TSTP Solution File: GEO544+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GEO544+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n008.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 05:56:52 EDT 2022
% Result : Theorem 26.50s 26.80s
% Output : Refutation 26.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GEO544+1 : TPTP v8.1.0. Released v7.5.0.
% 0.04/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.15/0.35 % Computer : n008.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Sat Jun 18 06:45:37 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.89/1.14 ============================== Prover9 ===============================
% 0.89/1.14 Prover9 (32) version 2009-11A, November 2009.
% 0.89/1.14 Process 19042 was started by sandbox on n008.cluster.edu,
% 0.89/1.14 Sat Jun 18 06:45:38 2022
% 0.89/1.14 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_18889_n008.cluster.edu".
% 0.89/1.14 ============================== end of head ===========================
% 0.89/1.14
% 0.89/1.14 ============================== INPUT =================================
% 0.89/1.14
% 0.89/1.14 % Reading from file /tmp/Prover9_18889_n008.cluster.edu
% 0.89/1.14
% 0.89/1.14 set(prolog_style_variables).
% 0.89/1.14 set(auto2).
% 0.89/1.14 % set(auto2) -> set(auto).
% 0.89/1.14 % set(auto) -> set(auto_inference).
% 0.89/1.14 % set(auto) -> set(auto_setup).
% 0.89/1.14 % set(auto_setup) -> set(predicate_elim).
% 0.89/1.14 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.89/1.14 % set(auto) -> set(auto_limits).
% 0.89/1.14 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.89/1.14 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.89/1.14 % set(auto) -> set(auto_denials).
% 0.89/1.14 % set(auto) -> set(auto_process).
% 0.89/1.14 % set(auto2) -> assign(new_constants, 1).
% 0.89/1.14 % set(auto2) -> assign(fold_denial_max, 3).
% 0.89/1.14 % set(auto2) -> assign(max_weight, "200.000").
% 0.89/1.14 % set(auto2) -> assign(max_hours, 1).
% 0.89/1.14 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.89/1.14 % set(auto2) -> assign(max_seconds, 0).
% 0.89/1.14 % set(auto2) -> assign(max_minutes, 5).
% 0.89/1.14 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.89/1.14 % set(auto2) -> set(sort_initial_sos).
% 0.89/1.14 % set(auto2) -> assign(sos_limit, -1).
% 0.89/1.14 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.89/1.14 % set(auto2) -> assign(max_megs, 400).
% 0.89/1.14 % set(auto2) -> assign(stats, some).
% 0.89/1.14 % set(auto2) -> clear(echo_input).
% 0.89/1.14 % set(auto2) -> set(quiet).
% 0.89/1.14 % set(auto2) -> clear(print_initial_clauses).
% 0.89/1.14 % set(auto2) -> clear(print_given).
% 0.89/1.14 assign(lrs_ticks,-1).
% 0.89/1.14 assign(sos_limit,10000).
% 0.89/1.14 assign(order,kbo).
% 0.89/1.14 set(lex_order_vars).
% 0.89/1.14 clear(print_given).
% 0.89/1.14
% 0.89/1.14 % formulas(sos). % not echoed (95 formulas)
% 0.89/1.14
% 0.89/1.14 ============================== end of input ==========================
% 0.89/1.14
% 0.89/1.14 % From the command line: assign(max_seconds, 300).
% 0.89/1.14
% 0.89/1.14 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.89/1.14
% 0.89/1.14 % Formulas that are not ordinary clauses:
% 0.89/1.14 1 (all A all B all C (coll(A,B,C) -> coll(A,C,B))) # label(ruleD1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 2 (all A all B all C (coll(A,B,C) -> coll(B,A,C))) # label(ruleD2) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 3 (all A all B all C all D (coll(A,B,C) & coll(A,B,D) -> coll(C,D,A))) # label(ruleD3) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 4 (all A all B all C all D (para(A,B,C,D) -> para(A,B,D,C))) # label(ruleD4) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 5 (all A all B all C all D (para(A,B,C,D) -> para(C,D,A,B))) # label(ruleD5) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 6 (all A all B all C all D all E all F (para(A,B,C,D) & para(C,D,E,F) -> para(A,B,E,F))) # label(ruleD6) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 7 (all A all B all C all D (perp(A,B,C,D) -> perp(A,B,D,C))) # label(ruleD7) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 8 (all A all B all C all D (perp(A,B,C,D) -> perp(C,D,A,B))) # label(ruleD8) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 9 (all A all B all C all D all E all F (perp(A,B,C,D) & perp(C,D,E,F) -> para(A,B,E,F))) # label(ruleD9) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 10 (all A all B all C all D all E all F (para(A,B,C,D) & perp(C,D,E,F) -> perp(A,B,E,F))) # label(ruleD10) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 11 (all A all B all M (midp(M,B,A) -> midp(M,A,B))) # label(ruleD11) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 12 (all A all B all C all O (cong(O,A,O,B) & cong(O,A,O,C) -> circle(O,A,B,C))) # label(ruleD12) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 13 (all A all B all C all D all O (cong(O,A,O,B) & cong(O,A,O,C) & cong(O,A,O,D) -> cyclic(A,B,C,D))) # label(ruleD13) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 14 (all A all B all C all D (cyclic(A,B,C,D) -> cyclic(A,B,D,C))) # label(ruleD14) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 15 (all A all B all C all D (cyclic(A,B,C,D) -> cyclic(A,C,B,D))) # label(ruleD15) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 16 (all A all B all C all D (cyclic(A,B,C,D) -> cyclic(B,A,C,D))) # label(ruleD16) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 17 (all A all B all C all D all E (cyclic(A,B,C,D) & cyclic(A,B,C,E) -> cyclic(B,C,D,E))) # label(ruleD17) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 18 (all A all B all C all D all P all Q all U all V (eqangle(A,B,C,D,P,Q,U,V) -> eqangle(B,A,C,D,P,Q,U,V))) # label(ruleD18) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 19 (all A all B all C all D all P all Q all U all V (eqangle(A,B,C,D,P,Q,U,V) -> eqangle(C,D,A,B,U,V,P,Q))) # label(ruleD19) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 20 (all A all B all C all D all P all Q all U all V (eqangle(A,B,C,D,P,Q,U,V) -> eqangle(P,Q,U,V,A,B,C,D))) # label(ruleD20) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 21 (all A all B all C all D all P all Q all U all V (eqangle(A,B,C,D,P,Q,U,V) -> eqangle(A,B,P,Q,C,D,U,V))) # label(ruleD21) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 22 (all A all B all C all D all P all Q all U all V all E all F all G all H (eqangle(A,B,C,D,P,Q,U,V) & eqangle(P,Q,U,V,E,F,G,H) -> eqangle(A,B,C,D,E,F,G,H))) # label(ruleD22) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 23 (all A all B all C all D (cong(A,B,C,D) -> cong(A,B,D,C))) # label(ruleD23) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 24 (all A all B all C all D (cong(A,B,C,D) -> cong(C,D,A,B))) # label(ruleD24) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 25 (all A all B all C all D all E all F (cong(A,B,C,D) & cong(C,D,E,F) -> cong(A,B,E,F))) # label(ruleD25) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 26 (all A all B all C all D all P all Q all U all V (eqratio(A,B,C,D,P,Q,U,V) -> eqratio(B,A,C,D,P,Q,U,V))) # label(ruleD26) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 27 (all A all B all C all D all P all Q all U all V (eqratio(A,B,C,D,P,Q,U,V) -> eqratio(C,D,A,B,U,V,P,Q))) # label(ruleD27) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 28 (all A all B all C all D all P all Q all U all V (eqratio(A,B,C,D,P,Q,U,V) -> eqratio(P,Q,U,V,A,B,C,D))) # label(ruleD28) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 29 (all A all B all C all D all P all Q all U all V (eqratio(A,B,C,D,P,Q,U,V) -> eqratio(A,B,P,Q,C,D,U,V))) # label(ruleD29) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 30 (all A all B all C all D all E all F all G all H all P all Q all U all V (eqratio(A,B,C,D,P,Q,U,V) & eqratio(P,Q,U,V,E,F,G,H) -> eqratio(A,B,C,D,E,F,G,H))) # label(ruleD30) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 31 (all A all B all C all P all Q all R (simtri(A,C,B,P,R,Q) -> simtri(A,B,C,P,Q,R))) # label(ruleD31) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 32 (all A all B all C all P all Q all R (simtri(B,A,C,Q,P,R) -> simtri(A,B,C,P,Q,R))) # label(ruleD32) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 33 (all A all B all C all P all Q all R (simtri(P,Q,R,A,B,C) -> simtri(A,B,C,P,Q,R))) # label(ruleD33) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 34 (all A all B all C all E all F all G all P all Q all R (simtri(A,B,C,E,F,G) & simtri(E,F,G,P,Q,R) -> simtri(A,B,C,P,Q,R))) # label(ruleD34) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 35 (all A all B all C all P all Q all R (contri(A,C,B,P,R,Q) -> contri(A,B,C,P,Q,R))) # label(ruleD35) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 36 (all A all B all C all P all Q all R (contri(B,A,C,Q,P,R) -> contri(A,B,C,P,Q,R))) # label(ruleD36) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 37 (all A all B all C all P all Q all R (contri(P,Q,R,A,B,C) -> contri(A,B,C,P,Q,R))) # label(ruleD37) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 38 (all A all B all C all E all F all G all P all Q all R (contri(A,B,C,E,F,G) & contri(E,F,G,P,Q,R) -> contri(A,B,C,P,Q,R))) # label(ruleD38) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 39 (all A all B all C all D all P all Q (eqangle(A,B,P,Q,C,D,P,Q) -> para(A,B,C,D))) # label(ruleD39) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 40 (all A all B all C all D all P all Q (para(A,B,C,D) -> eqangle(A,B,P,Q,C,D,P,Q))) # label(ruleD40) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 41 (all A all B all P all Q (cyclic(A,B,P,Q) -> eqangle(P,A,P,B,Q,A,Q,B))) # label(ruleD41) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 42 (all A all B all P all Q (eqangle(P,A,P,B,Q,A,Q,B) & -coll(P,Q,A) -> cyclic(A,B,P,Q))) # label(ruleD42a) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 43 (all A all B all P all Q (eqangle(P,A,P,B,Q,A,Q,B) & coll(P,Q,B) -> cyclic(A,B,P,Q))) # label(ruleD42b) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 44 (all A all B all C all P all Q all R (cyclic(A,B,C,P) & cyclic(A,B,C,Q) & cyclic(A,B,C,R) & eqangle(C,A,C,B,R,P,R,Q) -> cong(A,B,P,Q))) # label(ruleD43) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 45 (all A all B all C all E all F (midp(E,A,B) & midp(F,A,C) -> para(E,F,B,C))) # label(ruleD44) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 46 (all A all B all C all E all F (midp(E,A,B) & para(E,F,B,C) & coll(F,A,C) -> midp(F,A,C))) # label(ruleD45) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 47 (all A all B all O (cong(O,A,O,B) -> eqangle(O,A,A,B,A,B,O,B))) # label(ruleD46) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 48 (all A all B all O (eqangle(O,A,A,B,A,B,O,B) & -coll(O,A,B) -> cong(O,A,O,B))) # label(ruleD47) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 49 (all A all B all C all O all X (circle(O,A,B,C) & perp(O,A,A,X) -> eqangle(A,X,A,B,C,A,C,B))) # label(ruleD48) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 50 (all A all B all C all O all X (circle(O,A,B,C) & eqangle(A,X,A,B,C,A,C,B) -> perp(O,A,A,X))) # label(ruleD49) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 51 (all A all B all C all O all M (circle(O,A,B,C) & midp(M,B,C) -> eqangle(A,B,A,C,O,B,O,M))) # label(ruleD50) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 52 (all A all B all C all O all M (circle(O,A,B,C) & coll(M,B,C) & eqangle(A,B,A,C,O,B,O,M) -> midp(M,B,C))) # label(ruleD51) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 53 (all A all B all C all M (perp(A,B,B,C) & midp(M,A,C) -> cong(A,M,B,M))) # label(ruleD52) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 54 (all A all B all C all O (circle(O,A,B,C) & coll(O,A,C) -> perp(A,B,B,C))) # label(ruleD53) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 55 (all A all B all C all D (cyclic(A,B,C,D) & para(A,B,C,D) -> eqangle(A,D,C,D,C,D,C,B))) # label(ruleD54) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 56 (all A all B all M all O (midp(M,A,B) & perp(O,M,A,B) -> cong(O,A,O,B))) # label(ruleD55) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 57 (all A all B all P all Q (cong(A,P,B,P) & cong(A,Q,B,Q) -> perp(A,B,P,Q))) # label(ruleD56) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 58 (all A all B all P all Q (cong(A,P,B,P) & cong(A,Q,B,Q) & cyclic(A,B,P,Q) -> perp(P,A,A,Q))) # label(ruleD57) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 59 (all A all B all C all P all Q all R (eqangle(A,B,B,C,P,Q,Q,R) & eqangle(A,C,B,C,P,R,Q,R) & -coll(A,B,C) -> simtri(A,B,C,P,Q,R))) # label(ruleD58) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 60 (all A all B all C all P all Q all R (simtri(A,B,C,P,Q,R) -> eqratio(A,B,A,C,P,Q,P,R))) # label(ruleD59) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 61 (all A all B all C all P all Q all R (simtri(A,B,C,P,Q,R) -> eqangle(A,B,B,C,P,Q,Q,R))) # label(ruleD60) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 62 (all A all B all C all P all Q all R (simtri(A,B,C,P,Q,R) & cong(A,B,P,Q) -> contri(A,B,C,P,Q,R))) # label(ruleD61) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 63 (all A all B all C all P all Q all R (contri(A,B,C,P,Q,R) -> cong(A,B,P,Q))) # label(ruleD62) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 64 (all A all B all C all D all M (midp(M,A,B) & midp(M,C,D) -> para(A,C,B,D))) # label(ruleD63) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 65 (all A all B all C all D all M (midp(M,A,B) & para(A,C,B,D) & para(A,D,B,C) -> midp(M,C,D))) # label(ruleD64) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.15 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].
% 0.89/1.15 67 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.15 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].
% 0.89/1.15 69 (all A all B all C (midp(A,B,C) -> cong(A,B,A,C))) # label(ruleD68) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.15 70 (all A all B all C (midp(A,B,C) -> coll(A,B,C))) # label(ruleD69) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.15 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].
% 0.89/1.15 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].
% 0.89/1.15 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].
% 0.89/1.15 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].
% 0.89/1.15 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].
% 0.89/1.15 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].
% 0.89/1.15 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].
% 0.89/1.15 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].
% 0.89/1.15 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].
% 0.89/1.15 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].
% 0.89/1.15 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].
% 0.89/1.15 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].
% 0.89/1.15 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].
% 0.89/1.15 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].
% 0.89/1.15 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].
% 0.89/1.15 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].
% 0.89/1.15 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].
% 0.89/1.15 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].
% 0.89/1.15 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].
% 0.89/1.15 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].
% 0.89/1.15 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].
% 0.89/1.15 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].
% 0.89/1.15 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].
% 0.89/1.15 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].
