TSTP Solution File: GEO542+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GEO542+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 05:56:52 EDT 2022
% Result : Theorem 5.75s 6.04s
% Output : Refutation 5.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO542+1 : TPTP v8.1.0. Released v7.5.0.
% 0.12/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n012.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 18 08:22:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.41/1.06 ============================== Prover9 ===============================
% 0.41/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.41/1.06 Process 4743 was started by sandbox2 on n012.cluster.edu,
% 0.41/1.06 Sat Jun 18 08:22:54 2022
% 0.41/1.06 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_4590_n012.cluster.edu".
% 0.41/1.06 ============================== end of head ===========================
% 0.41/1.06
% 0.41/1.06 ============================== INPUT =================================
% 0.41/1.06
% 0.41/1.06 % Reading from file /tmp/Prover9_4590_n012.cluster.edu
% 0.41/1.06
% 0.41/1.06 set(prolog_style_variables).
% 0.41/1.06 set(auto2).
% 0.41/1.06 % set(auto2) -> set(auto).
% 0.41/1.06 % set(auto) -> set(auto_inference).
% 0.41/1.06 % set(auto) -> set(auto_setup).
% 0.41/1.06 % set(auto_setup) -> set(predicate_elim).
% 0.41/1.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.41/1.06 % set(auto) -> set(auto_limits).
% 0.41/1.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.41/1.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.41/1.06 % set(auto) -> set(auto_denials).
% 0.41/1.06 % set(auto) -> set(auto_process).
% 0.41/1.06 % set(auto2) -> assign(new_constants, 1).
% 0.41/1.06 % set(auto2) -> assign(fold_denial_max, 3).
% 0.41/1.06 % set(auto2) -> assign(max_weight, "200.000").
% 0.41/1.06 % set(auto2) -> assign(max_hours, 1).
% 0.41/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.41/1.06 % set(auto2) -> assign(max_seconds, 0).
% 0.41/1.06 % set(auto2) -> assign(max_minutes, 5).
% 0.41/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.41/1.06 % set(auto2) -> set(sort_initial_sos).
% 0.41/1.06 % set(auto2) -> assign(sos_limit, -1).
% 0.41/1.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.41/1.06 % set(auto2) -> assign(max_megs, 400).
% 0.41/1.06 % set(auto2) -> assign(stats, some).
% 0.41/1.06 % set(auto2) -> clear(echo_input).
% 0.41/1.06 % set(auto2) -> set(quiet).
% 0.41/1.06 % set(auto2) -> clear(print_initial_clauses).
% 0.41/1.06 % set(auto2) -> clear(print_given).
% 0.41/1.06 assign(lrs_ticks,-1).
% 0.41/1.06 assign(sos_limit,10000).
% 0.41/1.06 assign(order,kbo).
% 0.41/1.06 set(lex_order_vars).
% 0.41/1.06 clear(print_given).
% 0.41/1.06
% 0.41/1.06 % formulas(sos). % not echoed (95 formulas)
% 0.41/1.06
% 0.41/1.06 ============================== end of input ==========================
% 0.41/1.06
% 0.41/1.06 % From the command line: assign(max_seconds, 300).
% 0.41/1.06
% 0.41/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.41/1.06
% 0.41/1.06 % Formulas that are not ordinary clauses:
% 0.41/1.06 1 (all A all B all C (coll(A,B,C) -> coll(A,C,B))) # label(ruleD1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.06 2 (all A all B all C (coll(A,B,C) -> coll(B,A,C))) # label(ruleD2) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.06 11 (all A all B all M (midp(M,B,A) -> midp(M,A,B))) # label(ruleD11) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.06 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 67 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.07 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].
% 0.41/1.07 69 (all A all B all C (midp(A,B,C) -> cong(A,B,A,C))) # label(ruleD68) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.07 70 (all A all B all C (midp(A,B,C) -> coll(A,B,C))) # label(ruleD69) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 95 -(all A all B all C all A1 all B1 all C1 all O (midp(A1,C,B) & midp(B1,C,A) & midp(C1,B,A) & circle(O,A,B,C) -> perp(O,A1,B1,C1))) # label(exemplo6GDDFULL012002) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.41/1.07
% 0.41/1.07 ============================== end of process non-clausal formulas ===
% 0.41/1.07
% 0.41/1.07 ============================== PROCESS INITIAL CLAUSES ===============
% 0.41/1.07
% 0.41/1.07 ============================== PREDICATE ELIMINATION =================
% 0.41/1.07 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)].
