TSTP Solution File: GEO648+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GEO648+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.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 05:57:24 EDT 2022
% Result : Theorem 17.84s 18.14s
% Output : Refutation 17.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO648+1 : TPTP v8.1.0. Released v7.5.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jun 17 18:00:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.78/1.10 ============================== Prover9 ===============================
% 0.78/1.10 Prover9 (32) version 2009-11A, November 2009.
% 0.78/1.10 Process 17463 was started by sandbox on n019.cluster.edu,
% 0.78/1.10 Fri Jun 17 18:00:40 2022
% 0.78/1.10 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_17309_n019.cluster.edu".
% 0.78/1.10 ============================== end of head ===========================
% 0.78/1.10
% 0.78/1.10 ============================== INPUT =================================
% 0.78/1.10
% 0.78/1.10 % Reading from file /tmp/Prover9_17309_n019.cluster.edu
% 0.78/1.10
% 0.78/1.10 set(prolog_style_variables).
% 0.78/1.10 set(auto2).
% 0.78/1.10 % set(auto2) -> set(auto).
% 0.78/1.10 % set(auto) -> set(auto_inference).
% 0.78/1.10 % set(auto) -> set(auto_setup).
% 0.78/1.10 % set(auto_setup) -> set(predicate_elim).
% 0.78/1.10 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.78/1.10 % set(auto) -> set(auto_limits).
% 0.78/1.10 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.78/1.10 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.78/1.10 % set(auto) -> set(auto_denials).
% 0.78/1.10 % set(auto) -> set(auto_process).
% 0.78/1.10 % set(auto2) -> assign(new_constants, 1).
% 0.78/1.10 % set(auto2) -> assign(fold_denial_max, 3).
% 0.78/1.10 % set(auto2) -> assign(max_weight, "200.000").
% 0.78/1.10 % set(auto2) -> assign(max_hours, 1).
% 0.78/1.10 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.78/1.10 % set(auto2) -> assign(max_seconds, 0).
% 0.78/1.10 % set(auto2) -> assign(max_minutes, 5).
% 0.78/1.10 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.78/1.10 % set(auto2) -> set(sort_initial_sos).
% 0.78/1.10 % set(auto2) -> assign(sos_limit, -1).
% 0.78/1.10 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.78/1.10 % set(auto2) -> assign(max_megs, 400).
% 0.78/1.10 % set(auto2) -> assign(stats, some).
% 0.78/1.10 % set(auto2) -> clear(echo_input).
% 0.78/1.10 % set(auto2) -> set(quiet).
% 0.78/1.10 % set(auto2) -> clear(print_initial_clauses).
% 0.78/1.10 % set(auto2) -> clear(print_given).
% 0.78/1.10 assign(lrs_ticks,-1).
% 0.78/1.10 assign(sos_limit,10000).
% 0.78/1.10 assign(order,kbo).
% 0.78/1.10 set(lex_order_vars).
% 0.78/1.10 clear(print_given).
% 0.78/1.10
% 0.78/1.10 % formulas(sos). % not echoed (95 formulas)
% 0.78/1.10
% 0.78/1.10 ============================== end of input ==========================
% 0.78/1.10
% 0.78/1.10 % From the command line: assign(max_seconds, 300).
% 0.78/1.10
% 0.78/1.10 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.78/1.10
% 0.78/1.10 % Formulas that are not ordinary clauses:
% 0.78/1.10 1 (all A all B all C (coll(A,B,C) -> coll(A,C,B))) # label(ruleD1) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 2 (all A all B all C (coll(A,B,C) -> coll(B,A,C))) # label(ruleD2) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 3 (all A all B all C all D (coll(A,B,C) & coll(A,B,D) -> coll(C,D,A))) # label(ruleD3) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 4 (all A all B all C all D (para(A,B,C,D) -> para(A,B,D,C))) # label(ruleD4) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 5 (all A all B all C all D (para(A,B,C,D) -> para(C,D,A,B))) # label(ruleD5) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 6 (all A all B all C all D all E all F (para(A,B,C,D) & para(C,D,E,F) -> para(A,B,E,F))) # label(ruleD6) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 7 (all A all B all C all D (perp(A,B,C,D) -> perp(A,B,D,C))) # label(ruleD7) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 8 (all A all B all C all D (perp(A,B,C,D) -> perp(C,D,A,B))) # label(ruleD8) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 9 (all A all B all C all D all E all F (perp(A,B,C,D) & perp(C,D,E,F) -> para(A,B,E,F))) # label(ruleD9) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 10 (all A all B all C all D all E all F (para(A,B,C,D) & perp(C,D,E,F) -> perp(A,B,E,F))) # label(ruleD10) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 11 (all A all B all M (midp(M,B,A) -> midp(M,A,B))) # label(ruleD11) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 12 (all A all B all C all O (cong(O,A,O,B) & cong(O,A,O,C) -> circle(O,A,B,C))) # label(ruleD12) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 13 (all A all B all C all D all O (cong(O,A,O,B) & cong(O,A,O,C) & cong(O,A,O,D) -> cyclic(A,B,C,D))) # label(ruleD13) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 14 (all A all B all C all D (cyclic(A,B,C,D) -> cyclic(A,B,D,C))) # label(ruleD14) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 15 (all A all B all C all D (cyclic(A,B,C,D) -> cyclic(A,C,B,D))) # label(ruleD15) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 16 (all A all B all C all D (cyclic(A,B,C,D) -> cyclic(B,A,C,D))) # label(ruleD16) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 17 (all A all B all C all D all E (cyclic(A,B,C,D) & cyclic(A,B,C,E) -> cyclic(B,C,D,E))) # label(ruleD17) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 18 (all A all B all C all D all P all Q all U all V (eqangle(A,B,C,D,P,Q,U,V) -> eqangle(B,A,C,D,P,Q,U,V))) # label(ruleD18) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 19 (all A all B all C all D all P all Q all U all V (eqangle(A,B,C,D,P,Q,U,V) -> eqangle(C,D,A,B,U,V,P,Q))) # label(ruleD19) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 20 (all A all B all C all D all P all Q all U all V (eqangle(A,B,C,D,P,Q,U,V) -> eqangle(P,Q,U,V,A,B,C,D))) # label(ruleD20) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 21 (all A all B all C all D all P all Q all U all V (eqangle(A,B,C,D,P,Q,U,V) -> eqangle(A,B,P,Q,C,D,U,V))) # label(ruleD21) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 22 (all A all B all C all D all P all Q all U all V all E all F all G all H (eqangle(A,B,C,D,P,Q,U,V) & eqangle(P,Q,U,V,E,F,G,H) -> eqangle(A,B,C,D,E,F,G,H))) # label(ruleD22) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 23 (all A all B all C all D (cong(A,B,C,D) -> cong(A,B,D,C))) # label(ruleD23) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 24 (all A all B all C all D (cong(A,B,C,D) -> cong(C,D,A,B))) # label(ruleD24) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 25 (all A all B all C all D all E all F (cong(A,B,C,D) & cong(C,D,E,F) -> cong(A,B,E,F))) # label(ruleD25) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 26 (all A all B all C all D all P all Q all U all V (eqratio(A,B,C,D,P,Q,U,V) -> eqratio(B,A,C,D,P,Q,U,V))) # label(ruleD26) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 27 (all A all B all C all D all P all Q all U all V (eqratio(A,B,C,D,P,Q,U,V) -> eqratio(C,D,A,B,U,V,P,Q))) # label(ruleD27) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 28 (all A all B all C all D all P all Q all U all V (eqratio(A,B,C,D,P,Q,U,V) -> eqratio(P,Q,U,V,A,B,C,D))) # label(ruleD28) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 29 (all A all B all C all D all P all Q all U all V (eqratio(A,B,C,D,P,Q,U,V) -> eqratio(A,B,P,Q,C,D,U,V))) # label(ruleD29) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 30 (all A all B all C all D all E all F all G all H all P all Q all U all V (eqratio(A,B,C,D,P,Q,U,V) & eqratio(P,Q,U,V,E,F,G,H) -> eqratio(A,B,C,D,E,F,G,H))) # label(ruleD30) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 31 (all A all B all C all P all Q all R (simtri(A,C,B,P,R,Q) -> simtri(A,B,C,P,Q,R))) # label(ruleD31) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 32 (all A all B all C all P all Q all R (simtri(B,A,C,Q,P,R) -> simtri(A,B,C,P,Q,R))) # label(ruleD32) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 33 (all A all B all C all P all Q all R (simtri(P,Q,R,A,B,C) -> simtri(A,B,C,P,Q,R))) # label(ruleD33) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 34 (all A all B all C all E all F all G all P all Q all R (simtri(A,B,C,E,F,G) & simtri(E,F,G,P,Q,R) -> simtri(A,B,C,P,Q,R))) # label(ruleD34) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 35 (all A all B all C all P all Q all R (contri(A,C,B,P,R,Q) -> contri(A,B,C,P,Q,R))) # label(ruleD35) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 36 (all A all B all C all P all Q all R (contri(B,A,C,Q,P,R) -> contri(A,B,C,P,Q,R))) # label(ruleD36) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 37 (all A all B all C all P all Q all R (contri(P,Q,R,A,B,C) -> contri(A,B,C,P,Q,R))) # label(ruleD37) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 38 (all A all B all C all E all F all G all P all Q all R (contri(A,B,C,E,F,G) & contri(E,F,G,P,Q,R) -> contri(A,B,C,P,Q,R))) # label(ruleD38) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 39 (all A all B all C all D all P all Q (eqangle(A,B,P,Q,C,D,P,Q) -> para(A,B,C,D))) # label(ruleD39) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 40 (all A all B all C all D all P all Q (para(A,B,C,D) -> eqangle(A,B,P,Q,C,D,P,Q))) # label(ruleD40) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 41 (all A all B all P all Q (cyclic(A,B,P,Q) -> eqangle(P,A,P,B,Q,A,Q,B))) # label(ruleD41) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 42 (all A all B all P