% 0.89/1.15 95 -(all A all B all C all O all D all Q all S all J all M all I all NWPNT1 (circle(O,A,B,C) & circle(O,A,D,NWPNT1) & midp(Q,C,B) & midp(S,A,D) & midp(J,S,Q) & coll(O,J,M) & cong(O,J,O,M) & coll(I,A,D) & coll(I,B,C) -> perp(S,M,B,C))) # label(exemplo6GDDFULL012004) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.89/1.15
% 0.89/1.15 ============================== end of process non-clausal formulas ===
% 0.89/1.15
% 0.89/1.15 ============================== PROCESS INITIAL CLAUSES ===============
% 0.89/1.15
% 0.89/1.15 ============================== PREDICATE ELIMINATION =================
% 0.89/1.15 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)].
% 0.89/1.15 97 -cong(A,B,A,C) | -cong(A,B,A,D) | circle(A,B,C,D) # label(ruleD12) # label(axiom). [clausify(12)].
% 0.89/1.15 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)].
% 0.89/1.15 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)].
% 0.89/1.15 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)].
% 0.89/1.15 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)].
% 0.89/1.15 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)].
% 0.89/1.15 100 -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)].
% 0.89/1.15 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)].
% 0.89/1.15 101 -circle(A,B,C,D) | -coll(A,B,D) | perp(B,C,C,D) # label(ruleD53) # label(axiom). [clausify(54)].
% 0.89/1.15 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)].
% 0.89/1.15 102 -circle(A,B,C,D) | perp(f12(B,C,D,A),B,B,A) # label(ruleX11) # label(axiom). [clausify(87)].
% 0.89/1.15 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)].
% 0.89/1.15 103 -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)].
% 0.89/1.15 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)].
% 0.89/1.15 104 -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)].
% 0.89/1.15 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)].
% 0.89/1.15 105 -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)].
% 0.89/1.15 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)].
% 0.89/1.15 106 -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)].
% 0.89/1.15 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)].
% 0.89/1.15 107 -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)].
% 0.89/1.15 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)].
% 0.89/1.15 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)].
% 0.89/1.15 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)].
% 0.89/1.15 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)].
% 0.89/1.15 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)].
% 0.89/1.15 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)].
% 0.89/1.15 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)].
% 0.89/1.15 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)].
% 0.89/1.15 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)].
% 0.89/1.15 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)].
% 0.89/1.15 108 -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)].
% 0.89/1.15 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)].
% 0.89/1.15 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)].
% 0.89/1.15 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)].
% 0.89/1.15 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)].
% 0.89/1.15 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)].
% 0.89/1.15 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)].
% 0.89/1.15 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)].
% 0.89/1.15 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)].
% 0.89/1.15 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)].
% 0.89/1.15 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)].
% 0.89/1.15 109 circle(c4,c1,c2,c3) # label(exemplo6GDDFULL012004) # label(negated_conjecture). [clausify(95)].
% 0.89/1.15 Derived: -perp(c4,c1,c1,A) | eqangle(c1,A,c1,c2,c3,c1,c3,c2). [resolve(109,a,96,a)].
% 0.89/1.15 Derived: -eqangle(c1,A,c1,c2,c3,c1,c3,c2) | perp(c4,c1,c1,A). [resolve(109,a,98,a)].
% 0.89/1.15 Derived: -midp(A,c2,c3) | eqangle(c1,c2,c1,c3,c4,c2,c4,A). [resolve(109,a,99,a)].
% 0.89/1.15 Derived: -coll(A,c2,c3) | -eqangle(c1,c2,c1,c3,c4,c2,c4,A) | midp(A,c2,c3). [resolve(109,a,100,a)].
% 0.89/1.15 Derived: -coll(c4,c1,c3) | perp(c1,c2,c2,c3). [resolve(109,a,101,a)].
% 0.89/1.15 Derived: perp(f12(c1,c2,c3,c4),c1,c1,c4). [resolve(109,a,102,a)].
% 0.89/1.15 Derived: -cong(c4,c1,c4,A) | -cong(B,c1,B,c2) | B = c4 | coll(f13(c1,c2,c3,A,c4,B),c1,c3). [resolve(109,a,103,a)].
% 26.50/26.80 Derived: -cong(c4,c1,c4,A) | -cong(B,c1,B,c2) | B = c4 | cong(f13(c1,c2,c3,A,c4,B),B,B,c1). [resolve(109,a,104,a)].
% 26.50/26.80 Derived: -cong(c4,c1,c4,A) | -cong(B,c1,B,c2) | B = c4 | coll(f14(c1,c2,c3,A,c4,B),c2,A). [resolve(109,a,105,a)].
% 26.50/26.80 Derived: -cong(c4,c1,c4,A) | -cong(B,c1,B,c2) | B = c4 | cong(f14(c1,c2,c3,A,c4,B),B,B,c1). [resolve(109,a,106,a)].
% 26.50/26.80 110 circle(c4,c1,c5,c11) # label(exemplo6GDDFULL012004) # label(negated_conjecture). [clausify(95)].
% 26.50/26.80 Derived: -perp(c4,c1,c1,A) | eqangle(c1,A,c1,c5,c11,c1,c11,c5). [resolve(110,a,96,a)].
% 26.50/26.80 Derived: -eqangle(c1,A,c1,c5,c11,c1,c11,c5) | perp(c4,c1,c1,A). [resolve(110,a,98,a)].
