0.03/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.12/0.13	% Command    : tptp2X_and_run_prover9 %d %s
0.13/0.34	% Computer   : n013.cluster.edu
0.13/0.34	% Model      : x86_64 x86_64
0.13/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory     : 8042.1875MB
0.13/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit   : 1200
0.13/0.34	% DateTime   : Wed Jul 14 14:08:33 EDT 2021
0.13/0.34	% CPUTime    : 
0.44/1.04	============================== Prover9 ===============================
0.44/1.04	Prover9 (32) version 2009-11A, November 2009.
0.44/1.04	Process 25037 was started by sandbox on n013.cluster.edu,
0.44/1.04	Wed Jul 14 14:08:33 2021
0.44/1.04	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1200 -f /tmp/Prover9_24869_n013.cluster.edu".
0.44/1.04	============================== end of head ===========================
0.44/1.04	
0.44/1.04	============================== INPUT =================================
0.44/1.04	
0.44/1.04	% Reading from file /tmp/Prover9_24869_n013.cluster.edu
0.44/1.04	
0.44/1.04	set(prolog_style_variables).
0.44/1.04	set(auto2).
0.44/1.04	    % set(auto2) -> set(auto).
0.44/1.04	    % set(auto) -> set(auto_inference).
0.44/1.04	    % set(auto) -> set(auto_setup).
0.44/1.04	    % set(auto_setup) -> set(predicate_elim).
0.44/1.04	    % set(auto_setup) -> assign(eq_defs, unfold).
0.44/1.04	    % set(auto) -> set(auto_limits).
0.44/1.04	    % set(auto_limits) -> assign(max_weight, "100.000").
0.44/1.04	    % set(auto_limits) -> assign(sos_limit, 20000).
0.44/1.04	    % set(auto) -> set(auto_denials).
0.44/1.04	    % set(auto) -> set(auto_process).
0.44/1.04	    % set(auto2) -> assign(new_constants, 1).
0.44/1.04	    % set(auto2) -> assign(fold_denial_max, 3).
0.44/1.04	    % set(auto2) -> assign(max_weight, "200.000").
0.44/1.04	    % set(auto2) -> assign(max_hours, 1).
0.44/1.04	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.44/1.04	    % set(auto2) -> assign(max_seconds, 0).
0.44/1.04	    % set(auto2) -> assign(max_minutes, 5).
0.44/1.04	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.44/1.04	    % set(auto2) -> set(sort_initial_sos).
0.44/1.04	    % set(auto2) -> assign(sos_limit, -1).
0.44/1.04	    % set(auto2) -> assign(lrs_ticks, 3000).
0.44/1.04	    % set(auto2) -> assign(max_megs, 400).
0.44/1.04	    % set(auto2) -> assign(stats, some).
0.44/1.04	    % set(auto2) -> clear(echo_input).
0.44/1.04	    % set(auto2) -> set(quiet).
0.44/1.04	    % set(auto2) -> clear(print_initial_clauses).
0.44/1.04	    % set(auto2) -> clear(print_given).
0.44/1.04	assign(lrs_ticks,-1).
0.44/1.04	assign(sos_limit,10000).
0.44/1.04	assign(order,kbo).
0.44/1.04	set(lex_order_vars).
0.44/1.04	clear(print_given).
0.44/1.04	
0.44/1.04	% formulas(sos).  % not echoed (63 formulas)
0.44/1.04	
0.44/1.04	============================== end of input ==========================
0.44/1.04	
0.44/1.04	% From the command line: assign(max_seconds, 1200).
0.44/1.04	
0.44/1.04	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.44/1.04	
0.44/1.04	% Formulas that are not ordinary clauses:
0.44/1.04	1 (all U less_than(U,U)) # label(reflexivity) # label(axiom) # label(non_clause).  [assumption].
0.44/1.04	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].
0.44/1.04	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].
0.44/1.04	4 (all U all V (less_than(V,U) | less_than(U,V))) # label(totality) # label(axiom) # label(non_clause).  [assumption].
0.44/1.04	5 (all U less_than(bottom,U)) # label(bottom_smallest) # label(axiom) # label(non_clause).  [assumption].
0.44/1.04	6 (all U all V all W (contains_pq(insert_pq(U,V),W) <-> contains_pq(U,W) | W = V)) # label(ax9) # label(axiom) # label(non_clause).  [assumption].