all Q (eqangle(P,A,P,B,Q,A,Q,B) & -coll(P,Q,A) -> cyclic(A,B,P,Q))) # label(ruleD42a) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 43 (all A all B all P all Q (eqangle(P,A,P,B,Q,A,Q,B) & coll(P,Q,B) -> cyclic(A,B,P,Q))) # label(ruleD42b) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 44 (all A all B all C all P all Q all R (cyclic(A,B,C,P) & cyclic(A,B,C,Q) & cyclic(A,B,C,R) & eqangle(C,A,C,B,R,P,R,Q) -> cong(A,B,P,Q))) # label(ruleD43) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 45 (all A all B all C all E all F (midp(E,A,B) & midp(F,A,C) -> para(E,F,B,C))) # label(ruleD44) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 46 (all A all B all C all E all F (midp(E,A,B) & para(E,F,B,C) & coll(F,A,C) -> midp(F,A,C))) # label(ruleD45) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 47 (all A all B all O (cong(O,A,O,B) -> eqangle(O,A,A,B,A,B,O,B))) # label(ruleD46) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 48 (all A all B all O (eqangle(O,A,A,B,A,B,O,B) & -coll(O,A,B) -> cong(O,A,O,B))) # label(ruleD47) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 49 (all A all B all C all O all X (circle(O,A,B,C) & perp(O,A,A,X) -> eqangle(A,X,A,B,C,A,C,B))) # label(ruleD48) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 50 (all A all B all C all O all X (circle(O,A,B,C) & eqangle(A,X,A,B,C,A,C,B) -> perp(O,A,A,X))) # label(ruleD49) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 51 (all A all B all C all O all M (circle(O,A,B,C) & midp(M,B,C) -> eqangle(A,B,A,C,O,B,O,M))) # label(ruleD50) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 52 (all A all B all C all O all M (circle(O,A,B,C) & coll(M,B,C) & eqangle(A,B,A,C,O,B,O,M) -> midp(M,B,C))) # label(ruleD51) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 53 (all A all B all C all M (perp(A,B,B,C) & midp(M,A,C) -> cong(A,M,B,M))) # label(ruleD52) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 54 (all A all B all C all O (circle(O,A,B,C) & coll(O,A,C) -> perp(A,B,B,C))) # label(ruleD53) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 55 (all A all B all C all D (cyclic(A,B,C,D) & para(A,B,C,D) -> eqangle(A,D,C,D,C,D,C,B))) # label(ruleD54) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 56 (all A all B all M all O (midp(M,A,B) & perp(O,M,A,B) -> cong(O,A,O,B))) # label(ruleD55) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 57 (all A all B all P all Q (cong(A,P,B,P) & cong(A,Q,B,Q) -> perp(A,B,P,Q))) # label(ruleD56) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 58 (all A all B all P all Q (cong(A,P,B,P) & cong(A,Q,B,Q) & cyclic(A,B,P,Q) -> perp(P,A,A,Q))) # label(ruleD57) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 59 (all A all B all C all P all Q all R (eqangle(A,B,B,C,P,Q,Q,R) & eqangle(A,C,B,C,P,R,Q,R) & -coll(A,B,C) -> simtri(A,B,C,P,Q,R))) # label(ruleD58) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 60 (all A all B all C all P all Q all R (simtri(A,B,C,P,Q,R) -> eqratio(A,B,A,C,P,Q,P,R))) # label(ruleD59) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 61 (all A all B all C all P all Q all R (simtri(A,B,C,P,Q,R) -> eqangle(A,B,B,C,P,Q,Q,R))) # label(ruleD60) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 62 (all A all B all C all P all Q all R (simtri(A,B,C,P,Q,R) & cong(A,B,P,Q) -> contri(A,B,C,P,Q,R))) # label(ruleD61) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 63 (all A all B all C all P all Q all R (contri(A,B,C,P,Q,R) -> cong(A,B,P,Q))) # label(ruleD62) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 64 (all A all B all C all D all M (midp(M,A,B) & midp(M,C,D) -> para(A,C,B,D))) # label(ruleD63) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 65 (all A all B all C all D all M (midp(M,A,B) & para(A,C,B,D) & para(A,D,B,C) -> midp(M,C,D))) # label(ruleD64) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 66 (all A all B all C all D all O (para(A,B,C,D) & coll(O,A,C) & coll(O,B,D) -> eqratio(O,A,A,C,O,B,B,D))) # label(ruleD65) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 67 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 68 (all A all B all C (cong(A,B,A,C) & coll(A,B,C) -> midp(A,B,C))) # label(ruleD67) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 69 (all A all B all C (midp(A,B,C) -> cong(A,B,A,C))) # label(ruleD68) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 70 (all A all B all C (midp(A,B,C) -> coll(A,B,C))) # label(ruleD69) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 71 (all A all B all C all D all M all N (midp(M,A,B) & midp(N,C,D) -> eqratio(M,A,A,B,N,C,C,D))) # label(ruleD70) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 72 (all A all B all C all D (eqangle(A,B,C,D,C,D,A,B) & -para(A,B,C,D) -> perp(A,B,C,D))) # label(ruleD71) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 73 (all A all B all C all D (eqangle(A,B,C,D,C,D,A,B) & -perp(A,B,C,D) -> para(A,B,C,D))) # label(ruleD72) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 74 (all A all B all C all D all P all Q all U all V (eqangle(A,B,C,D,P,Q,U,V) & para(P,Q,U,V) -> para(A,B,C,D))) # label(ruleD73) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 75 (all A all B all C all D all P all Q all U all V (eqangle(A,B,C,D,P,Q,U,V) & perp(P,Q,U,V) -> perp(A,B,C,D))) # label(ruleD74) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 76 (all A all B all C all D all P all Q all U all V (eqratio(A,B,C,D,P,Q,U,V) & cong(P,Q,U,V) -> cong(A,B,C,D))) # label(ruleD75) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 77 (all A all M all O all X exists B (perp(O,M,M,A) & eqangle(X,O,M,O,M,O,A,O) -> coll(B,A,M) & coll(B,O,X))) # label(ruleX1) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 78 (all A all B all O all X exists M (cong(O,A,O,B) & eqangle(A,O,O,X,O,X,O,B) -> coll(B,A,M) & coll(M,O,X))) # label(ruleX2) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 79 (all A all B all O all X exists M (perp(O,X,A,B) & eqangle(A,O,O,X,O,X,O,B) -> coll(B,A,M) & coll(M,O,X))) # label(ruleX3) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 80 (all A all B all O all X exists M (perp(O,X,A,B) & cong(O,A,O,B) -> coll(B,A,M) & coll(M,O,X))) # label(ruleX4) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 81 (all A all B all P all X all Y exists Q (eqangle(A,P,B,P,A,X,B,Y) & -coll(A,B,P) -> eqangle(A,P,B,P,A,Q,B,Q) & cyclic(X,B,P,Q))) # label(ruleX5) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 82 (all A all B all C all D all M all N exists P (midp(M,A,B) & midp(N,C,D) -> midp(P,A,D) & para(P,M,B,D) & para(P,N,A,C))) # label(ruleX6) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 83 (all A all B all C all D all M all N all Q exists P (midp(M,A,B) & midp(N,C,D) & coll(C,A,B) & coll(D,A,B) -> midp(P,A,Q))) # label(ruleX7) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 84 (all A all B all M all P all Q all R all M exists X (midp(M,A,B) & para(A,P,R,M) & para(A,P,B,Q) & coll(P,Q,R) -> coll(X,A,Q) & coll(X,M,R))) # label(ruleX8) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 85 (all A all B all C all D all O exists P (cong(O,C,O,D) & perp(A,B,B,O) -> cong(O,C,O,P) & para(P,C,A,B) & cong(B,C,B,P))) # label(ruleX9) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 86 (all A all B all C all H exists P exists Q (perp(A,H,B,C) & perp(B,H,A,C) -> coll(P,C,B) & perp(A,P,C,B) & coll(Q,C,A) & perp(B,Q,C,A))) # label(ruleX10) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 87 (all A all B all C all O exists P (circle(O,A,B,C) -> perp(P,A,A,O))) # label(ruleX11) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 88 (all A all B all C all D all M all N exists P exists Q (circle(M,A,B,C) & cong(M,A,M,D) & cong(N,A,N,B) & M != N -> coll(P,A,C) & cong(P,N,N,A) & coll(Q,B,D) & cong(Q,N,N,A))) # label(ruleX12) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 89 (all A all B all C all D all M exists O (cyclic(A,B,C,D) & para(A,B,C,D) & midp(M,A,B) -> circle(O,A,B,C))) # label(ruleX13) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.11 90 (all A all B all C all D exists O (perp(A,C,C,B) & cyclic(A,B,C,D) -> circle(O,A,B,C))) # label(ruleX14) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.11 91 (all A all B all C all E all F exists P (perp(A,C,C,B) & coll(B,E,F) -> coll(P,E,F) & perp(P,A,E,F))) # label(ruleX15) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.11 92 (all A all B all C all D all M exists P (perp(A,B,A,C) & perp(C,A,C,D) & midp(M,B,D) -> midp(P,A,C))) # label(ruleX16) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.11 93 (all A all B all O exists C (cong(O,A,O,B) & perp(A,O,O,B) -> coll(A,O,C) & cong(O,A,O,C))) # label(ruleX17) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.11 94 (all A all B all C all D all P all Q exists R (para(A,B,C,D) & coll(P,A,C) & coll(P,B,D) & coll(Q,A,B) -> coll(P,Q,R) & coll(R,C,D))) # label(ruleX18) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.11 95 -(all A all B all C all D all E all NWPNT1 all NWPNT2 all NWPNT3 all NWPNT4 (circle(A,B,NWPNT1,NWPNT2) & circle(A,B,C,NWPNT3) & perp(A,C,C,D) & perp(A,B,B,D) & coll(C,A,E) & circle(A,C,E,NWPNT4) -> para(A,D,B,E))) # label(exemplo6GDDFULLmoreE0213) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.78/1.11
% 0.78/1.11 ============================== end of process non-clausal formulas ===
% 0.78/1.11
% 0.78/1.11 ============================== PROCESS INITIAL CLAUSES ===============
% 0.78/1.11
% 0.78/1.11 ============================== PREDICATE ELIMINATION =================
% 0.78/1.11 96 -circle(A,B,C,D) | -perp(A,B,B,E) | eqangle(B,E,B,C,D,B,D,C) # label(ruleD48) # label(axiom). [clausify(49)].
