0.08/0.13	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.08/0.13	% Command  : tptp2X_and_run_prover9 %d %s
0.14/0.35	% Computer : n011.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 : 960
0.14/0.35	% WCLimit  : 120
0.14/0.35	% DateTime : Tue Aug  9 01:57:06 EDT 2022
0.14/0.35	% CPUTime  : 
0.76/1.04	============================== Prover9 ===============================
0.76/1.04	Prover9 (32) version 2009-11A, November 2009.
0.76/1.04	Process 20006 was started by sandbox2 on n011.cluster.edu,
0.76/1.04	Tue Aug  9 01:57:07 2022
0.76/1.04	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_19852_n011.cluster.edu".
0.76/1.04	============================== end of head ===========================
0.76/1.04	
0.76/1.04	============================== INPUT =================================
0.76/1.04	
0.76/1.04	% Reading from file /tmp/Prover9_19852_n011.cluster.edu
0.76/1.04	
0.76/1.04	set(prolog_style_variables).
0.76/1.04	set(auto2).
0.76/1.04	    % set(auto2) -> set(auto).
0.76/1.04	    % set(auto) -> set(auto_inference).
0.76/1.04	    % set(auto) -> set(auto_setup).
0.76/1.04	    % set(auto_setup) -> set(predicate_elim).
0.76/1.04	    % set(auto_setup) -> assign(eq_defs, unfold).
0.76/1.04	    % set(auto) -> set(auto_limits).
0.76/1.04	    % set(auto_limits) -> assign(max_weight, "100.000").
0.76/1.04	    % set(auto_limits) -> assign(sos_limit, 20000).
0.76/1.04	    % set(auto) -> set(auto_denials).
0.76/1.04	    % set(auto) -> set(auto_process).
0.76/1.04	    % set(auto2) -> assign(new_constants, 1).
0.76/1.04	    % set(auto2) -> assign(fold_denial_max, 3).
0.76/1.04	    % set(auto2) -> assign(max_weight, "200.000").
0.76/1.04	    % set(auto2) -> assign(max_hours, 1).
0.76/1.04	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.76/1.04	    % set(auto2) -> assign(max_seconds, 0).
0.76/1.04	    % set(auto2) -> assign(max_minutes, 5).
0.76/1.04	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.76/1.04	    % set(auto2) -> set(sort_initial_sos).
0.76/1.04	    % set(auto2) -> assign(sos_limit, -1).
0.76/1.04	    % set(auto2) -> assign(lrs_ticks, 3000).
0.76/1.04	    % set(auto2) -> assign(max_megs, 400).
0.76/1.04	    % set(auto2) -> assign(stats, some).
0.76/1.04	    % set(auto2) -> clear(echo_input).
0.76/1.04	    % set(auto2) -> set(quiet).
0.76/1.04	    % set(auto2) -> clear(print_initial_clauses).
0.76/1.04	    % set(auto2) -> clear(print_given).
0.76/1.04	assign(lrs_ticks,-1).
0.76/1.04	assign(sos_limit,10000).
0.76/1.04	assign(order,kbo).
0.76/1.04	set(lex_order_vars).
0.76/1.04	clear(print_given).
0.76/1.04	
0.76/1.04	% formulas(sos).  % not echoed (64 formulas)
0.76/1.04	
0.76/1.04	============================== end of input ==========================
0.76/1.04	
0.76/1.04	% From the command line: assign(max_seconds, 960).
0.76/1.04	
0.76/1.04	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.76/1.04	
0.76/1.04	% Formulas that are not ordinary clauses:
0.76/1.04	1 (all U all V (less_than(V,U) | less_than(U,V))) # label(totality) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	2 (all U less_than(U,U)) # label(reflexivity) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	3 (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].
0.76/1.04	4 (all U less_than(bottom,U)) # label(bottom_smallest) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	5 (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].
0.76/1.04	6 (all U all V (contains_pq(U,V) & issmallestelement_pq(U,V) -> V = findmin_pq_res(U,V))) # label(ax14) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	7 (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].
