TSTP Solution File: GEO577+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GEO577+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 05:57:03 EDT 2022
% Result : Theorem 9.54s 9.81s
% Output : Refutation 9.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO577+1 : TPTP v8.1.0. Released v7.5.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % 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 18:58:37 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.43/1.08 ============================== Prover9 ===============================
% 0.43/1.08 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.08 Process 13658 was started by sandbox2 on n016.cluster.edu,
% 0.43/1.08 Sat Jun 18 18:58:38 2022
% 0.43/1.08 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_13505_n016.cluster.edu".
% 0.43/1.08 ============================== end of head ===========================
% 0.43/1.08
% 0.43/1.08 ============================== INPUT =================================
% 0.43/1.08
% 0.43/1.08 % Reading from file /tmp/Prover9_13505_n016.cluster.edu
% 0.43/1.08
% 0.43/1.08 set(prolog_style_variables).
% 0.43/1.08 set(auto2).
% 0.43/1.08 % set(auto2) -> set(auto).
% 0.43/1.08 % set(auto) -> set(auto_inference).
% 0.43/1.08 % set(auto) -> set(auto_setup).
% 0.43/1.08 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.08 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.08 % set(auto) -> set(auto_limits).
% 0.43/1.08 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.08 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.08 % set(auto) -> set(auto_denials).
% 0.43/1.08 % set(auto) -> set(auto_process).
% 0.43/1.08 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.08 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.08 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.08 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.08 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.08 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.08 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.08 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.08 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.08 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.08 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.08 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.08 % set(auto2) -> assign(stats, some).
% 0.43/1.08 % set(auto2) -> clear(echo_input).
% 0.43/1.08 % set(auto2) -> set(quiet).
% 0.43/1.08 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.08 % set(auto2) -> clear(print_given).
% 0.43/1.08 assign(lrs_ticks,-1).
% 0.43/1.08 assign(sos_limit,10000).
% 0.43/1.08 assign(order,kbo).
% 0.43/1.08 set(lex_order_vars).
% 0.43/1.08 clear(print_given).
% 0.43/1.08
% 0.43/1.08 % formulas(sos). % not echoed (95 formulas)
% 0.43/1.08
% 0.43/1.08 ============================== end of input ==========================
% 0.43/1.08
% 0.43/1.08 % From the command line: assign(max_seconds, 300).
% 0.43/1.08
% 0.43/1.08 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.08
% 0.43/1.08 % Formulas that are not ordinary clauses:
% 0.43/1.08 1 (all A all B all C (coll(A,B,C) -> coll(A,C,B))) # label(ruleD1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 2 (all A all B all C (coll(A,B,C) -> coll(B,A,C))) # label(ruleD2) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 11 (all A all B all M (midp(M,B,A) -> midp(M,A,B))) # label(ruleD11) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.08 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].
% 0.43/1.09 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].
% 0.43/1.09 67 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.09 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].
% 0.43/1.09 69 (all A all B all C (midp(A,B,C) -> cong(A,B,A,C))) # label(ruleD68) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.09 70 (all A all B all C (midp(A,B,C) -> coll(A,B,C))) # label(ruleD69) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.09 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].
% 0.43/1.09 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].
% 0.43/1.09 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].
% 0.43/1.09 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].
% 0.43/1.09 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].
% 0.43/1.09 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].
% 0.43/1.09 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].
% 0.43/1.09 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].
% 0.43/1.09 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].
% 0.43/1.09 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].
% 0.43/1.09 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].
% 0.43/1.09 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].
% 0.43/1.09 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].
% 0.43/1.09 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].
% 0.43/1.09 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].
% 0.43/1.09 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].
% 0.43/1.09 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].
% 0.43/1.09 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].
% 0.43/1.09 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].
% 0.43/1.09 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].
% 0.43/1.09 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].
% 0.43/1.09 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].
% 0.43/1.09 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].
% 0.43/1.09 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].
% 0.43/1.09 95 -(all A all B all C all I all O all M all L1 all NWPNT1 all NWPNT2 (eqangle(I,A,A,B,I,A,A,C) & eqangle(I,B,B,C,I,B,B,A) & eqangle(I,C,C,A,I,C,C,B) & circle(O,A,B,C) & circle(O,C,M,NWPNT1) & coll(M,C,I) & perp(B,I,B,L1) & circle(O,A,L1,NWPNT2) -> para(M,L1,A,I))) # label(exemplo6GDDFULL214039) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.43/1.09
% 0.43/1.09 ============================== end of process non-clausal formulas ===
% 0.43/1.09
% 0.43/1.09 ============================== PROCESS INITIAL CLAUSES ===============
% 0.43/1.09
% 0.43/1.09 ============================== PREDICATE ELIMINATION =================
% 0.43/1.09 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)].
