TSTP Solution File: ANA002-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : ANA002-2 : TPTP v8.1.0. Bugfixed v1.0.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.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 : Thu Jul 14 19:21:15 EDT 2022
% Result : Unsatisfiable 2.65s 2.93s
% Output : Refutation 2.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ANA002-2 : TPTP v8.1.0. Bugfixed v1.0.1.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.33 % Computer : n017.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Fri Jul 8 03:36:15 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.63/0.89 ============================== Prover9 ===============================
% 0.63/0.89 Prover9 (32) version 2009-11A, November 2009.
% 0.63/0.89 Process 23880 was started by sandbox on n017.cluster.edu,
% 0.63/0.89 Fri Jul 8 03:36:16 2022
% 0.63/0.89 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_23727_n017.cluster.edu".
% 0.63/0.89 ============================== end of head ===========================
% 0.63/0.89
% 0.63/0.89 ============================== INPUT =================================
% 0.63/0.89
% 0.63/0.89 % Reading from file /tmp/Prover9_23727_n017.cluster.edu
% 0.63/0.89
% 0.63/0.89 set(prolog_style_variables).
% 0.63/0.89 set(auto2).
% 0.63/0.89 % set(auto2) -> set(auto).
% 0.63/0.89 % set(auto) -> set(auto_inference).
% 0.63/0.89 % set(auto) -> set(auto_setup).
% 0.63/0.89 % set(auto_setup) -> set(predicate_elim).
% 0.63/0.89 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.63/0.89 % set(auto) -> set(auto_limits).
% 0.63/0.89 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.63/0.89 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.63/0.89 % set(auto) -> set(auto_denials).
% 0.63/0.89 % set(auto) -> set(auto_process).
% 0.63/0.89 % set(auto2) -> assign(new_constants, 1).
% 0.63/0.89 % set(auto2) -> assign(fold_denial_max, 3).
% 0.63/0.89 % set(auto2) -> assign(max_weight, "200.000").
% 0.63/0.89 % set(auto2) -> assign(max_hours, 1).
% 0.63/0.89 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.63/0.89 % set(auto2) -> assign(max_seconds, 0).
% 0.63/0.89 % set(auto2) -> assign(max_minutes, 5).
% 0.63/0.89 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.63/0.89 % set(auto2) -> set(sort_initial_sos).
% 0.63/0.89 % set(auto2) -> assign(sos_limit, -1).
% 0.63/0.89 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.63/0.89 % set(auto2) -> assign(max_megs, 400).
% 0.63/0.89 % set(auto2) -> assign(stats, some).
% 0.63/0.89 % set(auto2) -> clear(echo_input).
% 0.63/0.89 % set(auto2) -> set(quiet).
% 0.63/0.89 % set(auto2) -> clear(print_initial_clauses).
% 0.63/0.89 % set(auto2) -> clear(print_given).
% 0.63/0.89 assign(lrs_ticks,-1).
% 0.63/0.89 assign(sos_limit,10000).
% 0.63/0.89 assign(order,kbo).
% 0.63/0.89 set(lex_order_vars).
% 0.63/0.89 clear(print_given).
% 0.63/0.89
% 0.63/0.89 % formulas(sos). % not echoed (18 formulas)
% 0.63/0.89
% 0.63/0.89 ============================== end of input ==========================
% 0.63/0.89
% 0.63/0.89 % From the command line: assign(max_seconds, 300).
% 0.63/0.89
% 0.63/0.89 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.63/0.89
% 0.63/0.89 % Formulas that are not ordinary clauses:
% 0.63/0.89
% 0.63/0.89 ============================== end of process non-clausal formulas ===
% 0.63/0.89
% 0.63/0.89 ============================== PROCESS INITIAL CLAUSES ===============
% 0.63/0.89
% 0.63/0.89 ============================== PREDICATE ELIMINATION =================
% 0.63/0.89 1 in_interval(A,B,C) | -less_than_or_equal(A,B) | -less_than_or_equal(B,C) # label(in_interval) # label(axiom). [assumption].
