TSTP Solution File: GEO553+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GEO553+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 05:56:55 EDT 2022
% Result : Theorem 9.23s 9.56s
% Output : Refutation 9.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO553+1 : TPTP v8.1.0. Released v7.5.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n018.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 16:14:03 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.83/1.09 ============================== Prover9 ===============================
% 0.83/1.09 Prover9 (32) version 2009-11A, November 2009.
% 0.83/1.09 Process 20522 was started by sandbox2 on n018.cluster.edu,
% 0.83/1.09 Sat Jun 18 16:14:04 2022
% 0.83/1.09 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_20369_n018.cluster.edu".
% 0.83/1.09 ============================== end of head ===========================
% 0.83/1.09
% 0.83/1.09 ============================== INPUT =================================
% 0.83/1.09
% 0.83/1.09 % Reading from file /tmp/Prover9_20369_n018.cluster.edu
% 0.83/1.09
% 0.83/1.09 set(prolog_style_variables).
% 0.83/1.09 set(auto2).
% 0.83/1.09 % set(auto2) -> set(auto).
% 0.83/1.09 % set(auto) -> set(auto_inference).
% 0.83/1.09 % set(auto) -> set(auto_setup).
% 0.83/1.09 % set(auto_setup) -> set(predicate_elim).
% 0.83/1.09 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.83/1.09 % set(auto) -> set(auto_limits).
% 0.83/1.09 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.83/1.09 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.83/1.09 % set(auto) -> set(auto_denials).
% 0.83/1.09 % set(auto) -> set(auto_process).
% 0.83/1.09 % set(auto2) -> assign(new_constants, 1).
% 0.83/1.09 % set(auto2) -> assign(fold_denial_max, 3).
% 0.83/1.09 % set(auto2) -> assign(max_weight, "200.000").
% 0.83/1.09 % set(auto2) -> assign(max_hours, 1).
% 0.83/1.09 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.83/1.09 % set(auto2) -> assign(max_seconds, 0).
% 0.83/1.09 % set(auto2) -> assign(max_minutes, 5).
% 0.83/1.09 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.83/1.09 % set(auto2) -> set(sort_initial_sos).
% 0.83/1.09 % set(auto2) -> assign(sos_limit, -1).
% 0.83/1.09 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.83/1.09 % set(auto2) -> assign(max_megs, 400).
% 0.83/1.09 % set(auto2) -> assign(stats, some).
% 0.83/1.09 % set(auto2) -> clear(echo_input).
% 0.83/1.09 % set(auto2) -> set(quiet).
% 0.83/1.09 % set(auto2) -> clear(print_initial_clauses).
% 0.83/1.09 % set(auto2) -> clear(print_given).
% 0.83/1.09 assign(lrs_ticks,-1).
% 0.83/1.09 assign(sos_limit,10000).
% 0.83/1.09 assign(order,kbo).
% 0.83/1.09 set(lex_order_vars).
% 0.83/1.09 clear(print_given).
% 0.83/1.09
% 0.83/1.09 % formulas(sos). % not echoed (95 formulas)
% 0.83/1.09
% 0.83/1.09 ============================== end of input ==========================
% 0.83/1.09
% 0.83/1.09 % From the command line: assign(max_seconds, 300).
% 0.83/1.09
% 0.83/1.09 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.83/1.09
% 0.83/1.09 % Formulas that are not ordinary clauses:
% 0.83/1.09 1 (all A all B all C (coll(A,B,C) -> coll(A,C,B))) # label(ruleD1) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.09 2 (all A all B all C (coll(A,B,C) -> coll(B,A,C))) # label(ruleD2) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 11 (all A all B all M (midp(M,B,A) -> midp(M,A,B))) # label(ruleD11) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.09 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 67 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 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].
% 0.83/1.10 69 (all A all B all C (midp(A,B,C) -> cong(A,B,A,C))) # label(ruleD68) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 70 (all A all B all C (midp(A,B,C) -> coll(A,B,C))) # label(ruleD69) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 95 -(all A all B all C all D all E all F all G all H (para(A,B,C,D) & para(A,C,B,D) & perp(E,B,A,C) & coll(E,A,C) & perp(F,A,B,D) & coll(F,B,D) & perp(G,D,A,C) & coll(G,A,C) & perp(H,C,B,D) & coll(H,B,D) -> para(E,F,G,H))) # label(exemplo6GDDFULL012013) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.83/1.10
% 0.83/1.10 ============================== end of process non-clausal formulas ===
% 0.83/1.10
% 0.83/1.10 ============================== PROCESS INITIAL CLAUSES ===============
% 0.83/1.10
% 0.83/1.10 ============================== PREDICATE ELIMINATION =================
% 0.83/1.10 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)].