% 0.43/1.09 97 -cong(A,B,A,C) | -cong(A,B,A,D) | circle(A,B,C,D) # label(ruleD12) # label(axiom). [clausify(12)].
% 0.43/1.09 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)].
% 0.43/1.09 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)].
% 0.43/1.09 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)].
% 0.43/1.09 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)].
% 0.43/1.09 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)].
% 0.43/1.09 100 -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)].
% 0.43/1.09 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)].
% 0.43/1.09 101 -circle(A,B,C,D) | -coll(A,B,D) | perp(B,C,C,D) # label(ruleD53) # label(axiom). [clausify(54)].
% 0.43/1.09 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)].
% 0.43/1.09 102 -circle(A,B,C,D) | perp(f12(B,C,D,A),B,B,A) # label(ruleX11) # label(axiom). [clausify(87)].
% 0.43/1.09 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)].
% 0.43/1.09 103 -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)].
% 0.43/1.09 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)].
% 0.43/1.09 104 -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)].
% 0.43/1.09 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)].
% 0.43/1.09 105 -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)].
% 0.43/1.09 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)].
% 0.43/1.09 106 -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)].
% 0.43/1.09 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)].
% 0.82/1.09 107 -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)].
% 0.82/1.09 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)].
% 0.82/1.09 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)].
% 0.82/1.09 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)].
% 0.82/1.09 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)].
% 0.82/1.09 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)].
% 0.82/1.09 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)].
% 0.82/1.09 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)].
% 0.82/1.09 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)].
% 0.82/1.09 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)].
% 0.82/1.09 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)].
% 0.82/1.09 108 -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)].
% 0.82/1.09 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)].
% 0.82/1.09 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)].
% 0.82/1.09 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)].
% 0.82/1.09 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)].
% 0.82/1.09 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)].
% 0.82/1.09 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)].
% 0.82/1.09 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)].
% 0.82/1.09 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)].
% 0.82/1.09 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)].
% 0.82/1.09 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)].
% 0.82/1.09 109 circle(c5,c1,c2,c3) # label(exemplo6GDDFULL214039) # label(negated_conjecture). [clausify(95)].
% 0.82/1.09 Derived: -perp(c5,c1,c1,A) | eqangle(c1,A,c1,c2,c3,c1,c3,c2). [resolve(109,a,96,a)].
% 0.82/1.09 Derived: -eqangle(c1,A,c1,c2,c3,c1,c3,c2) | perp(c5,c1,c1,A). [resolve(109,a,98,a)].
% 0.82/1.09 Derived: -midp(A,c2,c3) | eqangle(c1,c2,c1,c3,c5,c2,c5,A). [resolve(109,a,99,a)].
% 0.82/1.09 Derived: -coll(A,c2,c3) | -eqangle(c1,c2,c1,c3,c5,c2,c5,A) | midp(A,c2,c3). [resolve(109,a,100,a)].
% 0.82/1.09 Derived: -coll(c5,c1,c3) | perp(c1,c2,c2,c3). [resolve(109,a,101,a)].
% 0.82/1.09 Derived: perp(f12(c1,c2,c3,c5),c1,c1,c5). [resolve(109,a,102,a)].
% 0.82/1.09 Derived: -cong(c5,c1,c5,A) | -cong(B,c1,B,c2) | B = c5 | coll(f13(c1,c2,c3,A,c5,B),c1,c3). [resolve(109,a,103,a)].
% 9.54/9.81 Derived: -cong(c5,c1,c5,A) | -cong(B,c1,B,c2) | B = c5 | cong(f13(c1,c2,c3,A,c5,B),B,B,c1). [resolve(109,a,104,a)].
% 9.54/9.81 Derived: -cong(c5,c1,c5,A) | -cong(B,c1,B,c2) | B = c5 | coll(f14(c1,c2,c3,A,c5,B),c2,A). [resolve(109,a,105,a)].
% 9.54/9.81 Derived: -cong(c5,c1,c5,A) | -cong(B,c1,B,c2) | B = c5 | cong(f14(c1,c2,c3,A,c5,B),B,B,c1). [resolve(109,a,106,a)].
% 9.54/9.81 110 circle(c5,c3,c6,c8) # label(exemplo6GDDFULL214039) # label(negated_conjecture). [clausify(95)].
% 9.54/9.81 Derived: -perp(c5,c3,c3,A) | eqangle(c3,A,c3,c6,c8,c3,c8,c6). [resolve(110,a,96,a)].
