TSTP Solution File: GEO562+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GEO562+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n016.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 05:56:58 EDT 2022
% Result : Theorem 6.91s 7.24s
% Output : Refutation 7.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : GEO562+1 : TPTP v8.1.0. Released v7.5.0.
% 0.04/0.15 % Command : tptp2X_and_run_prover9 %d %s
% 0.15/0.37 % Computer : n016.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 600
% 0.15/0.37 % DateTime : Sat Jun 18 17:12:07 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.91/1.16 ============================== Prover9 ===============================
% 0.91/1.16 Prover9 (32) version 2009-11A, November 2009.
% 0.91/1.16 Process 25648 was started by sandbox2 on n016.cluster.edu,
% 0.91/1.16 Sat Jun 18 17:12:08 2022
% 0.91/1.16 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_25495_n016.cluster.edu".
% 0.91/1.16 ============================== end of head ===========================
% 0.91/1.16
% 0.91/1.16 ============================== INPUT =================================
% 0.91/1.16
% 0.91/1.16 % Reading from file /tmp/Prover9_25495_n016.cluster.edu
% 0.91/1.16
% 0.91/1.16 set(prolog_style_variables).
% 0.91/1.16 set(auto2).
% 0.91/1.16 % set(auto2) -> set(auto).
% 0.91/1.16 % set(auto) -> set(auto_inference).
% 0.91/1.16 % set(auto) -> set(auto_setup).
% 0.91/1.16 % set(auto_setup) -> set(predicate_elim).
% 0.91/1.16 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.91/1.16 % set(auto) -> set(auto_limits).
% 0.91/1.16 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.91/1.16 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.91/1.16 % set(auto) -> set(auto_denials).
% 0.91/1.16 % set(auto) -> set(auto_process).
% 0.91/1.16 % set(auto2) -> assign(new_constants, 1).
% 0.91/1.16 % set(auto2) -> assign(fold_denial_max, 3).
% 0.91/1.16 % set(auto2) -> assign(max_weight, "200.000").
% 0.91/1.16 % set(auto2) -> assign(max_hours, 1).
% 0.91/1.16 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.91/1.16 % set(auto2) -> assign(max_seconds, 0).
% 0.91/1.16 % set(auto2) -> assign(max_minutes, 5).
% 0.91/1.16 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.91/1.16 % set(auto2) -> set(sort_initial_sos).
% 0.91/1.16 % set(auto2) -> assign(sos_limit, -1).
% 0.91/1.16 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.91/1.16 % set(auto2) -> assign(max_megs, 400).
% 0.91/1.16 % set(auto2) -> assign(stats, some).
% 0.91/1.16 % set(auto2) -> clear(echo_input).
% 0.91/1.16 % set(auto2) -> set(quiet).
% 0.91/1.16 % set(auto2) -> clear(print_initial_clauses).
% 0.91/1.16 % set(auto2) -> clear(print_given).
% 0.91/1.16 assign(lrs_ticks,-1).
% 0.91/1.16 assign(sos_limit,10000).
% 0.91/1.16 assign(order,kbo).
% 0.91/1.16 set(lex_order_vars).
% 0.91/1.16 clear(print_given).
% 0.91/1.16
% 0.91/1.16 % formulas(sos). % not echoed (95 formulas)
% 0.91/1.16
% 0.91/1.16 ============================== end of input ==========================
% 0.91/1.16
% 0.91/1.16 % From the command line: assign(max_seconds, 300).
% 0.91/1.16
% 0.91/1.16 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.91/1.16
% 0.91/1.16 % Formulas that are not ordinary clauses:
% 0.91/1.16 1 (all A all B all C (coll(A,B,C) -> coll(A,C,B))) # label(ruleD1) # label(axiom) # label(non_clause). [assumption].
% 0.91/1.16 2 (all A all B all C (coll(A,B,C) -> coll(B,A,C))) # label(ruleD2) # label(axiom) # label(non_clause). [assumption].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 11 (all A all B all M (midp(M,B,A) -> midp(M,A,B))) # label(ruleD11) # label(axiom) # label(non_clause). [assumption].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.16 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].
% 0.91/1.17 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].
% 0.91/1.17 67 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption].
% 0.91/1.17 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].
% 0.91/1.17 69 (all A all B all C (midp(A,B,C) -> cong(A,B,A,C))) # label(ruleD68) # label(axiom) # label(non_clause). [assumption].
