TSTP Solution File: GEO582+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GEO582+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 05:57:04 EDT 2022
% Result : Theorem 3.84s 4.09s
% Output : Refutation 3.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO582+1 : TPTP v8.1.0. Released v7.5.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n005.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 03:00:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.82/1.10 ============================== Prover9 ===============================
% 0.82/1.10 Prover9 (32) version 2009-11A, November 2009.
% 0.82/1.10 Process 15752 was started by sandbox on n005.cluster.edu,
% 0.82/1.10 Sat Jun 18 03:00:09 2022
% 0.82/1.10 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_15599_n005.cluster.edu".
% 0.82/1.10 ============================== end of head ===========================
% 0.82/1.10
% 0.82/1.10 ============================== INPUT =================================
% 0.82/1.10
% 0.82/1.10 % Reading from file /tmp/Prover9_15599_n005.cluster.edu
% 0.82/1.10
% 0.82/1.10 set(prolog_style_variables).
% 0.82/1.10 set(auto2).
% 0.82/1.10 % set(auto2) -> set(auto).
% 0.82/1.10 % set(auto) -> set(auto_inference).
% 0.82/1.10 % set(auto) -> set(auto_setup).
% 0.82/1.10 % set(auto_setup) -> set(predicate_elim).
% 0.82/1.10 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.82/1.10 % set(auto) -> set(auto_limits).
% 0.82/1.10 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.82/1.10 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.82/1.10 % set(auto) -> set(auto_denials).
% 0.82/1.10 % set(auto) -> set(auto_process).
% 0.82/1.10 % set(auto2) -> assign(new_constants, 1).
% 0.82/1.10 % set(auto2) -> assign(fold_denial_max, 3).
% 0.82/1.10 % set(auto2) -> assign(max_weight, "200.000").
% 0.82/1.10 % set(auto2) -> assign(max_hours, 1).
% 0.82/1.10 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.82/1.10 % set(auto2) -> assign(max_seconds, 0).
% 0.82/1.10 % set(auto2) -> assign(max_minutes, 5).
% 0.82/1.10 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.82/1.10 % set(auto2) -> set(sort_initial_sos).
% 0.82/1.10 % set(auto2) -> assign(sos_limit, -1).
% 0.82/1.10 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.82/1.10 % set(auto2) -> assign(max_megs, 400).
% 0.82/1.10 % set(auto2) -> assign(stats, some).
% 0.82/1.10 % set(auto2) -> clear(echo_input).
% 0.82/1.10 % set(auto2) -> set(quiet).
% 0.82/1.10 % set(auto2) -> clear(print_initial_clauses).
% 0.82/1.10 % set(auto2) -> clear(print_given).
% 0.82/1.10 assign(lrs_ticks,-1).
% 0.82/1.10 assign(sos_limit,10000).
% 0.82/1.10 assign(order,kbo).
% 0.82/1.10 set(lex_order_vars).
% 0.82/1.10 clear(print_given).
% 0.82/1.10
% 0.82/1.10 % formulas(sos). % not echoed (95 formulas)
% 0.82/1.10
% 0.82/1.10 ============================== end of input ==========================
% 0.82/1.10
% 0.82/1.10 % From the command line: assign(max_seconds, 300).
% 0.82/1.10
% 0.82/1.10 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.82/1.10
% 0.82/1.10 % Formulas that are not ordinary clauses:
% 0.82/1.10 1 (all A all B all C (coll(A,B,C) -> coll(A,C,B))) # label(ruleD1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.10 2 (all A all B all C (coll(A,B,C) -> coll(B,A,C))) # label(ruleD2) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 11 (all A all B all M (midp(M,B,A) -> midp(M,A,B))) # label(ruleD11) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 67 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.10 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].
% 0.82/1.10 69 (all A all B all C (midp(A,B,C) -> cong(A,B,A,C))) # label(ruleD68) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.10 70 (all A all B all C (midp(A,B,C) -> coll(A,B,C))) # label(ruleD69) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 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].
% 0.82/1.10 95 -(all A all B all C all O all D all A1 all C1 all NWPNT1 (circle(O,A,B,C) & circle(O,A,D,NWPNT1) & perp(A,B,A,A1) & coll(A1,C,D) & perp(C,D,C,C1) & coll(C1,A,B) -> para(D,B,A1,C1))) # label(exemplo6GDDFULL416044) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.82/1.10
% 0.82/1.10 ============================== end of process non-clausal formulas ===
% 0.82/1.10
% 0.82/1.10 ============================== PROCESS INITIAL CLAUSES ===============
% 0.82/1.10
% 0.82/1.10 ============================== PREDICATE ELIMINATION =================
% 0.82/1.10 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)].