% 0.63/0.89 2 -in_interval(f(l),n0,f(l)) # label(prove_there_is_x_which_crosses) # label(negated_conjecture). [assumption].
% 0.63/0.89 Derived: -less_than_or_equal(f(l),n0) | -less_than_or_equal(n0,f(l)). [resolve(1,a,2,a)].
% 0.63/0.89 3 less_than_or_equal(f(A),n0) | -less_than_or_equal(A,h(A)) | -in_interval(lower_bound,A,upper_bound) # label(continuity1) # label(axiom). [assumption].
% 0.63/0.89 Derived: less_than_or_equal(f(A),n0) | -less_than_or_equal(A,h(A)) | -less_than_or_equal(lower_bound,A) | -less_than_or_equal(A,upper_bound). [resolve(3,c,1,a)].
% 0.63/0.89 4 less_than_or_equal(n0,f(A)) | -less_than_or_equal(k(A),A) | -in_interval(lower_bound,A,upper_bound) # label(continuity3) # label(axiom). [assumption].
% 0.63/0.89 Derived: less_than_or_equal(n0,f(A)) | -less_than_or_equal(k(A),A) | -less_than_or_equal(lower_bound,A) | -less_than_or_equal(A,upper_bound). [resolve(4,c,1,a)].
% 0.63/0.89 5 less_than_or_equal(f(A),n0) | -less_than_or_equal(B,A) | -less_than_or_equal(f(B),n0) | less_than_or_equal(B,h(A)) | -in_interval(lower_bound,A,upper_bound) # label(continuity2) # label(axiom). [assumption].
% 0.63/0.89 Derived: less_than_or_equal(f(A),n0) | -less_than_or_equal(B,A) | -less_than_or_equal(f(B),n0) | less_than_or_equal(B,h(A)) | -less_than_or_equal(lower_bound,A) | -less_than_or_equal(A,upper_bound). [resolve(5,e,1,a)].
% 0.63/0.89 6 less_than_or_equal(n0,f(A)) | -less_than_or_equal(A,B) | -less_than_or_equal(n0,f(B)) | less_than_or_equal(k(A),B) | -in_interval(lower_bound,A,upper_bound) # label(continuity4) # label(axiom). [assumption].
% 0.63/0.89 Derived: less_than_or_equal(n0,f(A)) | -less_than_or_equal(A,B) | -less_than_or_equal(n0,f(B)) | less_than_or_equal(k(A),B) | -less_than_or_equal(lower_bound,A) | -less_than_or_equal(A,upper_bound). [resolve(6,e,1,a)].
% 2.65/2.93
% 2.65/2.93 ============================== end predicate elimination =============
% 2.65/2.93
% 2.65/2.93 Auto_denials: (non-Horn, no changes).
% 2.65/2.93
% 2.65/2.93 Term ordering decisions:
% 2.65/2.93 Function symbol KB weights: n0=1. upper_bound=1. lower_bound=1. l=1. q=1. f=1. g=1. h=1. k=1.
% 2.65/2.93
% 2.65/2.93 ============================== end of process initial clauses ========
% 2.65/2.93
% 2.65/2.93 ============================== CLAUSES FOR SEARCH ====================
% 2.65/2.93
% 2.65/2.93 ============================== end of clauses for search =============
% 2.65/2.93
% 2.65/2.93 ============================== SEARCH ================================
% 2.65/2.93
% 2.65/2.93 % Starting search at 0.01 seconds.
