14.29 ============================== SEARCH ================================
% 14.00/14.29
% 14.00/14.29 % Starting search at 0.04 seconds.
% 14.00/14.29
% 14.00/14.29 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 2147483647 (0.00 of 0.15 sec).
% 14.00/14.29
% 14.00/14.29 Low Water (keep): wt=26.000, iters=3346
% 14.00/14.29
% 14.00/14.29 Low Water (keep): wt=21.000, iters=3345
% 14.00/14.29
% 14.00/14.29 Low Water (keep): wt=18.000, iters=3333
% 14.00/14.29
% 14.00/14.29 Low Water (keep): wt=17.000, iters=3333
% 14.00/14.29
% 14.00/14.29 Low Water (keep): wt=16.000, iters=3334
% 14.00/14.29
% 14.00/14.29 Low Water (keep): wt=15.000, iters=3344
% 14.00/14.29
% 14.00/14.29 Low Water (keep): wt=14.000, iters=3337
% 14.00/14.29
% 14.00/14.29 Low Water (keep): wt=13.000, iters=3338
% 14.00/14.29
% 14.00/14.29 Low Water (keep): wt=12.000, iters=3383
% 14.00/14.29
% 14.00/14.29 Low Water (displace): id=2530, wt=33.000
% 14.00/14.29
% 14.00/14.29 Low Water (displace): id=15050, wt=9.000
% 14.00/14.29
% 14.00/14.29 Low Water (displace): id=17321, wt=8.000
% 14.00/14.29
% 14.00/14.29 Low Water (displace): id=17328, wt=5.000
% 14.00/14.29
% 14.00/14.29 Low Water (keep): wt=11.000, iters=3351
% 14.00/14.29
% 14.00/14.29 Low Water (keep): wt=10.000, iters=3339
% 14.00/14.29
% 14.00/14.29 ============================== PROOF =================================
% 14.00/14.29 % SZS status Theorem
% 14.00/14.29 % SZS output start Refutation
% 14.00/14.29
% 14.00/14.29 % Proof 1 at 13.04 (+ 0.16) seconds.
% 14.00/14.29 % Length of proof is 369.
% 14.00/14.29 % Level of proof is 38.
% 14.00/14.29 % Maximum clause weight is 29.000.
% 14.00/14.29 % Given clauses 17062.
% 14.00/14.29
% 14.00/14.29 1 (all A all B all C (coll(A,B,C) -> coll(A,C,B))) # label(ruleD1) # label(axiom) # label(non_clause). [assumption].
% 14.00/14.29 2 (all A all B all C (coll(A,B,C) -> coll(B,A,C))) # label(ruleD2) # label(axiom) # label(non_clause). [assumption].
% 14.00/14.29 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].
% 14.00/14.29 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].
% 14.00/14.29 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].
% 14.00/14.29 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].
% 14.00/14.29 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].
% 14.00/14.29 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].
% 14.00/14.29 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].
% 14.00/14.29 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].
% 14.00/14.29 11 (all A all B all M (midp(M,B,A) -> midp(M,A,B))) # label(ruleD11) # label(axiom) # label(non_clause). [assumption].
% 14.00/14.29 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].
% 14.00/14.29 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].
% 14.00/14.29 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].
% 14.00/14.29 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].
% 14.00/14.29 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].
% 14.00/14.29 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].
% 14.00/14.29 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].
% 14.00/14.29 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].
% 14.00/14.29 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].
% 14.00/14.29 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].
% 14.00/14.29 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].
% 14.00/14.29 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].
% 14.00/14.29 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].
% 14.00/14.29 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].
% 14.00/14.29 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].
% 14.00/14.29 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].
% 14.00/14.29 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].
% 14.00/14.29 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].
% 14.00/14.29 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].
% 14.00/14.29 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].
% 14.00/14.29 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].
% 14.00/14.29 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].
% 14.00/14.29 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].
% 14.00/14.29 67 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption].
% 14.00/14.29 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].
% 14.00/14.29 69 (all A all B all C (midp(A,B,C) -> cong(A,B,A,C))) # label(ruleD68) # label(axiom) # label(non_clause). [assumption].
% 14.00/14.29 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].
% 14.00/14.29 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].
% 14.00/14.29 95 -(all O all A all B all C all E all D all NWPNT1 all NWPNT2 all NWPNT3 (circle(O,A,NWPNT1,NWPNT2) & circle(O,A,B,NWPNT3) & perp(O,B,B,E) & perp(O,A,A,D) & coll(C,A,B) & perp(O,C,C,E) & coll(D,C,E) -> cong(O,E,O,D))) # label(exemplo6GDDFULL416053) # label(negated_conjecture) # label(non_clause). [assumption].
% 14.00/14.29 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)].
% 14.00/14.29 97 -cong(A,B,A,C) | -cong(A,B,A,D) | circle(A,B,C,D) # label(ruleD12) # label(axiom). [clausify(12)].
% 14.00/14.29 100 -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)].
% 14.00/14.29 101 -circle(A,B,C,D) | -coll(A,B,D) | perp(B,C,C,D) # label(ruleD53) # label(axiom). [clausify(54)].
% 14.00/14.29 109 circle(c1,c2,c7,c8) # label(exemplo6GDDFULL416053) # label(negated_conjecture). [clausify(95)].
% 14.00/14.29 111 -coll(A,B,C) | coll(A,C,B) # label(ruleD1) # label(axiom). [clausify(1)].
% 14.00/14.29 112 -coll(A,B,C) | coll(B,A,C) # label(ruleD2) # label(axiom). [clausify(2)].
% 14.00/14.29 113 -coll(A,B,C) | -coll(A,B,D) | coll(C,D,A) # label(ruleD3) # label(axiom). [clausify(3)].
% 14.00/14.29 114 -para(A,B,C,D) | para(A,B,D,C) # label(ruleD4) # label(axiom). [clausify(4)].
