TSTP Solution File: GEO612+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GEO612+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 05:57:13 EDT 2022
% Result : Theorem 4.15s 4.45s
% Output : Refutation 4.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO612+1 : TPTP v8.1.0. Released v7.5.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jun 17 19:01:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.83/1.10 ============================== Prover9 ===============================
% 0.83/1.10 Prover9 (32) version 2009-11A, November 2009.
% 0.83/1.10 Process 15488 was started by sandbox on n016.cluster.edu,
% 0.83/1.10 Fri Jun 17 19:01:51 2022
% 0.83/1.10 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_15335_n016.cluster.edu".
% 0.83/1.10 ============================== end of head ===========================
% 0.83/1.10
% 0.83/1.10 ============================== INPUT =================================
% 0.83/1.10
% 0.83/1.10 % Reading from file /tmp/Prover9_15335_n016.cluster.edu
% 0.83/1.10
% 0.83/1.10 set(prolog_style_variables).
% 0.83/1.10 set(auto2).
% 0.83/1.10 % set(auto2) -> set(auto).
% 0.83/1.10 % set(auto) -> set(auto_inference).
% 0.83/1.10 % set(auto) -> set(auto_setup).
% 0.83/1.10 % set(auto_setup) -> set(predicate_elim).
% 0.83/1.10 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.83/1.10 % set(auto) -> set(auto_limits).
% 0.83/1.10 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.83/1.10 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.83/1.10 % set(auto) -> set(auto_denials).
% 0.83/1.10 % set(auto) -> set(auto_process).
% 0.83/1.10 % set(auto2) -> assign(new_constants, 1).
% 0.83/1.10 % set(auto2) -> assign(fold_denial_max, 3).
% 0.83/1.10 % set(auto2) -> assign(max_weight, "200.000").
% 0.83/1.10 % set(auto2) -> assign(max_hours, 1).
% 0.83/1.10 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.83/1.10 % set(auto2) -> assign(max_seconds, 0).
% 0.83/1.10 % set(auto2) -> assign(max_minutes, 5).
% 0.83/1.10 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.83/1.10 % set(auto2) -> set(sort_initial_sos).
% 0.83/1.10 % set(auto2) -> assign(sos_limit, -1).
% 0.83/1.10 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.83/1.10 % set(auto2) -> assign(max_megs, 400).
% 0.83/1.10 % set(auto2) -> assign(stats, some).
% 0.83/1.10 % set(auto2) -> clear(echo_input).
% 0.83/1.10 % set(auto2) -> set(quiet).
% 0.83/1.10 % set(auto2) -> clear(print_initial_clauses).
% 0.83/1.10 % set(auto2) -> clear(print_given).
% 0.83/1.10 assign(lrs_ticks,-1).
% 0.83/1.10 assign(sos_limit,10000).
% 0.83/1.10 assign(order,kbo).
% 0.83/1.10 set(lex_order_vars).
% 0.83/1.10 clear(print_given).
% 0.83/1.10
% 0.83/1.10 % formulas(sos). % not echoed (95 formulas)
% 0.83/1.10
% 0.83/1.10 ============================== end of input ==========================
% 0.83/1.10
% 0.83/1.10 % From the command line: assign(max_seconds, 300).
% 0.83/1.10
% 0.83/1.10 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.83/1.10
% 0.83/1.10 % Formulas that are not ordinary clauses:
% 0.83/1.10 1 (all A all B all C (coll(A,B,C) -> coll(A,C,B))) # label(ruleD1) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 2 (all A all B all C (coll(A,B,C) -> coll(B,A,C))) # label(ruleD2) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 11 (all A all B all M (midp(M,B,A) -> midp(M,A,B))) # label(ruleD11) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 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].
% 0.83/1.10 40 (all A all B all C all D all P all Q (para(A,B,C,D) -> eqangle(A,B,P,Q,C,D,P,Q))) # label(ruleD40) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 41 (all A all B all P all Q (cyclic(A,B,P,Q) -> eqangle(P,A,P,B,Q,A,Q,B))) # label(ruleD41) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 42 (all A all B all P all Q (eqangle(P,A,P,B,Q,A,Q,B) & -coll(P,Q,A) -> cyclic(A,B,P,Q))) # label(ruleD42a) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 43 (all A all B all P all Q (eqangle(P,A,P,B,Q,A,Q,B) & coll(P,Q,B) -> cyclic(A,B,P,Q))) # label(ruleD42b) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 44 (all A all B all C all P all Q all R (cyclic(A,B,C,P) & cyclic(A,B,C,Q) & cyclic(A,B,C,R) & eqangle(C,A,C,B,R,P,R,Q) -> cong(A,B,P,Q))) # label(ruleD43) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 45 (all A all B all C all E all F (midp(E,A,B) & midp(F,A,C) -> para(E,F,B,C))) # label(ruleD44) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 46 (all A all B all C all E all F (midp(E,A,B) & para(E,F,B,C) & coll(F,A,C) -> midp(F,A,C))) # label(ruleD45) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 47 (all A all B all O (cong(O,A,O,B) -> eqangle(O,A,A,B,A,B,O,B))) # label(ruleD46) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 48 (all A all B all O (eqangle(O,A,A,B,A,B,O,B) & -coll(O,A,B) -> cong(O,A,O,B))) # label(ruleD47) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 49 (all A all B all C all O all X (circle(O,A,B,C) & perp(O,A,A,X) -> eqangle(A,X,A,B,C,A,C,B))) # label(ruleD48) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 50 (all A all B all C all O all X (circle(O,A,B,C) & eqangle(A,X,A,B,C,A,C,B) -> perp(O,A,A,X))) # label(ruleD49) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 51 (all A all B all C all O all M (circle(O,A,B,C) & midp(M,B,C) -> eqangle(A,B,A,C,O,B,O,M))) # label(ruleD50) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 52 (all A all B all C all O all M (circle(O,A,B,C) & coll(M,B,C) & eqangle(A,B,A,C,O,B,O,M) -> midp(M,B,C))) # label(ruleD51) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 53 (all A all B all C all M (perp(A,B,B,C) & midp(M,A,C) -> cong(A,M,B,M))) # label(ruleD52) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 54 (all A all B all C all O (circle(O,A,B,C) & coll(O,A,C) -> perp(A,B,B,C))) # label(ruleD53) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 55 (all A all B all C all D (cyclic(A,B,C,D) & para(A,B,C,D) -> eqangle(A,D,C,D,C,D,C,B))) # label(ruleD54) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 56 (all A all B all M all O (midp(M,A,B) & perp(O,M,A,B) -> cong(O,A,O,B))) # label(ruleD55) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 57 (all A all B all P all Q (cong(A,P,B,P) & cong(A,Q,B,Q) -> perp(A,B,P,Q))) # label(ruleD56) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 58 (all A all B all P all Q (cong(A,P,B,P) & cong(A,Q,B,Q) & cyclic(A,B,P,Q) -> perp(P,A,A,Q))) # label(ruleD57) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 59 (all A all B all C all P all Q all R (eqangle(A,B,B,C,P,Q,Q,R) & eqangle(A,C,B,C,P,R,Q,R) & -coll(A,B,C) -> simtri(A,B,C,P,Q,R))) # label(ruleD58) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 