% 2.65/2.93
% 2.65/2.93 Low Water (keep): wt=36.000, iters=3333
% 2.65/2.93
% 2.65/2.93 Low Water (keep): wt=34.000, iters=3336
% 2.65/2.93
% 2.65/2.93 Low Water (keep): wt=30.000, iters=3336
% 2.65/2.93
% 2.65/2.93 Low Water (keep): wt=29.000, iters=3394
% 2.65/2.93
% 2.65/2.93 Low Water (keep): wt=28.000, iters=3344
% 2.65/2.93
% 2.65/2.93 Low Water (keep): wt=27.000, iters=3339
% 2.65/2.93
% 2.65/2.93 Low Water (keep): wt=26.000, iters=3341
% 2.65/2.93
% 2.65/2.93 Low Water (keep): wt=21.000, iters=3366
% 2.65/2.93
% 2.65/2.93 ============================== PROOF =================================
% 2.65/2.93 % SZS status Unsatisfiable
% 2.65/2.93 % SZS output start Refutation
% 2.65/2.93
% 2.65/2.93 % Proof 1 at 2.01 (+ 0.03) seconds.
% 2.65/2.93 % Length of proof is 51.
% 2.65/2.93 % Level of proof is 16.
% 2.65/2.93 % Maximum clause weight is 22.000.
% 2.65/2.93 % Given clauses 564.
% 2.65/2.93
% 2.65/2.93 1 in_interval(A,B,C) | -less_than_or_equal(A,B) | -less_than_or_equal(B,C) # label(in_interval) # label(axiom). [assumption].
% 2.65/2.93 2 -in_interval(f(l),n0,f(l)) # label(prove_there_is_x_which_crosses) # label(negated_conjecture). [assumption].
% 2.65/2.93 3 less_than_or_equal(f(A),n0) | -less_than_or_equal(A,h(A)) | -in_interval(lower_bound,A,upper_bound) # label(continuity1) # label(axiom). [assumption].
% 2.65/2.93 4 less_than_or_equal(n0,f(A)) | -less_than_or_equal(k(A),A) | -in_interval(lower_bound,A,upper_bound) # label(continuity3) # label(axiom). [assumption].
% 2.65/2.93 5 less_than_or_equal(f(A),n0) | -less_than_or_equal(B,A) | -less_than_or_equal(f(B),n0) | less_than_or_equal(B,h(A)) | -in_interval(lower_bound,A,upper_bound) # label(continuity2) # label(axiom). [assumption].
% 2.65/2.93 6 less_than_or_equal(n0,f(A)) | -less_than_or_equal(A,B) | -less_than_or_equal(n0,f(B)) | less_than_or_equal(k(A),B) | -in_interval(lower_bound,A,upper_bound) # label(continuity4) # label(axiom). [assumption].
% 2.65/2.93 8 less_than_or_equal(lower_bound,upper_bound) # label(the_interval) # label(hypothesis). [assumption].
% 2.65/2.93 9 less_than_or_equal(f(lower_bound),n0) # label(lower_mapping) # label(hypothesis). [assumption].
% 2.65/2.93 10 less_than_or_equal(n0,f(upper_bound)) # label(upper_mapping) # label(hypothesis). [assumption].
% 2.65/2.93 11 less_than_or_equal(A,B) | less_than_or_equal(B,A) # label(totality_of_less) # label(axiom). [assumption].
% 2.65/2.93 12 less_than_or_equal(g(A),upper_bound) | less_than_or_equal(l,A) # label(crossover2_and_g_function1) # label(axiom). [assumption].
% 2.65/2.93 13 less_than_or_equal(f(g(A)),n0) | less_than_or_equal(l,A) # label(crossover3_and_g_function2) # label(axiom). [assumption].
% 2.65/2.93 14 -less_than_or_equal(g(A),A) | less_than_or_equal(l,A) # label(crossover4_and_g_function3) # label(axiom). [assumption].
% 2.65/2.93 15 -less_than_or_equal(A,q(B,A)) | less_than_or_equal(A,B) # label(interpolation1) # label(axiom). [assumption].
% 2.65/2.93 16 -less_than_or_equal(q(A,B),A) | less_than_or_equal(B,A) # label(interpolation2) # label(axiom). [assumption].
% 2.65/2.93 17 less_than_or_equal(A,B) | -less_than_or_equal(A,C) | -less_than_or_equal(C,B) # label(transitivity_of_less) # label(axiom). [assumption].
