TSTP Solution File: GEO660+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GEO660+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 05:57:28 EDT 2022
% Result : Theorem 2.84s 3.11s
% Output : Refutation 2.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO660+1 : TPTP v8.1.0. Released v7.5.0.
% 0.07/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Fri Jun 17 23:30:37 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.48/1.14 ============================== Prover9 ===============================
% 0.48/1.14 Prover9 (32) version 2009-11A, November 2009.
% 0.48/1.14 Process 28495 was started by sandbox on n011.cluster.edu,
% 0.48/1.14 Fri Jun 17 23:30:38 2022
% 0.48/1.14 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_28342_n011.cluster.edu".
% 0.48/1.14 ============================== end of head ===========================
% 0.48/1.14
% 0.48/1.14 ============================== INPUT =================================
% 0.48/1.14
% 0.48/1.14 % Reading from file /tmp/Prover9_28342_n011.cluster.edu
% 0.48/1.14
% 0.48/1.14 set(prolog_style_variables).
% 0.48/1.14 set(auto2).
% 0.48/1.14 % set(auto2) -> set(auto).
% 0.48/1.14 % set(auto) -> set(auto_inference).
% 0.48/1.14 % set(auto) -> set(auto_setup).
% 0.48/1.14 % set(auto_setup) -> set(predicate_elim).
% 0.48/1.14 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.48/1.14 % set(auto) -> set(auto_limits).
% 0.48/1.14 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.48/1.14 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.48/1.14 % set(auto) -> set(auto_denials).
% 0.48/1.14 % set(auto) -> set(auto_process).
% 0.48/1.14 % set(auto2) -> assign(new_constants, 1).
% 0.48/1.14 % set(auto2) -> assign(fold_denial_max, 3).
% 0.48/1.14 % set(auto2) -> assign(max_weight, "200.000").
% 0.48/1.14 % set(auto2) -> assign(max_hours, 1).
% 0.48/1.14 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.48/1.14 % set(auto2) -> assign(max_seconds, 0).
% 0.48/1.14 % set(auto2) -> assign(max_minutes, 5).
% 0.48/1.14 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.48/1.14 % set(auto2) -> set(sort_initial_sos).
% 0.48/1.14 % set(auto2) -> assign(sos_limit, -1).
% 0.48/1.14 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.48/1.14 % set(auto2) -> assign(max_megs, 400).
% 0.48/1.14 % set(auto2) -> assign(stats, some).
% 0.48/1.14 % set(auto2) -> clear(echo_input).
% 0.48/1.14 % set(auto2) -> set(quiet).
% 0.48/1.14 % set(auto2) -> clear(print_initial_clauses).
% 0.48/1.14 % set(auto2) -> clear(print_given).
% 0.48/1.14 assign(lrs_ticks,-1).
% 0.48/1.14 assign(sos_limit,10000).
% 0.48/1.14 assign(order,kbo).
% 0.48/1.14 set(lex_order_vars).
% 0.48/1.14 clear(print_given).
% 0.48/1.14
% 0.48/1.14 % formulas(sos). % not echoed (95 formulas)
% 0.48/1.14
% 0.48/1.14 ============================== end of input ==========================
% 0.48/1.14
% 0.48/1.14 % From the command line: assign(max_seconds, 300).
% 0.48/1.14
% 0.48/1.14 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.48/1.14
% 0.48/1.14 % Formulas that are not ordinary clauses:
% 0.48/1.14 1 (all A all B all C (coll(A,B,C) -> coll(A,C,B))) # label(ruleD1) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.14 2 (all A all B all C (coll(A,B,C) -> coll(B,A,C))) # label(ruleD2) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 11 (all A all B all M (midp(M,B,A) -> midp(M,A,B))) # label(ruleD11) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 67 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.14 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].
% 0.48/1.14 69 (all A all B all C (midp(A,B,C) -> cong(A,B,A,C))) # label(ruleD68) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.14 70 (all A all B all C (midp(A,B,C) -> coll(A,B,C))) # label(ruleD69) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 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].
% 0.48/1.14 95 -(all A all B all C all D all E all F all G (perp(C,A,C,B) & perp(D,C,A,B) & coll(D,A,B) & coll(E,C,D) & coll(F,A,B) & eqangle(B,A,A,E,E,A,A,C) & eqangle(D,C,C,F,F,C,C,B) & coll(G,B,C) & coll(G,A,E) -> para(E,F,C,B))) # label(exemplo7Book00EE02E02319) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.48/1.14
% 0.48/1.14 ============================== end of process non-clausal formulas ===
% 0.48/1.14
% 0.48/1.14 ============================== PROCESS INITIAL CLAUSES ===============
% 0.48/1.14
% 0.48/1.14 ============================== PREDICATE ELIMINATION =================
% 0.48/1.14 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)].