% 0.91/1.17 70 (all A all B all C (midp(A,B,C) -> coll(A,B,C))) # label(ruleD69) # label(axiom) # label(non_clause). [assumption].
% 0.91/1.17 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].
% 0.91/1.17 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].
% 0.91/1.17 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].
% 0.91/1.17 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].
% 0.91/1.17 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].
% 0.91/1.17 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].
% 0.91/1.17 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].
% 0.91/1.17 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].
% 0.91/1.17 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].
% 0.91/1.17 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].
% 0.91/1.17 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].
% 0.91/1.17 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].
% 0.91/1.17 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].
% 0.91/1.17 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].
% 0.91/1.17 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].
% 0.91/1.17 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].
% 0.91/1.17 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].
% 0.91/1.17 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].
% 0.91/1.17 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].
% 0.91/1.17 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].
% 0.91/1.17 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].
% 0.91/1.17 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].
% 0.91/1.17 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].
% 0.91/1.17 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].
% 0.91/1.17 95 -(all A all C all D all O all B all M all E all F all G all NWPNT1 all NWPNT2 (circle(O,A,C,D) & perp(C,O,A,B) & circle(O,A,B,NWPNT1) & coll(M,C,O) & coll(M,A,B) & circle(O,A,E,NWPNT2) & coll(F,A,B) & coll(F,C,D) & coll(G,A,B) & coll(G,C,E) -> eqangle(A,G,G,C,C,D,D,E))) # label(exemplo6GDDFULL214023) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.91/1.17
% 0.91/1.17 ============================== end of process non-clausal formulas ===
% 0.91/1.17
% 0.91/1.17 ============================== PROCESS INITIAL CLAUSES ===============
% 0.91/1.17
% 0.91/1.17 ============================== PREDICATE ELIMINATION =================
% 0.91/1.17 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)].
% 0.91/1.17 97 -cong(A,B,A,C) | -cong(A,B,A,D) | circle(A,B,C,D) # label(ruleD12) # label(axiom). [clausify(12)].
% 0.91/1.17 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)].
% 0.91/1.17 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)].
% 0.91/1.17 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)].
% 0.91/1.17 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)].
% 0.91/1.17 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)].
% 0.91/1.17 100 -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)].
% 0.91/1.17 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)].
% 0.91/1.17 101 -circle(A,B,C,D) | -coll(A,B,D) | perp(B,C,C,D) # label(ruleD53) # label(axiom). [clausify(54)].
% 0.91/1.17 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)].
% 0.91/1.17 102 -circle(A,B,C,D) | perp(f12(B,C,D,A),B,B,A) # label(ruleX11) # label(axiom). [clausify(87)].
% 0.91/1.17 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)].
% 0.91/1.17 103 -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)].
% 0.91/1.17 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)].
% 0.91/1.17 104 -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)].
% 0.91/1.17 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)].
% 0.91/1.17 105 -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)].
% 0.91/1.17 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)].
% 0.91/1.17 106 -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)].
% 0.91/1.17 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)].
% 0.91/1.17 107 -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)].
% 0.91/1.17 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)].
% 0.91/1.17 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)].
% 0.91/1.17 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)].
% 0.91/1.17 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)].
% 0.91/1.17 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)].
% 0.91/1.17 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)].
% 0.91/1.17 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)].
% 0.91/1.17 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)].
% 0.91/1.17 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)].
% 0.91/1.17 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)].
% 0.91/1.17 108 -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)].
% 0.91/1.17 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)].
% 0.91/1.17 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)].
% 0.91/1.17 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)].
% 0.91/1.17 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)].
% 0.91/1.17 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)].
% 0.91/1.17 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)].
% 0.91/1.17 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)].
% 0.91/1.17 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)].
% 0.91/1.17 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)].
% 0.91/1.17 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)].
% 0.91/1.17 109 circle(c4,c1,c2,c3) # label(exemplo6GDDFULL214023) # label(negated_conjecture). [clausify(95)].
% 0.91/1.17 Derived: -perp(c4,c1,c1,A) | eqangle(c1,A,c1,c2,c3,c1,c3,c2). [resolve(109,a,96,a)].
% 0.91/1.17 Derived: -eqangle(c1,A,c1,c2,c3,c1,c3,c2) | perp(c4,c1,c1,A). [resolve(109,a,98,a)].
% 0.91/1.17 Derived: -midp(A,c2,c3) | eqangle(c1,c2,c1,c3,c4,c2,c4,A). [resolve(109,a,99,a)].