% 0.83/1.10 97 -cong(A,B,A,C) | -cong(A,B,A,D) | circle(A,B,C,D) # label(ruleD12) # label(axiom). [clausify(12)].
% 0.83/1.10 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)].
% 0.83/1.10 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)].
% 0.83/1.10 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)].
% 0.83/1.10 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)].
% 0.83/1.10 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)].
% 0.83/1.10 100 -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)].
% 0.83/1.10 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)].
% 0.83/1.10 101 -circle(A,B,C,D) | -coll(A,B,D) | perp(B,C,C,D) # label(ruleD53) # label(axiom). [clausify(54)].
% 0.83/1.10 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)].
% 0.83/1.10 102 -circle(A,B,C,D) | perp(f12(B,C,D,A),B,B,A) # label(ruleX11) # label(axiom). [clausify(87)].
% 0.83/1.10 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)].
% 0.83/1.10 103 -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)].
% 0.83/1.10 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)].
% 0.83/1.10 104 -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)].
% 0.83/1.10 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)].
% 0.83/1.10 105 -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)].
% 0.83/1.10 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)].
% 0.83/1.10 106 -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)].
% 0.83/1.10 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)].
% 0.83/1.10 107 -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)].
% 0.83/1.12 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -perp(f15(A,B,C,D,E),A,A,F) | eqangle(A,F,A,B,C,A,C,B). [resolve(107,d,96,a)].
% 0.83/1.12 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -eqangle(A,F,A,B,C,A,C,B) | perp(f15(A,B,C,D,E),A,A,F). [resolve(107,d,98,a)].
% 0.83/1.12 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -midp(F,B,C) | eqangle(A,B,A,C,f15(A,B,C,D,E),B,f15(A,B,C,D,E),F). [resolve(107,d,99,a)].
% 0.83/1.12 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -coll(F,B,C) | -eqangle(A,B,A,C,f15(A,B,C,D,E),B,f15(A,B,C,D,E),F) | midp(F,B,C). [resolve(107,d,100,a)].
% 0.83/1.12 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -coll(f15(A,B,C,D,E),A,C) | perp(A,B,B,C). [resolve(107,d,101,a)].
% 0.83/1.12 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | perp(f12(A,B,C,f15(A,B,C,D,E)),A,A,f15(A,B,C,D,E)). [resolve(107,d,102,a)].
% 0.83/1.12 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -cong(f15(A,B,C,D,E),A,f15(A,B,C,D,E),F) | -cong(V6,A,V6,B) | V6 = f15(A,B,C,D,E) | coll(f13(A,B,C,F,f15(A,B,C,D,E),V6),A,C). [resolve(107,d,103,a)].
% 0.83/1.12 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -cong(f15(A,B,C,D,E),A,f15(A,B,C,D,E),F) | -cong(V6,A,V6,B) | V6 = f15(A,B,C,D,E) | cong(f13(A,B,C,F,f15(A,B,C,D,E),V6),V6,V6,A). [resolve(107,d,104,a)].
% 0.83/1.12 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -cong(f15(A,B,C,D,E),A,f15(A,B,C,D,E),F) | -cong(V6,A,V6,B) | V6 = f15(A,B,C,D,E) | coll(f14(A,B,C,F,f15(A,B,C,D,E),V6),B,F). [resolve(107,d,105,a)].
% 0.83/1.12 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -cong(f15(A,B,C,D,E),A,f15(A,B,C,D,E),F) | -cong(V6,A,V6,B) | V6 = f15(A,B,C,D,E) | cong(f14(A,B,C,F,f15(A,B,C,D,E),V6),V6,V6,A). [resolve(107,d,106,a)].
% 0.83/1.12 108 -perp(A,B,B,C) | -cyclic(A,C,B,D) | circle(f16(A,C,B,D),A,C,B) # label(ruleX14) # label(axiom). [clausify(90)].
% 0.83/1.12 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -perp(f16(A,C,B,D),A,A,E) | eqangle(A,E,A,C,B,A,B,C). [resolve(108,c,96,a)].
% 0.83/1.12 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -eqangle(A,E,A,C,B,A,B,C) | perp(f16(A,C,B,D),A,A,E). [resolve(108,c,98,a)].
