0.04/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.04/0.14	% Command    : tptp2X_and_run_prover9 %d %s
0.14/0.35	% Computer   : n003.cluster.edu
0.14/0.35	% Model      : x86_64 x86_64
0.14/0.35	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.14/0.35	% Memory     : 8042.1875MB
0.14/0.35	% OS         : Linux 3.10.0-693.el7.x86_64
0.14/0.35	% CPULimit   : 180
0.14/0.35	% DateTime   : Thu Aug 29 10:33:02 EDT 2019
0.14/0.35	% CPUTime    : 
0.80/1.09	============================== Prover9 ===============================
0.80/1.09	Prover9 (32) version 2009-11A, November 2009.
0.80/1.09	Process 7270 was started by sandbox2 on n003.cluster.edu,
0.80/1.09	Thu Aug 29 10:33:03 2019
0.80/1.09	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 180 -f /tmp/Prover9_7117_n003.cluster.edu".
0.80/1.09	============================== end of head ===========================
0.80/1.09	
0.80/1.09	============================== INPUT =================================
0.80/1.09	
0.80/1.09	% Reading from file /tmp/Prover9_7117_n003.cluster.edu
0.80/1.09	
0.80/1.09	set(prolog_style_variables).
0.80/1.09	set(auto2).
0.80/1.09	    % set(auto2) -> set(auto).
0.80/1.09	    % set(auto) -> set(auto_inference).
0.80/1.09	    % set(auto) -> set(auto_setup).
0.80/1.09	    % set(auto_setup) -> set(predicate_elim).
0.80/1.09	    % set(auto_setup) -> assign(eq_defs, unfold).
0.80/1.09	    % set(auto) -> set(auto_limits).
0.80/1.09	    % set(auto_limits) -> assign(max_weight, "100.000").
0.80/1.09	    % set(auto_limits) -> assign(sos_limit, 20000).
0.80/1.09	    % set(auto) -> set(auto_denials).
0.80/1.09	    % set(auto) -> set(auto_process).
0.80/1.09	    % set(auto2) -> assign(new_constants, 1).
0.80/1.09	    % set(auto2) -> assign(fold_denial_max, 3).
0.80/1.09	    % set(auto2) -> assign(max_weight, "200.000").
0.80/1.09	    % set(auto2) -> assign(max_hours, 1).
0.80/1.09	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.80/1.09	    % set(auto2) -> assign(max_seconds, 0).
0.80/1.09	    % set(auto2) -> assign(max_minutes, 5).
0.80/1.09	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.80/1.09	    % set(auto2) -> set(sort_initial_sos).
0.80/1.09	    % set(auto2) -> assign(sos_limit, -1).
0.80/1.09	    % set(auto2) -> assign(lrs_ticks, 3000).
0.80/1.09	    % set(auto2) -> assign(max_megs, 400).
0.80/1.09	    % set(auto2) -> assign(stats, some).
0.80/1.09	    % set(auto2) -> clear(echo_input).
0.80/1.09	    % set(auto2) -> set(quiet).
0.80/1.09	    % set(auto2) -> clear(print_initial_clauses).
0.80/1.09	    % set(auto2) -> clear(print_given).
0.80/1.09	assign(lrs_ticks,-1).
0.80/1.09	assign(sos_limit,10000).
0.80/1.09	assign(order,kbo).
0.80/1.09	set(lex_order_vars).
0.80/1.09	clear(print_given).
0.80/1.09	
0.80/1.09	% formulas(sos).  % not echoed (66 formulas)
0.80/1.09	
0.80/1.09	============================== end of input ==========================
0.80/1.09	
0.80/1.09	% From the command line: assign(max_seconds, 180).
0.80/1.09	
0.80/1.09	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.80/1.09	
0.80/1.09	% Formulas that are not ordinary clauses:
0.80/1.09	1 (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].
0.80/1.09	2 (all U less_than(U,U)) # label(reflexivity) # label(axiom) # label(non_clause).  [assumption].
0.80/1.09	3 (all U all V (less_than(U,V) | less_than(V,U))) # label(totality) # label(axiom) # label(non_clause).  [assumption].
0.80/1.09	4 (all U all V all W (less_than(V,W) & less_than(U,V) -> less_than(U,W))) # label(transitivity) # label(axiom) # label(non_clause).  [assumption].