% 0.41/1.07 97 -cong(A,B,A,C) | -cong(A,B,A,D) | circle(A,B,C,D) # label(ruleD12) # label(axiom). [clausify(12)].
% 0.41/1.07 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)].
% 0.41/1.07 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)].
% 0.41/1.07 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)].
% 0.41/1.07 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)].
% 0.41/1.07 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)].
% 0.41/1.07 100 -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)].
% 0.41/1.07 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)].
% 0.41/1.07 101 -circle(A,B,C,D) | -coll(A,B,D) | perp(B,C,C,D) # label(ruleD53) # label(axiom). [clausify(54)].
% 0.41/1.07 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)].
% 0.41/1.07 102 -circle(A,B,C,D) | perp(f12(B,C,D,A),B,B,A) # label(ruleX11) # label(axiom). [clausify(87)].
% 0.41/1.07 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)].
% 0.41/1.07 103 -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)].
% 0.41/1.07 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)].
% 0.41/1.07 104 -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)].
% 0.41/1.07 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)].
% 0.41/1.07 105 -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)].
% 0.41/1.07 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)].
% 0.41/1.07 106 -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)].
% 0.41/1.07 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)].
% 0.41/1.07 107 -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)].
% 0.41/1.07 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)].
% 0.41/1.07 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)].
% 0.41/1.07 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)].
% 0.41/1.07 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)].
% 0.41/1.07 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)].
% 0.41/1.07 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)].
% 0.41/1.07 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)].
% 0.41/1.07 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)].
% 0.41/1.07 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)].
% 0.41/1.07 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)].
% 0.41/1.07 108 -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)].
% 0.41/1.07 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)].
% 0.41/1.07 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)].
% 0.41/1.07 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)].
% 0.41/1.07 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)].
% 0.41/1.07 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)].
% 0.41/1.07 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)].
% 0.41/1.07 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)].
% 0.41/1.07 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)].
% 0.41/1.07 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)].
% 0.41/1.07 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)].
% 0.41/1.07 109 circle(c7,c1,c2,c3) # label(exemplo6GDDFULL012002) # label(negated_conjecture). [clausify(95)].
% 0.41/1.07 Derived: -perp(c7,c1,c1,A) | eqangle(c1,A,c1,c2,c3,c1,c3,c2). [resolve(109,a,96,a)].
% 0.41/1.07 Derived: -eqangle(c1,A,c1,c2,c3,c1,c3,c2) | perp(c7,c1,c1,A). [resolve(109,a,98,a)].
% 0.41/1.07 Derived: -midp(A,c2,c3) | eqangle(c1,c2,c1,c3,c7,c2,c7,A). [resolve(109,a,99,a)].
% 0.41/1.07 Derived: -coll(A,c2,c3) | -eqangle(c1,c2,c1,c3,c7,c2,c7,A) | midp(A,c2,c3). [resolve(109,a,100,a)].
% 0.41/1.07 Derived: -coll(c7,c1,c3) | perp(c1,c2,c2,c3). [resolve(109,a,101,a)].
% 0.41/1.07 Derived: perp(f12(c1,c2,c3,c7),c1,c1,c7). [resolve(109,a,102,a)].
% 0.41/1.07 Derived: -cong(c7,c1,c7,A) | -cong(B,c1,B,c2) | B = c7 | coll(f13(c1,c2,c3,A,c7,B),c1,c3). [resolve(109,a,103,a)].
% 0.41/1.07 Derived: -cong(c7,c1,c7,A) | -cong(B,c1,B,c2) | B = c7 | cong(f13(c1,c2,c3,A,c7,B),B,B,c1). [resolve(109,a,104,a)].
% 5.75/6.04 Derived: -cong(c7,c1,c7,A) | -cong(B,c1,B,c2) | B = c7 | coll(f14(c1,c2,c3,A,c7,B),c2,A). [resolve(109,a,105,a)].
