TSTP Solution File: GEO546+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GEO546+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 05:56:53 EDT 2022
% Result : Theorem 4.02s 4.35s
% Output : Refutation 4.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GEO546+1 : TPTP v8.1.0. Released v7.5.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 18 15:02:02 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.41/1.08 ============================== Prover9 ===============================
% 0.41/1.08 Prover9 (32) version 2009-11A, November 2009.
% 0.41/1.08 Process 16558 was started by sandbox on n022.cluster.edu,
% 0.41/1.08 Sat Jun 18 15:02:02 2022
% 0.41/1.08 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_16405_n022.cluster.edu".
% 0.41/1.08 ============================== end of head ===========================
% 0.41/1.08
% 0.41/1.08 ============================== INPUT =================================
% 0.41/1.08
% 0.41/1.08 % Reading from file /tmp/Prover9_16405_n022.cluster.edu
% 0.41/1.08
% 0.41/1.08 set(prolog_style_variables).
% 0.41/1.08 set(auto2).
% 0.41/1.08 % set(auto2) -> set(auto).
% 0.41/1.08 % set(auto) -> set(auto_inference).
% 0.41/1.08 % set(auto) -> set(auto_setup).
% 0.41/1.08 % set(auto_setup) -> set(predicate_elim).
% 0.41/1.08 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.41/1.08 % set(auto) -> set(auto_limits).
% 0.41/1.08 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.41/1.08 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.41/1.08 % set(auto) -> set(auto_denials).
% 0.41/1.08 % set(auto) -> set(auto_process).
% 0.41/1.08 % set(auto2) -> assign(new_constants, 1).
% 0.41/1.08 % set(auto2) -> assign(fold_denial_max, 3).
% 0.41/1.08 % set(auto2) -> assign(max_weight, "200.000").
% 0.41/1.08 % set(auto2) -> assign(max_hours, 1).
% 0.41/1.08 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.41/1.08 % set(auto2) -> assign(max_seconds, 0).
% 0.41/1.08 % set(auto2) -> assign(max_minutes, 5).
% 0.41/1.08 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.41/1.08 % set(auto2) -> set(sort_initial_sos).
% 0.41/1.08 % set(auto2) -> assign(sos_limit, -1).
% 0.41/1.08 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.41/1.08 % set(auto2) -> assign(max_megs, 400).
% 0.41/1.08 % set(auto2) -> assign(stats, some).
% 0.41/1.08 % set(auto2) -> clear(echo_input).
% 0.41/1.08 % set(auto2) -> set(quiet).
% 0.41/1.08 % set(auto2) -> clear(print_initial_clauses).
% 0.41/1.08 % set(auto2) -> clear(print_given).
% 0.41/1.08 assign(lrs_ticks,-1).
% 0.41/1.08 assign(sos_limit,10000).
% 0.41/1.08 assign(order,kbo).
% 0.41/1.08 set(lex_order_vars).
% 0.41/1.08 clear(print_given).
% 0.41/1.08
% 0.41/1.08 % formulas(sos). % not echoed (95 formulas)
% 0.41/1.08
% 0.41/1.08 ============================== end of input ==========================
% 0.41/1.08
% 0.41/1.08 % From the command line: assign(max_seconds, 300).
% 0.41/1.08
% 0.41/1.08 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.41/1.08
% 0.41/1.08 % Formulas that are not ordinary clauses:
% 0.41/1.08 1 (all A all B all C (coll(A,B,C) -> coll(A,C,B))) # label(ruleD1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.08 2 (all A all B all C (coll(A,B,C) -> coll(B,A,C))) # label(ruleD2) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.41/1.08 11 (all A all B all M (midp(M,B,A) -> midp(M,A,B))) # label(ruleD11) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.41/1.08 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].