% 26.50/26.80 Derived: -midp(A,c5,c11) | eqangle(c1,c5,c1,c11,c4,c5,c4,A). [resolve(110,a,99,a)].
% 26.50/26.80 Derived: -coll(A,c5,c11) | -eqangle(c1,c5,c1,c11,c4,c5,c4,A) | midp(A,c5,c11). [resolve(110,a,100,a)].
% 26.50/26.80 Derived: -coll(c4,c1,c11) | perp(c1,c5,c5,c11). [resolve(110,a,101,a)].
% 26.50/26.80 Derived: perp(f12(c1,c5,c11,c4),c1,c1,c4). [resolve(110,a,102,a)].
% 26.50/26.80 Derived: -cong(c4,c1,c4,A) | -cong(B,c1,B,c5) | B = c4 | coll(f13(c1,c5,c11,A,c4,B),c1,c11). [resolve(110,a,103,a)].
% 26.50/26.80 Derived: -cong(c4,c1,c4,A) | -cong(B,c1,B,c5) | B = c4 | cong(f13(c1,c5,c11,A,c4,B),B,B,c1). [resolve(110,a,104,a)].
% 26.50/26.80 Derived: -cong(c4,c1,c4,A) | -cong(B,c1,B,c5) | B = c4 | coll(f14(c1,c5,c11,A,c4,B),c5,A). [resolve(110,a,105,a)].
% 26.50/26.80 Derived: -cong(c4,c1,c4,A) | -cong(B,c1,B,c5) | B = c4 | cong(f14(c1,c5,c11,A,c4,B),B,B,c1). [resolve(110,a,106,a)].
% 26.50/26.80
% 26.50/26.80 ============================== end predicate elimination =============
% 26.50/26.80
% 26.50/26.80 Auto_denials: (non-Horn, no changes).
% 26.50/26.80
% 26.50/26.80 Term ordering decisions:
% 26.50/26.80 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. c10=1. c11=1. 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.
% 26.50/26.80
% 26.50/26.80 ============================== end of process initial clauses ========
% 26.50/26.80
% 26.50/26.80 ============================== CLAUSES FOR SEARCH ====================
% 26.50/26.80
% 26.50/26.80 ============================== end of clauses for search =============
% 26.50/26.80
% 26.50/26.80 ============================== SEARCH ================================
% 26.50/26.80
% 26.50/26.80 % Starting search at 0.04 seconds.
% 26.50/26.80
% 26.50/26.80 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 714 (0.00 of 0.24 sec).
% 26.50/26.80
% 26.50/26.80 Low Water (keep): wt=48.000, iters=3337
% 26.50/26.80
% 26.50/26.80 Low Water (keep): wt=40.000, iters=3416
% 26.50/26.80
% 26.50/26.80 Low Water (keep): wt=33.000, iters=3519
% 26.50/26.80
% 26.50/26.80 Low Water (keep): wt=29.000, iters=3511
% 26.50/26.80
% 26.50/26.80 Low Water (keep): wt=27.000, iters=3333
% 26.50/26.80
% 26.50/26.80 Low Water (keep): wt=25.000, iters=3473
% 26.50/26.80
% 26.50/26.80 Low Water (keep): wt=23.000, iters=3461
% 26.50/26.80
% 26.50/26.80 Low Water (keep): wt=22.000, iters=3461
% 26.50/26.80
% 26.50/26.80 Low Water (keep): wt=18.000, iters=3334
% 26.50/26.80
% 26.50/26.80 Low Water (keep): wt=17.000, iters=3349
% 26.50/26.80
% 26.50/26.80 Low Water (keep): wt=16.000, iters=3347
% 26.50/26.80
% 26.50/26.80 Low Water (keep): wt=15.000, iters=3334
% 26.50/26.80
% 26.50/26.80 Low Water (keep): wt=14.000, iters=3333
% 26.50/26.80
% 26.50/26.80 Low Water (keep): wt=13.000, iters=3336
% 26.50/26.80
% 26.50/26.80 Low Water (displace): id=4565, wt=53.000
% 26.50/26.80
% 26.50/26.80 Low Water (displace): id=13268, wt=12.000
% 26.50/26.80
% 26.50/26.80 Low Water (displace): id=13270, wt=10.000
% 26.50/26.80
% 26.50/26.80 Low Water (keep): wt=12.000, iters=3413
% 26.50/26.80
% 26.50/26.80 Low Water (displace): id=14186, wt=9.000
% 26.50/26.80
% 26.50/26.80 Low Water (displace): id=14264, wt=8.000
% 26.50/26.80
% 26.50/26.80 Low Water (keep): wt=11.000, iters=3336
% 26.50/26.80
% 26.50/26.80 Low Water (keep): wt=10.000, iters=3338
% 26.50/26.80
% 26.50/26.80 Low Water (displace): id=21336, wt=7.000
% 26.50/26.80
% 26.50/26.80 Low Water (displace): id=22667, wt=5.000
% 26.50/26.80
% 26.50/26.80 Low Water (keep): wt=9.000, iters=3333
% 26.50/26.80
% 26.50/26.80 Low Water (keep): wt=8.000, iters=3335
% 26.50/26.80
% 26.50/26.80 ============================== PROOF =================================
% 26.50/26.80 % SZS status Theorem
% 26.50/26.80 % SZS output start Refutation
% 26.50/26.80
% 26.50/26.80 % Proof 1 at 25.40 (+ 0.27) seconds.