% 0.91/1.17 Derived: -coll(A,c2,c3) | -eqangle(c1,c2,c1,c3,c4,c2,c4,A) | midp(A,c2,c3). [resolve(109,a,100,a)].
% 0.91/1.17 Derived: -coll(c4,c1,c3) | perp(c1,c2,c2,c3). [resolve(109,a,101,a)].
% 0.91/1.17 Derived: perp(f12(c1,c2,c3,c4),c1,c1,c4). [resolve(109,a,102,a)].
% 3.37/3.66 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)].
% 3.37/3.66 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)].
% 3.37/3.66 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)].
% 3.37/3.66 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)].
% 3.37/3.66 110 circle(c4,c1,c5,c10) # label(exemplo6GDDFULL214023) # label(negated_conjecture). [clausify(95)].
% 3.37/3.66 Derived: -perp(c4,c1,c1,A) | eqangle(c1,A,c1,c5,c10,c1,c10,c5). [resolve(110,a,96,a)].
% 3.37/3.66 Derived: -eqangle(c1,A,c1,c5,c10,c1,c10,c5) | perp(c4,c1,c1,A). [resolve(110,a,98,a)].
% 3.37/3.66 Derived: -midp(A,c5,c10) | eqangle(c1,c5,c1,c10,c4,c5,c4,A). [resolve(110,a,99,a)].
% 3.37/3.66 Derived: -coll(A,c5,c10) | -eqangle(c1,c5,c1,c10,c4,c5,c4,A) | midp(A,c5,c10). [resolve(110,a,100,a)].
% 3.37/3.66 Derived: -coll(c4,c1,c10) | perp(c1,c5,c5,c10). [resolve(110,a,101,a)].
% 3.37/3.66 Derived: perp(f12(c1,c5,c10,c4),c1,c1,c4). [resolve(110,a,102,a)].
% 3.37/3.66 Derived: -cong(c4,c1,c4,A) | -cong(B,c1,B,c5) | B = c4 | coll(f13(c1,c5,c10,A,c4,B),c1,c10). [resolve(110,a,103,a)].
% 3.37/3.66 Derived: -cong(c4,c1,c4,A) | -cong(B,c1,B,c5) | B = c4 | cong(f13(c1,c5,c10,A,c4,B),B,B,c1). [resolve(110,a,104,a)].
% 3.37/3.66 Derived: -cong(c4,c1,c4,A) | -cong(B,c1,B,c5) | B = c4 | coll(f14(c1,c5,c10,A,c4,B),c5,A). [resolve(110,a,105,a)].
% 3.37/3.66 Derived: -cong(c4,c1,c4,A) | -cong(B,c1,B,c5) | B = c4 | cong(f14(c1,c5,c10,A,c4,B),B,B,c1). [resolve(110,a,106,a)].
% 3.37/3.66 111 circle(c4,c1,c7,c11) # label(exemplo6GDDFULL214023) # label(negated_conjecture). [clausify(95)].
% 3.37/3.66 Derived: -perp(c4,c1,c1,A) | eqangle(c1,A,c1,c7,c11,c1,c11,c7). [resolve(111,a,96,a)].
% 3.37/3.66 Derived: -eqangle(c1,A,c1,c7,c11,c1,c11,c7) | perp(c4,c1,c1,A). [resolve(111,a,98,a)].
% 3.37/3.66 Derived: -midp(A,c7,c11) | eqangle(c1,c7,c1,c11,c4,c7,c4,A). [resolve(111,a,99,a)].
% 3.37/3.66 Derived: -coll(A,c7,c11) | -eqangle(c1,c7,c1,c11,c4,c7,c4,A) | midp(A,c7,c11). [resolve(111,a,100,a)].
% 3.37/3.66 Derived: -coll(c4,c1,c11) | perp(c1,c7,c7,c11). [resolve(111,a,101,a)].
% 3.37/3.66 Derived: perp(f12(c1,c7,c11,c4),c1,c1,c4). [resolve(111,a,102,a)].
% 3.37/3.66 Derived: -cong(c4,c1,c4,A) | -cong(B,c1,B,c7) | B = c4 | coll(f13(c1,c7,c11,A,c4,B),c1,c11). [resolve(111,a,103,a)].
% 3.37/3.66 Derived: -cong(c4,c1,c4,A) | -cong(B,c1,B,c7) | B = c4 | cong(f13(c1,c7,c11,A,c4,B),B,B,c1). [resolve(111,a,104,a)].