% 9.54/9.81 Derived: -eqangle(c3,A,c3,c6,c8,c3,c8,c6) | perp(c5,c3,c3,A). [resolve(110,a,98,a)].
% 9.54/9.81 Derived: -midp(A,c6,c8) | eqangle(c3,c6,c3,c8,c5,c6,c5,A). [resolve(110,a,99,a)].
% 9.54/9.81 Derived: -coll(A,c6,c8) | -eqangle(c3,c6,c3,c8,c5,c6,c5,A) | midp(A,c6,c8). [resolve(110,a,100,a)].
% 9.54/9.81 Derived: -coll(c5,c3,c8) | perp(c3,c6,c6,c8). [resolve(110,a,101,a)].
% 9.54/9.81 Derived: perp(f12(c3,c6,c8,c5),c3,c3,c5). [resolve(110,a,102,a)].
% 9.54/9.81 Derived: -cong(c5,c3,c5,A) | -cong(B,c3,B,c6) | B = c5 | coll(f13(c3,c6,c8,A,c5,B),c3,c8). [resolve(110,a,103,a)].
% 9.54/9.81 Derived: -cong(c5,c3,c5,A) | -cong(B,c3,B,c6) | B = c5 | cong(f13(c3,c6,c8,A,c5,B),B,B,c3). [resolve(110,a,104,a)].
% 9.54/9.81 Derived: -cong(c5,c3,c5,A) | -cong(B,c3,B,c6) | B = c5 | coll(f14(c3,c6,c8,A,c5,B),c6,A). [resolve(110,a,105,a)].
% 9.54/9.81 Derived: -cong(c5,c3,c5,A) | -cong(B,c3,B,c6) | B = c5 | cong(f14(c3,c6,c8,A,c5,B),B,B,c3). [resolve(110,a,106,a)].
% 9.54/9.81 111 circle(c5,c1,c7,c9) # label(exemplo6GDDFULL214039) # label(negated_conjecture). [clausify(95)].
% 9.54/9.81 Derived: -perp(c5,c1,c1,A) | eqangle(c1,A,c1,c7,c9,c1,c9,c7). [resolve(111,a,96,a)].
% 9.54/9.81 Derived: -eqangle(c1,A,c1,c7,c9,c1,c9,c7) | perp(c5,c1,c1,A). [resolve(111,a,98,a)].
% 9.54/9.81 Derived: -midp(A,c7,c9) | eqangle(c1,c7,c1,c9,c5,c7,c5,A). [resolve(111,a,99,a)].
% 9.54/9.81 Derived: -coll(A,c7,c9) | -eqangle(c1,c7,c1,c9,c5,c7,c5,A) | midp(A,c7,c9). [resolve(111,a,100,a)].
% 9.54/9.81 Derived: -coll(c5,c1,c9) | perp(c1,c7,c7,c9). [resolve(111,a,101,a)].
% 9.54/9.81 Derived: perp(f12(c1,c7,c9,c5),c1,c1,c5). [resolve(111,a,102,a)].
% 9.54/9.81 Derived: -cong(c5,c1,c5,A) | -cong(B,c1,B,c7) | B = c5 | coll(f13(c1,c7,c9,A,c5,B),c1,c9). [resolve(111,a,103,a)].
% 9.54/9.81 Derived: -cong(c5,c1,c5,A) | -cong(B,c1,B,c7) | B = c5 | cong(f13(c1,c7,c9,A,c5,B),B,B,c1). [resolve(111,a,104,a)].
% 9.54/9.81 Derived: -cong(c5,c1,c5,A) | -cong(B,c1,B,c7) | B = c5 | coll(f14(c1,c7,c9,A,c5,B),c7,A). [resolve(111,a,105,a)].
% 9.54/9.81 Derived: -cong(c5,c1,c5,A) | -cong(B,c1,B,c7) | B = c5 | cong(f14(c1,c7,c9,A,c5,B),B,B,c1). [resolve(111,a,106,a)].
% 9.54/9.81
% 9.54/9.81 ============================== end predicate elimination =============
% 9.54/9.81
% 9.54/9.81 Auto_denials: (non-Horn, no changes).
% 9.54/9.81
% 9.54/9.81 Term ordering decisions:
% 9.54/9.81 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.
% 9.54/9.81
% 9.54/9.81 ============================== end of process initial clauses ========
% 9.54/9.81
% 9.54/9.81 ============================== CLAUSES FOR SEARCH ====================
% 9.54/9.81
% 9.54/9.81 ============================== end of clauses for search =============
% 9.54/9.81
% 9.54/9.81 ============================== SEARCH ================================
% 9.54/9.81
% 9.54/9.81 % Starting search at 0.05 seconds.