0.80/1.09	5 (all U less_than(bottom,U)) # label(bottom_smallest) # label(axiom) # label(non_clause).  [assumption].
0.80/1.09	6 (all U all V (issmallestelement_pq(U,V) & contains_pq(U,V) -> U = findmin_pq_eff(U,V))) # label(ax13) # label(axiom) # label(non_clause).  [assumption].
0.80/1.09	7 (all U all V remove_pq(insert_pq(U,V),V) = U) # label(ax11) # label(axiom) # label(non_clause).  [assumption].
0.80/1.09	8 (all U all V (issmallestelement_pq(U,V) & contains_pq(U,V) -> removemin_pq_res(U,V) = V)) # label(ax16) # label(axiom) # label(non_clause).  [assumption].
0.80/1.09	9 (all U all V ((all W (contains_pq(U,W) -> less_than(V,W))) <-> issmallestelement_pq(U,V))) # label(ax10) # label(axiom) # label(non_clause).  [assumption].
0.80/1.09	10 (all U all V (issmallestelement_pq(U,V) & contains_pq(U,V) -> remove_pq(U,V) = removemin_pq_eff(U,V))) # label(ax15) # label(axiom) # label(non_clause).  [assumption].
0.80/1.09	11 (all U all V (issmallestelement_pq(U,V) & contains_pq(U,V) -> V = findmin_pq_res(U,V))) # label(ax14) # label(axiom) # label(non_clause).  [assumption].
0.80/1.09	12 (all U all V all W (W = V | contains_pq(U,W) <-> contains_pq(insert_pq(U,V),W))) # label(ax9) # label(axiom) # label(non_clause).  [assumption].
0.80/1.09	13 (all U all V isnonempty_pq(insert_pq(U,V))) # label(ax7) # label(axiom) # label(non_clause).  [assumption].
0.80/1.09	14 (all U all V all W (contains_pq(U,W) & W != V -> remove_pq(insert_pq(U,V),W) = insert_pq(remove_pq(U,W),V))) # label(ax12) # label(axiom) # label(non_clause).  [assumption].
0.80/1.09	15 (all U -contains_pq(create_pq,U)) # label(ax8) # label(axiom) # label(non_clause).  [assumption].
0.80/1.09	16 (all U all V all W insert_pq(insert_pq(U,V),W) = insert_pq(insert_pq(U,W),V)) # label(ax17) # label(axiom) # label(non_clause).  [assumption].
0.80/1.09	17 (all U all V all W lookup_slb(insert_slb(U,pair(V,W)),V) = W) # label(ax26) # label(axiom) # label(non_clause).  [assumption].
0.80/1.09	18 (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].
0.80/1.09	19 (all U all V all W isnonempty_slb(insert_slb(U,pair(V,W)))) # label(ax19) # label(axiom) # label(non_clause).  [assumption].
0.80/1.09	20 (all U create_slb = update_slb(create_slb,U)) # label(ax28) # label(axiom) # label(non_clause).  [assumption].
0.80/1.09	21 (all U all V all W remove_slb(insert_slb(U,pair(V,W)),V) = U) # label(ax24) # label(axiom) # label(non_clause).  [assumption].
0.80/1.09	22 (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].
0.80/1.09	23 (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].
0.80/1.09	24 (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].
0.80/1.09	25 (all U -contains_slb(create_slb,U)) # label(ax20) # label(axiom) # label(non_clause).  [assumption].
0.80/1.09	26 (all U all V all W all X all Y (pair_in_list(insert_slb(U,pair(V,X)),W,Y) <-> Y = X & V = W | pair_in_list(U,W,Y))) # label(ax23) # label(axiom) # label(non_clause).  [assumption].
0.80/1.09	27 (all U all V -pair_in_list(create_slb,U,V)) # label(ax22) # label(axiom) # label(non_clause).  [assumption].
0.80/1.09	28 (all U all V all W all X (V != W & contains_slb(U,W) -> lookup_slb(U,W) = lookup_slb(insert_slb(U,pair(V,X)),W))) # label(ax27) # label(axiom) # label(non_clause).  [assumption].
0.80/1.09	29 (all U all V all W all X (-contains_slb(V,X) -> remove_cpq(triple(U,V,W),X) = triple(U,V,bad))) # label(ax43) # label(axiom) # label(non_clause).  [assumption].
0.80/1.09	30 (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].
