TSTP Solution File: GEO084+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GEO084+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n013.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 05:53:51 EDT 2022
% Result : Theorem 0.81s 1.47s
% Output : Refutation 0.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO084+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 18 04:00:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.42/1.08 ============================== Prover9 ===============================
% 0.42/1.08 Prover9 (32) version 2009-11A, November 2009.
% 0.42/1.08 Process 31722 was started by sandbox2 on n013.cluster.edu,
% 0.42/1.08 Sat Jun 18 04:00:14 2022
% 0.42/1.08 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_31568_n013.cluster.edu".
% 0.42/1.08 ============================== end of head ===========================
% 0.42/1.08
% 0.42/1.08 ============================== INPUT =================================
% 0.42/1.08
% 0.42/1.08 % Reading from file /tmp/Prover9_31568_n013.cluster.edu
% 0.42/1.08
% 0.42/1.08 set(prolog_style_variables).
% 0.42/1.08 set(auto2).
% 0.42/1.08 % set(auto2) -> set(auto).
% 0.42/1.08 % set(auto) -> set(auto_inference).
% 0.42/1.08 % set(auto) -> set(auto_setup).
% 0.42/1.08 % set(auto_setup) -> set(predicate_elim).
% 0.42/1.08 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/1.08 % set(auto) -> set(auto_limits).
% 0.42/1.08 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/1.08 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/1.08 % set(auto) -> set(auto_denials).
% 0.42/1.08 % set(auto) -> set(auto_process).
% 0.42/1.08 % set(auto2) -> assign(new_constants, 1).
% 0.42/1.08 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/1.08 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/1.08 % set(auto2) -> assign(max_hours, 1).
% 0.42/1.08 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/1.08 % set(auto2) -> assign(max_seconds, 0).
% 0.42/1.08 % set(auto2) -> assign(max_minutes, 5).
% 0.42/1.08 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/1.08 % set(auto2) -> set(sort_initial_sos).
% 0.42/1.08 % set(auto2) -> assign(sos_limit, -1).
% 0.42/1.08 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/1.08 % set(auto2) -> assign(max_megs, 400).
% 0.42/1.08 % set(auto2) -> assign(stats, some).
% 0.42/1.08 % set(auto2) -> clear(echo_input).
% 0.42/1.08 % set(auto2) -> set(quiet).
% 0.42/1.08 % set(auto2) -> clear(print_initial_clauses).
% 0.42/1.08 % set(auto2) -> clear(print_given).
% 0.42/1.08 assign(lrs_ticks,-1).
% 0.42/1.08 assign(sos_limit,10000).
% 0.42/1.08 assign(order,kbo).
% 0.42/1.08 set(lex_order_vars).
% 0.42/1.08 clear(print_given).
% 0.42/1.08
% 0.42/1.08 % formulas(sos). % not echoed (17 formulas)
% 0.42/1.08
% 0.42/1.08 ============================== end of input ==========================
% 0.42/1.08
% 0.42/1.08 % From the command line: assign(max_seconds, 300).
% 0.42/1.08
% 0.42/1.08 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/1.08
% 0.42/1.08 % Formulas that are not ordinary clauses:
% 0.42/1.08 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].
% 0.42/1.08 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].
% 0.42/1.08 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].
% 0.42/1.08 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].
% 0.42/1.08 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].
% 0.42/1.08 6 (all C (closed(C) <-> -(exists P end_point(P,C)))) # label(closed_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.08 7 (all C (open(C) <-> (exists P end_point(P,C)))) # label(open_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.08 8 (all C all C1 (part_of(C1,C) & C1 != C -> open(C1))) # label(c1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.08 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].
% 0.42/1.08 10 (all C exists P inner_point(P,C)) # label(c3) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.08 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].
% 0.42/1.08 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].
% 0.81/1.47 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].
% 0.81/1.47 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].
% 0.81/1.47 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].
% 0.81/1.47 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].