% 9.54/9.81
% 9.54/9.81 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 51 (0.00 of 0.16 sec).
% 9.54/9.81
% 9.54/9.81 Low Water (keep): wt=30.000, iters=3349
% 9.54/9.81
% 9.54/9.81 Low Water (keep): wt=26.000, iters=3333
% 9.54/9.81
% 9.54/9.81 Low Water (keep): wt=22.000, iters=3340
% 9.54/9.81
% 9.54/9.81 Low Water (keep): wt=21.000, iters=3354
% 9.54/9.81
% 9.54/9.81 Low Water (keep): wt=18.000, iters=3344
% 9.54/9.81
% 9.54/9.81 Low Water (keep): wt=17.000, iters=3333
% 9.54/9.81
% 9.54/9.81 Low Water (keep): wt=16.000, iters=3335
% 9.54/9.81
% 9.54/9.81 Low Water (keep): wt=15.000, iters=3340
% 9.54/9.81
% 9.54/9.81 Low Water (keep): wt=14.000, iters=3336
% 9.54/9.81
% 9.54/9.81 Low Water (keep): wt=13.000, iters=3343
% 9.54/9.81
% 9.54/9.81 Low Water (keep): wt=12.000, iters=3333
% 9.54/9.81
% 9.54/9.81 Low Water (displace): id=16415, wt=9.000
% 9.54/9.81
% 9.54/9.81 Low Water (displace): id=16889, wt=8.000
% 9.54/9.81
% 9.54/9.81 Low Water (displace): id=20457, wt=5.000
% 9.54/9.81
% 9.54/9.81 Low Water (keep): wt=11.000, iters=3341
% 9.54/9.81
% 9.54/9.81 Low Water (keep): wt=10.000, iters=3333
% 9.54/9.81
% 9.54/9.81 Low Water (keep): wt=9.000, iters=3334
% 9.54/9.81
% 9.54/9.81 ============================== PROOF =================================
% 9.54/9.81 % SZS status Theorem
% 9.54/9.81 % SZS output start Refutation
% 9.54/9.81
% 9.54/9.81 % Proof 1 at 8.65 (+ 0.10) seconds.
% 9.54/9.81 % Length of proof is 127.
% 9.54/9.81 % Level of proof is 26.
% 9.54/9.81 % Maximum clause weight is 29.000.
% 9.54/9.81 % Given clauses 12960.
% 9.54/9.81
% 9.54/9.81 3 (all A all B all C all D (coll(A,B,C) & coll(A,B,D) -> coll(C,D,A))) # label(ruleD3) # label(axiom) # label(non_clause). [assumption].
% 9.54/9.81 4 (all A all B all C all D (para(A,B,C,D) -> para(A,B,D,C))) # label(ruleD4) # label(axiom) # label(non_clause). [assumption].
% 9.54/9.81 5 (all A all B all C all D (para(A,B,C,D) -> para(C,D,A,B))) # label(ruleD5) # label(axiom) # label(non_clause). [assumption].
% 9.54/9.81 6 (all A all B all C all D all E all F (para(A,B,C,D) & para(C,D,E,F) -> para(A,B,E,F))) # label(ruleD6) # label(axiom) # label(non_clause). [assumption].
% 9.54/9.81 8 (all A all B all C all D (perp(A,B,C,D) -> perp(C,D,A,B))) # label(ruleD8) # label(axiom) # label(non_clause). [assumption].
% 9.54/9.81 9 (all A all B all C all D all E all F (perp(A,B,C,D) & perp(C,D,E,F) -> para(A,B,E,F))) # label(ruleD9) # label(axiom) # label(non_clause). [assumption].
% 9.54/9.81 10 (all A all B all C all D all E all F (para(A,B,C,D) & perp(C,D,E,F) -> perp(A,B,E,F))) # label(ruleD10) # label(axiom) # label(non_clause). [assumption].
% 9.54/9.81 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].
% 9.54/9.81 15 (all A all B all C all D (cyclic(A,B,C,D) -> cyclic(A,C,B,D))) # label(ruleD15) # label(axiom) # label(non_clause). [assumption].
% 9.54/9.81 16 (all A all B all C all D (cyclic(A,B,C,D) -> cyclic(B,A,C,D))) # label(ruleD16) # label(axiom) # label(non_clause). [assumption].
% 9.54/9.81 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].
% 9.54/9.81 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].
% 9.54/9.81 20 (all A all B all C all D all P all Q all U all V (eqangle(A,B,C,D,P,Q,U,V) -> eqangle(P,Q,U,V,A,B,C,D))) # label(ruleD20) # label(axiom) # label(non_clause). [assumption].