% 26.50/26.80 % Length of proof is 115.
% 26.50/26.80 % Level of proof is 17.
% 26.50/26.80 % Maximum clause weight is 27.000.
% 26.50/26.80 % Given clauses 23244.
% 26.50/26.80
% 26.50/26.80 1 (all A all B all C (coll(A,B,C) -> coll(A,C,B))) # label(ruleD1) # label(axiom) # label(non_clause). [assumption].
% 26.50/26.80 2 (all A all B all C (coll(A,B,C) -> coll(B,A,C))) # label(ruleD2) # label(axiom) # label(non_clause). [assumption].
% 26.50/26.80 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].
% 26.50/26.80 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].
% 26.50/26.80 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].
% 26.50/26.80 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].
% 26.50/26.80 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].
% 26.50/26.80 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].
% 26.50/26.80 11 (all A all B all M (midp(M,B,A) -> midp(M,A,B))) # label(ruleD11) # label(axiom) # label(non_clause). [assumption].
% 26.50/26.80 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].
% 26.50/26.80 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].
% 26.50/26.80 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].
% 26.50/26.80 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].
% 26.50/26.80 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].
% 26.50/26.80 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].
% 26.50/26.80 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].
% 26.50/26.80 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].
% 26.50/26.80 69 (all A all B all C (midp(A,B,C) -> cong(A,B,A,C))) # label(ruleD68) # label(axiom) # label(non_clause). [assumption].
% 26.50/26.80 70 (all A all B all C (midp(A,B,C) -> coll(A,B,C))) # label(ruleD69) # label(axiom) # label(non_clause). [assumption].
% 26.50/26.80 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].
% 26.50/26.80 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].
% 26.50/26.80 95 -(all A all B all C all O all D all Q all S all J all M all I all NWPNT1 (circle(O,A,B,C) & circle(O,A,D,NWPNT1) & midp(Q,C,B) & midp(S,A,D) & midp(J,S,Q) & coll(O,J,M) & cong(O,J,O,M) & coll(I,A,D) & coll(I,B,C) -> perp(S,M,B,C))) # label(exemplo6GDDFULL012004) # label(negated_conjecture) # label(non_clause). [assumption].
% 26.50/26.80 102 -circle(A,B,C,D) | perp(f12(B,C,D,A),B,B,A) # label(ruleX11) # label(axiom). [clausify(87)].
% 26.50/26.80 109 circle(c4,c1,c2,c3) # label(exemplo6GDDFULL012004) # label(negated_conjecture). [clausify(95)].
% 26.50/26.80 111 -coll(A,B,C) | coll(A,C,B) # label(ruleD1) # label(axiom). [clausify(1)].
% 26.50/26.80 112 -coll(A,B,C) | coll(B,A,C) # label(ruleD2) # label(axiom). [clausify(2)].
% 26.50/26.80 113 -coll(A,B,C) | -coll(A,B,D) | coll(C,D,A) # label(ruleD3) # label(axiom). [clausify(3)].
% 26.50/26.80 114 -para(A,B,C,D) | para(A,B,D,C) # label(ruleD4) # label(axiom). [clausify(4)].
% 26.50/26.80 115 -para(A,B,C,D) | para(C,D,A,B) # label(ruleD5) # label(axiom). [clausify(5)].
% 26.50/26.80 118 -perp(A,B,C,D) | perp(C,D,A,B) # label(ruleD8) # label(axiom). [clausify(8)].
% 26.50/26.80 119 -perp(A,B,C,D) | -perp(C,D,E,F) | para(A,B,E,F) # label(ruleD9) # label(axiom). [clausify(9)].
% 26.50/26.80 120 -para(A,B,C,D) | -perp(C,D,E,F) | perp(A,B,E,F) # label(ruleD10) # label(axiom). [clausify(10)].
% 26.50/26.80 121 -midp(A,B,C) | midp(A,C,B) # label(ruleD11) # label(axiom). [clausify(11)].
% 26.50/26.80 132 -cong(A,B,C,D) | cong(A,B,D,C) # label(ruleD23) # label(axiom). [clausify(23)].
% 26.50/26.80 133 -cong(A,B,C,D) | cong(C,D,A,B) # label(ruleD24) # label(axiom). [clausify(24)].
% 26.50/26.80 134 -cong(A,B,C,D) | -cong(C,D,E,F) | cong(A,B,E,F) # label(ruleD25) # label(axiom). [clausify(25)].
% 26.50/26.80 154 -midp(A,B,C) | -midp(D,B,E) | para(A,D,C,E) # label(ruleD44) # label(axiom). [clausify(45)].
% 26.50/26.80 161 -cong(A,B,C,B) | -cong(A,D,C,D) | perp(A,C,B,D) # label(ruleD56) # label(axiom). [clausify(57)].
% 26.50/26.80 168 -midp(A,B,C) | -midp(A,D,E) | para(B,D,C,E) # label(ruleD63) # label(axiom). [clausify(64)].
% 26.50/26.80 169 -midp(A,B,C) | -para(B,D,C,E) | -para(B,E,C,D) | midp(A,D,E) # label(ruleD64) # label(axiom). [clausify(65)].
