TSTP Solution File: GEO112+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GEO112+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 05:54:05 EDT 2022
% Result : Theorem 0.80s 1.09s
% Output : Refutation 0.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GEO112+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.32 % Computer : n029.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Fri Jun 17 23:38:28 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.40/1.05 ============================== Prover9 ===============================
% 0.40/1.05 Prover9 (32) version 2009-11A, November 2009.
% 0.40/1.05 Process 14145 was started by sandbox on n029.cluster.edu,
% 0.40/1.05 Fri Jun 17 23:38:29 2022
% 0.40/1.05 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_13992_n029.cluster.edu".
% 0.40/1.05 ============================== end of head ===========================
% 0.40/1.05
% 0.40/1.05 ============================== INPUT =================================
% 0.40/1.05
% 0.40/1.05 % Reading from file /tmp/Prover9_13992_n029.cluster.edu
% 0.40/1.05
% 0.40/1.05 set(prolog_style_variables).
% 0.40/1.05 set(auto2).
% 0.40/1.05 % set(auto2) -> set(auto).
% 0.40/1.05 % set(auto) -> set(auto_inference).
% 0.40/1.05 % set(auto) -> set(auto_setup).
% 0.40/1.05 % set(auto_setup) -> set(predicate_elim).
% 0.40/1.05 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.40/1.05 % set(auto) -> set(auto_limits).
% 0.40/1.05 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.40/1.05 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.40/1.05 % set(auto) -> set(auto_denials).
% 0.40/1.05 % set(auto) -> set(auto_process).
% 0.40/1.05 % set(auto2) -> assign(new_constants, 1).
% 0.40/1.05 % set(auto2) -> assign(fold_denial_max, 3).
% 0.40/1.05 % set(auto2) -> assign(max_weight, "200.000").
% 0.40/1.05 % set(auto2) -> assign(max_hours, 1).
% 0.40/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.40/1.05 % set(auto2) -> assign(max_seconds, 0).
% 0.40/1.05 % set(auto2) -> assign(max_minutes, 5).
% 0.40/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.40/1.05 % set(auto2) -> set(sort_initial_sos).
% 0.40/1.05 % set(auto2) -> assign(sos_limit, -1).
% 0.40/1.05 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.40/1.05 % set(auto2) -> assign(max_megs, 400).
% 0.40/1.05 % set(auto2) -> assign(stats, some).
% 0.40/1.05 % set(auto2) -> clear(echo_input).
% 0.40/1.05 % set(auto2) -> set(quiet).
% 0.40/1.05 % set(auto2) -> clear(print_initial_clauses).
% 0.40/1.05 % set(auto2) -> clear(print_given).
% 0.40/1.05 assign(lrs_ticks,-1).
% 0.40/1.05 assign(sos_limit,10000).
% 0.40/1.05 assign(order,kbo).
% 0.40/1.05 set(lex_order_vars).
% 0.40/1.05 clear(print_given).
% 0.40/1.05
% 0.40/1.05 % formulas(sos). % not echoed (18 formulas)
% 0.40/1.05
% 0.40/1.05 ============================== end of input ==========================
% 0.40/1.05
% 0.40/1.05 % From the command line: assign(max_seconds, 300).
% 0.40/1.05
% 0.40/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.40/1.05
% 0.40/1.05 % Formulas that are not ordinary clauses:
% 0.40/1.05 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].
% 0.40/1.05 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].
% 0.40/1.05 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].
% 0.40/1.05 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].
% 0.40/1.05 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].
% 0.40/1.05 6 (all C (closed(C) <-> -(exists P end_point(P,C)))) # label(closed_defn) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.05 7 (all C (open(C) <-> (exists P end_point(P,C)))) # label(open_defn) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.05 8 (all C all C1 (part_of(C1,C) & C1 != C -> open(C1))) # label(c1) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.05 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].
% 0.40/1.05 10 (all C exists P inner_point(P,C)) # label(c3) # label(axiom) # label(non_clause). [assumption].
% 0.40/1.05 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].
% 0.40/1.05 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].
% 0.40/1.06 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].
% 0.40/1.06 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].
% 0.40/1.06 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].
% 0.40/1.06 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].
% 0.40/1.06 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].