% 0.82/1.10 97 -cong(A,B,A,C) | -cong(A,B,A,D) | circle(A,B,C,D) # label(ruleD12) # label(axiom). [clausify(12)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 100 -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)].
% 0.82/1.10 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)].
% 0.82/1.10 101 -circle(A,B,C,D) | -coll(A,B,D) | perp(B,C,C,D) # label(ruleD53) # label(axiom). [clausify(54)].
% 0.82/1.10 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)].
% 0.82/1.10 102 -circle(A,B,C,D) | perp(f12(B,C,D,A),B,B,A) # label(ruleX11) # label(axiom). [clausify(87)].
% 0.82/1.10 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)].
% 0.82/1.10 103 -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)].
% 0.82/1.10 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)].
% 0.82/1.10 104 -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)].
% 0.82/1.10 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)].
% 0.82/1.10 105 -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)].
% 0.82/1.10 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)].
% 0.82/1.10 106 -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)].
% 0.82/1.10 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)].
% 0.82/1.10 107 -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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 108 -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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 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)].
% 0.82/1.10 109 circle(c4,c1,c2,c3) # label(exemplo6GDDFULL416044) # label(negated_conjecture). [clausify(95)].
% 0.82/1.10 Derived: -perp(c4,c1,c1,A) | eqangle(c1,A,c1,c2,c3,c1,c3,c2). [resolve(109,a,96,a)].
% 0.82/1.10 Derived: -eqangle(c1,A,c1,c2,c3,c1,c3,c2) | perp(c4,c1,c1,A). [resolve(109,a,98,a)].
% 0.82/1.10 Derived: -midp(A,c2,c3) | eqangle(c1,c2,c1,c3,c4,c2,c4,A). [resolve(109,a,99,a)].
% 0.82/1.10 Derived: -coll(A,c2,c3) | -eqangle(c1,c2,c1,c3,c4,c2,c4,A) | midp(A,c2,c3). [resolve(109,a,100,a)].
% 0.82/1.10 Derived: -coll(c4,c1,c3) | perp(c1,c2,c2,c3). [resolve(109,a,101,a)].
% 0.82/1.10 Derived: perp(f12(c1,c2,c3,c4),c1,c1,c4). [resolve(109,a,102,a)].
% 0.82/1.10 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)].
% 3.84/4.09 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)].
% 3.84/4.09 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)].
% 3.84/4.09 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)].
% 3.84/4.09 110 circle(c4,c1,c5,c8) # label(exemplo6GDDFULL416044) # label(negated_conjecture). [clausify(95)].
% 3.84/4.09 Derived: -perp(c4,c1,c1,A) | eqangle(c1,A,c1,c5,c8,c1,c8,c5). [resolve(110,a,96,a)].
% 3.84/4.09 Derived: -eqangle(c1,A,c1,c5,c8,c1,c8,c5) | perp(c4,c1,c1,A). [resolve(110,a,98,a)].
% 3.84/4.09 Derived: -midp(A,c5,c8) | eqangle(c1,c5,c1,c8,c4,c5,c4,A). [resolve(110,a,99,a)].
% 3.84/4.09 Derived: -coll(A,c5,c8) | -eqangle(c1,c5,c1,c8,c4,c5,c4,A) | midp(A,c5,c8). [resolve(110,a,100,a)].
% 3.84/4.09 Derived: -coll(c4,c1,c8) | perp(c1,c5,c5,c8). [resolve(110,a,101,a)].
% 3.84/4.09 Derived: perp(f12(c1,c5,c8,c4),c1,c1,c4). [resolve(110,a,102,a)].
% 3.84/4.09 Derived: -cong(c4,c1,c4,A) | -cong(B,c1,B,c5) | B = c4 | coll(f13(c1,c5,c8,A,c4,B),c1,c8). [resolve(110,a,103,a)].
% 3.84/4.09 Derived: -cong(c4,c1,c4,A) | -cong(B,c1,B,c5) | B = c4 | cong(f13(c1,c5,c8,A,c4,B),B,B,c1). [resolve(110,a,104,a)].
% 3.84/4.09 Derived: -cong(c4,c1,c4,A) | -cong(B,c1,B,c5) | B = c4 | coll(f14(c1,c5,c8,A,c4,B),c5,A). [resolve(110,a,105,a)].