% 14.00/14.29 115 -para(A,B,C,D) | para(C,D,A,B) # label(ruleD5) # label(axiom). [clausify(5)].
% 14.00/14.29 116 -para(A,B,C,D) | -para(C,D,E,F) | para(A,B,E,F) # label(ruleD6) # label(axiom). [clausify(6)].
% 14.00/14.29 117 -perp(A,B,C,D) | perp(A,B,D,C) # label(ruleD7) # label(axiom). [clausify(7)].
% 14.00/14.29 118 -perp(A,B,C,D) | perp(C,D,A,B) # label(ruleD8) # label(axiom). [clausify(8)].
% 14.00/14.29 119 -perp(A,B,C,D) | -perp(C,D,E,F) | para(A,B,E,F) # label(ruleD9) # label(axiom). [clausify(9)].
% 14.00/14.29 120 -para(A,B,C,D) | -perp(C,D,E,F) | perp(A,B,E,F) # label(ruleD10) # label(axiom). [clausify(10)].
% 14.00/14.29 121 -midp(A,B,C) | midp(A,C,B) # label(ruleD11) # label(axiom). [clausify(11)].
% 14.00/14.29 123 -cyclic(A,B,C,D) | cyclic(A,B,D,C) # label(ruleD14) # label(axiom). [clausify(14)].
% 14.00/14.29 124 -cyclic(A,B,C,D) | cyclic(A,C,B,D) # label(ruleD15) # label(axiom). [clausify(15)].
% 14.00/14.29 125 -cyclic(A,B,C,D) | cyclic(B,A,C,D) # label(ruleD16) # label(axiom). [clausify(16)].
% 14.00/14.29 126 -cyclic(A,B,C,D) | -cyclic(A,B,C,E) | cyclic(B,C,D,E) # label(ruleD17) # label(axiom). [clausify(17)].
% 14.00/14.29 128 -eqangle(A,B,C,D,E,F,V6,V7) | eqangle(C,D,A,B,V6,V7,E,F) # label(ruleD19) # label(axiom). [clausify(19)].
% 14.00/14.29 130 -eqangle(A,B,C,D,E,F,V6,V7) | eqangle(A,B,E,F,C,D,V6,V7) # label(ruleD21) # label(axiom). [clausify(21)].
% 14.00/14.29 132 -cong(A,B,C,D) | cong(A,B,D,C) # label(ruleD23) # label(axiom). [clausify(23)].
% 14.00/14.29 133 -cong(A,B,C,D) | cong(C,D,A,B) # label(ruleD24) # label(axiom). [clausify(24)].
% 14.00/14.29 148 -eqangle(A,B,C,D,E,F,C,D) | para(A,B,E,F) # label(ruleD39) # label(axiom). [clausify(39)].
% 14.00/14.29 149 -para(A,B,C,D) | eqangle(A,B,E,F,C,D,E,F) # label(ruleD40) # label(axiom). [clausify(40)].
% 14.00/14.29 152 -eqangle(A,B,A,C,D,B,D,C) | -coll(A,D,C) | cyclic(B,C,A,D) # label(ruleD42b) # label(axiom). [clausify(43)].
% 14.00/14.29 153 -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)].
% 14.00/14.29 155 -midp(A,B,C) | -para(A,D,C,E) | -coll(D,B,E) | midp(D,B,E) # label(ruleD45) # label(axiom). [clausify(46)].
% 14.00/14.29 158 -perp(A,B,B,C) | -midp(D,A,C) | cong(A,D,B,D) # label(ruleD52) # label(axiom). [clausify(53)].
% 14.00/14.29 160 -midp(A,B,C) | -perp(D,A,B,C) | cong(D,B,D,C) # label(ruleD55) # label(axiom). [clausify(56)].
% 14.00/14.29 161 -cong(A,B,C,B) | -cong(A,D,C,D) | perp(A,C,B,D) # label(ruleD56) # label(axiom). [clausify(57)].
% 14.00/14.29 162 -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)].
% 14.00/14.29 169 -midp(A,B,C) | -para(B,D,C,E) | -para(B,E,C,D) | midp(A,D,E) # label(ruleD64) # label(axiom). [clausify(65)].
% 14.00/14.29 170 -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)].
% 14.00/14.29 171 -para(A,B,A,C) | coll(A,B,C) # label(ruleD66) # label(axiom). [clausify(67)].
% 14.00/14.29 172 -cong(A,B,A,C) | -coll(A,B,C) | midp(A,B,C) # label(ruleD67) # label(axiom). [clausify(68)].
% 14.00/14.29 173 -midp(A,B,C) | cong(A,B,A,C) # label(ruleD68) # label(axiom). [clausify(69)].
% 14.00/14.29 178 -eqangle(A,B,C,D,E,F,V6,V7) | -perp(E,F,V6,V7) | perp(A,B,C,D) # label(ruleD74) # label(axiom). [clausify(75)].
% 14.00/14.29 179 -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)].
% 14.00/14.29 210 perp(c1,c3,c3,c5) # label(exemplo6GDDFULL416053) # label(negated_conjecture). [clausify(95)].
% 14.00/14.29 211 perp(c1,c2,c2,c6) # label(exemplo6GDDFULL416053) # label(negated_conjecture). [clausify(95)].
% 14.00/14.29 212 coll(c4,c2,c3) # label(exemplo6GDDFULL416053) # label(negated_conjecture). [clausify(95)].
% 14.00/14.29 213 perp(c1,c4,c4,c5) # label(exemplo6GDDFULL416053) # label(negated_conjecture). [clausify(95)].
% 14.00/14.29 214 coll(c6,c4,c5) # label(exemplo6GDDFULL416053) # label(negated_conjecture). [clausify(95)].
% 14.00/14.29 215 -cong(c1,c5,c1,c6) # label(exemplo6GDDFULL416053) # label(negated_conjecture). [clausify(95)].