0.76/1.04	8 (all U all V all W (V != W & contains_pq(U,W) -> remove_pq(insert_pq(U,V),W) = insert_pq(remove_pq(U,W),V))) # label(ax12) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	9 (all U -contains_pq(create_pq,U)) # label(ax8) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	10 (all U all V (contains_pq(U,V) & issmallestelement_pq(U,V) -> U = findmin_pq_eff(U,V))) # label(ax13) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	11 (all U all V (contains_pq(U,V) & issmallestelement_pq(U,V) -> removemin_pq_eff(U,V) = remove_pq(U,V))) # label(ax15) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	12 (all U all V all W (contains_pq(U,W) | W = V <-> contains_pq(insert_pq(U,V),W))) # label(ax9) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	13 (all U all V isnonempty_pq(insert_pq(U,V))) # label(ax7) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	14 (all U all V all W insert_pq(insert_pq(U,W),V) = insert_pq(insert_pq(U,V),W)) # label(ax17) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	15 (all U all V (contains_pq(U,V) & issmallestelement_pq(U,V) -> V = removemin_pq_res(U,V))) # label(ax16) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	16 (all U all V U = remove_pq(insert_pq(U,V),V)) # label(ax11) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	17 (all U all V all W all X (strictly_less_than(X,W) -> update_slb(insert_slb(U,pair(V,X)),W) = insert_slb(update_slb(U,W),pair(V,W)))) # label(ax29) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	18 (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].
0.76/1.04	19 (all U create_slb = update_slb(create_slb,U)) # label(ax28) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	20 (all U all V all W all X (contains_slb(insert_slb(U,pair(V,X)),W) <-> contains_slb(U,W) | W = V)) # label(ax21) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	21 (all U all V -pair_in_list(create_slb,U,V)) # label(ax22) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	22 (all U all V all W all X (W != V & 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].
0.76/1.04	23 (all U -contains_slb(create_slb,U)) # label(ax20) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	24 (all U all V all W all X all Y (W = V & Y = X | pair_in_list(U,W,Y) <-> pair_in_list(insert_slb(U,pair(V,X)),W,Y))) # label(ax23) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	25 (all U all V all W U = remove_slb(insert_slb(U,pair(V,W)),V)) # label(ax24) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	26 (all U all V all W all X (less_than(W,X) -> insert_slb(update_slb(U,W),pair(V,X)) = update_slb(insert_slb(U,pair(V,X)),W))) # label(ax30) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	27 (all U all V all W isnonempty_slb(insert_slb(U,pair(V,W)))) # label(ax19) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	28 (all U all V all W W = lookup_slb(insert_slb(U,pair(V,W)),V)) # label(ax26) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	29 (all U all V (succ_cpq(U,V) -> succ_cpq(U,removemin_cpq_eff(V)))) # label(ax35) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	30 (all U succ_cpq(U,U)) # label(ax31) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	31 (all U all V check_cpq(triple(U,create_slb,V))) # label(ax36) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	32 (all U all V all W all X (strictly_less_than(X,lookup_slb(V,X)) & contains_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].
0.76/1.04	33 (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].
0.76/1.04	34 (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].
0.76/1.04	35 (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].
0.76/1.04	36 (all U all V bottom = findmin_cpq_res(triple(U,create_slb,V))) # label(ax50) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	37 (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].
0.76/1.04	38 (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].
0.76/1.04	39 (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].
0.76/1.04	40 (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].
0.76/1.04	41 (all U all V all W (-ok(triple(U,V,W)) -> W = bad)) # label(ax41) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	42 (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].
0.76/1.04	43 (all U remove_cpq(findmin_cpq_eff(U),findmin_cpq_res(U)) = removemin_cpq_eff(U)) # label(ax52) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	44 (all U findmin_cpq_res(U) = removemin_cpq_res(U)) # label(ax53) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	45 (all U all V (succ_cpq(U,V) -> succ_cpq(U,findmin_cpq_eff(V)))) # label(ax34) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	46 (all U all V all W all X (-contains_slb(V,findmin_pqp_res(U)) & create_slb != V -> 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].
0.76/1.04	47 (all U all V all W all X (create_slb != V & contains_slb(V,findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U),lookup_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].
0.76/1.04	48 (all U all V all W all X (less_than(lookup_slb(V,X),X) & contains_slb(V,X) -> triple(remove_pqp(U,X),remove_slb(V,X),W) = remove_cpq(triple(U,V,W),X))) # label(ax44) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	49 (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].