% 3.84/4.09 Derived: -cong(c4,c1,c4,A) | -cong(B,c1,B,c5) | B = c4 | cong(f14(c1,c5,c8,A,c4,B),B,B,c1). [resolve(110,a,106,a)].
% 3.84/4.09
% 3.84/4.09 ============================== end predicate elimination =============
% 3.84/4.09
% 3.84/4.09 Auto_denials: (non-Horn, no changes).
% 3.84/4.09
% 3.84/4.09 Term ordering decisions:
% 3.84/4.09 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.
% 3.84/4.09
% 3.84/4.09 ============================== end of process initial clauses ========
% 3.84/4.09
% 3.84/4.09 ============================== CLAUSES FOR SEARCH ====================
% 3.84/4.09
% 3.84/4.09 ============================== end of clauses for search =============
% 3.84/4.09
% 3.84/4.09 ============================== SEARCH ================================
% 3.84/4.09
% 3.84/4.09 % Starting search at 0.04 seconds.
% 3.84/4.09
% 3.84/4.09 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 2147483647 (0.00 of 0.11 sec).
% 3.84/4.09
% 3.84/4.09 Low Water (keep): wt=26.000, iters=3393
% 3.84/4.09
% 3.84/4.09 Low Water (keep): wt=22.000, iters=3355
% 3.84/4.09
% 3.84/4.09 Low Water (keep): wt=21.000, iters=3333
% 3.84/4.09
% 3.84/4.09 Low Water (keep): wt=18.000, iters=3341
% 3.84/4.09
% 3.84/4.09 Low Water (keep): wt=17.000, iters=3336
% 3.84/4.09
% 3.84/4.09 Low Water (keep): wt=16.000, iters=3337
% 3.84/4.09
% 3.84/4.09 Low Water (keep): wt=14.000, iters=3506
% 3.84/4.09
% 3.84/4.09 Low Water (keep): wt=13.000, iters=3365
% 3.84/4.09
% 3.84/4.09 Low Water (keep): wt=12.000, iters=3333
% 3.84/4.09
% 3.84/4.09 ============================== PROOF =================================
% 3.84/4.09 % SZS status Theorem
% 3.84/4.09 % SZS output start Refutation
% 3.84/4.09
% 3.84/4.09 % Proof 1 at 2.96 (+ 0.05) seconds.
% 3.84/4.09 % Length of proof is 108.
% 3.84/4.09 % Level of proof is 23.
% 3.84/4.09 % Maximum clause weight is 29.000.
% 3.84/4.09 % Given clauses 6466.
% 3.84/4.09
% 3.84/4.09 2 (all A all B all C (coll(A,B,C) -> coll(B,A,C))) # label(ruleD2) # label(axiom) # label(non_clause). [assumption].
% 3.84/4.09 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].
% 3.84/4.09 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].
% 3.84/4.09 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].
% 3.84/4.09 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].
% 3.84/4.09 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].
% 3.84/4.09 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].
% 3.84/4.09 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].
% 3.84/4.09 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].
% 3.84/4.09 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].
% 3.84/4.09 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].
% 3.84/4.09 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].
% 3.84/4.09 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].
% 3.84/4.09 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].
% 3.84/4.09 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].
% 3.84/4.09 40 (all A all B all C all D all P all Q (para(A,B,C,D) -> eqangle(A,B,P,Q,C,D,P,Q))) # label(ruleD40) # label(axiom) # label(non_clause). [assumption].
% 3.84/4.09 43 (all A all B all P all Q (eqangle(P,A,P,B,Q,A,Q,B) & coll(P,Q,B) -> cyclic(A,B,P,Q))) # label(ruleD42b) # label(axiom) # label(non_clause). [assumption].
% 3.84/4.09 44 (all A all B all C all P all Q all R (cyclic(A,B,C,P) & cyclic(A,B,C,Q) & cyclic(A,B,C,R) & eqangle(C,A,C,B,R,P,R,Q) -> cong(A,B,P,Q))) # label(ruleD43) # label(axiom) # label(non_clause). [assumption].
% 3.84/4.09 57 (all A all B all P all Q (cong(A,P,B,P) & cong(A,Q,B,Q) -> perp(A,B,P,Q))) # label(ruleD56) # label(axiom) # label(non_clause). [assumption].
% 3.84/4.09 67 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption].