% 3.37/3.66 Derived: -cong(c4,c1,c4,A) | -cong(B,c1,B,c7) | B = c4 | coll(f14(c1,c7,c11,A,c4,B),c7,A). [resolve(111,a,105,a)].
% 3.37/3.66 Derived: -cong(c4,c1,c4,A) | -cong(B,c1,B,c7) | B = c4 | cong(f14(c1,c7,c11,A,c4,B),B,B,c1). [resolve(111,a,106,a)].
% 3.37/3.66
% 3.37/3.66 ============================== end predicate elimination =============
% 3.37/3.66
% 3.37/3.66 Auto_denials: (non-Horn, no changes).
% 3.37/3.66
% 3.37/3.66 Term ordering decisions:
% 3.37/3.66 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.
% 3.37/3.66
% 3.37/3.66 ============================== end of process initial clauses ========
% 3.37/3.66
% 3.37/3.66 ============================== CLAUSES FOR SEARCH ====================
% 3.37/3.66
% 3.37/3.66 ============================== end of clauses for search =============
% 3.37/3.66
% 3.37/3.66 ============================== SEARCH ================================
% 3.37/3.66
% 3.37/3.66 % Starting search at 0.05 seconds.
% 3.37/3.66
% 3.37/3.66 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 2147483647 (0.00 of 0.14 sec).
% 3.37/3.66
% 3.37/3.66 Low Water (keep): wt=57.000, iters=3368
% 3.37/3.66
% 3.37/3.66 Low Water (keep): wt=49.000, iters=3358
% 3.37/3.66
% 3.37/3.66 Low Water (keep): wt=48.000, iters=3334
% 3.37/3.66
% 3.37/3.66 Low Water (keep): wt=44.000, iters=3367
% 3.37/3.66
% 3.37/3.66 Low Water (keep): wt=39.000, iters=3336
% 3.37/3.66
% 3.37/3.66 Low Water (keep): wt=36.000, iters=3333
% 3.37/3.66
% 3.37/3.66 Low Water (keep): wt=27.000, iters=3358
% 3.37/3.66
% 3.37/3.66 Low Water (keep): wt=26.000, iters=3337
% 3.37/3.66
% 3.37/3.66 Low Water (keep): wt=23.000, iters=3340
% 3.37/3.66
% 3.37/3.66 Low Water (keep): wt=22.000, iters=3334
% 3.37/3.66
% 3.37/3.66 Low Water (keep): wt=21.000, iters=3336
% 3.37/3.66
% 3.37/3.66 Low Water (keep): wt=18.000, iters=3335
% 3.37/3.66
% 3.37/3.66 Low Water (keep): wt=17.000, iters=3335
% 3.37/3.66
% 3.37/3.66 Low Water (keep): wt=16.000, iters=3333
% 3.37/3.66
% 3.37/3.66 Low Water (keep): wt=14.000, iters=3337
% 3.37/3.66
% 3.37/3.66 Low Water (displace): id=9012, wt=57.000
% 3.37/3.66
% 3.37/3.66 Low Water (displace): id=16443, wt=13.000
% 6.91/7.24
% 6.91/7.24 Low Water (keep): wt=13.000, iters=3346
% 6.91/7.24
% 6.91/7.24 ============================== PROOF =================================
% 6.91/7.24 % SZS status Theorem
% 6.91/7.24 % SZS output start Refutation
% 6.91/7.24
% 6.91/7.24 % Proof 1 at 6.02 (+ 0.08) seconds.
% 6.91/7.24 % Length of proof is 143.
% 6.91/7.24 % Level of proof is 30.
% 6.91/7.24 % Maximum clause weight is 29.000.
% 6.91/7.24 % Given clauses 10932.
% 6.91/7.24
% 6.91/7.24 1 (all A all B all C (coll(A,B,C) -> coll(A,C,B))) # label(ruleD1) # label(axiom) # label(non_clause). [assumption].
% 6.91/7.24 2 (all A all B all C (coll(A,B,C) -> coll(B,A,C))) # label(ruleD2) # label(axiom) # label(non_clause). [assumption].
% 6.91/7.24 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].
% 6.91/7.24 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].
% 6.91/7.24 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].
% 6.91/7.24 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].
% 6.91/7.24 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].
% 6.91/7.24 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].
% 6.91/7.24 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].
% 6.91/7.24 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].