% 0.48/1.14 97 -cong(A,B,A,C) | -cong(A,B,A,D) | circle(A,B,C,D) # label(ruleD12) # label(axiom). [clausify(12)].
% 0.48/1.14 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)].
% 0.48/1.14 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)].
% 0.48/1.14 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)].
% 0.48/1.14 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)].
% 0.48/1.14 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)].
% 0.48/1.14 100 -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)].
% 0.48/1.14 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)].
% 0.48/1.14 101 -circle(A,B,C,D) | -coll(A,B,D) | perp(B,C,C,D) # label(ruleD53) # label(axiom). [clausify(54)].
% 0.48/1.14 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)].
% 0.48/1.14 102 -circle(A,B,C,D) | perp(f12(B,C,D,A),B,B,A) # label(ruleX11) # label(axiom). [clausify(87)].
% 0.48/1.14 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)].
% 0.48/1.14 103 -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)].
% 0.48/1.14 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)].
% 0.48/1.14 104 -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)].
% 0.48/1.14 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)].
% 0.48/1.14 105 -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)].
% 0.48/1.14 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)].
% 0.48/1.14 106 -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)].
% 0.48/1.14 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)].
% 0.48/1.14 107 -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)].
% 0.48/1.16 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)].
% 0.48/1.16 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)].
% 0.48/1.16 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)].
% 0.48/1.16 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)].
% 0.48/1.16 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)].
% 0.48/1.16 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)].
% 0.48/1.16 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)].
% 0.48/1.16 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)].
% 0.48/1.16 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)].
% 0.48/1.16 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)].
% 0.48/1.16 108 -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)].
% 0.48/1.16 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)].
% 0.48/1.16 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)].
% 0.48/1.16 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)].
% 0.48/1.16 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)].
% 0.48/1.16 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)].
% 0.48/1.16 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)].
% 0.48/1.16 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)].
% 0.48/1.16 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)].
% 0.48/1.16 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)].
% 0.48/1.16 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)].
% 0.48/1.16
% 0.48/1.16 ============================== end predicate elimination =============
% 0.48/1.16
% 0.48/1.16 Auto_denials: (non-Horn, no changes).
% 0.48/1.16
% 0.48/1.16 Term ordering decisions:
% 0.48/1.16 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. f19=1. f1=1. f2=1. f3=1. f4=1. f10=1. f11=1. f12=1. f16=1. f5=1. f9=1. f15=1. f17=1. f18=1. f6=1. f13=1. f14=1. f20=1. f7=1. f8=1.
% 0.48/1.16
% 0.48/1.16 ============================== end of process initial clauses ========
% 0.48/1.16
% 0.48/1.16 ============================== CLAUSES FOR SEARCH ====================
% 0.48/1.16
% 0.48/1.16 ============================== end of clauses for search =============
% 0.48/1.16
% 0.48/1.16 ============================== SEARCH ================================
% 0.48/1.16
% 0.48/1.16 % Starting search at 0.04 seconds.
% 2.84/3.11
% 2.84/3.11 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 1365 (0.00 of 0.15 sec).