60 (all A all B all C all P all Q all R (simtri(A,B,C,P,Q,R) -> eqratio(A,B,A,C,P,Q,P,R))) # label(ruleD59) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 61 (all A all B all C all P all Q all R (simtri(A,B,C,P,Q,R) -> eqangle(A,B,B,C,P,Q,Q,R))) # label(ruleD60) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 62 (all A all B all C all P all Q all R (simtri(A,B,C,P,Q,R) & cong(A,B,P,Q) -> contri(A,B,C,P,Q,R))) # label(ruleD61) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 63 (all A all B all C all P all Q all R (contri(A,B,C,P,Q,R) -> cong(A,B,P,Q))) # label(ruleD62) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 64 (all A all B all C all D all M (midp(M,A,B) & midp(M,C,D) -> para(A,C,B,D))) # label(ruleD63) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 65 (all A all B all C all D all M (midp(M,A,B) & para(A,C,B,D) & para(A,D,B,C) -> midp(M,C,D))) # label(ruleD64) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 66 (all A all B all C all D all O (para(A,B,C,D) & coll(O,A,C) & coll(O,B,D) -> eqratio(O,A,A,C,O,B,B,D))) # label(ruleD65) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 67 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 68 (all A all B all C (cong(A,B,A,C) & coll(A,B,C) -> midp(A,B,C))) # label(ruleD67) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 69 (all A all B all C (midp(A,B,C) -> cong(A,B,A,C))) # label(ruleD68) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 70 (all A all B all C (midp(A,B,C) -> coll(A,B,C))) # label(ruleD69) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 71 (all A all B all C all D all M all N (midp(M,A,B) & midp(N,C,D) -> eqratio(M,A,A,B,N,C,C,D))) # label(ruleD70) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 72 (all A all B all C all D (eqangle(A,B,C,D,C,D,A,B) & -para(A,B,C,D) -> perp(A,B,C,D))) # label(ruleD71) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 73 (all A all B all C all D (eqangle(A,B,C,D,C,D,A,B) & -perp(A,B,C,D) -> para(A,B,C,D))) # label(ruleD72) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 74 (all A all B all C all D all P all Q all U all V (eqangle(A,B,C,D,P,Q,U,V) & para(P,Q,U,V) -> para(A,B,C,D))) # label(ruleD73) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 75 (all A all B all C all D all P all Q all U all V (eqangle(A,B,C,D,P,Q,U,V) & perp(P,Q,U,V) -> perp(A,B,C,D))) # label(ruleD74) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 76 (all A all B all C all D all P all Q all U all V (eqratio(A,B,C,D,P,Q,U,V) & cong(P,Q,U,V) -> cong(A,B,C,D))) # label(ruleD75) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 77 (all A all M all O all X exists B (perp(O,M,M,A) & eqangle(X,O,M,O,M,O,A,O) -> coll(B,A,M) & coll(B,O,X))) # label(ruleX1) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 78 (all A all B all O all X exists M (cong(O,A,O,B) & eqangle(A,O,O,X,O,X,O,B) -> coll(B,A,M) & coll(M,O,X))) # label(ruleX2) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 79 (all A all B all O all X exists M (perp(O,X,A,B) & eqangle(A,O,O,X,O,X,O,B) -> coll(B,A,M) & coll(M,O,X))) # label(ruleX3) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 80 (all A all B all O all X exists M (perp(O,X,A,B) & cong(O,A,O,B) -> coll(B,A,M) & coll(M,O,X))) # label(ruleX4) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 81 (all A all B all P all X all Y exists Q (eqangle(A,P,B,P,A,X,B,Y) & -coll(A,B,P) -> eqangle(A,P,B,P,A,Q,B,Q) & cyclic(X,B,P,Q))) # label(ruleX5) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 82 (all A all B all C all D all M all N exists P (midp(M,A,B) & midp(N,C,D) -> midp(P,A,D) & para(P,M,B,D) & para(P,N,A,C))) # label(ruleX6) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 83 (all A all B all C all D all M all N all Q exists P (midp(M,A,B) & midp(N,C,D) & coll(C,A,B) & coll(D,A,B) -> midp(P,A,Q))) # label(ruleX7) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 84 (all A all B all M all P all Q all R all M exists X (midp(M,A,B) & para(A,P,R,M) & para(A,P,B,Q) & coll(P,Q,R) -> coll(X,A,Q) & coll(X,M,R))) # label(ruleX8) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 85 (all A all B all C all D all O exists P (cong(O,C,O,D) & perp(A,B,B,O) -> cong(O,C,O,P) & para(P,C,A,B) & cong(B,C,B,P))) # label(ruleX9) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 86 (all A all B all C all H exists P exists Q (perp(A,H,B,C) & perp(B,H,A,C) -> coll(P,C,B) & perp(A,P,C,B) & coll(Q,C,A) & perp(B,Q,C,A))) # label(ruleX10) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 87 (all A all B all C all O exists P (circle(O,A,B,C) -> perp(P,A,A,O))) # label(ruleX11) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 88 (all A all B all C all D all M all N exists P exists Q (circle(M,A,B,C) & cong(M,A,M,D) & cong(N,A,N,B) & M != N -> coll(P,A,C) & cong(P,N,N,A) & coll(Q,B,D) & cong(Q,N,N,A))) # label(ruleX12) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 89 (all A all B all C all D all M exists O (cyclic(A,B,C,D) & para(A,B,C,D) & midp(M,A,B) -> circle(O,A,B,C))) # label(ruleX13) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.11 90 (all A all B all C all D exists O (perp(A,C,C,B) & cyclic(A,B,C,D) -> circle(O,A,B,C))) # label(ruleX14) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.11 91 (all A all B all C all E all F exists P (perp(A,C,C,B) & coll(B,E,F) -> coll(P,E,F) & perp(P,A,E,F))) # label(ruleX15) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.11 92 (all A all B all C all D all M exists P (perp(A,B,A,C) & perp(C,A,C,D) & midp(M,B,D) -> midp(P,A,C))) # label(ruleX16) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.11 93 (all A all B all O exists C (cong(O,A,O,B) & perp(A,O,O,B) -> coll(A,O,C) & cong(O,A,O,C))) # label(ruleX17) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.11 94 (all A all B all C all D all P all Q exists R (para(A,B,C,D) & coll(P,A,C) & coll(P,B,D) & coll(Q,A,B) -> coll(P,Q,R) & coll(R,C,D))) # label(ruleX18) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.11 95 -(all A all B all C all O all G all D all E all F all NWPNT1 (circle(O,A,B,C) & perp(G,C,A,B) & coll(G,A,B) & circle(O,C,D,NWPNT1) & coll(D,C,G) & perp(E,D,A,C) & coll(E,A,C) & perp(F,D,B,C) & coll(F,B,C) -> cyclic(A,E,F,B))) # label(exemplo6GDDFULL618074) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.83/1.11
% 0.83/1.11 ============================== end of process non-clausal formulas ===
% 0.83/1.11
% 0.83/1.11 ============================== PROCESS INITIAL CLAUSES ===============
% 0.83/1.11
% 0.83/1.11 ============================== PREDICATE ELIMINATION =================
% 0.83/1.11 96 -circle(A,B,C,D) | -perp(A,B,B,E) | eqangle(B,E,B,C,D,B,D,C) # label(ruleD48) # label(axiom). [clausify(49)].