% 5.75/6.04 Derived: -cong(c7,c1,c7,A) | -cong(B,c1,B,c2) | B = c7 | cong(f14(c1,c2,c3,A,c7,B),B,B,c1). [resolve(109,a,106,a)].
% 5.75/6.04
% 5.75/6.04 ============================== end predicate elimination =============
% 5.75/6.04
% 5.75/6.04 Auto_denials: (non-Horn, no changes).
% 5.75/6.04
% 5.75/6.04 Term ordering decisions:
% 5.75/6.04 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=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.
% 5.75/6.04
% 5.75/6.04 ============================== end of process initial clauses ========
% 5.75/6.04
% 5.75/6.04 ============================== CLAUSES FOR SEARCH ====================
% 5.75/6.04
% 5.75/6.04 ============================== end of clauses for search =============
% 5.75/6.04
% 5.75/6.04 ============================== SEARCH ================================
% 5.75/6.04
% 5.75/6.04 % Starting search at 0.02 seconds.
% 5.75/6.04
% 5.75/6.04 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 496 (0.00 of 0.15 sec).
% 5.75/6.04
% 5.75/6.04 Low Water (keep): wt=33.000, iters=3386
% 5.75/6.04
% 5.75/6.04 Low Water (keep): wt=32.000, iters=3364
% 5.75/6.04
% 5.75/6.04 Low Water (keep): wt=30.000, iters=3345
% 5.75/6.04
% 5.75/6.04 Low Water (keep): wt=29.000, iters=3341
% 5.75/6.04
% 5.75/6.04 Low Water (keep): wt=28.000, iters=3394
% 5.75/6.04
% 5.75/6.04 Low Water (keep): wt=27.000, iters=3390
% 5.75/6.04
% 5.75/6.04 Low Water (keep): wt=24.000, iters=3400
% 5.75/6.04
% 5.75/6.04 Low Water (keep): wt=23.000, iters=3401
% 5.75/6.04
% 5.75/6.04 Low Water (keep): wt=22.000, iters=3350
% 5.75/6.04
% 5.75/6.04 Low Water (keep): wt=19.000, iters=3337
% 5.75/6.04
% 5.75/6.04 Low Water (keep): wt=18.000, iters=3355
% 5.75/6.04
% 5.75/6.04 Low Water (keep): wt=17.000, iters=4033
% 5.75/6.04
% 5.75/6.04 Low Water (keep): wt=15.000, iters=3344
% 5.75/6.04
% 5.75/6.04 Low Water (displace): id=3004, wt=53.000
% 5.75/6.04
% 5.75/6.04 Low Water (displace): id=12728, wt=11.000
% 5.75/6.04
% 5.75/6.04 Low Water (displace): id=12737, wt=10.000
% 5.75/6.04
% 5.75/6.04 Low Water (keep): wt=14.000, iters=3361
% 5.75/6.04
% 5.75/6.04 Low Water (displace): id=13399, wt=9.000
% 5.75/6.04
% 5.75/6.04 Low Water (keep): wt=13.000, iters=3363
% 5.75/6.04
% 5.75/6.04 Low Water (displace): id=14357, wt=8.000
% 5.75/6.04
% 5.75/6.04 Low Water (keep): wt=12.000, iters=3335
% 5.75/6.04
% 5.75/6.04 Low Water (keep): wt=11.000, iters=3344
% 5.75/6.04
% 5.75/6.04 Low Water (keep): wt=10.000, iters=3335
% 5.75/6.04
% 5.75/6.04 Low Water (displace): id=25726, wt=5.000
% 5.75/6.04
% 5.75/6.04 Low Water (keep): wt=9.000, iters=3335
% 5.75/6.04
% 5.75/6.04 ============================== PROOF =================================
% 5.75/6.04 % SZS status Theorem
% 5.75/6.04 % SZS output start Refutation
% 5.75/6.04
% 5.75/6.04 % Proof 1 at 4.90 (+ 0.09) seconds.
% 5.75/6.04 % Length of proof is 171.
% 5.75/6.04 % Level of proof is 23.
% 5.75/6.04 % Maximum clause weight is 29.000.
% 5.75/6.04 % Given clauses 8966.
% 5.75/6.04
% 5.75/6.04 1 (all A all B all C (coll(A,B,C) -> coll(A,C,B))) # label(ruleD1) # label(axiom) # label(non_clause). [assumption].