% 2.65/2.93 18 less_than_or_equal(A,l) | -less_than_or_equal(A,upper_bound) | -less_than_or_equal(f(A),n0) # label(crossover1) # label(axiom). [assumption].
% 2.65/2.93 19 -less_than_or_equal(f(l),n0) | -less_than_or_equal(n0,f(l)). [resolve(1,a,2,a)].
% 2.65/2.93 20 less_than_or_equal(f(A),n0) | -less_than_or_equal(A,h(A)) | -less_than_or_equal(lower_bound,A) | -less_than_or_equal(A,upper_bound). [resolve(3,c,1,a)].
% 2.65/2.93 21 less_than_or_equal(n0,f(A)) | -less_than_or_equal(k(A),A) | -less_than_or_equal(lower_bound,A) | -less_than_or_equal(A,upper_bound). [resolve(4,c,1,a)].
% 2.65/2.93 22 less_than_or_equal(f(A),n0) | -less_than_or_equal(B,A) | -less_than_or_equal(f(B),n0) | less_than_or_equal(B,h(A)) | -less_than_or_equal(lower_bound,A) | -less_than_or_equal(A,upper_bound). [resolve(5,e,1,a)].
% 2.65/2.93 23 less_than_or_equal(n0,f(A)) | -less_than_or_equal(A,B) | -less_than_or_equal(n0,f(B)) | less_than_or_equal(k(A),B) | -less_than_or_equal(lower_bound,A) | -less_than_or_equal(A,upper_bound). [resolve(6,e,1,a)].
% 2.65/2.93 25 less_than_or_equal(n0,f(A)) | -less_than_or_equal(A,upper_bound) | less_than_or_equal(k(A),upper_bound) | -less_than_or_equal(lower_bound,A). [factor(23,b,f),unit_del(c,10)].
% 2.65/2.93 26 less_than_or_equal(l,upper_bound). [resolve(14,a,12,a),merge(b)].
% 2.65/2.93 32 less_than_or_equal(A,B) | -less_than_or_equal(C,B) | less_than_or_equal(C,A). [resolve(17,b,11,b)].
% 2.65/2.93 42 less_than_or_equal(g(A),l) | -less_than_or_equal(g(A),upper_bound) | less_than_or_equal(l,A). [resolve(18,c,13,a)].
% 2.65/2.93 43 less_than_or_equal(A,l) | -less_than_or_equal(A,upper_bound) | less_than_or_equal(n0,f(A)). [resolve(18,c,11,b)].
% 2.65/2.93 44 less_than_or_equal(lower_bound,l). [resolve(18,c,9,a),unit_del(b,8)].
% 2.65/2.93 53 less_than_or_equal(f(A),n0) | -less_than_or_equal(g(B),A) | less_than_or_equal(g(B),h(A)) | -less_than_or_equal(lower_bound,A) | -less_than_or_equal(A,upper_bound) | less_than_or_equal(l,B). [resolve(22,c,13,a)].
% 2.65/2.93 68 less_than_or_equal(n0,f(A)) | -less_than_or_equal(A,B) | -less_than_or_equal(n0,f(B)) | less_than_or_equal(k(A),B) | -less_than_or_equal(lower_bound,A) | less_than_or_equal(upper_bound,A). [resolve(23,f,11,b)].
% 2.65/2.93 73 less_than_or_equal(n0,f(l)) | less_than_or_equal(k(l),upper_bound). [resolve(26,a,25,b),unit_del(c,44)].
% 2.65/2.93 311 less_than_or_equal(g(A),l) | less_than_or_equal(l,A). [resolve(42,b,12,a),merge(c)].
% 2.65/2.93 711 less_than_or_equal(f(l),n0) | less_than_or_equal(g(A),h(l)) | less_than_or_equal(l,A). [resolve(53,b,311,a),merge(f),unit_del(c,44),unit_del(d,26)].
% 2.65/2.93 7441 less_than_or_equal(f(l),n0) | less_than_or_equal(l,h(l)). [resolve(711,b,14,a),merge(c)].