% 14.00/14.29 219 -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)].
% 14.00/14.29 220 -coll(A,B,C) | perp(B,D,D,C) | -cong(A,B,A,D) | -cong(A,B,A,C). [resolve(101,a,97,c)].
% 14.00/14.29 254 -perp(c1,c2,c2,A) | eqangle(c2,A,c2,c7,c8,c2,c8,c7). [resolve(109,a,96,a)].
% 14.00/14.29 258 -coll(c1,c2,c8) | perp(c2,c7,c7,c8). [resolve(109,a,101,a)].
% 14.00/14.29 282 -coll(A,B,C) | coll(C,C,A). [factor(113,a,b)].
% 14.00/14.29 283 -perp(A,B,A,B) | para(A,B,A,B). [factor(119,a,b)].
% 14.00/14.29 287 -cyclic(A,B,C,D) | cyclic(B,C,D,D). [factor(126,a,b)].
% 14.00/14.29 288 -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)].
% 14.00/14.29 290 -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(153,b,c)].
% 14.00/14.29 292 -cong(A,B,C,B) | perp(A,C,B,B). [factor(161,a,b)].
% 14.00/14.29 293 -cong(A,B,C,B) | -cyclic(A,C,B,B) | perp(B,A,A,B). [factor(162,a,b)].
% 14.00/14.29 296 -midp(A,B,C) | -para(B,D,C,D) | midp(A,D,D). [factor(169,b,c)].
% 14.00/14.29 320 -coll(A,B,B) | -eqangle(C,B,C,B,D,B,D,A) | midp(A,B,B) | -cong(D,C,D,B). [factor(219,d,e)].
% 14.00/14.29 321 -coll(A,B,C) | perp(B,C,C,C) | -cong(A,B,A,C). [factor(220,c,d)].
% 14.00/14.29 362 -midp(c3,c3,c5) | cong(c1,c3,c1,c5). [resolve(210,a,160,b)].
% 14.00/14.29 363 -midp(A,c1,c5) | cong(c1,A,c3,A). [resolve(210,a,158,a)].
% 14.00/14.29 364 -perp(A,B,c1,c3) | para(A,B,c3,c5). [resolve(210,a,119,b)].
% 14.00/14.29 365 -perp(c3,c5,A,B) | para(c1,c3,A,B). [resolve(210,a,119,a)].
% 14.00/14.29 366 perp(c3,c5,c1,c3). [resolve(210,a,118,a)].
% 14.00/14.29 367 perp(c1,c3,c5,c3). [resolve(210,a,117,a)].
% 14.00/14.29 387 -perp(A,B,c1,c2) | para(A,B,c2,c6). [resolve(211,a,119,b)].
% 14.00/14.29 388 -perp(c2,c6,A,B) | para(c1,c2,A,B). [resolve(211,a,119,a)].
% 14.00/14.29 389 perp(c2,c6,c1,c2). [resolve(211,a,118,a)].
% 14.00/14.29 413 -midp(A,c1,c5) | cong(c1,A,c4,A). [resolve(213,a,158,a)].
% 14.00/14.29 414 -perp(A,B,c1,c4) | para(A,B,c4,c5). [resolve(213,a,119,b)].
% 14.00/14.29 415 -perp(c4,c5,A,B) | para(c1,c4,A,B). [resolve(213,a,119,a)].
% 14.00/14.29 416 perp(c4,c5,c1,c4). [resolve(213,a,118,a)].
% 14.00/14.29 417 perp(c1,c4,c5,c4). [resolve(213,a,117,a)].
% 14.00/14.29 418 -coll(c6,c4,A) | coll(A,c5,c6). [resolve(214,a,113,b)].
% 14.00/14.29 419 -coll(c6,c4,A) | coll(c5,A,c6). [resolve(214,a,113,a)].
% 14.00/14.29 420 coll(c4,c6,c5). [resolve(214,a,112,a)].
% 14.00/14.29 421 coll(c6,c5,c4). [resolve(214,a,111,a)].
% 14.00/14.29 428 eqangle(c2,c6,c2,c7,c8,c2,c8,c7). [resolve(254,a,211,a)].
% 14.00/14.29 481 coll(c3,c3,c4). [resolve(282,a,212,a)].
% 14.00/14.29 490 coll(c5,c5,c4). [resolve(420,a,282,a)].
% 14.00/14.29 494 coll(c4,c4,c6). [resolve(421,a,282,a)].
% 14.00/14.29 502 coll(c4,c4,c3). [resolve(481,a,282,a)].
% 14.00/14.29 503 -coll(c3,c3,A) | coll(A,c4,c3). [resolve(481,a,113,b)].
% 14.00/14.29 505 coll(c3,c4,c3). [resolve(481,a,111,a)].
% 14.00/14.29 521 coll(c4,c4,c5). [resolve(490,a,282,a)].
% 14.00/14.29 531 -coll(c4,c4,A) | coll(A,c6,c4). [resolve(494,a,113,b)].
% 14.00/14.29 533 coll(c4,c6,c4). [resolve(494,a,111,a)].
% 14.00/14.29 549 coll(c4,c3,c4). [resolve(502,a,111,a)].
% 14.00/14.29 550 coll(c3,c3,c3). [resolve(505,a,282,a)].
% 14.00/14.29 571 coll(c4,c5,c4). [resolve(521,a,111,a)].
% 14.00/14.29 584 coll(c4,c4,c4). [resolve(533,a,282,a)].
% 14.00/14.29 654 -perp(c1,c3,A,B) | para(c3,c5,A,B). [resolve(366,a,119,a)].
% 14.00/14.29 655 perp(c3,c5,c3,c1). [resolve(366,a,117,a)].
% 14.00/14.29 669 perp(c5,c3,c1,c3). [resolve(367,a,118,a)].
% 14.00/14.29 691 perp(c2,c6,c2,c1). [resolve(389,a,117,a)].