0.76/1.04	50 (all U all V ($F <-> ok(triple(U,V,bad)))) # label(ax40) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	51 (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 -> 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].
0.76/1.04	52 (all U all V (pi_sharp_removemin(U,V) <-> contains_pq(U,V) & issmallestelement_pq(U,V))) # label(ax60) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	53 (all U (pi_find_min(U) <-> (exists V pi_sharp_find_min(i(U),V)))) # label(ax59) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	54 (all U (phi(U) <-> (exists V (succ_cpq(U,V) & ok(V) & check_cpq(V))))) # label(ax62) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	55 (all U all V i(triple(U,create_slb,V)) = create_pq) # label(ax54) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	56 (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].
0.76/1.04	57 (all U all V (contains_pq(U,V) <-> pi_sharp_remove(U,V))) # label(ax56) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	58 (all U (pi_removemin(U) <-> (exists V pi_sharp_find_min(i(U),V)))) # label(ax61) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	59 (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].
0.76/1.04	60 (all U all V (pi_sharp_remove(i(U),V) <-> pi_remove(U,V))) # label(ax57) # label(axiom) # label(non_clause).  [assumption].
0.76/1.04	61 (all U all V all W all X all Y i(triple(V,W,Y)) = i(triple(U,W,X))) # label(main2_l12) # label(lemma) # label(non_clause).  [assumption].
0.76/1.04	62 -(all U all V all W all X insert_pq(i(triple(U,V,W)),X) = i(insert_cpq(triple(U,V,W),X))) # label(co2) # label(negated_conjecture) # label(non_clause).  [assumption].
0.76/1.04	
0.76/1.04	============================== end of process non-clausal formulas ===
0.76/1.04	
0.76/1.04	============================== PROCESS INITIAL CLAUSES ===============
0.76/1.04	
0.76/1.04	============================== PREDICATE ELIMINATION =================
0.76/1.04	63 -contains_pq(A,B) | less_than(C,B) | -issmallestelement_pq(A,C) # label(ax10) # label(axiom).  [clausify(7)].
0.76/1.04	64 contains_pq(A,f1(A,B)) | issmallestelement_pq(A,B) # label(ax10) # label(axiom).  [clausify(7)].
0.76/1.04	65 -pi_sharp_removemin(A,B) | issmallestelement_pq(A,B) # label(ax60) # label(axiom).  [clausify(52)].
0.76/1.04	66 issmallestelement_pq(A,B) | -pi_sharp_find_min(A,B) # label(ax58) # label(axiom).  [clausify(56)].
0.76/1.04	67 -less_than(A,f1(B,A)) | issmallestelement_pq(B,A) # label(ax10) # label(axiom).  [clausify(7)].
0.76/1.04	Derived: -contains_pq(A,B) | less_than(C,B) | contains_pq(A,f1(A,C)).  [resolve(63,c,64,b)].
0.76/1.04	Derived: -contains_pq(A,B) | less_than(C,B) | -pi_sharp_removemin(A,C).  [resolve(63,c,65,b)].
0.76/1.04	Derived: -contains_pq(A,B) | less_than(C,B) | -pi_sharp_find_min(A,C).  [resolve(63,c,66,a)].
0.76/1.04	Derived: -contains_pq(A,B) | less_than(C,B) | -less_than(C,f1(A,C)).  [resolve(63,c,67,b)].
0.76/1.04	68 pi_sharp_removemin(A,B) | -contains_pq(A,B) | -issmallestelement_pq(A,B) # label(ax60) # label(axiom).  [clausify(52)].
0.76/1.04	Derived: pi_sharp_removemin(A,B) | -contains_pq(A,B) | contains_pq(A,f1(A,B)).  [resolve(68,c,64,b)].
0.76/1.04	Derived: pi_sharp_removemin(A,B) | -contains_pq(A,B) | -pi_sharp_find_min(A,B).  [resolve(68,c,66,a)].
0.76/1.04	Derived: pi_sharp_removemin(A,B) | -contains_pq(A,B) | -less_than(B,f1(A,B)).  [resolve(68,c,67,b)].
0.76/1.04	69 -contains_pq(A,B) | -issmallestelement_pq(A,B) | pi_sharp_find_min(A,B) # label(ax58) # label(axiom).  [clausify(56)].