% 2.84/3.11
% 2.84/3.11 Low Water (keep): wt=45.000, iters=3345
% 2.84/3.11
% 2.84/3.11 Low Water (keep): wt=44.000, iters=3345
% 2.84/3.11
% 2.84/3.11 Low Water (keep): wt=32.000, iters=3333
% 2.84/3.11
% 2.84/3.11 Low Water (keep): wt=28.000, iters=3336
% 2.84/3.11
% 2.84/3.11 Low Water (keep): wt=26.000, iters=3337
% 2.84/3.11
% 2.84/3.11 Low Water (keep): wt=23.000, iters=3335
% 2.84/3.11
% 2.84/3.11 Low Water (keep): wt=22.000, iters=3506
% 2.84/3.11
% 2.84/3.11 Low Water (keep): wt=21.000, iters=3373
% 2.84/3.11
% 2.84/3.11 Low Water (keep): wt=19.000, iters=3342
% 2.84/3.11
% 2.84/3.11 Low Water (keep): wt=18.000, iters=3356
% 2.84/3.11
% 2.84/3.11 Low Water (keep): wt=17.000, iters=3421
% 2.84/3.11
% 2.84/3.11 Low Water (keep): wt=16.000, iters=3350
% 2.84/3.11
% 2.84/3.11 Low Water (keep): wt=15.000, iters=3340
% 2.84/3.11
% 2.84/3.11 Low Water (keep): wt=14.000, iters=3341
% 2.84/3.11
% 2.84/3.11 Low Water (keep): wt=13.000, iters=3335
% 2.84/3.11
% 2.84/3.11 Low Water (keep): wt=12.000, iters=3343
% 2.84/3.11
% 2.84/3.11 Low Water (displace): id=8473, wt=48.000
% 2.84/3.11
% 2.84/3.11 Low Water (displace): id=8469, wt=46.000
% 2.84/3.11
% 2.84/3.11 Low Water (displace): id=8474, wt=44.000
% 2.84/3.11
% 2.84/3.11 Low Water (displace): id=8470, wt=42.000
% 2.84/3.11
% 2.84/3.11 Low Water (displace): id=8476, wt=37.000
% 2.84/3.11
% 2.84/3.11 Low Water (displace): id=8434, wt=36.000
% 2.84/3.11
% 2.84/3.11 Low Water (displace): id=8467, wt=35.000
% 2.84/3.11
% 2.84/3.11 Low Water (displace): id=8430, wt=34.000
% 2.84/3.11
% 2.84/3.11 Low Water (displace): id=8521, wt=32.000
% 2.84/3.11
% 2.84/3.11 Low Water (displace): id=8429, wt=31.000
% 2.84/3.11
% 2.84/3.11 Low Water (displace): id=8431, wt=30.000
% 2.84/3.11
% 2.84/3.11 Low Water (displace): id=8276, wt=29.000
% 2.84/3.11
% 2.84/3.11 Low Water (displace): id=8560, wt=28.000
% 2.84/3.11
% 2.84/3.11 Low Water (displace): id=8427, wt=27.000
% 2.84/3.11
% 2.84/3.11 Low Water (displace): id=8392, wt=26.000
% 2.84/3.11
% 2.84/3.11 Low Water (displace): id=14430, wt=11.000
% 2.84/3.11
% 2.84/3.11 Low Water (displace): id=14432, wt=10.000
% 2.84/3.11
% 2.84/3.11 Low Water (displace): id=14465, wt=9.000
% 2.84/3.11
% 2.84/3.11 Low Water (displace): id=14540, wt=8.000
% 2.84/3.11
% 2.84/3.11 Low Water (displace): id=14579, wt=5.000
% 2.84/3.11
% 2.84/3.11 Low Water (keep): wt=11.000, iters=3508
% 2.84/3.11
% 2.84/3.11 Low Water (keep): wt=10.000, iters=3333
% 2.84/3.11
% 2.84/3.11 ============================== PROOF =================================
% 2.84/3.11 % SZS status Theorem
% 2.84/3.11 % SZS output start Refutation
% 2.84/3.11
% 2.84/3.11 % Proof 1 at 1.94 (+ 0.05) seconds.
% 2.84/3.11 % Length of proof is 108.
% 2.84/3.11 % Level of proof is 22.
% 2.84/3.11 % Maximum clause weight is 29.000.
% 2.84/3.11 % Given clauses 5056.
% 2.84/3.11
% 2.84/3.11 1 (all A all B all C (coll(A,B,C) -> coll(A,C,B))) # label(ruleD1) # label(axiom) # label(non_clause). [assumption].
% 2.84/3.11 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].
% 2.84/3.11 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].
% 2.84/3.11 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].
% 2.84/3.11 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].
% 2.84/3.11 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].
% 2.84/3.11 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].
% 2.84/3.11 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].
% 2.84/3.11 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].
% 2.84/3.11 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].
% 2.84/3.11 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].
% 2.84/3.11 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].
% 2.84/3.11 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].
% 2.84/3.11 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].
% 2.84/3.11 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].
% 2.84/3.11 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].
% 2.84/3.11 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].
% 2.84/3.11 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].
% 2.84/3.11 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].
% 2.84/3.11 67 (all A all B all C (para(A,B,A,C) -> coll(A,B,C))) # label(ruleD66) # label(axiom) # label(non_clause). [assumption].