% 14.00/14.29 727 perp(c4,c5,c4,c1). [resolve(416,a,117,a)].
% 14.00/14.29 741 perp(c5,c4,c1,c4). [resolve(417,a,118,a)].
% 14.00/14.29 758 -midp(c5,c3,c1) | cong(c3,c3,c3,c1). [resolve(655,a,160,b)].
% 14.00/14.29 761 perp(c3,c1,c3,c5). [resolve(655,a,118,a)].
% 14.00/14.29 779 perp(c2,c1,c2,c6). [resolve(691,a,118,a)].
% 14.00/14.29 813 -perp(A,B,c3,c1) | para(A,B,c3,c5). [resolve(761,a,119,b)].
% 14.00/14.29 849 -perp(c2,c6,A,B) | para(c2,c1,A,B). [resolve(779,a,119,a)].
% 14.00/14.29 948 para(c5,c3,c3,c5). [resolve(364,a,669,a)].
% 14.00/14.29 949 para(c3,c5,c3,c5). [resolve(364,a,366,a)].
% 14.00/14.29 960 -coll(A,c5,c3) | -coll(A,c3,c5) | eqratio(A,c5,c5,c3,A,c3,c3,c5). [resolve(948,a,170,a)].
% 14.00/14.29 961 -midp(c5,A,c3) | -coll(c3,A,c5) | midp(c3,A,c5). [resolve(948,a,155,b)].
% 14.00/14.29 965 para(c3,c5,c5,c3). [resolve(948,a,115,a)].
% 14.00/14.29 966 para(c5,c3,c5,c3). [resolve(948,a,114,a)].
% 14.00/14.29 969 -midp(A,c3,c3) | midp(A,c5,c5). [resolve(949,a,296,b)].
% 14.00/14.29 976 coll(c3,c5,c5). [resolve(949,a,171,a)].
% 14.00/14.29 978 -midp(c3,A,c3) | -coll(c5,A,c5) | midp(c5,A,c5). [resolve(949,a,155,b)].
% 14.00/14.29 979 eqangle(c3,c5,A,B,c3,c5,A,B). [resolve(949,a,149,a)].
% 14.00/14.29 980 coll(c5,c5,c3). [resolve(976,a,282,a)].
% 14.00/14.29 983 coll(c5,c3,c5). [resolve(976,a,112,a)].
% 14.00/14.29 988 coll(c3,c3,c5). [resolve(980,a,282,a)].
% 14.00/14.29 989 -coll(c5,c5,A) | coll(A,c3,c5). [resolve(980,a,113,b)].
% 14.00/14.29 990 -coll(c5,c5,A) | coll(c3,A,c5). [resolve(980,a,113,a)].
% 14.00/14.29 991 para(c1,c3,c3,c1). [resolve(365,a,655,a)].
% 14.00/14.29 992 para(c1,c3,c1,c3). [resolve(365,a,366,a)].
% 14.00/14.29 999 coll(c3,c5,c3). [resolve(988,a,111,a)].
% 14.00/14.29 1004 coll(c5,c3,c3). [resolve(999,a,112,a)].
% 14.00/14.29 1020 -midp(c3,A,c5) | -coll(c5,A,c3) | midp(c5,A,c3). [resolve(965,a,155,b)].
% 14.00/14.29 1035 eqangle(c5,c3,A,B,c5,c3,A,B). [resolve(966,a,149,a)].
% 14.00/14.29 1047 -midp(c1,A,c3) | -coll(c3,A,c1) | midp(c3,A,c1). [resolve(991,a,155,b)].
% 14.00/14.29 1051 para(c3,c1,c1,c3). [resolve(991,a,115,a)].
% 14.00/14.29 1061 coll(c1,c3,c3). [resolve(992,a,171,a)].
% 14.00/14.29 1063 -midp(c1,A,c1) | -coll(c3,A,c3) | midp(c3,A,c3). [resolve(992,a,155,b)].
% 14.00/14.29 1064 eqangle(c1,c3,A,B,c1,c3,A,B). [resolve(992,a,149,a)].
% 14.00/14.29 1065 coll(c3,c3,c1). [resolve(1061,a,282,a)].
% 14.00/14.29 1073 coll(c1,c1,c3). [resolve(1065,a,282,a)].
% 14.00/14.29 1080 coll(c1,c3,c1). [resolve(1073,a,111,a)].
% 14.00/14.29 1090 coll(c1,c1,c1). [resolve(1080,a,282,a)].
% 14.00/14.29 1112 para(c3,c1,c3,c1). [resolve(1051,a,114,a)].
% 14.00/14.29 1124 -midp(A,c3,c3) | midp(A,c1,c1). [resolve(1112,a,296,b)].
% 14.00/14.29 1132 -midp(c3,A,c3) | -coll(c1,A,c1) | midp(c1,A,c1). [resolve(1112,a,155,b)].
% 14.00/14.29 1133 eqangle(c3,c1,A,B,c3,c1,A,B). [resolve(1112,a,149,a)].
% 14.00/14.29 1353 para(c2,c6,c2,c6). [resolve(387,a,389,a)].
% 14.00/14.29 1368 para(c1,c2,c1,c2). [resolve(388,a,389,a)].
% 14.00/14.29 1413 -midp(A,c2,c2) | midp(A,c6,c6). [resolve(1353,a,296,b)].
% 14.00/14.29 1441 -midp(A,c1,c1) | midp(A,c2,c2). [resolve(1368,a,296,b)].
% 14.00/14.29 1578 coll(c1,c4,c3). [resolve(503,a,1065,a)].
% 14.00/14.29 1581 coll(c4,c1,c3). [resolve(1578,a,112,a)].
% 14.00/14.29 1582 coll(c1,c3,c4). [resolve(1578,a,111,a)].
% 14.00/14.29 1585 coll(c4,c3,c1). [resolve(1581,a,111,a)].
