0.06/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.06/0.12	% Command    : tptp2X_and_run_prover9 %d %s
0.12/0.33	% Computer   : n016.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   : 1200
0.12/0.33	% DateTime   : Wed Jul 14 14:18:22 EDT 2021
0.12/0.33	% CPUTime    : 
0.71/1.02	============================== Prover9 ===============================
0.71/1.02	Prover9 (32) version 2009-11A, November 2009.
0.71/1.02	Process 32382 was started by sandbox on n016.cluster.edu,
0.71/1.02	Wed Jul 14 14:18:23 2021
0.71/1.02	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1200 -f /tmp/Prover9_32209_n016.cluster.edu".
0.71/1.02	============================== end of head ===========================
0.71/1.02	
0.71/1.02	============================== INPUT =================================
0.71/1.02	
0.71/1.02	% Reading from file /tmp/Prover9_32209_n016.cluster.edu
0.71/1.02	
0.71/1.02	set(prolog_style_variables).
0.71/1.02	set(auto2).
0.71/1.02	    % set(auto2) -> set(auto).
0.71/1.02	    % set(auto) -> set(auto_inference).
0.71/1.02	    % set(auto) -> set(auto_setup).
0.71/1.02	    % set(auto_setup) -> set(predicate_elim).
0.71/1.02	    % set(auto_setup) -> assign(eq_defs, unfold).
0.71/1.02	    % set(auto) -> set(auto_limits).
0.71/1.02	    % set(auto_limits) -> assign(max_weight, "100.000").
0.71/1.02	    % set(auto_limits) -> assign(sos_limit, 20000).
0.71/1.02	    % set(auto) -> set(auto_denials).
0.71/1.02	    % set(auto) -> set(auto_process).
0.71/1.02	    % set(auto2) -> assign(new_constants, 1).
0.71/1.02	    % set(auto2) -> assign(fold_denial_max, 3).
0.71/1.02	    % set(auto2) -> assign(max_weight, "200.000").
0.71/1.02	    % set(auto2) -> assign(max_hours, 1).
0.71/1.02	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.71/1.02	    % set(auto2) -> assign(max_seconds, 0).
0.71/1.02	    % set(auto2) -> assign(max_minutes, 5).
0.71/1.02	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.71/1.02	    % set(auto2) -> set(sort_initial_sos).
0.71/1.02	    % set(auto2) -> assign(sos_limit, -1).
0.71/1.02	    % set(auto2) -> assign(lrs_ticks, 3000).
0.71/1.02	    % set(auto2) -> assign(max_megs, 400).
0.71/1.02	    % set(auto2) -> assign(stats, some).
0.71/1.02	    % set(auto2) -> clear(echo_input).
0.71/1.02	    % set(auto2) -> set(quiet).
0.71/1.02	    % set(auto2) -> clear(print_initial_clauses).
0.71/1.02	    % set(auto2) -> clear(print_given).
0.71/1.02	assign(lrs_ticks,-1).
0.71/1.02	assign(sos_limit,10000).
0.71/1.02	assign(order,kbo).
0.71/1.02	set(lex_order_vars).
0.71/1.02	clear(print_given).
0.71/1.02	
0.71/1.02	% formulas(sos).  % not echoed (43 formulas)
0.71/1.02	
0.71/1.02	============================== end of input ==========================
0.71/1.02	
0.71/1.02	% From the command line: assign(max_seconds, 1200).
0.71/1.02	
0.71/1.02	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.71/1.02	
0.71/1.02	% Formulas that are not ordinary clauses:
0.71/1.02	1 (all U less_than(U,U)) # label(reflexivity) # label(axiom) # label(non_clause).  [assumption].
0.71/1.02	2 (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].
0.71/1.02	3 (all U all V (strictly_less_than(U,V) <-> less_than(U,V) & -less_than(V,U))) # label(stricly_smaller_definition) # label(axiom) # label(non_clause).  [assumption].
0.71/1.02	4 (all U all V (less_than(V,U) | less_than(U,V))) # label(totality) # label(axiom) # label(non_clause).  [assumption].
0.71/1.02	5 (all U less_than(bottom,U)) # label(bottom_smallest) # label(axiom) # label(non_clause).  [assumption].