0.44/1.04	7 (all U all V U = remove_pq(insert_pq(U,V),V)) # label(ax11) # label(axiom) # label(non_clause).  [assumption].
0.44/1.04	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].
0.44/1.04	9 (all U all V (contains_pq(U,V) & issmallestelement_pq(U,V) -> findmin_pq_eff(U,V) = U)) # label(ax13) # label(axiom) # label(non_clause).  [assumption].
0.44/1.04	10 (all U all V isnonempty_pq(insert_pq(U,V))) # label(ax7) # label(axiom) # label(non_clause).  [assumption].
0.44/1.04	11 (all U all V all W (contains_pq(U,W) & W != V -> insert_pq(remove_pq(U,W),V) = remove_pq(insert_pq(U,V),W))) # label(ax12) # label(axiom) # label(non_clause).  [assumption].
0.44/1.04	12 (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].
0.44/1.04	13 (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].
0.44/1.04	14 (all U -contains_pq(create_pq,U)) # label(ax8) # label(axiom) # label(non_clause).  [assumption].
0.44/1.04	15 (all U all V (issmallestelement_pq(U,V) <-> (all W (contains_pq(U,W) -> less_than(V,W))))) # label(ax10) # label(axiom) # label(non_clause).  [assumption].
0.44/1.05	16 (all U all V (contains_pq(U,V) & issmallestelement_pq(U,V) -> findmin_pq_res(U,V) = V)) # label(ax14) # label(axiom) # label(non_clause).  [assumption].
0.44/1.05	17 (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].
0.44/1.05	18 (all U all V all W W = lookup_slb(insert_slb(U,pair(V,W)),V)) # label(ax26) # label(axiom) # label(non_clause).  [assumption].
0.44/1.05	19 (all U all V -pair_in_list(create_slb,U,V)) # label(ax22) # label(axiom) # label(non_clause).  [assumption].
0.44/1.05	20 (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].
0.44/1.05	21 (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].
0.44/1.05	22 (all U update_slb(create_slb,U) = create_slb) # label(ax28) # label(axiom) # label(non_clause).  [assumption].
0.44/1.05	23 (all U all V all W isnonempty_slb(insert_slb(U,pair(V,W)))) # label(ax19) # label(axiom) # label(non_clause).  [assumption].
0.44/1.05	24 (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].
0.44/1.05	25 (all U all V all W remove_slb(insert_slb(U,pair(V,W)),V) = U) # label(ax24) # label(axiom) # label(non_clause).  [assumption].
0.44/1.05	26 (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].
0.44/1.05	27 (all U -contains_slb(create_slb,U)) # label(ax20) # label(axiom) # label(non_clause).  [assumption].
0.44/1.05	28 (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].
0.44/1.05	29 (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].
0.44/1.05	30 (all U all V bottom = findmin_cpq_res(triple(U,create_slb,V))) # label(ax50) # label(axiom) # label(non_clause).  [assumption].
0.44/1.05	31 (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].
0.44/1.05	32 (all U all V all W (-ok(triple(U,V,W)) -> bad = W)) # label(ax41) # label(axiom) # label(non_clause).  [assumption].
0.44/1.05	33 (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].
0.44/1.05	34 (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].
0.44/1.05	35 (all U succ_cpq(U,U)) # label(ax31) # label(axiom) # label(non_clause).  [assumption].
0.44/1.05	36 (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)) <-> $F))) # label(ax38) # label(axiom) # label(non_clause).  [assumption].
0.44/1.05	37 (all U all V ($F <-> ok(triple(U,V,bad)))) # label(ax40) # label(axiom) # label(non_clause).  [assumption].
0.44/1.05	38 (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].
0.44/1.05	39 (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].
0.44/1.05	40 (all U all V check_cpq(triple(U,create_slb,V))) # label(ax36) # label(axiom) # label(non_clause).  [assumption].
0.44/1.05	41 (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].
0.44/1.05	42 (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].
0.44/1.05	43 (all U removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U),findmin_cpq_res(U))) # label(ax52) # label(axiom) # label(non_clause).  [assumption].
0.44/1.05	44 (all U all V (succ_cpq(U,V) -> succ_cpq(U,findmin_cpq_eff(V)))) # label(ax34) # label(axiom) # label(non_clause).  [assumption].
0.44/1.05	45 (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].
0.44/1.05	46 (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].
