TSTP Solution File: GEO633+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GEO633+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 05:57:20 EDT 2022
% Result : Theorem 7.27s 7.57s
% Output : Refutation 7.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO633+1 : TPTP v8.1.0. Released v7.5.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jun 18 02:35:27 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.80/1.11 ============================== Prover9 ===============================
% 0.80/1.11 Prover9 (32) version 2009-11A, November 2009.
% 0.80/1.11 Process 6484 was started by sandbox on n025.cluster.edu,
% 0.80/1.11 Sat Jun 18 02:35:28 2022
% 0.80/1.11 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_6324_n025.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_6324_n025.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].
% 0.80/1.11 90 (all A all B all C all D exists O (perp(A,C,C,B) & cyclic(A,B,C,D) -> circle(O,A,B,C))) # label(ruleX14) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.11 91 (all A all B all C all E all F exists P (perp(A,C,C,B) & coll(B,E,F) -> coll(P,E,F) & perp(P,A,E,F))) # label(ruleX15) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.11 92 (all A all B all C all D all M exists P (perp(A,B,A,C) & perp(C,A,C,D) & midp(M,B,D) -> midp(P,A,C))) # label(ruleX16) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.11 93 (all A all B all O exists C (cong(O,A,O,B) & perp(A,O,O,B) -> coll(A,O,C) & cong(O,A,O,C))) # label(ruleX17) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.11 94 (all A all B all C all D all P all Q exists R (para(A,B,C,D) & coll(P,A,C) & coll(P,B,D) & coll(Q,A,B) -> coll(P,Q,R) & coll(R,C,D))) # label(ruleX18) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.11 95 -(all A all B all C all A1 all S all N all G all H (midp(A1,C,B) & eqangle(S,A,A,B,C,A,A,A1) & coll(S,B,C) & coll(N,A,A1) & perp(G,N,A,B) & coll(G,A,B) & perp(H,N,A,C) & coll(H,A,C) -> perp(G,H,A,S))) # label(exemplo6GDDFULL8110996) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.80/1.11
% 0.80/1.11 ============================== end of process non-clausal formulas ===
% 0.80/1.11
% 0.80/1.11 ============================== PROCESS INITIAL CLAUSES ===============
% 0.80/1.11
% 0.80/1.11 ============================== PREDICATE ELIMINATION =================
% 0.80/1.11 96 -circle(A,B,C,D) | -perp(A,B,B,E) | eqangle(B,E,B,C,D,B,D,C) # label(ruleD48) # label(axiom). [clausify(49)].
% 0.80/1.11 97 -cong(A,B,A,C) | -cong(A,B,A,D) | circle(A,B,C,D) # label(ruleD12) # label(axiom). [clausify(12)].
% 0.80/1.11 Derived: -perp(A,B,B,C) | eqangle(B,C,B,D,E,B,E,D) | -cong(A,B,A,D) | -cong(A,B,A,E). [resolve(96,a,97,c)].
% 0.80/1.11 98 -circle(A,B,C,D) | -eqangle(B,E,B,C,D,B,D,C) | perp(A,B,B,E) # label(ruleD49) # label(axiom). [clausify(50)].
% 0.80/1.11 Derived: -eqangle(A,B,A,C,D,A,D,C) | perp(E,A,A,B) | -cong(E,A,E,C) | -cong(E,A,E,D). [resolve(98,a,97,c)].
% 0.80/1.11 99 -circle(A,B,C,D) | -midp(E,C,D) | eqangle(B,C,B,D,A,C,A,E) # label(ruleD50) # label(axiom). [clausify(51)].
% 0.80/1.11 Derived: -midp(A,B,C) | eqangle(D,B,D,C,E,B,E,A) | -cong(E,D,E,B) | -cong(E,D,E,C). [resolve(99,a,97,c)].
% 0.80/1.11 100 -circle(A,B,C,D) | -coll(E,C,D) | -eqangle(B,C,B,D,A,C,A,E) | midp(E,C,D) # label(ruleD51) # label(axiom). [clausify(52)].
