0.00/0.10	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.10	% Command    : tptp2X_and_run_prover9 %d %s
0.10/0.31	% Computer   : n023.cluster.edu
0.10/0.31	% Model      : x86_64 x86_64
0.10/0.31	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.10/0.31	% Memory     : 8042.1875MB
0.10/0.31	% OS         : Linux 3.10.0-693.el7.x86_64
0.10/0.31	% CPULimit   : 960
0.10/0.31	% DateTime   : Thu Jul  2 07:07:43 EDT 2020
0.10/0.31	% CPUTime    : 
0.73/1.06	============================== Prover9 ===============================
0.73/1.06	Prover9 (32) version 2009-11A, November 2009.
0.73/1.06	Process 19115 was started by sandbox2 on n023.cluster.edu,
0.73/1.06	Thu Jul  2 07:07:44 2020
0.73/1.06	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_18940_n023.cluster.edu".
0.73/1.06	============================== end of head ===========================
0.73/1.06	
0.73/1.06	============================== INPUT =================================
0.73/1.06	
0.73/1.06	% Reading from file /tmp/Prover9_18940_n023.cluster.edu
0.73/1.06	
0.73/1.06	set(prolog_style_variables).
0.73/1.06	set(auto2).
0.73/1.06	    % set(auto2) -> set(auto).
0.73/1.06	    % set(auto) -> set(auto_inference).
0.73/1.06	    % set(auto) -> set(auto_setup).
0.73/1.06	    % set(auto_setup) -> set(predicate_elim).
0.73/1.06	    % set(auto_setup) -> assign(eq_defs, unfold).
0.73/1.06	    % set(auto) -> set(auto_limits).
0.73/1.06	    % set(auto_limits) -> assign(max_weight, "100.000").
0.73/1.06	    % set(auto_limits) -> assign(sos_limit, 20000).
0.73/1.06	    % set(auto) -> set(auto_denials).
0.73/1.06	    % set(auto) -> set(auto_process).
0.73/1.06	    % set(auto2) -> assign(new_constants, 1).
0.73/1.06	    % set(auto2) -> assign(fold_denial_max, 3).
0.73/1.06	    % set(auto2) -> assign(max_weight, "200.000").
0.73/1.06	    % set(auto2) -> assign(max_hours, 1).
0.73/1.06	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.73/1.06	    % set(auto2) -> assign(max_seconds, 0).
0.73/1.06	    % set(auto2) -> assign(max_minutes, 5).
0.73/1.06	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.73/1.06	    % set(auto2) -> set(sort_initial_sos).
0.73/1.06	    % set(auto2) -> assign(sos_limit, -1).
0.73/1.06	    % set(auto2) -> assign(lrs_ticks, 3000).
0.73/1.06	    % set(auto2) -> assign(max_megs, 400).
0.73/1.06	    % set(auto2) -> assign(stats, some).
0.73/1.06	    % set(auto2) -> clear(echo_input).
0.73/1.06	    % set(auto2) -> set(quiet).
0.73/1.06	    % set(auto2) -> clear(print_initial_clauses).
0.73/1.06	    % set(auto2) -> clear(print_given).
0.73/1.06	assign(lrs_ticks,-1).
0.73/1.06	assign(sos_limit,10000).
0.73/1.06	assign(order,kbo).
0.73/1.06	set(lex_order_vars).
0.73/1.06	clear(print_given).
0.73/1.06	
0.73/1.06	% formulas(sos).  % not echoed (43 formulas)
0.73/1.06	
0.73/1.06	============================== end of input ==========================
0.73/1.06	
0.73/1.06	% From the command line: assign(max_seconds, 960).