% 0.40/1.06 18 -(all C all P all Q all R (between_c(C,P,Q,R) -> between_c(C,R,Q,P))) # label(theorem_3_8_2) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.40/1.06
% 0.40/1.06 ============================== end of process non-clausal formulas ===
% 0.40/1.06
% 0.40/1.06 ============================== PROCESS INITIAL CLAUSES ===============
% 0.40/1.06
% 0.40/1.06 ============================== PREDICATE ELIMINATION =================
% 0.40/1.06 19 -inner_point(A,B) | -end_point(A,B) # label(inner_point_defn) # label(axiom). [clausify(4)].
% 0.40/1.06 20 inner_point(f8(A),A) # label(c3) # label(axiom). [clausify(10)].
% 0.40/1.06 Derived: -end_point(f8(A),A). [resolve(19,a,20,a)].
% 0.40/1.06 21 -inner_point(A,B) | incident_c(A,B) # label(inner_point_defn) # label(axiom). [clausify(4)].
% 0.40/1.06 Derived: incident_c(f8(A),A). [resolve(21,a,20,a)].
% 0.40/1.06 22 inner_point(A,B) | -incident_c(A,B) | end_point(A,B) # label(inner_point_defn) # label(axiom). [clausify(4)].
% 0.40/1.06 23 -inner_point(A,B) | meet(A,f9(B,A),f10(B,A)) # label(c4) # label(axiom). [clausify(11)].
% 0.40/1.06 Derived: meet(f8(A),f9(A,f8(A)),f10(A,f8(A))). [resolve(23,a,20,a)].
% 0.40/1.06 Derived: meet(A,f9(B,A),f10(B,A)) | -incident_c(A,B) | end_point(A,B). [resolve(23,a,22,a)].
% 0.40/1.06 24 -inner_point(A,B) | sum(f9(B,A),f10(B,A)) = B # label(c4) # label(axiom). [clausify(11)].
% 0.40/1.06 Derived: sum(f9(A,f8(A)),f10(A,f8(A))) = A. [resolve(24,a,20,a)].
% 0.40/1.06 Derived: sum(f9(A,B),f10(A,B)) = A | -incident_c(B,A) | end_point(B,A). [resolve(24,a,22,a)].
% 0.40/1.06 25 -between_c(A,B,C,D) | inner_point(C,f14(A,B,C,D)) # label(between_c_defn) # label(axiom). [clausify(17)].
% 0.40/1.06 Derived: -between_c(A,B,C,D) | -end_point(C,f14(A,B,C,D)). [resolve(25,b,19,a)].
% 0.40/1.06 Derived: -between_c(A,B,C,D) | incident_c(C,f14(A,B,C,D)). [resolve(25,b,21,a)].
% 0.40/1.06 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)].
% 0.40/1.06 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)].
% 0.40/1.06 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)].
% 0.40/1.06 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)].
% 0.40/1.06 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)].
% 0.40/1.06 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)].
% 0.40/1.06 27 -closed(A) | -end_point(B,A) # label(closed_defn) # label(axiom). [clausify(6)].
% 0.40/1.06 28 closed(A) | end_point(f6(A),A) # label(closed_defn) # label(axiom). [clausify(6)].
% 0.40/1.06 Derived: -end_point(A,B) | end_point(f6(B),B). [resolve(27,a,28,a)].
% 0.40/1.06 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)].
% 0.40/1.06 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)].
% 0.40/1.06 30 -open(A) | end_point(f7(A),A) # label(open_defn) # label(axiom). [clausify(7)].
% 0.40/1.06 31 open(A) | -end_point(B,A) # label(open_defn) # label(axiom). [clausify(7)].
% 0.40/1.06 Derived: end_point(f7(A),A) | -end_point(B,A). [resolve(30,a,31,a)].
% 0.80/1.09 32 -part_of(A,B) | A = B | open(A) # label(c1) # label(axiom). [clausify(8)].
% 0.80/1.09 Derived: -part_of(A,B) | A = B | end_point(f7(A),A). [resolve(32,c,30,a)].
% 0.80/1.09
% 0.80/1.09 ============================== end predicate elimination =============
% 0.80/1.09
% 0.80/1.09 Auto_denials: (non-Horn, no changes).
% 0.80/1.09
% 0.80/1.09 Term ordering decisions:
% 0.80/1.09 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.
