TSTP Solution File: GEO638+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GEO638+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n008.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 05:57:21 EDT 2022
% Result : Theorem 6.51s 6.82s
% Output : Refutation 6.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO638+1 : TPTP v8.1.0. Released v7.5.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n008.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 03:13:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.42/1.08 ============================== Prover9 ===============================
% 0.42/1.08 Prover9 (32) version 2009-11A, November 2009.
% 0.42/1.08 Process 455 was started by sandbox2 on n008.cluster.edu,
% 0.42/1.08 Sat Jun 18 03:13:38 2022
% 0.42/1.08 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_32750_n008.cluster.edu".
% 0.42/1.08 ============================== end of head ===========================
% 0.42/1.08
% 0.42/1.08 ============================== INPUT =================================
% 0.42/1.08
% 0.42/1.08 % Reading from file /tmp/Prover9_32750_n008.cluster.edu
% 0.42/1.08
% 0.42/1.08 set(prolog_style_variables).
% 0.42/1.08 set(auto2).
% 0.42/1.08 % set(auto2) -> set(auto).
% 0.42/1.08 % set(auto) -> set(auto_inference).
% 0.42/1.08 % set(auto) -> set(auto_setup).
% 0.42/1.08 % set(auto_setup) -> set(predicate_elim).
% 0.42/1.08 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/1.08 % set(auto) -> set(auto_limits).
% 0.42/1.08 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/1.08 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/1.08 % set(auto) -> set(auto_denials).
% 0.42/1.08 % set(auto) -> set(auto_process).
% 0.42/1.08 % set(auto2) -> assign(new_constants, 1).
% 0.42/1.08 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/1.08 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/1.08 % set(auto2) -> assign(max_hours, 1).
% 0.42/1.08 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/1.08 % set(auto2) -> assign(max_seconds, 0).
% 0.42/1.08 % set(auto2) -> assign(max_minutes, 5).
% 0.42/1.08 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/1.08 % set(auto2) -> set(sort_initial_sos).
% 0.42/1.08 % set(auto2) -> assign(sos_limit, -1).
% 0.42/1.08 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/1.08 % set(auto2) -> assign(max_megs, 400).
% 0.42/1.08 % set(auto2) -> assign(stats, some).
% 0.42/1.08 % set(auto2) -> clear(echo_input).
% 0.42/1.08 % set(auto2) -> set(quiet).
% 0.42/1.08 % set(auto2) -> clear(print_initial_clauses).
% 0.42/1.08 % set(auto2) -> clear(print_given).
% 0.42/1.08 assign(lrs_ticks,-1).
% 0.42/1.08 assign(sos_limit,10000).
% 0.42/1.08 assign(order,kbo).
% 0.42/1.08 set(lex_order_vars).
% 0.42/1.08 clear(print_given).
% 0.42/1.08
% 0.42/1.08 % formulas(sos). % not echoed (95 formulas)
% 0.42/1.08
% 0.42/1.08 ============================== end of input ==========================
% 0.42/1.08
% 0.42/1.08 % From the command line: assign(max_seconds, 300).
% 0.42/1.08
% 0.42/1.08 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/1.08
% 0.42/1.08 % Formulas that are not ordinary clauses:
% 0.42/1.08 1 (all A all B all C (coll(A,B,C) -> coll(A,C,B))) # label(ruleD1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.08 2 (all A all B all C (coll(A,B,C) -> coll(B,A,C))) # label(ruleD2) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.08 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].
% 0.42/1.08 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].
% 0.42/1.08 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].
% 0.42/1.08 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].
% 0.42/1.08 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].
% 0.42/1.08 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].
% 0.42/1.08 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].
% 0.42/1.08 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].
% 0.42/1.08 11 (all A all B all M (midp(M,B,A) -> midp(M,A,B))) # label(ruleD11) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.08 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].
% 0.42/1.08 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].
% 0.42/1.08 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].
% 0.42/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 67 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.08 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].
% 0.81/1.08 69 (all A all B all C (midp(A,B,C) -> cong(A,B,A,C))) # label(ruleD68) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.08 70 (all A all B all C (midp(A,B,C) -> coll(A,B,C))) # label(ruleD69) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.08 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].
% 0.81/1.09 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].
% 0.81/1.09 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].
% 0.81/1.09 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].
% 0.81/1.09 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].
% 0.81/1.09 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].
% 0.81/1.09 95 -(all A all B all E all G all D all C all F all H all NWPNT1 all NWPNT2 all NWPNT3 (midp(E,A,B) & circle(E,A,NWPNT1,NWPNT2) & circle(E,A,G,NWPNT3) & perp(E,G,G,D) & para(A,D,C,B) & coll(C,G,D) & midp(F,C,D) & perp(H,F,A,B) & coll(H,A,B) -> perp(C,H,D,H))) # label(exemplo6GDDFULL81109104) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.81/1.09
% 0.81/1.09 ============================== end of process non-clausal formulas ===
% 0.81/1.09
% 0.81/1.09 ============================== PROCESS INITIAL CLAUSES ===============
% 0.81/1.09
% 0.81/1.09 ============================== PREDICATE ELIMINATION =================
% 0.81/1.09 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)].
% 0.81/1.09 97 -cong(A,B,A,C) | -cong(A,B,A,D) | circle(A,B,C,D) # label(ruleD12) # label(axiom). [clausify(12)].
% 0.81/1.09 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)].
% 0.81/1.09 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)].
% 0.81/1.09 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)].
% 0.81/1.09 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)].
% 0.81/1.09 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)].
% 0.81/1.09 100 -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)].
% 0.81/1.09 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)].
% 0.81/1.09 101 -circle(A,B,C,D) | -coll(A,B,D) | perp(B,C,C,D) # label(ruleD53) # label(axiom). [clausify(54)].
% 0.81/1.09 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)].
% 0.81/1.09 102 -circle(A,B,C,D) | perp(f12(B,C,D,A),B,B,A) # label(ruleX11) # label(axiom). [clausify(87)].
% 0.81/1.09 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)].
% 0.81/1.09 103 -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)].
% 0.81/1.09 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)].
% 0.81/1.09 104 -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)].
% 0.81/1.09 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)].
% 0.81/1.09 105 -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)].
% 0.81/1.09 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)].
% 0.81/1.09 106 -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)].
% 0.81/1.09 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)].
% 0.81/1.09 107 -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)].
% 0.81/1.09 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)].
% 0.81/1.09 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)].
% 0.81/1.09 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)].
% 0.81/1.09 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)].
% 0.81/1.09 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)].
% 0.81/1.09 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)].
% 0.81/1.09 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)].
% 0.81/1.09 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)].
% 0.81/1.09 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)].
% 0.81/1.09 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)].
% 0.81/1.09 108 -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)].
% 0.81/1.09 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)].
% 0.81/1.09 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)].
% 0.81/1.09 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)].
% 0.81/1.09 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)].
% 0.81/1.09 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)].
% 0.81/1.09 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)].
% 0.81/1.09 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)].
% 0.81/1.09 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)].
% 0.81/1.09 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)].
% 0.81/1.09 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)].
% 0.81/1.09 109 circle(c3,c1,c9,c10) # label(exemplo6GDDFULL81109104) # label(negated_conjecture). [clausify(95)].
% 0.81/1.09 Derived: -perp(c3,c1,c1,A) | eqangle(c1,A,c1,c9,c10,c1,c10,c9). [resolve(109,a,96,a)].
% 0.81/1.09 Derived: -eqangle(c1,A,c1,c9,c10,c1,c10,c9) | perp(c3,c1,c1,A). [resolve(109,a,98,a)].
% 0.81/1.09 Derived: -midp(A,c9,c10) | eqangle(c1,c9,c1,c10,c3,c9,c3,A). [resolve(109,a,99,a)].
% 0.81/1.09 Derived: -coll(A,c9,c10) | -eqangle(c1,c9,c1,c10,c3,c9,c3,A) | midp(A,c9,c10). [resolve(109,a,100,a)].