% 0.83/1.12 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -midp(E,C,B) | eqangle(A,C,A,B,f16(A,C,B,D),C,f16(A,C,B,D),E). [resolve(108,c,99,a)].
% 0.83/1.12 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -coll(E,C,B) | -eqangle(A,C,A,B,f16(A,C,B,D),C,f16(A,C,B,D),E) | midp(E,C,B). [resolve(108,c,100,a)].
% 0.83/1.12 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -coll(f16(A,C,B,D),A,B) | perp(A,C,C,B). [resolve(108,c,101,a)].
% 0.83/1.12 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | perp(f12(A,C,B,f16(A,C,B,D)),A,A,f16(A,C,B,D)). [resolve(108,c,102,a)].
% 0.83/1.12 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -cong(f16(A,C,B,D),A,f16(A,C,B,D),E) | -cong(F,A,F,C) | F = f16(A,C,B,D) | coll(f13(A,C,B,E,f16(A,C,B,D),F),A,B). [resolve(108,c,103,a)].
% 0.83/1.12 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -cong(f16(A,C,B,D),A,f16(A,C,B,D),E) | -cong(F,A,F,C) | F = f16(A,C,B,D) | cong(f13(A,C,B,E,f16(A,C,B,D),F),F,F,A). [resolve(108,c,104,a)].
% 0.83/1.12 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -cong(f16(A,C,B,D),A,f16(A,C,B,D),E) | -cong(F,A,F,C) | F = f16(A,C,B,D) | coll(f14(A,C,B,E,f16(A,C,B,D),F),C,E). [resolve(108,c,105,a)].
% 0.83/1.12 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -cong(f16(A,C,B,D),A,f16(A,C,B,D),E) | -cong(F,A,F,C) | F = f16(A,C,B,D) | cong(f14(A,C,B,E,f16(A,C,B,D),F),F,F,A). [resolve(108,c,106,a)].
% 0.83/1.12
% 0.83/1.12 ============================== end predicate elimination =============
% 0.83/1.12
% 0.83/1.12 Auto_denials: (non-Horn, no changes).
% 0.83/1.12
% 0.83/1.12 Term ordering decisions:
% 0.83/1.12 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.
% 0.83/1.12
% 0.83/1.12 ============================== end of process initial clauses ========
% 0.83/1.12
% 0.83/1.12 ============================== CLAUSES FOR SEARCH ====================
% 0.83/1.12
% 0.83/1.12 ============================== end of clauses for search =============
% 0.83/1.12
% 0.83/1.12 ============================== SEARCH ================================
% 0.83/1.12
% 0.83/1.12 % Starting search at 0.04 seconds.
% 9.23/9.56
% 9.23/9.56 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 2147483647 (0.00 of 0.19 sec).
% 9.23/9.56
% 9.23/9.56 Low Water (keep): wt=26.000, iters=3388
% 9.23/9.56
% 9.23/9.56 Low Water (keep): wt=22.000, iters=3355
% 9.23/9.56
% 9.23/9.56 Low Water (keep): wt=18.000, iters=3335
% 9.23/9.56
% 9.23/9.56 Low Water (keep): wt=17.000, iters=3368
% 9.23/9.56
% 9.23/9.56 Low Water (keep): wt=16.000, iters=3335
% 9.23/9.56
% 9.23/9.56 Low Water (keep): wt=15.000, iters=3333
% 9.23/9.56
% 9.23/9.56 Low Water (keep): wt=14.000, iters=3348
% 9.23/9.56
% 9.23/9.56 Low Water (keep): wt=13.000, iters=3402
% 9.23/9.56
% 9.23/9.56 Low Water (keep): wt=12.000, iters=3333
% 9.23/9.56
% 9.23/9.56 Low Water (keep): wt=11.000, iters=3340
% 9.23/9.56
% 9.23/9.56 Low Water (keep): wt=10.000, iters=3333
% 9.23/9.56
% 9.23/9.56 Low Water (displace): id=20831, wt=53.000
% 9.23/9.56
% 9.23/9.56 Low Water (displace): id=20955, wt=45.000
% 9.23/9.56
% 9.23/9.56 Low Water (displace): id=21445, wt=32.000
% 9.23/9.56
% 9.23/9.56 Low Water (keep): wt=9.000, iters=3334
% 9.23/9.56
% 9.23/9.56 ============================== PROOF =================================
% 9.23/9.56 % SZS status Theorem
% 9.23/9.56 % SZS output start Refutation
% 9.23/9.56
% 9.23/9.56 % Proof 1 at 8.35 (+ 0.10) seconds.
