TSTP Solution File: GEO111+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GEO111+1 : TPTP v8.1.0. Released v2.4.0.
% 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 05:54:04 EDT 2022
% Result : Theorem 0.99s 1.26s
% Output : Refutation 0.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GEO111+1 : TPTP v8.1.0. Released v2.4.0.
% 0.08/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.36 % Computer : n011.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sat Jun 18 18:09:23 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.49/1.09 ============================== Prover9 ===============================
% 0.49/1.09 Prover9 (32) version 2009-11A, November 2009.
% 0.49/1.09 Process 21741 was started by sandbox2 on n011.cluster.edu,
% 0.49/1.09 Sat Jun 18 18:09:24 2022
% 0.49/1.09 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_21587_n011.cluster.edu".
% 0.49/1.09 ============================== end of head ===========================
% 0.49/1.09
% 0.49/1.09 ============================== INPUT =================================
% 0.49/1.09
% 0.49/1.09 % Reading from file /tmp/Prover9_21587_n011.cluster.edu
% 0.49/1.09
% 0.49/1.09 set(prolog_style_variables).
% 0.49/1.09 set(auto2).
% 0.49/1.09 % set(auto2) -> set(auto).
% 0.49/1.09 % set(auto) -> set(auto_inference).
% 0.49/1.09 % set(auto) -> set(auto_setup).
% 0.49/1.09 % set(auto_setup) -> set(predicate_elim).
% 0.49/1.09 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.49/1.09 % set(auto) -> set(auto_limits).
% 0.49/1.09 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.49/1.09 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.49/1.09 % set(auto) -> set(auto_denials).
% 0.49/1.09 % set(auto) -> set(auto_process).
% 0.49/1.09 % set(auto2) -> assign(new_constants, 1).
% 0.49/1.09 % set(auto2) -> assign(fold_denial_max, 3).
% 0.49/1.09 % set(auto2) -> assign(max_weight, "200.000").
% 0.49/1.09 % set(auto2) -> assign(max_hours, 1).
% 0.49/1.09 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.49/1.09 % set(auto2) -> assign(max_seconds, 0).
% 0.49/1.09 % set(auto2) -> assign(max_minutes, 5).
% 0.49/1.09 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.49/1.09 % set(auto2) -> set(sort_initial_sos).
% 0.49/1.09 % set(auto2) -> assign(sos_limit, -1).
% 0.49/1.09 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.49/1.09 % set(auto2) -> assign(max_megs, 400).
% 0.49/1.09 % set(auto2) -> assign(stats, some).
% 0.49/1.09 % set(auto2) -> clear(echo_input).
% 0.49/1.09 % set(auto2) -> set(quiet).
% 0.49/1.09 % set(auto2) -> clear(print_initial_clauses).
% 0.49/1.09 % set(auto2) -> clear(print_given).
% 0.49/1.09 assign(lrs_ticks,-1).
% 0.49/1.09 assign(sos_limit,10000).
% 0.49/1.09 assign(order,kbo).
% 0.49/1.09 set(lex_order_vars).
% 0.49/1.09 clear(print_given).
% 0.49/1.09
% 0.49/1.09 % formulas(sos). % not echoed (18 formulas)
% 0.49/1.09
% 0.49/1.09 ============================== end of input ==========================
% 0.49/1.09
% 0.49/1.09 % From the command line: assign(max_seconds, 300).
% 0.49/1.09
% 0.49/1.09 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.49/1.09
% 0.49/1.09 % Formulas that are not ordinary clauses:
% 0.49/1.09 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].
% 0.49/1.09 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].
% 0.49/1.09 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].
% 0.49/1.09 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].
% 0.49/1.09 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].
% 0.49/1.09 6 (all C (closed(C) <-> -(exists P end_point(P,C)))) # label(closed_defn) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.09 7 (all C (open(C) <-> (exists P end_point(P,C)))) # label(open_defn) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.09 8 (all C all C1 (part_of(C1,C) & C1 != C -> open(C1))) # label(c1) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.09 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].
% 0.49/1.09 10 (all C exists P inner_point(P,C)) # label(c3) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.09 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].
% 0.49/1.09 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].
% 0.49/1.09 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].