% 0.81/1.09 Derived: -coll(c3,c1,c10) | perp(c1,c9,c9,c10). [resolve(109,a,101,a)].
% 0.81/1.09 Derived: perp(f12(c1,c9,c10,c3),c1,c1,c3). [resolve(109,a,102,a)].
% 6.51/6.82 Derived: -cong(c3,c1,c3,A) | -cong(B,c1,B,c9) | B = c3 | coll(f13(c1,c9,c10,A,c3,B),c1,c10). [resolve(109,a,103,a)].
% 6.51/6.82 Derived: -cong(c3,c1,c3,A) | -cong(B,c1,B,c9) | B = c3 | cong(f13(c1,c9,c10,A,c3,B),B,B,c1). [resolve(109,a,104,a)].
% 6.51/6.82 Derived: -cong(c3,c1,c3,A) | -cong(B,c1,B,c9) | B = c3 | coll(f14(c1,c9,c10,A,c3,B),c9,A). [resolve(109,a,105,a)].
% 6.51/6.82 Derived: -cong(c3,c1,c3,A) | -cong(B,c1,B,c9) | B = c3 | cong(f14(c1,c9,c10,A,c3,B),B,B,c1). [resolve(109,a,106,a)].
% 6.51/6.82 110 circle(c3,c1,c4,c11) # label(exemplo6GDDFULL81109104) # label(negated_conjecture). [clausify(95)].
% 6.51/6.82 Derived: -perp(c3,c1,c1,A) | eqangle(c1,A,c1,c4,c11,c1,c11,c4). [resolve(110,a,96,a)].
% 6.51/6.82 Derived: -eqangle(c1,A,c1,c4,c11,c1,c11,c4) | perp(c3,c1,c1,A). [resolve(110,a,98,a)].
% 6.51/6.82 Derived: -midp(A,c4,c11) | eqangle(c1,c4,c1,c11,c3,c4,c3,A). [resolve(110,a,99,a)].
% 6.51/6.82 Derived: -coll(A,c4,c11) | -eqangle(c1,c4,c1,c11,c3,c4,c3,A) | midp(A,c4,c11). [resolve(110,a,100,a)].
% 6.51/6.82 Derived: -coll(c3,c1,c11) | perp(c1,c4,c4,c11). [resolve(110,a,101,a)].
% 6.51/6.82 Derived: perp(f12(c1,c4,c11,c3),c1,c1,c3). [resolve(110,a,102,a)].
% 6.51/6.82 Derived: -cong(c3,c1,c3,A) | -cong(B,c1,B,c4) | B = c3 | coll(f13(c1,c4,c11,A,c3,B),c1,c11). [resolve(110,a,103,a)].
% 6.51/6.82 Derived: -cong(c3,c1,c3,A) | -cong(B,c1,B,c4) | B = c3 | cong(f13(c1,c4,c11,A,c3,B),B,B,c1). [resolve(110,a,104,a)].
% 6.51/6.82 Derived: -cong(c3,c1,c3,A) | -cong(B,c1,B,c4) | B = c3 | coll(f14(c1,c4,c11,A,c3,B),c4,A). [resolve(110,a,105,a)].
% 6.51/6.82 Derived: -cong(c3,c1,c3,A) | -cong(B,c1,B,c4) | B = c3 | cong(f14(c1,c4,c11,A,c3,B),B,B,c1). [resolve(110,a,106,a)].
% 6.51/6.82
% 6.51/6.82 ============================== end predicate elimination =============
% 6.51/6.82
% 6.51/6.82 Auto_denials: (non-Horn, no changes).
% 6.51/6.82
% 6.51/6.82 Term ordering decisions:
% 6.51/6.82 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. c10=1. c11=1. f19=1. f1=1. f2=1. f3=1. f4=1. f10=1. f11=1. f12=1. f16=1. f5=1. f9=1. f15=1. f17=1. f18=1. f6=1. f13=1. f14=1. f20=1. f7=1. f8=1.
% 6.51/6.82
% 6.51/6.82 ============================== end of process initial clauses ========
% 6.51/6.82
% 6.51/6.82 ============================== CLAUSES FOR SEARCH ====================
% 6.51/6.82
% 6.51/6.82 ============================== end of clauses for search =============
% 6.51/6.82
% 6.51/6.82 ============================== SEARCH ================================
% 6.51/6.82
% 6.51/6.82 % Starting search at 0.05 seconds.
% 6.51/6.82
% 6.51/6.82 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 1418 (0.00 of 0.24 sec).
% 6.51/6.82
% 6.51/6.82 Low Water (keep): wt=39.000, iters=3466
% 6.51/6.82
% 6.51/6.82 Low Water (keep): wt=25.000, iters=3359
% 6.51/6.82
% 6.51/6.82 Low Water (keep): wt=24.000, iters=3340
% 6.51/6.82
% 6.51/6.82 Low Water (keep): wt=23.000, iters=3353
% 6.51/6.82
% 6.51/6.82 Low Water (keep): wt=19.000, iters=3354
% 6.51/6.82
% 6.51/6.82 Low Water (keep): wt=18.000, iters=3366
% 6.51/6.82
% 6.51/6.82 Low Water (keep): wt=17.000, iters=3334
% 6.51/6.82
% 6.51/6.82 Low Water (keep): wt=15.000, iters=3336
% 6.51/6.82
% 6.51/6.82 Low Water (keep): wt=14.000, iters=3335
% 6.51/6.82
% 6.51/6.82 Low Water (keep): wt=13.000, iters=3351
% 6.51/6.82
% 6.51/6.82 Low Water (displace): id=2641, wt=53.000
% 6.51/6.82
% 6.51/6.82 Low Water (displace): id=12718, wt=12.000
% 6.51/6.82
% 6.51/6.82 Low Water (displace): id=12724, wt=10.000
% 6.51/6.82
% 6.51/6.82 Low Water (displace): id=12761, wt=9.000
% 6.51/6.82
% 6.51/6.82 Low Water (keep): wt=12.000, iters=3334
% 6.51/6.82
% 6.51/6.82 Low Water (keep): wt=11.000, iters=3386
% 6.51/6.82
% 6.51/6.82 Low Water (displace): id=13638, wt=8.000
% 6.51/6.82
% 6.51/6.82 Low Water (displace): id=15935, wt=7.000
% 6.51/6.82
% 6.51/6.82 Low Water (keep): wt=10.000, iters=3333
% 6.51/6.82
% 6.51/6.82 Low Water (displace): id=18264, wt=5.000
% 6.51/6.82
% 6.51/6.82 Low Water (keep): wt=9.000, iters=3339
% 6.51/6.82
% 6.51/6.82 Low Water (keep): wt=8.000, iters=3333
% 6.51/6.82
% 6.51/6.82 ============================== PROOF =================================
% 6.51/6.82 % SZS status Theorem
% 6.51/6.82 % SZS output start Refutation
% 6.51/6.82
% 6.51/6.82 % Proof 1 at 5.66 (+ 0.10) seconds.
% 6.51/6.82 % Length of proof is 388.
% 6.51/6.82 % Level of proof is 56.
% 6.51/6.82 % Maximum clause weight is 20.000.
% 6.51/6.82 % Given clauses 9622.
% 6.51/6.82
% 6.51/6.82 1 (all A all B all C (coll(A,B,C) -> coll(A,C,B))) # label(ruleD1) # label(axiom) # label(non_clause). [assumption].
% 6.51/6.82 2 (all A all B all C (coll(A,B,C) -> coll(B,A,C))) # label(ruleD2) # label(axiom) # label(non_clause). [assumption].
% 6.51/6.82 3 (all A all B all C all D (coll(A,B,C) & coll(A,B,D) -> coll(C,D,A))) # label(ruleD3) # label(axiom) # label(non_clause). [assumption].
% 6.51/6.82 4 (all A all B all C all D (para(A,B,C,D) -> para(A,B,D,C))) # label(ruleD4) # label(axiom) # label(non_clause). [assumption].
% 6.51/6.82 5 (all A all B all C all D (para(A,B,C,D) -> para(C,D,A,B))) # label(ruleD5) # label(axiom) # label(non_clause). [assumption].