% 14.00/14.29 1586 coll(c4,c4,c1). [resolve(1582,a,282,a)].
% 14.00/14.29 1592 coll(c1,c1,c4). [resolve(1585,a,282,a)].
% 14.00/14.29 1598 coll(c4,c1,c4). [resolve(1586,a,111,a)].
% 14.00/14.29 1609 coll(c1,c4,c1). [resolve(1592,a,111,a)].
% 14.00/14.29 1650 coll(c1,c6,c4). [resolve(531,a,1586,a)].
% 14.00/14.29 1653 coll(c6,c1,c4). [resolve(1650,a,112,a)].
% 14.00/14.29 1659 coll(c6,c4,c1). [resolve(1653,a,111,a)].
% 14.00/14.29 1664 coll(c5,c1,c6). [resolve(1659,a,419,a)].
% 14.00/14.29 1665 coll(c1,c5,c6). [resolve(1659,a,418,a)].
% 14.00/14.29 1685 coll(c5,c6,c1). [resolve(1664,a,111,a)].
% 14.00/14.29 1688 coll(c1,c6,c5). [resolve(1665,a,111,a)].
% 14.00/14.29 1705 coll(c1,c1,c5). [resolve(1685,a,282,a)].
% 14.00/14.29 1709 coll(c5,c5,c1). [resolve(1688,a,282,a)].
% 14.00/14.29 1730 coll(c1,c5,c1). [resolve(1705,a,111,a)].
% 14.00/14.29 1731 para(c5,c4,c4,c5). [resolve(414,a,741,a)].
% 14.00/14.29 1732 para(c4,c5,c4,c5). [resolve(414,a,416,a)].
% 14.00/14.29 1744 coll(c5,c1,c5). [resolve(1709,a,111,a)].
% 14.00/14.29 1753 para(c1,c4,c4,c1). [resolve(415,a,727,a)].
% 14.00/14.29 1754 para(c1,c4,c1,c4). [resolve(415,a,416,a)].
% 14.00/14.29 1802 para(c5,c4,c5,c4). [resolve(1731,a,114,a)].
% 14.00/14.29 1813 -midp(c4,A,c4) | -coll(c5,A,c5) | midp(c5,A,c5). [resolve(1732,a,155,b)].
% 14.00/14.29 1830 para(c4,c1,c1,c4). [resolve(1753,a,115,a)].
% 14.00/14.29 1841 -midp(c1,A,c1) | -coll(c4,A,c4) | midp(c4,A,c4). [resolve(1754,a,155,b)].
% 14.00/14.29 1842 eqangle(c1,c4,A,B,c1,c4,A,B). [resolve(1754,a,149,a)].
% 14.00/14.29 1868 -midp(c5,A,c5) | -coll(c4,A,c4) | midp(c4,A,c4). [resolve(1802,a,155,b)].
% 14.00/14.29 1885 para(c4,c1,c4,c1). [resolve(1830,a,114,a)].
% 14.00/14.29 1896 -midp(c4,A,c4) | -coll(c1,A,c1) | midp(c1,A,c1). [resolve(1885,a,155,b)].
% 14.00/14.29 1906 eqangle(c2,c6,c8,c2,c2,c7,c8,c7). [resolve(428,a,130,a)].
% 14.00/14.29 2086 coll(c1,c3,c5). [resolve(989,a,1709,a)].
% 14.00/14.29 2093 coll(c3,c1,c5). [resolve(2086,a,112,a)].
% 14.00/14.29 2094 coll(c1,c5,c3). [resolve(2086,a,111,a)].
% 14.00/14.29 2097 coll(c3,c5,c1). [resolve(2093,a,111,a)].
% 14.00/14.29 2102 coll(c5,c1,c3). [resolve(2094,a,112,a)].
% 14.00/14.29 8452 eqratio(c5,c5,c5,c3,c5,c3,c3,c5). [resolve(960,a,980,a),unit_del(a,983)].
% 14.00/14.29 8648 -cyclic(c5,c3,c3,c5) | -cyclic(c5,c3,c3,c3) | cong(c5,c3,c5,c3). [resolve(979,a,290,c)].
% 14.00/14.29 8653 -coll(c3,c3,A) | cyclic(c5,A,c3,c3). [resolve(979,a,152,a)].
% 14.00/14.29 8654 eqangle(c3,c5,c3,c5,A,B,A,B). [resolve(979,a,130,a)].
% 14.00/14.29 8655 eqangle(A,B,c3,c5,A,B,c3,c5). [resolve(979,a,128,a)].
% 14.00/14.29 9195 midp(c3,c3,c3) | -cong(c5,c5,c5,c3). [resolve(1035,a,320,b),unit_del(a,550)].
% 14.00/14.29 9506 -cyclic(c3,c3,c1,c3) | -cyclic(c3,c3,c1,c1) | cong(c3,c3,c3,c3). [resolve(1064,a,288,c)].
% 14.00/14.29 9512 eqangle(A,B,c1,c3,A,B,c1,c3). [resolve(1064,a,128,a)].
% 14.00/14.29 10070 midp(c1,c1,c1) | -cong(c3,c3,c3,c1). [resolve(1133,a,320,b),unit_del(a,1090)].
% 14.00/14.29 13206 midp(c4,c4,c4) | -cong(c1,c1,c1,c4). [resolve(1842,a,320,b),unit_del(a,584)].
% 14.00/14.29 13321 -perp(c2,c7,c8,c7) | perp(c2,c6,c8,c2). [resolve(1906,a,178,a)].
% 14.00/14.29 14153 -cong(c5,c3,c3,c5) | cong(c5,c5,c5,c3). [resolve(8452,a,179,a)].
% 14.00/14.29 14206 cyclic(c5,c1,c3,c3). [resolve(8653,a,1065,a)].
% 14.00/14.29 14207 cyclic(c5,c5,c3,c3). [resolve(8653,a,988,a)].