% 9.23/9.56 % Length of proof is 172.
% 9.23/9.56 % Level of proof is 26.
% 9.23/9.56 % Maximum clause weight is 29.000.
% 9.23/9.56 % Given clauses 12936.
% 9.23/9.56
% 9.23/9.56 1 (all A all B all C (coll(A,B,C) -> coll(A,C,B))) # label(ruleD1) # label(axiom) # label(non_clause). [assumption].
% 9.23/9.56 2 (all A all B all C (coll(A,B,C) -> coll(B,A,C))) # label(ruleD2) # label(axiom) # label(non_clause). [assumption].
% 9.23/9.56 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].
% 9.23/9.56 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].
% 9.23/9.56 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].
% 9.23/9.56 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].
% 9.23/9.56 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].
% 9.23/9.56 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].
% 9.23/9.56 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].
% 9.23/9.56 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].
% 9.23/9.56 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].
% 9.23/9.56 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].
% 9.23/9.56 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].
% 9.23/9.56 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].
% 9.23/9.56 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].
% 9.23/9.56 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].
% 9.23/9.56 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].
% 9.23/9.56 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].
% 9.23/9.56 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].
% 9.23/9.56 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].
% 9.23/9.56 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].
% 9.23/9.56 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].
% 9.23/9.56 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].
% 9.23/9.56 67 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption].
% 9.23/9.56 69 (all A all B all C (midp(A,B,C) -> cong(A,B,A,C))) # label(ruleD68) # label(axiom) # label(non_clause). [assumption].
% 9.23/9.56 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].
% 9.23/9.56 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].
% 9.23/9.56 95 -(all A all B all C all D all E all F all G all H (para(A,B,C,D) & para(A,C,B,D) & perp(E,B,A,C) & coll(E,A,C) & perp(F,A,B,D) & coll(F,B,D) & perp(G,D,A,C) & coll(G,A,C) & perp(H,C,B,D) & coll(H,B,D) -> para(E,F,G,H))) # label(exemplo6GDDFULL012013) # label(negated_conjecture) # label(non_clause). [assumption].
% 9.23/9.56 97 -cong(A,B,A,C) | -cong(A,B,A,D) | circle(A,B,C,D) # label(ruleD12) # label(axiom). [clausify(12)].
% 9.23/9.56 100 -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)].
% 9.23/9.56 109 -coll(A,B,C) | coll(A,C,B) # label(ruleD1) # label(axiom). [clausify(1)].
% 9.23/9.56 110 -coll(A,B,C) | coll(B,A,C) # label(ruleD2) # label(axiom). [clausify(2)].
% 9.23/9.56 111 -coll(A,B,C) | -coll(A,B,D) | coll(C,D,A) # label(ruleD3) # label(axiom). [clausify(3)].
% 9.23/9.56 112 -para(A,B,C,D) | para(A,B,D,C) # label(ruleD4) # label(axiom). [clausify(4)].
% 9.23/9.56 113 -para(A,B,C,D) | para(C,D,A,B) # label(ruleD5) # label(axiom). [clausify(5)].
% 9.23/9.56 114 -para(A,B,C,D) | -para(C,D,E,F) | para(A,B,E,F) # label(ruleD6) # label(axiom). [clausify(6)].
% 9.23/9.56 116 -perp(A,B,C,D) | perp(C,D,A,B) # label(ruleD8) # label(axiom). [clausify(8)].
% 9.23/9.56 117 -perp(A,B,C,D) | -perp(C,D,E,F) | para(A,B,E,F) # label(ruleD9) # label(axiom). [clausify(9)].
% 9.23/9.56 118 -para(A,B,C,D) | -perp(C,D,E,F) | perp(A,B,E,F) # label(ruleD10) # label(axiom). [clausify(10)].
% 9.23/9.56 122 -cyclic(A,B,C,D) | cyclic(A,C,B,D) # label(ruleD15) # label(axiom). [clausify(15)].
% 9.23/9.56 123 -cyclic(A,B,C,D) | cyclic(B,A,C,D) # label(ruleD16) # label(axiom). [clausify(16)].
% 9.23/9.56 127 -eqangle(A,B,C,D,E,F,V6,V7) | eqangle(E,F,V6,V7,A,B,C,D) # label(ruleD20) # label(axiom). [clausify(20)].