% 5.75/6.04 2 (all A all B all C (coll(A,B,C) -> coll(B,A,C))) # label(ruleD2) # label(axiom) # label(non_clause). [assumption].
% 5.75/6.04 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].
% 5.75/6.04 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].
% 5.75/6.04 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].
% 5.75/6.04 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].
% 5.75/6.04 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].
% 5.75/6.04 11 (all A all B all M (midp(M,B,A) -> midp(M,A,B))) # label(ruleD11) # label(axiom) # label(non_clause). [assumption].
% 5.75/6.04 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].
% 5.75/6.04 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].
% 5.75/6.04 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].
% 5.75/6.04 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].
% 5.75/6.04 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].
% 5.75/6.04 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].
% 5.75/6.04 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].
% 5.75/6.04 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].
% 5.75/6.04 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].
% 5.75/6.04 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].
% 5.75/6.04 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].
% 5.75/6.04 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].
% 5.75/6.04 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].
% 5.75/6.04 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].
% 5.75/6.04 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].
% 5.75/6.04 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].
% 5.75/6.04 67 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption].
% 5.75/6.04 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].
% 5.75/6.04 69 (all A all B all C (midp(A,B,C) -> cong(A,B,A,C))) # label(ruleD68) # label(axiom) # label(non_clause). [assumption].
% 5.75/6.04 70 (all A all B all C (midp(A,B,C) -> coll(A,B,C))) # label(ruleD69) # label(axiom) # label(non_clause). [assumption].
% 5.75/6.04 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].
% 5.75/6.04 95 -(all A all B all C all A1 all B1 all C1 all O (midp(A1,C,B) & midp(B1,C,A) & midp(C1,B,A) & circle(O,A,B,C) -> perp(O,A1,B1,C1))) # label(exemplo6GDDFULL012002) # label(negated_conjecture) # label(non_clause). [assumption].
% 5.75/6.04 97 -cong(A,B,A,C) | -cong(A,B,A,D) | circle(A,B,C,D) # label(ruleD12) # label(axiom). [clausify(12)].
% 5.75/6.04 100 -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)].
% 5.75/6.04 101 -circle(A,B,C,D) | -coll(A,B,D) | perp(B,C,C,D) # label(ruleD53) # label(axiom). [clausify(54)].
% 5.75/6.04 102 -circle(A,B,C,D) | perp(f12(B,C,D,A),B,B,A) # label(ruleX11) # label(axiom). [clausify(87)].
% 5.75/6.04 109 circle(c7,c1,c2,c3) # label(exemplo6GDDFULL012002) # label(negated_conjecture). [clausify(95)].
% 5.75/6.04 110 -coll(A,B,C) | coll(A,C,B) # label(ruleD1) # label(axiom). [clausify(1)].
% 5.75/6.04 111 -coll(A,B,C) | coll(B,A,C) # label(ruleD2) # label(axiom). [clausify(2)].
% 5.75/6.04 112 -coll(A,B,C) | -coll(A,B,D) | coll(C,D,A) # label(ruleD3) # label(axiom). [clausify(3)].
% 5.75/6.04 113 -para(A,B,C,D) | para(A,B,D,C) # label(ruleD4) # label(axiom). [clausify(4)].
% 5.75/6.04 117 -perp(A,B,C,D) | perp(C,D,A,B) # label(ruleD8) # label(axiom). [clausify(8)].
% 5.75/6.04 118 -perp(A,B,C,D) | -perp(C,D,E,F) | para(A,B,E,F) # label(ruleD9) # label(axiom). [clausify(9)].
% 5.75/6.04 119 -para(A,B,C,D) | -perp(C,D,E,F) | perp(A,B,E,F) # label(ruleD10) # label(axiom). [clausify(10)].
% 5.75/6.04 120 -midp(A,B,C) | midp(A,C,B) # label(ruleD11) # label(axiom). [clausify(11)].
% 5.75/6.04 121 -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)].
% 5.75/6.04 125 -cyclic(A,B,C,D) | -cyclic(A,B,C,E) | cyclic(B,C,D,E) # label(ruleD17) # label(axiom). [clausify(17)].