% 0.80/1.11 Derived: -coll(A,B,C) | -eqangle(D,B,D,C,E,B,E,A) | midp(A,B,C) | -cong(E,D,E,B) | -cong(E,D,E,C). [resolve(100,a,97,c)].
% 0.80/1.11 101 -circle(A,B,C,D) | -coll(A,B,D) | perp(B,C,C,D) # label(ruleD53) # label(axiom). [clausify(54)].
% 0.80/1.11 Derived: -coll(A,B,C) | perp(B,D,D,C) | -cong(A,B,A,D) | -cong(A,B,A,C). [resolve(101,a,97,c)].
% 0.80/1.11 102 -circle(A,B,C,D) | perp(f12(B,C,D,A),B,B,A) # label(ruleX11) # label(axiom). [clausify(87)].
% 0.80/1.11 Derived: perp(f12(A,B,C,D),A,A,D) | -cong(D,A,D,B) | -cong(D,A,D,C). [resolve(102,a,97,c)].
% 0.80/1.11 103 -circle(A,B,C,D) | -cong(A,B,A,E) | -cong(F,B,F,C) | F = A | coll(f13(B,C,D,E,A,F),B,D) # label(ruleX12) # label(axiom). [clausify(88)].
% 0.80/1.11 Derived: -cong(A,B,A,C) | -cong(D,B,D,E) | D = A | coll(f13(B,E,F,C,A,D),B,F) | -cong(A,B,A,E) | -cong(A,B,A,F). [resolve(103,a,97,c)].
% 0.80/1.11 104 -circle(A,B,C,D) | -cong(A,B,A,E) | -cong(F,B,F,C) | F = A | cong(f13(B,C,D,E,A,F),F,F,B) # label(ruleX12) # label(axiom). [clausify(88)].
% 0.80/1.11 Derived: -cong(A,B,A,C) | -cong(D,B,D,E) | D = A | cong(f13(B,E,F,C,A,D),D,D,B) | -cong(A,B,A,E) | -cong(A,B,A,F). [resolve(104,a,97,c)].
% 0.80/1.11 105 -circle(A,B,C,D) | -cong(A,B,A,E) | -cong(F,B,F,C) | F = A | coll(f14(B,C,D,E,A,F),C,E) # label(ruleX12) # label(axiom). [clausify(88)].
% 0.80/1.11 Derived: -cong(A,B,A,C) | -cong(D,B,D,E) | D = A | coll(f14(B,E,F,C,A,D),E,C) | -cong(A,B,A,E) | -cong(A,B,A,F). [resolve(105,a,97,c)].
% 0.80/1.11 106 -circle(A,B,C,D) | -cong(A,B,A,E) | -cong(F,B,F,C) | F = A | cong(f14(B,C,D,E,A,F),F,F,B) # label(ruleX12) # label(axiom). [clausify(88)].
% 0.80/1.11 Derived: -cong(A,B,A,C) | -cong(D,B,D,E) | D = A | cong(f14(B,E,F,C,A,D),D,D,B) | -cong(A,B,A,E) | -cong(A,B,A,F). [resolve(106,a,97,c)].
% 0.80/1.11 107 -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | circle(f15(A,B,C,D,E),A,B,C) # label(ruleX13) # label(axiom). [clausify(89)].
% 0.84/1.13 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)].
% 0.84/1.13 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)].
% 0.84/1.13 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)].
% 0.84/1.13 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)].
% 0.84/1.13 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)].
% 0.84/1.13 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)].
% 0.84/1.13 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)].
% 0.84/1.13 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)].
% 0.84/1.13 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)].
% 0.84/1.13 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)].
% 0.84/1.13 108 -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)].
% 0.84/1.13 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)].
% 0.84/1.13 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)].
% 0.84/1.13 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)].
% 0.84/1.13 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)].
% 0.84/1.13 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)].
% 0.84/1.13 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)].
% 0.84/1.13 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)].
% 0.84/1.13 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)].
% 0.84/1.13 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)].
% 0.84/1.13 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)].
% 0.84/1.13
% 0.84/1.13 ============================== end predicate elimination =============
% 0.84/1.13
% 0.84/1.13 Auto_denials: (non-Horn, no changes).