% 0.49/1.09 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].
% 0.49/1.09 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].
% 0.49/1.09 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].
% 0.49/1.09 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].
% 0.49/1.09 18 -(all C all P all Q all R (between_c(C,P,Q,R) -> incident_c(P,C) & incident_c(Q,C) & incident_c(R,C) & P != Q & Q != R & P != R)) # label(theorem_3_8_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.49/1.09
% 0.49/1.09 ============================== end of process non-clausal formulas ===
% 0.49/1.09
% 0.49/1.09 ============================== PROCESS INITIAL CLAUSES ===============
% 0.49/1.09
% 0.49/1.09 ============================== PREDICATE ELIMINATION =================
% 0.49/1.09 19 -inner_point(A,B) | -end_point(A,B) # label(inner_point_defn) # label(axiom). [clausify(4)].
% 0.49/1.09 20 inner_point(f8(A),A) # label(c3) # label(axiom). [clausify(10)].
% 0.49/1.09 Derived: -end_point(f8(A),A). [resolve(19,a,20,a)].
% 0.49/1.09 21 -inner_point(A,B) | incident_c(A,B) # label(inner_point_defn) # label(axiom). [clausify(4)].
% 0.49/1.09 Derived: incident_c(f8(A),A). [resolve(21,a,20,a)].
% 0.49/1.09 22 inner_point(A,B) | -incident_c(A,B) | end_point(A,B) # label(inner_point_defn) # label(axiom). [clausify(4)].
% 0.49/1.09 23 -inner_point(A,B) | meet(A,f9(B,A),f10(B,A)) # label(c4) # label(axiom). [clausify(11)].
% 0.49/1.09 Derived: meet(f8(A),f9(A,f8(A)),f10(A,f8(A))). [resolve(23,a,20,a)].
% 0.49/1.09 Derived: meet(A,f9(B,A),f10(B,A)) | -incident_c(A,B) | end_point(A,B). [resolve(23,a,22,a)].
% 0.49/1.09 24 -inner_point(A,B) | sum(f9(B,A),f10(B,A)) = B # label(c4) # label(axiom). [clausify(11)].
% 0.49/1.09 Derived: sum(f9(A,f8(A)),f10(A,f8(A))) = A. [resolve(24,a,20,a)].
% 0.49/1.09 Derived: sum(f9(A,B),f10(A,B)) = A | -incident_c(B,A) | end_point(B,A). [resolve(24,a,22,a)].
% 0.49/1.09 25 -between_c(A,B,C,D) | inner_point(C,f14(A,B,C,D)) # label(between_c_defn) # label(axiom). [clausify(17)].
% 0.49/1.09 Derived: -between_c(A,B,C,D) | -end_point(C,f14(A,B,C,D)). [resolve(25,b,19,a)].
% 0.49/1.09 Derived: -between_c(A,B,C,D) | incident_c(C,f14(A,B,C,D)). [resolve(25,b,21,a)].
% 0.49/1.09 Derived: -between_c(A,B,C,D) | meet(C,f9(f14(A,B,C,D),C),f10(f14(A,B,C,D),C)). [resolve(25,b,23,a)].
% 0.49/1.09 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(25,b,24,a)].
% 0.49/1.09 26 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)].
% 0.49/1.09 Derived: between_c(A,B,f8(C),D) | D = B | -part_of(C,A) | -end_point(B,C) | -end_point(D,C). [resolve(26,f,20,a)].
% 0.49/1.09 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(26,f,22,a)].
% 0.49/1.09 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(26,f,25,b)].
% 0.49/1.09 27 -closed(A) | -end_point(B,A) # label(closed_defn) # label(axiom). [clausify(6)].
% 0.49/1.09 28 closed(A) | end_point(f6(A),A) # label(closed_defn) # label(axiom). [clausify(6)].
% 0.49/1.09 Derived: -end_point(A,B) | end_point(f6(B),B). [resolve(27,a,28,a)].
% 0.49/1.09 29 -closed(A) | -meet(B,C,D) | sum(C,D) != A | -end_point(E,C) | meet(E,C,D) # label(c7) # label(axiom). [clausify(14)].