% 9.23/9.56 128 -eqangle(A,B,C,D,E,F,V6,V7) | eqangle(A,B,E,F,C,D,V6,V7) # label(ruleD21) # label(axiom). [clausify(21)].
% 9.23/9.56 130 -cong(A,B,C,D) | cong(A,B,D,C) # label(ruleD23) # label(axiom). [clausify(23)].
% 9.23/9.56 131 -cong(A,B,C,D) | cong(C,D,A,B) # label(ruleD24) # label(axiom). [clausify(24)].
% 9.23/9.56 147 -para(A,B,C,D) | eqangle(A,B,E,F,C,D,E,F) # label(ruleD40) # label(axiom). [clausify(40)].
% 9.23/9.56 150 -eqangle(A,B,A,C,D,B,D,C) | -coll(A,D,C) | cyclic(B,C,A,D) # label(ruleD42b) # label(axiom). [clausify(43)].
% 9.23/9.56 151 -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)].
% 9.23/9.56 159 -cong(A,B,C,B) | -cong(A,D,C,D) | perp(A,C,B,D) # label(ruleD56) # label(axiom). [clausify(57)].
% 9.23/9.56 167 -midp(A,B,C) | -para(B,D,C,E) | -para(B,E,C,D) | midp(A,D,E) # label(ruleD64) # label(axiom). [clausify(65)].
% 9.23/9.56 168 -para(A,B,C,D) | -coll(E,A,C) | -coll(E,B,D) | eqratio(E,A,A,C,E,B,B,D) # label(ruleD65) # label(axiom). [clausify(66)].
% 9.23/9.56 169 -para(A,B,A,C) | coll(A,B,C) # label(ruleD66) # label(axiom). [clausify(67)].
% 9.23/9.56 171 -midp(A,B,C) | cong(A,B,A,C) # label(ruleD68) # label(axiom). [clausify(69)].
% 9.23/9.56 175 -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)].
% 9.23/9.56 177 -eqratio(A,B,C,D,E,F,V6,V7) | -cong(E,F,V6,V7) | cong(A,B,C,D) # label(ruleD75) # label(axiom). [clausify(76)].
% 9.23/9.56 208 para(c1,c2,c3,c4) # label(exemplo6GDDFULL012013) # label(negated_conjecture). [clausify(95)].
% 9.23/9.56 209 para(c1,c3,c2,c4) # label(exemplo6GDDFULL012013) # label(negated_conjecture). [clausify(95)].
% 9.23/9.56 213 coll(c6,c2,c4) # label(exemplo6GDDFULL012013) # label(negated_conjecture). [clausify(95)].
% 9.23/9.56 215 coll(c7,c1,c3) # label(exemplo6GDDFULL012013) # label(negated_conjecture). [clausify(95)].
% 9.23/9.56 217 coll(c8,c2,c4) # label(exemplo6GDDFULL012013) # label(negated_conjecture). [clausify(95)].
% 9.23/9.56 218 -para(c5,c6,c7,c8) # label(exemplo6GDDFULL012013) # label(negated_conjecture). [clausify(95)].
% 9.23/9.56 222 -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)].
% 9.23/9.56 257 -coll(A,B,C) | coll(C,C,A). [factor(111,a,b)].
% 9.23/9.56 263 -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)].
% 9.23/9.56 265 -cyclic(A,B,C,D) | -cyclic(A,B,C,E) | -eqangle(C,A,C,B,E,D,E,E) | cong(A,B,D,E). [factor(151,b,c)].
% 9.23/9.56 267 -cong(A,B,C,B) | perp(A,C,B,B). [factor(159,a,b)].
% 9.23/9.56 271 -midp(A,B,C) | -para(B,D,C,D) | midp(A,D,D). [factor(167,b,c)].
% 9.23/9.56 295 -coll(A,B,B) | -eqangle(C,B,C,B,D,B,D,A) | midp(A,B,B) | -cong(D,C,D,B). [factor(222,d,e)].
% 9.23/9.56 330 eqangle(c1,c2,A,B,c3,c4,A,B). [resolve(208,a,147,a)].
% 9.23/9.56 332 -para(A,B,c1,c2) | para(A,B,c3,c4). [resolve(208,a,114,b)].
% 9.23/9.56 333 -para(c3,c4,A,B) | para(c1,c2,A,B). [resolve(208,a,114,a)].