% 6.51/6.82 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].
% 6.51/6.82 7 (all A all B all C all D (perp(A,B,C,D) -> perp(A,B,D,C))) # label(ruleD7) # label(axiom) # label(non_clause). [assumption].
% 6.51/6.82 8 (all A all B all C all D (perp(A,B,C,D) -> perp(C,D,A,B))) # label(ruleD8) # label(axiom) # label(non_clause). [assumption].
% 6.51/6.82 9 (all A all B all C all D all E all F (perp(A,B,C,D) & perp(C,D,E,F) -> para(A,B,E,F))) # label(ruleD9) # label(axiom) # label(non_clause). [assumption].
% 6.51/6.82 11 (all A all B all M (midp(M,B,A) -> midp(M,A,B))) # label(ruleD11) # label(axiom) # label(non_clause). [assumption].
% 6.51/6.82 12 (all A all B all C all O (cong(O,A,O,B) & cong(O,A,O,C) -> circle(O,A,B,C))) # label(ruleD12) # label(axiom) # label(non_clause). [assumption].
% 6.51/6.82 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].
% 6.51/6.82 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].
% 6.51/6.82 15 (all A all B all C all D (cyclic(A,B,C,D) -> cyclic(A,C,B,D))) # label(ruleD15) # label(axiom) # label(non_clause). [assumption].
% 6.51/6.82 16 (all A all B all C all D (cyclic(A,B,C,D) -> cyclic(B,A,C,D))) # label(ruleD16) # label(axiom) # label(non_clause). [assumption].
% 6.51/6.82 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].
% 6.51/6.82 23 (all A all B all C all D (cong(A,B,C,D) -> cong(A,B,D,C))) # label(ruleD23) # label(axiom) # label(non_clause). [assumption].
% 6.51/6.82 24 (all A all B all C all D (cong(A,B,C,D) -> cong(C,D,A,B))) # label(ruleD24) # label(axiom) # label(non_clause). [assumption].
% 6.51/6.82 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].
% 6.51/6.82 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].
% 6.51/6.82 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].
% 6.51/6.82 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].
% 6.51/6.82 57 (all A all B all P all Q (cong(A,P,B,P) & cong(A,Q,B,Q) -> perp(A,B,P,Q))) # label(ruleD56) # label(axiom) # label(non_clause). [assumption].
% 6.51/6.82 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].
% 6.51/6.82 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].
% 6.51/6.82 65 (all A all B all C all D all M (midp(M,A,B) & para(A,C,B,D) & para(A,D,B,C) -> midp(M,C,D))) # label(ruleD64) # label(axiom) # label(non_clause). [assumption].
% 6.51/6.82 67 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption].
% 6.51/6.82 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].
% 6.51/6.82 69 (all A all B all C (midp(A,B,C) -> cong(A,B,A,C))) # label(ruleD68) # label(axiom) # label(non_clause). [assumption].
% 6.51/6.82 70 (all A all B all C (midp(A,B,C) -> coll(A,B,C))) # label(ruleD69) # label(axiom) # label(non_clause). [assumption].
% 6.51/6.82 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].
% 6.51/6.82 76 (all A all B all C all D all P all Q all U all V (eqratio(A,B,C,D,P,Q,U,V) & cong(P,Q,U,V) -> cong(A,B,C,D))) # label(ruleD75) # label(axiom) # label(non_clause). [assumption].
% 6.51/6.82 95 -(all A all B all E all G all D all C all F all H all NWPNT1 all NWPNT2 all NWPNT3 (midp(E,A,B) & circle(E,A,NWPNT1,NWPNT2) & circle(E,A,G,NWPNT3) & perp(E,G,G,D) & para(A,D,C,B) & coll(C,G,D) & midp(F,C,D) & perp(H,F,A,B) & coll(H,A,B) -> perp(C,H,D,H))) # label(exemplo6GDDFULL81109104) # label(negated_conjecture) # label(non_clause). [assumption].
% 6.51/6.82 97 -cong(A,B,A,C) | -cong(A,B,A,D) | circle(A,B,C,D) # label(ruleD12) # label(axiom). [clausify(12)].
% 6.51/6.82 101 -circle(A,B,C,D) | -coll(A,B,D) | perp(B,C,C,D) # label(ruleD53) # label(axiom). [clausify(54)].
% 6.51/6.82 111 -coll(A,B,C) | coll(A,C,B) # label(ruleD1) # label(axiom). [clausify(1)].
% 6.51/6.82 112 -coll(A,B,C) | coll(B,A,C) # label(ruleD2) # label(axiom). [clausify(2)].
% 6.51/6.82 113 -coll(A,B,C) | -coll(A,B,D) | coll(C,D,A) # label(ruleD3) # label(axiom). [clausify(3)].
% 6.51/6.82 114 -para(A,B,C,D) | para(A,B,D,C) # label(ruleD4) # label(axiom). [clausify(4)].
% 6.51/6.82 115 -para(A,B,C,D) | para(C,D,A,B) # label(ruleD5) # label(axiom). [clausify(5)].
% 6.51/6.82 116 -para(A,B,C,D) | -para(C,D,E,F) | para(A,B,E,F) # label(ruleD6) # label(axiom). [clausify(6)].
% 6.51/6.82 117 -perp(A,B,C,D) | perp(A,B,D,C) # label(ruleD7) # label(axiom). [clausify(7)].
% 6.51/6.82 118 -perp(A,B,C,D) | perp(C,D,A,B) # label(ruleD8) # label(axiom). [clausify(8)].
% 6.51/6.82 119 -perp(A,B,C,D) | -perp(C,D,E,F) | para(A,B,E,F) # label(ruleD9) # label(axiom). [clausify(9)].
% 6.51/6.82 121 -midp(A,B,C) | midp(A,C,B) # label(ruleD11) # label(axiom). [clausify(11)].
% 6.51/6.82 122 -cong(A,B,A,C) | -cong(A,B,A,D) | -cong(A,B,A,E) | cyclic(B,C,D,E) # label(ruleD13) # label(axiom). [clausify(13)].
% 6.51/6.82 123 -cyclic(A,B,C,D) | cyclic(A,B,D,C) # label(ruleD14) # label(axiom). [clausify(14)].
% 6.51/6.82 124 -cyclic(A,B,C,D) | cyclic(A,C,B,D) # label(ruleD15) # label(axiom). [clausify(15)].
% 6.51/6.82 125 -cyclic(A,B,C,D) | cyclic(B,A,C,D) # label(ruleD16) # label(axiom). [clausify(16)].
% 6.51/6.82 126 -cyclic(A,B,C,D) | -cyclic(A,B,C,E) | cyclic(B,C,D,E) # label(ruleD17) # label(axiom). [clausify(17)].
% 6.51/6.82 132 -cong(A,B,C,D) | cong(A,B,D,C) # label(ruleD23) # label(axiom). [clausify(23)].
% 6.51/6.82 133 -cong(A,B,C,D) | cong(C,D,A,B) # label(ruleD24) # label(axiom). [clausify(24)].
% 6.51/6.82 134 -cong(A,B,C,D) | -cong(C,D,E,F) | cong(A,B,E,F) # label(ruleD25) # label(axiom). [clausify(25)].
% 6.51/6.82 155 -midp(A,B,C) | -para(A,D,C,E) | -coll(D,B,E) | midp(D,B,E) # label(ruleD45) # label(axiom). [clausify(46)].
% 6.51/6.82 160 -midp(A,B,C) | -perp(D,A,B,C) | cong(D,B,D,C) # label(ruleD55) # label(axiom). [clausify(56)].
% 6.51/6.82 161 -cong(A,B,C,B) | -cong(A,D,C,D) | perp(A,C,B,D) # label(ruleD56) # label(axiom). [clausify(57)].
% 6.51/6.82 162 -cong(A,B,C,B) | -cong(A,D,C,D) | -cyclic(A,C,B,D) | perp(B,A,A,D) # label(ruleD57) # label(axiom). [clausify(58)].