0.80/1.09	31 (all U all V findmin_cpq_res(triple(U,create_slb,V)) = bottom) # label(ax50) # label(axiom) # label(non_clause).  [assumption].
0.80/1.09	32 (all U all V all W (-ok(triple(U,V,W)) -> bad = W)) # label(ax41) # label(axiom) # label(non_clause).  [assumption].
0.80/1.09	33 (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].
0.80/1.09	34 (all U succ_cpq(U,U)) # label(ax31) # label(axiom) # label(non_clause).  [assumption].
0.80/1.09	35 (all U removemin_cpq_res(U) = findmin_cpq_res(U)) # label(ax53) # label(axiom) # label(non_clause).  [assumption].
0.80/1.09	36 (all U all V all W all X (V != create_slb -> findmin_pqp_res(U) = findmin_cpq_res(triple(U,V,W)))) # label(ax51) # label(axiom) # label(non_clause).  [assumption].
0.80/1.09	37 (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].
0.80/1.09	38 (all U all V all W all X (contains_slb(V,X) & strictly_less_than(X,lookup_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].
0.80/1.09	39 (all U all V (succ_cpq(U,V) -> succ_cpq(U,removemin_cpq_eff(V)))) # label(ax35) # label(axiom) # label(non_clause).  [assumption].
0.80/1.09	40 (all U all V all W all X (-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(ax47) # label(axiom) # label(non_clause).  [assumption].
0.80/1.09	41 (all U all V (ok(triple(U,V,bad)) <-> $F)) # label(ax40) # label(axiom) # label(non_clause).  [assumption].
0.80/1.09	42 (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].
0.80/1.10	43 (all U all V all W all X (V != create_slb & contains_slb(V,findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U),lookup_slb(V,findmin_pqp_res(U))) -> 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].
0.80/1.10	44 (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].
0.80/1.10	45 (all U all V check_cpq(triple(U,create_slb,V))) # label(ax36) # label(axiom) # label(non_clause).  [assumption].
0.80/1.10	46 (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].
0.80/1.10	47 (all U all V (succ_cpq(U,V) -> succ_cpq(U,findmin_cpq_eff(V)))) # label(ax34) # label(axiom) # label(non_clause).  [assumption].
0.80/1.10	48 (all U removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U),findmin_cpq_res(U))) # label(ax52) # label(axiom) # label(non_clause).  [assumption].
0.80/1.10	49 (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].
0.80/1.10	50 (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].
0.80/1.10	51 (all U all V all W all X (create_slb != V & less_than(lookup_slb(V,findmin_pqp_res(U)),findmin_pqp_res(U)) & contains_slb(V,findmin_pqp_res(U)) -> 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].
0.80/1.10	52 (all U all V (contains_pq(U,V) <-> pi_sharp_remove(U,V))) # label(ax56) # label(axiom) # label(non_clause).  [assumption].
0.80/1.10	53 (all U all V (pi_sharp_removemin(U,V) <-> issmallestelement_pq(U,V) & contains_pq(U,V))) # label(ax60) # label(axiom) # label(non_clause).  [assumption].
0.80/1.10	54 (all U all V i(triple(U,create_slb,V)) = create_pq) # label(ax54) # label(axiom) # label(non_clause).  [assumption].
0.80/1.10	55 (all U ((exists V pi_sharp_find_min(i(U),V)) <-> pi_find_min(U))) # label(ax59) # label(axiom) # label(non_clause).  [assumption].
0.80/1.10	56 (all U all V all W all X all Y i(triple(U,insert_slb(V,pair(X,Y)),W)) = insert_pq(i(triple(U,V,W)),X)) # label(ax55) # label(axiom) # label(non_clause).  [assumption].
0.80/1.10	57 (all U all V (pi_sharp_remove(i(U),V) <-> pi_remove(U,V))) # label(ax57) # label(axiom) # label(non_clause).  [assumption].
0.80/1.10	58 (all U ((exists V (succ_cpq(U,V) & ok(V) & check_cpq(V))) <-> phi(U))) # label(ax62) # label(axiom) # label(non_clause).  [assumption].
0.80/1.10	59 (all U all V (contains_pq(U,V) & issmallestelement_pq(U,V) <-> pi_sharp_find_min(U,V))) # label(ax58) # label(axiom) # label(non_clause).  [assumption].
