0.03/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.12	% Command    : tptp2X_and_run_prover9 %d %s
0.12/0.33	% Computer   : n029.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   : 960
0.12/0.33	% DateTime   : Thu Jul  2 07:53:03 EDT 2020
0.12/0.33	% CPUTime    : 
0.80/1.12	============================== Prover9 ===============================
0.80/1.12	Prover9 (32) version 2009-11A, November 2009.
0.80/1.12	Process 21092 was started by sandbox2 on n029.cluster.edu,
0.80/1.12	Thu Jul  2 07:53:03 2020
0.80/1.12	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_20937_n029.cluster.edu".
0.80/1.12	============================== end of head ===========================
0.80/1.12	
0.80/1.12	============================== INPUT =================================
0.80/1.12	
0.80/1.12	% Reading from file /tmp/Prover9_20937_n029.cluster.edu
0.80/1.12	
0.80/1.12	set(prolog_style_variables).
0.80/1.12	set(auto2).
0.80/1.12	    % set(auto2) -> set(auto).
0.80/1.12	    % set(auto) -> set(auto_inference).
0.80/1.12	    % set(auto) -> set(auto_setup).
0.80/1.12	    % set(auto_setup) -> set(predicate_elim).
0.80/1.12	    % set(auto_setup) -> assign(eq_defs, unfold).
0.80/1.12	    % set(auto) -> set(auto_limits).
0.80/1.12	    % set(auto_limits) -> assign(max_weight, "100.000").
0.80/1.12	    % set(auto_limits) -> assign(sos_limit, 20000).
0.80/1.12	    % set(auto) -> set(auto_denials).
0.80/1.12	    % set(auto) -> set(auto_process).
0.80/1.12	    % set(auto2) -> assign(new_constants, 1).
0.80/1.12	    % set(auto2) -> assign(fold_denial_max, 3).
0.80/1.12	    % set(auto2) -> assign(max_weight, "200.000").
0.80/1.12	    % set(auto2) -> assign(max_hours, 1).
0.80/1.12	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.80/1.12	    % set(auto2) -> assign(max_seconds, 0).
0.80/1.12	    % set(auto2) -> assign(max_minutes, 5).
0.80/1.12	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.80/1.12	    % set(auto2) -> set(sort_initial_sos).
0.80/1.12	    % set(auto2) -> assign(sos_limit, -1).
0.80/1.12	    % set(auto2) -> assign(lrs_ticks, 3000).
0.80/1.12	    % set(auto2) -> assign(max_megs, 400).
0.80/1.12	    % set(auto2) -> assign(stats, some).
0.80/1.12	    % set(auto2) -> clear(echo_input).
0.80/1.12	    % set(auto2) -> set(quiet).
0.80/1.12	    % set(auto2) -> clear(print_initial_clauses).
0.80/1.12	    % set(auto2) -> clear(print_given).
0.80/1.12	assign(lrs_ticks,-1).
0.80/1.12	assign(sos_limit,10000).
0.80/1.12	assign(order,kbo).
0.80/1.12	set(lex_order_vars).
0.80/1.12	clear(print_given).
0.80/1.12	
0.80/1.12	% formulas(sos).  % not echoed (49 formulas)
0.80/1.12	
0.80/1.12	============================== end of input ==========================
0.80/1.12	
0.80/1.12	% From the command line: assign(max_seconds, 960).
0.80/1.12	
0.80/1.12	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.80/1.12	
0.80/1.12	% Formulas that are not ordinary clauses:
0.80/1.12	1 (all B (bool(B) -> or1(true,B) = true)) # label(or1_axiom3) # label(axiom) # label(non_clause).  [assumption].
0.80/1.12	2 (all B phi(B) = lazy_impl(true,B)) # label(lazy_impl_axiom3) # label(axiom) # label(non_clause).  [assumption].
0.80/1.12	3 (all P all R f6(P,R) = lazy_impl(prop(R),impl(f5(P,R),R))) # label(def_f6) # label(axiom) # label(non_clause).  [assumption].
0.80/1.12	4 (all B lazy_and1(true,B) = phi(B)) # label(lazy_and1_axiom3) # label(axiom) # label(non_clause).  [assumption].