0.76/1.04	Derived: -contains_pq(A,B) | pi_sharp_find_min(A,B) | contains_pq(A,f1(A,B)).  [resolve(69,b,64,b)].
0.76/1.04	Derived: -contains_pq(A,B) | pi_sharp_find_min(A,B) | -pi_sharp_removemin(A,B).  [resolve(69,b,65,b)].
0.76/1.04	Derived: -contains_pq(A,B) | pi_sharp_find_min(A,B) | -less_than(B,f1(A,B)).  [resolve(69,b,67,b)].
0.76/1.04	70 -contains_pq(A,B) | -issmallestelement_pq(A,B) | findmin_pq_res(A,B) = B # label(ax14) # label(axiom).  [clausify(6)].
0.76/1.04	Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | contains_pq(A,f1(A,B)).  [resolve(70,b,64,b)].
0.76/1.04	Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | -pi_sharp_removemin(A,B).  [resolve(70,b,65,b)].
0.76/1.04	Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | -pi_sharp_find_min(A,B).  [resolve(70,b,66,a)].
0.76/1.04	Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | -less_than(B,f1(A,B)).  [resolve(70,b,67,b)].
0.76/1.04	71 -contains_pq(A,B) | -issmallestelement_pq(A,B) | findmin_pq_eff(A,B) = A # label(ax13) # label(axiom).  [clausify(10)].
0.76/1.04	Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | contains_pq(A,f1(A,B)).  [resolve(71,b,64,b)].
0.76/1.04	Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -pi_sharp_removemin(A,B).  [resolve(71,b,65,b)].
0.76/1.04	Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -pi_sharp_find_min(A,B).  [resolve(71,b,66,a)].
0.76/1.04	Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -less_than(B,f1(A,B)).  [resolve(71,b,67,b)].
0.76/1.04	72 -contains_pq(A,B) | -issmallestelement_pq(A,B) | removemin_pq_res(A,B) = B # label(ax16) # label(axiom).  [clausify(15)].
0.76/1.04	Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | contains_pq(A,f1(A,B)).  [resolve(72,b,64,b)].
0.76/1.04	Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | -pi_sharp_removemin(A,B).  [resolve(72,b,65,b)].
0.76/1.04	Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | -pi_sharp_find_min(A,B).  [resolve(72,b,66,a)].
0.76/1.04	Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | -less_than(B,f1(A,B)).  [resolve(72,b,67,b)].
0.76/1.04	73 -contains_pq(A,B) | -issmallestelement_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) # label(ax15) # label(axiom).  [clausify(11)].
0.76/1.04	Derived: -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | contains_pq(A,f1(A,B)).  [resolve(73,b,64,b)].
0.76/1.04	Derived: -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | -pi_sharp_removemin(A,B).  [resolve(73,b,65,b)].
0.76/1.04	Derived: -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | -pi_sharp_find_min(A,B).  [resolve(73,b,66,a)].
0.76/1.04	Derived: -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | -less_than(B,f1(A,B)).  [resolve(73,b,67,b)].
0.76/1.04	74 phi(A) | -succ_cpq(A,B) | -ok(B) | -check_cpq(B) # label(ax62) # label(axiom).  [clausify(54)].
0.76/1.04	75 -phi(A) | ok(f3(A)) # label(ax62) # label(axiom).  [clausify(54)].
0.76/1.04	76 -phi(A) | check_cpq(f3(A)) # label(ax62) # label(axiom).  [clausify(54)].
0.76/1.04	77 -phi(A) | succ_cpq(A,f3(A)) # label(ax62) # label(axiom).  [clausify(54)].
0.76/1.04	Derived: -succ_cpq(A,B) | -ok(B) | -check_cpq(B) | ok(f3(A)).  [resolve(74,a,75,a)].
0.76/1.04	Derived: -succ_cpq(A,B) | -ok(B) | -check_cpq(B) | check_cpq(f3(A)).  [resolve(74,a,76,a)].
0.76/1.04	Derived: -succ_cpq(A,B) | -ok(B) | -check_cpq(B) | succ_cpq(A,f3(A)).  [resolve(74,a,77,a)].