% 0.78/1.11 97 -cong(A,B,A,C) | -cong(A,B,A,D) | circle(A,B,C,D) # label(ruleD12) # label(axiom). [clausify(12)].
% 0.78/1.11 Derived: -perp(A,B,B,C) | eqangle(B,C,B,D,E,B,E,D) | -cong(A,B,A,D) | -cong(A,B,A,E). [resolve(96,a,97,c)].
% 0.78/1.11 98 -circle(A,B,C,D) | -eqangle(B,E,B,C,D,B,D,C) | perp(A,B,B,E) # label(ruleD49) # label(axiom). [clausify(50)].
% 0.78/1.11 Derived: -eqangle(A,B,A,C,D,A,D,C) | perp(E,A,A,B) | -cong(E,A,E,C) | -cong(E,A,E,D). [resolve(98,a,97,c)].
% 0.78/1.11 99 -circle(A,B,C,D) | -midp(E,C,D) | eqangle(B,C,B,D,A,C,A,E) # label(ruleD50) # label(axiom). [clausify(51)].
% 0.78/1.11 Derived: -midp(A,B,C) | eqangle(D,B,D,C,E,B,E,A) | -cong(E,D,E,B) | -cong(E,D,E,C). [resolve(99,a,97,c)].
% 0.78/1.11 100 -circle(A,B,C,D) | -coll(E,C,D) | -eqangle(B,C,B,D,A,C,A,E) | midp(E,C,D) # label(ruleD51) # label(axiom). [clausify(52)].
% 0.78/1.11 Derived: -coll(A,B,C) | -eqangle(D,B,D,C,E,B,E,A) | midp(A,B,C) | -cong(E,D,E,B) | -cong(E,D,E,C). [resolve(100,a,97,c)].
% 0.78/1.11 101 -circle(A,B,C,D) | -coll(A,B,D) | perp(B,C,C,D) # label(ruleD53) # label(axiom). [clausify(54)].
% 0.78/1.11 Derived: -coll(A,B,C) | perp(B,D,D,C) | -cong(A,B,A,D) | -cong(A,B,A,C). [resolve(101,a,97,c)].
% 0.78/1.11 102 -circle(A,B,C,D) | perp(f12(B,C,D,A),B,B,A) # label(ruleX11) # label(axiom). [clausify(87)].
% 0.78/1.11 Derived: perp(f12(A,B,C,D),A,A,D) | -cong(D,A,D,B) | -cong(D,A,D,C). [resolve(102,a,97,c)].
% 0.78/1.11 103 -circle(A,B,C,D) | -cong(A,B,A,E) | -cong(F,B,F,C) | F = A | coll(f13(B,C,D,E,A,F),B,D) # label(ruleX12) # label(axiom). [clausify(88)].
% 0.78/1.11 Derived: -cong(A,B,A,C) | -cong(D,B,D,E) | D = A | coll(f13(B,E,F,C,A,D),B,F) | -cong(A,B,A,E) | -cong(A,B,A,F). [resolve(103,a,97,c)].
% 0.78/1.11 104 -circle(A,B,C,D) | -cong(A,B,A,E) | -cong(F,B,F,C) | F = A | cong(f13(B,C,D,E,A,F),F,F,B) # label(ruleX12) # label(axiom). [clausify(88)].
% 0.78/1.11 Derived: -cong(A,B,A,C) | -cong(D,B,D,E) | D = A | cong(f13(B,E,F,C,A,D),D,D,B) | -cong(A,B,A,E) | -cong(A,B,A,F). [resolve(104,a,97,c)].
% 0.78/1.11 105 -circle(A,B,C,D) | -cong(A,B,A,E) | -cong(F,B,F,C) | F = A | coll(f14(B,C,D,E,A,F),C,E) # label(ruleX12) # label(axiom). [clausify(88)].
% 0.78/1.11 Derived: -cong(A,B,A,C) | -cong(D,B,D,E) | D = A | coll(f14(B,E,F,C,A,D),E,C) | -cong(A,B,A,E) | -cong(A,B,A,F). [resolve(105,a,97,c)].
% 0.78/1.11 106 -circle(A,B,C,D) | -cong(A,B,A,E) | -cong(F,B,F,C) | F = A | cong(f14(B,C,D,E,A,F),F,F,B) # label(ruleX12) # label(axiom). [clausify(88)].
% 0.78/1.11 Derived: -cong(A,B,A,C) | -cong(D,B,D,E) | D = A | cong(f14(B,E,F,C,A,D),D,D,B) | -cong(A,B,A,E) | -cong(A,B,A,F). [resolve(106,a,97,c)].
% 0.78/1.11 107 -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | circle(f15(A,B,C,D,E),A,B,C) # label(ruleX13) # label(axiom). [clausify(89)].
% 0.78/1.11 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -perp(f15(A,B,C,D,E),A,A,F) | eqangle(A,F,A,B,C,A,C,B). [resolve(107,d,96,a)].
% 0.78/1.11 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -eqangle(A,F,A,B,C,A,C,B) | perp(f15(A,B,C,D,E),A,A,F). [resolve(107,d,98,a)].
% 0.78/1.11 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -midp(F,B,C) | eqangle(A,B,A,C,f15(A,B,C,D,E),B,f15(A,B,C,D,E),F). [resolve(107,d,99,a)].
% 0.78/1.11 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -coll(F,B,C) | -eqangle(A,B,A,C,f15(A,B,C,D,E),B,f15(A,B,C,D,E),F) | midp(F,B,C). [resolve(107,d,100,a)].
% 0.78/1.11 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -coll(f15(A,B,C,D,E),A,C) | perp(A,B,B,C). [resolve(107,d,101,a)].
% 0.78/1.11 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | perp(f12(A,B,C,f15(A,B,C,D,E)),A,A,f15(A,B,C,D,E)). [resolve(107,d,102,a)].
% 0.78/1.11 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -cong(f15(A,B,C,D,E),A,f15(A,B,C,D,E),F) | -cong(V6,A,V6,B) | V6 = f15(A,B,C,D,E) | coll(f13(A,B,C,F,f15(A,B,C,D,E),V6),A,C). [resolve(107,d,103,a)].
% 0.78/1.11 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -cong(f15(A,B,C,D,E),A,f15(A,B,C,D,E),F) | -cong(V6,A,V6,B) | V6 = f15(A,B,C,D,E) | cong(f13(A,B,C,F,f15(A,B,C,D,E),V6),V6,V6,A). [resolve(107,d,104,a)].
% 0.78/1.11 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -cong(f15(A,B,C,D,E),A,f15(A,B,C,D,E),F) | -cong(V6,A,V6,B) | V6 = f15(A,B,C,D,E) | coll(f14(A,B,C,F,f15(A,B,C,D,E),V6),B,F). [resolve(107,d,105,a)].
% 0.78/1.11 Derived: -cyclic(A,B,C,D) | -para(A,B,C,D) | -midp(E,A,B) | -cong(f15(A,B,C,D,E),A,f15(A,B,C,D,E),F) | -cong(V6,A,V6,B) | V6 = f15(A,B,C,D,E) | cong(f14(A,B,C,F,f15(A,B,C,D,E),V6),V6,V6,A). [resolve(107,d,106,a)].
% 0.78/1.11 108 -perp(A,B,B,C) | -cyclic(A,C,B,D) | circle(f16(A,C,B,D),A,C,B) # label(ruleX14) # label(axiom). [clausify(90)].
% 0.78/1.11 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -perp(f16(A,C,B,D),A,A,E) | eqangle(A,E,A,C,B,A,B,C). [resolve(108,c,96,a)].
% 0.78/1.11 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -eqangle(A,E,A,C,B,A,B,C) | perp(f16(A,C,B,D),A,A,E). [resolve(108,c,98,a)].
% 0.78/1.11 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -midp(E,C,B) | eqangle(A,C,A,B,f16(A,C,B,D),C,f16(A,C,B,D),E). [resolve(108,c,99,a)].
% 0.78/1.11 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -coll(E,C,B) | -eqangle(A,C,A,B,f16(A,C,B,D),C,f16(A,C,B,D),E) | midp(E,C,B). [resolve(108,c,100,a)].
% 0.78/1.11 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -coll(f16(A,C,B,D),A,B) | perp(A,C,C,B). [resolve(108,c,101,a)].
% 0.78/1.11 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | perp(f12(A,C,B,f16(A,C,B,D)),A,A,f16(A,C,B,D)). [resolve(108,c,102,a)].
% 0.78/1.11 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -cong(f16(A,C,B,D),A,f16(A,C,B,D),E) | -cong(F,A,F,C) | F = f16(A,C,B,D) | coll(f13(A,C,B,E,f16(A,C,B,D),F),A,B). [resolve(108,c,103,a)].
% 0.78/1.11 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -cong(f16(A,C,B,D),A,f16(A,C,B,D),E) | -cong(F,A,F,C) | F = f16(A,C,B,D) | cong(f13(A,C,B,E,f16(A,C,B,D),F),F,F,A). [resolve(108,c,104,a)].
% 0.78/1.11 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -cong(f16(A,C,B,D),A,f16(A,C,B,D),E) | -cong(F,A,F,C) | F = f16(A,C,B,D) | coll(f14(A,C,B,E,f16(A,C,B,D),F),C,E). [resolve(108,c,105,a)].
% 0.78/1.11 Derived: -perp(A,B,B,C) | -cyclic(A,C,B,D) | -cong(f16(A,C,B,D),A,f16(A,C,B,D),E) | -cong(F,A,F,C) | F = f16(A,C,B,D) | cong(f14(A,C,B,E,f16(A,C,B,D),F),F,F,A). [resolve(108,c,106,a)].