% 6.51/6.82 168 -midp(A,B,C) | -midp(A,D,E) | para(B,D,C,E) # label(ruleD63) # label(axiom). [clausify(64)].
% 6.51/6.82 169 -midp(A,B,C) | -para(B,D,C,E) | -para(B,E,C,D) | midp(A,D,E) # label(ruleD64) # label(axiom). [clausify(65)].
% 6.51/6.82 171 -para(A,B,A,C) | coll(A,B,C) # label(ruleD66) # label(axiom). [clausify(67)].
% 6.51/6.82 172 -cong(A,B,A,C) | -coll(A,B,C) | midp(A,B,C) # label(ruleD67) # label(axiom). [clausify(68)].
% 6.51/6.82 173 -midp(A,B,C) | cong(A,B,A,C) # label(ruleD68) # label(axiom). [clausify(69)].
% 6.51/6.82 174 -midp(A,B,C) | coll(A,B,C) # label(ruleD69) # label(axiom). [clausify(70)].
% 6.51/6.82 175 -midp(A,B,C) | -midp(D,E,F) | eqratio(A,B,B,C,D,E,E,F) # label(ruleD70) # label(axiom). [clausify(71)].
% 6.51/6.82 179 -eqratio(A,B,C,D,E,F,V6,V7) | -cong(E,F,V6,V7) | cong(A,B,C,D) # label(ruleD75) # label(axiom). [clausify(76)].
% 6.51/6.82 210 midp(c3,c1,c2) # label(exemplo6GDDFULL81109104) # label(negated_conjecture). [clausify(95)].
% 6.51/6.82 211 perp(c3,c4,c4,c5) # label(exemplo6GDDFULL81109104) # label(negated_conjecture). [clausify(95)].
% 6.51/6.82 212 para(c1,c5,c6,c2) # label(exemplo6GDDFULL81109104) # label(negated_conjecture). [clausify(95)].
% 6.51/6.82 213 coll(c6,c4,c5) # label(exemplo6GDDFULL81109104) # label(negated_conjecture). [clausify(95)].
% 6.51/6.82 214 midp(c7,c6,c5) # label(exemplo6GDDFULL81109104) # label(negated_conjecture). [clausify(95)].
% 6.51/6.82 215 perp(c8,c7,c1,c2) # label(exemplo6GDDFULL81109104) # label(negated_conjecture). [clausify(95)].
% 6.51/6.82 216 coll(c8,c1,c2) # label(exemplo6GDDFULL81109104) # label(negated_conjecture). [clausify(95)].
% 6.51/6.82 217 -perp(c6,c8,c5,c8) # label(exemplo6GDDFULL81109104) # label(negated_conjecture). [clausify(95)].
% 6.51/6.82 222 -coll(A,B,C) | perp(B,D,D,C) | -cong(A,B,A,D) | -cong(A,B,A,C). [resolve(101,a,97,c)].
% 6.51/6.82 284 -coll(A,B,C) | coll(C,C,A). [factor(113,a,b)].
% 6.51/6.82 286 -cong(A,B,A,C) | -cong(A,B,A,D) | cyclic(B,C,C,D). [factor(122,a,b)].
% 6.51/6.82 298 -midp(A,B,C) | -para(B,D,C,D) | midp(A,D,D). [factor(169,b,c)].
% 6.51/6.82 323 -coll(A,B,C) | perp(B,C,C,C) | -cong(A,B,A,C). [factor(222,c,d)].
% 6.51/6.82 338 -cong(A,B,A,C) | cyclic(B,C,C,C). [factor(286,a,b)].
% 6.51/6.82 355 -midp(A,B,C) | eqratio(A,B,B,C,c3,c1,c1,c2). [resolve(210,a,175,b)].
% 6.51/6.82 356 -midp(A,B,C) | eqratio(c3,c1,c1,c2,A,B,B,C). [resolve(210,a,175,a)].
% 6.51/6.82 357 coll(c3,c1,c2). [resolve(210,a,174,a)].
% 6.51/6.82 358 cong(c3,c1,c3,c2). [resolve(210,a,173,a)].
% 6.51/6.82 359 -midp(c3,A,B) | para(A,c1,B,c2). [resolve(210,a,168,b)].
% 6.51/6.82 363 midp(c3,c2,c1). [resolve(210,a,121,a)].
% 6.51/6.82 382 -midp(c4,c4,c5) | cong(c3,c4,c3,c5). [resolve(211,a,160,b)].
% 6.51/6.82 384 -perp(A,B,c3,c4) | para(A,B,c4,c5). [resolve(211,a,119,b)].
% 6.51/6.82 385 -perp(c4,c5,A,B) | para(c3,c4,A,B). [resolve(211,a,119,a)].
% 6.51/6.82 386 perp(c4,c5,c3,c4). [resolve(211,a,118,a)].
% 6.51/6.82 387 perp(c3,c4,c5,c4). [resolve(211,a,117,a)].
% 6.51/6.82 400 -para(A,B,c1,c5) | para(A,B,c6,c2). [resolve(212,a,116,b)].
% 6.51/6.82 401 -para(c6,c2,A,B) | para(c1,c5,A,B). [resolve(212,a,116,a)].
% 6.51/6.82 402 para(c6,c2,c1,c5). [resolve(212,a,115,a)].
% 6.51/6.82 403 para(c1,c5,c2,c6). [resolve(212,a,114,a)].
% 6.51/6.82 404 -coll(c6,c4,A) | coll(A,c5,c6). [resolve(213,a,113,b)].
% 6.51/6.82 405 -coll(c6,c4,A) | coll(c5,A,c6). [resolve(213,a,113,a)].
% 6.51/6.82 406 coll(c4,c6,c5). [resolve(213,a,112,a)].
% 6.51/6.82 407 coll(c6,c5,c4). [resolve(213,a,111,a)].
% 6.51/6.82 418 coll(c7,c6,c5). [resolve(214,a,174,a)].
% 6.51/6.82 419 cong(c7,c6,c7,c5). [resolve(214,a,173,a)].
% 6.51/6.82 420 -midp(c7,A,B) | para(A,c6,B,c5). [resolve(214,a,168,b)].
% 6.51/6.82 421 -midp(c7,A,B) | para(c6,A,c5,B). [resolve(214,a,168,a)].
% 6.51/6.82 424 midp(c7,c5,c6). [resolve(214,a,121,a)].
% 6.51/6.82 438 -perp(c1,c2,A,B) | para(c8,c7,A,B). [resolve(215,a,119,a)].
% 6.51/6.82 441 -coll(c8,c1,A) | coll(A,c2,c8). [resolve(216,a,113,b)].
% 6.51/6.82 443 coll(c1,c8,c2). [resolve(216,a,112,a)].
% 6.51/6.82 444 coll(c8,c2,c1). [resolve(216,a,111,a)].
% 6.51/6.82 497 coll(c2,c2,c8). [resolve(284,a,216,a)].
% 6.51/6.82 498 coll(c5,c5,c6). [resolve(284,a,213,a)].
% 6.51/6.82 516 coll(c2,c2,c3). [resolve(357,a,284,a)].
% 6.51/6.82 520 coll(c3,c2,c1). [resolve(357,a,111,a)].
% 6.51/6.82 540 cong(c3,c2,c3,c1). [resolve(363,a,173,a)].
% 6.51/6.82 545 coll(c5,c5,c4). [resolve(406,a,284,a)].
% 6.51/6.82 546 -coll(c4,c6,A) | coll(A,c5,c4). [resolve(406,a,113,b)].
% 6.51/6.82 547 -coll(c4,c6,A) | coll(c5,A,c4). [resolve(406,a,113,a)].
% 6.51/6.82 549 coll(c4,c4,c6). [resolve(407,a,284,a)].
% 6.51/6.82 551 -coll(c6,c5,A) | coll(c4,A,c6). [resolve(407,a,113,a)].
% 6.51/6.82 555 coll(c5,c5,c7). [resolve(418,a,284,a)].