% 3.84/4.09 95 -(all A all B all C all O all D all A1 all C1 all NWPNT1 (circle(O,A,B,C) & circle(O,A,D,NWPNT1) & perp(A,B,A,A1) & coll(A1,C,D) & perp(C,D,C,C1) & coll(C1,A,B) -> para(D,B,A1,C1))) # label(exemplo6GDDFULL416044) # label(negated_conjecture) # label(non_clause). [assumption].
% 3.84/4.09 112 -coll(A,B,C) | coll(B,A,C) # label(ruleD2) # label(axiom). [clausify(2)].
% 3.84/4.09 113 -coll(A,B,C) | -coll(A,B,D) | coll(C,D,A) # label(ruleD3) # label(axiom). [clausify(3)].
% 3.84/4.09 114 -para(A,B,C,D) | para(A,B,D,C) # label(ruleD4) # label(axiom). [clausify(4)].
% 3.84/4.09 117 -perp(A,B,C,D) | perp(A,B,D,C) # label(ruleD7) # label(axiom). [clausify(7)].
% 3.84/4.09 118 -perp(A,B,C,D) | perp(C,D,A,B) # label(ruleD8) # label(axiom). [clausify(8)].
% 3.84/4.09 119 -perp(A,B,C,D) | -perp(C,D,E,F) | para(A,B,E,F) # label(ruleD9) # label(axiom). [clausify(9)].
% 3.84/4.09 123 -cyclic(A,B,C,D) | cyclic(A,B,D,C) # label(ruleD14) # label(axiom). [clausify(14)].
% 3.84/4.09 124 -cyclic(A,B,C,D) | cyclic(A,C,B,D) # label(ruleD15) # label(axiom). [clausify(15)].
% 3.84/4.09 125 -cyclic(A,B,C,D) | cyclic(B,A,C,D) # label(ruleD16) # label(axiom). [clausify(16)].
% 3.84/4.09 126 -cyclic(A,B,C,D) | -cyclic(A,B,C,E) | cyclic(B,C,D,E) # label(ruleD17) # label(axiom). [clausify(17)].
% 3.84/4.09 128 -eqangle(A,B,C,D,E,F,V6,V7) | eqangle(C,D,A,B,V6,V7,E,F) # label(ruleD19) # label(axiom). [clausify(19)].
% 3.84/4.09 130 -eqangle(A,B,C,D,E,F,V6,V7) | eqangle(A,B,E,F,C,D,V6,V7) # label(ruleD21) # label(axiom). [clausify(21)].
% 3.84/4.09 132 -cong(A,B,C,D) | cong(A,B,D,C) # label(ruleD23) # label(axiom). [clausify(23)].
% 3.84/4.09 133 -cong(A,B,C,D) | cong(C,D,A,B) # label(ruleD24) # label(axiom). [clausify(24)].
% 3.84/4.09 148 -eqangle(A,B,C,D,E,F,C,D) | para(A,B,E,F) # label(ruleD39) # label(axiom). [clausify(39)].
% 3.84/4.09 149 -para(A,B,C,D) | eqangle(A,B,E,F,C,D,E,F) # label(ruleD40) # label(axiom). [clausify(40)].
% 3.84/4.09 152 -eqangle(A,B,A,C,D,B,D,C) | -coll(A,D,C) | cyclic(B,C,A,D) # label(ruleD42b) # label(axiom). [clausify(43)].
% 3.84/4.09 153 -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)].
% 3.84/4.09 161 -cong(A,B,C,B) | -cong(A,D,C,D) | perp(A,C,B,D) # label(ruleD56) # label(axiom). [clausify(57)].
% 3.84/4.09 171 -para(A,B,A,C) | coll(A,B,C) # label(ruleD66) # label(axiom). [clausify(67)].
% 3.84/4.09 210 perp(c1,c2,c1,c6) # label(exemplo6GDDFULL416044) # label(negated_conjecture). [clausify(95)].
% 3.84/4.09 213 coll(c7,c1,c2) # label(exemplo6GDDFULL416044) # label(negated_conjecture). [clausify(95)].
% 3.84/4.09 214 -para(c5,c2,c6,c7) # label(exemplo6GDDFULL416044) # label(negated_conjecture). [clausify(95)].
% 3.84/4.09 281 -coll(A,B,C) | coll(C,C,A). [factor(113,a,b)].
% 3.84/4.09 353 -perp(A,B,c1,c2) | para(A,B,c1,c6). [resolve(210,a,119,b)].