0.71/1.02	6 (all U all V all W all X (contains_slb(U,W) & V != W -> insert_slb(remove_slb(U,W),pair(V,X)) = remove_slb(insert_slb(U,pair(V,X)),W))) # label(ax25) # label(axiom) # label(non_clause).  [assumption].
0.71/1.02	7 (all U all V all W W = lookup_slb(insert_slb(U,pair(V,W)),V)) # label(ax26) # label(axiom) # label(non_clause).  [assumption].
0.71/1.02	8 (all U all V -pair_in_list(create_slb,U,V)) # label(ax22) # label(axiom) # label(non_clause).  [assumption].
0.71/1.02	9 (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].
0.71/1.02	10 (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].
0.71/1.02	11 (all U update_slb(create_slb,U) = create_slb) # label(ax28) # label(axiom) # label(non_clause).  [assumption].
0.71/1.02	12 (all U all V all W isnonempty_slb(insert_slb(U,pair(V,W)))) # label(ax19) # label(axiom) # label(non_clause).  [assumption].
0.71/1.02	13 (all U all V all W all X all Y (pair_in_list(U,W,Y) | W = V & Y = X <-> pair_in_list(insert_slb(U,pair(V,X)),W,Y))) # label(ax23) # label(axiom) # label(non_clause).  [assumption].
0.71/1.02	14 (all U all V all W remove_slb(insert_slb(U,pair(V,W)),V) = U) # label(ax24) # label(axiom) # label(non_clause).  [assumption].
0.71/1.02	15 (all U all V all W all X (W = V | contains_slb(U,W) <-> contains_slb(insert_slb(U,pair(V,X)),W))) # label(ax21) # label(axiom) # label(non_clause).  [assumption].
0.71/1.02	16 (all U -contains_slb(create_slb,U)) # label(ax20) # label(axiom) # label(non_clause).  [assumption].
0.71/1.02	17 (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].
0.71/1.02	18 (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].
0.71/1.02	19 (all U all V bottom = findmin_cpq_res(triple(U,create_slb,V))) # label(ax50) # label(axiom) # label(non_clause).  [assumption].
0.71/1.02	20 (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].
0.71/1.02	21 (all U all V all W (-ok(triple(U,V,W)) -> bad = W)) # label(ax41) # label(axiom) # label(non_clause).  [assumption].
0.71/1.02	22 (all U all V findmin_cpq_eff(triple(U,create_slb,V)) = triple(U,create_slb,bad)) # label(ax46) # label(axiom) # label(non_clause).  [assumption].
0.71/1.02	23 (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].
0.71/1.02	24 (all U succ_cpq(U,U)) # label(ax31) # label(axiom) # label(non_clause).  [assumption].
0.71/1.02	25 (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)) <-> $F))) # label(ax38) # label(axiom) # label(non_clause).  [assumption].
0.71/1.02	26 (all U all V ($F <-> ok(triple(U,V,bad)))) # label(ax40) # label(axiom) # label(non_clause).  [assumption].
0.71/1.02	27 (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].
0.71/1.02	28 (all U all V all W all X (strictly_less_than(findmin_pqp_res(U),lookup_slb(V,findmin_pqp_res(U))) & contains_slb(V,findmin_pqp_res(U)) & V != create_slb -> triple(U,update_slb(V,findmin_pqp_res(U)),bad) = findmin_cpq_eff(triple(U,V,W)))) # label(ax48) # label(axiom) # label(non_clause).  [assumption].
0.71/1.02	29 (all U all V check_cpq(triple(U,create_slb,V))) # label(ax36) # label(axiom) # label(non_clause).  [assumption].
0.71/1.02	30 (all U all V all W all X all Y (less_than(Y,X) -> (check_cpq(triple(U,V,W)) <-> check_cpq(triple(U,insert_slb(V,pair(X,Y)),W))))) # label(ax37) # label(axiom) # label(non_clause).  [assumption].
0.71/1.02	31 (all U all V all W all X (contains_slb(V,X) <-> contains_cpq(triple(U,V,W),X))) # label(ax39) # label(axiom) # label(non_clause).  [assumption].