% 0.83/1.11 97 -cong(A,B,A,C) | -cong(A,B,A,D) | circle(A,B,C,D) # label(ruleD12) # label(axiom). [clausify(12)].
% 0.83/1.11 Derived: -perp(A,B,B,C) | eqangle(B,C,B,D,E,B,E,D) | -cong(A,B,A,D) | -cong(A,B,A,E). [resolve(96,a,97,c)].
% 0.83/1.11 98 -circle(A,B,C,D) | -eqangle(B,E,B,C,D,B,D,C) | perp(A,B,B,E) # label(ruleD49) # label(axiom). [clausify(50)].
% 0.83/1.11 Derived: -eqangle(A,B,A,C,D,A,D,C) | perp(E,A,A,B) | -cong(E,A,E,C) | -cong(E,A,E,D). [resolve(98,a,97,c)].
% 0.83/1.11 99 -circle(A,B,C,D) | -midp(E,C,D) | eqangle(B,C,B,D,A,C,A,E) # label(ruleD50) # label(axiom). [clausify(51)].
% 0.83/1.11 Derived: -midp(A,B,C) | eqangle(D,B,D,C,E,B,E,A) | -cong(E,D,E,B) | -cong(E,D,E,C). [resolve(99,a,97,c)].
% 0.83/1.11 100 -circle(A,B,C,D) | -coll(E,C,D) | -eqangle(B,C,B,D,A,C,A,E) | midp(E,C,D) # label(ruleD51) # label(axiom). [clausify(52)].
% 0.83/1.11 Derived: -coll(A,B,C) | -eqangle(D,B,D,C,E,B,E,A) | midp(A,B,C) | -cong(E,D,E,B) | -cong(E,D,E,C). [resolve(100,a,97,c)].
% 0.83/1.11 101 -circle(A,B,C,D) | -coll(A,B,D) | perp(B,C,C,D) # label(ruleD53) # label(axiom). [clausify(54)].
% 0.83/1.11 Derived: -coll(A,B,C) | perp(B,D,D,C) | -cong(A,B,A,D) | -cong(A,B,A,C). [resolve(101,a,97,c)].
% 0.83/1.11 102 -circle(A,B,C,D) | perp(f12(B,C,D,A),B,B,A) # label(ruleX11) # label(axiom). [clausify(87)].
% 0.83/1.11 Derived: perp(f12(A,B,C,D),A,A,D) | -cong(D,A,D,B) | -cong(D,A,D,C). [resolve(102,a,97,c)].
% 0.83/1.11 103 -circle(A,B,C,D) | -cong(A,B,A,E) | -cong(F,B,F,C) | F = A | coll(f13(B,C,D,E,A,F),B,D) # label(ruleX12) # label(axiom). [clausify(88)].
% 0.83/1.11 Derived: -cong(A,B,A,C) | -cong(D,B,D,E) | D = A | coll(f13(B,E,F,C,A,D),B,F) | -cong(A,B,A,E) | -cong(A,B,A,F). [resolve(103,a,97,c)].
% 0.83/1.11 104 -circle(A,B,C,D) | -cong(A,B,A,E) | -cong(F,B,F,C) | F = A | cong(f13(B,C,D,E,A,F),F,F,B) # label(ruleX12) # label(axiom). [clausify(88)].
% 0.83/1.11 Derived: -cong(A,B,A,C) | -cong(D,B,D,E) | D = A | cong(f13(B,E,F,C,A,D),D,D,B) | -cong(A,B,A,E) | -cong(A,B,A,F). [resolve(104,a,97,c)].
% 0.83/1.11 105 -circle(A,B,C,D) | -cong(A,B,A,E) | -cong(F,B,F,C) | F = A | coll(f14(B,C,D,E,A,F),C,E) # label(ruleX12) # label(axiom). [clausify(88)].
% 0.83/1.11 Derived: -cong(A,B,A,C) | -cong(D,B,D,E) | D = A | coll(f14(B,E,F,C,A,D),E,C) | -cong(A,B,A,E) | -cong(A,B,A,F). [resolve(105,a,97,c)].
% 0.83/1.11 106 -circle(A,B,C,D) | -cong(A,B,A,E) | -cong(F,B,F,C) | F = A | cong(f14(B,C,D,E,A,F),F,F,B) # label(ruleX12) # label(axiom). [clausify(88)].
% 0.83/1.11 Derived: -cong(A,B,A,C) | -cong(D,B,D,E) | D = A | cong(f14(B,E,F,C,A,D),D,D,B) | -cong(A,B,A,E) | -cong(A,B,A,F). [resolve(106,a,97,c)].
% 0.83/1.11 107 -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | circle(f15(A,B,C,D,E),A,B,C) # label(ruleX13) # label(axiom). [clausify(89)].
% 0.83/1.11 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -perp(f15(A,B,C,D,E),A,A,F) | eqangle(A,F,A,B,C,A,C,B). [resolve(107,d,96,a)].
% 0.83/1.11 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -eqangle(A,F,A,B,C,A,C,B) | perp(f15(A,B,C,D,E),A,A,F). [resolve(107,d,98,a)].
% 0.83/1.11 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -midp(F,B,C) | eqangle(A,B,A,C,f15(A,B,C,D,E),B,f15(A,B,C,D,E),F). [resolve(107,d,99,a)].