% 0.78/1.11 109 circle(c1,c2,c6,c7) # label(exemplo6GDDFULLmoreE0213) # label(negated_conjecture). [clausify(95)].
% 0.78/1.11 Derived: -perp(c1,c2,c2,A) | eqangle(c2,A,c2,c6,c7,c2,c7,c6). [resolve(109,a,96,a)].
% 0.78/1.11 Derived: -eqangle(c2,A,c2,c6,c7,c2,c7,c6) | perp(c1,c2,c2,A). [resolve(109,a,98,a)].
% 0.78/1.11 Derived: -midp(A,c6,c7) | eqangle(c2,c6,c2,c7,c1,c6,c1,A). [resolve(109,a,99,a)].
% 0.78/1.11 Derived: -coll(A,c6,c7) | -eqangle(c2,c6,c2,c7,c1,c6,c1,A) | midp(A,c6,c7). [resolve(109,a,100,a)].
% 0.78/1.11 Derived: -coll(c1,c2,c7) | perp(c2,c6,c6,c7). [resolve(109,a,101,a)].
% 0.78/1.11 Derived: perp(f12(c2,c6,c7,c1),c2,c2,c1). [resolve(109,a,102,a)].
% 0.78/1.11 Derived: -cong(c1,c2,c1,A) | -cong(B,c2,B,c6) | B = c1 | coll(f13(c2,c6,c7,A,c1,B),c2,c7). [resolve(109,a,103,a)].
% 1.72/2.01 Derived: -cong(c1,c2,c1,A) | -cong(B,c2,B,c6) | B = c1 | cong(f13(c2,c6,c7,A,c1,B),B,B,c2). [resolve(109,a,104,a)].
% 1.72/2.01 Derived: -cong(c1,c2,c1,A) | -cong(B,c2,B,c6) | B = c1 | coll(f14(c2,c6,c7,A,c1,B),c6,A). [resolve(109,a,105,a)].
% 1.72/2.01 Derived: -cong(c1,c2,c1,A) | -cong(B,c2,B,c6) | B = c1 | cong(f14(c2,c6,c7,A,c1,B),B,B,c2). [resolve(109,a,106,a)].
% 1.72/2.01 110 circle(c1,c2,c3,c8) # label(exemplo6GDDFULLmoreE0213) # label(negated_conjecture). [clausify(95)].
% 1.72/2.01 Derived: -perp(c1,c2,c2,A) | eqangle(c2,A,c2,c3,c8,c2,c8,c3). [resolve(110,a,96,a)].
% 1.72/2.01 Derived: -eqangle(c2,A,c2,c3,c8,c2,c8,c3) | perp(c1,c2,c2,A). [resolve(110,a,98,a)].
% 1.72/2.01 Derived: -midp(A,c3,c8) | eqangle(c2,c3,c2,c8,c1,c3,c1,A). [resolve(110,a,99,a)].
% 1.72/2.01 Derived: -coll(A,c3,c8) | -eqangle(c2,c3,c2,c8,c1,c3,c1,A) | midp(A,c3,c8). [resolve(110,a,100,a)].
% 1.72/2.01 Derived: -coll(c1,c2,c8) | perp(c2,c3,c3,c8). [resolve(110,a,101,a)].
% 1.72/2.01 Derived: perp(f12(c2,c3,c8,c1),c2,c2,c1). [resolve(110,a,102,a)].
% 1.72/2.01 Derived: -cong(c1,c2,c1,A) | -cong(B,c2,B,c3) | B = c1 | coll(f13(c2,c3,c8,A,c1,B),c2,c8). [resolve(110,a,103,a)].
% 1.72/2.01 Derived: -cong(c1,c2,c1,A) | -cong(B,c2,B,c3) | B = c1 | cong(f13(c2,c3,c8,A,c1,B),B,B,c2). [resolve(110,a,104,a)].
% 1.72/2.01 Derived: -cong(c1,c2,c1,A) | -cong(B,c2,B,c3) | B = c1 | coll(f14(c2,c3,c8,A,c1,B),c3,A). [resolve(110,a,105,a)].
% 1.72/2.01 Derived: -cong(c1,c2,c1,A) | -cong(B,c2,B,c3) | B = c1 | cong(f14(c2,c3,c8,A,c1,B),B,B,c2). [resolve(110,a,106,a)].
% 1.72/2.01 111 circle(c1,c3,c5,c9) # label(exemplo6GDDFULLmoreE0213) # label(negated_conjecture). [clausify(95)].
% 1.72/2.01 Derived: -perp(c1,c3,c3,A) | eqangle(c3,A,c3,c5,c9,c3,c9,c5). [resolve(111,a,96,a)].
% 1.72/2.01 Derived: -eqangle(c3,A,c3,c5,c9,c3,c9,c5) | perp(c1,c3,c3,A). [resolve(111,a,98,a)].
% 1.72/2.01 Derived: -midp(A,c5,c9) | eqangle(c3,c5,c3,c9,c1,c5,c1,A). [resolve(111,a,99,a)].
% 1.72/2.01 Derived: -coll(A,c5,c9) | -eqangle(c3,c5,c3,c9,c1,c5,c1,A) | midp(A,c5,c9). [resolve(111,a,100,a)].
% 1.72/2.01 Derived: -coll(c1,c3,c9) | perp(c3,c5,c5,c9). [resolve(111,a,101,a)].
% 1.72/2.01 Derived: perp(f12(c3,c5,c9,c1),c3,c3,c1). [resolve(111,a,102,a)].
% 1.72/2.01 Derived: -cong(c1,c3,c1,A) | -cong(B,c3,B,c5) | B = c1 | coll(f13(c3,c5,c9,A,c1,B),c3,c9). [resolve(111,a,103,a)].
% 1.72/2.01 Derived: -cong(c1,c3,c1,A) | -cong(B,c3,B,c5) | B = c1 | cong(f13(c3,c5,c9,A,c1,B),B,B,c3). [resolve(111,a,104,a)].
% 1.72/2.01 Derived: -cong(c1,c3,c1,A) | -cong(B,c3,B,c5) | B = c1 | coll(f14(c3,c5,c9,A,c1,B),c5,A). [resolve(111,a,105,a)].
% 1.72/2.01 Derived: -cong(c1,c3,c1,A) | -cong(B,c3,B,c5) | B = c1 | cong(f14(c3,c5,c9,A,c1,B),B,B,c3). [resolve(111,a,106,a)].
% 1.72/2.01
% 1.72/2.01 ============================== end predicate elimination =============
% 1.72/2.01
% 1.72/2.01 Auto_denials: (non-Horn, no changes).
% 1.72/2.01
% 1.72/2.01 Term ordering decisions:
% 1.72/2.01 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. f19=1. f1=1. f2=1. f3=1. f4=1. f10=1. f11=1. f12=1. f16=1. f5=1. f9=1. f15=1. f17=1. f18=1. f6=1. f13=1. f14=1. f20=1. f7=1. f8=1.
% 1.72/2.01
% 1.72/2.01 ============================== end of process initial clauses ========
% 1.72/2.01
% 1.72/2.01 ============================== CLAUSES FOR SEARCH ====================
% 1.72/2.01
% 1.72/2.01 ============================== end of clauses for search =============
% 1.72/2.01
% 1.72/2.01 ============================== SEARCH ================================
% 1.72/2.01
% 1.72/2.01 % Starting search at 0.05 seconds.
% 1.72/2.01
% 1.72/2.01 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 2147483647 (0.00 of 0.15 sec).
% 1.72/2.01
% 1.72/2.01 Low Water (keep): wt=39.000, iters=3344
% 1.72/2.01
% 1.72/2.01 Low Water (keep): wt=33.000, iters=3343
% 1.72/2.01
% 1.72/2.01 Low Water (keep): wt=29.000, iters=3351
% 1.72/2.01
% 1.72/2.01 Low Water (keep): wt=26.000, iters=3348
% 1.72/2.01
% 1.72/2.01 Low Water (keep): wt=25.000, iters=3343
% 1.72/2.01
% 1.72/2.01 Low Water (keep): wt=22.000, iters=3336
% 1.72/2.01
% 1.72/2.01 Low Water (keep): wt=21.000, iters=3340
% 1.72/2.01
% 1.72/2.01 Low Water (keep): wt=20.000, iters=3357
% 1.72/2.01
% 1.72/2.01 Low Water (keep): wt=19.000, iters=3333
% 1.72/2.01
% 1.72/2.01 Low Water (keep): wt=18.000, iters=3333
% 1.72/2.01
% 1.72/2.01 Low Water (keep): wt=17.000, iters=3338
% 1.72/2.01
% 1.72/2.01 Low Water (keep): wt=15.000, iters=3338
% 1.72/2.01
% 1.72/2.01 Low Water (keep): wt=14.000, iters=3338
% 1.72/2.01
% 1.72/2.01 Low Water (displace): id=7232, wt=39.000
% 1.72/2.01
% 1.72/2.01 Low Water (displace): id=7203, wt=33.000
% 1.72/2.01
% 1.72/2.01 Low Water (displace): id=6690, wt=30.000
% 1.72/2.01
% 1.72/2.01 Low Water (displace): id=7429, wt=29.000
% 1.72/2.01
% 1.72/2.01 Low Water (displace): id=7509, wt=28.000
% 1.72/2.01
% 1.72/2.01 Low Water (displace): id=7510, wt=27.000
% 17.84/18.14
% 17.84/18.14 Low Water (displace): id=7622, wt=26.000
% 17.84/18.14
% 17.84/18.14 Low Water (displace): id=13778, wt=13.000
% 17.84/18.14
% 17.84/18.14 Low Water (keep): wt=13.000, iters=3338
% 17.84/18.14
% 17.84/18.14 Low Water (displace): id=13835, wt=12.000
% 17.84/18.14
% 17.84/18.14 Low Water (displace): id=13875, wt=10.000
% 17.84/18.14
% 17.84/18.14 Low Water (displace): id=14056, wt=9.000
% 17.84/18.14
% 17.84/18.14 Low Water (displace): id=14136, wt=8.000
% 17.84/18.14
% 17.84/18.14 Low Water (displace): id=14765, wt=7.000
% 17.84/18.14
% 17.84/18.14 Low Water (displace): id=14889, wt=5.000
% 17.84/18.14
% 17.84/18.14 Low Water (keep): wt=12.000, iters=3335
% 17.84/18.14
% 17.84/18.14 Low Water (keep): wt=11.000, iters=3333
% 17.84/18.14
% 17.84/18.14 Low Water (keep): wt=10.000, iters=3561
% 17.84/18.14
% 17.84/18.14 Low Water (keep): wt=9.000, iters=3340
% 17.84/18.14
% 17.84/18.14 ============================== PROOF =================================
% 17.84/18.14 % SZS status Theorem
% 17.84/18.14 % SZS output start Refutation
% 17.84/18.14
% 17.84/18.14 % Proof 1 at 16.93 (+ 0.13) seconds.