0.76/1.05	78 pi_sharp_removemin(A,B) | -contains_pq(A,B) | contains_pq(A,f1(A,B)).  [resolve(68,c,64,b)].
0.76/1.05	79 -pi_sharp_removemin(A,B) | contains_pq(A,B) # label(ax60) # label(axiom).  [clausify(52)].
0.76/1.05	80 -contains_pq(A,B) | less_than(C,B) | -pi_sharp_removemin(A,C).  [resolve(63,c,65,b)].
0.76/1.05	Derived: -contains_pq(A,B) | contains_pq(A,f1(A,B)) | -contains_pq(A,C) | less_than(B,C).  [resolve(78,a,80,c)].
0.76/1.05	81 pi_sharp_removemin(A,B) | -contains_pq(A,B) | -pi_sharp_find_min(A,B).  [resolve(68,c,66,a)].
0.76/1.05	Derived: -contains_pq(A,B) | -pi_sharp_find_min(A,B) | -contains_pq(A,C) | less_than(B,C).  [resolve(81,a,80,c)].
0.76/1.05	82 pi_sharp_removemin(A,B) | -contains_pq(A,B) | -less_than(B,f1(A,B)).  [resolve(68,c,67,b)].
0.76/1.05	Derived: -contains_pq(A,B) | -less_than(B,f1(A,B)) | -contains_pq(A,C) | less_than(B,C).  [resolve(82,a,80,c)].
0.76/1.05	83 -contains_pq(A,B) | pi_sharp_find_min(A,B) | -pi_sharp_removemin(A,B).  [resolve(69,b,65,b)].
0.76/1.05	Derived: -contains_pq(A,B) | pi_sharp_find_min(A,B) | -contains_pq(A,B) | contains_pq(A,f1(A,B)).  [resolve(83,c,78,a)].
0.76/1.05	84 -contains_pq(A,B) | findmin_pq_res(A,B) = B | -pi_sharp_removemin(A,B).  [resolve(70,b,65,b)].
0.76/1.05	Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | -contains_pq(A,B) | contains_pq(A,f1(A,B)).  [resolve(84,c,78,a)].
0.76/1.05	85 -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -pi_sharp_removemin(A,B).  [resolve(71,b,65,b)].
0.76/1.05	Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -contains_pq(A,B) | contains_pq(A,f1(A,B)).  [resolve(85,c,78,a)].
0.76/1.05	86 -contains_pq(A,B) | removemin_pq_res(A,B) = B | -pi_sharp_removemin(A,B).  [resolve(72,b,65,b)].
0.76/1.05	Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | -contains_pq(A,B) | contains_pq(A,f1(A,B)).  [resolve(86,c,78,a)].
0.76/1.05	87 -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | -pi_sharp_removemin(A,B).  [resolve(73,b,65,b)].
0.76/1.05	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(87,c,78,a)].
0.76/1.05	88 -pi_find_min(A) | pi_sharp_find_min(i(A),f2(A)) # label(ax59) # label(axiom).  [clausify(53)].
0.76/1.05	89 pi_find_min(A) | -pi_sharp_find_min(i(A),B) # label(ax59) # label(axiom).  [clausify(53)].
0.76/1.05	Derived: pi_sharp_find_min(i(A),f2(A)) | -pi_sharp_find_min(i(A),B).  [resolve(88,a,89,a)].
0.76/1.05	90 -pi_removemin(A) | pi_sharp_find_min(i(A),f4(A)) # label(ax61) # label(axiom).  [clausify(58)].
0.76/1.05	91 pi_removemin(A) | -pi_sharp_find_min(i(A),B) # label(ax61) # label(axiom).  [clausify(58)].
0.76/1.05	Derived: pi_sharp_find_min(i(A),f4(A)) | -pi_sharp_find_min(i(A),B).  [resolve(90,a,91,a)].
0.76/1.05	92 pi_sharp_remove(i(A),B) | -pi_remove(A,B) # label(ax57) # label(axiom).  [clausify(60)].
0.76/1.05	93 -pi_sharp_remove(i(A),B) | pi_remove(A,B) # label(ax57) # label(axiom).  [clausify(60)].
0.76/1.05	94 contains_pq(A,B) | -pi_sharp_remove(A,B) # label(ax56) # label(axiom).  [clausify(57)].