% 0.83/1.11 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -coll(F,B,C) | -eqangle(A,B,A,C,f15(A,B,C,D,E),B,f15(A,B,C,D,E),F) | midp(F,B,C). [resolve(107,d,100,a)].
% 0.83/1.11 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -coll(f15(A,B,C,D,E),A,C) | perp(A,B,B,C). [resolve(107,d,101,a)].
% 0.83/1.11 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | perp(f12(A,B,C,f15(A,B,C,D,E)),A,A,f15(A,B,C,D,E)). [resolve(107,d,102,a)].
% 0.83/1.11 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -cong(f15(A,B,C,D,E),A,f15(A,B,C,D,E),F) | -cong(V6,A,V6,B) | V6 = f15(A,B,C,D,E) | coll(f13(A,B,C,F,f15(A,B,C,D,E),V6),A,C). [resolve(107,d,103,a)].
% 0.83/1.11 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -cong(f15(A,B,C,D,E),A,f15(A,B,C,D,E),F) | -cong(V6,A,V6,B) | V6 = f15(A,B,C,D,E) | cong(f13(A,B,C,F,f15(A,B,C,D,E),V6),V6,V6,A). [resolve(107,d,104,a)].
% 0.83/1.11 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -cong(f15(A,B,C,D,E),A,f15(A,B,C,D,E),F) | -cong(V6,A,V6,B) | V6 = f15(A,B,C,D,E) | coll(f14(A,B,C,F,f15(A,B,C,D,E),V6),B,F). [resolve(107,d,105,a)].
% 0.83/1.11 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -cong(f15(A,B,C,D,E),A,f15(A,B,C,D,E),F) | -cong(V6,A,V6,B) | V6 = f15(A,B,C,D,E) | cong(f14(A,B,C,F,f15(A,B,C,D,E),V6),V6,V6,A). [resolve(107,d,106,a)].
% 0.83/1.11 108 -perp(A,B,B,C) | -cyclic(A,C,B,D) | circle(f16(A,C,B,D),A,C,B) # label(ruleX14) # label(axiom). [clausify(90)].
% 0.83/1.11 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -perp(f16(A,C,B,D),A,A,E) | eqangle(A,E,A,C,B,A,B,C). [resolve(108,c,96,a)].
% 0.83/1.11 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -eqangle(A,E,A,C,B,A,B,C) | perp(f16(A,C,B,D),A,A,E). [resolve(108,c,98,a)].
% 0.83/1.11 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -midp(E,C,B) | eqangle(A,C,A,B,f16(A,C,B,D),C,f16(A,C,B,D),E). [resolve(108,c,99,a)].
% 0.83/1.11 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -coll(E,C,B) | -eqangle(A,C,A,B,f16(A,C,B,D),C,f16(A,C,B,D),E) | midp(E,C,B). [resolve(108,c,100,a)].
% 0.83/1.11 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -coll(f16(A,C,B,D),A,B) | perp(A,C,C,B). [resolve(108,c,101,a)].
% 0.83/1.11 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | perp(f12(A,C,B,f16(A,C,B,D)),A,A,f16(A,C,B,D)). [resolve(108,c,102,a)].
% 0.83/1.11 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -cong(f16(A,C,B,D),A,f16(A,C,B,D),E) | -cong(F,A,F,C) | F = f16(A,C,B,D) | coll(f13(A,C,B,E,f16(A,C,B,D),F),A,B). [resolve(108,c,103,a)].
% 0.83/1.11 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -cong(f16(A,C,B,D),A,f16(A,C,B,D),E) | -cong(F,A,F,C) | F = f16(A,C,B,D) | cong(f13(A,C,B,E,f16(A,C,B,D),F),F,F,A). [resolve(108,c,104,a)].
% 0.83/1.11 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -cong(f16(A,C,B,D),A,f16(A,C,B,D),E) | -cong(F,A,F,C) | F = f16(A,C,B,D) | coll(f14(A,C,B,E,f16(A,C,B,D),F),C,E). [resolve(108,c,105,a)].
% 0.83/1.11 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -cong(f16(A,C,B,D),A,f16(A,C,B,D),E) | -cong(F,A,F,C) | F = f16(A,C,B,D) | cong(f14(A,C,B,E,f16(A,C,B,D),F),F,F,A). [resolve(108,c,106,a)].
% 0.83/1.11 109 circle(c4,c1,c2,c3) # label(exemplo6GDDFULL618074) # label(negated_conjecture). [clausify(95)].
% 0.83/1.11 Derived: -perp(c4,c1,c1,A) | eqangle(c1,A,c1,c2,c3,c1,c3,c2). [resolve(109,a,96,a)].
% 0.83/1.11 Derived: -eqangle(c1,A,c1,c2,c3,c1,c3,c2) | perp(c4,c1,c1,A). [resolve(109,a,98,a)].
% 0.83/1.11 Derived: -midp(A,c2,c3) | eqangle(c1,c2,c1,c3,c4,c2,c4,A). [resolve(109,a,99,a)].
% 0.83/1.11 Derived: -coll(A,c2,c3) | -eqangle(c1,c2,c1,c3,c4,c2,c4,A) | midp(A,c2,c3). [resolve(109,a,100,a)].
% 0.83/1.11 Derived: -coll(c4,c1,c3) | perp(c1,c2,c2,c3). [resolve(109,a,101,a)].
% 0.83/1.11 Derived: perp(f12(c1,c2,c3,c4),c1,c1,c4). [resolve(109,a,102,a)].
% 0.83/1.11 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)].
% 4.15/4.45 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)].
% 4.15/4.45 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)].
% 4.15/4.45 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)].
% 4.15/4.45 110 circle(c4,c3,c6,c9) # label(exemplo6GDDFULL618074) # label(negated_conjecture). [clausify(95)].
% 4.15/4.45 Derived: -perp(c4,c3,c3,A) | eqangle(c3,A,c3,c6,c9,c3,c9,c6). [resolve(110,a,96,a)].
% 4.15/4.45 Derived: -eqangle(c3,A,c3,c6,c9,c3,c9,c6) | perp(c4,c3,c3,A). [resolve(110,a,98,a)].
% 4.15/4.45 Derived: -midp(A,c6,c9) | eqangle(c3,c6,c3,c9,c4,c6,c4,A). [resolve(110,a,99,a)].
% 4.15/4.45 Derived: -coll(A,c6,c9) | -eqangle(c3,c6,c3,c9,c4,c6,c4,A) | midp(A,c6,c9). [resolve(110,a,100,a)].
% 4.15/4.45 Derived: -coll(c4,c3,c9) | perp(c3,c6,c6,c9). [resolve(110,a,101,a)].