% 17.84/18.14 % Length of proof is 321.
% 17.84/18.14 % Level of proof is 58.
% 17.84/18.14 % Maximum clause weight is 29.000.
% 17.84/18.14 % Given clauses 19436.
% 17.84/18.14
% 17.84/18.14 1 (all A all B all C (coll(A,B,C) -> coll(A,C,B))) # label(ruleD1) # label(axiom) # label(non_clause). [assumption].
% 17.84/18.14 2 (all A all B all C (coll(A,B,C) -> coll(B,A,C))) # label(ruleD2) # label(axiom) # label(non_clause). [assumption].
% 17.84/18.14 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].
% 17.84/18.14 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].
% 17.84/18.14 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].
% 17.84/18.14 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].
% 17.84/18.14 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].
% 17.84/18.14 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].
% 17.84/18.14 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].
% 17.84/18.14 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].
% 17.84/18.14 11 (all A all B all M (midp(M,B,A) -> midp(M,A,B))) # label(ruleD11) # label(axiom) # label(non_clause). [assumption].
% 17.84/18.14 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].
% 17.84/18.14 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].
% 17.84/18.14 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].
% 17.84/18.14 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].
% 17.84/18.14 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].
% 17.84/18.14 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].
% 17.84/18.14 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].
% 17.84/18.14 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].
% 17.84/18.14 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].
% 17.84/18.14 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].
% 17.84/18.14 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].
% 17.84/18.14 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].
% 17.84/18.14 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].
% 17.84/18.14 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].
% 17.84/18.14 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].
% 17.84/18.14 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].
% 17.84/18.14 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].
% 17.84/18.14 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].
% 17.84/18.14 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].
% 17.84/18.14 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].
% 17.84/18.14 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].
% 17.84/18.14 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].
% 17.84/18.14 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].
% 17.84/18.14 67 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption].
% 17.84/18.14 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].
% 17.84/18.14 69 (all A all B all C (midp(A,B,C) -> cong(A,B,A,C))) # label(ruleD68) # label(axiom) # label(non_clause). [assumption].
% 17.84/18.14 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].
% 17.84/18.14 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].
% 17.84/18.14 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].
% 17.84/18.14 95 -(all A all B all C all D all E all NWPNT1 all NWPNT2 all NWPNT3 all NWPNT4 (circle(A,B,NWPNT1,NWPNT2) & circle(A,B,C,NWPNT3) & perp(A,C,C,D) & perp(A,B,B,D) & coll(C,A,E) & circle(A,C,E,NWPNT4) -> para(A,D,B,E))) # label(exemplo6GDDFULLmoreE0213) # label(negated_conjecture) # label(non_clause). [assumption].
% 17.84/18.14 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)].
% 17.84/18.14 97 -cong(A,B,A,C) | -cong(A,B,A,D) | circle(A,B,C,D) # label(ruleD12) # label(axiom). [clausify(12)].
% 17.84/18.14 100 -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)].
% 17.84/18.14 101 -circle(A,B,C,D) | -coll(A,B,D) | perp(B,C,C,D) # label(ruleD53) # label(axiom). [clausify(54)].
% 17.84/18.14 110 circle(c1,c2,c3,c8) # label(exemplo6GDDFULLmoreE0213) # label(negated_conjecture). [clausify(95)].
% 17.84/18.14 112 -coll(A,B,C) | coll(A,C,B) # label(ruleD1) # label(axiom). [clausify(1)].
% 17.84/18.14 113 -coll(A,B,C) | coll(B,A,C) # label(ruleD2) # label(axiom). [clausify(2)].
% 17.84/18.14 114 -coll(A,B,C) | -coll(A,B,D) | coll(C,D,A) # label(ruleD3) # label(axiom). [clausify(3)].
% 17.84/18.14 115 -para(A,B,C,D) | para(A,B,D,C) # label(ruleD4) # label(axiom). [clausify(4)].
% 17.84/18.14 116 -para(A,B,C,D) | para(C,D,A,B) # label(ruleD5) # label(axiom). [clausify(5)].
% 17.84/18.14 117 -para(A,B,C,D) | -para(C,D,E,F) | para(A,B,E,F) # label(ruleD6) # label(axiom). [clausify(6)].
% 17.84/18.14 118 -perp(A,B,C,D) | perp(A,B,D,C) # label(ruleD7) # label(axiom). [clausify(7)].
% 17.84/18.14 119 -perp(A,B,C,D) | perp(C,D,A,B) # label(ruleD8) # label(axiom). [clausify(8)].
% 17.84/18.14 120 -perp(A,B,C,D) | -perp(C,D,E,F) | para(A,B,E,F) # label(ruleD9) # label(axiom). [clausify(9)].
% 17.84/18.14 121 -para(A,B,C,D) | -perp(C,D,E,F) | perp(A,B,E,F) # label(ruleD10) # label(axiom). [clausify(10)].
% 17.84/18.14 122 -midp(A,B,C) | midp(A,C,B) # label(ruleD11) # label(axiom). [clausify(11)].
% 17.84/18.14 124 -cyclic(A,B,C,D) | cyclic(A,B,D,C) # label(ruleD14) # label(axiom). [clausify(14)].
% 17.84/18.14 125 -cyclic(A,B,C,D) | cyclic(A,C,B,D) # label(ruleD15) # label(axiom). [clausify(15)].
% 17.84/18.14 126 -cyclic(A,B,C,D) | cyclic(B,A,C,D) # label(ruleD16) # label(axiom). [clausify(16)].
% 17.84/18.14 127 -cyclic(A,B,C,D) | -cyclic(A,B,C,E) | cyclic(B,C,D,E) # label(ruleD17) # label(axiom). [clausify(17)].
% 17.84/18.14 129 -eqangle(A,B,C,D,E,F,V6,V7) | eqangle(C,D,A,B,V6,V7,E,F) # label(ruleD19) # label(axiom). [clausify(19)].
% 17.84/18.14 130 -eqangle(A,B,C,D,E,F,V6,V7) | eqangle(E,F,V6,V7,A,B,C,D) # label(ruleD20) # label(axiom). [clausify(20)].
% 17.84/18.14 133 -cong(A,B,C,D) | cong(A,B,D,C) # label(ruleD23) # label(axiom). [clausify(23)].
% 17.84/18.14 134 -cong(A,B,C,D) | cong(C,D,A,B) # label(ruleD24) # label(axiom). [clausify(24)].
% 17.84/18.14 149 -eqangle(A,B,C,D,E,F,C,D) | para(A,B,E,F) # label(ruleD39) # label(axiom). [clausify(39)].
% 17.84/18.14 150 -para(A,B,C,D) | eqangle(A,B,E,F,C,D,E,F) # label(ruleD40) # label(axiom). [clausify(40)].
% 17.84/18.14 153 -eqangle(A,B,A,C,D,B,D,C) | -coll(A,D,C) | cyclic(B,C,A,D) # label(ruleD42b) # label(axiom). [clausify(43)].
% 17.84/18.14 154 -cyclic(A,B,C,D) | -cyclic(A,B,C,E) | -cyclic(A,B,C,F) | -eqangle(C,A,C,B,F,D,F,E) | cong(A,B,D,E) # label(ruleD43) # label(axiom). [clausify(44)].
% 17.84/18.14 156 -midp(A,B,C) | -para(A,D,C,E) | -coll(D,B,E) | midp(D,B,E) # label(ruleD45) # label(axiom). [clausify(46)].
% 17.84/18.14 159 -perp(A,B,B,C) | -midp(D,A,C) | cong(A,D,B,D) # label(ruleD52) # label(axiom). [clausify(53)].
% 17.84/18.14 161 -midp(A,B,C) | -perp(D,A,B,C) | cong(D,B,D,C) # label(ruleD55) # label(axiom). [clausify(56)].
% 17.84/18.14 162 -cong(A,B,C,B) | -cong(A,D,C,D) | perp(A,C,B,D) # label(ruleD56) # label(axiom). [clausify(57)].
% 17.84/18.14 163 -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)].
% 17.84/18.14 170 -midp(A,B,C) | -para(B,D,C,E) | -para(B,E,C,D) | midp(A,D,E) # label(ruleD64) # label(axiom). [clausify(65)].
% 17.84/18.14 171 -para(A,B,C,D) | -coll(E,A,C) | -coll(E,B,D) | eqratio(E,A,A,C,E,B,B,D) # label(ruleD65) # label(axiom). [clausify(66)].
% 17.84/18.14 172 -para(A,B,A,C) | coll(A,B,C) # label(ruleD66) # label(axiom). [clausify(67)].
% 17.84/18.14 173 -cong(A,B,A,C) | -coll(A,B,C) | midp(A,B,C) # label(ruleD67) # label(axiom). [clausify(68)].
% 17.84/18.14 174 -midp(A,B,C) | cong(A,B,A,C) # label(ruleD68) # label(axiom). [clausify(69)].
% 17.84/18.14 179 -eqangle(A,B,C,D,E,F,V6,V7) | -perp(E,F,V6,V7) | perp(A,B,C,D) # label(ruleD74) # label(axiom). [clausify(75)].