% 9.54/9.81 21 (all A all B all C all D all P all Q all U all V (eqangle(A,B,C,D,P,Q,U,V) -> eqangle(A,B,P,Q,C,D,U,V))) # label(ruleD21) # label(axiom) # label(non_clause). [assumption].
% 9.54/9.81 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].
% 9.54/9.81 23 (all A all B all C all D (cong(A,B,C,D) -> cong(A,B,D,C))) # label(ruleD23) # label(axiom) # label(non_clause). [assumption].
% 9.54/9.81 24 (all A all B all C all D (cong(A,B,C,D) -> cong(C,D,A,B))) # label(ruleD24) # label(axiom) # label(non_clause). [assumption].
% 9.54/9.81 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].
% 9.54/9.81 40 (all A all B all C all D all P all Q (para(A,B,C,D) -> eqangle(A,B,P,Q,C,D,P,Q))) # label(ruleD40) # label(axiom) # label(non_clause). [assumption].
% 9.54/9.81 43 (all A all B all P all Q (eqangle(P,A,P,B,Q,A,Q,B) & coll(P,Q,B) -> cyclic(A,B,P,Q))) # label(ruleD42b) # label(axiom) # label(non_clause). [assumption].
% 9.54/9.81 44 (all A all B all C all P all Q all R (cyclic(A,B,C,P) & cyclic(A,B,C,Q) & cyclic(A,B,C,R) & eqangle(C,A,C,B,R,P,R,Q) -> cong(A,B,P,Q))) # label(ruleD43) # label(axiom) # label(non_clause). [assumption].
% 9.54/9.81 57 (all A all B all P all Q (cong(A,P,B,P) & cong(A,Q,B,Q) -> perp(A,B,P,Q))) # label(ruleD56) # label(axiom) # label(non_clause). [assumption].
% 9.54/9.81 67 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption].
% 9.54/9.81 74 (all A all B all C all D all P all Q all U all V (eqangle(A,B,C,D,P,Q,U,V) & para(P,Q,U,V) -> para(A,B,C,D))) # label(ruleD73) # label(axiom) # label(non_clause). [assumption].
% 9.54/9.81 95 -(all A all B all C all I all O all M all L1 all NWPNT1 all NWPNT2 (eqangle(I,A,A,B,I,A,A,C) & eqangle(I,B,B,C,I,B,B,A) & eqangle(I,C,C,A,I,C,C,B) & circle(O,A,B,C) & circle(O,C,M,NWPNT1) & coll(M,C,I) & perp(B,I,B,L1) & circle(O,A,L1,NWPNT2) -> para(M,L1,A,I))) # label(exemplo6GDDFULL214039) # label(negated_conjecture) # label(non_clause). [assumption].
% 9.54/9.81 114 -coll(A,B,C) | -coll(A,B,D) | coll(C,D,A) # label(ruleD3) # label(axiom). [clausify(3)].
% 9.54/9.81 115 -para(A,B,C,D) | para(A,B,D,C) # label(ruleD4) # label(axiom). [clausify(4)].
% 9.54/9.81 116 -para(A,B,C,D) | para(C,D,A,B) # label(ruleD5) # label(axiom). [clausify(5)].
% 9.54/9.81 117 -para(A,B,C,D) | -para(C,D,E,F) | para(A,B,E,F) # label(ruleD6) # label(axiom). [clausify(6)].
% 9.54/9.81 119 -perp(A,B,C,D) | perp(C,D,A,B) # label(ruleD8) # label(axiom). [clausify(8)].
% 9.54/9.81 120 -perp(A,B,C,D) | -perp(C,D,E,F) | para(A,B,E,F) # label(ruleD9) # label(axiom). [clausify(9)].
% 9.54/9.81 121 -para(A,B,C,D) | -perp(C,D,E,F) | perp(A,B,E,F) # label(ruleD10) # label(axiom). [clausify(10)].
% 9.54/9.81 124 -cyclic(A,B,C,D) | cyclic(A,B,D,C) # label(ruleD14) # label(axiom). [clausify(14)].
% 9.54/9.81 125 -cyclic(A,B,C,D) | cyclic(A,C,B,D) # label(ruleD15) # label(axiom). [clausify(15)].
% 9.54/9.81 126 -cyclic(A,B,C,D) | cyclic(B,A,C,D) # label(ruleD16) # label(axiom). [clausify(16)].
% 9.54/9.81 127 -cyclic(A,B,C,D) | -cyclic(A,B,C,E) | cyclic(B,C,D,E) # label(ruleD17) # label(axiom). [clausify(17)].