0.73/1.06	
0.73/1.06	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.73/1.06	
0.73/1.06	% Formulas that are not ordinary clauses:
0.73/1.06	1 (all U all V (less_than(U,V) | less_than(V,U))) # label(totality) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	2 (all U less_than(bottom,U)) # label(bottom_smallest) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	3 (all U all V (-less_than(V,U) & less_than(U,V) <-> strictly_less_than(U,V))) # label(stricly_smaller_definition) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	4 (all U less_than(U,U)) # label(reflexivity) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	5 (all U all V all W (less_than(U,V) & less_than(V,W) -> less_than(U,W))) # label(transitivity) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	6 (all U -contains_slb(create_slb,U)) # label(ax20) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	7 (all U all V -pair_in_list(create_slb,U,V)) # label(ax22) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	8 (all U all V all W all X all Y (pair_in_list(insert_slb(U,pair(V,X)),W,Y) <-> Y = X & W = V | pair_in_list(U,W,Y))) # label(ax23) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	9 (all U all V all W all X (V = W | contains_slb(U,W) <-> contains_slb(insert_slb(U,pair(V,X)),W))) # label(ax21) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	10 (all U all V all W lookup_slb(insert_slb(U,pair(V,W)),V) = W) # label(ax26) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	11 (all U all V all W isnonempty_slb(insert_slb(U,pair(V,W)))) # label(ax19) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	12 (all U all V all W all X (strictly_less_than(X,W) -> insert_slb(update_slb(U,W),pair(V,W)) = update_slb(insert_slb(U,pair(V,X)),W))) # label(ax29) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	13 (all U update_slb(create_slb,U) = create_slb) # label(ax28) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	14 (all U all V all W all X (V != W & contains_slb(U,W) -> remove_slb(insert_slb(U,pair(V,X)),W) = insert_slb(remove_slb(U,W),pair(V,X)))) # label(ax25) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	15 (all U all V all W all X (less_than(W,X) -> update_slb(insert_slb(U,pair(V,X)),W) = insert_slb(update_slb(U,W),pair(V,X)))) # label(ax30) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	16 (all U all V all W remove_slb(insert_slb(U,pair(V,W)),V) = U) # label(ax24) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	17 (all U all V all W all X (V != W & contains_slb(U,W) -> lookup_slb(insert_slb(U,pair(V,X)),W) = lookup_slb(U,W))) # label(ax27) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	18 (all U all V check_cpq(triple(U,create_slb,V))) # label(ax36) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	19 (all U all V all W all X (contains_cpq(triple(U,V,W),X) <-> contains_slb(V,X))) # label(ax39) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	20 (all U all V (succ_cpq(U,V) -> succ_cpq(U,findmin_cpq_eff(V)))) # label(ax34) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	21 (all U all V all W (succ_cpq(U,V) -> succ_cpq(U,insert_cpq(V,W)))) # label(ax32) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	22 (all U findmin_cpq_res(U) = removemin_cpq_res(U)) # label(ax53) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	23 (all U all V all W all X (contains_slb(V,findmin_pqp_res(U)) & less_than(lookup_slb(V,findmin_pqp_res(U)),findmin_pqp_res(U)) & create_slb != V -> findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),W))) # label(ax49) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	24 (all U all V ($F <-> ok(triple(U,V,bad)))) # label(ax40) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	25 (all U all V all W all X (contains_slb(V,X) & less_than(lookup_slb(V,X),X) -> remove_cpq(triple(U,V,W),X) = triple(remove_pqp(U,X),remove_slb(V,X),W))) # label(ax44) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	26 (all U all V all W (succ_cpq(U,V) -> succ_cpq(U,remove_cpq(V,W)))) # label(ax33) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	27 (all U all V all W all X all Y (less_than(Y,X) -> (check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) <-> check_cpq(triple(U,V,W))))) # label(ax37) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	28 (all U all V all W (-ok(triple(U,V,W)) -> W = bad)) # label(ax41) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	29 (all U succ_cpq(U,U)) # label(ax31) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	30 (all U all V all W all X (-contains_slb(V,X) -> triple(U,V,bad) = remove_cpq(triple(U,V,W),X))) # label(ax43) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	31 (all U all V all W all X triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),W) = insert_cpq(triple(U,V,W),X)) # label(ax42) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	32 (all U all V all W all X (create_slb != V & strictly_less_than(findmin_pqp_res(U),lookup_slb(V,findmin_pqp_res(U))) & contains_slb(V,findmin_pqp_res(U)) -> findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),bad))) # label(ax48) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	33 (all U all V bottom = findmin_cpq_res(triple(U,create_slb,V))) # label(ax50) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	34 (all U all V triple(U,create_slb,bad) = findmin_cpq_eff(triple(U,create_slb,V))) # label(ax46) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	35 (all U all V all W all X all Y (strictly_less_than(X,Y) -> (check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) <-> $F))) # label(ax38) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	36 (all U all V (succ_cpq(U,V) -> succ_cpq(U,removemin_cpq_eff(V)))) # label(ax35) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	37 (all U removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U),findmin_cpq_res(U))) # label(ax52) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	38 (all U all V all W all X (V != create_slb -> findmin_cpq_res(triple(U,V,W)) = findmin_pqp_res(U))) # label(ax51) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	39 (all U all V all W all X (-contains_slb(V,findmin_pqp_res(U)) & V != create_slb -> findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),bad))) # label(ax47) # label(axiom) # label(non_clause).  [assumption].