% 17.84/18.14 180 -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)].
% 17.84/18.14 202 -perp(A,B,C,D) | -perp(C,B,A,D) | coll(f11(A,C,D,B),D,A) # label(ruleX10) # label(axiom). [clausify(86)].
% 17.84/18.14 211 perp(c1,c3,c3,c4) # label(exemplo6GDDFULLmoreE0213) # label(negated_conjecture). [clausify(95)].
% 17.84/18.14 212 perp(c1,c2,c2,c4) # label(exemplo6GDDFULLmoreE0213) # label(negated_conjecture). [clausify(95)].
% 17.84/18.14 213 coll(c3,c1,c5) # label(exemplo6GDDFULLmoreE0213) # label(negated_conjecture). [clausify(95)].
% 17.84/18.14 214 -para(c1,c4,c2,c5) # label(exemplo6GDDFULLmoreE0213) # label(negated_conjecture). [clausify(95)].
% 17.84/18.14 218 -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)].
% 17.84/18.14 219 -coll(A,B,C) | perp(B,D,D,C) | -cong(A,B,A,D) | -cong(A,B,A,C). [resolve(101,a,97,c)].
% 17.84/18.14 267 -perp(c1,c2,c2,A) | eqangle(c2,A,c2,c3,c8,c2,c8,c3). [resolve(110,a,96,a)].
% 17.84/18.14 271 -coll(c1,c2,c8) | perp(c2,c3,c3,c8). [resolve(110,a,101,a)].
% 17.84/18.14 295 -coll(A,B,C) | coll(C,C,A). [factor(114,a,b)].
% 17.84/18.14 300 -cyclic(A,B,C,D) | cyclic(B,C,D,D). [factor(127,a,b)].
% 17.84/18.14 303 -cyclic(A,B,C,D) | -cyclic(A,B,C,E) | -eqangle(C,A,C,B,E,D,E,E) | cong(A,B,D,E). [factor(154,b,c)].
% 17.84/18.14 305 -cong(A,B,C,B) | perp(A,C,B,B). [factor(162,a,b)].
% 17.84/18.14 309 -midp(A,B,C) | -para(B,D,C,D) | midp(A,D,D). [factor(170,b,c)].
% 17.84/18.14 321 -perp(A,B,A,C) | coll(f11(A,A,C,B),C,A). [factor(202,a,b)].
% 17.84/18.14 333 -coll(A,B,B) | -eqangle(C,B,C,B,D,B,D,A) | midp(A,B,B) | -cong(D,C,D,B). [factor(218,d,e)].
% 17.84/18.14 334 -coll(A,B,C) | perp(B,C,C,C) | -cong(A,B,A,C). [factor(219,c,d)].
% 17.84/18.14 375 -midp(c3,c3,c4) | cong(c1,c3,c1,c4). [resolve(211,a,161,b)].
% 17.84/18.14 377 -perp(A,B,c1,c3) | para(A,B,c3,c4). [resolve(211,a,120,b)].
% 17.84/18.14 378 -perp(c3,c4,A,B) | para(c1,c3,A,B). [resolve(211,a,120,a)].
% 17.84/18.14 379 perp(c3,c4,c1,c3). [resolve(211,a,119,a)].
% 17.84/18.14 380 perp(c1,c3,c4,c3). [resolve(211,a,118,a)].
% 17.84/18.14 399 -midp(A,c1,c4) | cong(c1,A,c2,A). [resolve(212,a,159,a)].
% 17.84/18.14 400 -perp(A,B,c1,c2) | para(A,B,c2,c4). [resolve(212,a,120,b)].
% 17.84/18.14 401 -perp(c2,c4,A,B) | para(c1,c2,A,B). [resolve(212,a,120,a)].
% 17.84/18.14 402 perp(c2,c4,c1,c2). [resolve(212,a,119,a)].
% 17.84/18.14 403 perp(c1,c2,c4,c2). [resolve(212,a,118,a)].
% 17.84/18.14 406 coll(c1,c3,c5). [resolve(213,a,113,a)].
% 17.84/18.14 407 coll(c3,c5,c1). [resolve(213,a,112,a)].
% 17.84/18.14 438 eqangle(c2,c4,c2,c3,c8,c2,c8,c3). [resolve(267,a,212,a)].
% 17.84/18.14 490 coll(c5,c5,c3). [resolve(295,a,213,a)].
% 17.84/18.14 494 coll(c1,c5,c3). [resolve(406,a,112,a)].
% 17.84/18.14 495 coll(c1,c1,c3). [resolve(407,a,295,a)].
% 17.84/18.14 499 coll(c3,c3,c5). [resolve(490,a,295,a)].
% 17.84/18.14 507 coll(c3,c3,c1). [resolve(494,a,295,a)].
% 17.84/18.14 513 coll(c1,c3,c1). [resolve(495,a,112,a)].
% 17.84/18.14 518 coll(c3,c5,c3). [resolve(499,a,112,a)].
% 17.84/18.14 529 -coll(c3,c3,A) | coll(A,c1,c3). [resolve(507,a,114,b)].
% 17.84/18.14 530 -coll(c3,c3,A) | coll(c1,A,c3). [resolve(507,a,114,a)].
% 17.84/18.14 531 coll(c3,c1,c3). [resolve(507,a,112,a)].
% 17.84/18.14 534 coll(c1,c1,c1). [resolve(513,a,295,a)].
% 17.84/18.14 536 -coll(c1,c3,A) | coll(c1,A,c1). [resolve(513,a,114,a)].
% 17.84/18.14 538 coll(c3,c3,c3). [resolve(518,a,295,a)].
% 17.84/18.14 556 -coll(c3,c3,A) | coll(A,c3,c3). [resolve(538,a,114,b)].
% 17.84/18.14 576 perp(c3,c4,c3,c1). [resolve(379,a,118,a)].
% 17.84/18.14 590 perp(c4,c3,c1,c3). [resolve(380,a,119,a)].
% 17.84/18.14 612 perp(c2,c4,c2,c1). [resolve(402,a,118,a)].
% 17.84/18.14 626 perp(c4,c2,c1,c2). [resolve(403,a,119,a)].
% 17.84/18.14 643 -midp(c4,c3,c1) | cong(c3,c3,c3,c1). [resolve(576,a,161,b)].
% 17.84/18.14 646 perp(c3,c1,c3,c4). [resolve(576,a,119,a)].
% 17.84/18.14 652 perp(c4,c3,c3,c1). [resolve(590,a,118,a)].
% 17.84/18.14 664 perp(c2,c1,c2,c4). [resolve(612,a,119,a)].
% 17.84/18.14 670 perp(c4,c2,c2,c1). [resolve(626,a,118,a)].
% 17.84/18.14 682 perp(c3,c1,c4,c3). [resolve(646,a,118,a)].
% 17.84/18.14 703 -midp(A,c4,c1) | cong(c4,A,c3,A). [resolve(652,a,159,a)].
% 17.84/18.14 717 perp(c2,c1,c4,c2). [resolve(664,a,118,a)].
% 17.84/18.14 738 -midp(A,c4,c1) | cong(c4,A,c2,A). [resolve(670,a,159,a)].
% 17.84/18.14 739 -perp(A,B,c4,c2) | para(A,B,c2,c1). [resolve(670,a,120,b)].
% 17.84/18.14 753 -perp(c4,c3,A,B) | para(c3,c1,A,B). [resolve(682,a,120,a)].
% 17.84/18.14 766 -perp(c4,c2,A,B) | para(c2,c1,A,B). [resolve(717,a,120,a)].
% 17.84/18.14 767 para(c4,c3,c3,c4). [resolve(377,a,590,a)].
% 17.84/18.14 768 para(c3,c4,c3,c4). [resolve(377,a,379,a)].
% 17.84/18.14 779 -coll(A,c4,c3) | -coll(A,c3,c4) | eqratio(A,c4,c4,c3,A,c3,c3,c4). [resolve(767,a,171,a)].
% 17.84/18.14 780 -midp(c4,A,c3) | -coll(c3,A,c4) | midp(c3,A,c4). [resolve(767,a,156,b)].
% 17.84/18.14 784 para(c3,c4,c4,c3). [resolve(767,a,116,a)].
% 17.84/18.14 785 para(c4,c3,c4,c3). [resolve(767,a,115,a)].
% 17.84/18.14 788 -midp(A,c3,c3) | midp(A,c4,c4). [resolve(768,a,309,b)].
% 17.84/18.14 795 coll(c3,c4,c4). [resolve(768,a,172,a)].
% 17.84/18.14 796 -coll(A,c3,c3) | -coll(A,c4,c4) | eqratio(A,c3,c3,c3,A,c4,c4,c4). [resolve(768,a,171,a)].
% 17.84/18.14 797 -midp(c3,A,c3) | -coll(c4,A,c4) | midp(c4,A,c4). [resolve(768,a,156,b)].
% 17.84/18.14 798 eqangle(c3,c4,A,B,c3,c4,A,B). [resolve(768,a,150,a)].
% 17.84/18.14 799 coll(c4,c4,c3). [resolve(795,a,295,a)].
% 17.84/18.14 807 coll(c3,c3,c4). [resolve(799,a,295,a)].
% 17.84/18.14 808 -coll(c4,c4,A) | coll(A,c3,c4). [resolve(799,a,114,b)].
% 17.84/18.14 810 para(c1,c3,c3,c1). [resolve(378,a,576,a)].
% 17.84/18.14 811 para(c1,c3,c1,c3). [resolve(378,a,379,a)].
% 17.84/18.14 817 coll(c1,c4,c3). [resolve(807,a,530,a)].
% 17.84/18.14 818 coll(c4,c1,c3). [resolve(807,a,529,a)].
% 17.84/18.14 822 -coll(c3,c3,A) | coll(c4,A,c3). [resolve(807,a,114,a)].
% 17.84/18.14 823 coll(c3,c4,c3). [resolve(807,a,112,a)].
% 17.84/18.14 831 coll(c1,c3,c4). [resolve(817,a,112,a)].