% 6.91/7.24 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].
% 6.91/7.24 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].
% 6.91/7.24 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].
% 6.91/7.24 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].
% 6.91/7.24 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].
% 6.91/7.24 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].
% 6.91/7.24 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].
% 6.91/7.24 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].
% 6.91/7.24 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].
% 6.91/7.24 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].
% 6.91/7.24 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].
% 6.91/7.24 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].
% 6.91/7.24 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].
% 6.91/7.24 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].
% 6.91/7.24 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].
% 6.91/7.24 67 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption].
% 6.91/7.24 69 (all A all B all C (midp(A,B,C) -> cong(A,B,A,C))) # label(ruleD68) # label(axiom) # label(non_clause). [assumption].
% 6.91/7.24 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].
% 6.91/7.24 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].
% 6.91/7.24 95 -(all A all C all D all O all B all M all E all F all G all NWPNT1 all NWPNT2 (circle(O,A,C,D) & perp(C,O,A,B) & circle(O,A,B,NWPNT1) & coll(M,C,O) & coll(M,A,B) & circle(O,A,E,NWPNT2) & coll(F,A,B) & coll(F,C,D) & coll(G,A,B) & coll(G,C,E) -> eqangle(A,G,G,C,C,D,D,E))) # label(exemplo6GDDFULL214023) # label(negated_conjecture) # label(non_clause). [assumption].
% 6.91/7.24 97 -cong(A,B,A,C) | -cong(A,B,A,D) | circle(A,B,C,D) # label(ruleD12) # label(axiom). [clausify(12)].
% 6.91/7.24 100 -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)].
% 6.91/7.24 102 -circle(A,B,C,D) | perp(f12(B,C,D,A),B,B,A) # label(ruleX11) # label(axiom). [clausify(87)].
% 6.91/7.24 109 circle(c4,c1,c2,c3) # label(exemplo6GDDFULL214023) # label(negated_conjecture). [clausify(95)].
% 6.91/7.24 112 -coll(A,B,C) | coll(A,C,B) # label(ruleD1) # label(axiom). [clausify(1)].
% 6.91/7.24 113 -coll(A,B,C) | coll(B,A,C) # label(ruleD2) # label(axiom). [clausify(2)].
% 6.91/7.24 114 -coll(A,B,C) | -coll(A,B,D) | coll(C,D,A) # label(ruleD3) # label(axiom). [clausify(3)].
% 6.91/7.24 115 -para(A,B,C,D) | para(A,B,D,C) # label(ruleD4) # label(axiom). [clausify(4)].
% 6.91/7.24 116 -para(A,B,C,D) | para(C,D,A,B) # label(ruleD5) # label(axiom). [clausify(5)].
% 6.91/7.24 118 -perp(A,B,C,D) | perp(A,B,D,C) # label(ruleD7) # label(axiom). [clausify(7)].
% 6.91/7.24 119 -perp(A,B,C,D) | perp(C,D,A,B) # label(ruleD8) # label(axiom). [clausify(8)].
% 6.91/7.24 120 -perp(A,B,C,D) | -perp(C,D,E,F) | para(A,B,E,F) # label(ruleD9) # label(axiom). [clausify(9)].
% 6.91/7.24 125 -cyclic(A,B,C,D) | cyclic(A,C,B,D) # label(ruleD15) # label(axiom). [clausify(15)].
% 6.91/7.24 126 -cyclic(A,B,C,D) | cyclic(B,A,C,D) # label(ruleD16) # label(axiom). [clausify(16)].
% 6.91/7.24 129 -eqangle(A,B,C,D,E,F,V6,V7) | eqangle(C,D,A,B,V6,V7,E,F) # label(ruleD19) # label(axiom). [clausify(19)].
% 6.91/7.24 130 -eqangle(A,B,C,D,E,F,V6,V7) | eqangle(E,F,V6,V7,A,B,C,D) # label(ruleD20) # label(axiom). [clausify(20)].
% 6.91/7.24 131 -eqangle(A,B,C,D,E,F,V6,V7) | eqangle(A,B,E,F,C,D,V6,V7) # label(ruleD21) # label(axiom). [clausify(21)].
% 6.91/7.24 132 -eqangle(A,B,C,D,E,F,V6,V7) | -eqangle(E,F,V6,V7,V8,V9,V10,V11) | eqangle(A,B,C,D,V8,V9,V10,V11) # label(ruleD22) # label(axiom). [clausify(22)].