% 0.84/1.13
% 0.84/1.13 Term ordering decisions:
% 0.84/1.13 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=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.
% 0.84/1.13
% 0.84/1.13 ============================== end of process initial clauses ========
% 0.84/1.13
% 0.84/1.13 ============================== CLAUSES FOR SEARCH ====================
% 0.84/1.13
% 0.84/1.13 ============================== end of clauses for search =============
% 0.84/1.13
% 0.84/1.13 ============================== SEARCH ================================
% 0.84/1.13
% 0.84/1.13 % Starting search at 0.04 seconds.
% 7.27/7.57
% 7.27/7.57 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 1002 (0.00 of 0.18 sec).
% 7.27/7.57
% 7.27/7.57 Low Water (keep): wt=25.000, iters=3384
% 7.27/7.57
% 7.27/7.57 Low Water (keep): wt=22.000, iters=3334
% 7.27/7.57
% 7.27/7.57 Low Water (keep): wt=19.000, iters=3386
% 7.27/7.57
% 7.27/7.57 Low Water (keep): wt=18.000, iters=3340
% 7.27/7.57
% 7.27/7.57 Low Water (keep): wt=17.000, iters=3335
% 7.27/7.57
% 7.27/7.57 Low Water (keep): wt=16.000, iters=3335
% 7.27/7.57
% 7.27/7.57 Low Water (keep): wt=15.000, iters=3358
% 7.27/7.57
% 7.27/7.57 Low Water (keep): wt=14.000, iters=3378
% 7.27/7.57
% 7.27/7.57 Low Water (keep): wt=13.000, iters=3343
% 7.27/7.57
% 7.27/7.57 Low Water (keep): wt=12.000, iters=3337
% 7.27/7.57
% 7.27/7.57 Low Water (displace): id=7330, wt=55.000
% 7.27/7.57
% 7.27/7.57 Low Water (displace): id=7346, wt=53.000
% 7.27/7.57
% 7.27/7.57 Low Water (displace): id=7340, wt=50.000
% 7.27/7.57
% 7.27/7.57 Low Water (displace): id=7347, wt=49.000
% 7.27/7.57
% 7.27/7.57 Low Water (displace): id=7291, wt=48.000
% 7.27/7.57
% 7.27/7.57 Low Water (displace): id=13969, wt=11.000
% 7.27/7.57
% 7.27/7.57 Low Water (displace): id=13975, wt=10.000
% 7.27/7.57
% 7.27/7.57 Low Water (displace): id=14047, wt=9.000
% 7.27/7.57
% 7.27/7.57 Low Water (displace): id=14094, wt=8.000
% 7.27/7.57
% 7.27/7.57 Low Water (keep): wt=11.000, iters=3337
% 7.27/7.57
% 7.27/7.57 Low Water (displace): id=15511, wt=7.000
% 7.27/7.57
% 7.27/7.57 Low Water (keep): wt=10.000, iters=3336
% 7.27/7.57
% 7.27/7.57 ============================== PROOF =================================
% 7.27/7.57 % SZS status Theorem
% 7.27/7.57 % SZS output start Refutation
% 7.27/7.57
% 7.27/7.57 % Proof 1 at 6.35 (+ 0.14) seconds.
% 7.27/7.57 % Length of proof is 165.
% 7.27/7.57 % Level of proof is 22.
% 7.27/7.57 % Maximum clause weight is 29.000.
% 7.27/7.57 % Given clauses 11381.
% 7.27/7.57
% 7.27/7.57 1 (all A all B all C (coll(A,B,C) -> coll(A,C,B))) # label(ruleD1) # label(axiom) # label(non_clause). [assumption].
% 7.27/7.57 2 (all A all B all C (coll(A,B,C) -> coll(B,A,C))) # label(ruleD2) # label(axiom) # label(non_clause). [assumption].
% 7.27/7.57 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].
% 7.27/7.57 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].
% 7.27/7.57 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].
% 7.27/7.57 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].
% 7.27/7.57 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].
% 7.27/7.57 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].
% 7.27/7.57 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].
