TSTP Solution File: GEO127+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GEO127+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.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 05:54:13 EDT 2022
% Result : Theorem 0.93s 1.21s
% Output : Refutation 0.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO127+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n009.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 : Sat Jun 18 16:53:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.42/1.01 ============================== Prover9 ===============================
% 0.42/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.42/1.01 Process 24997 was started by sandbox on n009.cluster.edu,
% 0.42/1.01 Sat Jun 18 16:53:38 2022
% 0.42/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_24844_n009.cluster.edu".
% 0.42/1.01 ============================== end of head ===========================
% 0.42/1.01
% 0.42/1.01 ============================== INPUT =================================
% 0.42/1.01
% 0.42/1.01 % Reading from file /tmp/Prover9_24844_n009.cluster.edu
% 0.42/1.01
% 0.42/1.01 set(prolog_style_variables).
% 0.42/1.01 set(auto2).
% 0.42/1.01 % set(auto2) -> set(auto).
% 0.42/1.01 % set(auto) -> set(auto_inference).
% 0.42/1.01 % set(auto) -> set(auto_setup).
% 0.42/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.42/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/1.01 % set(auto) -> set(auto_limits).
% 0.42/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/1.01 % set(auto) -> set(auto_denials).
% 0.42/1.01 % set(auto) -> set(auto_process).
% 0.42/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.42/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.42/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.42/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.42/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.42/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.42/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.42/1.01 % set(auto2) -> assign(stats, some).
% 0.42/1.01 % set(auto2) -> clear(echo_input).
% 0.42/1.01 % set(auto2) -> set(quiet).
% 0.42/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.42/1.01 % set(auto2) -> clear(print_given).
% 0.42/1.01 assign(lrs_ticks,-1).
% 0.42/1.01 assign(sos_limit,10000).
% 0.42/1.01 assign(order,kbo).
% 0.42/1.01 set(lex_order_vars).
% 0.42/1.01 clear(print_given).
% 0.42/1.01
% 0.42/1.01 % formulas(sos). % not echoed (28 formulas)
% 0.42/1.01
% 0.42/1.01 ============================== end of input ==========================
% 0.42/1.01
% 0.42/1.01 % From the command line: assign(max_seconds, 300).
% 0.42/1.01
% 0.42/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/1.01
% 0.42/1.01 % Formulas that are not ordinary clauses:
% 0.42/1.01 1 (all C all C1 (part_of(C1,C) <-> (all P (incident_c(P,C1) -> incident_c(P,C))))) # label(part_of_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.01 2 (all C all C1 all C2 (C = sum(C1,C2) <-> (all Q (incident_c(Q,C) <-> incident_c(Q,C1) | incident_c(Q,C2))))) # label(sum_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.01 3 (all P all C (end_point(P,C) <-> incident_c(P,C) & (all C1 all C2 (part_of(C1,C) & part_of(C2,C) & incident_c(P,C1) & incident_c(P,C2) -> part_of(C1,C2) | part_of(C2,C1))))) # label(end_point_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.01 4 (all P all C (inner_point(P,C) <-> incident_c(P,C) & -end_point(P,C))) # label(inner_point_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.01 5 (all P all C all C1 (meet(P,C,C1) <-> incident_c(P,C) & incident_c(P,C1) & (all Q (incident_c(Q,C) & incident_c(Q,C1) -> end_point(Q,C) & end_point(Q,C1))))) # label(meet_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.01 6 (all C (closed(C) <-> -(exists P end_point(P,C)))) # label(closed_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.01 7 (all C (open(C) <-> (exists P end_point(P,C)))) # label(open_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.01 8 (all C all C1 (part_of(C1,C) & C1 != C -> open(C1))) # label(c1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.01 9 (all C all C1 all C2 all C3 (part_of(C1,C) & part_of(C2,C) & part_of(C3,C) & (exists P (end_point(P,C1) & end_point(P,C2) & end_point(P,C3))) -> part_of(C2,C3) | part_of(C3,C2) | part_of(C1,C2) | part_of(C2,C1) | part_of(C1,C3) | part_of(C3,C1))) # label(c2) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.01 10 (all C exists P inner_point(P,C)) # label(c3) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.01 11 (all C all P (inner_point(P,C) -> (exists C1 exists C2 (meet(P,C1,C2) & C = sum(C1,C2))))) # label(c4) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.01 12 (all C all P all Q all R (end_point(P,C) & end_point(Q,C) & end_point(R,C) -> P = Q | P = R | Q = R)) # label(c5) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 13 (all C all P (end_point(P,C) -> (exists Q (end_point(Q,C) & P != Q)))) # label(c6) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 14 (all C all C1 all C2 all P (closed(C) & meet(P,C1,C2) & C = sum(C1,C2) -> (all Q (end_point(Q,C1) -> meet(Q,C1,C2))))) # label(c7) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 15 (all C1 all C2 ((exists P meet(P,C1,C2)) -> (exists C C = sum(C1,C2)))) # label(c8) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 16 (all C all C1 ((all P (incident_c(P,C) <-> incident_c(P,C1))) -> C = C1)) # label(c9) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 17 (all C all P all Q all R (between_c(C,P,Q,R) <-> P != R & (exists Cpp (part_of(Cpp,C) & end_point(P,Cpp) & end_point(R,Cpp) & inner_point(Q,Cpp))))) # label(between_c_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 18 (all O all P all Q all R (between_o(O,P,Q,R) <-> ordered_by(O,P,Q) & ordered_by(O,Q,R) | ordered_by(O,R,Q) & ordered_by(O,Q,P))) # label(between_o_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 19 (all P all O (start_point(P,O) <-> incident_o(P,O) & (all Q (P != Q & incident_o(Q,O) -> ordered_by(O,P,Q))))) # label(start_point_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 20 (all P all O (finish_point(P,O) <-> incident_o(P,O) & (all Q (P != Q & incident_o(Q,O) -> ordered_by(O,Q,P))))) # label(finish_point_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 21 (all O all P all Q (ordered_by(O,P,Q) -> incident_o(P,O) & incident_o(Q,O))) # label(o1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 22 (all O exists C (open(C) & (all P (incident_o(P,O) <-> incident_c(P,C))))) # label(o2) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 23 (all P all Q all R all O (between_o(O,P,Q,R) <-> (exists C ((all P (incident_o(P,O) <-> incident_c(P,C))) & between_c(C,P,Q,R))))) # label(o3) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 24 (all O exists P start_point(P,O)) # label(o4) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 25 (all P all Q all C (open(C) & P != Q & incident_c(P,C) & incident_c(Q,C) -> (exists O ((all R (incident_o(R,O) <-> incident_c(R,C))) & ordered_by(O,P,Q))))) # label(o5) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 26 (all O1 all O2 ((all P all Q (ordered_by(O1,P,Q) <-> ordered_by(O2,P,Q))) -> O1 = O2)) # label(o6) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 27 (all C all O (C = underlying_curve(O) <-> (all P (incident_o(P,O) <-> incident_c(P,C))))) # label(underlying_curve_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.02 28 -(all O all P (incident_o(P,O) <-> (exists Q (ordered_by(O,P,Q) | ordered_by(O,Q,P))))) # label(theorem_4_12) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.42/1.02
% 0.42/1.02 ============================== end of process non-clausal formulas ===
% 0.42/1.02
% 0.42/1.02 ============================== PROCESS INITIAL CLAUSES ===============
% 0.42/1.02
% 0.42/1.02 ============================== PREDICATE ELIMINATION =================
% 0.42/1.02 29 -open(A) | end_point(f7(A),A) # label(open_defn) # label(axiom). [clausify(7)].
% 0.42/1.02 30 open(f17(A)) # label(o2) # label(axiom). [clausify(22)].
% 0.42/1.02 31 open(A) | -end_point(B,A) # label(open_defn) # label(axiom). [clausify(7)].
% 0.42/1.02 Derived: end_point(f7(f17(A)),f17(A)). [resolve(29,a,30,a)].
% 0.42/1.02 Derived: end_point(f7(A),A) | -end_point(B,A). [resolve(29,a,31,a)].
% 0.42/1.02 32 -part_of(A,B) | A = B | open(A) # label(c1) # label(axiom). [clausify(8)].
% 0.42/1.02 Derived: -part_of(A,B) | A = B | end_point(f7(A),A). [resolve(32,c,29,a)].
% 0.42/1.02 33 -open(A) | B = C | -incident_c(C,A) | -incident_c(B,A) | ordered_by(f21(C,B,A),C,B) # label(o5) # label(axiom). [clausify(25)].
% 0.42/1.02 Derived: A = B | -incident_c(B,f17(C)) | -incident_c(A,f17(C)) | ordered_by(f21(B,A,f17(C)),B,A). [resolve(33,a,30,a)].
% 0.42/1.02 Derived: A = B | -incident_c(B,C) | -incident_c(A,C) | ordered_by(f21(B,A,C),B,A) | -end_point(D,C). [resolve(33,a,31,a)].
% 0.42/1.02 Derived: A = B | -incident_c(B,C) | -incident_c(A,C) | ordered_by(f21(B,A,C),B,A) | -part_of(C,D) | C = D. [resolve(33,a,32,c)].
% 0.42/1.02 34 -open(A) | B = C | -incident_c(C,A) | -incident_c(B,A) | -incident_o(D,f21(C,B,A)) | incident_c(D,A) # label(o5) # label(axiom). [clausify(25)].
% 0.42/1.02 Derived: A = B | -incident_c(B,f17(C)) | -incident_c(A,f17(C)) | -incident_o(D,f21(B,A,f17(C))) | incident_c(D,f17(C)). [resolve(34,a,30,a)].