% 9.23/9.56 334 para(c3,c4,c1,c2). [resolve(208,a,113,a)].
% 9.23/9.56 335 para(c1,c2,c4,c3). [resolve(208,a,112,a)].
% 9.23/9.56 350 para(c2,c4,c1,c3). [resolve(209,a,113,a)].
% 9.23/9.56 389 coll(c6,c4,c2). [resolve(213,a,109,a)].
% 9.23/9.56 407 coll(c1,c7,c3). [resolve(215,a,110,a)].
% 9.23/9.56 408 coll(c7,c3,c1). [resolve(215,a,109,a)].
% 9.23/9.56 427 coll(c8,c4,c2). [resolve(217,a,109,a)].
% 9.23/9.56 428 coll(c4,c4,c8). [resolve(257,a,217,a)].
% 9.23/9.56 429 coll(c3,c3,c7). [resolve(257,a,215,a)].
% 9.23/9.56 450 coll(c2,c2,c6). [resolve(389,a,257,a)].
% 9.23/9.56 457 -coll(c1,c7,A) | coll(c3,A,c1). [resolve(407,a,111,a)].
% 9.23/9.56 461 -coll(c7,c3,A) | coll(c1,A,c7). [resolve(408,a,111,a)].
% 9.23/9.56 468 -coll(c8,c4,A) | coll(c2,A,c8). [resolve(427,a,111,a)].
% 9.23/9.56 471 -coll(c4,c4,A) | coll(A,c8,c4). [resolve(428,a,111,b)].
% 9.23/9.56 476 -coll(c3,c3,A) | coll(c7,A,c3). [resolve(429,a,111,a)].
% 9.23/9.56 509 coll(c2,c6,c2). [resolve(450,a,109,a)].
% 9.23/9.56 581 eqangle(c1,c2,c3,c4,A,B,A,B). [resolve(330,a,128,a)].
% 9.23/9.56 596 coll(c2,c2,c2). [resolve(509,a,257,a)].
% 9.23/9.56 630 para(c1,c2,c1,c2). [resolve(334,a,333,a)].
% 9.23/9.56 631 para(c3,c4,c3,c4). [resolve(334,a,332,a)].
% 9.23/9.56 680 para(c4,c3,c1,c2). [resolve(335,a,113,a)].
% 9.23/9.56 753 -coll(A,c2,c1) | -coll(A,c4,c3) | eqratio(A,c2,c2,c1,A,c4,c4,c3). [resolve(350,a,168,a)].
% 9.23/9.56 761 para(c2,c4,c3,c1). [resolve(350,a,112,a)].
% 9.23/9.56 906 coll(c1,c2,c2). [resolve(630,a,169,a)].
% 9.23/9.56 907 -coll(A,c1,c1) | -coll(A,c2,c2) | eqratio(A,c1,c1,c1,A,c2,c2,c2). [resolve(630,a,168,a)].
% 9.23/9.56 909 eqangle(c1,c2,A,B,c1,c2,A,B). [resolve(630,a,147,a)].
% 9.23/9.56 910 para(c1,c2,c2,c1). [resolve(630,a,112,a)].
% 9.23/9.56 911 coll(c2,c2,c1). [resolve(906,a,257,a)].
% 9.23/9.56 917 coll(c1,c1,c2). [resolve(911,a,257,a)].
% 9.23/9.56 928 coll(c1,c2,c1). [resolve(917,a,109,a)].
% 9.23/9.56 931 coll(c2,c1,c1). [resolve(928,a,110,a)].
% 9.23/9.56 948 coll(c3,c4,c4). [resolve(631,a,169,a)].
% 9.23/9.56 951 eqangle(c3,c4,A,B,c3,c4,A,B). [resolve(631,a,147,a)].
% 9.23/9.56 955 coll(c4,c4,c3). [resolve(948,a,257,a)].
% 9.23/9.56 961 coll(c3,c3,c4). [resolve(955,a,257,a)].
% 9.23/9.56 976 coll(c3,c4,c3). [resolve(961,a,109,a)].
% 9.23/9.56 1000 para(c4,c3,c3,c4). [resolve(680,a,332,a)].
% 9.23/9.56 1031 -perp(c3,c1,A,B) | perp(c2,c4,A,B). [resolve(761,a,118,a)].
% 9.23/9.56 1188 para(c2,c1,c1,c2). [resolve(910,a,113,a)].
% 9.23/9.56 1282 para(c4,c3,c4,c3). [resolve(1000,a,112,a)].