0.76/1.05	95 -contains_pq(A,B) | pi_sharp_remove(A,B) # label(ax56) # label(axiom).  [clausify(57)].
0.76/1.05	
0.76/1.05	============================== end predicate elimination =============
0.76/1.05	
0.76/1.05	Auto_denials:  (non-Horn, no changes).
0.76/1.05	
0.76/1.05	Term ordering decisions:
0.76/1.05	Function symbol KB weights:  create_slb=1. bad=1. bottom=1. create_pq=1. c1=1. c2=1. c3=1. c4=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.
0.76/1.05	
0.76/1.05	============================== end of process initial clauses ========
0.76/1.05	
0.76/1.05	============================== CLAUSES FOR SEARCH ====================
0.76/1.05	
0.76/1.05	============================== end of clauses for search =============
0.76/1.05	
0.76/1.05	============================== SEARCH ================================
0.76/1.05	
0.76/1.05	% Starting search at 0.02 seconds.
0.76/1.05	
0.76/1.05	============================== PROOF =================================
0.76/1.05	% SZS status Theorem
0.76/1.05	% SZS output start Refutation
0.76/1.05	
0.76/1.05	% Proof 1 at 0.02 (+ 0.00) seconds.
0.76/1.05	% Length of proof is 11.
0.76/1.05	% Level of proof is 4.
0.76/1.05	% Maximum clause weight is 17.000.
0.76/1.05	% Given clauses 22.
0.76/1.05	
0.76/1.05	39 (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].
0.76/1.05	59 (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].
0.76/1.05	61 (all U all V all W all X all Y i(triple(V,W,Y)) = i(triple(U,W,X))) # label(main2_l12) # label(lemma) # label(non_clause).  [assumption].
0.76/1.05	62 -(all U all V all W all X insert_pq(i(triple(U,V,W)),X) = i(insert_cpq(triple(U,V,W),X))) # label(co2) # label(negated_conjecture) # label(non_clause).  [assumption].
0.76/1.05	117 i(triple(A,B,C)) = i(triple(D,B,E)) # label(main2_l12) # label(lemma).  [clausify(61)].
0.76/1.05	119 insert_cpq(triple(A,B,C),D) = triple(insert_pqp(A,D),insert_slb(B,pair(D,bottom)),C) # label(ax42) # label(axiom).  [clausify(39)].
0.76/1.05	120 triple(insert_pqp(A,B),insert_slb(C,pair(B,bottom)),D) = insert_cpq(triple(A,C,D),B).  [copy(119),flip(a)].
0.76/1.05	121 i(triple(A,insert_slb(B,pair(C,D)),E)) = insert_pq(i(triple(A,B,E)),C) # label(ax55) # label(axiom).  [clausify(59)].
0.76/1.05	131 i(insert_cpq(triple(c1,c2,c3),c4)) != insert_pq(i(triple(c1,c2,c3)),c4) # label(co2) # label(negated_conjecture).  [clausify(62)].
0.76/1.05	199 i(insert_cpq(triple(A,B,C),D)) = insert_pq(i(triple(E,B,F)),D).  [para(120(a,1),117(a,1,1)),rewrite([121(8)])].
0.76/1.05	200 $F.  [resolve(199,a,131,a)].
0.76/1.05	
0.76/1.05	% SZS output end Refutation
0.76/1.05	============================== end of proof ==========================
0.76/1.05	
0.76/1.05	============================== STATISTICS ============================
0.76/1.05	
0.76/1.05	Given=22. Generated=130. Kept=93. proofs=1.
0.76/1.05	Usable=22. Sos=68. Demods=13. Limbo=2, Disabled=127. Hints=0.
0.76/1.05	Megabytes=0.32.
0.76/1.05	User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
0.76/1.05	
0.76/1.05	============================== end of statistics =====================
0.76/1.05	
0.76/1.05	============================== end of search =========================
0.76/1.05	
0.76/1.05	THEOREM PROVED
0.76/1.05	% SZS status Theorem
0.76/1.05	
0.76/1.05	Exiting with 1 proof.
0.76/1.05	
0.76/1.05	Process 20006 exit (max_proofs) Tue Aug  9 01:57:07 2022
0.76/1.05	Prover9 interrupted
0.76/1.05	EOF