% 2.84/3.11 95 -(all A all B all C all D all E all F all G (perp(C,A,C,B) & perp(D,C,A,B) & coll(D,A,B) & coll(E,C,D) & coll(F,A,B) & eqangle(B,A,A,E,E,A,A,C) & eqangle(D,C,C,F,F,C,C,B) & coll(G,B,C) & coll(G,A,E) -> para(E,F,C,B))) # label(exemplo7Book00EE02E02319) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.84/3.11 109 -coll(A,B,C) | coll(A,C,B) # label(ruleD1) # label(axiom). [clausify(1)].
% 2.84/3.11 111 -coll(A,B,C) | -coll(A,B,D) | coll(C,D,A) # label(ruleD3) # label(axiom). [clausify(3)].
% 2.84/3.11 112 -para(A,B,C,D) | para(A,B,D,C) # label(ruleD4) # label(axiom). [clausify(4)].
% 2.84/3.11 113 -para(A,B,C,D) | para(C,D,A,B) # label(ruleD5) # label(axiom). [clausify(5)].
% 2.84/3.11 116 -perp(A,B,C,D) | perp(C,D,A,B) # label(ruleD8) # label(axiom). [clausify(8)].
% 2.84/3.11 117 -perp(A,B,C,D) | -perp(C,D,E,F) | para(A,B,E,F) # label(ruleD9) # label(axiom). [clausify(9)].
% 2.84/3.11 121 -cyclic(A,B,C,D) | cyclic(A,B,D,C) # label(ruleD14) # label(axiom). [clausify(14)].
% 2.84/3.11 122 -cyclic(A,B,C,D) | cyclic(A,C,B,D) # label(ruleD15) # label(axiom). [clausify(15)].
% 2.84/3.11 123 -cyclic(A,B,C,D) | cyclic(B,A,C,D) # label(ruleD16) # label(axiom). [clausify(16)].
% 2.84/3.11 124 -cyclic(A,B,C,D) | -cyclic(A,B,C,E) | cyclic(B,C,D,E) # label(ruleD17) # label(axiom). [clausify(17)].
% 2.84/3.11 126 -eqangle(A,B,C,D,E,F,V6,V7) | eqangle(C,D,A,B,V6,V7,E,F) # label(ruleD19) # label(axiom). [clausify(19)].
% 2.84/3.11 128 -eqangle(A,B,C,D,E,F,V6,V7) | eqangle(A,B,E,F,C,D,V6,V7) # label(ruleD21) # label(axiom). [clausify(21)].
% 2.84/3.11 130 -cong(A,B,C,D) | cong(A,B,D,C) # label(ruleD23) # label(axiom). [clausify(23)].
% 2.84/3.11 131 -cong(A,B,C,D) | cong(C,D,A,B) # label(ruleD24) # label(axiom). [clausify(24)].
% 2.84/3.11 146 -eqangle(A,B,C,D,E,F,C,D) | para(A,B,E,F) # label(ruleD39) # label(axiom). [clausify(39)].
% 2.84/3.11 147 -para(A,B,C,D) | eqangle(A,B,E,F,C,D,E,F) # label(ruleD40) # label(axiom). [clausify(40)].
% 2.84/3.11 150 -eqangle(A,B,A,C,D,B,D,C) | -coll(A,D,C) | cyclic(B,C,A,D) # label(ruleD42b) # label(axiom). [clausify(43)].
% 2.84/3.11 151 -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)].
% 2.84/3.11 159 -cong(A,B,C,B) | -cong(A,D,C,D) | perp(A,C,B,D) # label(ruleD56) # label(axiom). [clausify(57)].
% 2.84/3.11 169 -para(A,B,A,C) | coll(A,B,C) # label(ruleD66) # label(axiom). [clausify(67)].
% 2.84/3.11 208 perp(c3,c1,c3,c2) # label(exemplo7Book00EE02E02319) # label(negated_conjecture). [clausify(95)].
% 2.84/3.11 209 perp(c4,c3,c1,c2) # label(exemplo7Book00EE02E02319) # label(negated_conjecture). [clausify(95)].
% 2.84/3.11 215 coll(c7,c2,c3) # label(exemplo7Book00EE02E02319) # label(negated_conjecture). [clausify(95)].
% 2.84/3.11 217 -para(c5,c6,c3,c2) # label(exemplo7Book00EE02E02319) # label(negated_conjecture). [clausify(95)].
% 2.84/3.11 256 -coll(A,B,C) | coll(C,C,A). [factor(111,a,b)].