0.80/1.10	60 (all U (pi_removemin(U) <-> (exists V pi_sharp_find_min(i(U),V)))) # label(ax61) # label(axiom) # label(non_clause).  [assumption].
0.80/1.10	61 (all U all V all W (-ok(triple(U,V,W)) -> -phi(triple(U,V,W)))) # label(l8_lX) # label(lemma) # label(non_clause).  [assumption].
0.80/1.10	62 (all U all V all W (-contains_cpq(triple(U,V,W),findmin_cpq_res(triple(U,V,W))) -> -ok(findmin_cpq_eff(triple(U,V,W))))) # label(l8_l9) # label(lemma) # label(non_clause).  [assumption].
0.80/1.10	63 (all U all V all W all X (contains_pq(i(triple(U,V,W)),X) <-> contains_cpq(triple(U,V,W),X))) # label(l8_li56) # label(lemma) # label(non_clause).  [assumption].
0.80/1.10	64 -(all U all V all W (phi(findmin_cpq_eff(triple(U,V,W))) -> contains_pq(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W))))) # label(l8_co) # label(negated_conjecture) # label(non_clause).  [assumption].
0.80/1.10	
0.80/1.10	============================== end of process non-clausal formulas ===
0.80/1.10	
0.80/1.10	============================== PROCESS INITIAL CLAUSES ===============
0.80/1.10	
0.80/1.10	============================== PREDICATE ELIMINATION =================
0.80/1.10	65 -contains_pq(A,B) | less_than(C,B) | -issmallestelement_pq(A,C) # label(ax10) # label(axiom).  [clausify(9)].
0.80/1.10	66 contains_pq(A,f1(A,B)) | issmallestelement_pq(A,B) # label(ax10) # label(axiom).  [clausify(9)].
0.80/1.10	67 -pi_sharp_removemin(A,B) | issmallestelement_pq(A,B) # label(ax60) # label(axiom).  [clausify(53)].
0.80/1.10	68 issmallestelement_pq(A,B) | -pi_sharp_find_min(A,B) # label(ax58) # label(axiom).  [clausify(59)].
0.80/1.10	69 -less_than(A,f1(B,A)) | issmallestelement_pq(B,A) # label(ax10) # label(axiom).  [clausify(9)].
0.80/1.10	Derived: -contains_pq(A,B) | less_than(C,B) | contains_pq(A,f1(A,C)).  [resolve(65,c,66,b)].
0.80/1.10	Derived: -contains_pq(A,B) | less_than(C,B) | -pi_sharp_removemin(A,C).  [resolve(65,c,67,b)].
0.80/1.10	Derived: -contains_pq(A,B) | less_than(C,B) | -pi_sharp_find_min(A,C).  [resolve(65,c,68,a)].
0.80/1.10	Derived: -contains_pq(A,B) | less_than(C,B) | -less_than(C,f1(A,C)).  [resolve(65,c,69,b)].
0.80/1.10	70 pi_sharp_removemin(A,B) | -issmallestelement_pq(A,B) | -contains_pq(A,B) # label(ax60) # label(axiom).  [clausify(53)].
0.80/1.10	Derived: pi_sharp_removemin(A,B) | -contains_pq(A,B) | contains_pq(A,f1(A,B)).  [resolve(70,b,66,b)].
0.80/1.10	Derived: pi_sharp_removemin(A,B) | -contains_pq(A,B) | -pi_sharp_find_min(A,B).  [resolve(70,b,68,a)].
0.80/1.10	Derived: pi_sharp_removemin(A,B) | -contains_pq(A,B) | -less_than(B,f1(A,B)).  [resolve(70,b,69,b)].
0.80/1.10	71 -contains_pq(A,B) | -issmallestelement_pq(A,B) | pi_sharp_find_min(A,B) # label(ax58) # label(axiom).  [clausify(59)].
0.80/1.10	Derived: -contains_pq(A,B) | pi_sharp_find_min(A,B) | contains_pq(A,f1(A,B)).  [resolve(71,b,66,b)].
0.80/1.10	Derived: -contains_pq(A,B) | pi_sharp_find_min(A,B) | -pi_sharp_removemin(A,B).  [resolve(71,b,67,b)].
0.80/1.10	Derived: -contains_pq(A,B) | pi_sharp_find_min(A,B) | -less_than(B,f1(A,B)).  [resolve(71,b,69,b)].