% 0.81/1.09 40 (all A all B all C all D all P all Q (para(A,B,C,D) -> eqangle(A,B,P,Q,C,D,P,Q))) # label(ruleD40) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 41 (all A all B all P all Q (cyclic(A,B,P,Q) -> eqangle(P,A,P,B,Q,A,Q,B))) # label(ruleD41) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 42 (all A all B all P all Q (eqangle(P,A,P,B,Q,A,Q,B) & -coll(P,Q,A) -> cyclic(A,B,P,Q))) # label(ruleD42a) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 43 (all A all B all P all Q (eqangle(P,A,P,B,Q,A,Q,B) & coll(P,Q,B) -> cyclic(A,B,P,Q))) # label(ruleD42b) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 44 (all A all B all C all P all Q all R (cyclic(A,B,C,P) & cyclic(A,B,C,Q) & cyclic(A,B,C,R) & eqangle(C,A,C,B,R,P,R,Q) -> cong(A,B,P,Q))) # label(ruleD43) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 45 (all A all B all C all E all F (midp(E,A,B) & midp(F,A,C) -> para(E,F,B,C))) # label(ruleD44) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 46 (all A all B all C all E all F (midp(E,A,B) & para(E,F,B,C) & coll(F,A,C) -> midp(F,A,C))) # label(ruleD45) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 47 (all A all B all O (cong(O,A,O,B) -> eqangle(O,A,A,B,A,B,O,B))) # label(ruleD46) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 48 (all A all B all O (eqangle(O,A,A,B,A,B,O,B) & -coll(O,A,B) -> cong(O,A,O,B))) # label(ruleD47) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 49 (all A all B all C all O all X (circle(O,A,B,C) & perp(O,A,A,X) -> eqangle(A,X,A,B,C,A,C,B))) # label(ruleD48) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 50 (all A all B all C all O all X (circle(O,A,B,C) & eqangle(A,X,A,B,C,A,C,B) -> perp(O,A,A,X))) # label(ruleD49) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 51 (all A all B all C all O all M (circle(O,A,B,C) & midp(M,B,C) -> eqangle(A,B,A,C,O,B,O,M))) # label(ruleD50) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 52 (all A all B all C all O all M (circle(O,A,B,C) & coll(M,B,C) & eqangle(A,B,A,C,O,B,O,M) -> midp(M,B,C))) # label(ruleD51) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 53 (all A all B all C all M (perp(A,B,B,C) & midp(M,A,C) -> cong(A,M,B,M))) # label(ruleD52) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 54 (all A all B all C all O (circle(O,A,B,C) & coll(O,A,C) -> perp(A,B,B,C))) # label(ruleD53) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 55 (all A all B all C all D (cyclic(A,B,C,D) & para(A,B,C,D) -> eqangle(A,D,C,D,C,D,C,B))) # label(ruleD54) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 56 (all A all B all M all O (midp(M,A,B) & perp(O,M,A,B) -> cong(O,A,O,B))) # label(ruleD55) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 57 (all A all B all P all Q (cong(A,P,B,P) & cong(A,Q,B,Q) -> perp(A,B,P,Q))) # label(ruleD56) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 58 (all A all B all P all Q (cong(A,P,B,P) & cong(A,Q,B,Q) & cyclic(A,B,P,Q) -> perp(P,A,A,Q))) # label(ruleD57) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 59 (all A all B all C all P all Q all R (eqangle(A,B,B,C,P,Q,Q,R) & eqangle(A,C,B,C,P,R,Q,R) & -coll(A,B,C) -> simtri(A,B,C,P,Q,R))) # label(ruleD58) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 60 (all A all B all C all P all Q all R (simtri(A,B,C,P,Q,R) -> eqratio(A,B,A,C,P,Q,P,R))) # label(ruleD59) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 61 (all A all B all C all P all Q all R (simtri(A,B,C,P,Q,R) -> eqangle(A,B,B,C,P,Q,Q,R))) # label(ruleD60) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 62 (all A all B all C all P all Q all R (simtri(A,B,C,P,Q,R) & cong(A,B,P,Q) -> contri(A,B,C,P,Q,R))) # label(ruleD61) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 63 (all A all B all C all P all Q all R (contri(A,B,C,P,Q,R) -> cong(A,B,P,Q))) # label(ruleD62) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 64 (all A all B all C all D all M (midp(M,A,B) & midp(M,C,D) -> para(A,C,B,D))) # label(ruleD63) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 65 (all A all B all C all D all M (midp(M,A,B) & para(A,C,B,D) & para(A,D,B,C) -> midp(M,C,D))) # label(ruleD64) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 66 (all A all B all C all D all O (para(A,B,C,D) & coll(O,A,C) & coll(O,B,D) -> eqratio(O,A,A,C,O,B,B,D))) # label(ruleD65) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 67 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 68 (all A all B all C (cong(A,B,A,C) & coll(A,B,C) -> midp(A,B,C))) # label(ruleD67) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 69 (all A all B all C (midp(A,B,C) -> cong(A,B,A,C))) # label(ruleD68) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 70 (all A all B all C (midp(A,B,C) -> coll(A,B,C))) # label(ruleD69) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 71 (all A all B all C all D all M all N (midp(M,A,B) & midp(N,C,D) -> eqratio(M,A,A,B,N,C,C,D))) # label(ruleD70) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 72 (all A all B all C all D (eqangle(A,B,C,D,C,D,A,B) & -para(A,B,C,D) -> perp(A,B,C,D))) # label(ruleD71) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 73 (all A all B all C all D (eqangle(A,B,C,D,C,D,A,B) & -perp(A,B,C,D) -> para(A,B,C,D))) # label(ruleD72) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 74 (all A all B all C all D all P all Q all U all V (eqangle(A,B,C,D,P,Q,U,V) & para(P,Q,U,V) -> para(A,B,C,D))) # label(ruleD73) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 75 (all A all B all C all D all P all Q all U all V (eqangle(A,B,C,D,P,Q,U,V) & perp(P,Q,U,V) -> perp(A,B,C,D))) # label(ruleD74) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 76 (all A all B all C all D all P all Q all U all V (eqratio(A,B,C,D,P,Q,U,V) & cong(P,Q,U,V) -> cong(A,B,C,D))) # label(ruleD75) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 77 (all A all M all O all X exists B (perp(O,M,M,A) & eqangle(X,O,M,O,M,O,A,O) -> coll(B,A,M) & coll(B,O,X))) # label(ruleX1) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 78 (all A all B all O all X exists M (cong(O,A,O,B) & eqangle(A,O,O,X,O,X,O,B) -> coll(B,A,M) & coll(M,O,X))) # label(ruleX2) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 79 (all A all B all O all X exists M (perp(O,X,A,B) & eqangle(A,O,O,X,O,X,O,B) -> coll(B,A,M) & coll(M,O,X))) # label(ruleX3) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 80 (all A all B all O all X exists M (perp(O,X,A,B) & cong(O,A,O,B) -> coll(B,A,M) & coll(M,O,X))) # label(ruleX4) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 81 (all A all B all P all X all Y exists Q (eqangle(A,P,B,P,A,X,B,Y) & -coll(A,B,P) -> eqangle(A,P,B,P,A,Q,B,Q) & cyclic(X,B,P,Q))) # label(ruleX5) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 82 (all A all B all C all D all M all N exists P (midp(M,A,B) & midp(N,C,D) -> midp(P,A,D) & para(P,M,B,D) & para(P,N,A,C))) # label(ruleX6) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 83 (all A all B all C all D all M all N all Q exists P (midp(M,A,B) & midp(N,C,D) & coll(C,A,B) & coll(D,A,B) -> midp(P,A,Q))) # label(ruleX7) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 84 (all A all B all M all P all Q all R all M exists X (midp(M,A,B) & para(A,P,R,M) & para(A,P,B,Q) & coll(P,Q,R) -> coll(X,A,Q) & coll(X,M,R))) # label(ruleX8) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 85 (all A all B all C all D all O exists P (cong(O,C,O,D) & perp(A,B,B,O) -> cong(O,C,O,P) & para(P,C,A,B) & cong(B,C,B,P))) # label(ruleX9) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 86 (all A all B all C all H exists P exists Q (perp(A,H,B,C) & perp(B,H,A,C) -> coll(P,C,B) & perp(A,P,C,B) & coll(Q,C,A) & perp(B,Q,C,A))) # label(ruleX10) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 87 (all A all B all C all O exists P (circle(O,A,B,C) -> perp(P,A,A,O))) # label(ruleX11) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 88 (all A all B all C all D all M all N exists P exists Q (circle(M,A,B,C) & cong(M,A,M,D) & cong(N,A,N,B) & M != N -> coll(P,A,C) & cong(P,N,N,A) & coll(Q,B,D) & cong(Q,N,N,A))) # label(ruleX12) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 89 (all A all B all C all D all M exists O (cyclic(A,B,C,D) & para(A,B,C,D) & midp(M,A,B) -> circle(O,A,B,C))) # label(ruleX13) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 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].
% 0.81/1.09 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].
% 0.81/1.09 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].
% 0.81/1.09 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].
% 0.81/1.09 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].
% 0.81/1.09 95 -(all A all B all C all E all F all H (perp(E,C,A,B) & coll(E,A,B) & perp(F,A,B,C) & coll(F,B,C) & coll(H,C,E) & coll(H,A,F) -> perp(B,H,A,C))) # label(exemplo6GDDFULL012006) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.81/1.09
% 0.81/1.09 ============================== end of process non-clausal formulas ===
% 0.81/1.09
% 0.81/1.09 ============================== PROCESS INITIAL CLAUSES ===============
% 0.81/1.09
% 0.81/1.09 ============================== PREDICATE ELIMINATION =================
% 0.81/1.09 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)].
% 0.81/1.09 97 -cong(A,B,A,C) | -cong(A,B,A,D) | circle(A,B,C,D) # label(ruleD12) # label(axiom). [clausify(12)].
% 0.81/1.09 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)].
% 0.81/1.09 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)].
% 0.81/1.09 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)].
% 0.81/1.09 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)].
% 0.81/1.09 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)].
% 0.81/1.09 100 -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)].
% 0.81/1.09 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)].
% 0.81/1.09 101 -circle(A,B,C,D) | -coll(A,B,D) | perp(B,C,C,D) # label(ruleD53) # label(axiom). [clausify(54)].
% 0.81/1.09 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)].
% 0.81/1.09 102 -circle(A,B,C,D) | perp(f12(B,C,D,A),B,B,A) # label(ruleX11) # label(axiom). [clausify(87)].
% 0.81/1.09 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)].
% 0.81/1.09 103 -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)].
% 0.81/1.09 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)].
% 0.81/1.09 104 -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)].
% 0.81/1.09 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)].
% 0.81/1.09 105 -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)].
% 0.81/1.09 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)].
% 0.81/1.09 106 -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)].
% 0.81/1.09 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)].
% 0.81/1.09 107 -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)].
% 0.93/1.21 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)].
% 0.93/1.21 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)].
% 0.93/1.21 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)].
% 0.93/1.21 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)].
% 0.93/1.21 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)].
% 0.93/1.21 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)].
% 0.93/1.21 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)].
% 0.93/1.21 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)].
% 0.93/1.21 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)].
% 0.93/1.21 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)].
% 0.93/1.21 108 -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)].
% 0.93/1.21 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)].
% 0.93/1.21 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)].
% 0.93/1.21 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)].