% 17.84/18.14 836 coll(c4,c3,c1). [resolve(818,a,112,a)].
% 17.84/18.14 847 coll(c4,c3,c3). [resolve(823,a,113,a)].
% 17.84/18.14 848 coll(c1,c4,c1). [resolve(831,a,536,a)].
% 17.84/18.14 852 coll(c4,c4,c1). [resolve(831,a,295,a)].
% 17.84/18.14 853 -coll(c1,c3,A) | coll(A,c4,c1). [resolve(831,a,114,b)].
% 17.84/18.14 858 coll(c1,c1,c4). [resolve(836,a,295,a)].
% 17.84/18.14 861 coll(c3,c4,c1). [resolve(836,a,113,a)].
% 17.84/18.14 919 coll(c4,c1,c4). [resolve(852,a,112,a)].
% 17.84/18.14 989 -midp(c3,A,c4) | -coll(c4,A,c3) | midp(c4,A,c3). [resolve(784,a,156,b)].
% 17.84/18.14 1003 -midp(c4,A,c4) | -coll(c3,A,c3) | midp(c3,A,c3). [resolve(785,a,156,b)].
% 17.84/18.14 1016 -midp(c1,A,c3) | -coll(c3,A,c1) | midp(c3,A,c1). [resolve(810,a,156,b)].
% 17.84/18.14 1020 para(c3,c1,c1,c3). [resolve(810,a,116,a)].
% 17.84/18.14 1031 -midp(c1,A,c1) | -coll(c3,A,c3) | midp(c3,A,c3). [resolve(811,a,156,b)].
% 17.84/18.14 1048 para(c3,c1,c3,c1). [resolve(1020,a,115,a)].
% 17.84/18.14 1059 -midp(c3,A,c3) | -coll(c1,A,c1) | midp(c1,A,c1). [resolve(1048,a,156,b)].
% 17.84/18.14 1060 eqangle(c3,c1,A,B,c3,c1,A,B). [resolve(1048,a,150,a)].
% 17.84/18.14 1141 para(c4,c2,c2,c4). [resolve(400,a,626,a)].
% 17.84/18.14 1142 para(c2,c4,c2,c4). [resolve(400,a,402,a)].
% 17.84/18.14 1154 -midp(c4,A,c2) | -coll(c2,A,c4) | midp(c2,A,c4). [resolve(1141,a,156,b)].
% 17.84/18.14 1158 para(c2,c4,c4,c2). [resolve(1141,a,116,a)].
% 17.84/18.14 1162 -midp(A,c2,c2) | midp(A,c4,c4). [resolve(1142,a,309,b)].
% 17.84/18.14 1169 coll(c2,c4,c4). [resolve(1142,a,172,a)].
% 17.84/18.14 1173 coll(c4,c4,c2). [resolve(1169,a,295,a)].
% 17.84/18.14 1180 coll(c2,c3,c4). [resolve(1173,a,808,a)].
% 17.84/18.14 1188 para(c1,c2,c2,c1). [resolve(401,a,612,a)].
% 17.84/18.14 1201 coll(c2,c4,c3). [resolve(1180,a,112,a)].
% 17.84/18.14 1212 coll(c3,c3,c2). [resolve(1201,a,295,a)].
% 17.84/18.14 1234 coll(c2,c3,c3). [resolve(1212,a,556,a)].
% 17.84/18.14 1235 coll(c1,c2,c3). [resolve(1212,a,530,a)].
% 17.84/18.14 1236 coll(c2,c1,c3). [resolve(1212,a,529,a)].
% 17.84/18.14 1239 -coll(c3,c3,A) | coll(A,c2,c3). [resolve(1212,a,114,b)].
% 17.84/18.14 1240 -coll(c3,c3,A) | coll(c2,A,c3). [resolve(1212,a,114,a)].
% 17.84/18.14 1241 coll(c3,c2,c3). [resolve(1212,a,112,a)].
% 17.84/18.14 1256 coll(c1,c3,c2). [resolve(1235,a,112,a)].
% 17.84/18.14 1259 coll(c2,c3,c1). [resolve(1236,a,112,a)].
% 17.84/18.14 1291 coll(c1,c1,c2). [resolve(1259,a,295,a)].
% 17.84/18.14 1293 -coll(c2,c3,A) | coll(c1,A,c2). [resolve(1259,a,114,a)].
% 17.84/18.14 1415 -perp(c4,c2,A,B) | perp(c2,c4,A,B). [resolve(1158,a,121,a)].
% 17.84/18.14 1443 -para(c2,c1,A,B) | para(c1,c2,A,B). [resolve(1188,a,117,a)].
% 17.84/18.14 1485 coll(c2,c4,c1). [resolve(853,a,1256,a)].
% 17.84/18.14 1488 coll(c4,c2,c1). [resolve(1485,a,113,a)].
% 17.84/18.14 1489 coll(c2,c1,c4). [resolve(1485,a,112,a)].
% 17.84/18.14 1589 eqangle(c8,c2,c8,c3,c2,c4,c2,c3). [resolve(438,a,130,a)].
% 17.84/18.14 6303 eqratio(c2,c4,c4,c3,c2,c3,c3,c4). [resolve(779,a,1201,a),unit_del(a,1180)].
% 17.84/18.14 6574 eqratio(c2,c3,c3,c3,c2,c4,c4,c4). [resolve(796,b,1169,a),unit_del(a,1234)].
% 17.84/18.14 6613 -cyclic(c4,c3,c3,c4) | -cyclic(c4,c3,c3,c3) | cong(c4,c3,c4,c3). [resolve(798,a,303,c)].
% 17.84/18.14 6623 -coll(c3,c3,A) | cyclic(c4,A,c3,c3). [resolve(798,a,153,a)].
% 17.84/18.14 6625 eqangle(A,B,c3,c4,A,B,c3,c4). [resolve(798,a,129,a)].
% 17.84/18.14 8959 midp(c1,c1,c1) | -cong(c3,c3,c3,c1). [resolve(1060,a,333,b),unit_del(a,534)].
% 17.84/18.14 9247 -perp(c2,c4,c2,c3) | perp(c8,c2,c8,c3). [resolve(1589,a,179,a)].
% 17.84/18.14 9992 -cong(c2,c3,c3,c4) | cong(c2,c4,c4,c3). [resolve(6303,a,180,a)].
% 17.84/18.14 10013 -cong(c2,c4,c4,c4) | cong(c2,c3,c3,c3). [resolve(6574,a,180,a)].
% 17.84/18.14 10065 cyclic(c4,c2,c3,c3). [resolve(6623,a,1212,a)].
% 17.84/18.14 10070 cyclic(c4,c4,c3,c3). [resolve(6623,a,807,a)].
% 17.84/18.14 10071 cyclic(c4,c3,c3,c3). [resolve(6623,a,538,a)].
% 17.84/18.14 10075 -cyclic(c4,c3,c3,c4) | cong(c4,c3,c4,c3). [back_unit_del(6613),unit_del(b,10071)].
% 17.84/18.14 10082 cyclic(c2,c4,c3,c3). [resolve(10065,a,126,a)].
% 17.84/18.14 10089 cyclic(c4,c3,c4,c3). [resolve(10070,a,125,a)].
% 17.84/18.14 10121 cyclic(c2,c3,c4,c3). [resolve(10082,a,125,a)].
% 17.84/18.14 10133 cyclic(c4,c3,c3,c4). [resolve(10089,a,124,a)].
% 17.84/18.14 10135 cong(c4,c3,c4,c3). [back_unit_del(10075),unit_del(a,10133)].
% 17.84/18.14 10183 -cong(c2,c4,c3,c4) | -cong(c2,c3,c3,c3) | perp(c4,c2,c2,c3). [resolve(10121,a,163,c)].
% 17.84/18.14 10187 cyclic(c3,c2,c4,c3). [resolve(10121,a,126,a)].
% 17.84/18.14 10237 midp(c4,c3,c3). [resolve(10135,a,173,a),unit_del(a,847)].
% 17.84/18.14 10253 midp(c4,c4,c4). [resolve(10237,a,788,a)].
% 17.84/18.14 10254 midp(c3,c3,c4). [resolve(10237,a,780,a),unit_del(a,807)].
% 17.84/18.14 10276 cong(c1,c3,c1,c4). [back_unit_del(375),unit_del(a,10254)].
% 17.84/18.14 10338 midp(c3,c4,c3). [resolve(10253,a,1003,a),unit_del(a,823)].
% 17.84/18.14 10503 midp(c1,c4,c1). [resolve(10338,a,1059,a),unit_del(a,848)].
% 17.84/18.14 10605 midp(c1,c1,c4). [resolve(10503,a,122,a)].
% 17.84/18.14 10609 cong(c1,c1,c2,c1). [resolve(10605,a,399,a)].
% 17.84/18.14 10625 cong(c1,c1,c1,c4). [resolve(10605,a,174,a)].
% 17.84/18.14 10718 cyclic(c3,c2,c3,c4). [resolve(10187,a,124,a)].
% 17.84/18.14 10859 midp(c1,c3,c4). [resolve(10276,a,173,a),unit_del(a,831)].
% 17.84/18.14 10888 midp(c1,c4,c3). [resolve(10859,a,122,a)].
% 17.84/18.14 10893 midp(c3,c4,c1). [resolve(10888,a,1016,a),unit_del(a,861)].
% 17.84/18.14 10911 cong(c4,c3,c2,c3). [resolve(10893,a,738,a)].
% 17.84/18.14 10930 midp(c3,c1,c4). [resolve(10893,a,122,a)].
% 17.84/18.14 10933 midp(c4,c1,c3). [resolve(10930,a,989,a),unit_del(a,818)].
% 17.84/18.14 10983 midp(c4,c3,c1). [resolve(10933,a,122,a)].
% 17.84/18.14 10988 cong(c3,c3,c3,c1). [back_unit_del(643),unit_del(a,10983)].
% 17.84/18.14 10992 midp(c1,c1,c1). [back_unit_del(8959),unit_del(b,10988)].