% 6.91/7.24 133 -cong(A,B,C,D) | cong(A,B,D,C) # label(ruleD23) # label(axiom). [clausify(23)].
% 6.91/7.24 134 -cong(A,B,C,D) | cong(C,D,A,B) # label(ruleD24) # label(axiom). [clausify(24)].
% 6.91/7.24 149 -eqangle(A,B,C,D,E,F,C,D) | para(A,B,E,F) # label(ruleD39) # label(axiom). [clausify(39)].
% 6.91/7.24 150 -para(A,B,C,D) | eqangle(A,B,E,F,C,D,E,F) # label(ruleD40) # label(axiom). [clausify(40)].
% 6.91/7.24 153 -eqangle(A,B,A,C,D,B,D,C) | -coll(A,D,C) | cyclic(B,C,A,D) # label(ruleD42b) # label(axiom). [clausify(43)].
% 6.91/7.24 154 -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)].
% 6.91/7.24 162 -cong(A,B,C,B) | -cong(A,D,C,D) | perp(A,C,B,D) # label(ruleD56) # label(axiom). [clausify(57)].
% 6.91/7.24 170 -midp(A,B,C) | -para(B,D,C,E) | -para(B,E,C,D) | midp(A,D,E) # label(ruleD64) # label(axiom). [clausify(65)].
% 6.91/7.24 171 -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)].
% 6.91/7.24 172 -para(A,B,A,C) | coll(A,B,C) # label(ruleD66) # label(axiom). [clausify(67)].
% 6.91/7.24 174 -midp(A,B,C) | cong(A,B,A,C) # label(ruleD68) # label(axiom). [clausify(69)].
% 6.91/7.24 180 -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)].
% 6.91/7.24 211 perp(c2,c4,c1,c5) # label(exemplo6GDDFULL214023) # label(negated_conjecture). [clausify(95)].
% 6.91/7.24 213 coll(c6,c1,c5) # label(exemplo6GDDFULL214023) # label(negated_conjecture). [clausify(95)].
% 6.91/7.24 216 coll(c9,c1,c5) # label(exemplo6GDDFULL214023) # label(negated_conjecture). [clausify(95)].
% 6.91/7.24 218 -eqangle(c1,c9,c9,c2,c2,c3,c3,c7) # label(exemplo6GDDFULL214023) # label(negated_conjecture). [clausify(95)].
% 6.91/7.24 222 -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)].
% 6.91/7.24 262 perp(f12(c1,c2,c3,c4),c1,c1,c4). [resolve(109,a,102,a)].
% 6.91/7.24 299 -coll(A,B,C) | coll(C,C,A). [factor(114,a,b)].
% 6.91/7.24 305 -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(154,a,b)].
% 6.91/7.24 313 -midp(A,B,C) | -para(B,D,C,D) | midp(A,D,D). [factor(170,b,c)].
% 6.91/7.24 337 -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)].
% 6.91/7.24 373 -perp(A,B,c2,c4) | para(A,B,c1,c5). [resolve(211,a,120,b)].
% 6.91/7.24 374 -perp(c1,c5,A,B) | para(c2,c4,A,B). [resolve(211,a,120,a)].
% 6.91/7.24 375 perp(c1,c5,c2,c4). [resolve(211,a,119,a)].
% 6.91/7.24 376 perp(c2,c4,c5,c1). [resolve(211,a,118,a)].
% 6.91/7.24 383 coll(c1,c6,c5). [resolve(213,a,113,a)].
% 6.91/7.24 421 -perp(A,B,f12(c1,c2,c3,c4),c1) | para(A,B,c1,c4). [resolve(262,a,120,b)].
% 6.91/7.24 423 perp(c1,c4,f12(c1,c2,c3,c4),c1). [resolve(262,a,119,a)].
% 6.91/7.24 477 coll(c5,c5,c9). [resolve(299,a,216,a)].
% 6.91/7.24 490 coll(c5,c5,c1). [resolve(383,a,299,a)].
% 6.91/7.24 535 coll(c5,c9,c5). [resolve(477,a,112,a)].
% 6.91/7.24 565 coll(c1,c1,c5). [resolve(490,a,299,a)].
% 6.91/7.24 632 coll(c5,c5,c5). [resolve(535,a,299,a)].
% 6.91/7.24 662 para(c2,c4,c2,c4). [resolve(375,a,374,a)].
% 6.91/7.24 663 para(c1,c5,c1,c5). [resolve(375,a,373,a)].