0.44/1.05	47 (all U all V (succ_cpq(U,V) -> succ_cpq(U,removemin_cpq_eff(V)))) # label(ax35) # label(axiom) # label(non_clause).  [assumption].
0.44/1.05	48 (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].
0.44/1.05	49 (all U removemin_cpq_res(U) = findmin_cpq_res(U)) # label(ax53) # label(axiom) # label(non_clause).  [assumption].
0.44/1.05	50 (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].
0.44/1.05	51 (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].
0.44/1.05	52 (all U all V (pi_sharp_remove(U,V) <-> contains_pq(U,V))) # label(ax56) # label(axiom) # label(non_clause).  [assumption].
0.44/1.05	53 (all U all V (contains_pq(U,V) & issmallestelement_pq(U,V) <-> pi_sharp_removemin(U,V))) # label(ax60) # label(axiom) # label(non_clause).  [assumption].
0.44/1.05	54 (all U all V create_pq = i(triple(U,create_slb,V))) # label(ax54) # label(axiom) # label(non_clause).  [assumption].
0.44/1.05	55 (all U all V (pi_sharp_find_min(U,V) <-> issmallestelement_pq(U,V) & contains_pq(U,V))) # label(ax58) # label(axiom) # label(non_clause).  [assumption].
0.44/1.05	56 (all U (pi_removemin(U) <-> (exists V pi_sharp_find_min(i(U),V)))) # label(ax61) # label(axiom) # label(non_clause).  [assumption].
0.44/1.05	57 (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].
0.44/1.05	58 (all U all V (pi_remove(U,V) <-> pi_sharp_remove(i(U),V))) # label(ax57) # label(axiom) # label(non_clause).  [assumption].
0.44/1.05	59 (all U (pi_find_min(U) <-> (exists V pi_sharp_find_min(i(U),V)))) # label(ax59) # label(axiom) # label(non_clause).  [assumption].
0.44/1.05	60 (all U (phi(U) <-> (exists V (succ_cpq(U,V) & ok(V) & check_cpq(V))))) # label(ax62) # label(axiom) # label(non_clause).  [assumption].
0.44/1.05	61 -(all U ((all V all W all X all Y i(triple(V,U,X)) = i(triple(W,U,Y))) -> (all Z all X1 all X2 all X3 all X4 all X5 i(triple(Z,insert_slb(U,pair(X4,X5)),X2)) = i(triple(X1,insert_slb(U,pair(X4,X5)),X3))))) # label(l2_co) # label(negated_conjecture) # label(non_clause).  [assumption].
0.44/1.05	
0.44/1.05	============================== end of process non-clausal formulas ===
0.44/1.05	
0.44/1.05	============================== PROCESS INITIAL CLAUSES ===============
0.44/1.05	
0.44/1.05	============================== PREDICATE ELIMINATION =================
0.44/1.05	62 -issmallestelement_pq(A,B) | -contains_pq(A,C) | less_than(B,C) # label(ax10) # label(axiom).  [clausify(15)].
0.44/1.05	63 issmallestelement_pq(A,B) | contains_pq(A,f1(A,B)) # label(ax10) # label(axiom).  [clausify(15)].
0.44/1.05	64 issmallestelement_pq(A,B) | -pi_sharp_removemin(A,B) # label(ax60) # label(axiom).  [clausify(53)].
0.44/1.05	65 -pi_sharp_find_min(A,B) | issmallestelement_pq(A,B) # label(ax58) # label(axiom).  [clausify(55)].
0.44/1.05	66 issmallestelement_pq(A,B) | -less_than(B,f1(A,B)) # label(ax10) # label(axiom).  [clausify(15)].
0.44/1.05	Derived: -contains_pq(A,B) | less_than(C,B) | contains_pq(A,f1(A,C)).  [resolve(62,a,63,a)].
0.44/1.05	Derived: -contains_pq(A,B) | less_than(C,B) | -pi_sharp_removemin(A,C).  [resolve(62,a,64,a)].
0.44/1.05	Derived: -contains_pq(A,B) | less_than(C,B) | -pi_sharp_find_min(A,C).  [resolve(62,a,65,b)].
0.44/1.05	Derived: -contains_pq(A,B) | less_than(C,B) | -less_than(C,f1(A,C)).  [resolve(62,a,66,a)].
0.44/1.05	67 -contains_pq(A,B) | -issmallestelement_pq(A,B) | pi_sharp_removemin(A,B) # label(ax60) # label(axiom).  [clausify(53)].