% 9.23/9.56 1540 para(c2,c1,c2,c1). [resolve(1188,a,112,a)].
% 9.23/9.56 1613 eqangle(c4,c3,A,B,c4,c3,A,B). [resolve(1282,a,147,a)].
% 9.23/9.56 1747 eqangle(c2,c1,A,B,c2,c1,A,B). [resolve(1540,a,147,a)].
% 9.23/9.56 2588 coll(c3,c8,c4). [resolve(471,a,955,a)].
% 9.23/9.56 2592 coll(c8,c3,c4). [resolve(2588,a,110,a)].
% 9.23/9.56 2603 coll(c8,c4,c3). [resolve(2592,a,109,a)].
% 9.23/9.56 2617 coll(c2,c3,c8). [resolve(2603,a,468,a)].
% 9.23/9.56 2648 coll(c2,c8,c3). [resolve(2617,a,109,a)].
% 9.23/9.56 2679 coll(c3,c3,c2). [resolve(2648,a,257,a)].
% 9.23/9.56 3280 coll(c7,c2,c3). [resolve(476,a,2679,a)].
% 9.23/9.56 3302 coll(c7,c3,c2). [resolve(3280,a,109,a)].
% 9.23/9.56 3344 coll(c1,c2,c7). [resolve(3302,a,461,a)].
% 9.23/9.56 3453 coll(c1,c7,c2). [resolve(3344,a,109,a)].
% 9.23/9.56 3581 coll(c3,c2,c1). [resolve(3453,a,457,a)].
% 9.23/9.56 4215 eqangle(A,B,A,B,c1,c2,c3,c4). [resolve(581,a,127,a)].
% 9.23/9.56 4627 eqratio(c3,c2,c2,c1,c3,c4,c4,c3). [resolve(753,b,976,a),unit_del(a,3581)].
% 9.23/9.56 5085 eqratio(c2,c1,c1,c1,c2,c2,c2,c2). [resolve(907,b,596,a),unit_del(a,931)].
% 9.23/9.56 5086 midp(c2,c2,c2) | -cong(c1,c1,c1,c2). [resolve(909,a,295,b),unit_del(a,596)].
% 9.23/9.56 5088 -cyclic(c2,c2,c1,c2) | -cyclic(c2,c2,c1,c1) | cong(c2,c2,c2,c2). [resolve(909,a,263,c)].
% 9.23/9.56 5097 -coll(c1,c1,A) | cyclic(c2,A,c1,c1). [resolve(909,a,150,a)].
% 9.23/9.56 5190 -cyclic(c4,c3,c3,c4) | -cyclic(c4,c3,c3,c3) | cong(c4,c3,c4,c3). [resolve(951,a,265,c)].
% 9.23/9.56 5200 -coll(c3,c3,A) | cyclic(c4,A,c3,c3). [resolve(951,a,150,a)].
% 9.23/9.56 13505 -coll(c4,c4,A) | cyclic(c3,A,c4,c4). [resolve(1613,a,150,a)].
% 9.23/9.56 14137 -coll(c2,c2,A) | cyclic(c1,A,c2,c2). [resolve(1747,a,150,a)].
% 9.23/9.56 18165 para(A,B,A,B). [resolve(4215,a,175,a),unit_del(a,208)].
% 9.23/9.56 18168 -midp(A,B,B) | midp(A,C,C). [resolve(18165,a,271,b)].
% 9.23/9.56 18169 coll(A,B,B). [resolve(18165,a,169,a)].
% 9.23/9.56 18229 coll(A,A,B). [resolve(18169,a,257,a)].
% 9.23/9.56 18248 cyclic(c1,A,c2,c2). [back_unit_del(14137),unit_del(a,18229)].
% 9.23/9.56 18284 cyclic(c3,A,c4,c4). [back_unit_del(13505),unit_del(a,18229)].
% 9.23/9.56 18511 cyclic(c4,A,c3,c3). [back_unit_del(5200),unit_del(a,18229)].
% 9.23/9.56 18512 cyclic(c2,A,c1,c1). [back_unit_del(5097),unit_del(a,18229)].
% 9.23/9.56 18644 -cyclic(c4,c3,c3,c4) | cong(c4,c3,c4,c3). [back_unit_del(5190),unit_del(b,18511)].
% 9.23/9.56 18645 -cyclic(c2,c2,c1,c2) | cong(c2,c2,c2,c2). [back_unit_del(5088),unit_del(b,18512)].