% 6.51/6.82 558 coll(c6,c7,c5). [resolve(418,a,112,a)].
% 6.51/6.82 559 coll(c7,c5,c6). [resolve(418,a,111,a)].
% 6.51/6.82 580 cong(c7,c5,c7,c6). [resolve(424,a,173,a)].
% 6.51/6.82 585 coll(c2,c2,c1). [resolve(443,a,284,a)].
% 6.51/6.82 587 -coll(c1,c8,A) | coll(c2,A,c1). [resolve(443,a,113,a)].
% 6.51/6.82 588 coll(c1,c2,c8). [resolve(443,a,111,a)].
% 6.51/6.82 591 coll(c1,c1,c8). [resolve(444,a,284,a)].
% 6.51/6.82 599 -coll(c2,c2,A) | coll(A,c8,c2). [resolve(497,a,113,b)].
% 6.51/6.82 603 -coll(c5,c5,A) | coll(A,c6,c5). [resolve(498,a,113,b)].
% 6.51/6.82 608 -coll(c2,c2,A) | coll(A,c3,c2). [resolve(516,a,113,b)].
% 6.51/6.82 610 coll(c2,c3,c2). [resolve(516,a,111,a)].
% 6.51/6.82 620 coll(c2,c3,c1). [resolve(520,a,112,a)].
% 6.51/6.82 621 coll(c4,c4,c5). [resolve(545,a,284,a)].
% 6.51/6.82 629 -coll(c4,c4,A) | coll(A,c6,c4). [resolve(549,a,113,b)].
% 6.51/6.82 630 -coll(c4,c4,A) | coll(c6,A,c4). [resolve(549,a,113,a)].
% 6.51/6.82 638 -coll(c5,c5,A) | coll(A,c7,c5). [resolve(555,a,113,b)].
% 6.51/6.82 640 coll(c5,c7,c5). [resolve(555,a,111,a)].
% 6.51/6.82 644 coll(c6,c6,c7). [resolve(559,a,284,a)].
% 6.51/6.82 647 coll(c5,c7,c6). [resolve(559,a,112,a)].
% 6.51/6.82 653 -coll(c2,c2,A) | coll(c1,A,c2). [resolve(585,a,113,a)].
% 6.51/6.82 661 -coll(c1,c1,A) | coll(A,c8,c1). [resolve(591,a,113,b)].
% 6.51/6.82 692 coll(c3,c2,c2). [resolve(610,a,112,a)].
% 6.51/6.82 702 eqratio(c7,c6,c6,c5,c3,c1,c1,c2). [resolve(355,a,214,a)].
% 6.51/6.82 715 eqratio(c3,c1,c1,c2,c3,c2,c2,c1). [resolve(356,a,363,a)].
% 6.51/6.82 775 perp(c1,c2,c2,c2). [resolve(358,a,323,c),unit_del(a,357)].
% 6.51/6.82 814 -cong(A,B,c3,c1) | cong(A,B,c3,c2). [resolve(358,a,134,b)].
% 6.51/6.82 826 coll(c6,c7,c6). [resolve(644,a,111,a)].
% 6.51/6.82 834 para(c2,c1,c1,c2). [resolve(359,a,363,a)].
% 6.51/6.82 987 perp(c4,c5,c4,c3). [resolve(386,a,117,a)].
% 6.51/6.82 1001 perp(c5,c4,c3,c4). [resolve(387,a,118,a)].
% 6.51/6.82 1021 -midp(c6,A,c1) | -coll(c2,A,c5) | midp(c2,A,c5). [resolve(402,a,155,b)].
% 6.51/6.82 1026 para(c6,c2,c5,c1). [resolve(402,a,114,a)].
% 6.51/6.82 1038 -midp(c1,A,c2) | -coll(c5,A,c6) | midp(c5,A,c6). [resolve(403,a,155,b)].
% 6.51/6.82 1043 para(c2,c6,c1,c5). [resolve(403,a,115,a)].
% 6.51/6.82 1052 cyclic(c6,c5,c5,c5). [resolve(419,a,338,a)].
% 6.51/6.82 1123 cong(c7,c6,c5,c7). [resolve(419,a,132,a)].
% 6.51/6.82 1282 perp(c2,c1,c1,c1). [resolve(540,a,323,c),unit_del(a,520)].
% 6.51/6.82 1315 cong(c3,c2,c1,c3). [resolve(540,a,132,a)].
% 6.51/6.82 1354 cyclic(c5,c6,c6,c6). [resolve(580,a,338,a)].
% 6.51/6.82 1392 perp(c5,c6,c6,c6). [resolve(580,a,323,c),unit_del(a,559)].
% 6.51/6.82 1425 cong(c7,c5,c6,c7). [resolve(580,a,132,a)].
% 6.51/6.82 1494 -midp(c2,A,c1) | -coll(c1,A,c2) | midp(c1,A,c2). [resolve(834,a,155,b)].
% 6.51/6.82 1544 -midp(c6,A,c5) | -coll(c2,A,c1) | midp(c2,A,c1). [resolve(1026,a,155,b)].
% 6.51/6.82 1549 para(c5,c1,c6,c2). [resolve(1026,a,115,a)].
% 6.51/6.82 1586 cyclic(c5,c6,c5,c5). [resolve(1052,a,125,a)].
% 6.51/6.82 1620 cong(c5,c7,c7,c6). [resolve(1123,a,133,a)].
% 6.51/6.82 1730 perp(c1,c1,c2,c1). [resolve(1282,a,118,a)].
% 6.51/6.82 1740 -cong(c1,c3,A,B) | cong(c3,c2,A,B). [resolve(1315,a,134,a)].
% 6.51/6.82 1741 cong(c1,c3,c3,c2). [resolve(1315,a,133,a)].
% 6.51/6.82 1774 cyclic(c6,c5,c6,c6). [resolve(1354,a,125,a)].
% 6.51/6.82 1793 -midp(c6,c6,c6) | cong(c5,c6,c5,c6). [resolve(1392,a,160,b)].
% 6.51/6.82 1808 cong(c6,c7,c7,c5). [resolve(1425,a,133,a)].
% 6.51/6.82 1899 para(c5,c4,c4,c5). [resolve(384,a,1001,a)].
% 6.51/6.82 1900 para(c4,c5,c4,c5). [resolve(384,a,386,a)].
% 6.51/6.82 1935 -midp(c5,A,c6) | -coll(c1,A,c2) | midp(c1,A,c2). [resolve(1549,a,155,b)].
% 6.51/6.82 1974 para(c3,c4,c4,c3). [resolve(385,a,987,a)].
% 6.51/6.82 1975 para(c3,c4,c3,c4). [resolve(385,a,386,a)].
% 6.51/6.82 1996 cyclic(c5,c5,c6,c5). [resolve(1586,a,124,a)].
% 6.51/6.82 2011 -cong(c7,c6,A,B) | cong(c5,c7,A,B). [resolve(1620,a,134,a)].
% 6.51/6.82 2012 cong(c5,c7,c6,c7). [resolve(1620,a,132,a)].
% 6.51/6.82 2082 perp(c1,c1,c1,c2). [resolve(1730,a,117,a)].
% 6.51/6.82 2093 cong(c1,c3,c2,c3). [resolve(1741,a,132,a)].
% 6.51/6.82 2131 cyclic(c6,c6,c5,c6). [resolve(1774,a,124,a)].
% 6.51/6.82 2148 cong(c6,c7,c5,c7). [resolve(1808,a,132,a)].
% 6.51/6.82 2217 -midp(c5,A,c4) | -coll(c4,A,c5) | midp(c4,A,c5). [resolve(1899,a,155,b)].
% 6.51/6.82 2222 para(c5,c4,c5,c4). [resolve(1899,a,114,a)].
% 6.51/6.82 2225 -midp(A,c4,c4) | midp(A,c5,c5). [resolve(1900,a,298,b)].
% 6.51/6.82 2233 -midp(c4,A,c4) | -coll(c5,A,c5) | midp(c5,A,c5). [resolve(1900,a,155,b)].
