TSTP Solution File: GEO083+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GEO083+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n010.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 05:53:50 EDT 2022
% Result : Theorem 7.33s 7.63s
% Output : Refutation 7.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO083+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.33 % Computer : n010.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Sat Jun 18 18:42:53 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.73/0.99 ============================== Prover9 ===============================
% 0.73/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.73/0.99 Process 4981 was started by sandbox2 on n010.cluster.edu,
% 0.73/0.99 Sat Jun 18 18:42:53 2022
% 0.73/0.99 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_4825_n010.cluster.edu".
% 0.73/0.99 ============================== end of head ===========================
% 0.73/0.99
% 0.73/0.99 ============================== INPUT =================================
% 0.73/0.99
% 0.73/0.99 % Reading from file /tmp/Prover9_4825_n010.cluster.edu
% 0.73/0.99
% 0.73/0.99 set(prolog_style_variables).
% 0.73/0.99 set(auto2).
% 0.73/0.99 % set(auto2) -> set(auto).
% 0.73/0.99 % set(auto) -> set(auto_inference).
% 0.73/0.99 % set(auto) -> set(auto_setup).
% 0.73/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.73/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.73/0.99 % set(auto) -> set(auto_limits).
% 0.73/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.73/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.73/0.99 % set(auto) -> set(auto_denials).
% 0.73/0.99 % set(auto) -> set(auto_process).
% 0.73/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.73/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.73/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.73/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.73/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.73/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.73/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.73/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.73/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.73/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.73/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.73/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.73/0.99 % set(auto2) -> assign(stats, some).
% 0.73/0.99 % set(auto2) -> clear(echo_input).
% 0.73/0.99 % set(auto2) -> set(quiet).
% 0.73/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.73/0.99 % set(auto2) -> clear(print_given).
% 0.73/0.99 assign(lrs_ticks,-1).
% 0.73/0.99 assign(sos_limit,10000).
% 0.73/0.99 assign(order,kbo).
% 0.73/0.99 set(lex_order_vars).
% 0.73/0.99 clear(print_given).
% 0.73/0.99
% 0.73/0.99 % formulas(sos). % not echoed (17 formulas)
% 0.73/0.99
% 0.73/0.99 ============================== end of input ==========================
% 0.73/0.99
% 0.73/0.99 % From the command line: assign(max_seconds, 300).
% 0.73/0.99
% 0.73/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.73/0.99
% 0.73/0.99 % Formulas that are not ordinary clauses:
% 0.73/0.99 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].
% 0.73/0.99 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].
% 0.73/0.99 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].
% 0.73/0.99 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].
% 0.73/0.99 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].
% 0.73/0.99 6 (all C (closed(C) <-> -(exists P end_point(P,C)))) # label(closed_defn) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 7 (all C (open(C) <-> (exists P end_point(P,C)))) # label(open_defn) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 8 (all C all C1 (part_of(C1,C) & C1 != C -> open(C1))) # label(c1) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 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].
% 0.73/0.99 10 (all C exists P inner_point(P,C)) # label(c3) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 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].
% 0.73/0.99 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].
% 1.91/2.19 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].
% 1.91/2.19 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].
% 1.91/2.19 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].
% 1.91/2.19 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].
% 1.91/2.19 17 -(all C1 all C2 all C3 all P (part_of(C2,C3) & meet(P,C1,C2) & meet(P,C1,C3) -> part_of(sum(C1,C2),sum(C1,C3)))) # label(corollary_2_6_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.91/2.19
% 1.91/2.19 ============================== end of process non-clausal formulas ===
% 1.91/2.19
% 1.91/2.19 ============================== PROCESS INITIAL CLAUSES ===============
% 1.91/2.19
% 1.91/2.19 ============================== PREDICATE ELIMINATION =================
% 1.91/2.19 18 -inner_point(A,B) | -end_point(A,B) # label(inner_point_defn) # label(axiom). [clausify(4)].
% 1.91/2.19 19 inner_point(f8(A),A) # label(c3) # label(axiom). [clausify(10)].
% 1.91/2.19 Derived: -end_point(f8(A),A). [resolve(18,a,19,a)].
% 1.91/2.19 20 -inner_point(A,B) | incident_c(A,B) # label(inner_point_defn) # label(axiom). [clausify(4)].
% 1.91/2.19 Derived: incident_c(f8(A),A). [resolve(20,a,19,a)].
% 1.91/2.19 21 inner_point(A,B) | -incident_c(A,B) | end_point(A,B) # label(inner_point_defn) # label(axiom). [clausify(4)].