0.78/1.09	40 (all U all V all W all X (contains_slb(V,X) & strictly_less_than(X,lookup_slb(V,X)) -> remove_cpq(triple(U,V,W),X) = triple(remove_pqp(U,X),remove_slb(V,X),bad))) # label(ax45) # label(axiom) # label(non_clause).  [assumption].
0.78/1.09	41 (all U all V all W (check_cpq(triple(U,V,W)) <-> (all X all Y (pair_in_list(V,X,Y) -> less_than(Y,X))))) # label(l26_li4142) # label(lemma) # label(non_clause).  [assumption].
0.78/1.09	42 -(all U all V all W (-check_cpq(triple(U,V,W)) -> (all X -check_cpq(insert_cpq(triple(U,V,W),X))))) # label(l26_co) # label(negated_conjecture) # label(non_clause).  [assumption].
0.78/1.09	
0.78/1.09	============================== end of process non-clausal formulas ===
0.78/1.09	
0.78/1.09	============================== PROCESS INITIAL CLAUSES ===============
0.78/1.09	
0.78/1.09	============================== PREDICATE ELIMINATION =================
0.78/1.09	
0.78/1.09	============================== end predicate elimination =============
0.78/1.09	
0.78/1.09	Auto_denials:  (non-Horn, no changes).
0.78/1.09	
0.78/1.09	Term ordering decisions:
0.78/1.09	Function symbol KB weights:  create_slb=1. bad=1. bottom=1. c1=1. c2=1. c3=1. c4=1. insert_slb=1. pair=1. update_slb=1. lookup_slb=1. remove_cpq=1. remove_slb=1. insert_cpq=1. remove_pqp=1. insert_pqp=1. findmin_pqp_res=1. findmin_cpq_eff=1. findmin_cpq_res=1. removemin_cpq_eff=1. removemin_cpq_res=1. triple=1. f1=1. f2=1.
0.78/1.09	
0.78/1.09	============================== end of process initial clauses ========
0.78/1.09	
0.78/1.09	============================== CLAUSES FOR SEARCH ====================
0.78/1.09	
0.78/1.09	============================== end of clauses for search =============
0.78/1.09	
0.78/1.09	============================== SEARCH ================================
0.78/1.09	
0.78/1.09	% Starting search at 0.01 seconds.
0.78/1.09	
0.78/1.09	============================== PROOF =================================
0.78/1.09	% SZS status Theorem
0.78/1.09	% SZS output start Refutation
0.78/1.09	
0.78/1.09	% Proof 1 at 0.03 (+ 0.00) seconds.
0.78/1.09	% Length of proof is 20.
0.78/1.09	% Level of proof is 6.
0.78/1.09	% Maximum clause weight is 19.000.
0.78/1.09	% Given clauses 176.
0.78/1.09	
0.78/1.09	2 (all U less_than(bottom,U)) # label(bottom_smallest) # label(axiom) # label(non_clause).  [assumption].
0.78/1.09	27 (all U all V all W all X all Y (less_than(Y,X) -> (check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) <-> check_cpq(triple(U,V,W))))) # label(ax37) # label(axiom) # label(non_clause).  [assumption].
0.78/1.09	31 (all U all V all W all X triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),W) = insert_cpq(triple(U,V,W),X)) # label(ax42) # label(axiom) # label(non_clause).  [assumption].