0.44/1.05	Derived: -contains_pq(A,B) | pi_sharp_removemin(A,B) | contains_pq(A,f1(A,B)).  [resolve(67,b,63,a)].
0.44/1.05	Derived: -contains_pq(A,B) | pi_sharp_removemin(A,B) | -pi_sharp_find_min(A,B).  [resolve(67,b,65,b)].
0.44/1.05	Derived: -contains_pq(A,B) | pi_sharp_removemin(A,B) | -less_than(B,f1(A,B)).  [resolve(67,b,66,a)].
0.44/1.05	68 pi_sharp_find_min(A,B) | -issmallestelement_pq(A,B) | -contains_pq(A,B) # label(ax58) # label(axiom).  [clausify(55)].
0.44/1.05	Derived: pi_sharp_find_min(A,B) | -contains_pq(A,B) | contains_pq(A,f1(A,B)).  [resolve(68,b,63,a)].
0.44/1.05	Derived: pi_sharp_find_min(A,B) | -contains_pq(A,B) | -pi_sharp_removemin(A,B).  [resolve(68,b,64,a)].
0.44/1.05	Derived: pi_sharp_find_min(A,B) | -contains_pq(A,B) | -less_than(B,f1(A,B)).  [resolve(68,b,66,a)].
0.44/1.05	69 -issmallestelement_pq(A,B) | -contains_pq(A,B) | removemin_pq_res(A,B) = B # label(ax16) # label(axiom).  [clausify(8)].
0.44/1.05	Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | contains_pq(A,f1(A,B)).  [resolve(69,a,63,a)].
0.44/1.05	Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | -pi_sharp_removemin(A,B).  [resolve(69,a,64,a)].
0.44/1.05	Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | -pi_sharp_find_min(A,B).  [resolve(69,a,65,b)].
0.44/1.05	Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | -less_than(B,f1(A,B)).  [resolve(69,a,66,a)].
0.44/1.05	70 -contains_pq(A,B) | -issmallestelement_pq(A,B) | findmin_pq_eff(A,B) = A # label(ax13) # label(axiom).  [clausify(9)].
0.44/1.05	Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | contains_pq(A,f1(A,B)).  [resolve(70,b,63,a)].
0.44/1.05	Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -pi_sharp_removemin(A,B).  [resolve(70,b,64,a)].
0.44/1.05	Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -pi_sharp_find_min(A,B).  [resolve(70,b,65,b)].
0.44/1.05	Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -less_than(B,f1(A,B)).  [resolve(70,b,66,a)].
0.44/1.05	71 -contains_pq(A,B) | -issmallestelement_pq(A,B) | findmin_pq_res(A,B) = B # label(ax14) # label(axiom).  [clausify(16)].
0.44/1.05	Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | contains_pq(A,f1(A,B)).  [resolve(71,b,63,a)].
0.44/1.05	Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | -pi_sharp_removemin(A,B).  [resolve(71,b,64,a)].
0.44/1.05	Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | -pi_sharp_find_min(A,B).  [resolve(71,b,65,b)].
0.44/1.05	Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | -less_than(B,f1(A,B)).  [resolve(71,b,66,a)].
0.44/1.05	72 -issmallestelement_pq(A,B) | -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) # label(ax15) # label(axiom).  [clausify(13)].
0.44/1.05	Derived: -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | contains_pq(A,f1(A,B)).  [resolve(72,a,63,a)].
0.44/1.05	Derived: -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | -pi_sharp_removemin(A,B).  [resolve(72,a,64,a)].
0.44/1.05	Derived: -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | -pi_sharp_find_min(A,B).  [resolve(72,a,65,b)].
0.44/1.05	Derived: -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | -less_than(B,f1(A,B)).  [resolve(72,a,66,a)].
0.44/1.05	73 phi(A) | -succ_cpq(A,B) | -ok(B) | -check_cpq(B) # label(ax62) # label(axiom).  [clausify(60)].
0.44/1.05	74 -phi(A) | ok(f4(A)) # label(ax62) # label(axiom).  [clausify(60)].
0.44/1.05	75 -phi(A) | check_cpq(f4(A)) # label(ax62) # label(axiom).  [clausify(60)].
0.44/1.05	76 -phi(A) | succ_cpq(A,f4(A)) # label(ax62) # label(axiom).  [clausify(60)].