% 0.93/1.21 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)].
% 0.93/1.21 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)].
% 0.93/1.21 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)].
% 0.93/1.21 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)].
% 0.93/1.21 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)].
% 0.93/1.21 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)].
% 0.93/1.21 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)].
% 0.93/1.21
% 0.93/1.21 ============================== end predicate elimination =============
% 0.93/1.21
% 0.93/1.21 Auto_denials: (non-Horn, no changes).
% 0.93/1.21
% 0.93/1.21 Term ordering decisions:
% 0.93/1.21 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. c6=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.
% 0.93/1.21
% 0.93/1.21 ============================== end of process initial clauses ========
% 0.93/1.21
% 0.93/1.21 ============================== CLAUSES FOR SEARCH ====================
% 0.93/1.21
% 0.93/1.21 ============================== end of clauses for search =============
% 0.93/1.21
% 0.93/1.21 ============================== SEARCH ================================
% 0.93/1.21
% 0.93/1.21 % Starting search at 0.04 seconds.
% 0.93/1.21
% 0.93/1.21 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 2147483647 (0.00 of 0.14 sec).
% 4.02/4.35
% 4.02/4.35 Low Water (keep): wt=45.000, iters=3454
% 4.02/4.35
% 4.02/4.35 Low Water (keep): wt=44.000, iters=3398
% 4.02/4.35
% 4.02/4.35 Low Water (keep): wt=40.000, iters=3413
% 4.02/4.35
% 4.02/4.35 Low Water (keep): wt=39.000, iters=3365
% 4.02/4.35
% 4.02/4.35 Low Water (keep): wt=32.000, iters=3353
% 4.02/4.35
% 4.02/4.35 Low Water (keep): wt=28.000, iters=3335
% 4.02/4.35
% 4.02/4.35 Low Water (keep): wt=24.000, iters=3375
% 4.02/4.35
% 4.02/4.35 Low Water (keep): wt=23.000, iters=3340
% 4.02/4.35
% 4.02/4.35 Low Water (keep): wt=22.000, iters=3354
% 4.02/4.35
% 4.02/4.35 Low Water (keep): wt=21.000, iters=3347
% 4.02/4.35
% 4.02/4.35 Low Water (keep): wt=19.000, iters=3351
% 4.02/4.35
% 4.02/4.35 Low Water (keep): wt=18.000, iters=3342
% 4.02/4.35
% 4.02/4.35 Low Water (keep): wt=17.000, iters=3348
% 4.02/4.35
% 4.02/4.35 Low Water (keep): wt=15.000, iters=3345
% 4.02/4.35
% 4.02/4.35 Low Water (displace): id=6914, wt=53.000
% 4.02/4.35
% 4.02/4.35 Low Water (displace): id=13225, wt=14.000
% 4.02/4.35
% 4.02/4.35 Low Water (keep): wt=14.000, iters=3340
% 4.02/4.35
% 4.02/4.35 Low Water (displace): id=13276, wt=13.000
% 4.02/4.35
% 4.02/4.35 Low Water (displace): id=13279, wt=10.000
% 4.02/4.35
% 4.02/4.35 Low Water (displace): id=13364, wt=9.000
% 4.02/4.35
% 4.02/4.35 Low Water (keep): wt=13.000, iters=3333
% 4.02/4.35
% 4.02/4.35 Low Water (displace): id=16128, wt=8.000
% 4.02/4.35
% 4.02/4.35 Low Water (keep): wt=11.000, iters=3345
% 4.02/4.35
% 4.02/4.35 Low Water (keep): wt=10.000, iters=3339
% 4.02/4.35
% 4.02/4.35 Low Water (keep): wt=9.000, iters=3383
% 4.02/4.35
% 4.02/4.35 ============================== PROOF =================================
% 4.02/4.35 % SZS status Theorem
% 4.02/4.35 % SZS output start Refutation
% 4.02/4.35
% 4.02/4.35 % Proof 1 at 3.22 (+ 0.06) seconds.
% 4.02/4.35 % Length of proof is 171.
% 4.02/4.35 % Level of proof is 22.
% 4.02/4.35 % Maximum clause weight is 29.000.
% 4.02/4.35 % Given clauses 7423.
% 4.02/4.35
% 4.02/4.35 1 (all A all B all C (coll(A,B,C) -> coll(A,C,B))) # label(ruleD1) # label(axiom) # label(non_clause). [assumption].
% 4.02/4.35 2 (all A all B all C (coll(A,B,C) -> coll(B,A,C))) # label(ruleD2) # label(axiom) # label(non_clause). [assumption].
% 4.02/4.35 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].
% 4.02/4.35 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].
% 4.02/4.35 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].
% 4.02/4.35 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].
% 4.02/4.35 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].
% 4.02/4.35 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].
% 4.02/4.35 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].
% 4.02/4.35 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].
% 4.02/4.35 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].
% 4.02/4.35 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].
% 4.02/4.35 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].
% 4.02/4.35 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].
% 4.02/4.35 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].
% 4.02/4.35 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].
% 4.02/4.35 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].
% 4.02/4.35 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].