% 0.81/1.47 17 -(all C1 all C2 all C3 all P (part_of(C1,C3) & part_of(C2,C3) & meet(P,C1,C2) -> part_of(sum(C1,C2),C3))) # label(corollary_2_6_2) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.81/1.47
% 0.81/1.47 ============================== end of process non-clausal formulas ===
% 0.81/1.47
% 0.81/1.47 ============================== PROCESS INITIAL CLAUSES ===============
% 0.81/1.47
% 0.81/1.47 ============================== PREDICATE ELIMINATION =================
% 0.81/1.47 18 -inner_point(A,B) | -end_point(A,B) # label(inner_point_defn) # label(axiom). [clausify(4)].
% 0.81/1.47 19 inner_point(f8(A),A) # label(c3) # label(axiom). [clausify(10)].
% 0.81/1.47 Derived: -end_point(f8(A),A). [resolve(18,a,19,a)].
% 0.81/1.47 20 -inner_point(A,B) | incident_c(A,B) # label(inner_point_defn) # label(axiom). [clausify(4)].
% 0.81/1.47 Derived: incident_c(f8(A),A). [resolve(20,a,19,a)].
% 0.81/1.47 21 inner_point(A,B) | -incident_c(A,B) | end_point(A,B) # label(inner_point_defn) # label(axiom). [clausify(4)].
% 0.81/1.47 22 -inner_point(A,B) | meet(A,f9(B,A),f10(B,A)) # label(c4) # label(axiom). [clausify(11)].
% 0.81/1.47 Derived: meet(f8(A),f9(A,f8(A)),f10(A,f8(A))). [resolve(22,a,19,a)].
% 0.81/1.47 Derived: meet(A,f9(B,A),f10(B,A)) | -incident_c(A,B) | end_point(A,B). [resolve(22,a,21,a)].
% 0.81/1.47 23 -inner_point(A,B) | sum(f9(B,A),f10(B,A)) = B # label(c4) # label(axiom). [clausify(11)].
% 0.81/1.47 Derived: sum(f9(A,f8(A)),f10(A,f8(A))) = A. [resolve(23,a,19,a)].
% 0.81/1.47 Derived: sum(f9(A,B),f10(A,B)) = A | -incident_c(B,A) | end_point(B,A). [resolve(23,a,21,a)].
% 0.81/1.47 24 -closed(A) | -end_point(B,A) # label(closed_defn) # label(axiom). [clausify(6)].
% 0.81/1.47 25 closed(A) | end_point(f6(A),A) # label(closed_defn) # label(axiom). [clausify(6)].
% 0.81/1.47 Derived: -end_point(A,B) | end_point(f6(B),B). [resolve(24,a,25,a)].
% 0.81/1.47 26 -closed(A) | -meet(B,C,D) | sum(C,D) != A | -end_point(E,C) | meet(E,C,D) # label(c7) # label(axiom). [clausify(14)].
% 0.81/1.47 Derived: -meet(A,B,C) | sum(B,C) != D | -end_point(E,B) | meet(E,B,C) | end_point(f6(D),D). [resolve(26,a,25,a)].
% 0.81/1.47 27 -open(A) | end_point(f7(A),A) # label(open_defn) # label(axiom). [clausify(7)].
% 0.81/1.47 28 open(A) | -end_point(B,A) # label(open_defn) # label(axiom). [clausify(7)].
% 0.81/1.47 Derived: end_point(f7(A),A) | -end_point(B,A). [resolve(27,a,28,a)].
% 0.81/1.47 29 -part_of(A,B) | A = B | open(A) # label(c1) # label(axiom). [clausify(8)].
% 0.81/1.47 Derived: -part_of(A,B) | A = B | end_point(f7(A),A). [resolve(29,c,27,a)].
% 0.81/1.47
% 0.81/1.47 ============================== end predicate elimination =============
% 0.81/1.47
% 0.81/1.47 Auto_denials: (non-Horn, no changes).
% 0.81/1.47
% 0.81/1.47 Term ordering decisions:
% 0.81/1.47 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.
% 0.81/1.47
% 0.81/1.47 ============================== end of process initial clauses ========
% 0.81/1.47
% 0.81/1.47 ============================== CLAUSES FOR SEARCH ====================
% 0.81/1.47
% 0.81/1.47 ============================== end of clauses for search =============
% 0.81/1.47
% 0.81/1.47 ============================== SEARCH ================================
% 0.81/1.47
% 0.81/1.47 % Starting search at 0.02 seconds.