0.80/1.12	5 (all B (bool(B) -> impl(true,B) = B)) # label(impl_axiom4) # label(axiom) # label(non_clause).  [assumption].
0.80/1.12	6 (all A (-bool(A) -> not1(A) = phi(A))) # label(not1_axiom1) # label(axiom) # label(non_clause).  [assumption].
0.80/1.12	7 (all P exists R (exists2(P) = phi(f6(P,R)) & -(exists R1 forallprefers(f6(P,R1),f6(P,R))))) # label(def_exists2) # label(axiom) # label(non_clause).  [assumption].
0.80/1.12	8 (all A all B (-bool(A) -> lazy_impl(A,B) = phi(A))) # label(lazy_impl_axiom1) # label(axiom) # label(non_clause).  [assumption].
0.80/1.12	9 (all B (bool(B) -> and1(false,B) = false)) # label(and1_axiom3) # label(axiom) # label(non_clause).  [assumption].
0.80/1.12	10 (all P all Q all R lazy_impl(prop(R),impl(impl(P,R),impl(impl(Q,R),R))) = f3(P,Q,R)) # label(def_f3) # label(axiom) # label(non_clause).  [assumption].
0.80/1.12	11 (all A all B (-bool(B) & bool(A) -> or1(A,B) = phi(B))) # label(or1_axiom2) # label(axiom) # label(non_clause).  [assumption].
0.80/1.12	12 (all X (-bool(X) <-> prop(X) = false)) # label(prop_false) # label(axiom) # label(non_clause).  [assumption].
0.80/1.12	13 (all B (bool(B) -> true = impl(false,B))) # label(impl_axiom3) # label(axiom) # label(non_clause).  [assumption].
0.80/1.12	14 (all P all X all R f4(P,X,R) = impl(apply(P,X),R)) # label(def_f4) # label(axiom) # label(non_clause).  [assumption].
0.80/1.12	15 (all A all B (-bool(B) & bool(A) -> impl(A,B) = phi(B))) # label(impl_axiom2) # label(axiom) # label(non_clause).  [assumption].
0.80/1.12	16 (exists P (-(exists P1 forallprefers(f7(P1),f7(P))) & false2 = phi(f7(P)))) # label(def_false2) # label(axiom) # label(non_clause).  [assumption].
0.80/1.13	17 (all P all Q all R lazy_impl(prop(R),impl(impl(P,impl(Q,R)),R)) = f1(P,Q,R)) # label(def_f1) # label(axiom) # label(non_clause).  [assumption].
0.80/1.13	18 (all X all Y (existsprefers(X,Y) <-> X = true & Y = false | d(Y) & d(X) & bool(Y) & -bool(X) | d(Y) & -d(X))) # label(def_existsprefers) # label(axiom) # label(non_clause).  [assumption].
0.80/1.13	19 (all P exists X (-(exists X1 existsprefers(apply(P,X1),apply(P,X))) & exists1(P) = phi(apply(P,X)))) # label(exists1_axiom1) # label(axiom) # label(non_clause).  [assumption].
0.80/1.13	20 (all X all Y (forallprefers(X,Y) <-> -d(X) & d(Y) | Y = true & X = false | d(Y) & d(X) & -bool(X) & bool(Y))) # label(def_forallprefers) # label(axiom) # label(non_clause).  [assumption].
0.80/1.13	21 (all X (phi(X) = err & -d(X) | d(X) & phi(X) = X)) # label(def_phi) # label(axiom) # label(non_clause).  [assumption].
0.80/1.13	22 (all B true = lazy_impl(false,B)) # label(lazy_impl_axiom2) # label(axiom) # label(non_clause).  [assumption].
0.80/1.13	23 (all A all B (-bool(A) -> phi(A) = and1(A,B))) # label(and1_axiom1) # label(axiom) # label(non_clause).  [assumption].
0.80/1.13	24 (all A all B (-bool(A) -> phi(A) = lazy_and1(A,B))) # label(lazy_and1_axiom1) # label(axiom) # label(non_clause).  [assumption].
0.80/1.13	25 (all B (bool(B) -> B = and1(true,B))) # label(and1_axiom4) # label(axiom) # label(non_clause).  [assumption].