% 3.84/4.09 354 -perp(c1,c6,A,B) | para(c1,c2,A,B). [resolve(210,a,119,a)].
% 3.84/4.09 355 perp(c1,c6,c1,c2). [resolve(210,a,118,a)].
% 3.84/4.09 356 perp(c1,c2,c6,c1). [resolve(210,a,117,a)].
% 3.84/4.09 376 coll(c1,c7,c2). [resolve(213,a,112,a)].
% 3.84/4.09 438 coll(c2,c2,c1). [resolve(376,a,281,a)].
% 3.84/4.09 482 coll(c1,c1,c2). [resolve(438,a,281,a)].
% 3.84/4.09 484 -coll(c2,c2,A) | coll(c1,A,c2). [resolve(438,a,113,a)].
% 3.84/4.09 600 para(c1,c2,c1,c2). [resolve(355,a,354,a)].
% 3.84/4.09 601 para(c1,c6,c1,c6). [resolve(355,a,353,a)].
% 3.84/4.09 633 perp(c6,c1,c1,c2). [resolve(356,a,118,a)].
% 3.84/4.09 679 eqangle(c1,c2,A,B,c1,c2,A,B). [resolve(600,a,149,a)].
% 3.84/4.09 690 coll(c1,c6,c6). [resolve(601,a,171,a)].
% 3.84/4.09 693 eqangle(c1,c6,A,B,c1,c6,A,B). [resolve(601,a,149,a)].
% 3.84/4.09 695 coll(c6,c6,c1). [resolve(690,a,281,a)].
% 3.84/4.09 701 coll(c1,c1,c6). [resolve(695,a,281,a)].
% 3.84/4.09 728 para(c6,c1,c1,c6). [resolve(633,a,353,a)].
% 3.84/4.09 876 para(c6,c1,c6,c1). [resolve(728,a,114,a)].
% 3.84/4.09 964 eqangle(c6,c1,A,B,c6,c1,A,B). [resolve(876,a,149,a)].
% 3.84/4.09 2595 -coll(c1,c1,A) | cyclic(c2,A,c1,c1). [resolve(679,a,152,a)].
% 3.84/4.09 2596 eqangle(c1,c2,c1,c2,A,B,A,B). [resolve(679,a,130,a)].
% 3.84/4.09 2597 eqangle(A,B,c1,c2,A,B,c1,c2). [resolve(679,a,128,a)].
% 3.84/4.09 2685 -coll(c1,c1,A) | cyclic(c6,A,c1,c1). [resolve(693,a,152,a)].
% 3.84/4.09 2687 eqangle(A,B,c1,c6,A,B,c1,c6). [resolve(693,a,128,a)].
% 3.84/4.09 6903 -coll(c6,c6,A) | cyclic(c1,A,c6,c6). [resolve(964,a,152,a)].
% 3.84/4.09 14815 cyclic(c2,c6,c1,c1). [resolve(2595,a,701,a)].
% 3.84/4.09 14819 cyclic(c2,c2,c1,c1). [resolve(2595,a,482,a)].
% 3.84/4.09 14847 cyclic(c2,c1,c6,c1). [resolve(14815,a,124,a)].
% 3.84/4.09 14852 -coll(c1,A,c2) | cyclic(c2,c2,c1,A). [resolve(2596,a,152,a)].
% 3.84/4.09 14861 -cyclic(c2,c2,c1,A) | cyclic(c2,c1,A,c1). [resolve(14819,a,126,b)].
% 3.84/4.09 14862 -cyclic(c2,c2,c1,A) | cyclic(c2,c1,c1,A). [resolve(14819,a,126,a)].
% 3.84/4.09 14877 para(A,B,A,B). [resolve(2597,a,148,a)].
% 3.84/4.09 14942 cyclic(c2,c1,c1,c6). [resolve(14847,a,123,a)].
% 3.84/4.09 14996 coll(A,B,B). [resolve(14877,a,171,a)].
% 3.84/4.09 15084 coll(A,A,B). [resolve(14996,a,281,a)].
% 3.84/4.09 15289 cyclic(c1,A,c6,c6). [back_unit_del(6903),unit_del(a,15084)].
% 3.84/4.09 15368 cyclic(c6,A,c1,c1). [back_unit_del(2685),unit_del(a,15084)].
% 3.84/4.09 15453 coll(c1,A,c2). [back_unit_del(484),unit_del(a,15084)].
% 3.84/4.09 15661 cyclic(c2,c2,c1,A). [back_unit_del(14852),unit_del(a,15453)].