% 9.23/9.56 19243 cyclic(A,c1,c2,c2). [resolve(18248,a,123,a)].
% 9.23/9.56 19276 cyclic(c3,c4,A,c4). [resolve(18284,a,122,a)].
% 9.23/9.56 19744 cyclic(A,c2,c1,c2). [resolve(19243,a,122,a)].
% 9.23/9.56 19745 cong(c2,c2,c2,c2). [back_unit_del(18645),unit_del(a,19744)].
% 9.23/9.56 19823 cyclic(c4,c3,A,c4). [resolve(19276,a,123,a)].
% 9.23/9.56 19825 cong(c4,c3,c4,c3). [back_unit_del(18644),unit_del(a,19823)].
% 9.23/9.56 20821 cong(c4,c3,c3,c4). [resolve(19825,a,130,a)].
% 9.23/9.56 21706 cong(c3,c4,c4,c3). [resolve(20821,a,131,a)].
% 9.23/9.56 24428 cong(c3,c2,c2,c1). [resolve(4627,a,177,a),unit_del(a,21706)].
% 9.23/9.56 24435 cong(c3,c2,c1,c2). [resolve(24428,a,130,a)].
% 9.23/9.56 24443 perp(c3,c1,c2,c2). [resolve(24435,a,267,a)].
% 9.23/9.56 24465 perp(c2,c4,c2,c2). [resolve(24443,a,1031,a)].
% 9.23/9.56 24569 -perp(c2,c2,A,B) | para(c2,c4,A,B). [resolve(24465,a,117,a)].
% 9.23/9.56 24570 perp(c2,c2,c2,c4). [resolve(24465,a,116,a)].
% 9.23/9.56 24662 -perp(A,B,c2,c2) | para(A,B,c2,c4). [resolve(24570,a,117,b)].
% 9.23/9.56 24999 cong(c2,c1,c1,c1). [resolve(5085,a,177,a),unit_del(a,19745)].
% 9.23/9.56 25009 cong(c1,c1,c2,c1). [resolve(24999,a,131,a)].
% 9.23/9.56 25016 cong(c1,c1,c1,c2). [resolve(25009,a,130,a)].
% 9.23/9.56 25018 midp(c2,c2,c2). [back_unit_del(5086),unit_del(b,25016)].
% 9.23/9.56 25027 midp(c2,A,A). [resolve(25018,a,18168,a)].
% 9.23/9.56 25181 cong(c2,A,c2,A). [resolve(25027,a,171,a)].
% 9.23/9.56 29296 perp(c2,c2,A,B). [resolve(25181,a,159,b),unit_del(a,25181)].
% 9.23/9.56 29300 para(c2,c4,A,B). [back_unit_del(24569),unit_del(a,29296)].
% 9.23/9.56 30123 perp(A,B,c2,c2). [resolve(29296,a,116,a)].
% 9.23/9.56 30124 para(A,B,c2,c4). [back_unit_del(24662),unit_del(a,30123)].
% 9.23/9.56 30155 para(A,B,C,D). [resolve(29300,a,114,b),unit_del(a,30124)].
% 9.23/9.56 30156 $F. [resolve(30155,a,218,a)].
% 9.23/9.56
% 9.23/9.56 % SZS output end Refutation
% 9.23/9.56 ============================== end of proof ==========================
% 9.23/9.56
% 9.23/9.56 ============================== STATISTICS ============================
% 9.23/9.56
% 9.23/9.56 Given=12936. Generated=190572. Kept=30039. proofs=1.
% 9.23/9.56 Usable=10194. Sos=9010. Demods=0. Limbo=1, Disabled=10987. Hints=0.
% 9.23/9.56 Megabytes=16.82.
% 9.23/9.56 User_CPU=8.35, System_CPU=0.10, Wall_clock=8.
% 9.23/9.56
% 9.23/9.56 ============================== end of statistics =====================
% 9.23/9.56
% 9.23/9.56 ============================== end of search =========================
% 9.23/9.56
% 9.23/9.56 THEOREM PROVED
% 9.23/9.56 % SZS status Theorem
% 9.23/9.56
% 9.23/9.56 Exiting with 1 proof.
% 9.23/9.56
% 9.23/9.56 Process 20522 exit (max_proofs) Sat Jun 18 16:14:12 2022
% 9.23/9.56 Prover9 interrupted
%------------------------------------------------------------------------------