% 5.75/6.04 131 -cong(A,B,C,D) | cong(A,B,D,C) # label(ruleD23) # label(axiom). [clausify(23)].
% 5.75/6.04 132 -cong(A,B,C,D) | cong(C,D,A,B) # label(ruleD24) # label(axiom). [clausify(24)].
% 5.75/6.04 133 -cong(A,B,C,D) | -cong(C,D,E,F) | cong(A,B,E,F) # label(ruleD25) # label(axiom). [clausify(25)].
% 5.75/6.04 149 -cyclic(A,B,C,D) | eqangle(C,A,C,B,D,A,D,B) # label(ruleD41) # label(axiom). [clausify(41)].
% 5.75/6.04 152 -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)].
% 5.75/6.04 153 -midp(A,B,C) | -midp(D,B,E) | para(A,D,C,E) # label(ruleD44) # label(axiom). [clausify(45)].
% 5.75/6.04 157 -perp(A,B,B,C) | -midp(D,A,C) | cong(A,D,B,D) # label(ruleD52) # label(axiom). [clausify(53)].
% 5.75/6.04 159 -midp(A,B,C) | -perp(D,A,B,C) | cong(D,B,D,C) # label(ruleD55) # label(axiom). [clausify(56)].
% 5.75/6.04 160 -cong(A,B,C,B) | -cong(A,D,C,D) | perp(A,C,B,D) # label(ruleD56) # label(axiom). [clausify(57)].
% 5.75/6.04 167 -midp(A,B,C) | -midp(A,D,E) | para(B,D,C,E) # label(ruleD63) # label(axiom). [clausify(64)].
% 5.75/6.04 168 -midp(A,B,C) | -para(B,D,C,E) | -para(B,E,C,D) | midp(A,D,E) # label(ruleD64) # label(axiom). [clausify(65)].
% 5.75/6.04 170 -para(A,B,A,C) | coll(A,B,C) # label(ruleD66) # label(axiom). [clausify(67)].
% 5.75/6.04 171 -cong(A,B,A,C) | -coll(A,B,C) | midp(A,B,C) # label(ruleD67) # label(axiom). [clausify(68)].
% 5.75/6.04 172 -midp(A,B,C) | cong(A,B,A,C) # label(ruleD68) # label(axiom). [clausify(69)].
% 5.75/6.04 173 -midp(A,B,C) | coll(A,B,C) # label(ruleD69) # label(axiom). [clausify(70)].
% 5.75/6.04 209 midp(c4,c3,c2) # label(exemplo6GDDFULL012002) # label(negated_conjecture). [clausify(95)].
% 5.75/6.04 210 midp(c5,c3,c1) # label(exemplo6GDDFULL012002) # label(negated_conjecture). [clausify(95)].
% 5.75/6.04 211 midp(c6,c2,c1) # label(exemplo6GDDFULL012002) # label(negated_conjecture). [clausify(95)].
% 5.75/6.04 212 -perp(c7,c4,c5,c6) # label(exemplo6GDDFULL012002) # label(negated_conjecture). [clausify(95)].
% 5.75/6.04 216 -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)].
% 5.75/6.04 217 -coll(A,B,C) | perp(B,D,D,C) | -cong(A,B,A,D) | -cong(A,B,A,C). [resolve(101,a,97,c)].
% 5.75/6.04 256 perp(f12(c1,c2,c3,c7),c1,c1,c7). [resolve(109,a,102,a)].
% 5.75/6.04 265 -coll(A,B,C) | coll(C,C,A). [factor(112,a,b)].
% 5.75/6.04 267 -cong(A,B,A,C) | -cong(A,B,A,D) | cyclic(B,C,C,D). [factor(121,a,b)].
% 5.75/6.04 270 -cyclic(A,B,C,D) | cyclic(B,C,D,D). [factor(125,a,b)].
% 5.75/6.04 271 -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(152,a,b)].
% 5.75/6.04 279 -midp(A,B,C) | -para(B,D,C,D) | midp(A,D,D). [factor(168,b,c)].
% 5.75/6.04 303 -coll(A,B,B) | -eqangle(C,B,C,B,D,B,D,A) | midp(A,B,B) | -cong(D,C,D,B). [factor(216,d,e)].