% 0.49/1.09 Derived: -meet(A,B,C) | sum(B,C) != D | -end_point(E,B) | meet(E,B,C) | end_point(f6(D),D). [resolve(29,a,28,a)].
% 0.49/1.09 30 -open(A) | end_point(f7(A),A) # label(open_defn) # label(axiom). [clausify(7)].
% 0.49/1.09 31 open(A) | -end_point(B,A) # label(open_defn) # label(axiom). [clausify(7)].
% 0.49/1.09 Derived: end_point(f7(A),A) | -end_point(B,A). [resolve(30,a,31,a)].
% 0.99/1.26 32 -part_of(A,B) | A = B | open(A) # label(c1) # label(axiom). [clausify(8)].
% 0.99/1.26 Derived: -part_of(A,B) | A = B | end_point(f7(A),A). [resolve(32,c,30,a)].
% 0.99/1.26
% 0.99/1.26 ============================== end predicate elimination =============
% 0.99/1.26
% 0.99/1.26 Auto_denials: (non-Horn, no changes).
% 0.99/1.26
% 0.99/1.26 Term ordering decisions:
% 0.99/1.26 Function symbol KB weights: c10=1. c11=1. c12=1. c13=1. sum=1. f1=1. f3=1. f4=1. f9=1. f10=1. f11=1. f12=1. f13=1. f6=1. f7=1. f8=1. f2=1. f5=1. f14=1.
% 0.99/1.26
% 0.99/1.26 ============================== end of process initial clauses ========
% 0.99/1.26
% 0.99/1.26 ============================== CLAUSES FOR SEARCH ====================
% 0.99/1.26
% 0.99/1.26 ============================== end of clauses for search =============
% 0.99/1.26
% 0.99/1.26 ============================== SEARCH ================================
% 0.99/1.26
% 0.99/1.26 % Starting search at 0.02 seconds.
% 0.99/1.26
% 0.99/1.26 ============================== PROOF =================================
% 0.99/1.26 % SZS status Theorem
% 0.99/1.26 % SZS output start Refutation
% 0.99/1.26
% 0.99/1.26 % Proof 1 at 0.18 (+ 0.01) seconds.
% 0.99/1.26 % Length of proof is 35.
% 0.99/1.26 % Level of proof is 8.
% 0.99/1.26 % Maximum clause weight is 18.000.
% 0.99/1.26 % Given clauses 151.
% 0.99/1.26
% 0.99/1.26 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].
% 0.99/1.26 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].
% 0.99/1.26 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].
% 0.99/1.26 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].
% 0.99/1.26 18 -(all C all P all Q all R (between_c(C,P,Q,R) -> incident_c(P,C) & incident_c(Q,C) & incident_c(R,C) & P != Q & Q != R & P != R)) # label(theorem_3_8_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.99/1.26 19 -inner_point(A,B) | -end_point(A,B) # label(inner_point_defn) # label(axiom). [clausify(4)].
% 0.99/1.26 21 -inner_point(A,B) | incident_c(A,B) # label(inner_point_defn) # label(axiom). [clausify(4)].
% 0.99/1.26 25 -between_c(A,B,C,D) | inner_point(C,f14(A,B,C,D)) # label(between_c_defn) # label(axiom). [clausify(17)].
% 0.99/1.26 33 between_c(c10,c11,c12,c13) # label(theorem_3_8_1) # label(negated_conjecture). [clausify(18)].
% 0.99/1.26 38 -between_c(A,B,C,D) | D != B # label(between_c_defn) # label(axiom). [clausify(17)].
% 0.99/1.26 39 -end_point(A,B) | incident_c(A,B) # label(end_point_defn) # label(axiom). [clausify(3)].
% 0.99/1.26 44 -part_of(A,B) | -incident_c(C,A) | incident_c(C,B) # label(part_of_defn) # label(axiom). [clausify(1)].
% 0.99/1.26 53 -between_c(A,B,C,D) | part_of(f14(A,B,C,D),A) # label(between_c_defn) # label(axiom). [clausify(17)].
% 0.99/1.26 54 -between_c(A,B,C,D) | end_point(B,f14(A,B,C,D)) # label(between_c_defn) # label(axiom). [clausify(17)].