% 2.65/2.93 7474 less_than_or_equal(l,h(l)) | less_than_or_equal(A,n0) | less_than_or_equal(f(l),A). [resolve(7441,a,32,b)].
% 2.65/2.93 7650 less_than_or_equal(A,n0) | less_than_or_equal(f(l),A) | less_than_or_equal(f(l),n0). [resolve(7474,a,20,b),unit_del(d,44),unit_del(e,26)].
% 2.65/2.93 7966 less_than_or_equal(A,n0) | less_than_or_equal(f(l),A) | less_than_or_equal(B,n0) | less_than_or_equal(f(l),B). [resolve(7650,c,32,b)].
% 2.65/2.93 8004 less_than_or_equal(A,n0) | less_than_or_equal(f(l),A). [factor(7966,a,c),merge(c)].
% 2.65/2.93 8073 less_than_or_equal(q(A,f(l)),n0) | less_than_or_equal(f(l),A). [resolve(8004,b,15,a)].
% 2.65/2.93 8607 less_than_or_equal(f(l),n0). [resolve(8073,a,16,a),merge(b)].
% 2.65/2.93 8634 -less_than_or_equal(n0,f(l)). [back_unit_del(19),unit_del(a,8607)].
% 2.65/2.93 8847 less_than_or_equal(k(l),upper_bound). [back_unit_del(73),unit_del(a,8634)].
% 2.65/2.93 8878 -less_than_or_equal(k(l),l). [ur(21,a,8634,a,c,44,a,d,26,a)].
% 2.65/2.93 8886 -less_than_or_equal(q(l,k(l)),l). [ur(16,b,8878,a)].
% 2.65/2.93 8887 -less_than_or_equal(k(l),q(l,k(l))). [ur(15,b,8878,a)].
% 2.65/2.93 8920 -less_than_or_equal(upper_bound,l). [ur(17,a,8878,a,b,8847,a)].
% 2.65/2.93 9452 less_than_or_equal(l,q(l,k(l))). [resolve(8886,a,11,b)].
% 2.65/2.93 9725 -less_than_or_equal(n0,f(q(l,k(l)))). [resolve(9452,a,68,b),unit_del(a,8634),unit_del(c,8887),unit_del(d,44),unit_del(e,8920)].
% 2.65/2.93 9770 -less_than_or_equal(upper_bound,q(l,k(l))). [ur(17,a,8887,a,b,8847,a)].
% 2.65/2.93 9780 less_than_or_equal(q(l,k(l)),upper_bound). [resolve(9770,a,11,b)].
% 2.65/2.93 9939 $F. [resolve(9780,a,43,b),unit_del(a,8886),unit_del(b,9725)].
% 2.65/2.93
% 2.65/2.93 % SZS output end Refutation
% 2.65/2.93 ============================== end of proof ==========================
% 2.65/2.93
% 2.65/2.93 ============================== STATISTICS ============================
% 2.65/2.93
% 2.65/2.93 Given=564. Generated=44390. Kept=9932. proofs=1.
% 2.65/2.93 Usable=426. Sos=5643. Demods=0. Limbo=9, Disabled=3877. Hints=0.
% 2.65/2.93 Megabytes=8.53.
% 2.65/2.93 User_CPU=2.01, System_CPU=0.03, Wall_clock=2.
% 2.65/2.93
% 2.65/2.93 ============================== end of statistics =====================
% 2.65/2.93
% 2.65/2.93 ============================== end of search =========================
% 2.65/2.93
% 2.65/2.93 THEOREM PROVED
% 2.65/2.93 % SZS status Unsatisfiable
% 2.65/2.93
% 2.65/2.93 Exiting with 1 proof.
% 2.65/2.93
% 2.65/2.93 Process 23880 exit (max_proofs) Fri Jul 8 03:36:18 2022
% 2.65/2.93 Prover9 interrupted
%------------------------------------------------------------------------------