% 4.15/4.45 Derived: perp(f12(c3,c6,c9,c4),c3,c3,c4). [resolve(110,a,102,a)].
% 4.15/4.45 Derived: -cong(c4,c3,c4,A) | -cong(B,c3,B,c6) | B = c4 | coll(f13(c3,c6,c9,A,c4,B),c3,c9). [resolve(110,a,103,a)].
% 4.15/4.45 Derived: -cong(c4,c3,c4,A) | -cong(B,c3,B,c6) | B = c4 | cong(f13(c3,c6,c9,A,c4,B),B,B,c3). [resolve(110,a,104,a)].
% 4.15/4.45 Derived: -cong(c4,c3,c4,A) | -cong(B,c3,B,c6) | B = c4 | coll(f14(c3,c6,c9,A,c4,B),c6,A). [resolve(110,a,105,a)].
% 4.15/4.45 Derived: -cong(c4,c3,c4,A) | -cong(B,c3,B,c6) | B = c4 | cong(f14(c3,c6,c9,A,c4,B),B,B,c3). [resolve(110,a,106,a)].
% 4.15/4.45
% 4.15/4.45 ============================== end predicate elimination =============
% 4.15/4.45
% 4.15/4.45 Auto_denials: (non-Horn, no changes).
% 4.15/4.45
% 4.15/4.45 Term ordering decisions:
% 4.15/4.45 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=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.
% 4.15/4.45
% 4.15/4.45 ============================== end of process initial clauses ========
% 4.15/4.45
% 4.15/4.45 ============================== CLAUSES FOR SEARCH ====================
% 4.15/4.45
% 4.15/4.45 ============================== end of clauses for search =============
% 4.15/4.45
% 4.15/4.45 ============================== SEARCH ================================
% 4.15/4.45
% 4.15/4.45 % Starting search at 0.05 seconds.
% 4.15/4.45
% 4.15/4.45 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 2147483647 (0.00 of 0.15 sec).
% 4.15/4.45
% 4.15/4.45 Low Water (keep): wt=26.000, iters=3340
% 4.15/4.45
% 4.15/4.45 Low Water (keep): wt=23.000, iters=3355
% 4.15/4.45
% 4.15/4.45 Low Water (keep): wt=22.000, iters=3390
% 4.15/4.45
% 4.15/4.45 Low Water (keep): wt=21.000, iters=3345
% 4.15/4.45
% 4.15/4.45 Low Water (keep): wt=18.000, iters=3336
% 4.15/4.45
% 4.15/4.45 Low Water (keep): wt=17.000, iters=3335
% 4.15/4.45
% 4.15/4.45 Low Water (keep): wt=16.000, iters=3334
% 4.15/4.45
% 4.15/4.45 Low Water (keep): wt=15.000, iters=3340
% 4.15/4.45
% 4.15/4.45 Low Water (keep): wt=14.000, iters=3336
% 4.15/4.45
% 4.15/4.45 Low Water (keep): wt=13.000, iters=3340
% 4.15/4.45
% 4.15/4.45 Low Water (keep): wt=12.000, iters=3408
% 4.15/4.45
% 4.15/4.45 Low Water (displace): id=8730, wt=48.000
% 4.15/4.45
% 4.15/4.45 Low Water (displace): id=8725, wt=46.000
% 4.15/4.45
% 4.15/4.45 Low Water (displace): id=8727, wt=44.000
% 4.15/4.45
% 4.15/4.45 Low Water (displace): id=8726, wt=42.000
% 4.15/4.45
% 4.15/4.45 Low Water (displace): id=8732, wt=37.000
% 4.15/4.45
% 4.15/4.45 Low Water (displace): id=8918, wt=34.000
% 4.15/4.45
% 4.15/4.45 Low Water (displace): id=8951, wt=26.000
% 4.15/4.45
% 4.15/4.45 Low Water (displace): id=15834, wt=10.000
% 4.15/4.45
% 4.15/4.45 Low Water (displace): id=15888, wt=9.000
% 4.15/4.45
% 4.15/4.45 Low Water (displace): id=16217, wt=8.000
% 4.15/4.45
% 4.15/4.45 Low Water (displace): id=17041, wt=7.000
% 4.15/4.45
% 4.15/4.45 Low Water (displace): id=17116, wt=5.000
% 4.15/4.45
% 4.15/4.45 Low Water (keep): wt=11.000, iters=3385
% 4.15/4.45
% 4.15/4.45 Low Water (keep): wt=10.000, iters=3335
% 4.15/4.45
% 4.15/4.45 ============================== PROOF =================================
% 4.15/4.45 % SZS status Theorem
% 4.15/4.45 % SZS output start Refutation
% 4.15/4.45
% 4.15/4.45 % Proof 1 at 3.32 (+ 0.05) seconds.
% 4.15/4.45 % Length of proof is 170.
% 4.15/4.45 % Level of proof is 32.
% 4.15/4.45 % Maximum clause weight is 29.000.
% 4.15/4.45 % Given clauses 7007.
% 4.15/4.45
% 4.15/4.45 1 (all A all B all C (coll(A,B,C) -> coll(A,C,B))) # label(ruleD1) # label(axiom) # label(non_clause). [assumption].
% 4.15/4.45 2 (all A all B all C (coll(A,B,C) -> coll(B,A,C))) # label(ruleD2) # label(axiom) # label(non_clause). [assumption].
% 4.15/4.45 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].
% 4.15/4.45 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].
% 4.15/4.45 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].
% 4.15/4.45 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].
% 4.15/4.45 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].
% 4.15/4.45 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].
% 4.15/4.45 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].
% 4.15/4.45 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].
% 4.15/4.45 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].
% 4.15/4.45 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].
% 4.15/4.45 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].
% 4.15/4.45 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].
% 4.15/4.45 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].
% 4.15/4.45 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].
% 4.15/4.45 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].
% 4.15/4.45 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].
% 4.15/4.45 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].
% 4.15/4.45 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].
% 4.15/4.45 67 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption].
% 4.15/4.45 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].
% 4.15/4.45 69 (all A all B all C (midp(A,B,C) -> cong(A,B,A,C))) # label(ruleD68) # label(axiom) # label(non_clause). [assumption].
% 4.15/4.45 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].
% 4.15/4.45 95 -(all A all B all C all O all G all D all E all F all NWPNT1 (circle(O,A,B,C) & perp(G,C,A,B) & coll(G,A,B) & circle(O,C,D,NWPNT1) & coll(D,C,G) & perp(E,D,A,C) & coll(E,A,C) & perp(F,D,B,C) & coll(F,B,C) -> cyclic(A,E,F,B))) # label(exemplo6GDDFULL618074) # label(negated_conjecture) # label(non_clause). [assumption].