0.80/1.10	72 -issmallestelement_pq(A,B) | -contains_pq(A,B) | findmin_pq_eff(A,B) = A # label(ax13) # label(axiom).  [clausify(6)].
0.80/1.10	Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | contains_pq(A,f1(A,B)).  [resolve(72,a,66,b)].
0.80/1.10	Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -pi_sharp_removemin(A,B).  [resolve(72,a,67,b)].
0.80/1.10	Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -pi_sharp_find_min(A,B).  [resolve(72,a,68,a)].
0.80/1.10	Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -less_than(B,f1(A,B)).  [resolve(72,a,69,b)].
0.80/1.10	73 -issmallestelement_pq(A,B) | -contains_pq(A,B) | removemin_pq_res(A,B) = B # label(ax16) # label(axiom).  [clausify(8)].
0.80/1.10	Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | contains_pq(A,f1(A,B)).  [resolve(73,a,66,b)].
0.80/1.10	Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | -pi_sharp_removemin(A,B).  [resolve(73,a,67,b)].
0.80/1.10	Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | -pi_sharp_find_min(A,B).  [resolve(73,a,68,a)].
0.80/1.10	Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | -less_than(B,f1(A,B)).  [resolve(73,a,69,b)].
0.80/1.10	74 -issmallestelement_pq(A,B) | -contains_pq(A,B) | findmin_pq_res(A,B) = B # label(ax14) # label(axiom).  [clausify(11)].
0.80/1.10	Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | contains_pq(A,f1(A,B)).  [resolve(74,a,66,b)].
0.80/1.10	Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | -pi_sharp_removemin(A,B).  [resolve(74,a,67,b)].
0.80/1.10	Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | -pi_sharp_find_min(A,B).  [resolve(74,a,68,a)].
0.80/1.10	Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | -less_than(B,f1(A,B)).  [resolve(74,a,69,b)].
0.80/1.10	75 -issmallestelement_pq(A,B) | -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) # label(ax15) # label(axiom).  [clausify(10)].
0.80/1.10	Derived: -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | contains_pq(A,f1(A,B)).  [resolve(75,a,66,b)].
0.80/1.10	Derived: -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | -pi_sharp_removemin(A,B).  [resolve(75,a,67,b)].
0.80/1.10	Derived: -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | -pi_sharp_find_min(A,B).  [resolve(75,a,68,a)].
0.80/1.10	Derived: -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | -less_than(B,f1(A,B)).  [resolve(75,a,69,b)].
0.80/1.10	76 pi_sharp_removemin(A,B) | -contains_pq(A,B) | contains_pq(A,f1(A,B)).  [resolve(70,b,66,b)].
0.80/1.10	77 -pi_sharp_removemin(A,B) | contains_pq(A,B) # label(ax60) # label(axiom).  [clausify(53)].
0.80/1.10	78 -contains_pq(A,B) | less_than(C,B) | -pi_sharp_removemin(A,C).  [resolve(65,c,67,b)].
1.71/2.05	Derived: -contains_pq(A,B) | contains_pq(A,f1(A,B)) | -contains_pq(A,C) | less_than(B,C).  [resolve(76,a,78,c)].
1.71/2.05	79 pi_sharp_removemin(A,B) | -contains_pq(A,B) | -pi_sharp_find_min(A,B).  [resolve(70,b,68,a)].
1.71/2.05	Derived: -contains_pq(A,B) | -pi_sharp_find_min(A,B) | -contains_pq(A,C) | less_than(B,C).  [resolve(79,a,78,c)].
1.71/2.05	80 pi_sharp_removemin(A,B) | -contains_pq(A,B) | -less_than(B,f1(A,B)).  [resolve(70,b,69,b)].
1.71/2.05	Derived: -contains_pq(A,B) | -less_than(B,f1(A,B)) | -contains_pq(A,C) | less_than(B,C).  [resolve(80,a,78,c)].
1.71/2.05	81 -contains_pq(A,B) | pi_sharp_find_min(A,B) | -pi_sharp_removemin(A,B).  [resolve(71,b,67,b)].
1.71/2.05	Derived: -contains_pq(A,B) | pi_sharp_find_min(A,B) | -contains_pq(A,B) | contains_pq(A,f1(A,B)).  [resolve(81,c,76,a)].
1.71/2.05	82 -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -pi_sharp_removemin(A,B).  [resolve(72,a,67,b)].