% 7.27/7.57 11 (all A all B all M (midp(M,B,A) -> midp(M,A,B))) # label(ruleD11) # label(axiom) # label(non_clause). [assumption].
% 7.27/7.57 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].
% 7.27/7.57 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].
% 7.27/7.57 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].
% 7.27/7.57 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].
% 7.27/7.57 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].
% 7.27/7.57 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].
% 7.27/7.57 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].
% 7.27/7.57 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].
% 7.27/7.57 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].
% 7.27/7.57 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].
% 7.27/7.57 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].
% 7.27/7.57 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].
% 7.27/7.57 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].
% 7.27/7.57 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].
% 7.27/7.57 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].
% 7.27/7.57 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].
% 7.27/7.57 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].
% 7.27/7.57 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].
% 7.27/7.57 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].
% 7.27/7.57 69 (all A all B all C (midp(A,B,C) -> cong(A,B,A,C))) # label(ruleD68) # label(axiom) # label(non_clause). [assumption].
% 7.27/7.57 70 (all A all B all C (midp(A,B,C) -> coll(A,B,C))) # label(ruleD69) # label(axiom) # label(non_clause). [assumption].
% 7.27/7.57 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].
% 7.27/7.57 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].
% 7.27/7.57 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].
% 7.27/7.57 95 -(all A all B all C all A1 all S all N all G all H (midp(A1,C,B) & eqangle(S,A,A,B,C,A,A,A1) & coll(S,B,C) & coll(N,A,A1) & perp(G,N,A,B) & coll(G,A,B) & perp(H,N,A,C) & coll(H,A,C) -> perp(G,H,A,S))) # label(exemplo6GDDFULL8110996) # label(negated_conjecture) # label(non_clause). [assumption].
% 7.27/7.57 97 -cong(A,B,A,C) | -cong(A,B,A,D) | circle(A,B,C,D) # label(ruleD12) # label(axiom). [clausify(12)].
% 7.27/7.57 100 -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)].
% 7.27/7.57 101 -circle(A,B,C,D) | -coll(A,B,D) | perp(B,C,C,D) # label(ruleD53) # label(axiom). [clausify(54)].
% 7.27/7.57 109 -coll(A,B,C) | coll(A,C,B) # label(ruleD1) # label(axiom). [clausify(1)].
% 7.27/7.57 110 -coll(A,B,C) | coll(B,A,C) # label(ruleD2) # label(axiom). [clausify(2)].
% 7.27/7.57 111 -coll(A,B,C) | -coll(A,B,D) | coll(C,D,A) # label(ruleD3) # label(axiom). [clausify(3)].
% 7.27/7.57 112 -para(A,B,C,D) | para(A,B,D,C) # label(ruleD4) # label(axiom). [clausify(4)].
% 7.27/7.57 113 -para(A,B,C,D) | para(C,D,A,B) # label(ruleD5) # label(axiom). [clausify(5)].
% 7.27/7.57 115 -perp(A,B,C,D) | perp(A,B,D,C) # label(ruleD7) # label(axiom). [clausify(7)].
% 7.27/7.57 116 -perp(A,B,C,D) | perp(C,D,A,B) # label(ruleD8) # label(axiom). [clausify(8)].
% 7.27/7.57 117 -perp(A,B,C,D) | -perp(C,D,E,F) | para(A,B,E,F) # label(ruleD9) # label(axiom). [clausify(9)].
% 7.27/7.57 118 -para(A,B,C,D) | -perp(C,D,E,F) | perp(A,B,E,F) # label(ruleD10) # label(axiom). [clausify(10)].
% 7.27/7.57 119 -midp(A,B,C) | midp(A,C,B) # label(ruleD11) # label(axiom). [clausify(11)].
% 7.27/7.57 120 -cong(A,B,A,C) | -cong(A,B,A,D) | -cong(A,B,A,E) | cyclic(B,C,D,E) # label(ruleD13) # label(axiom). [clausify(13)].
% 7.27/7.57 124 -cyclic(A,B,C,D) | -cyclic(A,B,C,E) | cyclic(B,C,D,E) # label(ruleD17) # label(axiom). [clausify(17)].