% 4.15/4.45 101 -circle(A,B,C,D) | -coll(A,B,D) | perp(B,C,C,D) # label(ruleD53) # label(axiom). [clausify(54)].
% 4.15/4.45 102 -circle(A,B,C,D) | perp(f12(B,C,D,A),B,B,A) # label(ruleX11) # label(axiom). [clausify(87)].
% 4.15/4.45 109 circle(c4,c1,c2,c3) # label(exemplo6GDDFULL618074) # label(negated_conjecture). [clausify(95)].
% 4.15/4.45 110 circle(c4,c3,c6,c9) # label(exemplo6GDDFULL618074) # label(negated_conjecture). [clausify(95)].
% 4.15/4.45 111 -coll(A,B,C) | coll(A,C,B) # label(ruleD1) # label(axiom). [clausify(1)].
% 4.15/4.45 112 -coll(A,B,C) | coll(B,A,C) # label(ruleD2) # label(axiom). [clausify(2)].
% 4.15/4.45 113 -coll(A,B,C) | -coll(A,B,D) | coll(C,D,A) # label(ruleD3) # label(axiom). [clausify(3)].
% 4.15/4.45 114 -para(A,B,C,D) | para(A,B,D,C) # label(ruleD4) # label(axiom). [clausify(4)].
% 4.15/4.45 115 -para(A,B,C,D) | para(C,D,A,B) # label(ruleD5) # label(axiom). [clausify(5)].
% 4.15/4.45 117 -perp(A,B,C,D) | perp(A,B,D,C) # label(ruleD7) # label(axiom). [clausify(7)].
% 4.19/4.45 118 -perp(A,B,C,D) | perp(C,D,A,B) # label(ruleD8) # label(axiom). [clausify(8)].
% 4.19/4.45 119 -perp(A,B,C,D) | -perp(C,D,E,F) | para(A,B,E,F) # label(ruleD9) # label(axiom). [clausify(9)].
% 4.19/4.45 122 -cong(A,B,A,C) | -cong(A,B,A,D) | -cong(A,B,A,E) | cyclic(B,C,D,E) # label(ruleD13) # label(axiom). [clausify(13)].
% 4.19/4.45 123 -cyclic(A,B,C,D) | cyclic(A,B,D,C) # label(ruleD14) # label(axiom). [clausify(14)].
% 4.19/4.45 124 -cyclic(A,B,C,D) | cyclic(A,C,B,D) # label(ruleD15) # label(axiom). [clausify(15)].
% 4.19/4.45 125 -cyclic(A,B,C,D) | cyclic(B,A,C,D) # label(ruleD16) # label(axiom). [clausify(16)].
% 4.19/4.45 126 -cyclic(A,B,C,D) | -cyclic(A,B,C,E) | cyclic(B,C,D,E) # label(ruleD17) # label(axiom). [clausify(17)].
% 4.19/4.45 128 -eqangle(A,B,C,D,E,F,V6,V7) | eqangle(C,D,A,B,V6,V7,E,F) # label(ruleD19) # label(axiom). [clausify(19)].
% 4.19/4.45 149 -para(A,B,C,D) | eqangle(A,B,E,F,C,D,E,F) # label(ruleD40) # label(axiom). [clausify(40)].
% 4.19/4.45 152 -eqangle(A,B,A,C,D,B,D,C) | -coll(A,D,C) | cyclic(B,C,A,D) # label(ruleD42b) # label(axiom). [clausify(43)].
% 4.19/4.45 153 -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)].
% 4.19/4.45 155 -midp(A,B,C) | -para(A,D,C,E) | -coll(D,B,E) | midp(D,B,E) # label(ruleD45) # label(axiom). [clausify(46)].
% 4.19/4.45 169 -midp(A,B,C) | -para(B,D,C,E) | -para(B,E,C,D) | midp(A,D,E) # label(ruleD64) # label(axiom). [clausify(65)].
% 4.19/4.45 171 -para(A,B,A,C) | coll(A,B,C) # label(ruleD66) # label(axiom). [clausify(67)].
% 4.19/4.45 172 -cong(A,B,A,C) | -coll(A,B,C) | midp(A,B,C) # label(ruleD67) # label(axiom). [clausify(68)].
% 4.19/4.45 173 -midp(A,B,C) | cong(A,B,A,C) # label(ruleD68) # label(axiom). [clausify(69)].
% 4.19/4.45 210 perp(c5,c3,c1,c2) # label(exemplo6GDDFULL618074) # label(negated_conjecture). [clausify(95)].
% 4.19/4.45 211 coll(c5,c1,c2) # label(exemplo6GDDFULL618074) # label(negated_conjecture). [clausify(95)].
% 4.19/4.45 212 coll(c6,c3,c5) # label(exemplo6GDDFULL618074) # label(negated_conjecture). [clausify(95)].
% 4.19/4.45 213 perp(c7,c6,c1,c3) # label(exemplo6GDDFULL618074) # label(negated_conjecture). [clausify(95)].
% 4.19/4.45 214 coll(c7,c1,c3) # label(exemplo6GDDFULL618074) # label(negated_conjecture). [clausify(95)].
% 4.19/4.45 216 coll(c8,c2,c3) # label(exemplo6GDDFULL618074) # label(negated_conjecture). [clausify(95)].
% 4.19/4.45 217 -cyclic(c1,c7,c8,c2) # label(exemplo6GDDFULL618074) # label(negated_conjecture). [clausify(95)].
% 4.19/4.45 260 -coll(c4,c1,c3) | perp(c1,c2,c2,c3). [resolve(109,a,101,a)].
% 4.19/4.45 275 perp(f12(c3,c6,c9,c4),c3,c3,c4). [resolve(110,a,102,a)].
% 4.19/4.45 284 -coll(A,B,C) | coll(C,C,A). [factor(113,a,b)].
% 4.19/4.45 286 -cong(A,B,A,C) | -cong(A,B,A,D) | cyclic(B,C,C,D). [factor(122,a,b)].
% 4.19/4.45 289 -cyclic(A,B,C,D) | cyclic(B,C,D,D). [factor(126,a,b)].
% 4.19/4.45 290 -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(153,a,b)].
% 4.19/4.45 298 -midp(A,B,C) | -para(B,D,C,D) | midp(A,D,D). [factor(169,b,c)].
% 4.19/4.45 338 -cong(A,B,A,C) | cyclic(B,C,C,C). [factor(286,a,b)].
% 4.19/4.45 359 -perp(c1,c2,A,B) | para(c5,c3,A,B). [resolve(210,a,119,a)].