% 0.42/1.02 Derived: A = B | -incident_c(B,C) | -incident_c(A,C) | -incident_o(D,f21(B,A,C)) | incident_c(D,C) | -end_point(E,C). [resolve(34,a,31,a)].
% 0.42/1.02 Derived: A = B | -incident_c(B,C) | -incident_c(A,C) | -incident_o(D,f21(B,A,C)) | incident_c(D,C) | -part_of(C,E) | C = E. [resolve(34,a,32,c)].
% 0.42/1.02 35 -open(A) | B = C | -incident_c(C,A) | -incident_c(B,A) | incident_o(D,f21(C,B,A)) | -incident_c(D,A) # label(o5) # label(axiom). [clausify(25)].
% 0.42/1.02 Derived: A = B | -incident_c(B,f17(C)) | -incident_c(A,f17(C)) | incident_o(D,f21(B,A,f17(C))) | -incident_c(D,f17(C)). [resolve(35,a,30,a)].
% 0.42/1.02 Derived: A = B | -incident_c(B,C) | -incident_c(A,C) | incident_o(D,f21(B,A,C)) | -incident_c(D,C) | -end_point(E,C). [resolve(35,a,31,a)].
% 0.42/1.02 Derived: A = B | -incident_c(B,C) | -incident_c(A,C) | incident_o(D,f21(B,A,C)) | -incident_c(D,C) | -part_of(C,E) | C = E. [resolve(35,a,32,c)].
% 0.42/1.02 36 -inner_point(A,B) | -end_point(A,B) # label(inner_point_defn) # label(axiom). [clausify(4)].
% 0.42/1.02 37 inner_point(f8(A),A) # label(c3) # label(axiom). [clausify(10)].
% 0.42/1.02 Derived: -end_point(f8(A),A). [resolve(36,a,37,a)].
% 0.42/1.02 38 -inner_point(A,B) | incident_c(A,B) # label(inner_point_defn) # label(axiom). [clausify(4)].
% 0.42/1.02 Derived: incident_c(f8(A),A). [resolve(38,a,37,a)].
% 0.42/1.02 39 inner_point(A,B) | -incident_c(A,B) | end_point(A,B) # label(inner_point_defn) # label(axiom). [clausify(4)].
% 0.42/1.02 40 -inner_point(A,B) | meet(A,f9(B,A),f10(B,A)) # label(c4) # label(axiom). [clausify(11)].
% 0.42/1.02 Derived: meet(f8(A),f9(A,f8(A)),f10(A,f8(A))). [resolve(40,a,37,a)].
% 0.42/1.02 Derived: meet(A,f9(B,A),f10(B,A)) | -incident_c(A,B) | end_point(A,B). [resolve(40,a,39,a)].
% 0.42/1.02 41 -inner_point(A,B) | sum(f9(B,A),f10(B,A)) = B # label(c4) # label(axiom). [clausify(11)].
% 0.42/1.02 Derived: sum(f9(A,f8(A)),f10(A,f8(A))) = A. [resolve(41,a,37,a)].
% 0.42/1.02 Derived: sum(f9(A,B),f10(A,B)) = A | -incident_c(B,A) | end_point(B,A). [resolve(41,a,39,a)].
% 0.42/1.02 42 -between_c(A,B,C,D) | inner_point(C,f14(A,B,C,D)) # label(between_c_defn) # label(axiom). [clausify(17)].
% 0.42/1.02 Derived: -between_c(A,B,C,D) | -end_point(C,f14(A,B,C,D)). [resolve(42,b,36,a)].
% 0.42/1.02 Derived: -between_c(A,B,C,D) | incident_c(C,f14(A,B,C,D)). [resolve(42,b,38,a)].
% 0.42/1.02 Derived: -between_c(A,B,C,D) | meet(C,f9(f14(A,B,C,D),C),f10(f14(A,B,C,D),C)). [resolve(42,b,40,a)].
% 0.42/1.02 Derived: -between_c(A,B,C,D) | sum(f9(f14(A,B,C,D),C),f10(f14(A,B,C,D),C)) = f14(A,B,C,D). [resolve(42,b,41,a)].
% 0.42/1.02 43 between_c(A,B,C,D) | D = B | -part_of(E,A) | -end_point(B,E) | -end_point(D,E) | -inner_point(C,E) # label(between_c_defn) # label(axiom). [clausify(17)].
% 0.42/1.02 Derived: between_c(A,B,f8(C),D) | D = B | -part_of(C,A) | -end_point(B,C) | -end_point(D,C). [resolve(43,f,37,a)].
% 0.42/1.02 Derived: between_c(A,B,C,D) | D = B | -part_of(E,A) | -end_point(B,E) | -end_point(D,E) | -incident_c(C,E) | end_point(C,E). [resolve(43,f,39,a)].
% 0.42/1.02 Derived: between_c(A,B,C,D) | D = B | -part_of(f14(E,F,C,V6),A) | -end_point(B,f14(E,F,C,V6)) | -end_point(D,f14(E,F,C,V6)) | -between_c(E,F,C,V6). [resolve(43,f,42,b)].