% 2.84/3.11 261 -cyclic(A,B,C,D) | cyclic(B,C,D,D). [factor(124,a,b)].
% 2.84/3.11 262 -cyclic(A,B,C,D) | -cyclic(A,B,C,E) | -eqangle(C,A,C,B,E,D,E,D) | cong(A,B,D,D). [factor(151,a,b)].
% 2.84/3.11 329 -perp(c3,c2,A,B) | para(c3,c1,A,B). [resolve(208,a,117,a)].
% 2.84/3.11 330 perp(c3,c2,c3,c1). [resolve(208,a,116,a)].
% 2.84/3.11 344 -perp(c1,c2,A,B) | para(c4,c3,A,B). [resolve(209,a,117,a)].
% 2.84/3.11 345 perp(c1,c2,c4,c3). [resolve(209,a,116,a)].
% 2.84/3.11 386 coll(c3,c3,c7). [resolve(256,a,215,a)].
% 2.84/3.11 451 coll(c3,c7,c3). [resolve(386,a,109,a)].
% 2.84/3.11 560 coll(c3,c3,c3). [resolve(451,a,256,a)].
% 2.84/3.11 584 para(c3,c1,c3,c1). [resolve(330,a,329,a)].
% 2.84/3.11 760 para(c4,c3,c4,c3). [resolve(345,a,344,a)].
% 2.84/3.11 823 coll(c3,c1,c1). [resolve(584,a,169,a)].
% 2.84/3.11 826 eqangle(c3,c1,A,B,c3,c1,A,B). [resolve(584,a,147,a)].
% 2.84/3.11 827 para(c3,c1,c1,c3). [resolve(584,a,112,a)].
% 2.84/3.11 828 coll(c1,c1,c3). [resolve(823,a,256,a)].
% 2.84/3.11 834 coll(c3,c3,c1). [resolve(828,a,256,a)].
% 2.84/3.11 836 -coll(c1,c1,A) | coll(c3,A,c1). [resolve(828,a,111,a)].
% 2.84/3.11 910 eqangle(c4,c3,A,B,c4,c3,A,B). [resolve(760,a,147,a)].
% 2.84/3.11 969 para(c1,c3,c3,c1). [resolve(827,a,113,a)].
% 2.84/3.11 1127 para(c1,c3,c1,c3). [resolve(969,a,112,a)].
% 2.84/3.11 1197 eqangle(c1,c3,A,B,c1,c3,A,B). [resolve(1127,a,147,a)].
% 2.84/3.11 2145 -coll(c3,c3,A) | cyclic(c1,A,c3,c3). [resolve(826,a,150,a)].
% 2.84/3.11 2146 eqangle(c3,c1,c3,c1,A,B,A,B). [resolve(826,a,128,a)].
% 2.84/3.11 2147 eqangle(A,B,c3,c1,A,B,c3,c1). [resolve(826,a,126,a)].
% 2.84/3.11 2389 eqangle(A,B,c4,c3,A,B,c4,c3). [resolve(910,a,126,a)].
% 2.84/3.11 7342 -cyclic(c3,c3,c1,c3) | -cyclic(c3,c3,c1,c1) | cong(c3,c3,c3,c3). [resolve(1197,a,262,c)].
% 2.84/3.11 8503 cyclic(c1,c1,c3,c3). [resolve(2145,a,834,a)].
% 2.84/3.11 8504 cyclic(c1,c3,c3,c3). [resolve(2145,a,560,a)].
% 2.84/3.11 8538 -cyclic(c1,c1,c3,A) | cyclic(c1,c3,A,c3). [resolve(8503,a,124,b)].
% 2.84/3.11 8540 cyclic(c1,c3,c1,c3). [resolve(8503,a,122,a)].
% 2.84/3.11 8551 cyclic(c3,c1,c3,c3). [resolve(8504,a,123,a)].
% 2.84/3.11 8640 cyclic(c1,c3,c3,c1). [resolve(8540,a,121,a)].
% 2.84/3.11 8655 cyclic(c3,c3,c1,c3). [resolve(8551,a,122,a)].
% 2.84/3.11 8656 -cyclic(c3,c3,c1,c1) | cong(c3,c3,c3,c3). [back_unit_del(7342),unit_del(a,8655)].
% 2.84/3.11 8906 cyclic(c3,c3,c1,c1). [resolve(8640,a,261,a)].
% 2.84/3.11 8914 cong(c3,c3,c3,c3). [back_unit_del(8656),unit_del(a,8906)].