% 4.19/4.45 360 perp(c1,c2,c5,c3). [resolve(210,a,118,a)].
% 4.19/4.45 364 coll(c1,c5,c2). [resolve(211,a,112,a)].
% 4.19/4.45 368 coll(c3,c6,c5). [resolve(212,a,112,a)].
% 4.19/4.45 381 -perp(A,B,c7,c6) | para(A,B,c1,c3). [resolve(213,a,119,b)].
% 4.19/4.45 384 perp(c7,c6,c3,c1). [resolve(213,a,117,a)].
% 4.19/4.45 387 coll(c1,c7,c3). [resolve(214,a,112,a)].
% 4.19/4.45 388 coll(c7,c3,c1). [resolve(214,a,111,a)].
% 4.19/4.45 406 coll(c2,c8,c3). [resolve(216,a,112,a)].
% 4.19/4.45 453 -perp(A,B,f12(c3,c6,c9,c4),c3) | para(A,B,c3,c4). [resolve(275,a,119,b)].
% 4.19/4.45 455 perp(c3,c4,f12(c3,c6,c9,c4),c3). [resolve(275,a,118,a)].
% 4.19/4.45 459 coll(c3,c3,c7). [resolve(284,a,214,a)].
% 4.19/4.45 460 coll(c5,c5,c6). [resolve(284,a,212,a)].
% 4.19/4.45 462 coll(c2,c2,c1). [resolve(364,a,284,a)].
% 4.19/4.45 465 coll(c1,c2,c5). [resolve(364,a,111,a)].
% 4.19/4.45 470 coll(c5,c5,c3). [resolve(368,a,284,a)].
% 4.19/4.45 479 -coll(c1,c7,A) | coll(A,c3,c1). [resolve(387,a,113,b)].
% 4.19/4.45 484 -coll(c7,c3,A) | coll(c1,A,c7). [resolve(388,a,113,a)].
% 4.19/4.45 486 coll(c3,c3,c2). [resolve(406,a,284,a)].
% 4.19/4.45 500 -coll(c3,c3,A) | coll(c7,A,c3). [resolve(459,a,113,a)].
% 4.19/4.45 505 coll(c5,c6,c5). [resolve(460,a,111,a)].
% 4.19/4.45 510 coll(c1,c1,c2). [resolve(462,a,284,a)].
% 4.19/4.45 514 coll(c5,c5,c1). [resolve(465,a,284,a)].
% 4.19/4.45 552 coll(c3,c2,c3). [resolve(486,a,111,a)].
% 4.19/4.45 578 coll(c5,c5,c5). [resolve(505,a,284,a)].
% 4.19/4.45 591 coll(c1,c2,c1). [resolve(510,a,111,a)].
% 4.19/4.45 635 para(c5,c3,c5,c3). [resolve(360,a,359,a)].
% 4.19/4.45 797 perp(c3,c1,c7,c6). [resolve(384,a,118,a)].
% 4.19/4.45 828 -midp(A,c5,c5) | midp(A,c3,c3). [resolve(635,a,298,b)].
% 4.19/4.45 836 -midp(c5,A,c5) | -coll(c3,A,c3) | midp(c3,A,c3). [resolve(635,a,155,b)].
% 4.19/4.45 837 eqangle(c5,c3,A,B,c5,c3,A,B). [resolve(635,a,149,a)].
% 4.19/4.45 838 para(c5,c3,c3,c5). [resolve(635,a,114,a)].
% 4.19/4.45 952 para(c3,c5,c5,c3). [resolve(838,a,115,a)].
% 4.19/4.45 1065 para(c3,c1,c1,c3). [resolve(381,a,797,a)].
% 4.19/4.45 1082 para(c3,c5,c3,c5). [resolve(952,a,114,a)].
% 4.19/4.45 1152 para(c3,c1,c3,c1). [resolve(1065,a,114,a)].
% 4.19/4.45 1176 eqangle(c3,c5,A,B,c3,c5,A,B). [resolve(1082,a,149,a)].
% 4.19/4.45 1252 -midp(c3,A,c3) | -coll(c1,A,c1) | midp(c1,A,c1). [resolve(1152,a,155,b)].
% 4.19/4.45 2130 para(c3,c4,c3,c4). [resolve(455,a,453,a)].
% 4.19/4.45 2208 coll(c3,c4,c4). [resolve(2130,a,171,a)].
% 4.19/4.45 2213 coll(c4,c4,c3). [resolve(2208,a,284,a)].
% 4.19/4.45 2223 coll(c3,c3,c4). [resolve(2213,a,284,a)].
% 4.19/4.45 2232 coll(c7,c4,c3). [resolve(2223,a,500,a)].
% 4.19/4.45 2241 coll(c7,c3,c4). [resolve(2232,a,111,a)].
% 4.19/4.45 2262 coll(c1,c4,c7). [resolve(2241,a,484,a)].
% 4.19/4.45 2298 coll(c1,c7,c4). [resolve(2262,a,111,a)].
% 4.19/4.45 2345 coll(c4,c3,c1). [resolve(2298,a,479,a)].
% 4.19/4.45 2400 coll(c4,c1,c3). [resolve(2345,a,111,a)].
% 4.19/4.45 2401 perp(c1,c2,c2,c3). [back_unit_del(260),unit_del(a,2400)].
% 4.19/4.45 2723 para(c5,c3,c2,c3). [resolve(2401,a,359,a)].
% 4.19/4.45 2780 para(c2,c3,c5,c3). [resolve(2723,a,115,a)].
% 4.19/4.45 2781 para(c5,c3,c3,c2). [resolve(2723,a,114,a)].
% 4.19/4.45 2846 para(c2,c3,c3,c5). [resolve(2780,a,114,a)].
% 4.19/4.45 2865 para(c3,c2,c5,c3). [resolve(2781,a,115,a)].
% 4.19/4.45 2920 para(c3,c5,c2,c3). [resolve(2846,a,115,a)].
% 4.19/4.45 2937 para(c3,c2,c3,c5). [resolve(2865,a,114,a)].
% 4.19/4.45 3023 para(c3,c5,c3,c2). [resolve(2920,a,114,a)].
% 4.19/4.45 3034 -midp(A,c3,c3) | midp(A,c2,c5). [resolve(2937,a,169,b),unit_del(b,3023)].
% 4.19/4.45 3470 -coll(c5,c5,A) | cyclic(c3,A,c5,c5). [resolve(837,a,152,a)].
% 4.19/4.45 3472 eqangle(A,B,c5,c3,A,B,c5,c3). [resolve(837,a,128,a)].
% 4.19/4.45 7248 -cyclic(c5,c5,c3,c5) | -cyclic(c5,c5,c3,c3) | cong(c5,c5,c5,c5). [resolve(1176,a,290,c)].