% 17.84/18.14 11025 midp(c3,c1,c3). [resolve(10992,a,1031,a),unit_del(a,531)].
% 17.84/18.14 11082 midp(c4,c1,c4). [resolve(11025,a,797,a),unit_del(a,919)].
% 17.84/18.14 11142 cong(c1,c4,c2,c4). [resolve(11082,a,399,a)].
% 17.84/18.14 11162 midp(c4,c4,c1). [resolve(11082,a,122,a)].
% 17.84/18.14 11181 cong(c4,c4,c2,c4). [resolve(11162,a,738,a)].
% 17.84/18.14 11656 cong(c1,c1,c1,c2). [resolve(10609,a,133,a)].
% 17.84/18.14 11767 perp(c1,c4,c4,c4). [resolve(10625,a,334,c),unit_del(a,858)].
% 17.84/18.14 12055 cyclic(c2,c3,c4,c4). [resolve(10718,a,300,a)].
% 17.84/18.14 12186 cong(c2,c3,c4,c3). [resolve(10911,a,134,a)].
% 17.84/18.14 12505 cong(c1,c4,c4,c2). [resolve(11142,a,133,a)].
% 17.84/18.14 12569 cong(c2,c4,c4,c4). [resolve(11181,a,134,a)].
% 17.84/18.14 12570 cong(c4,c4,c4,c2). [resolve(11181,a,133,a)].
% 17.84/18.14 12571 cong(c2,c3,c3,c3). [back_unit_del(10013),unit_del(a,12569)].
% 17.84/18.14 12574 -cong(c2,c4,c3,c4) | perp(c4,c2,c2,c3). [back_unit_del(10183),unit_del(b,12571)].
% 17.84/18.14 13013 midp(c1,c1,c2). [resolve(11656,a,173,a),unit_del(a,1291)].
% 17.84/18.14 13035 midp(c1,c2,c1). [resolve(13013,a,122,a)].
% 17.84/18.14 13037 midp(c3,c2,c3). [resolve(13035,a,1031,a),unit_del(a,1241)].
% 17.84/18.14 13203 -perp(c4,c4,A,B) | para(c1,c4,A,B). [resolve(11767,a,120,a)].
% 17.84/18.14 13530 cyclic(c2,c4,c3,c4). [resolve(12055,a,125,a)].
% 17.84/18.14 13701 cong(c2,c3,c3,c4). [resolve(12186,a,133,a)].
% 17.84/18.14 13702 cong(c2,c4,c4,c3). [back_unit_del(9992),unit_del(a,13701)].
% 17.84/18.14 13805 cong(c4,c2,c1,c4). [resolve(12505,a,134,a)].
% 17.84/18.14 13894 perp(c4,c2,c2,c2). [resolve(12570,a,334,c),unit_del(a,1173)].
% 17.84/18.14 14610 perp(c3,c2,c2,c4). [resolve(13530,a,163,c),unit_del(a,12186),unit_del(b,12569)].
% 17.84/18.14 14870 cong(c2,c4,c3,c4). [resolve(13702,a,133,a)].
% 17.84/18.14 14872 perp(c4,c2,c2,c3). [back_unit_del(12574),unit_del(a,14870)].
% 17.84/18.14 14961 cong(c4,c2,c4,c1). [resolve(13805,a,133,a)].
% 17.84/18.14 15093 para(c2,c1,c2,c2). [resolve(13894,a,766,a)].
% 17.84/18.14 15451 perp(c3,c2,c4,c2). [resolve(14610,a,118,a)].
% 17.84/18.14 15743 perp(c2,c4,c2,c3). [resolve(14872,a,1415,a)].
% 17.84/18.14 15755 perp(c8,c2,c8,c3). [back_unit_del(9247),unit_del(a,15743)].
% 17.84/18.14 15943 midp(c4,c2,c1). [resolve(14961,a,173,a),unit_del(a,1488)].
% 17.84/18.14 15956 midp(c4,c1,c2). [resolve(15943,a,122,a)].
% 17.84/18.14 15957 midp(c2,c1,c4). [resolve(15956,a,1154,a),unit_del(a,1489)].
% 17.84/18.14 15979 midp(c2,c4,c1). [resolve(15957,a,122,a)].
% 17.84/18.14 15982 cong(c4,c2,c3,c2). [resolve(15979,a,703,a)].
% 17.84/18.14 16140 para(c1,c2,c2,c2). [resolve(1443,a,15093,a)].
% 17.84/18.14 16240 para(c3,c2,c2,c1). [resolve(15451,a,739,a)].
% 17.84/18.14 16391 coll(f11(c8,c8,c3,c2),c3,c8). [resolve(15755,a,321,a)].
% 17.84/18.14 16543 perp(c4,c3,c2,c2). [resolve(15982,a,305,a)].
% 17.84/18.14 16605 -midp(A,c1,c2) | midp(A,c2,c2). [resolve(16140,a,309,b)].
% 17.84/18.14 16827 para(c3,c1,c2,c2). [resolve(16543,a,753,a)].
% 17.84/18.14 17193 -midp(A,c3,c2) | midp(A,c1,c2). [resolve(16827,a,170,b),unit_del(b,16240)].
% 17.84/18.14 25393 coll(f11(c8,c8,c3,c2),c8,c3). [resolve(16391,a,112,a)].
% 17.84/18.14 29484 coll(c8,f11(c8,c8,c3,c2),c3). [resolve(25393,a,113,a)].
% 17.84/18.14 36353 coll(c3,c3,c8). [resolve(29484,a,295,a)].
% 17.84/18.14 36380 coll(c2,c8,c3). [resolve(36353,a,1240,a)].
% 17.84/18.14 36381 coll(c8,c2,c3). [resolve(36353,a,1239,a)].
% 17.84/18.14 36382 coll(c4,c8,c3). [resolve(36353,a,822,a)].
% 17.84/18.14 36395 coll(c2,c3,c8). [resolve(36380,a,112,a)].
% 17.84/18.14 36403 coll(c4,c3,c8). [resolve(36382,a,112,a)].
% 17.84/18.14 36446 coll(c1,c8,c2). [resolve(36395,a,1293,a)].
% 17.84/18.14 36491 coll(c8,c8,c4). [resolve(36403,a,295,a)].
% 17.84/18.14 36583 coll(c1,c2,c8). [resolve(36446,a,112,a)].
% 17.84/18.14 36584 perp(c2,c3,c3,c8). [back_unit_del(271),unit_del(a,36583)].
% 17.84/18.14 36674 coll(c8,c4,c8). [resolve(36491,a,112,a)].
% 17.84/18.14 36855 coll(c4,c8,c8). [resolve(36674,a,113,a)].
% 17.84/18.14 36902 perp(c2,c3,c8,c3). [resolve(36584,a,118,a)].
% 17.84/18.14 36914 perp(c8,c3,c2,c3). [resolve(36902,a,119,a)].
% 17.84/18.14 36946 cong(c8,c2,c8,c3). [resolve(36914,a,161,b),unit_del(a,13037)].
% 17.84/18.14 36988 midp(c8,c2,c3). [resolve(36946,a,173,a),unit_del(a,36381)].
% 17.84/18.14 36998 midp(c8,c3,c2). [resolve(36988,a,122,a)].
% 17.84/18.14 36999 midp(c8,c1,c2). [resolve(36998,a,17193,a)].
% 17.84/18.14 37009 midp(c8,c2,c2). [resolve(36999,a,16605,a)].
% 17.84/18.14 37046 midp(c8,c4,c4). [resolve(37009,a,1162,a)].
% 17.84/18.14 37092 cong(c8,c4,c8,c4). [resolve(37046,a,174,a)].
% 17.84/18.14 37220 cong(c8,c4,c4,c8). [resolve(37092,a,133,a)].
% 17.84/18.14 37317 cong(c4,c8,c8,c4). [resolve(37220,a,134,a)].
% 17.84/18.14 37416 cong(c4,c8,c4,c8). [resolve(37317,a,133,a)].
% 17.84/18.14 37523 midp(c4,c8,c8). [resolve(37416,a,173,a),unit_del(a,36855)].
% 17.84/18.14 38082 para(A,B,A,B). [resolve(6625,a,149,a)].
% 17.84/18.14 38085 -midp(A,B,B) | midp(A,C,C). [resolve(38082,a,309,b)].
% 17.84/18.14 43945 midp(c4,A,A). [resolve(38085,a,37523,a)].
% 17.84/18.14 43955 cong(c4,A,c4,A). [resolve(43945,a,174,a)].
% 17.84/18.14 44012 perp(c4,c4,A,B). [resolve(43955,a,162,b),unit_del(a,43955)].
% 17.84/18.14 44032 para(c1,c4,A,B). [back_unit_del(13203),unit_del(a,44012)].
% 17.84/18.14 44033 $F. [resolve(44032,a,214,a)].
% 17.84/18.14
% 17.84/18.14 % SZS output end Refutation
% 17.84/18.14 ============================== end of proof ==========================
% 17.84/18.14
% 17.84/18.14 ============================== STATISTICS ============================
% 17.84/18.14
% 17.84/18.14 Given=19436. Generated=260511. Kept=43901. proofs=1.
% 17.84/18.14 Usable=17194. Sos=8234. Demods=0. Limbo=20, Disabled=18632. Hints=0.
% 17.84/18.14 Megabytes=21.65.
% 17.84/18.14 User_CPU=16.93, System_CPU=0.13, Wall_clock=17.
% 17.84/18.14
% 17.84/18.14 ============================== end of statistics =====================
% 17.84/18.14
% 17.84/18.14 ============================== end of search =========================
% 17.84/18.14
% 17.84/18.14 THEOREM PROVED
% 17.84/18.14 % SZS status Theorem
% 17.84/18.14
% 17.84/18.14 Exiting with 1 proof.
% 17.84/18.14
% 17.84/18.14 Process 17463 exit (max_proofs) Fri Jun 17 18:00:57 2022
% 17.84/18.14 Prover9 interrupted
%------------------------------------------------------------------------------