0.71/1.02	32 (all U removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U),findmin_cpq_res(U))) # label(ax52) # label(axiom) # label(non_clause).  [assumption].
0.71/1.02	33 (all U all V (succ_cpq(U,V) -> succ_cpq(U,findmin_cpq_eff(V)))) # label(ax34) # label(axiom) # label(non_clause).  [assumption].
0.71/1.02	34 (all U all V all W all X (strictly_less_than(X,lookup_slb(V,X)) & contains_slb(V,X) -> triple(remove_pqp(U,X),remove_slb(V,X),bad) = remove_cpq(triple(U,V,W),X))) # label(ax45) # label(axiom) # label(non_clause).  [assumption].
0.71/1.02	35 (all U all V all W all X (less_than(lookup_slb(V,X),X) & contains_slb(V,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].
0.71/1.02	36 (all U all V (succ_cpq(U,V) -> succ_cpq(U,removemin_cpq_eff(V)))) # label(ax35) # label(axiom) # label(non_clause).  [assumption].
0.71/1.02	37 (all U all V all W all X (create_slb != V -> findmin_cpq_res(triple(U,V,W)) = findmin_pqp_res(U))) # label(ax51) # label(axiom) # label(non_clause).  [assumption].
0.71/1.02	38 (all U removemin_cpq_res(U) = findmin_cpq_res(U)) # label(ax53) # label(axiom) # label(non_clause).  [assumption].
0.71/1.02	39 (all U all V all W all X (create_slb != V & -contains_slb(V,findmin_pqp_res(U)) -> triple(U,update_slb(V,findmin_pqp_res(U)),bad) = findmin_cpq_eff(triple(U,V,W)))) # label(ax47) # label(axiom) # label(non_clause).  [assumption].
0.71/1.02	40 (all U all V all W all X (less_than(lookup_slb(V,findmin_pqp_res(U)),findmin_pqp_res(U)) & contains_slb(V,findmin_pqp_res(U)) & V != create_slb -> triple(U,update_slb(V,findmin_pqp_res(U)),W) = findmin_cpq_eff(triple(U,V,W)))) # label(ax49) # label(axiom) # label(non_clause).  [assumption].
0.71/1.08	41 (all U all V all W ((all X all Y (pair_in_list(V,X,Y) -> less_than(Y,X))) <-> check_cpq(triple(U,V,W)))) # label(l26_li4142) # label(lemma) # label(non_clause).  [assumption].
0.71/1.08	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].
0.71/1.08	
0.71/1.08	============================== end of process non-clausal formulas ===
0.71/1.08	
0.71/1.08	============================== PROCESS INITIAL CLAUSES ===============
0.71/1.08	
0.71/1.08	============================== PREDICATE ELIMINATION =================
0.71/1.08	
0.71/1.08	============================== end predicate elimination =============
0.71/1.08	
0.71/1.08	Auto_denials:  (non-Horn, no changes).
0.71/1.08	
0.71/1.08	Term ordering decisions:
0.71/1.08	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.
0.71/1.08	
0.71/1.08	============================== end of process initial clauses ========
0.71/1.08	
0.71/1.08	============================== CLAUSES FOR SEARCH ====================
0.71/1.08	
0.71/1.08	============================== end of clauses for search =============
0.71/1.08	
0.71/1.08	============================== SEARCH ================================
0.71/1.08	
0.71/1.08	% Starting search at 0.02 seconds.
0.71/1.08	
0.71/1.08	============================== PROOF =================================
0.71/1.08	% SZS status Theorem
0.71/1.08	% SZS output start Refutation
0.71/1.08	
0.71/1.08	% Proof 1 at 0.07 (+ 0.00) seconds.
0.71/1.08	% Length of proof is 20.
0.71/1.08	% Level of proof is 6.
0.71/1.08	% Maximum clause weight is 19.000.
0.71/1.08	% Given clauses 178.
0.71/1.08	
0.71/1.08	5 (all U less_than(bottom,U)) # label(bottom_smallest) # label(axiom) # label(non_clause).  [assumption].
0.71/1.08	23 (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].