% 4.19/4.45 12464 cyclic(c3,c5,c5,c5). [resolve(3470,a,578,a)].
% 4.19/4.45 12465 cyclic(c3,c1,c5,c5). [resolve(3470,a,514,a)].
% 4.19/4.45 12467 cyclic(c3,c3,c5,c5). [resolve(3470,a,470,a)].
% 4.19/4.45 12499 cyclic(c5,c3,c5,c5). [resolve(12464,a,125,a)].
% 4.19/4.45 12506 cyclic(c3,c5,c1,c5). [resolve(12465,a,124,a)].
% 4.19/4.45 12518 cyclic(c3,c5,c3,c5). [resolve(12467,a,124,a)].
% 4.19/4.45 12583 cyclic(c5,c5,c3,c5). [resolve(12499,a,124,a)].
% 4.19/4.45 12584 -cyclic(c5,c5,c3,c3) | cong(c5,c5,c5,c5). [back_unit_del(7248),unit_del(a,12583)].
% 4.19/4.45 12600 cyclic(c3,c5,c5,c1). [resolve(12506,a,123,a)].
% 4.19/4.45 12625 cyclic(c3,c5,c5,c3). [resolve(12518,a,123,a)].
% 4.19/4.45 12743 cyclic(c5,c5,c1,c1). [resolve(12600,a,289,a)].
% 4.19/4.45 12747 -cyclic(c3,c5,c5,A) | cyclic(c5,c5,A,c1). [resolve(12600,a,126,b)].
% 4.19/4.45 12748 -cyclic(c3,c5,c5,A) | cyclic(c5,c5,c1,A). [resolve(12600,a,126,a)].
% 4.19/4.45 12781 cyclic(c5,c5,c3,c3). [resolve(12625,a,289,a)].
% 4.19/4.45 12787 cong(c5,c5,c5,c5). [back_unit_del(12584),unit_del(a,12781)].
% 4.19/4.45 13483 cyclic(c5,c1,c1,c1). [resolve(12743,a,289,a)].
% 4.19/4.45 13487 -cyclic(c5,c5,c1,A) | cyclic(c5,c1,c1,A). [resolve(12743,a,126,a)].
% 4.19/4.45 13554 midp(c5,c5,c5). [resolve(12787,a,172,a),unit_del(a,578)].
% 4.19/4.45 13559 midp(c5,c3,c3). [resolve(13554,a,828,a)].
% 4.19/4.45 13612 midp(c5,c2,c5). [resolve(13559,a,3034,a)].
% 4.19/4.45 13709 midp(c3,c2,c3). [resolve(13612,a,836,a),unit_del(a,552)].
% 4.19/4.45 13869 midp(c1,c2,c1). [resolve(13709,a,1252,a),unit_del(a,591)].
% 4.19/4.45 13971 cong(c1,c2,c1,c1). [resolve(13869,a,173,a)].
% 4.19/4.45 15102 -cyclic(c5,c1,c1,A) | cyclic(c1,c1,c1,A). [resolve(13483,a,126,a)].
% 4.19/4.45 15545 cyclic(c2,c1,c1,c1). [resolve(13971,a,338,a)].
% 4.19/4.45 17024 cyclic(c1,c2,c1,c1). [resolve(15545,a,125,a)].
% 4.19/4.45 18731 cyclic(c1,c1,c2,c1). [resolve(17024,a,124,a)].
% 4.19/4.45 19964 cyclic(c1,c1,c1,c2). [resolve(18731,a,123,a)].
% 4.19/4.45 21420 -cyclic(c1,c1,c1,A) | cyclic(c1,c1,A,c2). [resolve(19964,a,126,b)].
% 4.19/4.45 25105 cyclic(A,c3,c5,c5). [resolve(3472,a,152,a),unit_del(a,470)].
% 4.19/4.45 25108 cyclic(c3,A,c5,c5). [resolve(25105,a,125,a)].
% 4.19/4.45 25526 cyclic(c3,c5,A,c5). [resolve(25108,a,124,a)].
% 4.19/4.45 25576 cyclic(c3,c5,c5,A). [resolve(25526,a,123,a)].
% 4.19/4.45 25583 cyclic(c5,c5,c1,A). [back_unit_del(12748),unit_del(a,25576)].
% 4.19/4.45 25584 cyclic(c5,c5,A,c1). [back_unit_del(12747),unit_del(a,25576)].
% 4.19/4.45 25616 cyclic(c5,c1,c1,A). [back_unit_del(13487),unit_del(a,25583)].
% 4.19/4.45 25680 cyclic(c1,c1,c1,A). [back_unit_del(15102),unit_del(a,25616)].
% 4.19/4.45 25766 cyclic(c1,c1,A,c2). [back_unit_del(21420),unit_del(a,25680)].
% 4.19/4.45 25893 cyclic(c5,c5,A,B). [resolve(25576,a,126,b),unit_del(a,25576)].
% 4.19/4.45 25919 cyclic(c5,A,c1,B). [resolve(25584,a,126,a),unit_del(a,25893)].
% 4.19/4.45 26031 cyclic(c1,c1,A,B). [resolve(25616,a,126,b),unit_del(a,25919)].
% 4.19/4.45 26289 cyclic(c1,A,B,c2). [resolve(25766,a,126,b),unit_del(a,26031)].
% 4.19/4.45 26290 $F. [resolve(26289,a,217,a)].
% 4.19/4.45
% 4.19/4.45 % SZS output end Refutation
% 4.19/4.45 ============================== end of proof ==========================
% 4.19/4.45
% 4.19/4.45 ============================== STATISTICS ============================
% 4.19/4.45
% 4.19/4.45 Given=7007. Generated=96811. Kept=26163. proofs=1.
% 4.19/4.45 Usable=5493. Sos=7150. Demods=0. Limbo=1, Disabled=13691. Hints=0.
% 4.19/4.45 Megabytes=14.49.
% 4.19/4.45 User_CPU=3.32, System_CPU=0.05, Wall_clock=4.
% 4.19/4.45
% 4.19/4.45 ============================== end of statistics =====================
% 4.19/4.45
% 4.19/4.45 ============================== end of search =========================
% 4.19/4.45
% 4.19/4.45 THEOREM PROVED
% 4.19/4.45 % SZS status Theorem
% 4.19/4.45
% 4.19/4.45 Exiting with 1 proof.
% 4.19/4.45
% 4.19/4.45 Process 15488 exit (max_proofs) Fri Jun 17 19:01:55 2022
% 4.19/4.45 Prover9 interrupted
%------------------------------------------------------------------------------