% 0.42/1.02 44 -start_point(A,B) | incident_o(A,B) # label(start_point_defn) # label(axiom). [clausify(19)].
% 0.42/1.02 45 start_point(f20(A),A) # label(o4) # label(axiom). [clausify(24)].
% 0.42/1.02 Derived: incident_o(f20(A),A). [resolve(44,a,45,a)].
% 0.42/1.02 46 start_point(A,B) | -incident_o(A,B) | f15(A,B) != A # label(start_point_defn) # label(axiom). [clausify(19)].
% 0.42/1.02 47 start_point(A,B) | -incident_o(A,B) | incident_o(f15(A,B),B) # label(start_point_defn) # label(axiom). [clausify(19)].
% 0.42/1.02 48 start_point(A,B) | -incident_o(A,B) | -ordered_by(B,A,f15(A,B)) # label(start_point_defn) # label(axiom). [clausify(19)].
% 0.42/1.02 49 -start_point(A,B) | C = A | -incident_o(C,B) | ordered_by(B,A,C) # label(start_point_defn) # label(axiom). [clausify(19)].
% 0.42/1.02 Derived: A = f20(B) | -incident_o(A,B) | ordered_by(B,f20(B),A). [resolve(49,a,45,a)].
% 0.42/1.02 Derived: A = B | -incident_o(A,C) | ordered_by(C,B,A) | -incident_o(B,C) | f15(B,C) != B. [resolve(49,a,46,a)].
% 0.42/1.02 Derived: A = B | -incident_o(A,C) | ordered_by(C,B,A) | -incident_o(B,C) | incident_o(f15(B,C),C). [resolve(49,a,47,a)].
% 0.42/1.02 Derived: A = B | -incident_o(A,C) | ordered_by(C,B,A) | -incident_o(B,C) | -ordered_by(C,B,f15(B,C)). [resolve(49,a,48,a)].
% 0.42/1.02 50 -closed(A) | -end_point(B,A) # label(closed_defn) # label(axiom). [clausify(6)].
% 0.42/1.02 51 closed(A) | end_point(f6(A),A) # label(closed_defn) # label(axiom). [clausify(6)].
% 0.42/1.02 Derived: -end_point(A,B) | end_point(f6(B),B). [resolve(50,a,51,a)].
% 0.42/1.02 52 -closed(A) | -meet(B,C,D) | sum(C,D) != A | -end_point(E,C) | meet(E,C,D) # label(c7) # label(axiom). [clausify(14)].
% 0.42/1.02 Derived: -meet(A,B,C) | sum(B,C) != D | -end_point(E,B) | meet(E,B,C) | end_point(f6(D),D). [resolve(52,a,51,a)].
% 0.42/1.02 53 finish_point(A,B) | -incident_o(A,B) | f16(A,B) != A # label(finish_point_defn) # label(axiom). [clausify(20)].
% 0.42/1.02 54 -finish_point(A,B) | incident_o(A,B) # label(finish_point_defn) # label(axiom). [clausify(20)].
% 0.42/1.02 55 finish_point(A,B) | -incident_o(A,B) | incident_o(f16(A,B),B) # label(finish_point_defn) # label(axiom). [clausify(20)].
% 0.42/1.02 56 finish_point(A,B) | -incident_o(A,B) | -ordered_by(B,f16(A,B),A) # label(finish_point_defn) # label(axiom). [clausify(20)].
% 0.42/1.02 57 -finish_point(A,B) | C = A | -incident_o(C,B) | ordered_by(B,C,A) # label(finish_point_defn) # label(axiom). [clausify(20)].
% 0.42/1.02 Derived: A = B | -incident_o(A,C) | ordered_by(C,A,B) | -incident_o(B,C) | f16(B,C) != B. [resolve(57,a,53,a)].
% 0.42/1.02 Derived: A = B | -incident_o(A,C) | ordered_by(C,A,B) | -incident_o(B,C) | incident_o(f16(B,C),C). [resolve(57,a,55,a)].
% 0.42/1.02 Derived: A = B | -incident_o(A,C) | ordered_by(C,A,B) | -incident_o(B,C) | -ordered_by(C,f16(B,C),B). [resolve(57,a,56,a)].
% 0.42/1.02 58 between_o(A,B,C,D) | -ordered_by(A,B,C) | -ordered_by(A,C,D) # label(between_o_defn) # label(axiom). [clausify(18)].
% 0.42/1.02 59 -between_o(A,B,C,D) | ordered_by(A,B,C) | ordered_by(A,D,C) # label(between_o_defn) # label(axiom). [clausify(18)].
% 0.42/1.02 60 -between_o(A,B,C,D) | ordered_by(A,B,C) | ordered_by(A,C,B) # label(between_o_defn) # label(axiom). [clausify(18)].