% 14.00/14.29 14208 cyclic(c5,c3,c3,c3). [resolve(8653,a,550,a)].
% 14.00/14.29 14212 -cyclic(c5,c3,c3,c5) | cong(c5,c3,c5,c3). [back_unit_del(8648),unit_del(b,14208)].
% 14.00/14.29 14220 cyclic(c1,c3,c3,c3). [resolve(14206,a,287,a)].
% 14.00/14.29 14223 cyclic(c1,c5,c3,c3). [resolve(14206,a,125,a)].
% 14.00/14.29 14224 cyclic(c5,c3,c1,c3). [resolve(14206,a,124,a)].
% 14.00/14.29 14229 cyclic(c5,c3,c5,c3). [resolve(14207,a,124,a)].
% 14.00/14.29 14264 cyclic(c3,c1,c3,c3). [resolve(14220,a,125,a)].
% 14.00/14.29 14268 cyclic(c1,c3,c5,c3). [resolve(14223,a,124,a)].
% 14.00/14.29 14273 cyclic(c5,c3,c3,c1). [resolve(14224,a,123,a)].
% 14.00/14.29 14278 cyclic(c5,c3,c3,c5). [resolve(14229,a,123,a)].
% 14.00/14.29 14280 cong(c5,c3,c5,c3). [back_unit_del(14212),unit_del(a,14278)].
% 14.00/14.29 14336 cyclic(c3,c3,c1,c3). [resolve(14264,a,124,a)].
% 14.00/14.29 14337 -cyclic(c3,c3,c1,c1) | cong(c3,c3,c3,c3). [back_unit_del(9506),unit_del(a,14336)].
% 14.00/14.29 14341 cyclic(c3,c1,c5,c3). [resolve(14268,a,125,a)].
% 14.00/14.29 14347 cyclic(c3,c3,c1,c1). [resolve(14273,a,287,a)].
% 14.00/14.29 14351 cong(c3,c3,c3,c3). [back_unit_del(14337),unit_del(a,14347)].
% 14.00/14.29 14379 midp(c5,c3,c3). [resolve(14280,a,172,a),unit_del(a,1004)].
% 14.00/14.29 14383 cong(c5,c3,c3,c5). [resolve(14280,a,132,a)].
% 14.00/14.29 14386 cong(c5,c5,c5,c3). [back_unit_del(14153),unit_del(a,14383)].
% 14.00/14.29 14387 midp(c3,c3,c3). [back_unit_del(9195),unit_del(b,14386)].
% 14.00/14.29 14391 midp(c5,c5,c5). [resolve(14379,a,969,a)].
% 14.00/14.29 14392 midp(c3,c3,c5). [resolve(14379,a,961,a),unit_del(a,988)].
% 14.00/14.29 14407 cong(c1,c3,c1,c5). [back_unit_del(362),unit_del(a,14392)].
% 14.00/14.29 14410 midp(c1,c3,c1). [resolve(14387,a,1132,a),unit_del(a,1080)].
% 14.00/14.29 14411 midp(c3,c1,c1). [resolve(14387,a,1124,a)].
% 14.00/14.29 14445 midp(c4,c5,c4). [resolve(14391,a,1868,a),unit_del(a,571)].
% 14.00/14.29 14482 midp(c4,c3,c4). [resolve(14410,a,1841,a),unit_del(a,549)].
% 14.00/14.29 14504 cong(c3,c1,c3,c1). [resolve(14411,a,173,a)].
% 14.00/14.29 14566 midp(c1,c5,c1). [resolve(14445,a,1896,a),unit_del(a,1730)].
% 14.00/14.29 14602 midp(c4,c4,c3). [resolve(14482,a,121,a)].
% 14.00/14.29 14692 midp(c1,c1,c5). [resolve(14566,a,121,a)].
% 14.00/14.29 14699 cong(c4,c4,c4,c3). [resolve(14602,a,173,a)].
% 14.00/14.29 14748 cong(c1,c1,c4,c1). [resolve(14692,a,413,a)].
% 14.00/14.29 14891 perp(c1,c3,c3,c3). [resolve(14336,a,162,c),unit_del(a,14504),unit_del(b,14351)].
% 14.00/14.29 14902 cyclic(c3,c1,c3,c5). [resolve(14341,a,123,a)].
% 14.00/14.29 14998 midp(c1,c3,c5). [resolve(14407,a,172,a),unit_del(a,2086)].
% 14.00/14.29 15016 midp(c1,c5,c3). [resolve(14998,a,121,a)].
% 14.00/14.29 15017 midp(c3,c5,c1). [resolve(15016,a,1047,a),unit_del(a,2097)].
% 14.00/14.29 15033 cong(c3,c5,c3,c1). [resolve(15017,a,173,a)].
% 14.00/14.29 15038 midp(c3,c1,c5). [resolve(15017,a,121,a)].
% 14.00/14.29 15041 midp(c5,c1,c3). [resolve(15038,a,1020,a),unit_del(a,2102)].
% 14.00/14.29 15070 midp(c5,c3,c1). [resolve(15041,a,121,a)].
% 14.00/14.29 15073 cong(c3,c3,c3,c1). [back_unit_del(758),unit_del(a,15070)].
% 14.00/14.29 15074 midp(c1,c1,c1). [back_unit_del(10070),unit_del(b,15073)].
% 14.00/14.29 15091 midp(c4,c1,c4). [resolve(15074,a,1841,a),unit_del(a,1598)].
% 14.00/14.29 15094 midp(c1,c2,c2). [resolve(15074,a,1441,a)].
% 14.00/14.29 15122 midp(c5,c1,c5). [resolve(15091,a,1813,a),unit_del(a,1744)].
% 14.00/14.29 15174 midp(c1,c6,c6). [resolve(15094,a,1413,a)].
% 14.00/14.29 15210 cong(c1,c5,c3,c5). [resolve(15122,a,363,a)].