% 5.75/6.04 304 -coll(A,B,C) | perp(B,C,C,C) | -cong(A,B,A,C). [factor(217,c,d)].
% 5.75/6.04 319 -cong(A,B,A,C) | cyclic(B,C,C,C). [factor(267,a,b)].
% 5.75/6.04 320 -cyclic(A,B,C,D) | -eqangle(C,A,C,B,D,D,D,D) | cong(A,B,D,D). [factor(271,a,b)].
% 5.75/6.04 338 coll(c4,c3,c2). [resolve(209,a,173,a)].
% 5.75/6.04 339 cong(c4,c3,c4,c2). [resolve(209,a,172,a)].
% 5.75/6.04 340 -midp(c4,A,B) | para(A,c3,B,c2). [resolve(209,a,167,b)].
% 5.75/6.04 341 -midp(c4,A,B) | para(c3,A,c2,B). [resolve(209,a,167,a)].
% 5.75/6.04 344 midp(c4,c2,c3). [resolve(209,a,120,a)].
% 5.75/6.04 362 midp(c5,c1,c3). [resolve(210,a,120,a)].
% 5.75/6.04 374 coll(c6,c2,c1). [resolve(211,a,173,a)].
% 5.75/6.04 375 cong(c6,c2,c6,c1). [resolve(211,a,172,a)].
% 5.75/6.04 376 -midp(c6,A,B) | para(A,c2,B,c1). [resolve(211,a,167,b)].
% 5.75/6.04 377 -midp(c6,A,B) | para(c2,A,c1,B). [resolve(211,a,167,a)].
% 5.75/6.04 380 midp(c6,c1,c2). [resolve(211,a,120,a)].
% 5.75/6.04 402 -perp(A,B,f12(c1,c2,c3,c7),c1) | para(A,B,c1,c7). [resolve(256,a,118,b)].
% 5.75/6.04 404 perp(c1,c7,f12(c1,c2,c3,c7),c1). [resolve(256,a,117,a)].
% 5.75/6.04 430 coll(c2,c2,c4). [resolve(338,a,265,a)].
% 5.75/6.04 434 coll(c4,c2,c3). [resolve(338,a,110,a)].
% 5.75/6.04 455 cong(c4,c2,c4,c3). [resolve(344,a,172,a)].
% 5.75/6.04 456 -midp(c4,A,B) | para(A,c2,B,c3). [resolve(344,a,167,b)].
% 5.75/6.04 488 -midp(A,c1,B) | para(c5,A,c3,B). [resolve(362,a,153,a)].
% 5.75/6.04 493 coll(c1,c1,c6). [resolve(374,a,265,a)].
% 5.75/6.04 496 coll(c2,c6,c1). [resolve(374,a,111,a)].
% 5.75/6.04 497 coll(c6,c1,c2). [resolve(374,a,110,a)].
% 5.75/6.04 518 cong(c6,c1,c6,c2). [resolve(380,a,172,a)].
% 5.75/6.04 519 -midp(c6,A,B) | para(A,c1,B,c2). [resolve(380,a,167,b)].
% 5.75/6.04 520 -midp(c6,A,B) | para(c1,A,c2,B). [resolve(380,a,167,a)].
% 5.75/6.04 526 coll(c2,c4,c2). [resolve(430,a,110,a)].
% 5.75/6.04 563 coll(c1,c6,c1). [resolve(493,a,110,a)].
% 5.75/6.04 564 coll(c1,c1,c2). [resolve(496,a,265,a)].
% 5.75/6.04 581 coll(c2,c2,c2). [resolve(526,a,265,a)].
% 5.75/6.04 584 coll(c4,c2,c2). [resolve(526,a,111,a)].
% 5.75/6.04 646 coll(c6,c1,c1). [resolve(563,a,111,a)].
% 5.75/6.04 647 coll(c2,c2,c1). [resolve(564,a,265,a)].
% 5.75/6.04 700 cyclic(c3,c2,c2,c2). [resolve(339,a,319,a)].
% 5.75/6.04 769 -cong(A,B,c4,c3) | cong(A,B,c4,c2). [resolve(339,a,133,b)].
% 5.75/6.04 771 cong(c4,c3,c2,c4). [resolve(339,a,131,a)].