% 7.27/7.57 125 -eqangle(A,B,C,D,E,F,V6,V7) | eqangle(B,A,C,D,E,F,V6,V7) # label(ruleD18) # label(axiom). [clausify(18)].
% 7.27/7.57 130 -cong(A,B,C,D) | cong(A,B,D,C) # label(ruleD23) # label(axiom). [clausify(23)].
% 7.27/7.57 131 -cong(A,B,C,D) | cong(C,D,A,B) # label(ruleD24) # label(axiom). [clausify(24)].
% 7.27/7.57 132 -cong(A,B,C,D) | -cong(C,D,E,F) | cong(A,B,E,F) # label(ruleD25) # label(axiom). [clausify(25)].
% 7.27/7.57 147 -para(A,B,C,D) | eqangle(A,B,E,F,C,D,E,F) # label(ruleD40) # label(axiom). [clausify(40)].
% 7.27/7.57 148 -cyclic(A,B,C,D) | eqangle(C,A,C,B,D,A,D,B) # label(ruleD41) # label(axiom). [clausify(41)].
% 7.27/7.57 151 -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)].
% 7.27/7.57 152 -midp(A,B,C) | -midp(D,B,E) | para(A,D,C,E) # label(ruleD44) # label(axiom). [clausify(45)].
% 7.27/7.57 153 -midp(A,B,C) | -para(A,D,C,E) | -coll(D,B,E) | midp(D,B,E) # label(ruleD45) # label(axiom). [clausify(46)].
% 7.27/7.57 158 -midp(A,B,C) | -perp(D,A,B,C) | cong(D,B,D,C) # label(ruleD55) # label(axiom). [clausify(56)].
% 7.27/7.57 159 -cong(A,B,C,B) | -cong(A,D,C,D) | perp(A,C,B,D) # label(ruleD56) # label(axiom). [clausify(57)].
% 7.27/7.57 166 -midp(A,B,C) | -midp(A,D,E) | para(B,D,C,E) # label(ruleD63) # label(axiom). [clausify(64)].
% 7.27/7.57 167 -midp(A,B,C) | -para(B,D,C,E) | -para(B,E,C,D) | midp(A,D,E) # label(ruleD64) # label(axiom). [clausify(65)].
% 7.27/7.57 170 -cong(A,B,A,C) | -coll(A,B,C) | midp(A,B,C) # label(ruleD67) # label(axiom). [clausify(68)].
% 7.27/7.57 171 -midp(A,B,C) | cong(A,B,A,C) # label(ruleD68) # label(axiom). [clausify(69)].
% 7.27/7.57 172 -midp(A,B,C) | coll(A,B,C) # label(ruleD69) # label(axiom). [clausify(70)].
% 7.27/7.57 175 -eqangle(A,B,C,D,E,F,V6,V7) | -para(E,F,V6,V7) | para(A,B,C,D) # label(ruleD73) # label(axiom). [clausify(74)].
% 7.27/7.57 176 -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)].
% 7.27/7.57 191 -midp(A,B,C) | -midp(D,E,F) | -coll(E,B,C) | -coll(F,B,C) | midp(f7(B,C,E,F,A,D,V6),B,V6) # label(ruleX7) # label(axiom). [clausify(83)].
% 7.27/7.57 208 midp(c4,c3,c2) # label(exemplo6GDDFULL8110996) # label(negated_conjecture). [clausify(95)].
% 7.27/7.57 209 eqangle(c5,c1,c1,c2,c3,c1,c1,c4) # label(exemplo6GDDFULL8110996) # label(negated_conjecture). [clausify(95)].
% 7.27/7.57 210 coll(c5,c2,c3) # label(exemplo6GDDFULL8110996) # label(negated_conjecture). [clausify(95)].
% 7.27/7.57 212 perp(c7,c6,c1,c2) # label(exemplo6GDDFULL8110996) # label(negated_conjecture). [clausify(95)].
% 7.27/7.57 213 coll(c7,c1,c2) # label(exemplo6GDDFULL8110996) # label(negated_conjecture). [clausify(95)].
% 7.27/7.57 216 -perp(c7,c8,c1,c5) # label(exemplo6GDDFULL8110996) # label(negated_conjecture). [clausify(95)].