% 6.51/6.82 2263 -midp(c3,A,c4) | -coll(c4,A,c3) | midp(c4,A,c3). [resolve(1974,a,155,b)].
% 6.51/6.82 2270 -midp(A,c3,c3) | midp(A,c4,c4). [resolve(1975,a,298,b)].
% 6.51/6.82 2277 coll(c3,c4,c4). [resolve(1975,a,171,a)].
% 6.51/6.82 2281 coll(c4,c4,c3). [resolve(2277,a,284,a)].
% 6.51/6.82 2319 cyclic(c5,c5,c5,c6). [resolve(1996,a,123,a)].
% 6.51/6.82 2343 -cong(c5,A,c6,A) | perp(c5,c6,c7,A). [resolve(2012,a,161,a)].
% 6.51/6.82 2396 perp(c1,c2,c1,c1). [resolve(2082,a,118,a)].
% 6.51/6.82 2401 -cong(c2,c3,A,B) | cong(c1,c3,A,B). [resolve(2093,a,134,a)].
% 6.51/6.82 2418 cyclic(c6,c6,c6,c5). [resolve(2131,a,123,a)].
% 6.51/6.82 2444 -cong(c5,c7,A,B) | cong(c6,c7,A,B). [resolve(2148,a,134,a)].
% 6.51/6.82 2508 -midp(A,c5,c5) | midp(A,c4,c4). [resolve(2222,a,298,b)].
% 6.51/6.82 2558 -cyclic(c5,c5,c5,A) | cyclic(c5,c5,c6,A). [resolve(2319,a,126,a)].
% 6.51/6.82 2649 -cyclic(c6,c6,c6,A) | cyclic(c6,c6,A,c5). [resolve(2418,a,126,b)].
% 6.51/6.82 2662 para(c2,c6,c6,c2). [resolve(400,a,1043,a)].
% 6.51/6.82 2663 para(c6,c2,c6,c2). [resolve(400,a,402,a)].
% 6.51/6.82 2721 para(c1,c5,c5,c1). [resolve(401,a,1026,a)].
% 6.51/6.82 2722 para(c1,c5,c1,c5). [resolve(401,a,402,a)].
% 6.51/6.82 2822 para(c2,c6,c2,c6). [resolve(2662,a,114,a)].
% 6.51/6.82 2832 coll(c6,c2,c2). [resolve(2663,a,171,a)].
% 6.51/6.82 2834 -midp(c6,A,c6) | -coll(c2,A,c2) | midp(c2,A,c2). [resolve(2663,a,155,b)].
% 6.51/6.82 2836 coll(c2,c2,c6). [resolve(2832,a,284,a)].
% 6.51/6.82 2911 para(c5,c1,c1,c5). [resolve(2721,a,115,a)].
% 6.51/6.82 2927 coll(c1,c5,c5). [resolve(2722,a,171,a)].
% 6.51/6.82 2931 coll(c5,c5,c1). [resolve(2927,a,284,a)].
% 6.51/6.82 2941 coll(c1,c1,c5). [resolve(2931,a,284,a)].
% 6.51/6.82 3042 -midp(A,c2,c2) | midp(A,c6,c6). [resolve(2822,a,298,b)].
% 6.51/6.82 3050 -midp(c2,A,c2) | -coll(c6,A,c6) | midp(c6,A,c6). [resolve(2822,a,155,b)].
% 6.51/6.82 3105 para(c5,c1,c5,c1). [resolve(2911,a,114,a)].
% 6.51/6.82 3146 -midp(A,c5,c5) | midp(A,c1,c1). [resolve(3105,a,298,b)].
% 6.51/6.82 3203 para(c5,c6,c6,c5). [resolve(420,a,424,a)].
% 6.51/6.82 3225 para(c6,c5,c5,c6). [resolve(421,a,424,a)].
% 6.51/6.82 3255 para(c5,c6,c5,c6). [resolve(3203,a,114,a)].
% 6.51/6.82 3275 -midp(c6,A,c5) | -coll(c5,A,c6) | midp(c5,A,c6). [resolve(3225,a,155,b)].
% 6.51/6.82 3279 para(c6,c5,c6,c5). [resolve(3225,a,114,a)].
% 6.51/6.82 3290 -midp(A,c5,c5) | midp(A,c6,c6). [resolve(3255,a,298,b)].
% 6.51/6.82 3298 -midp(c5,A,c5) | -coll(c6,A,c6) | midp(c6,A,c6). [resolve(3255,a,155,b)].
% 6.51/6.82 3302 -midp(A,c6,c6) | midp(A,c5,c5). [resolve(3279,a,298,b)].
% 6.51/6.82 3312 coll(c6,c8,c2). [resolve(599,a,2836,a)].
% 6.51/6.82 3316 coll(c8,c6,c2). [resolve(3312,a,112,a)].
% 6.51/6.82 3324 coll(c8,c2,c6). [resolve(3316,a,111,a)].
% 6.51/6.82 3338 coll(c6,c6,c8). [resolve(3324,a,284,a)].
% 6.51/6.82 3366 coll(c6,c8,c6). [resolve(3338,a,111,a)].
% 6.51/6.82 3464 para(c8,c7,c1,c1). [resolve(438,a,2396,a)].
% 6.51/6.82 3466 para(c8,c7,c2,c2). [resolve(438,a,775,a)].
% 6.51/6.82 3501 para(c1,c1,c8,c7). [resolve(3464,a,115,a)].
% 6.51/6.82 3534 para(c2,c2,c8,c7). [resolve(3466,a,115,a)].
% 6.51/6.82 3602 para(c1,c1,c7,c8). [resolve(3501,a,114,a)].
% 6.51/6.82 3635 para(c2,c2,c7,c8). [resolve(3534,a,114,a)].
% 6.51/6.82 3664 -midp(c1,A,c7) | -coll(c1,A,c8) | midp(c1,A,c8). [resolve(3602,a,155,b)].
% 6.51/6.82 3693 -midp(c2,A,c7) | -coll(c2,A,c8) | midp(c2,A,c8). [resolve(3635,a,155,b)].
% 6.51/6.82 3747 coll(c1,c6,c5). [resolve(603,a,2931,a)].
% 6.51/6.82 3752 coll(c6,c1,c5). [resolve(3747,a,112,a)].
% 6.51/6.82 3780 coll(c6,c5,c1). [resolve(3752,a,111,a)].
% 6.51/6.82 3788 coll(c4,c1,c6). [resolve(3780,a,551,a)].
% 6.51/6.82 3818 coll(c4,c6,c1). [resolve(3788,a,111,a)].
% 6.51/6.82 3828 coll(c1,c1,c4). [resolve(3818,a,284,a)].
% 6.51/6.82 3878 coll(c6,c3,c2). [resolve(608,a,2836,a)].
% 6.51/6.82 3882 coll(c6,c2,c3). [resolve(3878,a,111,a)].
% 6.51/6.82 3888 coll(c3,c3,c6). [resolve(3882,a,284,a)].
% 6.51/6.82 3902 coll(c3,c6,c3). [resolve(3888,a,111,a)].
% 6.51/6.82 3914 coll(c6,c3,c3). [resolve(3902,a,112,a)].
% 6.51/6.82 3952 coll(c3,c6,c4). [resolve(629,a,2281,a)].
% 6.51/6.82 3957 coll(c6,c3,c4). [resolve(3952,a,112,a)].
% 6.51/6.82 3961 coll(c6,c4,c3). [resolve(3957,a,111,a)].
% 6.51/6.82 3967 coll(c5,c3,c6). [resolve(3961,a,405,a)].
% 6.51/6.82 3968 coll(c3,c5,c6). [resolve(3961,a,404,a)].
% 6.51/6.82 3971 coll(c4,c6,c3). [resolve(3961,a,112,a)].
% 6.51/6.82 3978 coll(c5,c6,c3). [resolve(3967,a,111,a)].
% 6.51/6.82 3983 coll(c3,c6,c5). [resolve(3968,a,111,a)].
% 6.51/6.82 3984 coll(c5,c3,c4). [resolve(3971,a,547,a)].