% 0.81/1.47
% 0.81/1.47 ============================== PROOF =================================
% 0.81/1.47 % SZS status Theorem
% 0.81/1.47 % SZS output start Refutation
% 0.81/1.47
% 0.81/1.47 % Proof 1 at 0.39 (+ 0.01) seconds.
% 0.81/1.47 % Length of proof is 16.
% 0.81/1.47 % Level of proof is 4.
% 0.81/1.47 % Maximum clause weight is 14.000.
% 0.81/1.47 % Given clauses 388.
% 0.81/1.47
% 0.81/1.47 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].
% 0.81/1.47 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].
% 0.81/1.47 17 -(all C1 all C2 all C3 all P (part_of(C1,C3) & part_of(C2,C3) & meet(P,C1,C2) -> part_of(sum(C1,C2),C3))) # label(corollary_2_6_2) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.81/1.47 30 part_of(c10,c12) # label(corollary_2_6_2) # label(negated_conjecture). [clausify(17)].
% 0.81/1.47 31 part_of(c11,c12) # label(corollary_2_6_2) # label(negated_conjecture). [clausify(17)].
% 0.81/1.47 33 part_of(A,B) | incident_c(f1(B,A),A) # label(part_of_defn) # label(axiom). [clausify(1)].
% 0.81/1.47 36 -part_of(sum(c10,c11),c12) # label(corollary_2_6_2) # label(negated_conjecture). [clausify(17)].
% 0.81/1.47 41 part_of(A,B) | -incident_c(f1(B,A),B) # label(part_of_defn) # label(axiom). [clausify(1)].
% 0.81/1.47 43 -part_of(A,B) | -incident_c(C,A) | incident_c(C,B) # label(part_of_defn) # label(axiom). [clausify(1)].
% 0.81/1.47 57 sum(A,B) != C | -incident_c(D,C) | incident_c(D,A) | incident_c(D,B) # label(sum_defn) # label(axiom). [clausify(2)].
% 0.81/1.47 89 incident_c(f1(c12,sum(c10,c11)),sum(c10,c11)). [resolve(36,a,33,a)].
% 0.81/1.47 92 -incident_c(f1(c12,sum(c10,c11)),c12). [ur(41,a,36,a)].
% 0.81/1.47 94 -incident_c(A,c11) | incident_c(A,c12). [resolve(43,a,31,a)].
% 0.81/1.47 477 -incident_c(f1(c12,sum(c10,c11)),c11). [ur(94,b,92,a)].
% 0.81/1.47 484 -incident_c(f1(c12,sum(c10,c11)),c10). [ur(43,a,30,a,c,92,a)].
% 0.81/1.47 2858 $F. [ur(57,b,89,a,c,484,a,d,477,a),xx(a)].
% 0.81/1.47
% 0.81/1.47 % SZS output end Refutation
% 0.81/1.47 ============================== end of proof ==========================
% 0.81/1.47
% 0.81/1.47 ============================== STATISTICS ============================
% 0.81/1.47
% 0.81/1.47 Given=388. Generated=4879. Kept=2827. proofs=1.
% 0.81/1.47 Usable=360. Sos=2156. Demods=5. Limbo=6, Disabled=362. Hints=0.
% 0.81/1.47 Megabytes=2.73.
% 0.81/1.47 User_CPU=0.39, System_CPU=0.01, Wall_clock=1.
% 0.81/1.47
% 0.81/1.47 ============================== end of statistics =====================
% 0.81/1.47
% 0.81/1.47 ============================== end of search =========================
% 0.81/1.47
% 0.81/1.47 THEOREM PROVED
% 0.81/1.47 % SZS status Theorem
% 0.81/1.47
% 0.81/1.47 Exiting with 1 proof.
% 0.81/1.47
% 0.81/1.47 Process 31722 exit (max_proofs) Sat Jun 18 04:00:15 2022
% 0.81/1.47 Prover9 interrupted
%------------------------------------------------------------------------------