% 5.75/6.04 800 para(c3,c2,c2,c3). [resolve(341,a,344,a)].
% 5.75/6.04 812 coll(c2,c1,c2). [resolve(647,a,110,a)].
% 5.75/6.04 868 coll(c1,c2,c2). [resolve(812,a,111,a)].
% 5.75/6.04 1060 -cong(A,B,c6,c2) | cong(A,B,c6,c1). [resolve(375,a,133,b)].
% 5.75/6.04 1228 perp(c2,c3,c3,c3). [resolve(455,a,304,c),unit_del(a,434)].
% 5.75/6.04 1456 perp(c1,c2,c2,c2). [resolve(518,a,304,c),unit_del(a,497)].
% 5.75/6.04 1498 cyclic(c2,c2,c2,c2). [resolve(700,a,270,a)].
% 5.75/6.04 1554 cong(c2,c4,c4,c3). [resolve(771,a,132,a)].
% 5.75/6.04 1584 -perp(c2,c3,A,B) | perp(c3,c2,A,B). [resolve(800,a,119,a)].
% 5.75/6.04 1823 -midp(A,c2,c3) | cong(c2,A,c3,A). [resolve(1228,a,157,a)].
% 5.75/6.04 1957 -midp(c2,c2,c2) | cong(c1,c2,c1,c2). [resolve(1456,a,159,b)].
% 5.75/6.04 1989 eqangle(c2,c2,c2,c2,c2,c2,c2,c2). [resolve(1498,a,149,a)].
% 5.75/6.04 2029 cong(c2,c4,c3,c4). [resolve(1554,a,131,a)].
% 5.75/6.04 2431 -cong(c2,A,c3,A) | perp(c2,c3,A,c4). [resolve(2029,a,160,b)].
% 5.75/6.04 2525 para(c1,c2,c2,c1). [resolve(376,a,380,a)].
% 5.75/6.04 2581 para(c2,c1,c1,c2). [resolve(377,a,380,a)].
% 5.75/6.04 2820 para(c1,c2,c1,c2). [resolve(2525,a,113,a)].
% 5.75/6.04 2882 para(c2,c1,c2,c1). [resolve(2581,a,113,a)].
% 5.75/6.04 3121 -midp(A,c1,c1) | midp(A,c2,c2). [resolve(2820,a,279,b)].
% 5.75/6.04 3165 -midp(A,c2,c2) | midp(A,c1,c1). [resolve(2882,a,279,b)].
% 5.75/6.04 3695 para(c1,c7,c1,c7). [resolve(404,a,402,a)].
% 5.75/6.04 4067 -midp(A,c1,c1) | midp(A,c7,c7). [resolve(3695,a,279,b)].
% 5.75/6.04 4074 coll(c1,c7,c7). [resolve(3695,a,170,a)].
% 5.75/6.04 4079 coll(c7,c7,c1). [resolve(4074,a,265,a)].
% 5.75/6.04 4087 coll(c1,c1,c7). [resolve(4079,a,265,a)].
% 5.75/6.04 4114 coll(c1,c7,c1). [resolve(4087,a,110,a)].
% 5.75/6.04 4120 coll(c7,c1,c1). [resolve(4114,a,111,a)].
% 5.75/6.04 5206 para(c5,c6,c3,c2). [resolve(488,a,380,a)].
% 5.75/6.04 5254 -perp(c3,c2,A,B) | perp(c5,c6,A,B). [resolve(5206,a,119,a)].
% 5.75/6.04 8037 cong(c4,c2,c4,c2). [resolve(769,a,455,a)].
% 5.75/6.04 8103 midp(c4,c2,c2). [resolve(8037,a,171,a),unit_del(a,584)].
% 5.75/6.04 8119 midp(c4,c1,c1). [resolve(8103,a,3165,a)].
% 5.75/6.04 8247 para(c1,c2,c1,c3). [resolve(8119,a,456,a)].
% 5.75/6.04 8280 para(c1,c3,c1,c2). [resolve(8119,a,340,a)].
% 5.75/6.04 8979 -midp(A,c1,c1) | midp(A,c2,c3). [resolve(8247,a,168,b),unit_del(b,8280)].