% 1.91/2.19 22 -inner_point(A,B) | meet(A,f9(B,A),f10(B,A)) # label(c4) # label(axiom). [clausify(11)].
% 1.91/2.19 Derived: meet(f8(A),f9(A,f8(A)),f10(A,f8(A))). [resolve(22,a,19,a)].
% 1.91/2.19 Derived: meet(A,f9(B,A),f10(B,A)) | -incident_c(A,B) | end_point(A,B). [resolve(22,a,21,a)].
% 1.91/2.19 23 -inner_point(A,B) | sum(f9(B,A),f10(B,A)) = B # label(c4) # label(axiom). [clausify(11)].
% 1.91/2.19 Derived: sum(f9(A,f8(A)),f10(A,f8(A))) = A. [resolve(23,a,19,a)].
% 1.91/2.19 Derived: sum(f9(A,B),f10(A,B)) = A | -incident_c(B,A) | end_point(B,A). [resolve(23,a,21,a)].
% 1.91/2.19 24 -closed(A) | -end_point(B,A) # label(closed_defn) # label(axiom). [clausify(6)].
% 1.91/2.19 25 closed(A) | end_point(f6(A),A) # label(closed_defn) # label(axiom). [clausify(6)].
% 1.91/2.19 Derived: -end_point(A,B) | end_point(f6(B),B). [resolve(24,a,25,a)].
% 1.91/2.19 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)].
% 1.91/2.19 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)].
% 1.91/2.19 27 -open(A) | end_point(f7(A),A) # label(open_defn) # label(axiom). [clausify(7)].
% 1.91/2.19 28 open(A) | -end_point(B,A) # label(open_defn) # label(axiom). [clausify(7)].
% 1.91/2.19 Derived: end_point(f7(A),A) | -end_point(B,A). [resolve(27,a,28,a)].
% 1.91/2.19 29 -part_of(A,B) | A = B | open(A) # label(c1) # label(axiom). [clausify(8)].
% 1.91/2.19 Derived: -part_of(A,B) | A = B | end_point(f7(A),A). [resolve(29,c,27,a)].
% 1.91/2.19
% 1.91/2.19 ============================== end predicate elimination =============
% 1.91/2.19
% 1.91/2.19 Auto_denials: (non-Horn, no changes).
% 1.91/2.19
% 1.91/2.19 Term ordering decisions:
% 1.91/2.19 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.
% 1.91/2.19
% 1.91/2.19 ============================== end of process initial clauses ========
% 1.91/2.19
% 1.91/2.19 ============================== CLAUSES FOR SEARCH ====================
% 1.91/2.19
% 1.91/2.19 ============================== end of clauses for search =============
% 1.91/2.19
% 1.91/2.19 ============================== SEARCH ================================
% 1.91/2.19
% 1.91/2.19 % Starting search at 0.02 seconds.
% 1.91/2.19
% 1.91/2.19 Low Water (keep): wt=43.000, iters=3378
% 1.91/2.19
% 1.91/2.19 Low Water (keep): wt=36.000, iters=3367
% 1.91/2.19
% 1.91/2.19 Low Water (keep): wt=34.000, iters=3343
% 1.91/2.19
% 1.91/2.19 Low Water (keep): wt=32.000, iters=3346
% 1.91/2.19
% 1.91/2.19 Low Water (keep): wt=30.000, iters=3391
% 1.91/2.19
% 1.91/2.19 Low Water (keep): wt=28.000, iters=3334
% 1.91/2.19
% 1.91/2.19 Low Water (keep): wt=26.000, iters=3379
% 1.91/2.19
% 1.91/2.19 Low Water (keep): wt=25.000, iters=3542
% 1.91/2.19
% 1.91/2.19 Low Water (keep): wt=24.000, iters=3433
% 1.91/2.19
% 1.91/2.19 Low Water (keep): wt=23.000, iters=3351
% 1.91/2.19
% 1.91/2.19 Low Water (keep): wt=19.000, iters=3402
% 1.91/2.19
% 1.91/2.19 Low Water (keep): wt=15.000, iters=3393
% 1.91/2.19
% 1.91/2.19 Low Water (keep): wt=14.000, iters=3400
% 7.33/7.63
% 7.33/7.63 Low Water (keep): wt=13.000, iters=3384
% 7.33/7.63
% 7.33/7.63 ============================== PROOF =================================
% 7.33/7.63 % SZS status Theorem
% 7.33/7.63 % SZS output start Refutation
% 7.33/7.63
% 7.33/7.63 % Proof 1 at 6.62 (+ 0.04) seconds.