% 0.99/1.26 55 -between_c(A,B,C,D) | end_point(D,f14(A,B,C,D)) # label(between_c_defn) # label(axiom). [clausify(17)].
% 0.99/1.26 67 -incident_c(c11,c10) | -incident_c(c12,c10) | -incident_c(c13,c10) | c12 = c11 | c13 = c12 | c13 = c11 # label(theorem_3_8_1) # label(negated_conjecture). [clausify(18)].
% 0.99/1.26 77 -between_c(A,B,C,D) | -end_point(C,f14(A,B,C,D)). [resolve(25,b,19,a)].
% 0.99/1.26 78 -between_c(A,B,C,D) | incident_c(C,f14(A,B,C,D)). [resolve(25,b,21,a)].
% 0.99/1.26 101 c13 != c11. [resolve(38,a,33,a)].
% 0.99/1.26 103 -incident_c(c11,c10) | -incident_c(c12,c10) | -incident_c(c13,c10) | c12 = c11 | c13 = c12. [back_unit_del(67),unit_del(f,101)].
% 0.99/1.26 175 part_of(f14(c10,c11,c12,c13),c10). [resolve(53,a,33,a)].
% 0.99/1.26 176 end_point(c11,f14(c10,c11,c12,c13)). [resolve(54,a,33,a)].
% 0.99/1.26 177 end_point(c13,f14(c10,c11,c12,c13)). [resolve(55,a,33,a)].
% 0.99/1.26 307 -end_point(c12,f14(c10,c11,c12,c13)). [resolve(77,a,33,a)].
% 0.99/1.26 308 incident_c(c12,f14(c10,c11,c12,c13)). [resolve(78,a,33,a)].
% 0.99/1.26 402 -incident_c(A,f14(c10,c11,c12,c13)) | incident_c(A,c10). [resolve(175,a,44,a)].
% 0.99/1.26 407 incident_c(c11,f14(c10,c11,c12,c13)). [resolve(176,a,39,a)].
% 0.99/1.26 414 incident_c(c13,f14(c10,c11,c12,c13)). [resolve(177,a,39,a)].
% 0.99/1.26 1090 incident_c(c13,c10). [resolve(402,a,414,a)].
% 0.99/1.26 1091 incident_c(c11,c10). [resolve(402,a,407,a)].
% 0.99/1.26 1092 incident_c(c12,c10). [resolve(402,a,308,a)].
% 0.99/1.26 1101 c12 = c11 | c13 = c12. [back_unit_del(103),unit_del(a,1091),unit_del(b,1092),unit_del(c,1090)].
% 0.99/1.26 1175 c12 = c11. [para(1101(b,1),177(a,1)),unit_del(b,307)].
% 0.99/1.26 1297 -end_point(c11,f14(c10,c11,c11,c13)). [back_rewrite(307),rewrite([1175(1),1175(4)])].
% 0.99/1.26 1299 $F. [back_rewrite(176),rewrite([1175(4)]),unit_del(a,1297)].
% 0.99/1.26
% 0.99/1.26 % SZS output end Refutation
% 0.99/1.26 ============================== end of proof ==========================
% 0.99/1.26
% 0.99/1.26 ============================== STATISTICS ============================
% 0.99/1.26
% 0.99/1.26 Given=151. Generated=1910. Kept=1265. proofs=1.
% 0.99/1.26 Usable=135. Sos=797. Demods=6. Limbo=124, Disabled=277. Hints=0.
% 0.99/1.26 Megabytes=1.48.
% 0.99/1.26 User_CPU=0.18, System_CPU=0.01, Wall_clock=0.
% 0.99/1.26
% 0.99/1.26 ============================== end of statistics =====================
% 0.99/1.26
% 0.99/1.26 ============================== end of search =========================
% 0.99/1.26
% 0.99/1.26 THEOREM PROVED
% 0.99/1.26 % SZS status Theorem
% 0.99/1.26
% 0.99/1.26 Exiting with 1 proof.
% 0.99/1.26
% 0.99/1.26 Process 21741 exit (max_proofs) Sat Jun 18 18:09:24 2022
% 0.99/1.26 Prover9 interrupted
%------------------------------------------------------------------------------