1.71/2.05	Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -contains_pq(A,B) | contains_pq(A,f1(A,B)).  [resolve(82,c,76,a)].
1.71/2.05	83 -contains_pq(A,B) | removemin_pq_res(A,B) = B | -pi_sharp_removemin(A,B).  [resolve(73,a,67,b)].
1.71/2.05	Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | -contains_pq(A,B) | contains_pq(A,f1(A,B)).  [resolve(83,c,76,a)].
1.71/2.05	84 -contains_pq(A,B) | findmin_pq_res(A,B) = B | -pi_sharp_removemin(A,B).  [resolve(74,a,67,b)].
1.71/2.05	Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | -contains_pq(A,B) | contains_pq(A,f1(A,B)).  [resolve(84,c,76,a)].
1.71/2.05	85 -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | -pi_sharp_removemin(A,B).  [resolve(75,a,67,b)].
1.71/2.05	Derived: -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | -contains_pq(A,B) | contains_pq(A,f1(A,B)).  [resolve(85,c,76,a)].
1.71/2.05	86 pi_sharp_find_min(i(A),f2(A)) | -pi_find_min(A) # label(ax59) # label(axiom).  [clausify(55)].
1.71/2.05	87 -pi_sharp_find_min(i(A),B) | pi_find_min(A) # label(ax59) # label(axiom).  [clausify(55)].
1.71/2.05	Derived: pi_sharp_find_min(i(A),f2(A)) | -pi_sharp_find_min(i(A),B).  [resolve(86,b,87,b)].
1.71/2.05	88 -pi_removemin(A) | pi_sharp_find_min(i(A),f4(A)) # label(ax61) # label(axiom).  [clausify(60)].
1.71/2.05	89 pi_removemin(A) | -pi_sharp_find_min(i(A),B) # label(ax61) # label(axiom).  [clausify(60)].
1.71/2.05	Derived: pi_sharp_find_min(i(A),f4(A)) | -pi_sharp_find_min(i(A),B).  [resolve(88,a,89,a)].
1.71/2.05	90 pi_sharp_remove(i(A),B) | -pi_remove(A,B) # label(ax57) # label(axiom).  [clausify(57)].
1.71/2.05	91 -pi_sharp_remove(i(A),B) | pi_remove(A,B) # label(ax57) # label(axiom).  [clausify(57)].
1.71/2.05	92 contains_pq(A,B) | -pi_sharp_remove(A,B) # label(ax56) # label(axiom).  [clausify(52)].
1.71/2.05	93 -contains_pq(A,B) | pi_sharp_remove(A,B) # label(ax56) # label(axiom).  [clausify(52)].
1.71/2.05	
1.71/2.05	============================== end predicate elimination =============
1.71/2.05	
1.71/2.05	Auto_denials:  (non-Horn, no changes).
1.71/2.05	
1.71/2.05	Term ordering decisions:
1.71/2.05	Function symbol KB weights:  create_slb=1. bad=1. bottom=1. create_pq=1. c1=1. c2=1. c3=1. insert_slb=1. pair=1. insert_pq=1. update_slb=1. lookup_slb=1. remove_pq=1. remove_cpq=1. remove_slb=1. findmin_pq_eff=1. findmin_pq_res=1. removemin_pq_eff=1. removemin_pq_res=1. insert_cpq=1. remove_pqp=1. insert_pqp=1. f1=1. findmin_pqp_res=1. i=1. findmin_cpq_eff=1. findmin_cpq_res=1. removemin_cpq_eff=1. removemin_cpq_res=1. f2=1. f3=1. f4=1. triple=1.
1.71/2.05	
1.71/2.05	============================== end of process initial clauses ========
1.71/2.05	
1.71/2.05	============================== CLAUSES FOR SEARCH ====================
1.71/2.05	
1.71/2.05	============================== end of clauses for search =============
1.71/2.05	
1.71/2.05	============================== SEARCH ================================
1.71/2.05	
1.71/2.05	% Starting search at 0.03 seconds.
1.71/2.05	
1.71/2.05	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 22 (0.00 of 0.28 sec).