% 6.91/7.24 702 perp(c5,c1,c2,c4). [resolve(376,a,119,a)].
% 6.91/7.24 709 coll(c1,c5,c1). [resolve(565,a,112,a)].
% 6.91/7.24 816 coll(c5,c1,c1). [resolve(709,a,113,a)].
% 6.91/7.24 919 eqangle(c2,c4,A,B,c2,c4,A,B). [resolve(662,a,150,a)].
% 6.91/7.24 920 para(c2,c4,c4,c2). [resolve(662,a,115,a)].
% 6.91/7.24 930 -coll(A,c1,c1) | -coll(A,c5,c5) | eqratio(A,c1,c1,c1,A,c5,c5,c5). [resolve(663,a,171,a)].
% 6.91/7.24 932 eqangle(c1,c5,A,B,c1,c5,A,B). [resolve(663,a,150,a)].
% 6.91/7.24 948 para(c5,c1,c1,c5). [resolve(702,a,373,a)].
% 6.91/7.24 975 eqangle(c2,c4,A,B,c4,c2,A,B). [resolve(920,a,150,a)].
% 6.91/7.24 978 para(c4,c2,c2,c4). [resolve(920,a,116,a)].
% 6.91/7.24 1023 para(c5,c1,c5,c1). [resolve(948,a,115,a)].
% 6.91/7.24 1049 eqangle(c4,c2,A,B,c2,c4,A,B). [resolve(978,a,150,a)].
% 6.91/7.24 1052 para(c4,c2,c4,c2). [resolve(978,a,115,a)].
% 6.91/7.24 1068 -midp(A,c5,c5) | midp(A,c1,c1). [resolve(1023,a,313,b)].
% 6.91/7.24 1077 eqangle(c5,c1,A,B,c5,c1,A,B). [resolve(1023,a,150,a)].
% 6.91/7.24 1080 -midp(A,c4,c4) | midp(A,c2,c2). [resolve(1052,a,313,b)].
% 6.91/7.24 1163 para(c1,c4,c1,c4). [resolve(423,a,421,a)].
% 6.91/7.24 1238 -midp(A,c1,c1) | midp(A,c4,c4). [resolve(1163,a,313,b)].
% 6.91/7.24 3459 eqangle(A,B,c2,c4,A,B,c2,c4). [resolve(919,a,129,a)].
% 6.91/7.24 3695 eqratio(c5,c1,c1,c1,c5,c5,c5,c5). [resolve(930,b,632,a),unit_del(a,816)].
% 6.91/7.24 3696 midp(c5,c5,c5) | -cong(c1,c1,c1,c5). [resolve(932,a,337,b),unit_del(a,632)].
% 6.91/7.24 3698 -cyclic(c5,c5,c1,c5) | -cyclic(c5,c5,c1,c1) | cong(c5,c5,c5,c5). [resolve(932,a,305,c)].
% 6.91/7.24 3707 -coll(c1,c1,A) | cyclic(c5,A,c1,c1). [resolve(932,a,153,a)].
% 6.91/7.24 3708 eqangle(c1,c5,c1,c5,A,B,A,B). [resolve(932,a,131,a)].
% 6.91/7.24 3922 -eqangle(A,B,C,D,c2,c4,E,F) | eqangle(A,B,C,D,c4,c2,E,F). [resolve(975,a,132,b)].
% 6.91/7.24 4165 eqangle(c4,c2,c2,c4,A,B,A,B). [resolve(1049,a,131,a)].
% 6.91/7.24 4260 -coll(c5,c5,A) | cyclic(c1,A,c5,c5). [resolve(1077,a,153,a)].
% 6.91/7.24 16288 para(A,B,A,B). [resolve(3459,a,149,a)].
% 6.91/7.24 16444 -midp(A,B,B) | midp(A,C,C). [resolve(16288,a,313,b)].
% 6.91/7.24 16445 coll(A,B,B). [resolve(16288,a,172,a)].
% 6.91/7.24 16579 coll(A,A,B). [resolve(16445,a,299,a)].
% 6.91/7.24 16772 cyclic(c1,A,c5,c5). [back_unit_del(4260),unit_del(a,16579)].
% 6.91/7.24 16773 cyclic(c5,A,c1,c1). [back_unit_del(3707),unit_del(a,16579)].
% 6.91/7.24 16927 -cyclic(c5,c5,c1,c5) | cong(c5,c5,c5,c5). [back_unit_del(3698),unit_del(b,16773)].