0.71/1.08	30 (all U all V all W all X all Y (less_than(Y,X) -> (check_cpq(triple(U,V,W)) <-> check_cpq(triple(U,insert_slb(V,pair(X,Y)),W))))) # label(ax37) # label(axiom) # label(non_clause).  [assumption].
0.71/1.08	41 (all U all V all W ((all X all Y (pair_in_list(V,X,Y) -> less_than(Y,X))) <-> check_cpq(triple(U,V,W)))) # label(l26_li4142) # label(lemma) # label(non_clause).  [assumption].
0.71/1.08	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].
0.71/1.08	44 less_than(bottom,A) # label(bottom_smallest) # label(axiom).  [clausify(5)].
0.71/1.08	52 check_cpq(insert_cpq(triple(c1,c2,c3),c4)) # label(l26_co) # label(negated_conjecture).  [clausify(42)].
0.71/1.08	62 pair_in_list(A,f1(B,A,C),f2(B,A,C)) | check_cpq(triple(B,A,C)) # label(l26_li4142) # label(lemma).  [clausify(41)].
0.71/1.08	63 insert_cpq(triple(A,B,C),D) = triple(insert_pqp(A,D),insert_slb(B,pair(D,bottom)),C) # label(ax42) # label(axiom).  [clausify(23)].
0.71/1.08	64 triple(insert_pqp(A,B),insert_slb(C,pair(B,bottom)),D) = insert_cpq(triple(A,C,D),B).  [copy(63),flip(a)].
0.71/1.08	70 -check_cpq(triple(c1,c2,c3)) # label(l26_co) # label(negated_conjecture).  [clausify(42)].
0.71/1.08	86 -pair_in_list(A,B,C) | less_than(C,B) | -check_cpq(triple(D,A,E)) # label(l26_li4142) # label(lemma).  [clausify(41)].
0.71/1.08	89 -less_than(f2(A,B,C),f1(A,B,C)) | check_cpq(triple(A,B,C)) # label(l26_li4142) # label(lemma).  [clausify(41)].
0.71/1.08	94 -less_than(A,B) | check_cpq(triple(C,D,E)) | -check_cpq(triple(C,insert_slb(D,pair(B,A)),E)) # label(ax37) # label(axiom).  [clausify(30)].
0.71/1.08	131 less_than(f2(A,B,C),f1(A,B,C)) | -check_cpq(triple(D,B,E)) | check_cpq(triple(A,B,C)).  [resolve(86,a,62,a)].
0.71/1.08	156 -check_cpq(triple(c1,insert_slb(c2,pair(A,bottom)),c3)).  [ur(94,a,44,a,b,70,a)].
0.71/1.08	207 -less_than(f2(c1,insert_slb(c2,pair(A,bottom)),c3),f1(c1,insert_slb(c2,pair(A,bottom)),c3)).  [ur(89,b,156,a)].
0.71/1.08	579 -check_cpq(triple(A,insert_slb(c2,pair(B,bottom)),C)).  [ur(131,a,207,a,c,156,a)].
0.71/1.08	593 -check_cpq(insert_cpq(triple(A,c2,B),C)).  [para(64(a,1),579(a,1))].
0.71/1.08	594 $F.  [resolve(593,a,52,a)].
0.71/1.08	
0.71/1.08	% SZS output end Refutation
0.71/1.08	============================== end of proof ==========================
0.71/1.08	
0.71/1.08	============================== STATISTICS ============================
0.71/1.08	
0.71/1.08	Given=178. Generated=863. Kept=545. proofs=1.
0.71/1.08	Usable=168. Sos=333. Demods=12. Limbo=4, Disabled=94. Hints=0.
0.71/1.08	Megabytes=0.88.
0.71/1.08	User_CPU=0.07, System_CPU=0.00, Wall_clock=0.
0.71/1.08	
0.71/1.08	============================== end of statistics =====================
0.71/1.08	
0.71/1.08	============================== end of search =========================
0.71/1.08	
0.71/1.08	THEOREM PROVED
0.71/1.08	% SZS status Theorem
0.71/1.08	
0.71/1.08	Exiting with 1 proof.
0.71/1.08	
0.71/1.08	Process 32382 exit (max_proofs) Wed Jul 14 14:18:23 2021
0.71/1.08	Prover9 interrupted
0.71/1.08	EOF