1.71/2.05	
1.71/2.05	Low Water (keep): wt=132.000, iters=3777
1.71/2.05	
1.71/2.05	Low Water (keep): wt=48.000, iters=3478
1.71/2.05	
1.71/2.05	Low Water (keep): wt=43.000, iters=3462
1.71/2.05	
1.71/2.05	Low Water (keep): wt=42.000, iters=3386
1.71/2.05	
1.71/2.05	Low Water (keep): wt=40.000, iters=3364
1.71/2.05	
1.71/2.05	Low Water (keep): wt=39.000, iters=3414
1.71/2.05	
1.71/2.05	Low Water (keep): wt=38.000, iters=3386
1.71/2.05	
1.71/2.05	Low Water (keep): wt=36.000, iters=3390
1.71/2.05	
1.71/2.05	Low Water (keep): wt=35.000, iters=3377
1.71/2.05	
1.71/2.05	Low Water (keep): wt=33.000, iters=3351
2.60/2.90	
2.60/2.90	Low Water (keep): wt=32.000, iters=3363
2.60/2.90	
2.60/2.90	Low Water (keep): wt=31.000, iters=3412
2.60/2.90	
2.60/2.90	Low Water (keep): wt=30.000, iters=3355
2.60/2.90	
2.60/2.90	Low Water (keep): wt=29.000, iters=3472
2.60/2.90	
2.60/2.90	Low Water (keep): wt=28.000, iters=3432
2.60/2.90	
2.60/2.90	============================== PROOF =================================
2.60/2.90	% SZS status Theorem
2.60/2.90	% SZS output start Refutation
2.60/2.90	
2.60/2.90	% Proof 1 at 1.80 (+ 0.02) seconds.
2.60/2.90	% Length of proof is 35.
2.60/2.90	% Level of proof is 8.
2.60/2.90	% Maximum clause weight is 20.000.
2.60/2.90	% Given clauses 1407.
2.60/2.90	
2.60/2.90	30 (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].
2.60/2.90	36 (all U all V all W all X (V != create_slb -> findmin_pqp_res(U) = findmin_cpq_res(triple(U,V,W)))) # label(ax51) # label(axiom) # label(non_clause).  [assumption].
2.60/2.90	40 (all U all V all W all X (-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(ax47) # label(axiom) # label(non_clause).  [assumption].
2.60/2.90	41 (all U all V (ok(triple(U,V,bad)) <-> $F)) # label(ax40) # label(axiom) # label(non_clause).  [assumption].
2.60/2.90	49 (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].
2.60/2.90	58 (all U ((exists V (succ_cpq(U,V) & ok(V) & check_cpq(V))) <-> phi(U))) # label(ax62) # label(axiom) # label(non_clause).  [assumption].
2.60/2.90	61 (all U all V all W (-ok(triple(U,V,W)) -> -phi(triple(U,V,W)))) # label(l8_lX) # label(lemma) # label(non_clause).  [assumption].
2.60/2.90	63 (all U all V all W all X (contains_pq(i(triple(U,V,W)),X) <-> contains_cpq(triple(U,V,W),X))) # label(l8_li56) # label(lemma) # label(non_clause).  [assumption].
2.60/2.90	64 -(all U all V all W (phi(findmin_cpq_eff(triple(U,V,W))) -> contains_pq(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W))))) # label(l8_co) # label(negated_conjecture) # label(non_clause).  [assumption].
2.60/2.90	103 phi(findmin_cpq_eff(triple(c1,c2,c3))) # label(l8_co) # label(negated_conjecture).  [clausify(64)].
2.60/2.90	111 findmin_cpq_eff(triple(A,create_slb,B)) = triple(A,create_slb,bad) # label(ax46) # label(axiom).  [clausify(49)].
2.60/2.90	113 create_slb = A | findmin_pqp_res(B) = findmin_cpq_res(triple(B,A,C)) # label(ax51) # label(axiom).  [clausify(36)].
2.60/2.90	114 create_slb = A | findmin_cpq_res(triple(B,A,C)) = findmin_pqp_res(B).  [copy(113),flip(b)].
2.60/2.90	119 contains_slb(A,findmin_pqp_res(B)) | create_slb = A | findmin_cpq_eff(triple(B,A,C)) = triple(B,update_slb(A,findmin_pqp_res(B)),bad) # label(ax47) # label(axiom).  [clausify(40)].
2.60/2.90	125 -ok(triple(A,B,bad)) # label(ax40) # label(axiom).  [clausify(41)].