% 26.50/26.80 172 -cong(A,B,A,C) | -coll(A,B,C) | midp(A,B,C) # label(ruleD67) # label(axiom). [clausify(68)].
% 26.50/26.80 173 -midp(A,B,C) | cong(A,B,A,C) # label(ruleD68) # label(axiom). [clausify(69)].
% 26.50/26.80 174 -midp(A,B,C) | coll(A,B,C) # label(ruleD69) # label(axiom). [clausify(70)].
% 26.50/26.80 193 -midp(A,B,C) | -midp(D,E,F) | -coll(E,B,C) | -coll(F,B,C) | midp(f7(B,C,E,F,A,D,V6),B,V6) # label(ruleX7) # label(axiom). [clausify(83)].
% 26.50/26.80 210 midp(c6,c3,c2) # label(exemplo6GDDFULL012004) # label(negated_conjecture). [clausify(95)].
% 26.50/26.80 211 midp(c7,c1,c5) # label(exemplo6GDDFULL012004) # label(negated_conjecture). [clausify(95)].
% 26.50/26.80 213 coll(c4,c8,c9) # label(exemplo6GDDFULL012004) # label(negated_conjecture). [clausify(95)].
% 26.50/26.80 214 cong(c4,c8,c4,c9) # label(exemplo6GDDFULL012004) # label(negated_conjecture). [clausify(95)].
% 26.50/26.80 217 -perp(c7,c9,c2,c3) # label(exemplo6GDDFULL012004) # label(negated_conjecture). [clausify(95)].
% 26.50/26.80 261 perp(f12(c1,c2,c3,c4),c1,c1,c4). [resolve(109,a,102,a)].
% 26.50/26.80 284 -coll(A,B,C) | coll(C,C,A). [factor(113,a,b)].
% 26.50/26.80 293 -midp(A,B,C) | para(A,A,C,C). [factor(154,a,b)].
% 26.50/26.80 297 -midp(A,B,C) | para(B,B,C,C). [factor(168,a,b)].
% 26.50/26.80 298 -midp(A,B,C) | -para(B,D,C,D) | midp(A,D,D). [factor(169,b,c)].
% 26.50/26.80 304 -midp(A,B,C) | -coll(B,B,C) | -coll(C,B,C) | midp(f7(B,C,B,C,A,A,D),B,D). [factor(193,a,b)].
% 26.50/26.80 357 coll(c6,c3,c2). [resolve(210,a,174,a)].
% 26.50/26.80 358 cong(c6,c3,c6,c2). [resolve(210,a,173,a)].
% 26.50/26.80 359 -midp(c6,A,B) | para(A,c3,B,c2). [resolve(210,a,168,b)].
% 26.50/26.80 363 midp(c6,c2,c3). [resolve(210,a,121,a)].
% 26.50/26.80 375 coll(c7,c1,c5). [resolve(211,a,174,a)].
% 26.50/26.80 376 cong(c7,c1,c7,c5). [resolve(211,a,173,a)].
% 26.50/26.80 377 -midp(c7,A,B) | para(A,c1,B,c5). [resolve(211,a,168,b)].
% 26.50/26.80 381 midp(c7,c5,c1). [resolve(211,a,121,a)].
% 26.50/26.80 403 coll(c8,c4,c9). [resolve(213,a,112,a)].
% 26.50/26.80 405 midp(c4,c8,c9). [resolve(214,a,172,a),unit_del(a,213)].
% 26.50/26.80 407 -cong(A,B,c4,c8) | cong(A,B,c4,c9). [resolve(214,a,134,b)].
% 26.50/26.80 409 cong(c4,c9,c4,c8). [resolve(214,a,133,a)].
% 26.50/26.80 495 -perp(A,B,f12(c1,c2,c3,c4),c1) | para(A,B,c1,c4). [resolve(261,a,119,b)].
% 26.50/26.80 497 perp(c1,c4,f12(c1,c2,c3,c4),c1). [resolve(261,a,118,a)].
% 26.50/26.80 574 coll(c2,c2,c6). [resolve(357,a,284,a)].
% 26.50/26.80 599 cong(c6,c2,c6,c3). [resolve(363,a,173,a)].
% 26.50/26.80 604 coll(c5,c5,c7). [resolve(375,a,284,a)].
% 26.50/26.80 628 cong(c7,c5,c7,c1). [resolve(381,a,173,a)].
% 26.50/26.80 667 coll(c9,c9,c8). [resolve(403,a,284,a)].
% 26.50/26.80 684 -coll(c8,c8,c9) | -coll(c9,c8,c9) | midp(f7(c8,c9,c8,c9,c4,c4,A),c8,A). [resolve(405,a,304,a)].
% 26.50/26.80 705 midp(c4,c9,c8). [resolve(405,a,121,a)].
% 26.50/26.80 752 coll(c2,c6,c2). [resolve(574,a,111,a)].
% 26.50/26.80 766 coll(c5,c7,c5). [resolve(604,a,111,a)].
% 26.50/26.80 799 coll(c8,c8,c9). [resolve(667,a,284,a)].
% 26.50/26.80 802 coll(c9,c8,c9). [resolve(667,a,111,a)].