% 6.51/6.82 3985 coll(c3,c5,c4). [resolve(3971,a,546,a)].
% 6.51/6.82 3990 coll(c3,c3,c5). [resolve(3978,a,284,a)].
% 6.51/6.82 3993 coll(c6,c5,c3). [resolve(3978,a,112,a)].
% 6.51/6.82 3996 coll(c5,c5,c3). [resolve(3983,a,284,a)].
% 6.51/6.82 4004 coll(c5,c4,c3). [resolve(3984,a,111,a)].
% 6.51/6.82 4009 coll(c3,c4,c5). [resolve(3985,a,111,a)].
% 6.51/6.82 4014 coll(c3,c5,c3). [resolve(3990,a,111,a)].
% 6.51/6.82 4022 coll(c5,c3,c5). [resolve(3996,a,111,a)].
% 6.51/6.82 4029 coll(c4,c5,c3). [resolve(4004,a,112,a)].
% 6.51/6.82 4038 coll(c5,c3,c3). [resolve(4014,a,112,a)].
% 6.51/6.82 4152 coll(c1,c7,c5). [resolve(638,a,2931,a)].
% 6.51/6.82 4161 coll(c7,c1,c5). [resolve(4152,a,112,a)].
% 6.51/6.82 4176 coll(c7,c5,c1). [resolve(4161,a,111,a)].
% 6.51/6.82 4192 coll(c1,c1,c7). [resolve(4176,a,284,a)].
% 6.51/6.82 4371 coll(c7,c8,c1). [resolve(661,a,4192,a)].
% 6.51/6.82 4372 coll(c4,c8,c1). [resolve(661,a,3828,a)].
% 6.51/6.82 4373 coll(c5,c8,c1). [resolve(661,a,2941,a)].
% 6.51/6.82 4376 coll(c8,c7,c1). [resolve(4371,a,112,a)].
% 6.51/6.82 4380 coll(c8,c4,c1). [resolve(4372,a,112,a)].
% 6.51/6.82 4386 coll(c8,c5,c1). [resolve(4373,a,112,a)].
% 6.51/6.82 4390 coll(c8,c1,c7). [resolve(4376,a,111,a)].
% 6.51/6.82 4398 coll(c8,c1,c4). [resolve(4380,a,111,a)].
% 6.51/6.82 4405 coll(c8,c1,c5). [resolve(4386,a,111,a)].
% 6.51/6.82 4415 coll(c7,c2,c8). [resolve(4390,a,441,a)].
% 6.51/6.82 4427 coll(c4,c4,c8). [resolve(4398,a,284,a)].
% 6.51/6.82 4439 coll(c5,c2,c8). [resolve(4405,a,441,a)].
% 6.51/6.82 4445 coll(c1,c8,c5). [resolve(4405,a,112,a)].
% 6.51/6.82 4460 coll(c7,c8,c2). [resolve(4415,a,111,a)].
% 6.51/6.82 4471 coll(c6,c8,c4). [resolve(4427,a,630,a)].
% 6.51/6.82 4490 coll(c5,c8,c2). [resolve(4439,a,111,a)].
% 6.51/6.82 4502 coll(c2,c5,c1). [resolve(4445,a,587,a)].
% 6.51/6.82 4518 coll(c2,c2,c7). [resolve(4460,a,284,a)].
% 6.51/6.82 4538 coll(c6,c4,c8). [resolve(4471,a,111,a)].
% 6.51/6.82 4560 coll(c2,c2,c5). [resolve(4490,a,284,a)].
% 6.51/6.82 4627 coll(c2,c1,c5). [resolve(4502,a,111,a)].
% 6.51/6.82 4646 coll(c1,c7,c2). [resolve(4518,a,653,a)].
% 6.51/6.82 4651 coll(c2,c7,c2). [resolve(4518,a,111,a)].
% 6.51/6.82 4680 coll(c5,c8,c6). [resolve(4538,a,405,a)].
% 6.51/6.82 4806 coll(c1,c5,c2). [resolve(4560,a,653,a)].
% 6.51/6.82 6713 -cong(c3,c1,c1,c2) | cong(c7,c6,c6,c5). [resolve(702,a,179,a)].
% 6.51/6.82 6742 -cong(c3,c2,c2,c1) | cong(c3,c1,c1,c2). [resolve(715,a,179,a)].
% 6.51/6.82 7127 cong(c3,c2,c3,c2). [resolve(814,a,540,a)].
% 6.51/6.82 7215 midp(c3,c2,c2). [resolve(7127,a,172,a),unit_del(a,692)].
% 6.51/6.82 7236 midp(c3,c6,c6). [resolve(7215,a,3042,a)].
% 6.51/6.82 7338 midp(c3,c5,c5). [resolve(7236,a,3302,a)].
% 6.51/6.82 7400 cong(c3,c6,c3,c6). [resolve(7236,a,173,a)].
% 6.51/6.82 7503 midp(c3,c4,c4). [resolve(7338,a,2508,a)].
% 6.51/6.82 7565 cong(c3,c5,c3,c5). [resolve(7338,a,173,a)].
% 6.51/6.82 8555 cong(c3,c6,c6,c3). [resolve(7400,a,132,a)].
% 6.51/6.82 8860 cong(c3,c5,c5,c3). [resolve(7565,a,132,a)].
% 6.51/6.82 10124 cong(c6,c3,c3,c6). [resolve(8555,a,133,a)].
% 6.51/6.82 10269 cong(c5,c3,c3,c5). [resolve(8860,a,133,a)].
% 6.51/6.82 10839 cong(c6,c3,c6,c3). [resolve(10124,a,132,a)].
% 6.51/6.82 10886 cong(c5,c3,c5,c3). [resolve(10269,a,132,a)].
% 6.51/6.82 11244 midp(c6,c3,c3). [resolve(10839,a,172,a),unit_del(a,3914)].
% 6.51/6.82 11248 midp(c6,c4,c4). [resolve(11244,a,2270,a)].
% 6.51/6.82 11301 midp(c6,c5,c5). [resolve(11248,a,2225,a)].
% 6.51/6.82 11364 midp(c6,c6,c6). [resolve(11301,a,3290,a)].
% 6.51/6.82 11365 midp(c6,c1,c1). [resolve(11301,a,3146,a)].
% 6.51/6.82 11421 cong(c5,c6,c5,c6). [back_unit_del(1793),unit_del(a,11364)].
% 6.51/6.82 11651 midp(c5,c3,c3). [resolve(10886,a,172,a),unit_del(a,4038)].
% 6.51/6.82 11655 midp(c5,c4,c4). [resolve(11651,a,2270,a)].
% 6.51/6.82 12446 midp(c2,c1,c5). [resolve(1021,a,11365,a),unit_del(a,4627)].
% 6.51/6.82 12505 midp(c2,c5,c1). [resolve(12446,a,121,a)].
% 6.51/6.82 17715 midp(c1,c5,c2). [resolve(1494,a,12505,a),unit_del(a,4806)].
% 6.51/6.82 17724 midp(c5,c5,c6). [resolve(17715,a,1038,a),unit_del(a,498)].
% 6.51/6.82 17793 cong(c5,c5,c5,c6). [resolve(17724,a,173,a)].
% 6.51/6.82 18014 cong(c5,c5,c6,c5). [resolve(17793,a,132,a)].
% 6.51/6.82 20722 midp(c4,c4,c5). [resolve(2217,a,11655,a),unit_del(a,621)].
% 6.51/6.82 20723 cong(c3,c4,c3,c5). [back_unit_del(382),unit_del(a,20722)].
% 6.51/6.82 20768 midp(c3,c4,c5). [resolve(20723,a,172,a),unit_del(a,4009)].
% 6.51/6.82 20788 midp(c3,c5,c4). [resolve(20768,a,121,a)].
% 6.51/6.82 21046 midp(c4,c5,c3). [resolve(2263,a,20788,a),unit_del(a,4029)].
% 6.51/6.82 21047 midp(c4,c4,c3). [resolve(2263,a,7503,a),unit_del(a,2281)].