% 0.42/1.02 61 -between_o(A,B,C,D) | ordered_by(A,C,D) | ordered_by(A,D,C) # label(between_o_defn) # label(axiom). [clausify(18)].
% 0.42/1.02 62 -between_o(A,B,C,D) | ordered_by(A,C,D) | ordered_by(A,C,B) # label(between_o_defn) # label(axiom). [clausify(18)].
% 0.42/1.02 63 between_o(A,B,C,D) | -ordered_by(A,D,C) | -ordered_by(A,C,B) # label(between_o_defn) # label(axiom). [clausify(18)].
% 0.42/1.02 64 -between_o(A,B,C,D) | between_c(f18(B,C,D,A),B,C,D) # label(o3) # label(axiom). [clausify(23)].
% 0.42/1.02 Derived: between_c(f18(A,B,C,D),A,B,C) | -ordered_by(D,A,B) | -ordered_by(D,B,C). [resolve(64,a,58,a)].
% 0.42/1.02 Derived: between_c(f18(A,B,C,D),A,B,C) | -ordered_by(D,C,B) | -ordered_by(D,B,A). [resolve(64,a,63,a)].
% 0.42/1.02 65 -between_o(A,B,C,D) | -incident_o(E,A) | incident_c(E,f18(B,C,D,A)) # label(o3) # label(axiom). [clausify(23)].
% 0.42/1.02 Derived: -incident_o(A,B) | incident_c(A,f18(C,D,E,B)) | -ordered_by(B,C,D) | -ordered_by(B,D,E). [resolve(65,a,58,a)].
% 0.42/1.02 Derived: -incident_o(A,B) | incident_c(A,f18(C,D,E,B)) | -ordered_by(B,E,D) | -ordered_by(B,D,C). [resolve(65,a,63,a)].
% 0.42/1.02 66 -between_o(A,B,C,D) | incident_o(E,A) | -incident_c(E,f18(B,C,D,A)) # label(o3) # label(axiom). [clausify(23)].
% 0.42/1.02 Derived: incident_o(A,B) | -incident_c(A,f18(C,D,E,B)) | -ordered_by(B,C,D) | -ordered_by(B,D,E). [resolve(66,a,58,a)].
% 0.42/1.02 Derived: incident_o(A,B) | -incident_c(A,f18(C,D,E,B)) | -ordered_by(B,E,D) | -ordered_by(B,D,C). [resolve(66,a,63,a)].
% 0.42/1.02 67 between_o(A,B,C,D) | incident_o(f19(B,C,D,A,E),A) | incident_c(f19(B,C,D,A,E),E) | -between_c(E,B,C,D) # label(o3) # label(axiom). [clausify(23)].
% 0.42/1.02 Derived: incident_o(f19(A,B,C,D,E),D) | incident_c(f19(A,B,C,D,E),E) | -between_c(E,A,B,C) | ordered_by(D,A,B) | ordered_by(D,C,B). [resolve(67,a,59,a)].
% 0.42/1.02 Derived: incident_o(f19(A,B,C,D,E),D) | incident_c(f19(A,B,C,D,E),E) | -between_c(E,A,B,C) | ordered_by(D,A,B) | ordered_by(D,B,A). [resolve(67,a,60,a)].
% 0.42/1.02 Derived: incident_o(f19(A,B,C,D,E),D) | incident_c(f19(A,B,C,D,E),E) | -between_c(E,A,B,C) | ordered_by(D,B,C) | ordered_by(D,C,B). [resolve(67,a,61,a)].
% 0.42/1.02 Derived: incident_o(f19(A,B,C,D,E),D) | incident_c(f19(A,B,C,D,E),E) | -between_c(E,A,B,C) | ordered_by(D,B,C) | ordered_by(D,B,A). [resolve(67,a,62,a)].
% 0.93/1.21 Derived: incident_o(f19(A,B,C,D,E),D) | incident_c(f19(A,B,C,D,E),E) | -between_c(E,A,B,C) | between_c(f18(A,B,C,D),A,B,C). [resolve(67,a,64,a)].
% 0.93/1.21 Derived: incident_o(f19(A,B,C,D,E),D) | incident_c(f19(A,B,C,D,E),E) | -between_c(E,A,B,C) | -incident_o(F,D) | incident_c(F,f18(A,B,C,D)). [resolve(67,a,65,a)].
% 0.93/1.21 Derived: incident_o(f19(A,B,C,D,E),D) | incident_c(f19(A,B,C,D,E),E) | -between_c(E,A,B,C) | incident_o(F,D) | -incident_c(F,f18(A,B,C,D)). [resolve(67,a,66,a)].
% 0.93/1.21 68 between_o(A,B,C,D) | -incident_o(f19(B,C,D,A,E),A) | -incident_c(f19(B,C,D,A,E),E) | -between_c(E,B,C,D) # label(o3) # label(axiom). [clausify(23)].