% 4.02/4.35 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].
% 4.02/4.35 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].
% 4.02/4.35 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].
% 4.02/4.35 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].
% 4.02/4.35 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].
% 4.02/4.35 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].
% 4.02/4.35 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].
% 4.02/4.35 69 (all A all B all C (midp(A,B,C) -> cong(A,B,A,C))) # label(ruleD68) # label(axiom) # label(non_clause). [assumption].
% 4.02/4.35 95 -(all A all B all C all E all F all H (perp(E,C,A,B) & coll(E,A,B) & perp(F,A,B,C) & coll(F,B,C) & coll(H,C,E) & coll(H,A,F) -> perp(B,H,A,C))) # label(exemplo6GDDFULL012006) # label(negated_conjecture) # label(non_clause). [assumption].
% 4.02/4.35 97 -cong(A,B,A,C) | -cong(A,B,A,D) | circle(A,B,C,D) # label(ruleD12) # label(axiom). [clausify(12)].
% 4.02/4.35 101 -circle(A,B,C,D) | -coll(A,B,D) | perp(B,C,C,D) # label(ruleD53) # label(axiom). [clausify(54)].
% 4.02/4.35 109 -coll(A,B,C) | coll(A,C,B) # label(ruleD1) # label(axiom). [clausify(1)].
% 4.02/4.35 110 -coll(A,B,C) | coll(B,A,C) # label(ruleD2) # label(axiom). [clausify(2)].
% 4.02/4.35 111 -coll(A,B,C) | -coll(A,B,D) | coll(C,D,A) # label(ruleD3) # label(axiom). [clausify(3)].
% 4.02/4.35 112 -para(A,B,C,D) | para(A,B,D,C) # label(ruleD4) # label(axiom). [clausify(4)].
% 4.02/4.35 113 -para(A,B,C,D) | para(C,D,A,B) # label(ruleD5) # label(axiom). [clausify(5)].
% 4.02/4.35 115 -perp(A,B,C,D) | perp(A,B,D,C) # label(ruleD7) # label(axiom). [clausify(7)].
% 4.02/4.35 116 -perp(A,B,C,D) | perp(C,D,A,B) # label(ruleD8) # label(axiom). [clausify(8)].
% 4.02/4.35 117 -perp(A,B,C,D) | -perp(C,D,E,F) | para(A,B,E,F) # label(ruleD9) # label(axiom). [clausify(9)].
% 4.02/4.35 118 -para(A,B,C,D) | -perp(C,D,E,F) | perp(A,B,E,F) # label(ruleD10) # label(axiom). [clausify(10)].
% 4.02/4.35 121 -cyclic(A,B,C,D) | cyclic(A,B,D,C) # label(ruleD14) # label(axiom). [clausify(14)].
% 4.02/4.35 122 -cyclic(A,B,C,D) | cyclic(A,C,B,D) # label(ruleD15) # label(axiom). [clausify(15)].
% 4.02/4.35 123 -cyclic(A,B,C,D) | cyclic(B,A,C,D) # label(ruleD16) # label(axiom). [clausify(16)].
% 4.02/4.35 124 -cyclic(A,B,C,D) | -cyclic(A,B,C,E) | cyclic(B,C,D,E) # label(ruleD17) # label(axiom). [clausify(17)].
% 4.02/4.35 126 -eqangle(A,B,C,D,E,F,V6,V7) | eqangle(C,D,A,B,V6,V7,E,F) # label(ruleD19) # label(axiom). [clausify(19)].
% 4.02/4.35 146 -eqangle(A,B,C,D,E,F,C,D) | para(A,B,E,F) # label(ruleD39) # label(axiom). [clausify(39)].
% 4.02/4.35 147 -para(A,B,C,D) | eqangle(A,B,E,F,C,D,E,F) # label(ruleD40) # label(axiom). [clausify(40)].
% 4.02/4.35 150 -eqangle(A,B,A,C,D,B,D,C) | -coll(A,D,C) | cyclic(B,C,A,D) # label(ruleD42b) # label(axiom). [clausify(43)].
% 4.02/4.35 151 -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)].
% 4.02/4.35 153 -midp(A,B,C) | -para(A,D,C,E) | -coll(D,B,E) | midp(D,B,E) # label(ruleD45) # label(axiom). [clausify(46)].
% 4.02/4.35 159 -cong(A,B,C,B) | -cong(A,D,C,D) | perp(A,C,B,D) # label(ruleD56) # label(axiom). [clausify(57)].
% 4.02/4.35 160 -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)].
% 4.02/4.35 167 -midp(A,B,C) | -para(B,D,C,E) | -para(B,E,C,D) | midp(A,D,E) # label(ruleD64) # label(axiom). [clausify(65)].
% 4.02/4.35 170 -cong(A,B,A,C) | -coll(A,B,C) | midp(A,B,C) # label(ruleD67) # label(axiom). [clausify(68)].
% 4.02/4.35 171 -midp(A,B,C) | cong(A,B,A,C) # label(ruleD68) # label(axiom). [clausify(69)].
% 4.02/4.35 208 perp(c4,c3,c1,c2) # label(exemplo6GDDFULL012006) # label(negated_conjecture). [clausify(95)].