% 6.51/6.82 21067 midp(c4,c3,c5). [resolve(21046,a,121,a)].
% 6.51/6.82 21084 midp(c4,c3,c4). [resolve(21047,a,121,a)].
% 6.51/6.82 21100 cong(c4,c3,c4,c5). [resolve(21067,a,173,a)].
% 6.51/6.82 21107 midp(c5,c3,c5). [resolve(21084,a,2233,a),unit_del(a,4022)].
% 6.51/6.82 21143 midp(c5,c5,c3). [resolve(21107,a,121,a)].
% 6.51/6.82 21329 cyclic(c3,c5,c5,c5). [resolve(21100,a,338,a)].
% 6.51/6.82 21522 perp(c5,c6,c7,c5). [resolve(2343,a,18014,a)].
% 6.51/6.82 21544 cyclic(c5,c3,c5,c5). [resolve(21329,a,125,a)].
% 6.51/6.82 21664 -midp(c6,c7,c5) | cong(c5,c7,c5,c5). [resolve(21522,a,160,b)].
% 6.51/6.82 21703 cyclic(c5,c5,c3,c5). [resolve(21544,a,124,a)].
% 6.51/6.82 21957 cyclic(c5,c5,c5,c3). [resolve(21703,a,123,a)].
% 6.51/6.82 22788 cyclic(c5,c5,c6,c3). [resolve(2558,a,21957,a)].
% 6.51/6.82 23069 perp(c6,c5,c5,c3). [resolve(22788,a,162,c),unit_del(a,11421),unit_del(b,10886)].
% 6.51/6.82 23439 cong(c6,c5,c6,c3). [resolve(23069,a,160,b),unit_del(a,21143)].
% 6.51/6.82 23974 midp(c6,c5,c3). [resolve(23439,a,172,a),unit_del(a,3993)].
% 6.51/6.82 23980 midp(c6,c3,c5). [resolve(23974,a,121,a)].
% 6.51/6.82 23981 midp(c2,c3,c1). [resolve(23980,a,1544,a),unit_del(a,620)].
% 6.51/6.82 23985 cong(c2,c3,c2,c1). [resolve(23981,a,173,a)].
% 6.51/6.82 24601 cong(c1,c3,c2,c1). [resolve(23985,a,2401,a)].
% 6.51/6.82 25262 cong(c3,c2,c2,c1). [resolve(24601,a,1740,a)].
% 6.51/6.82 25263 cong(c3,c1,c1,c2). [back_unit_del(6742),unit_del(a,25262)].
% 6.51/6.82 25264 cong(c7,c6,c6,c5). [back_unit_del(6713),unit_del(a,25263)].
% 6.51/6.82 25850 cong(c5,c7,c6,c5). [resolve(25264,a,2011,a)].
% 6.51/6.82 26217 cong(c6,c7,c6,c5). [resolve(25850,a,2444,a)].
% 6.51/6.82 26448 midp(c6,c7,c5). [resolve(26217,a,172,a),unit_del(a,558)].
% 6.51/6.82 26449 cong(c5,c7,c5,c5). [back_unit_del(21664),unit_del(a,26448)].
% 6.51/6.82 26450 midp(c5,c7,c6). [resolve(26448,a,3275,a),unit_del(a,647)].
% 6.51/6.82 26454 midp(c1,c7,c2). [resolve(26450,a,1935,a),unit_del(a,4646)].
% 6.51/6.82 26462 midp(c1,c2,c7). [resolve(26454,a,121,a)].
% 6.51/6.82 26469 midp(c1,c2,c8). [resolve(26462,a,3664,a),unit_del(a,588)].
% 6.51/6.82 26480 midp(c1,c8,c2). [resolve(26469,a,121,a)].
% 6.51/6.82 26483 midp(c5,c8,c6). [resolve(26480,a,1038,a),unit_del(a,4680)].
% 6.51/6.82 26487 cong(c5,c8,c5,c6). [resolve(26483,a,173,a)].
% 6.51/6.82 26488 midp(c5,c6,c8). [resolve(26483,a,121,a)].
% 6.51/6.82 26494 cong(c5,c6,c5,c8). [resolve(26488,a,173,a)].
% 6.51/6.82 26678 midp(c5,c7,c5). [resolve(26449,a,172,a),unit_del(a,640)].
% 6.51/6.82 26680 midp(c6,c7,c6). [resolve(26678,a,3298,a),unit_del(a,826)].
% 6.51/6.82 26684 midp(c2,c7,c2). [resolve(26680,a,2834,a),unit_del(a,4651)].
% 6.51/6.82 26694 midp(c2,c2,c7). [resolve(26684,a,121,a)].
% 6.51/6.82 26728 midp(c2,c2,c8). [resolve(26694,a,3693,a),unit_del(a,497)].
% 6.51/6.82 26745 midp(c2,c8,c2). [resolve(26728,a,121,a)].
% 6.51/6.82 26760 midp(c6,c8,c6). [resolve(26745,a,3050,a),unit_del(a,3366)].
% 6.51/6.82 26777 midp(c6,c6,c8). [resolve(26760,a,121,a)].
% 6.51/6.82 26789 cong(c6,c6,c6,c8). [resolve(26777,a,173,a)].
% 6.51/6.82 26825 cyclic(c8,c6,c6,c6). [resolve(26487,a,338,a)].
% 6.51/6.82 26849 cong(c5,c6,c8,c5). [resolve(26494,a,132,a)].
% 6.51/6.82 27164 cong(c6,c6,c8,c6). [resolve(26789,a,132,a)].
% 6.51/6.82 27225 cyclic(c6,c8,c6,c6). [resolve(26825,a,125,a)].
% 6.51/6.82 27263 cong(c8,c5,c5,c6). [resolve(26849,a,133,a)].
% 6.51/6.82 27504 cong(c8,c6,c6,c6). [resolve(27164,a,133,a)].
% 6.51/6.82 27626 cyclic(c6,c6,c8,c6). [resolve(27225,a,124,a)].
% 6.51/6.82 27681 cong(c8,c5,c6,c5). [resolve(27263,a,132,a)].
% 6.51/6.82 28073 cyclic(c6,c6,c6,c8). [resolve(27626,a,123,a)].
% 6.51/6.82 28414 cyclic(c6,c6,c8,c5). [resolve(28073,a,2649,a)].
% 6.51/6.82 28711 cyclic(c6,c8,c6,c5). [resolve(28414,a,124,a)].
% 6.51/6.82 29201 cyclic(c8,c6,c6,c5). [resolve(28711,a,125,a)].
% 6.51/6.82 29859 perp(c6,c8,c8,c5). [resolve(29201,a,162,c),unit_del(a,27504),unit_del(b,27681)].
% 6.51/6.82 30150 $F. [resolve(29859,a,117,a),unit_del(a,217)].
% 6.51/6.82
% 6.51/6.82 % SZS output end Refutation
% 6.51/6.82 ============================== end of proof ==========================
% 6.51/6.82
% 6.51/6.82 ============================== STATISTICS ============================
% 6.51/6.82
% 6.51/6.82 Given=9622. Generated=180378. Kept=30023. proofs=1.
% 6.51/6.82 Usable=9421. Sos=9971. Demods=0. Limbo=5, Disabled=10799. Hints=0.
% 6.51/6.82 Megabytes=16.30.
% 6.51/6.82 User_CPU=5.66, System_CPU=0.10, Wall_clock=6.
% 6.51/6.82
% 6.51/6.82 ============================== end of statistics =====================
% 6.51/6.82
% 6.51/6.82 ============================== end of search =========================
% 6.51/6.82
% 6.51/6.82 THEOREM PROVED
% 6.51/6.82 % SZS status Theorem
% 6.51/6.82
% 6.51/6.82 Exiting with 1 proof.
% 6.51/6.82
% 6.51/6.82 Process 455 exit (max_proofs) Sat Jun 18 03:13:44 2022
% 6.51/6.82 Prover9 interrupted
%------------------------------------------------------------------------------