% 0.93/1.21 Derived: -incident_o(f19(A,B,C,D,E),D) | -incident_c(f19(A,B,C,D,E),E) | -between_c(E,A,B,C) | ordered_by(D,A,B) | ordered_by(D,C,B). [resolve(68,a,59,a)].
% 0.93/1.21 Derived: -incident_o(f19(A,B,C,D,E),D) | -incident_c(f19(A,B,C,D,E),E) | -between_c(E,A,B,C) | ordered_by(D,A,B) | ordered_by(D,B,A). [resolve(68,a,60,a)].
% 0.93/1.21 Derived: -incident_o(f19(A,B,C,D,E),D) | -incident_c(f19(A,B,C,D,E),E) | -between_c(E,A,B,C) | ordered_by(D,B,C) | ordered_by(D,C,B). [resolve(68,a,61,a)].
% 0.93/1.21 Derived: -incident_o(f19(A,B,C,D,E),D) | -incident_c(f19(A,B,C,D,E),E) | -between_c(E,A,B,C) | ordered_by(D,B,C) | ordered_by(D,B,A). [resolve(68,a,62,a)].
% 0.93/1.21 Derived: -incident_o(f19(A,B,C,D,E),D) | -incident_c(f19(A,B,C,D,E),E) | -between_c(E,A,B,C) | between_c(f18(A,B,C,D),A,B,C). [resolve(68,a,64,a)].
% 0.93/1.21 Derived: -incident_o(f19(A,B,C,D,E),D) | -incident_c(f19(A,B,C,D,E),E) | -between_c(E,A,B,C) | -incident_o(F,D) | incident_c(F,f18(A,B,C,D)). [resolve(68,a,65,a)].
% 0.93/1.21 Derived: -incident_o(f19(A,B,C,D,E),D) | -incident_c(f19(A,B,C,D,E),E) | -between_c(E,A,B,C) | incident_o(F,D) | -incident_c(F,f18(A,B,C,D)). [resolve(68,a,66,a)].
% 0.93/1.21
% 0.93/1.21 ============================== end predicate elimination =============
% 0.93/1.21
% 0.93/1.21 Auto_denials: (non-Horn, no changes).
% 0.93/1.21
% 0.93/1.21 Term ordering decisions:
% 0.93/1.21 Function symbol KB weights: c10=1. c11=1. c12=1. sum=1. f1=1. f3=1. f4=1. f9=1. f10=1. f11=1. f12=1. f13=1. f15=1. f16=1. f22=1. f23=1. f24=1. underlying_curve=1. f6=1. f7=1. f8=1. f17=1. f20=1. f2=1. f5=1. f21=1. f14=1. f18=1. f19=1.
% 0.93/1.21
% 0.93/1.21 ============================== end of process initial clauses ========
% 0.93/1.21
% 0.93/1.21 ============================== CLAUSES FOR SEARCH ====================
% 0.93/1.21
% 0.93/1.21 ============================== end of clauses for search =============
% 0.93/1.21
% 0.93/1.21 ============================== SEARCH ================================
% 0.93/1.21
% 0.93/1.21 % Starting search at 0.02 seconds.
% 0.93/1.21
% 0.93/1.21 ============================== PROOF =================================
% 0.93/1.21 % SZS status Theorem
% 0.93/1.21 % SZS output start Refutation
% 0.93/1.21
% 0.93/1.21 % Proof 1 at 0.20 (+ 0.01) seconds.
% 0.93/1.21 % Length of proof is 68.
% 0.93/1.21 % Level of proof is 13.
% 0.93/1.21 % Maximum clause weight is 18.000.
% 0.93/1.21 % Given clauses 337.
% 0.93/1.21
% 0.93/1.21 3 (all P all C (end_point(P,C) <-> incident_c(P,C) & (all C1 all C2 (part_of(C1,C) & part_of(C2,C) & incident_c(P,C1) & incident_c(P,C2) -> part_of(C1,C2) | part_of(C2,C1))))) # label(end_point_defn) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 4 (all P all C (inner_point(P,C) <-> incident_c(P,C) & -end_point(P,C))) # label(inner_point_defn) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 6 (all C (closed(C) <-> -(exists P end_point(P,C)))) # label(closed_defn) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 7 (all C (open(C) <-> (exists P end_point(P,C)))) # label(open_defn) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 10 (all C exists P inner_point(P,C)) # label(c3) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 13 (all C all P (end_point(P,C) -> (exists Q (end_point(Q,C) & P != Q)))) # label(c6) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 19 (all P all O (start_point(P,O) <-> incident_o(P,O) & (all Q (P != Q & incident_o(Q,O) -> ordered_by(O,P,Q))))) # label(start_point_defn) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 20 (all P all O (finish_point(P,O) <-> incident_o(P,O) & (all Q (P != Q & incident_o(Q,O) -> ordered_by(O,Q,P))))) # label(finish_point_defn) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 21 (all O all P all Q (ordered_by(O,P,Q) -> incident_o(P,O) & incident_o(Q,O))) # label(o1) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 22 (all O exists C (open(C) & (all P (incident_o(P,O) <-> incident_c(P,C))))) # label(o2) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 24 (all O exists P start_point(P,O)) # label(o4) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 28 -(all O all P (incident_o(P,O) <-> (exists Q (ordered_by(O,P,Q) | ordered_by(O,Q,P))))) # label(theorem_4_12) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.93/1.21 29 -open(A) | end_point(f7(A),A) # label(open_defn) # label(axiom). [clausify(7)].