% 14.00/14.29 15221 midp(c5,c5,c1). [resolve(15122,a,121,a)].
% 14.00/14.29 15294 cong(c5,c5,c5,c1). [resolve(15221,a,173,a)].
% 14.00/14.29 15858 perp(c4,c3,c3,c3). [resolve(14699,a,321,c),unit_del(a,502)].
% 14.00/14.29 15940 cong(c1,c1,c1,c4). [resolve(14748,a,132,a)].
% 14.00/14.29 15941 midp(c4,c4,c4). [back_unit_del(13206),unit_del(b,15940)].
% 14.00/14.29 15943 midp(c1,c4,c1). [resolve(15941,a,1896,a),unit_del(a,1609)].
% 14.00/14.29 15963 midp(c3,c4,c3). [resolve(15943,a,1063,a),unit_del(a,505)].
% 14.00/14.29 16037 midp(c3,c3,c4). [resolve(15963,a,121,a)].
% 14.00/14.29 16104 cong(c3,c3,c3,c4). [resolve(16037,a,173,a)].
% 14.00/14.29 16439 para(c3,c5,c3,c3). [resolve(14891,a,654,a)].
% 14.00/14.29 16452 cyclic(c1,c3,c5,c5). [resolve(14902,a,287,a)].
% 14.00/14.29 16535 cong(c3,c5,c1,c3). [resolve(15033,a,132,a)].
% 14.00/14.29 17263 cong(c5,c5,c1,c5). [resolve(15294,a,132,a)].
% 14.00/14.29 17795 perp(c3,c3,c4,c3). [resolve(15858,a,118,a)].
% 14.00/14.29 18089 cong(c3,c3,c4,c3). [resolve(16104,a,132,a)].
% 14.00/14.29 18547 -perp(c3,c3,A,B) | perp(c3,c5,A,B). [resolve(16439,a,120,a)].
% 14.00/14.29 18578 perp(c5,c1,c1,c5). [resolve(16452,a,293,b),unit_del(a,15210)].
% 14.00/14.29 18582 cyclic(c3,c1,c5,c5). [resolve(16452,a,125,a)].
% 14.00/14.29 18583 cyclic(c1,c5,c3,c5). [resolve(16452,a,124,a)].
% 14.00/14.29 18735 cong(c1,c3,c3,c5). [resolve(16535,a,133,a)].
% 14.00/14.29 19325 cong(c1,c5,c5,c5). [resolve(17263,a,133,a)].
% 14.00/14.29 19595 perp(c3,c3,c3,c4). [resolve(17795,a,117,a)].
% 14.00/14.29 19681 perp(c3,c4,c3,c3). [resolve(18089,a,292,a)].
% 14.00/14.29 20078 perp(c5,c1,c5,c1). [resolve(18578,a,117,a)].
% 14.00/14.29 20082 cyclic(c3,c5,c1,c5). [resolve(18582,a,124,a)].
% 14.00/14.29 20088 cyclic(c1,c5,c5,c3). [resolve(18583,a,123,a)].
% 14.00/14.29 20195 cong(c1,c3,c5,c3). [resolve(18735,a,132,a)].
% 14.00/14.29 21314 -perp(A,B,c3,c3) | para(A,B,c3,c4). [resolve(19595,a,119,b)].
% 14.00/14.29 21365 -perp(c3,c3,A,B) | para(c3,c4,A,B). [resolve(19681,a,119,a)].
% 14.00/14.29 21561 para(c5,c1,c5,c1). [resolve(20078,a,283,a)].
% 14.00/14.29 21569 cyclic(c5,c3,c1,c5). [resolve(20082,a,125,a)].
% 14.00/14.29 21571 perp(c5,c1,c1,c3). [resolve(20088,a,162,c),unit_del(a,19325),unit_del(b,20195)].
% 14.00/14.29 22981 para(c5,c1,c1,c5). [resolve(21561,a,114,a)].
% 14.00/14.29 22996 cyclic(c5,c3,c5,c1). [resolve(21569,a,123,a)].
% 14.00/14.29 23019 perp(c5,c1,c3,c1). [resolve(21571,a,117,a)].
% 14.00/14.29 23705 para(c1,c5,c5,c1). [resolve(22981,a,115,a)].
% 14.00/14.29 23709 cyclic(c5,c5,c3,c1). [resolve(22996,a,124,a)].
% 14.00/14.29 23711 para(c5,c1,c3,c5). [resolve(23019,a,813,a)].
% 14.00/14.29 24146 -perp(c5,c1,A,B) | perp(c1,c5,A,B). [resolve(23705,a,120,a)].
% 14.00/14.29 24150 -cyclic(c5,c5,c3,A) | cyclic(c5,c3,A,c1). [resolve(23709,a,126,b)].
% 14.00/14.29 24165 -perp(c3,c5,A,B) | perp(c5,c1,A,B). [resolve(23711,a,120,a)].
% 14.00/14.29 34451 -coll(c3,A,c5) | cyclic(c5,c5,c3,A). [resolve(8654,a,152,a)].
% 14.00/14.29 34456 para(A,B,A,B). [resolve(8655,a,148,a)].
% 14.00/14.29 34460 -midp(A,B,B) | midp(A,C,C). [resolve(34456,a,296,b)].
% 14.00/14.29 34461 coll(A,B,B). [resolve(34456,a,171,a)].
% 14.00/14.29 34465 coll(A,A,B). [resolve(34461,a,282,a)].
% 14.00/14.29 34468 coll(A,B,A). [resolve(34461,a,112,a)].
% 14.00/14.29 34802 coll(c3,A,c5). [back_unit_del(990),unit_del(a,34465)].
% 14.00/14.29 34837 -midp(c1,A,c1) | midp(c3,A,c3). [back_unit_del(1063),unit_del(b,34468)].