% 3.84/4.09 15682 cyclic(c2,c1,c1,A). [back_unit_del(14862),unit_del(a,15661)].
% 3.84/4.09 15683 cyclic(c2,c1,A,c1). [back_unit_del(14861),unit_del(a,15661)].
% 3.84/4.09 15994 -cyclic(A,c6,c1,A) | -cyclic(A,c6,c1,c6) | -cyclic(A,c6,c1,c1) | cong(A,c6,A,c6). [resolve(2687,a,153,d)].
% 3.84/4.09 16041 cyclic(c1,c1,A,c6). [resolve(14942,a,126,b),unit_del(a,15682)].
% 3.84/4.09 16445 -cyclic(c1,A,c6,B) | cyclic(A,c6,B,c6). [resolve(15289,a,126,b)].
% 3.84/4.09 16473 cyclic(A,c6,c1,c1). [resolve(15368,a,125,a)].
% 3.84/4.09 16475 -cyclic(A,c6,c1,A) | -cyclic(A,c6,c1,c6) | cong(A,c6,A,c6). [back_unit_del(15994),unit_del(c,16473)].
% 3.84/4.09 16585 cyclic(c2,c1,A,B). [resolve(15661,a,126,b),unit_del(a,15661)].
% 3.84/4.09 16615 cyclic(c1,c1,A,B). [resolve(15682,a,126,b),unit_del(a,16585)].
% 3.84/4.09 16629 cyclic(c1,A,B,c1). [resolve(15683,a,126,b),unit_del(a,16585)].
% 3.84/4.09 17062 cyclic(c1,A,c6,B). [resolve(16041,a,126,a),unit_del(a,16615)].
% 3.84/4.09 17064 cyclic(A,c6,B,c6). [back_unit_del(16445),unit_del(a,17062)].
% 3.84/4.09 17067 -cyclic(A,c6,c1,A) | cong(A,c6,A,c6). [back_unit_del(16475),unit_del(b,17064)].
% 3.84/4.09 17763 cyclic(c1,A,B,C). [resolve(16585,a,126,b),unit_del(a,16585)].
% 3.84/4.09 17881 cyclic(A,B,c1,C). [resolve(16629,a,126,a),unit_del(a,17763)].
% 3.84/4.09 17882 cong(A,c6,A,c6). [back_unit_del(17067),unit_del(a,17881)].
% 3.84/4.09 19028 cong(A,c6,c6,A). [resolve(17882,a,132,a)].
% 3.84/4.09 19452 cong(c6,A,A,c6). [resolve(19028,a,133,a)].
% 3.84/4.09 19638 cong(c6,A,c6,A). [resolve(19452,a,132,a)].
% 3.84/4.09 19760 perp(c6,c6,A,B). [resolve(19638,a,161,b),unit_del(a,19638)].
% 3.84/4.09 20048 -perp(A,B,c6,c6) | para(A,B,C,D). [resolve(19760,a,119,b)].
% 3.84/4.09 20049 perp(A,B,c6,c6). [resolve(19760,a,118,a)].
% 3.84/4.09 20050 para(A,B,C,D). [back_unit_del(20048),unit_del(a,20049)].
% 3.84/4.09 20051 $F. [resolve(20050,a,214,a)].
% 3.84/4.09
% 3.84/4.09 % SZS output end Refutation
% 3.84/4.09 ============================== end of proof ==========================
% 3.84/4.09
% 3.84/4.09 ============================== STATISTICS ============================
% 3.84/4.09
% 3.84/4.09 Given=6466. Generated=73954. Kept=19924. proofs=1.
% 3.84/4.09 Usable=5268. Sos=6886. Demods=0. Limbo=1, Disabled=7938. Hints=0.
% 3.84/4.09 Megabytes=13.46.
% 3.84/4.09 User_CPU=2.96, System_CPU=0.05, Wall_clock=3.
% 3.84/4.09
% 3.84/4.09 ============================== end of statistics =====================
% 3.84/4.09
% 3.84/4.09 ============================== end of search =========================
% 3.84/4.09
% 3.84/4.09 THEOREM PROVED
% 3.84/4.09 % SZS status Theorem
% 3.84/4.09
% 3.84/4.09 Exiting with 1 proof.
% 3.84/4.09
% 3.84/4.09 Process 15752 exit (max_proofs) Sat Jun 18 03:00:12 2022
% 3.84/4.09 Prover9 interrupted
%------------------------------------------------------------------------------