% 0.93/1.21 30 open(f17(A)) # label(o2) # label(axiom). [clausify(22)].
% 0.93/1.21 36 -inner_point(A,B) | -end_point(A,B) # label(inner_point_defn) # label(axiom). [clausify(4)].
% 0.93/1.21 37 inner_point(f8(A),A) # label(c3) # label(axiom). [clausify(10)].
% 0.93/1.21 38 -inner_point(A,B) | incident_c(A,B) # label(inner_point_defn) # label(axiom). [clausify(4)].
% 0.93/1.21 45 start_point(f20(A),A) # label(o4) # label(axiom). [clausify(24)].
% 0.93/1.21 49 -start_point(A,B) | C = A | -incident_o(C,B) | ordered_by(B,A,C) # label(start_point_defn) # label(axiom). [clausify(19)].
% 0.93/1.21 50 -closed(A) | -end_point(B,A) # label(closed_defn) # label(axiom). [clausify(6)].
% 0.93/1.21 51 closed(A) | end_point(f6(A),A) # label(closed_defn) # label(axiom). [clausify(6)].
% 0.93/1.21 53 finish_point(A,B) | -incident_o(A,B) | f16(A,B) != A # label(finish_point_defn) # label(axiom). [clausify(20)].
% 0.93/1.21 55 finish_point(A,B) | -incident_o(A,B) | incident_o(f16(A,B),B) # label(finish_point_defn) # label(axiom). [clausify(20)].
% 0.93/1.21 57 -finish_point(A,B) | C = A | -incident_o(C,B) | ordered_by(B,C,A) # label(finish_point_defn) # label(axiom). [clausify(20)].
% 0.93/1.21 70 incident_o(c11,c10) | ordered_by(c10,c11,c12) | ordered_by(c10,c12,c11) # label(theorem_4_12) # label(negated_conjecture). [clausify(28)].
% 0.93/1.21 75 -incident_o(c11,c10) | -ordered_by(c10,c11,A) # label(theorem_4_12) # label(negated_conjecture). [clausify(28)].
% 0.93/1.21 76 -incident_o(c11,c10) | -ordered_by(c10,A,c11) # label(theorem_4_12) # label(negated_conjecture). [clausify(28)].
% 0.93/1.21 77 -end_point(A,B) | f11(B,A) != A # label(c6) # label(axiom). [clausify(13)].
% 0.93/1.21 79 -end_point(A,B) | incident_c(A,B) # label(end_point_defn) # label(axiom). [clausify(3)].
% 0.93/1.21 82 -ordered_by(A,B,C) | incident_o(B,A) # label(o1) # label(axiom). [clausify(21)].
% 0.93/1.21 83 -ordered_by(A,B,C) | incident_o(C,A) # label(o1) # label(axiom). [clausify(21)].
% 0.93/1.21 85 incident_o(A,B) | -incident_c(A,f17(B)) # label(o2) # label(axiom). [clausify(22)].
% 0.93/1.21 87 -end_point(A,B) | end_point(f11(B,A),B) # label(c6) # label(axiom). [clausify(13)].
% 0.93/1.21 118 end_point(f7(f17(A)),f17(A)). [resolve(29,a,30,a)].
% 0.93/1.21 130 -end_point(f8(A),A). [resolve(36,a,37,a)].
% 0.93/1.21 131 incident_c(f8(A),A). [resolve(38,a,37,a)].
% 0.93/1.21 144 A = f20(B) | -incident_o(A,B) | ordered_by(B,f20(B),A). [resolve(49,a,45,a)].
% 0.93/1.21 145 f20(A) = B | -incident_o(B,A) | ordered_by(A,f20(A),B). [copy(144),flip(a)].
% 0.93/1.21 149 -end_point(A,B) | end_point(f6(B),B). [resolve(50,a,51,a)].
% 0.93/1.21 151 A = B | -incident_o(A,C) | ordered_by(C,A,B) | -incident_o(B,C) | f16(B,C) != B. [resolve(57,a,53,a)].
% 0.93/1.21 152 A = B | -incident_o(A,C) | ordered_by(C,A,B) | -incident_o(B,C) | incident_o(f16(B,C),C). [resolve(57,a,55,a)].
% 0.93/1.21 216 incident_o(c11,c10) | ordered_by(c10,c11,c12). [resolve(83,a,70,c),merge(b)].