% 14.00/14.29 34839 -midp(c3,A,c3) | midp(c5,A,c5). [back_unit_del(978),unit_del(b,34468)].
% 14.00/14.29 34859 cyclic(c5,c5,c3,A). [back_unit_del(34451),unit_del(a,34802)].
% 14.00/14.29 34868 cyclic(c5,c3,A,c1). [back_unit_del(24150),unit_del(a,34859)].
% 14.00/14.29 35044 coll(A,B,C). [resolve(34465,a,113,b),unit_del(a,34465)].
% 14.00/14.29 35046 perp(c2,c7,c7,c8). [back_unit_del(258),unit_del(a,35044)].
% 14.00/14.29 35074 cyclic(c5,c3,A,B). [resolve(34859,a,126,b),unit_del(a,34859)].
% 14.00/14.29 35085 cyclic(c3,A,B,c1). [resolve(34868,a,126,b),unit_del(a,35074)].
% 14.00/14.29 35473 perp(c2,c7,c8,c7). [resolve(35046,a,117,a)].
% 14.00/14.29 35474 perp(c2,c6,c8,c2). [back_unit_del(13321),unit_del(a,35473)].
% 14.00/14.29 35515 cyclic(c3,A,B,C). [resolve(35074,a,126,b),unit_del(a,35074)].
% 14.00/14.29 35539 cyclic(A,B,C,c1). [resolve(35085,a,126,b),unit_del(a,35515)].
% 14.00/14.29 35540 cyclic(A,B,c1,C). [resolve(35085,a,126,a),unit_del(a,35515)].
% 14.00/14.29 35553 cong(A,c3,A,c3). [resolve(9512,a,153,d),unit_del(a,35540),unit_del(b,35540),unit_del(c,35539)].
% 14.00/14.29 35739 para(c2,c1,c8,c2). [resolve(35474,a,849,a)].
% 14.00/14.29 35776 cong(A,c3,c3,A). [resolve(35553,a,132,a)].
% 14.00/14.29 35828 para(c2,c1,c2,c8). [resolve(35739,a,114,a)].
% 14.00/14.29 35851 cong(c3,A,A,c3). [resolve(35776,a,133,a)].
% 14.00/14.29 35897 para(c2,c8,c2,c1). [resolve(35828,a,115,a)].
% 14.00/14.29 35907 cong(c3,A,c3,A). [resolve(35851,a,132,a)].
% 14.00/14.29 35929 -midp(A,c2,c2) | midp(A,c1,c8). [resolve(35897,a,169,c),unit_del(b,35828)].
% 14.00/14.29 35935 perp(c3,c3,A,B). [resolve(35907,a,161,b),unit_del(a,35907)].
% 14.00/14.29 35938 para(c3,c4,A,B). [back_unit_del(21365),unit_del(a,35935)].
% 14.00/14.29 35946 perp(c3,c5,A,B). [back_unit_del(18547),unit_del(a,35935)].
% 14.00/14.29 35966 perp(c5,c1,A,B). [back_unit_del(24165),unit_del(a,35946)].
% 14.00/14.29 35981 perp(c1,c5,A,B). [back_unit_del(24146),unit_del(a,35966)].
% 14.00/14.29 36034 perp(A,B,c3,c3). [resolve(35935,a,118,a)].
% 14.00/14.29 36035 para(A,B,c3,c4). [back_unit_del(21314),unit_del(a,36034)].
% 14.00/14.29 36057 para(A,B,C,D). [resolve(35938,a,116,b),unit_del(a,36035)].
% 14.00/14.29 36059 -midp(A,B,C) | midp(A,D,E). [back_unit_del(169),unit_del(b,36057),unit_del(c,36057)].
% 14.00/14.29 36116 -midp(c5,A,B) | cong(c1,A,c1,B). [resolve(35981,a,160,b)].
% 14.00/14.29 37521 midp(c1,A,A). [resolve(34460,a,15174,a)].
% 14.00/14.29 38841 midp(c1,c1,c8). [resolve(35929,a,37521,a)].
% 14.00/14.29 38856 midp(c1,c8,c1). [resolve(38841,a,121,a)].
% 14.00/14.29 38876 midp(c3,c8,c3). [resolve(38856,a,34837,a)].
% 14.00/14.29 38898 midp(c5,c8,c5). [resolve(38876,a,34839,a)].
% 14.00/14.29 38927 midp(c5,c5,c8). [resolve(38898,a,121,a)].
% 14.00/14.29 39392 midp(c5,A,B). [resolve(36059,a,38927,a)].
% 14.00/14.29 39399 cong(c1,A,c1,B). [back_unit_del(36116),unit_del(a,39392)].
% 14.00/14.29 39400 $F. [resolve(39399,a,215,a)].
% 14.00/14.29
% 14.00/14.29 % SZS output end Refutation
% 14.00/14.29 ============================== end of proof ==========================
% 14.00/14.29
% 14.00/14.29 ============================== STATISTICS ============================
% 14.00/14.29
% 14.00/14.29 Given=17062. Generated=231143. Kept=39273. proofs=1.
% 14.00/14.29 Usable=14849. Sos=6378. Demods=0. Limbo=7, Disabled=18209. Hints=0.
% 14.00/14.29 Megabytes=19.05.
% 14.00/14.29 User_CPU=13.04, System_CPU=0.16, Wall_clock=13.
% 14.00/14.29
% 14.00/14.29 ============================== end of statistics =====================
% 14.00/14.29
% 14.00/14.29 ============================== end of search =========================
% 14.00/14.29
% 14.00/14.29 THEOREM PROVED
% 14.00/14.29 % SZS status Theorem
% 14.00/14.29
% 14.00/14.29 Exiting with 1 proof.
% 14.00/14.29
% 14.00/14.29 Process 4439 exit (max_proofs) Fri Jun 17 23:06:12 2022
% 14.00/14.29 Prover9 interrupted
%------------------------------------------------------------------------------