% 5.75/6.04 13862 cong(c6,c1,c6,c1). [resolve(1060,a,518,a)].
% 5.75/6.04 13974 midp(c6,c1,c1). [resolve(13862,a,171,a),unit_del(a,646)].
% 5.75/6.04 13978 midp(c6,c7,c7). [resolve(13974,a,4067,a)].
% 5.75/6.04 13979 midp(c6,c2,c2). [resolve(13974,a,3121,a)].
% 5.75/6.04 14059 para(c1,c7,c2,c7). [resolve(13978,a,520,a)].
% 5.75/6.04 14136 para(c2,c1,c2,c2). [resolve(13979,a,519,a)].
% 5.75/6.04 14171 para(c2,c2,c2,c1). [resolve(13979,a,376,a)].
% 5.75/6.04 14659 -midp(A,c1,c2) | midp(A,c7,c7). [resolve(14059,a,279,b)].
% 5.75/6.04 14714 -midp(A,c2,c2) | midp(A,c1,c2). [resolve(14136,a,168,b),unit_del(b,14171)].
% 5.75/6.04 25499 cong(c2,c2,c2,c2). [resolve(1989,a,320,b),unit_del(a,1498)].
% 5.75/6.04 25500 midp(c2,c2,c2). [resolve(1989,a,303,b),unit_del(a,581),unit_del(c,25499)].
% 5.75/6.04 25514 cong(c1,c2,c1,c2). [back_unit_del(1957),unit_del(a,25500)].
% 5.75/6.04 26119 midp(c1,c2,c2). [resolve(25514,a,171,a),unit_del(a,868)].
% 5.75/6.04 26122 midp(c1,c1,c2). [resolve(26119,a,14714,a)].
% 5.75/6.04 26154 midp(c1,c7,c7). [resolve(26122,a,14659,a)].
% 5.75/6.04 26349 cong(c1,c7,c1,c7). [resolve(26154,a,172,a)].
% 5.75/6.04 26729 cong(c1,c7,c7,c1). [resolve(26349,a,131,a)].
% 5.75/6.04 27171 cong(c7,c1,c1,c7). [resolve(26729,a,132,a)].
% 5.75/6.04 27417 cong(c7,c1,c7,c1). [resolve(27171,a,131,a)].
% 5.75/6.04 27504 midp(c7,c1,c1). [resolve(27417,a,171,a),unit_del(a,4120)].
% 5.75/6.04 27510 midp(c7,c2,c3). [resolve(27504,a,8979,a)].
% 5.75/6.04 27629 cong(c2,c7,c3,c7). [resolve(27510,a,1823,a)].
% 5.75/6.04 28035 perp(c2,c3,c7,c4). [resolve(2431,a,27629,a)].
% 5.75/6.04 28363 perp(c3,c2,c7,c4). [resolve(28035,a,1584,a)].
% 5.75/6.04 34956 perp(c5,c6,c7,c4). [resolve(5254,a,28363,a)].
% 5.75/6.04 35453 $F. [resolve(34956,a,117,a),unit_del(a,212)].
% 5.75/6.04
% 5.75/6.04 % SZS output end Refutation
% 5.75/6.04 ============================== end of proof ==========================
% 5.75/6.04
% 5.75/6.04 ============================== STATISTICS ============================
% 5.75/6.04
% 5.75/6.04 Given=8966. Generated=151901. Kept=35331. proofs=1.
% 5.75/6.04 Usable=8892. Sos=9999. Demods=0. Limbo=4, Disabled=16594. Hints=0.
% 5.75/6.04 Megabytes=17.82.
% 5.75/6.04 User_CPU=4.90, System_CPU=0.09, Wall_clock=5.
% 5.75/6.04
% 5.75/6.04 ============================== end of statistics =====================
% 5.75/6.04
% 5.75/6.04 ============================== end of search =========================
% 5.75/6.04
% 5.75/6.04 THEOREM PROVED
% 5.75/6.04 % SZS status Theorem
% 5.75/6.04
% 5.75/6.04 Exiting with 1 proof.
% 5.75/6.04
% 5.75/6.04 Process 4743 exit (max_proofs) Sat Jun 18 08:22:59 2022
% 5.75/6.05 Prover9 interrupted
%------------------------------------------------------------------------------