0.44/1.05	Derived: -succ_cpq(A,B) | -ok(B) | -check_cpq(B) | ok(f4(A)).  [resolve(73,a,74,a)].
0.44/1.05	Derived: -succ_cpq(A,B) | -ok(B) | -check_cpq(B) | check_cpq(f4(A)).  [resolve(73,a,75,a)].
0.44/1.05	Derived: -succ_cpq(A,B) | -ok(B) | -check_cpq(B) | succ_cpq(A,f4(A)).  [resolve(73,a,76,a)].
0.44/1.06	77 -contains_pq(A,B) | pi_sharp_removemin(A,B) | contains_pq(A,f1(A,B)).  [resolve(67,b,63,a)].
0.44/1.06	78 contains_pq(A,B) | -pi_sharp_removemin(A,B) # label(ax60) # label(axiom).  [clausify(53)].
0.44/1.06	79 -contains_pq(A,B) | less_than(C,B) | -pi_sharp_removemin(A,C).  [resolve(62,a,64,a)].
0.44/1.06	Derived: -contains_pq(A,B) | contains_pq(A,f1(A,B)) | -contains_pq(A,C) | less_than(B,C).  [resolve(77,b,79,c)].
0.44/1.06	80 -contains_pq(A,B) | pi_sharp_removemin(A,B) | -pi_sharp_find_min(A,B).  [resolve(67,b,65,b)].
0.44/1.06	Derived: -contains_pq(A,B) | -pi_sharp_find_min(A,B) | -contains_pq(A,C) | less_than(B,C).  [resolve(80,b,79,c)].
0.44/1.06	81 -contains_pq(A,B) | pi_sharp_removemin(A,B) | -less_than(B,f1(A,B)).  [resolve(67,b,66,a)].
0.44/1.06	Derived: -contains_pq(A,B) | -less_than(B,f1(A,B)) | -contains_pq(A,C) | less_than(B,C).  [resolve(81,b,79,c)].
0.44/1.06	82 pi_sharp_find_min(A,B) | -contains_pq(A,B) | -pi_sharp_removemin(A,B).  [resolve(68,b,64,a)].
0.44/1.06	Derived: pi_sharp_find_min(A,B) | -contains_pq(A,B) | -contains_pq(A,B) | contains_pq(A,f1(A,B)).  [resolve(82,c,77,b)].
0.44/1.06	83 -contains_pq(A,B) | removemin_pq_res(A,B) = B | -pi_sharp_removemin(A,B).  [resolve(69,a,64,a)].
0.44/1.06	Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | -contains_pq(A,B) | contains_pq(A,f1(A,B)).  [resolve(83,c,77,b)].
0.44/1.06	84 -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -pi_sharp_removemin(A,B).  [resolve(70,b,64,a)].
0.44/1.06	Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -contains_pq(A,B) | contains_pq(A,f1(A,B)).  [resolve(84,c,77,b)].
0.44/1.06	85 -contains_pq(A,B) | findmin_pq_res(A,B) = B | -pi_sharp_removemin(A,B).  [resolve(71,b,64,a)].
0.44/1.06	Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | -contains_pq(A,B) | contains_pq(A,f1(A,B)).  [resolve(85,c,77,b)].
0.44/1.06	86 -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | -pi_sharp_removemin(A,B).  [resolve(72,a,64,a)].
0.44/1.06	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(86,c,77,b)].
0.44/1.06	87 -pi_removemin(A) | pi_sharp_find_min(i(A),f2(A)) # label(ax61) # label(axiom).  [clausify(56)].
0.44/1.06	88 pi_removemin(A) | -pi_sharp_find_min(i(A),B) # label(ax61) # label(axiom).  [clausify(56)].
0.44/1.06	Derived: pi_sharp_find_min(i(A),f2(A)) | -pi_sharp_find_min(i(A),B).  [resolve(87,a,88,a)].
0.44/1.06	89 -pi_find_min(A) | pi_sharp_find_min(i(A),f3(A)) # label(ax59) # label(axiom).  [clausify(59)].
0.44/1.06	90 pi_find_min(A) | -pi_sharp_find_min(i(A),B) # label(ax59) # label(axiom).  [clausify(59)].
0.44/1.06	Derived: pi_sharp_find_min(i(A),f3(A)) | -pi_sharp_find_min(i(A),B).  [resolve(89,a,90,a)].
0.44/1.06	91 pi_remove(A,B) | -pi_sharp_remove(i(A),B) # label(ax57) # label(axiom).  [clausify(58)].