% 9.54/9.81 129 -eqangle(A,B,C,D,E,F,V6,V7) | eqangle(C,D,A,B,V6,V7,E,F) # label(ruleD19) # label(axiom). [clausify(19)].
% 9.54/9.81 130 -eqangle(A,B,C,D,E,F,V6,V7) | eqangle(E,F,V6,V7,A,B,C,D) # label(ruleD20) # label(axiom). [clausify(20)].
% 9.54/9.81 131 -eqangle(A,B,C,D,E,F,V6,V7) | eqangle(A,B,E,F,C,D,V6,V7) # label(ruleD21) # label(axiom). [clausify(21)].
% 9.54/9.81 132 -eqangle(A,B,C,D,E,F,V6,V7) | -eqangle(E,F,V6,V7,V8,V9,V10,V11) | eqangle(A,B,C,D,V8,V9,V10,V11) # label(ruleD22) # label(axiom). [clausify(22)].
% 9.54/9.81 133 -cong(A,B,C,D) | cong(A,B,D,C) # label(ruleD23) # label(axiom). [clausify(23)].
% 9.54/9.81 134 -cong(A,B,C,D) | cong(C,D,A,B) # label(ruleD24) # label(axiom). [clausify(24)].
% 9.54/9.81 149 -eqangle(A,B,C,D,E,F,C,D) | para(A,B,E,F) # label(ruleD39) # label(axiom). [clausify(39)].
% 9.54/9.81 150 -para(A,B,C,D) | eqangle(A,B,E,F,C,D,E,F) # label(ruleD40) # label(axiom). [clausify(40)].
% 9.54/9.81 153 -eqangle(A,B,A,C,D,B,D,C) | -coll(A,D,C) | cyclic(B,C,A,D) # label(ruleD42b) # label(axiom). [clausify(43)].
% 9.54/9.81 154 -cyclic(A,B,C,D) | -cyclic(A,B,C,E) | -cyclic(A,B,C,F) | -eqangle(C,A,C,B,F,D,F,E) | cong(A,B,D,E) # label(ruleD43) # label(axiom). [clausify(44)].
% 9.54/9.81 162 -cong(A,B,C,B) | -cong(A,D,C,D) | perp(A,C,B,D) # label(ruleD56) # label(axiom). [clausify(57)].
% 9.54/9.81 172 -para(A,B,A,C) | coll(A,B,C) # label(ruleD66) # label(axiom). [clausify(67)].
% 9.54/9.81 178 -eqangle(A,B,C,D,E,F,V6,V7) | -para(E,F,V6,V7) | para(A,B,C,D) # label(ruleD73) # label(axiom). [clausify(74)].
% 9.54/9.81 211 eqangle(c4,c1,c1,c2,c4,c1,c1,c3) # label(exemplo6GDDFULL214039) # label(negated_conjecture). [clausify(95)].
% 9.54/9.81 212 eqangle(c4,c2,c2,c3,c4,c2,c2,c1) # label(exemplo6GDDFULL214039) # label(negated_conjecture). [clausify(95)].
% 9.54/9.81 213 eqangle(c4,c3,c3,c1,c4,c3,c3,c2) # label(exemplo6GDDFULL214039) # label(negated_conjecture). [clausify(95)].
% 9.54/9.81 216 -para(c6,c7,c1,c4) # label(exemplo6GDDFULL214039) # label(negated_conjecture). [clausify(95)].
% 9.54/9.81 297 -coll(A,B,C) | coll(C,C,A). [factor(114,a,b)].
% 9.54/9.81 302 -cyclic(A,B,C,D) | cyclic(B,C,D,D). [factor(127,a,b)].
% 9.54/9.81 305 -cyclic(A,B,C,D) | -cyclic(A,B,C,E) | -eqangle(C,A,C,B,E,D,E,E) | cong(A,B,D,E). [factor(154,b,c)].
% 9.54/9.81 307 -cong(A,B,C,B) | perp(A,C,B,B). [factor(162,a,b)].
% 9.54/9.81 365 eqangle(c4,c1,c4,c1,c1,c2,c1,c3). [resolve(211,a,131,a)].
% 9.54/9.81 367 eqangle(c1,c2,c4,c1,c1,c3,c4,c1). [resolve(211,a,129,a)].
% 9.54/9.81 374 eqangle(c4,c2,c4,c2,c2,c3,c2,c1). [resolve(212,a,131,a)].
% 9.54/9.81 376 eqangle(c2,c3,c4,c2,c2,c1,c4,c2). [resolve(212,a,129,a)].
% 9.54/9.81 385 eqangle(c3,c1,c4,c3,c3,c2,c4,c3). [resolve(213,a,129,a)].