% 7.27/7.57 220 -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)].
% 7.27/7.57 221 -coll(A,B,C) | perp(B,D,D,C) | -cong(A,B,A,D) | -cong(A,B,A,C). [resolve(101,a,97,c)].
% 7.27/7.57 255 -coll(A,B,C) | coll(C,C,A). [factor(111,a,b)].
% 7.27/7.57 257 -cong(A,B,A,C) | -cong(A,B,A,D) | cyclic(B,C,C,D). [factor(120,a,b)].
% 7.27/7.57 260 -cyclic(A,B,C,D) | cyclic(B,C,D,D). [factor(124,a,b)].
% 7.27/7.57 261 -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)].
% 7.27/7.57 268 -midp(A,B,C) | para(B,B,C,C). [factor(166,a,b)].
% 7.27/7.57 269 -midp(A,B,C) | -para(B,D,C,D) | midp(A,D,D). [factor(167,b,c)].
% 7.27/7.57 293 -coll(A,B,B) | -eqangle(C,B,C,B,D,B,D,A) | midp(A,B,B) | -cong(D,C,D,B). [factor(220,d,e)].
% 7.27/7.57 294 -coll(A,B,C) | perp(B,C,C,C) | -cong(A,B,A,C). [factor(221,c,d)].
% 7.27/7.57 309 -cong(A,B,A,C) | cyclic(B,C,C,C). [factor(257,a,b)].
% 7.27/7.57 310 -cyclic(A,B,C,D) | -eqangle(C,A,C,B,D,D,D,D) | cong(A,B,D,D). [factor(261,a,b)].
% 7.27/7.57 318 -midp(A,B,C) | -coll(c3,B,C) | -coll(c2,B,C) | midp(f7(B,C,c3,c2,A,c4,D),B,D). [resolve(208,a,191,b)].
% 7.27/7.57 328 coll(c4,c3,c2). [resolve(208,a,172,a)].
% 7.27/7.57 329 cong(c4,c3,c4,c2). [resolve(208,a,171,a)].
% 7.27/7.57 330 -midp(c4,A,B) | para(A,c3,B,c2). [resolve(208,a,166,b)].
% 7.27/7.57 334 midp(c4,c2,c3). [resolve(208,a,119,a)].
% 7.27/7.57 344 eqangle(c1,c5,c1,c2,c3,c1,c1,c4). [resolve(209,a,125,a)].
% 7.27/7.57 347 coll(c2,c5,c3). [resolve(210,a,110,a)].
% 7.27/7.57 364 -perp(A,B,c7,c6) | para(A,B,c1,c2). [resolve(212,a,117,b)].
% 7.27/7.57 367 perp(c7,c6,c2,c1). [resolve(212,a,115,a)].
% 7.27/7.57 370 coll(c1,c7,c2). [resolve(213,a,110,a)].
% 7.27/7.57 392 coll(c2,c2,c7). [resolve(255,a,213,a)].
% 7.27/7.57 402 coll(c2,c2,c4). [resolve(328,a,255,a)].
% 7.27/7.57 405 coll(c3,c4,c2). [resolve(328,a,110,a)].
% 7.27/7.57 407 -coll(c3,c2,c3) | -coll(c2,c2,c3) | midp(f7(c2,c3,c3,c2,c4,c4,A),c2,A). [resolve(334,a,318,a)].
% 7.27/7.57 426 cong(c4,c2,c4,c3). [resolve(334,a,171,a)].
% 7.27/7.57 430 -midp(A,c2,B) | para(c4,A,c3,B). [resolve(334,a,152,a)].
% 7.27/7.57 431 coll(c3,c3,c2). [resolve(347,a,255,a)].
% 7.27/7.57 449 coll(c2,c2,c1). [resolve(370,a,255,a)].
% 7.27/7.57 473 coll(c2,c7,c2). [resolve(392,a,109,a)].
% 7.27/7.57 486 coll(c2,c4,c2). [resolve(402,a,109,a)].
% 7.27/7.57 487 coll(c2,c2,c3). [resolve(405,a,255,a)].