% 0.93/1.21 496 incident_o(f8(f17(A)),A). [resolve(131,a,85,b)].
% 0.93/1.21 533 end_point(f6(f17(A)),f17(A)). [resolve(149,a,118,a)].
% 0.93/1.21 819 end_point(f11(f17(A),f6(f17(A))),f17(A)). [resolve(533,a,87,a)].
% 0.93/1.21 820 incident_c(f6(f17(A)),f17(A)). [resolve(533,a,79,a)].
% 0.93/1.21 821 f11(f17(A),f6(f17(A))) != f6(f17(A)). [resolve(533,a,77,a)].
% 0.93/1.21 841 incident_o(f6(f17(A)),A). [resolve(820,a,85,b)].
% 0.93/1.21 873 incident_o(c11,c10). [resolve(216,b,82,a),merge(b)].
% 0.93/1.21 874 -ordered_by(c10,A,c11). [back_unit_del(76),unit_del(a,873)].
% 0.93/1.21 875 -ordered_by(c10,c11,A). [back_unit_del(75),unit_del(a,873)].
% 0.93/1.21 876 c11 = A | -incident_o(A,c10) | incident_o(f16(c11,c10),c10). [resolve(873,a,152,d),flip(a),unit_del(c,874)].
% 0.93/1.21 878 c11 = A | -incident_o(A,c10) | f16(c11,c10) != c11. [resolve(873,a,151,d),flip(a),unit_del(c,874)].
% 0.93/1.21 884 f20(c10) = c11. [resolve(873,a,145,b),unit_del(b,874)].
% 0.93/1.21 1541 incident_c(f11(f17(A),f6(f17(A))),f17(A)). [resolve(819,a,79,a)].
% 0.93/1.21 1779 incident_o(f11(f17(A),f6(f17(A))),A). [resolve(1541,a,85,b)].
% 0.93/1.21 2491 f6(f17(c10)) = c11 | incident_o(f16(c11,c10),c10). [resolve(876,b,841,a),flip(a)].
% 0.93/1.21 2493 f8(f17(c10)) = c11 | incident_o(f16(c11,c10),c10). [resolve(876,b,496,a),flip(a)].
% 0.93/1.21 2522 f6(f17(c10)) = c11 | f16(c11,c10) = c11. [resolve(2491,b,145,b),rewrite([884(7),884(13)]),flip(b),unit_del(c,875)].
% 0.93/1.21 2544 f8(f17(c10)) = c11 | f16(c11,c10) = c11. [resolve(2493,b,145,b),rewrite([884(7),884(13)]),flip(b),unit_del(c,875)].
% 0.93/1.21 2601 f16(c11,c10) = c11 | end_point(c11,f17(c10)). [para(2522(a,1),533(a,1))].
% 0.93/1.21 2650 f16(c11,c10) = c11 | -end_point(c11,f17(c10)). [para(2544(a,1),130(a,1))].
% 0.93/1.21 2682 f16(c11,c10) = c11. [resolve(2650,b,2601,b),merge(b)].
% 0.93/1.21 2687 c11 = A | -incident_o(A,c10). [back_rewrite(878),rewrite([2682(7)]),xx(c)].
% 0.93/1.21 2690 f11(f17(c10),f6(f17(c10))) = c11. [resolve(2687,b,1779,a),flip(a)].
% 0.93/1.21 2697 f6(f17(c10)) = c11. [resolve(2687,b,841,a),flip(a)].
% 0.93/1.21 2708 f11(f17(c10),c11) = c11. [back_rewrite(2690),rewrite([2697(5)])].
% 0.93/1.21 2752 $F. [para(2697(a,1),821(a,1,2)),rewrite([2708(4),2697(4)]),xx(a)].
% 0.93/1.21
% 0.93/1.21 % SZS output end Refutation
% 0.93/1.21 ============================== end of proof ==========================
% 0.93/1.21
% 0.93/1.21 ============================== STATISTICS ============================
% 0.93/1.21
% 0.93/1.21 Given=337. Generated=4434. Kept=2681. proofs=1.
% 0.93/1.21 Usable=296. Sos=1753. Demods=18. Limbo=1, Disabled=774. Hints=0.
% 0.93/1.21 Megabytes=3.46.
% 0.93/1.21 User_CPU=0.20, System_CPU=0.01, Wall_clock=0.
% 0.93/1.21
% 0.93/1.21 ============================== end of statistics =====================
% 0.93/1.21
% 0.93/1.21 ============================== end of search =========================
% 0.93/1.21
% 0.93/1.21 THEOREM PROVED
% 0.93/1.21 % SZS status Theorem
% 0.93/1.21
% 0.93/1.21 Exiting with 1 proof.
% 0.93/1.21
% 0.93/1.21 Process 24997 exit (max_proofs) Sat Jun 18 16:53:38 2022
% 0.93/1.21 Prover9 interrupted
%------------------------------------------------------------------------------