% 4.02/4.35 209 coll(c4,c1,c2) # label(exemplo6GDDFULL012006) # label(negated_conjecture). [clausify(95)].
% 4.02/4.35 210 perp(c5,c1,c2,c3) # label(exemplo6GDDFULL012006) # label(negated_conjecture). [clausify(95)].
% 4.02/4.35 212 coll(c6,c3,c4) # label(exemplo6GDDFULL012006) # label(negated_conjecture). [clausify(95)].
% 4.02/4.35 214 -perp(c2,c6,c1,c3) # label(exemplo6GDDFULL012006) # label(negated_conjecture). [clausify(95)].
% 4.02/4.35 219 -coll(A,B,C) | perp(B,D,D,C) | -cong(A,B,A,D) | -cong(A,B,A,C). [resolve(101,a,97,c)].
% 4.02/4.35 253 -coll(A,B,C) | coll(C,C,A). [factor(111,a,b)].
% 4.02/4.35 258 -cyclic(A,B,C,D) | cyclic(B,C,D,D). [factor(124,a,b)].
% 4.02/4.35 259 -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(151,a,b)].
% 4.02/4.35 261 -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(151,b,c)].
% 4.02/4.35 267 -midp(A,B,C) | -para(B,D,C,D) | midp(A,D,D). [factor(167,b,c)].
% 4.02/4.35 292 -coll(A,B,C) | perp(B,C,C,C) | -cong(A,B,A,C). [factor(219,c,d)].
% 4.02/4.35 327 -perp(A,B,c4,c3) | para(A,B,c1,c2). [resolve(208,a,117,b)].
% 4.02/4.35 328 -perp(c1,c2,A,B) | para(c4,c3,A,B). [resolve(208,a,117,a)].
% 4.02/4.35 329 perp(c1,c2,c4,c3). [resolve(208,a,116,a)].
% 4.02/4.35 330 perp(c4,c3,c2,c1). [resolve(208,a,115,a)].
% 4.02/4.35 333 coll(c1,c4,c2). [resolve(209,a,110,a)].
% 4.02/4.35 346 -perp(A,B,c5,c1) | para(A,B,c2,c3). [resolve(210,a,117,b)].
% 4.02/4.35 349 perp(c5,c1,c3,c2). [resolve(210,a,115,a)].
% 4.02/4.35 356 coll(c3,c6,c4). [resolve(212,a,110,a)].
% 4.02/4.35 363 coll(c4,c4,c6). [resolve(253,a,212,a)].
% 4.02/4.35 369 coll(c1,c2,c4). [resolve(333,a,109,a)].
% 4.02/4.35 382 coll(c4,c4,c3). [resolve(356,a,253,a)].
% 4.02/4.35 385 coll(c3,c4,c6). [resolve(356,a,109,a)].
% 4.02/4.35 405 coll(c4,c6,c4). [resolve(363,a,109,a)].
% 4.02/4.35 418 coll(c4,c4,c1). [resolve(369,a,253,a)].
% 4.02/4.35 440 coll(c3,c3,c4). [resolve(382,a,253,a)].
% 4.02/4.35 443 coll(c4,c3,c4). [resolve(382,a,109,a)].
% 4.02/4.35 444 coll(c6,c6,c3). [resolve(385,a,253,a)].
% 4.02/4.35 476 coll(c4,c4,c4). [resolve(405,a,253,a)].
% 4.02/4.35 525 coll(c3,c4,c3). [resolve(440,a,109,a)].
% 4.02/4.35 528 coll(c3,c4,c4). [resolve(443,a,110,a)].
% 4.02/4.35 531 coll(c6,c3,c6). [resolve(444,a,109,a)].
% 4.02/4.35 540 para(c4,c3,c4,c3). [resolve(329,a,328,a)].
% 4.02/4.35 554 -perp(c4,c3,A,B) | para(c1,c2,A,B). [resolve(329,a,117,a)].
% 4.02/4.35 555 perp(c1,c2,c3,c4). [resolve(329,a,115,a)].
% 4.02/4.35 580 perp(c2,c1,c4,c3). [resolve(330,a,116,a)].
% 4.02/4.35 634 coll(c3,c6,c6). [resolve(531,a,110,a)].
% 4.02/4.35 699 perp(c3,c2,c5,c1). [resolve(349,a,116,a)].
% 4.02/4.35 702 -midp(A,c4,c4) | midp(A,c3,c3). [resolve(540,a,267,b)].
% 4.02/4.35 710 -midp(c4,A,c4) | -coll(c3,A,c3) | midp(c3,A,c3). [resolve(540,a,153,b)].
% 4.02/4.35 711 eqangle(c4,c3,A,B,c4,c3,A,B). [resolve(540,a,147,a)].
% 4.02/4.35 712 para(c4,c3,c3,c4). [resolve(540,a,112,a)].
% 4.02/4.35 739 perp(c3,c4,c1,c2). [resolve(555,a,116,a)].
% 4.02/4.35 740 para(c2,c1,c1,c2). [resolve(580,a,327,a)].