% 6.91/7.24 17850 cyclic(A,c1,c5,c5). [resolve(16772,a,126,a)].
% 6.91/7.24 18892 cyclic(A,c5,c1,c5). [resolve(17850,a,125,a)].
% 6.91/7.24 18893 cong(c5,c5,c5,c5). [back_unit_del(16927),unit_del(a,18892)].
% 6.91/7.24 20675 cong(c5,c1,c1,c1). [resolve(3695,a,180,a),unit_del(a,18893)].
% 6.91/7.24 20863 cong(c1,c1,c5,c1). [resolve(20675,a,134,a)].
% 6.91/7.24 20915 cong(c1,c1,c1,c5). [resolve(20863,a,133,a)].
% 6.91/7.24 20916 midp(c5,c5,c5). [back_unit_del(3696),unit_del(b,20915)].
% 6.91/7.24 20917 midp(c5,c1,c1). [resolve(20916,a,1068,a)].
% 7.00/7.24 20932 midp(c5,c4,c4). [resolve(20917,a,1238,a)].
% 7.00/7.24 20949 midp(c5,c2,c2). [resolve(20932,a,1080,a)].
% 7.00/7.24 21297 midp(c5,A,A). [resolve(16444,a,20949,a)].
% 7.00/7.24 21310 cong(c5,A,c5,A). [resolve(21297,a,174,a)].
% 7.00/7.24 21394 perp(c5,c5,A,B). [resolve(21310,a,162,b),unit_del(a,21310)].
% 7.00/7.24 21883 -perp(A,B,c5,c5) | para(A,B,C,D). [resolve(21394,a,120,b)].
% 7.00/7.24 21884 perp(A,B,c5,c5). [resolve(21394,a,119,a)].
% 7.00/7.24 21885 para(A,B,C,D). [back_unit_del(21883),unit_del(a,21884)].
% 7.00/7.24 21926 eqangle(A,B,C,D,E,F,C,D). [back_unit_del(150),unit_del(a,21885)].
% 7.00/7.24 22150 eqangle(c1,c5,c1,c5,c4,c2,c2,c4). [resolve(3922,a,3708,a)].
% 7.00/7.24 23765 -eqangle(A,B,A,B,C,D,E,F) | eqangle(c4,c2,c2,c4,C,D,E,F). [resolve(4165,a,132,a)].
% 7.00/7.24 26881 eqangle(A,B,C,D,E,F,E,F). [resolve(21926,a,131,a)].
% 7.00/7.24 26927 eqangle(A,B,C,D,c4,c2,c2,c4). [resolve(22150,a,132,b),unit_del(a,26881)].
% 7.00/7.24 29536 eqangle(A,B,A,B,C,D,E,F). [resolve(26881,a,130,a)].
% 7.00/7.24 29541 eqangle(c4,c2,c2,c4,A,B,C,D). [back_unit_del(23765),unit_del(a,29536)].
% 7.00/7.24 29575 eqangle(A,B,C,D,E,F,V6,V7). [resolve(26927,a,132,a),unit_del(a,29541)].
% 7.00/7.24 29576 $F. [resolve(29575,a,218,a)].
% 7.00/7.24
% 7.00/7.24 % SZS output end Refutation
% 7.00/7.24 ============================== end of proof ==========================
% 7.00/7.24
% 7.00/7.24 ============================== STATISTICS ============================
% 7.00/7.24
% 7.00/7.24 Given=10932. Generated=116929. Kept=29444. proofs=1.
% 7.00/7.24 Usable=8533. Sos=5716. Demods=0. Limbo=0, Disabled=15378. Hints=0.
% 7.00/7.24 Megabytes=18.92.
% 7.00/7.24 User_CPU=6.02, System_CPU=0.08, Wall_clock=6.
% 7.00/7.24
% 7.00/7.24 ============================== end of statistics =====================
% 7.00/7.24
% 7.00/7.24 ============================== end of search =========================
% 7.00/7.24
% 7.00/7.24 THEOREM PROVED
% 7.00/7.24 % SZS status Theorem
% 7.00/7.24
% 7.00/7.24 Exiting with 1 proof.
% 7.00/7.24
% 7.00/7.24 Process 25648 exit (max_proofs) Sat Jun 18 17:12:14 2022
% 7.00/7.24 Prover9 interrupted
%------------------------------------------------------------------------------