% 7.27/7.57 492 -coll(c3,c2,c3) | midp(f7(c2,c3,c3,c2,c4,c4,A),c2,A). [back_unit_del(407),unit_del(b,487)].
% 7.27/7.57 500 coll(c3,c2,c3). [resolve(431,a,109,a)].
% 7.27/7.57 501 midp(f7(c2,c3,c3,c2,c4,c4,A),c2,A). [back_unit_del(492),unit_del(a,500)].
% 7.27/7.57 527 coll(c1,c1,c2). [resolve(449,a,255,a)].
% 7.27/7.57 566 coll(c2,c2,c2). [resolve(473,a,255,a)].
% 7.27/7.57 588 cyclic(c3,c2,c2,c2). [resolve(329,a,309,a)].
% 7.27/7.57 626 perp(c3,c2,c2,c2). [resolve(329,a,294,c),unit_del(a,328)].
% 7.27/7.57 657 -cong(A,B,c4,c3) | cong(A,B,c4,c2). [resolve(329,a,132,b)].
% 7.27/7.57 671 coll(c4,c2,c2). [resolve(486,a,110,a)].
% 7.27/7.57 838 -para(c3,c1,c1,c4) | para(c1,c5,c1,c2). [resolve(344,a,175,a)].
% 7.27/7.57 914 perp(c2,c1,c7,c6). [resolve(367,a,116,a)].
% 7.27/7.57 1081 cyclic(c2,c2,c2,c2). [resolve(588,a,260,a)].
% 7.27/7.57 1122 perp(c2,c2,c3,c2). [resolve(626,a,116,a)].
% 7.27/7.57 1318 eqangle(c2,c2,c2,c2,c2,c2,c2,c2). [resolve(1081,a,148,a)].
% 7.27/7.57 1344 perp(c2,c2,c2,c3). [resolve(1122,a,115,a)].
% 7.27/7.57 1523 -perp(A,B,c2,c2) | para(A,B,c2,c3). [resolve(1344,a,117,b)].
% 7.27/7.57 1544 para(c2,c1,c1,c2). [resolve(364,a,914,a)].
% 7.27/7.57 1661 -midp(c2,A,c1) | -coll(c1,A,c2) | midp(c1,A,c2). [resolve(1544,a,153,b)].
% 7.27/7.57 1666 para(c2,c1,c2,c1). [resolve(1544,a,112,a)].
% 7.27/7.57 1823 -midp(A,c2,c2) | midp(A,c1,c1). [resolve(1666,a,269,b)].
% 7.27/7.57 2879 para(c2,c2,A,A). [resolve(501,a,268,a)].
% 7.27/7.57 2891 coll(f7(c2,c3,c3,c2,c4,c4,A),c2,A). [resolve(501,a,172,a)].
% 7.27/7.57 2892 cong(f7(c2,c3,c3,c2,c4,c4,A),c2,f7(c2,c3,c3,c2,c4,c4,A),A). [resolve(501,a,171,a)].
% 7.27/7.57 3534 -perp(A,A,B,C) | perp(c2,c2,B,C). [resolve(2879,a,118,a)].
% 7.27/7.57 3865 cong(c4,c2,c4,c2). [resolve(657,a,426,a)].
% 7.27/7.57 3947 midp(c4,c2,c2). [resolve(3865,a,170,a),unit_del(a,671)].
% 7.27/7.57 3987 para(c2,c3,c2,c2). [resolve(3947,a,330,a)].
% 7.27/7.57 4428 -perp(c2,c2,A,B) | perp(c2,c3,A,B). [resolve(3987,a,118,a)].
% 7.27/7.57 11678 cong(c2,c2,c2,c2). [resolve(1318,a,310,b),unit_del(a,1081)].
% 7.27/7.57 11679 midp(c2,c2,c2). [resolve(1318,a,293,b),unit_del(a,566),unit_del(c,11678)].
% 7.27/7.57 11710 midp(c2,c1,c1). [resolve(11679,a,1823,a)].
% 7.27/7.57 16651 midp(c1,c1,c2). [resolve(1661,a,11710,a),unit_del(a,527)].