% 26.50/26.80 803 midp(f7(c8,c9,c8,c9,c4,c4,A),c8,A). [back_unit_del(684),unit_del(a,799),unit_del(b,802)].
% 26.50/26.80 834 para(c4,c4,c8,c8). [resolve(705,a,293,a)].
% 26.50/26.80 975 -cong(A,B,c6,c3) | cong(A,B,c6,c2). [resolve(358,a,134,b)].
% 26.50/26.80 1002 coll(c6,c2,c2). [resolve(752,a,112,a)].
% 26.50/26.80 1023 coll(c7,c5,c5). [resolve(766,a,112,a)].
% 26.50/26.80 1311 -cong(A,B,c7,c1) | cong(A,B,c7,c5). [resolve(376,a,134,b)].
% 26.50/26.80 1326 para(c5,c1,c1,c5). [resolve(377,a,381,a)].
% 26.50/26.80 2137 para(c8,c8,c4,c4). [resolve(834,a,115,a)].
% 26.50/26.80 2295 para(c5,c1,c5,c1). [resolve(1326,a,114,a)].
% 26.50/26.80 2660 cong(c4,c9,c4,c9). [resolve(407,a,409,a)].
% 26.50/26.80 2740 -perp(c4,c4,A,B) | perp(c8,c8,A,B). [resolve(2137,a,120,a)].
% 26.50/26.80 2909 -midp(A,c5,c5) | midp(A,c1,c1). [resolve(2295,a,298,b)].
% 26.50/26.80 3270 -cong(c4,A,c4,A) | perp(c4,c4,A,c9). [resolve(2660,a,161,b)].
% 26.50/26.80 6030 para(c1,c4,c1,c4). [resolve(497,a,495,a)].
% 26.50/26.80 6424 -midp(A,c1,c1) | midp(A,c4,c4). [resolve(6030,a,298,b)].
% 26.50/26.80 10171 para(c8,c8,A,A). [resolve(803,a,297,a)].
% 26.50/26.80 10183 para(A,A,c8,c8). [resolve(10171,a,115,a)].
% 26.50/26.80 10186 -perp(c8,c8,A,B) | perp(C,C,A,B). [resolve(10183,a,120,a)].
% 26.50/26.80 11859 cong(c6,c2,c6,c2). [resolve(975,a,599,a)].
% 26.50/26.80 11898 midp(c6,c2,c2). [resolve(11859,a,172,a),unit_del(a,1002)].
% 26.50/26.80 11980 para(c2,c3,c2,c2). [resolve(11898,a,359,a)].
% 26.50/26.80 12421 -perp(c2,c2,A,B) | perp(c2,c3,A,B). [resolve(11980,a,120,a)].
% 26.50/26.80 14359 cong(c7,c5,c7,c5). [resolve(1311,a,628,a)].
% 26.50/26.80 14489 midp(c7,c5,c5). [resolve(14359,a,172,a),unit_del(a,1023)].
% 26.50/26.80 14493 midp(c7,c1,c1). [resolve(14489,a,2909,a)].
% 26.50/26.80 14541 midp(c7,c4,c4). [resolve(14493,a,6424,a)].
% 26.50/26.80 14626 cong(c7,c4,c7,c4). [resolve(14541,a,173,a)].
% 26.50/26.80 15072 cong(c7,c4,c4,c7). [resolve(14626,a,132,a)].
% 26.50/26.80 15381 cong(c4,c7,c7,c4). [resolve(15072,a,133,a)].
% 26.50/26.80 15530 cong(c4,c7,c4,c7). [resolve(15381,a,132,a)].
% 26.50/26.80 23435 perp(c4,c4,c7,c9). [resolve(3270,a,15530,a)].
% 26.50/26.80 23502 perp(c8,c8,c7,c9). [resolve(23435,a,2740,a)].
% 26.50/26.80 37901 perp(A,A,c7,c9). [resolve(10186,a,23502,a)].
% 26.50/26.80 42591 perp(c2,c3,c7,c9). [resolve(12421,a,37901,a)].
% 26.50/26.80 42735 $F. [resolve(42591,a,118,a),unit_del(a,217)].
% 26.50/26.80
% 26.50/26.80 % SZS output end Refutation
% 26.50/26.80 ============================== end of proof ==========================
% 26.50/26.80
% 26.50/26.80 ============================== STATISTICS ============================
% 26.50/26.80
% 26.50/26.80 Given=23244. Generated=455758. Kept=42608. proofs=1.
% 26.50/26.80 Usable=23161. Sos=8898. Demods=0. Limbo=0, Disabled=10722. Hints=0.
% 26.50/26.80 Megabytes=21.53.
% 26.50/26.80 User_CPU=25.40, System_CPU=0.27, Wall_clock=26.
% 26.50/26.80
% 26.50/26.80 ============================== end of statistics =====================
% 26.50/26.80
% 26.50/26.80 ============================== end of search =========================
% 26.50/26.80
% 26.50/26.80 THEOREM PROVED
% 26.50/26.80 % SZS status Theorem
% 26.50/26.80
% 26.50/26.80 Exiting with 1 proof.
% 26.50/26.80
% 26.50/26.80 Process 19042 exit (max_proofs) Sat Jun 18 06:46:04 2022
% 26.50/26.80 Prover9 interrupted
%------------------------------------------------------------------------------