% 7.33/7.63 % Length of proof is 19.
% 7.33/7.63 % Level of proof is 5.
% 7.33/7.63 % Maximum clause weight is 25.000.
% 7.33/7.63 % Given clauses 1851.
% 7.33/7.63
% 7.33/7.63 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].
% 7.33/7.63 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].
% 7.33/7.63 17 -(all C1 all C2 all C3 all P (part_of(C2,C3) & meet(P,C1,C2) & meet(P,C1,C3) -> part_of(sum(C1,C2),sum(C1,C3)))) # label(corollary_2_6_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 7.33/7.63 30 part_of(c11,c12) # label(corollary_2_6_1) # label(negated_conjecture). [clausify(17)].
% 7.33/7.63 33 part_of(A,B) | incident_c(f1(B,A),A) # label(part_of_defn) # label(axiom). [clausify(1)].
% 7.33/7.63 36 -part_of(sum(c10,c11),sum(c10,c12)) # label(corollary_2_6_1) # label(negated_conjecture). [clausify(17)].
% 7.33/7.63 41 part_of(A,B) | -incident_c(f1(B,A),B) # label(part_of_defn) # label(axiom). [clausify(1)].
% 7.33/7.63 43 -part_of(A,B) | -incident_c(C,A) | incident_c(C,B) # label(part_of_defn) # label(axiom). [clausify(1)].
% 7.33/7.63 44 sum(A,B) != C | incident_c(D,C) | -incident_c(D,A) # label(sum_defn) # label(axiom). [clausify(2)].
% 7.33/7.63 45 sum(A,B) != C | incident_c(D,C) | -incident_c(D,B) # label(sum_defn) # label(axiom). [clausify(2)].
% 7.33/7.63 57 sum(A,B) != C | -incident_c(D,C) | incident_c(D,A) | incident_c(D,B) # label(sum_defn) # label(axiom). [clausify(2)].
% 7.33/7.63 89 incident_c(f1(sum(c10,c12),sum(c10,c11)),sum(c10,c11)). [resolve(36,a,33,a)].
% 7.33/7.63 93 -incident_c(f1(sum(c10,c12),sum(c10,c11)),sum(c10,c12)). [ur(41,a,36,a)].
% 7.33/7.63 95 -incident_c(A,c11) | incident_c(A,c12). [resolve(43,a,30,a)].
% 7.33/7.63 383 sum(c10,c11) != sum(A,B) | incident_c(f1(sum(c10,c12),sum(c10,c11)),A) | incident_c(f1(sum(c10,c12),sum(c10,c11)),B). [resolve(89,a,57,b),flip(a)].
% 7.33/7.63 472 -incident_c(f1(sum(c10,c12),sum(c10,c11)),c12). [ur(45,a,xx,b,93,a)].
% 7.33/7.63 475 -incident_c(f1(sum(c10,c12),sum(c10,c11)),c10). [ur(44,a,xx,b,93,a)].
% 7.33/7.63 14264 incident_c(f1(sum(c10,c12),sum(c10,c11)),c11). [xx_res(383,a),unit_del(a,475)].
% 7.33/7.63 14305 $F. [resolve(14264,a,95,a),unit_del(a,472)].
% 7.33/7.63
% 7.33/7.63 % SZS output end Refutation
% 7.33/7.63 ============================== end of proof ==========================
% 7.33/7.63
% 7.33/7.63 ============================== STATISTICS ============================
% 7.33/7.63
% 7.33/7.63 Given=1851. Generated=52566. Kept=14274. proofs=1.
% 7.33/7.63 Usable=1630. Sos=8707. Demods=18. Limbo=6, Disabled=3988. Hints=0.
% 7.33/7.63 Megabytes=11.28.
% 7.33/7.63 User_CPU=6.62, System_CPU=0.04, Wall_clock=7.
% 7.33/7.63
% 7.33/7.63 ============================== end of statistics =====================
% 7.33/7.63
% 7.33/7.63 ============================== end of search =========================
% 7.33/7.63
% 7.33/7.63 THEOREM PROVED
% 7.33/7.63 % SZS status Theorem
% 7.33/7.63
% 7.33/7.63 Exiting with 1 proof.
% 7.33/7.63
% 7.33/7.63 Process 4981 exit (max_proofs) Sat Jun 18 18:43:00 2022
% 7.33/7.63 Prover9 interrupted
%------------------------------------------------------------------------------