% 4.02/4.35 798 para(c3,c4,c4,c3). [resolve(712,a,113,a)].
% 4.02/4.35 825 -perp(A,B,c3,c4) | para(A,B,c1,c2). [resolve(739,a,117,b)].
% 4.02/4.35 843 para(c2,c1,c2,c1). [resolve(740,a,112,a)].
% 4.02/4.35 871 para(c3,c2,c2,c3). [resolve(346,a,699,a)].
% 4.02/4.35 901 para(c3,c4,c3,c4). [resolve(798,a,112,a)].
% 4.02/4.35 917 -midp(A,c2,c2) | midp(A,c1,c1). [resolve(843,a,267,b)].
% 4.02/4.35 958 para(c3,c2,c3,c2). [resolve(871,a,112,a)].
% 4.02/4.35 982 eqangle(c3,c4,A,B,c3,c4,A,B). [resolve(901,a,147,a)].
% 4.02/4.35 1028 -midp(A,c3,c3) | midp(A,c2,c2). [resolve(958,a,267,b)].
% 4.02/4.35 1442 -cyclic(c3,c4,c4,c3) | -cyclic(c3,c4,c4,c4) | cong(c3,c4,c3,c4). [resolve(711,a,261,c)].
% 4.02/4.35 1451 -cyclic(c3,A,c4,c3) | -cyclic(c3,A,c4,A) | -cyclic(c3,A,c4,c4) | cong(c3,A,c3,A). [resolve(711,a,151,d)].
% 4.02/4.35 1452 -coll(c4,c4,A) | cyclic(c3,A,c4,c4). [resolve(711,a,150,a)].
% 4.02/4.35 1454 eqangle(A,B,c4,c3,A,B,c4,c3). [resolve(711,a,126,a)].
% 4.02/4.35 1567 -cyclic(c4,c4,c3,c4) | -cyclic(c4,c4,c3,c3) | cong(c4,c4,c4,c4). [resolve(982,a,259,c)].
% 4.02/4.35 1684 cyclic(c3,c4,c4,c4). [resolve(1452,a,476,a)].
% 4.02/4.35 1685 cyclic(c3,c1,c4,c4). [resolve(1452,a,418,a)].
% 4.02/4.35 1687 cyclic(c3,c3,c4,c4). [resolve(1452,a,382,a)].
% 4.02/4.35 1688 cyclic(c3,c6,c4,c4). [resolve(1452,a,363,a)].
% 4.02/4.35 1689 -cyclic(c3,c4,c4,c3) | cong(c3,c4,c3,c4). [back_unit_del(1442),unit_del(b,1684)].
% 4.02/4.35 1733 cyclic(c4,c3,c4,c4). [resolve(1684,a,123,a)].
% 4.02/4.35 1755 cyclic(c1,c3,c4,c4). [resolve(1685,a,123,a)].
% 4.02/4.35 1800 cyclic(c3,c4,c3,c4). [resolve(1687,a,122,a)].
% 4.02/4.35 1822 cyclic(c6,c3,c4,c4). [resolve(1688,a,123,a)].
% 4.02/4.35 1823 cyclic(c3,c4,c6,c4). [resolve(1688,a,122,a)].
% 4.02/4.35 1923 cyclic(c4,c4,c3,c4). [resolve(1733,a,122,a)].
% 4.02/4.35 1924 -cyclic(c4,c4,c3,c3) | cong(c4,c4,c4,c4). [back_unit_del(1567),unit_del(a,1923)].
% 4.02/4.35 1965 cyclic(c1,c4,c3,c4). [resolve(1755,a,122,a)].
% 4.02/4.35 2072 cyclic(c3,c4,c4,c3). [resolve(1800,a,121,a)].
% 4.02/4.35 2074 cong(c3,c4,c3,c4). [back_unit_del(1689),unit_del(a,2072)].
% 4.02/4.35 2118 cyclic(c6,c4,c3,c4). [resolve(1822,a,122,a)].
% 4.02/4.35 2139 cyclic(c4,c3,c6,c4). [resolve(1823,a,123,a)].
% 4.02/4.35 2287 cyclic(c4,c1,c3,c4). [resolve(1965,a,123,a)].
% 4.02/4.35 2439 cyclic(c4,c4,c3,c3). [resolve(2072,a,258,a)].
% 4.02/4.35 2460 cong(c4,c4,c4,c4). [back_unit_del(1924),unit_del(a,2439)].
% 4.02/4.35 2538 midp(c3,c4,c4). [resolve(2074,a,170,a),unit_del(a,528)].
% 4.02/4.35 2555 midp(c3,c3,c3). [resolve(2538,a,702,a)].
% 4.02/4.35 2594 midp(c3,c2,c2). [resolve(2555,a,1028,a)].
% 4.02/4.35 2628 midp(c3,c1,c1). [resolve(2594,a,917,a)].
% 4.02/4.35 2671 cong(c3,c1,c3,c1). [resolve(2628,a,171,a)].
% 4.02/4.35 2773 cyclic(c4,c6,c3,c4). [resolve(2118,a,123,a)].