% 7.27/7.57 16662 cong(c1,c1,c1,c2). [resolve(16651,a,171,a)].
% 7.27/7.57 16667 midp(c1,c2,c1). [resolve(16651,a,119,a)].
% 7.27/7.57 16668 para(c4,c1,c3,c1). [resolve(16667,a,430,a)].
% 7.27/7.57 16687 perp(c1,c2,c2,c2). [resolve(16662,a,294,c),unit_del(a,527)].
% 7.27/7.57 16704 para(c3,c1,c4,c1). [resolve(16668,a,113,a)].
% 7.27/7.57 16738 para(c1,c2,c2,c3). [resolve(16687,a,1523,a)].
% 7.27/7.57 16760 para(c3,c1,c1,c4). [resolve(16704,a,112,a)].
% 7.27/7.57 16761 para(c1,c5,c1,c2). [back_unit_del(838),unit_del(a,16760)].
% 7.27/7.57 16821 -perp(c2,c3,A,B) | perp(c1,c2,A,B). [resolve(16738,a,118,a)].
% 7.27/7.57 16965 eqangle(c1,c5,A,B,c1,c2,A,B). [resolve(16761,a,147,a)].
% 7.27/7.57 20047 perp(c2,A,A,A). [resolve(2892,a,294,c),unit_del(a,2891)].
% 7.27/7.57 20058 perp(A,A,c2,A). [resolve(20047,a,116,a)].
% 7.27/7.57 20076 perp(A,A,A,c2). [resolve(20058,a,115,a)].
% 7.27/7.57 21115 perp(c2,c2,A,c2). [resolve(3534,a,20076,a)].
% 7.27/7.57 21121 perp(A,c2,c2,c2). [resolve(21115,a,116,a)].
% 7.27/7.57 21160 cong(A,c2,A,c2). [resolve(21121,a,158,b),unit_del(a,11679)].
% 7.27/7.57 21244 cong(A,c2,c2,A). [resolve(21160,a,130,a)].
% 7.27/7.57 21314 cong(c2,A,A,c2). [resolve(21244,a,131,a)].
% 7.27/7.57 21338 cong(c2,A,c2,A). [resolve(21314,a,130,a)].
% 7.27/7.57 21370 perp(c2,c2,A,B). [resolve(21338,a,159,b),unit_del(a,21338)].
% 7.27/7.57 21395 perp(c2,c3,A,B). [back_unit_del(4428),unit_del(a,21370)].
% 7.27/7.57 21464 perp(c1,c2,A,B). [back_unit_del(16821),unit_del(a,21395)].
% 7.27/7.57 28014 perp(c1,c5,A,B). [resolve(16965,a,176,a),unit_del(a,21464)].
% 7.27/7.57 28023 perp(A,B,c1,c5). [resolve(28014,a,116,a)].
% 7.27/7.57 28024 $F. [resolve(28023,a,216,a)].
% 7.27/7.57
% 7.27/7.57 % SZS output end Refutation
% 7.27/7.57 ============================== end of proof ==========================
% 7.27/7.57
% 7.27/7.57 ============================== STATISTICS ============================
% 7.27/7.57
% 7.27/7.57 Given=11381. Generated=206500. Kept=27907. proofs=1.
% 7.27/7.57 Usable=9471. Sos=8173. Demods=0. Limbo=5, Disabled=10409. Hints=0.
% 7.27/7.57 Megabytes=15.29.
% 7.27/7.57 User_CPU=6.35, System_CPU=0.14, Wall_clock=7.
% 7.27/7.57
% 7.27/7.57 ============================== end of statistics =====================
% 7.27/7.57
% 7.27/7.57 ============================== end of search =========================
% 7.27/7.57
% 7.27/7.57 THEOREM PROVED
% 7.27/7.57 % SZS status Theorem
% 7.27/7.57
% 7.27/7.57 Exiting with 1 proof.
% 7.27/7.57
% 7.27/7.57 Process 6484 exit (max_proofs) Sat Jun 18 02:35:35 2022
% 7.27/7.57 Prover9 interrupted
%------------------------------------------------------------------------------