% 2.84/3.11 9498 -cong(c3,A,c3,A) | perp(c3,c3,c3,A). [resolve(8914,a,159,a)].
% 2.84/3.11 15377 -coll(c3,A,c1) | cyclic(c1,c1,c3,A). [resolve(2146,a,150,a)].
% 2.84/3.11 15402 para(A,B,A,B). [resolve(2147,a,146,a)].
% 2.84/3.11 16775 coll(A,B,B). [resolve(15402,a,169,a)].
% 2.84/3.11 16901 coll(A,A,B). [resolve(16775,a,256,a)].
% 2.84/3.11 17062 coll(c3,A,c1). [back_unit_del(836),unit_del(a,16901)].
% 2.84/3.11 17194 cyclic(c1,c1,c3,A). [back_unit_del(15377),unit_del(a,17062)].
% 2.84/3.11 17369 cyclic(c1,c3,A,c3). [back_unit_del(8538),unit_del(a,17194)].
% 2.84/3.11 18032 cyclic(c1,c3,A,B). [resolve(17194,a,124,b),unit_del(a,17194)].
% 2.84/3.11 18052 cyclic(c3,A,B,c3). [resolve(17369,a,124,b),unit_del(a,18032)].
% 2.84/3.11 18053 cyclic(c3,A,c3,B). [resolve(17369,a,124,a),unit_del(a,18032)].
% 2.84/3.11 18705 cyclic(c3,A,B,C). [resolve(18032,a,124,b),unit_del(a,18032)].
% 2.84/3.11 18721 cyclic(A,B,C,c3). [resolve(18052,a,124,b),unit_del(a,18705)].
% 2.84/3.11 18722 cyclic(A,B,c3,C). [resolve(18052,a,124,a),unit_del(a,18705)].
% 2.84/3.11 18725 cyclic(A,c3,B,B). [resolve(18053,a,261,a)].
% 2.84/3.11 18727 cyclic(A,c3,B,C). [resolve(18053,a,124,b),unit_del(a,18722)].
% 2.84/3.11 18738 cong(A,c3,A,c3). [resolve(2389,a,151,d),unit_del(a,18727),unit_del(b,18721),unit_del(c,18725)].
% 2.84/3.11 19035 cong(A,c3,c3,A). [resolve(18738,a,130,a)].
% 2.84/3.11 19184 cong(c3,A,A,c3). [resolve(19035,a,131,a)].
% 2.84/3.11 19270 cong(c3,A,c3,A). [resolve(19184,a,130,a)].
% 2.84/3.11 19292 perp(c3,c3,c3,A). [back_unit_del(9498),unit_del(a,19270)].
% 2.84/3.11 19380 perp(c3,c3,A,B). [resolve(19270,a,159,b),unit_del(a,19270)].
% 2.84/3.11 19601 -perp(A,B,c3,c3) | para(A,B,c3,C). [resolve(19292,a,117,b)].
% 2.84/3.11 19757 perp(A,B,c3,c3). [resolve(19380,a,116,a)].
% 2.84/3.11 19759 para(A,B,c3,C). [back_unit_del(19601),unit_del(a,19757)].
% 2.84/3.11 19760 $F. [resolve(19759,a,217,a)].
% 2.84/3.11
% 2.84/3.11 % SZS output end Refutation
% 2.84/3.11 ============================== end of proof ==========================
% 2.84/3.11
% 2.84/3.11 ============================== STATISTICS ============================
% 2.84/3.11
% 2.84/3.11 Given=5056. Generated=71148. Kept=19643. proofs=1.
% 2.84/3.11 Usable=3796. Sos=7892. Demods=0. Limbo=2, Disabled=8105. Hints=0.
% 2.84/3.11 Megabytes=11.62.
% 2.84/3.11 User_CPU=1.95, System_CPU=0.05, Wall_clock=2.
% 2.84/3.11
% 2.84/3.11 ============================== end of statistics =====================
% 2.84/3.11
% 2.84/3.11 ============================== end of search =========================
% 2.84/3.11
% 2.84/3.11 THEOREM PROVED
% 2.84/3.11 % SZS status Theorem
% 2.84/3.11
% 2.84/3.11 Exiting with 1 proof.
% 2.84/3.11
% 2.84/3.11 Process 28495 exit (max_proofs) Fri Jun 17 23:30:40 2022
% 2.84/3.11 Prover9 interrupted
%------------------------------------------------------------------------------