% 9.54/9.81 545 -eqangle(A,B,C,D,c4,c1,c4,c1) | eqangle(A,B,C,D,c1,c2,c1,c3). [resolve(365,a,132,b)].
% 9.54/9.81 547 eqangle(c1,c2,c1,c3,c4,c1,c4,c1). [resolve(365,a,130,a)].
% 9.54/9.81 597 para(c1,c2,c1,c3). [resolve(367,a,149,a)].
% 9.54/9.81 648 coll(c1,c2,c3). [resolve(597,a,172,a)].
% 9.54/9.81 653 eqangle(c1,c2,A,B,c1,c3,A,B). [resolve(597,a,150,a)].
% 9.54/9.81 656 -para(c1,c3,A,B) | para(c1,c2,A,B). [resolve(597,a,117,a)].
% 9.54/9.81 657 para(c1,c3,c1,c2). [resolve(597,a,116,a)].
% 9.54/9.81 661 coll(c3,c3,c1). [resolve(648,a,297,a)].
% 9.54/9.81 672 coll(c1,c1,c3). [resolve(661,a,297,a)].
% 9.54/9.81 743 -para(c2,c3,c2,c1) | para(c4,c2,c4,c2). [resolve(374,a,178,a)].
% 9.54/9.81 796 para(c2,c3,c2,c1). [resolve(376,a,149,a)].
% 9.54/9.81 800 para(c4,c2,c4,c2). [back_unit_del(743),unit_del(a,796)].
% 9.54/9.81 908 para(c2,c1,c2,c3). [resolve(796,a,116,a)].
% 9.54/9.81 924 eqangle(c4,c2,A,B,c4,c2,A,B). [resolve(800,a,150,a)].
% 9.54/9.81 1012 eqangle(c2,c1,A,B,c2,c3,A,B). [resolve(908,a,150,a)].
% 9.54/9.81 1253 para(c3,c1,c3,c2). [resolve(385,a,149,a)].
% 9.54/9.81 1275 para(c3,c1,c2,c3). [resolve(1253,a,115,a)].
% 9.54/9.81 1319 -perp(c2,c3,A,B) | perp(c3,c1,A,B). [resolve(1275,a,121,a)].
% 9.54/9.81 2942 eqangle(c1,c2,c1,c3,c1,c2,c1,c3). [resolve(547,a,545,a)].
% 9.54/9.81 3533 -cyclic(c2,c1,c1,c3) | -cyclic(c2,c1,c1,c1) | cong(c2,c1,c3,c1). [resolve(653,a,305,c)].
% 9.54/9.81 3619 para(c1,c2,c1,c2). [resolve(656,a,657,a)].
% 9.54/9.81 3667 eqangle(c1,c2,A,B,c1,c2,A,B). [resolve(3619,a,150,a)].
% 9.54/9.81 5527 eqangle(A,B,c4,c2,A,B,c4,c2). [resolve(924,a,129,a)].
% 9.54/9.81 7443 eqangle(A,B,c2,c1,A,B,c2,c3). [resolve(1012,a,129,a)].
% 9.54/9.81 18173 cyclic(c2,c3,c1,c1). [resolve(2942,a,153,a),unit_del(a,672)].
% 9.54/9.81 18180 cyclic(c3,c2,c1,c1). [resolve(18173,a,126,a)].
% 9.54/9.81 18181 cyclic(c2,c1,c3,c1). [resolve(18173,a,125,a)].
% 9.54/9.81 18188 cyclic(c2,c1,c1,c1). [resolve(18180,a,302,a)].
% 9.54/9.81 18191 cyclic(c3,c1,c2,c1). [resolve(18180,a,125,a)].
% 9.54/9.81 18192 -cyclic(c2,c1,c1,c3) | cong(c2,c1,c3,c1). [back_unit_del(3533),unit_del(b,18188)].
% 9.54/9.81 18198 cyclic(c2,c1,c1,c3). [resolve(18181,a,124,a)].
% 9.54/9.81 18199 cong(c2,c1,c3,c1). [back_unit_del(18192),unit_del(a,18198)].
% 9.54/9.81 18214 cyclic(c3,c1,c1,c2). [resolve(18191,a,124,a)].
% 9.54/9.81 18227 perp(c2,c3,c1,c1). [resolve(18199,a,307,a)].
% 9.54/9.81 18255 cyclic(c1,c1,c2,c2). [resolve(18214,a,302,a)].
% 9.54/9.81 18287 perp(c3,c1,c1,c1). [resolve(18227,a,1319,a)].
% 9.54/9.81 18323 cyclic(c1,c2,c1,c2). [resolve(18255,a,125,a)].