0.44/1.06	92 -pi_remove(A,B) | pi_sharp_remove(i(A),B) # label(ax57) # label(axiom).  [clausify(58)].
0.44/1.06	93 pi_sharp_remove(A,B) | -contains_pq(A,B) # label(ax56) # label(axiom).  [clausify(52)].
0.44/1.06	94 -pi_sharp_remove(A,B) | contains_pq(A,B) # label(ax56) # label(axiom).  [clausify(52)].
0.44/1.06	
0.44/1.06	============================== end predicate elimination =============
0.44/1.06	
0.44/1.06	Auto_denials:  (non-Horn, no changes).
0.44/1.06	
0.44/1.06	Term ordering decisions:
0.44/1.06	Function symbol KB weights:  create_slb=1. bad=1. bottom=1. create_pq=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=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.
0.44/1.06	
0.44/1.06	============================== end of process initial clauses ========
0.44/1.06	
0.44/1.06	============================== CLAUSES FOR SEARCH ====================
0.44/1.06	
0.44/1.06	============================== end of clauses for search =============
0.44/1.06	
0.44/1.06	============================== SEARCH ================================
0.44/1.06	
0.44/1.06	% Starting search at 0.03 seconds.
0.44/1.06	
0.44/1.06	============================== PROOF =================================
0.44/1.06	% SZS status Theorem
0.44/1.06	% SZS output start Refutation
0.44/1.06	
0.44/1.06	% Proof 1 at 0.03 (+ 0.00) seconds.
0.44/1.06	% Length of proof is 8.
0.44/1.06	% Level of proof is 3.
0.44/1.06	% Maximum clause weight is 17.000.
0.44/1.06	% Given clauses 23.
0.44/1.06	
0.44/1.06	57 (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].
0.44/1.06	61 -(all U ((all V all W all X all Y i(triple(V,U,X)) = i(triple(W,U,Y))) -> (all Z all X1 all X2 all X3 all X4 all X5 i(triple(Z,insert_slb(U,pair(X4,X5)),X2)) = i(triple(X1,insert_slb(U,pair(X4,X5)),X3))))) # label(l2_co) # label(negated_conjecture) # label(non_clause).  [assumption].
0.44/1.06	115 i(triple(A,c1,B)) = i(triple(C,c1,D)) # label(l2_co) # label(negated_conjecture).  [clausify(61)].
0.44/1.06	120 i(triple(A,insert_slb(B,pair(C,D)),E)) = insert_pq(i(triple(A,B,E)),C) # label(ax55) # label(axiom).  [clausify(57)].
0.44/1.06	130 i(triple(c3,insert_slb(c1,pair(c6,c7)),c5)) != i(triple(c2,insert_slb(c1,pair(c6,c7)),c4)) # label(l2_co) # label(negated_conjecture).  [clausify(61)].
0.44/1.06	131 insert_pq(i(triple(c3,c1,c5)),c6) != insert_pq(i(triple(c2,c1,c4)),c6).  [copy(130),rewrite([120(9),120(16)])].
0.44/1.06	199 insert_pq(i(triple(A,c1,B)),C) = insert_pq(i(triple(D,c1,E)),C).  [para(115(a,1),120(a,2,1)),rewrite([120(5)])].
0.44/1.06	200 $F.  [resolve(199,a,131,a)].
0.44/1.06	
0.44/1.06	% SZS output end Refutation
0.44/1.06	============================== end of proof ==========================
0.44/1.06	
0.44/1.06	============================== STATISTICS ============================
0.44/1.06	
0.44/1.06	Given=23. Generated=132. Kept=93. proofs=1.
0.44/1.06	Usable=23. Sos=69. Demods=13. Limbo=0, Disabled=127. Hints=0.
0.44/1.06	Megabytes=0.33.
0.44/1.06	User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
0.44/1.06	
0.44/1.06	============================== end of statistics =====================
0.44/1.06	
0.44/1.06	============================== end of search =========================
0.44/1.06	
0.44/1.06	THEOREM PROVED
0.44/1.06	% SZS status Theorem
0.44/1.06	
0.44/1.06	Exiting with 1 proof.
0.44/1.06	
0.44/1.06	Process 25037 exit (max_proofs) Wed Jul 14 14:08:33 2021
0.44/1.06	Prover9 interrupted
0.44/1.07	EOF