2.60/2.90	127 -contains_pq(i(triple(c1,c2,c3)),findmin_cpq_res(triple(c1,c2,c3))) # label(l8_co) # label(negated_conjecture).  [clausify(64)].
2.60/2.90	129 ok(f3(A)) | -phi(A) # label(ax62) # label(axiom).  [clausify(58)].
2.60/2.90	130 check_cpq(f3(A)) | -phi(A) # label(ax62) # label(axiom).  [clausify(58)].
2.60/2.90	132 succ_cpq(A,f3(A)) | -phi(A) # label(ax62) # label(axiom).  [clausify(58)].
2.60/2.90	144 contains_cpq(triple(A,B,C),D) | -contains_slb(B,D) # label(ax39) # label(axiom).  [clausify(30)].
2.60/2.90	145 -succ_cpq(A,B) | -ok(B) | -check_cpq(B) | phi(A) # label(ax62) # label(axiom).  [clausify(58)].
2.60/2.90	148 ok(triple(A,B,C)) | -phi(triple(A,B,C)) # label(l8_lX) # label(lemma).  [clausify(61)].
2.60/2.90	153 contains_pq(i(triple(A,B,C)),D) | -contains_cpq(triple(A,B,C),D) # label(l8_li56) # label(lemma).  [clausify(63)].
2.60/2.90	207 ok(f3(findmin_cpq_eff(triple(c1,c2,c3)))).  [resolve(129,b,103,a)].
2.60/2.90	208 check_cpq(f3(findmin_cpq_eff(triple(c1,c2,c3)))).  [resolve(130,b,103,a)].
2.60/2.90	209 succ_cpq(findmin_cpq_eff(triple(c1,c2,c3)),f3(findmin_cpq_eff(triple(c1,c2,c3)))).  [resolve(132,b,103,a)].
2.60/2.90	240 -phi(triple(A,B,bad)).  [ur(148,a,125,a)].
2.60/2.90	247 -contains_cpq(triple(c1,c2,c3),findmin_cpq_res(triple(c1,c2,c3))).  [ur(153,a,127,a)].
2.60/2.90	380 -contains_slb(c2,findmin_cpq_res(triple(c1,c2,c3))).  [ur(144,a,247,a)].
2.60/2.90	384 c2 = create_slb | -contains_slb(c2,findmin_pqp_res(c1)).  [para(114(b,1),380(a,2)),flip(a)].
2.60/2.90	446 -succ_cpq(triple(A,B,bad),f3(findmin_cpq_eff(triple(c1,c2,c3)))).  [ur(145,b,207,a,c,208,a,d,240,a)].
2.60/2.90	509 c2 = create_slb | findmin_cpq_eff(triple(c1,c2,A)) = triple(c1,update_slb(c2,findmin_pqp_res(c1)),bad).  [resolve(384,b,119,a),flip(b),merge(b)].
2.60/2.90	7668 c2 = create_slb.  [para(509(b,1),103(a,1)),unit_del(b,240)].
2.60/2.90	8112 -succ_cpq(triple(A,B,bad),f3(triple(c1,create_slb,bad))).  [back_rewrite(446),rewrite([7668(4),111(7)])].
2.60/2.90	8118 $F.  [back_rewrite(209),rewrite([7668(2),111(5),7668(6),111(9)]),unit_del(a,8112)].
2.60/2.90	
2.60/2.90	% SZS output end Refutation
2.60/2.90	============================== end of proof ==========================
2.60/2.90	
2.60/2.90	============================== STATISTICS ============================
2.60/2.90	
2.60/2.90	Given=1407. Generated=21841. Kept=8014. proofs=1.
2.60/2.90	Usable=967. Sos=5500. Demods=98. Limbo=450, Disabled=1225. Hints=0.
2.60/2.90	Megabytes=15.25.
2.60/2.90	User_CPU=1.80, System_CPU=0.02, Wall_clock=1.
2.60/2.90	
2.60/2.90	============================== end of statistics =====================
2.60/2.90	
2.60/2.90	============================== end of search =========================
2.60/2.90	
2.60/2.90	THEOREM PROVED
2.60/2.90	% SZS status Theorem
2.60/2.90	
2.60/2.90	Exiting with 1 proof.
2.60/2.90	
2.60/2.90	Process 7270 exit (max_proofs) Thu Aug 29 10:33:04 2019
2.60/2.90	Prover9 interrupted
2.60/2.90	EOF