% 9.54/9.81 18393 -perp(A,B,c3,c1) | para(A,B,c1,c1). [resolve(18287,a,120,b)].
% 9.54/9.81 18395 perp(c1,c1,c3,c1). [resolve(18287,a,119,a)].
% 9.54/9.81 18451 cyclic(c2,c1,c1,c2). [resolve(18323,a,126,a)].
% 9.54/9.81 18557 -perp(c3,c1,A,B) | para(c1,c1,A,B). [resolve(18395,a,120,a)].
% 9.54/9.81 20773 -cyclic(c2,c1,c1,A) | cyclic(c1,c1,A,c2). [resolve(18451,a,127,b)].
% 9.54/9.81 27862 -coll(c1,c1,A) | cyclic(c2,A,c1,c1). [resolve(3667,a,153,a)].
% 9.54/9.81 34672 para(A,B,A,B). [resolve(5527,a,149,a)].
% 9.54/9.81 34698 coll(A,B,B). [resolve(34672,a,172,a)].
% 9.54/9.81 34700 coll(A,A,B). [resolve(34698,a,297,a)].
% 9.54/9.81 34704 cyclic(c2,A,c1,c1). [back_unit_del(27862),unit_del(a,34700)].
% 9.54/9.81 35040 cyclic(c2,c1,A,c1). [resolve(34704,a,125,a)].
% 9.54/9.81 35124 cyclic(c2,c1,c1,A). [resolve(35040,a,124,a)].
% 9.54/9.81 35126 cyclic(c1,c1,A,c2). [back_unit_del(20773),unit_del(a,35124)].
% 9.54/9.81 35273 cyclic(c1,c1,A,B). [resolve(35124,a,127,b),unit_del(a,35124)].
% 9.54/9.81 35277 cyclic(c1,A,B,c2). [resolve(35126,a,127,b),unit_del(a,35273)].
% 9.54/9.81 35432 cyclic(c1,A,B,C). [resolve(35273,a,127,b),unit_del(a,35273)].
% 9.54/9.81 35441 cyclic(A,B,C,c2). [resolve(35277,a,127,b),unit_del(a,35432)].
% 9.54/9.81 35442 cyclic(A,B,c2,C). [resolve(35277,a,127,a),unit_del(a,35432)].
% 9.54/9.81 35448 cong(A,c1,A,c3). [resolve(7443,a,154,d),unit_del(a,35442),unit_del(b,35442),unit_del(c,35441)].
% 9.54/9.81 35576 cong(A,c1,c3,A). [resolve(35448,a,133,a)].
% 9.54/9.81 35649 cong(c3,A,A,c1). [resolve(35576,a,134,a)].
% 9.54/9.81 35681 cong(c3,A,c1,A). [resolve(35649,a,133,a)].
% 9.54/9.81 35693 perp(c3,c1,A,B). [resolve(35681,a,162,b),unit_del(a,35681)].
% 9.54/9.81 35697 para(c1,c1,A,B). [back_unit_del(18557),unit_del(a,35693)].
% 9.54/9.81 35728 perp(A,B,c3,c1). [resolve(35693,a,119,a)].
% 9.54/9.81 35729 para(A,B,c1,c1). [back_unit_del(18393),unit_del(a,35728)].
% 9.54/9.81 35753 para(A,B,C,D). [resolve(35697,a,117,b),unit_del(a,35729)].
% 9.54/9.81 35754 $F. [resolve(35753,a,216,a)].
% 9.54/9.81
% 9.54/9.81 % SZS output end Refutation
% 9.54/9.81 ============================== end of proof ==========================
% 9.54/9.81
% 9.54/9.81 ============================== STATISTICS ============================
% 9.54/9.81
% 9.54/9.81 Given=12960. Generated=190045. Kept=35622. proofs=1.
% 9.54/9.81 Usable=10926. Sos=9052. Demods=0. Limbo=1, Disabled=15824. Hints=0.
% 9.54/9.81 Megabytes=17.92.
% 9.54/9.81 User_CPU=8.65, System_CPU=0.10, Wall_clock=9.
% 9.54/9.81
% 9.54/9.81 ============================== end of statistics =====================
% 9.54/9.81
% 9.54/9.81 ============================== end of search =========================
% 9.54/9.81
% 9.54/9.81 THEOREM PROVED
% 9.54/9.81 % SZS status Theorem
% 9.54/9.81
% 9.54/9.81 Exiting with 1 proof.
% 9.54/9.81
% 9.54/9.81 Process 13658 exit (max_proofs) Sat Jun 18 18:58:47 2022
% 9.54/9.81 Prover9 interrupted
%------------------------------------------------------------------------------