% 0.80/1.09
% 0.80/1.09 ============================== end of process initial clauses ========
% 0.80/1.09
% 0.80/1.09 ============================== CLAUSES FOR SEARCH ====================
% 0.80/1.09
% 0.80/1.09 ============================== end of clauses for search =============
% 0.80/1.09
% 0.80/1.09 ============================== SEARCH ================================
% 0.80/1.09
% 0.80/1.09 % Starting search at 0.01 seconds.
% 0.80/1.09
% 0.80/1.09 ============================== PROOF =================================
% 0.80/1.09 % SZS status Theorem
% 0.80/1.09 % SZS output start Refutation
% 0.80/1.09
% 0.80/1.09 % Proof 1 at 0.05 (+ 0.00) seconds.
% 0.80/1.09 % Length of proof is 16.
% 0.80/1.09 % Level of proof is 3.
% 0.80/1.09 % Maximum clause weight is 34.000.
% 0.80/1.09 % Given clauses 71.
% 0.80/1.10
% 0.80/1.10 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].
% 0.80/1.10 18 -(all C all P all Q all R (between_c(C,P,Q,R) -> between_c(C,R,Q,P))) # label(theorem_3_8_2) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.80/1.10 25 -between_c(A,B,C,D) | inner_point(C,f14(A,B,C,D)) # label(between_c_defn) # label(axiom). [clausify(17)].
% 0.80/1.10 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)].
% 0.80/1.10 33 between_c(c10,c11,c12,c13) # label(theorem_3_8_2) # label(negated_conjecture). [clausify(18)].
% 0.80/1.10 37 -between_c(c10,c13,c12,c11) # label(theorem_3_8_2) # label(negated_conjecture). [clausify(18)].
% 0.80/1.10 39 -between_c(A,B,C,D) | D != B # label(between_c_defn) # label(axiom). [clausify(17)].
% 0.80/1.10 54 -between_c(A,B,C,D) | part_of(f14(A,B,C,D),A) # label(between_c_defn) # label(axiom). [clausify(17)].
% 0.80/1.10 55 -between_c(A,B,C,D) | end_point(B,f14(A,B,C,D)) # label(between_c_defn) # label(axiom). [clausify(17)].
% 0.80/1.10 56 -between_c(A,B,C,D) | end_point(D,f14(A,B,C,D)) # label(between_c_defn) # label(axiom). [clausify(17)].
% 0.80/1.10 83 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)].
% 0.80/1.10 101 c13 != c11. [resolve(39,a,33,a)].
% 0.80/1.10 174 part_of(f14(c10,c11,c12,c13),c10). [resolve(54,a,33,a)].
% 0.80/1.10 175 end_point(c11,f14(c10,c11,c12,c13)). [resolve(55,a,33,a)].
% 0.80/1.10 176 end_point(c13,f14(c10,c11,c12,c13)). [resolve(56,a,33,a)].
% 0.80/1.10 408 $F. [ur(83,a,37,a,b,101,a(flip),c,174,a,e,175,a,f,33,a),unit_del(a,176)].
% 0.80/1.10
% 0.80/1.10 % SZS output end Refutation
% 0.80/1.10 ============================== end of proof ==========================
% 0.80/1.10
% 0.80/1.10 ============================== STATISTICS ============================
% 0.80/1.10
% 0.80/1.10 Given=71. Generated=714. Kept=374. proofs=1.
% 0.80/1.10 Usable=69. Sos=254. Demods=3. Limbo=6, Disabled=113. Hints=0.
% 0.80/1.10 Megabytes=0.48.
% 0.80/1.10 User_CPU=0.05, System_CPU=0.00, Wall_clock=0.
% 0.80/1.10
% 0.80/1.10 ============================== end of statistics =====================
% 0.80/1.10
% 0.80/1.10 ============================== end of search =========================
% 0.80/1.10
% 0.80/1.10 THEOREM PROVED
% 0.80/1.10 % SZS status Theorem
% 0.80/1.10
% 0.80/1.10 Exiting with 1 proof.
% 0.80/1.10
% 0.80/1.10 Process 14145 exit (max_proofs) Fri Jun 17 23:38:29 2022
% 0.80/1.10 Prover9 interrupted
%------------------------------------------------------------------------------