0.78/1.09	41 (all U all V all W (check_cpq(triple(U,V,W)) <-> (all X all Y (pair_in_list(V,X,Y) -> less_than(Y,X))))) # label(l26_li4142) # label(lemma) # label(non_clause).  [assumption].
0.78/1.09	42 -(all U all V all W (-check_cpq(triple(U,V,W)) -> (all X -check_cpq(insert_cpq(triple(U,V,W),X))))) # label(l26_co) # label(negated_conjecture) # label(non_clause).  [assumption].
0.78/1.09	43 less_than(bottom,A) # label(bottom_smallest) # label(axiom).  [clausify(2)].
0.78/1.09	52 check_cpq(insert_cpq(triple(c1,c2,c3),c4)) # label(l26_co) # label(negated_conjecture).  [clausify(42)].
0.78/1.09	61 check_cpq(triple(A,B,C)) | pair_in_list(B,f1(A,B,C),f2(A,B,C)) # label(l26_li4142) # label(lemma).  [clausify(41)].
0.78/1.09	62 insert_cpq(triple(A,B,C),D) = triple(insert_pqp(A,D),insert_slb(B,pair(D,bottom)),C) # label(ax42) # label(axiom).  [clausify(31)].
0.78/1.09	63 triple(insert_pqp(A,B),insert_slb(C,pair(B,bottom)),D) = insert_cpq(triple(A,C,D),B).  [copy(62),flip(a)].
0.78/1.09	69 -check_cpq(triple(c1,c2,c3)) # label(l26_co) # label(negated_conjecture).  [clausify(42)].
0.78/1.09	85 -check_cpq(triple(A,B,C)) | -pair_in_list(B,D,E) | less_than(E,D) # label(l26_li4142) # label(lemma).  [clausify(41)].
0.78/1.09	88 check_cpq(triple(A,B,C)) | -less_than(f2(A,B,C),f1(A,B,C)) # label(l26_li4142) # label(lemma).  [clausify(41)].
0.78/1.09	92 -less_than(A,B) | -check_cpq(triple(C,insert_slb(D,pair(B,A)),E)) | check_cpq(triple(C,D,E)) # label(ax37) # label(axiom).  [clausify(27)].
0.78/1.09	130 -check_cpq(triple(A,B,C)) | less_than(f2(D,B,E),f1(D,B,E)) | check_cpq(triple(D,B,E)).  [resolve(85,b,61,b)].
0.78/1.09	153 -check_cpq(triple(c1,insert_slb(c2,pair(A,bottom)),c3)).  [ur(92,a,43,a,c,69,a)].
0.78/1.09	209 -less_than(f2(c1,insert_slb(c2,pair(A,bottom)),c3),f1(c1,insert_slb(c2,pair(A,bottom)),c3)).  [ur(88,a,153,a)].
0.78/1.09	577 -check_cpq(triple(A,insert_slb(c2,pair(B,bottom)),C)).  [ur(130,b,209,a,c,153,a)].
0.78/1.09	587 -check_cpq(insert_cpq(triple(A,c2,B),C)).  [para(63(a,1),577(a,1))].
0.78/1.09	588 $F.  [resolve(587,a,52,a)].
0.78/1.09	
0.78/1.09	% SZS output end Refutation
0.78/1.09	============================== end of proof ==========================
0.78/1.09	
0.78/1.09	============================== STATISTICS ============================
0.78/1.09	
0.78/1.09	Given=176. Generated=849. Kept=540. proofs=1.
0.78/1.09	Usable=170. Sos=330. Demods=12. Limbo=4, Disabled=90. Hints=0.
0.78/1.09	Megabytes=0.88.
0.78/1.09	User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
0.78/1.09	
0.78/1.09	============================== end of statistics =====================
0.78/1.09	
0.78/1.09	============================== end of search =========================
0.78/1.09	
0.78/1.09	THEOREM PROVED
0.78/1.09	% SZS status Theorem
0.78/1.09	
0.78/1.09	Exiting with 1 proof.
0.78/1.09	
0.78/1.09	Process 19115 exit (max_proofs) Thu Jul  2 07:07:44 2020
0.78/1.09	Prover9 interrupted
0.78/1.09	EOF