% 4.02/4.35 2796 cyclic(c4,c3,c4,c6). [resolve(2139,a,121,a)].
% 4.02/4.35 2985 cyclic(c4,c1,c4,c3). [resolve(2287,a,121,a)].
% 4.02/4.35 3355 midp(c4,c4,c4). [resolve(2460,a,170,a),unit_del(a,476)].
% 4.02/4.35 3362 midp(c3,c4,c3). [resolve(3355,a,710,a),unit_del(a,525)].
% 4.02/4.35 3404 cong(c3,c4,c3,c3). [resolve(3362,a,171,a)].
% 4.02/4.35 4203 cyclic(c4,c6,c4,c3). [resolve(2773,a,121,a)].
% 4.02/4.35 4224 cyclic(c3,c4,c6,c6). [resolve(2796,a,258,a)].
% 4.02/4.35 4435 cyclic(c1,c4,c3,c3). [resolve(2985,a,258,a)].
% 4.02/4.35 4902 perp(c4,c3,c3,c3). [resolve(3404,a,292,c),unit_del(a,525)].
% 4.02/4.35 6182 cyclic(c6,c4,c3,c3). [resolve(4203,a,258,a)].
% 4.02/4.35 6226 cyclic(c3,c6,c4,c6). [resolve(4224,a,122,a)].
% 4.02/4.35 6534 cyclic(c1,c3,c4,c3). [resolve(4435,a,122,a)].
% 4.02/4.35 7004 para(c1,c2,c3,c3). [resolve(4902,a,554,a)].
% 4.02/4.35 7955 cyclic(c6,c3,c4,c3). [resolve(6182,a,122,a)].
% 4.02/4.35 8303 cyclic(c3,c1,c4,c3). [resolve(6534,a,123,a)].
% 4.02/4.35 8799 -perp(c3,c3,A,B) | perp(c1,c2,A,B). [resolve(7004,a,118,a)].
% 4.02/4.35 9737 cyclic(c3,c6,c4,c3). [resolve(7955,a,123,a)].
% 4.02/4.35 10090 cyclic(c3,c1,c3,c4). [resolve(8303,a,121,a)].
% 4.02/4.35 11148 cyclic(c3,c3,c1,c4). [resolve(10090,a,122,a)].
% 4.02/4.35 11787 perp(c1,c3,c3,c4). [resolve(11148,a,160,c),unit_del(a,2671),unit_del(b,2074)].
% 4.02/4.35 12545 para(c1,c3,c1,c2). [resolve(11787,a,825,a)].
% 4.02/4.35 13206 -perp(c1,c2,A,B) | perp(c1,c3,A,B). [resolve(12545,a,118,a)].
% 4.02/4.35 18097 cong(c3,c6,c3,c6). [resolve(1451,b,6226,a),unit_del(a,9737),unit_del(b,1688)].
% 4.02/4.35 18105 midp(c3,c6,c6). [resolve(18097,a,170,a),unit_del(a,634)].
% 4.02/4.35 18158 para(A,B,A,B). [resolve(1454,a,146,a)].
% 4.02/4.35 18282 -midp(A,B,B) | midp(A,C,C). [resolve(18158,a,267,b)].
% 4.02/4.35 23734 midp(c3,A,A). [resolve(18282,a,18105,a)].
% 4.02/4.35 23795 cong(c3,A,c3,A). [resolve(23734,a,171,a)].
% 4.02/4.35 23987 perp(c3,c3,A,B). [resolve(23795,a,159,b),unit_del(a,23795)].
% 4.02/4.35 24002 perp(c1,c2,A,B). [back_unit_del(8799),unit_del(a,23987)].
% 4.02/4.35 24018 perp(c1,c3,A,B). [back_unit_del(13206),unit_del(a,24002)].
% 4.02/4.35 24136 perp(A,B,c1,c3). [resolve(24018,a,116,a)].
% 4.02/4.35 24137 $F. [resolve(24136,a,214,a)].
% 4.02/4.35
% 4.02/4.35 % SZS output end Refutation
% 4.02/4.35 ============================== end of proof ==========================
% 4.02/4.35
% 4.02/4.35 ============================== STATISTICS ============================
% 4.02/4.35
% 4.02/4.35 Given=7423. Generated=113505. Kept=24020. proofs=1.
% 4.02/4.35 Usable=6493. Sos=8395. Demods=0. Limbo=0, Disabled=9281. Hints=0.
% 4.02/4.35 Megabytes=14.97.
% 4.02/4.35 User_CPU=3.22, System_CPU=0.06, Wall_clock=4.
% 4.02/4.35
% 4.02/4.35 ============================== end of statistics =====================
% 4.02/4.35
% 4.02/4.35 ============================== end of search =========================
% 4.02/4.35
% 4.02/4.35 THEOREM PROVED
% 4.02/4.35 % SZS status Theorem
% 4.02/4.35
% 4.02/4.35 Exiting with 1 proof.
% 4.02/4.35
% 4.02/4.35 Process 16558 exit (max_proofs) Sat Jun 18 15:02:06 2022
% 4.02/4.35 Prover9 interrupted
%------------------------------------------------------------------------------