0.80/1.13	26 (all P all Q exists R (-(exists R1 forallprefers(f3(P,Q,R1),f3(P,Q,R))) & or2(P,Q) = phi(f3(P,Q,R)))) # label(def_or2) # label(axiom) # label(non_clause).  [assumption].
0.80/1.13	27 (all A all B (-bool(A) -> phi(A) = or1(A,B))) # label(or1_axiom1) # label(axiom) # label(non_clause).  [assumption].
0.80/1.13	28 (all P lazy_impl(prop(P),P) = f7(P)) # label(def_f7) # label(axiom) # label(non_clause).  [assumption].
0.80/1.13	29 (all A all B (-bool(A) -> phi(A) = impl(A,B))) # label(impl_axiom1) # label(axiom) # label(non_clause).  [assumption].
0.80/1.13	30 (all B false = lazy_and1(false,B)) # label(lazy_and1_axiom2) # label(axiom) # label(non_clause).  [assumption].
0.80/1.13	31 (all P all Q all R f2(P,Q,R) = lazy_impl(prop(R),impl(lazy_impl(P,impl(Q,R)),R))) # label(def_f2) # label(axiom) # label(non_clause).  [assumption].
0.80/1.13	32 (all P all Q exists R (phi(f2(P,Q,R)) = lazy_and2(P,Q) & -(exists R1 forallprefers(f2(P,Q,R1),f2(P,Q,R))))) # label(def_lazy_and2) # label(axiom) # label(non_clause).  [assumption].
0.80/1.13	33 (all P all R exists X (-(exists X1 forallprefers(f4(P,X1,R),f4(P,X,R))) & f5(P,R) = phi(f4(P,X,R)))) # label(def_f5) # label(axiom) # label(non_clause).  [assumption].
0.80/1.13	34 (all B (bool(B) -> B = or1(false,B))) # label(or1_axiom4) # label(axiom) # label(non_clause).  [assumption].
0.80/1.13	35 (all P impl(P,false2) = not2(P)) # label(def_not2) # label(axiom) # label(non_clause).  [assumption].
0.80/1.13	36 (all X (false = X | X = true <-> bool(X))) # label(def_bool) # label(axiom) # label(non_clause).  [assumption].
0.80/1.13	37 (all A all B (bool(A) & -bool(B) -> phi(B) = and1(A,B))) # label(and1_axiom2) # label(axiom) # label(non_clause).  [assumption].
0.80/1.13	38 (all P all Q exists R (-(exists R1 forallprefers(f1(P,Q,R1),f1(P,Q,R))) & phi(f1(P,Q,R)) = and2(P,Q))) # label(def_and2) # label(axiom) # label(non_clause).  [assumption].
0.80/1.13	39 (all X (bool(X) <-> true = prop(X))) # label(prop_true) # label(axiom) # label(non_clause).  [assumption].
0.80/1.13	
0.80/1.13	============================== end of process non-clausal formulas ===
0.80/1.13	
0.80/1.13	============================== PROCESS INITIAL CLAUSES ===============
0.80/1.13	
0.80/1.13	============================== PREDICATE ELIMINATION =================
0.80/1.13	
0.80/1.13	============================== end predicate elimination =============
0.80/1.13	
0.80/1.13	Auto_denials:  (non-Horn, no changes).
0.80/1.13	
0.80/1.13	Term ordering decisions:
0.80/1.13	Function symbol KB weights:  true=1. false=1. err=1. false2=1. false1=1. c1=1. impl=1. lazy_impl=1. and1=1. or1=1. lazy_and1=1. apply=1. f5=1. f6=1. and2=1. lazy_and2=1. or2=1. f3=1. f4=1. f7=1. f8=1. phi=1. prop=1. not1=1. f7=1. exists1=1. exists2=1. not2=1. f1=1. f2=1. f1=1. f2=1. f3=1. f4=1.
0.80/1.13	
0.80/1.13	============================== end of process initial clauses ========
0.80/1.13	
0.80/1.13	============================== CLAUSES FOR SEARCH ====================
0.80/1.13	
0.80/1.13	============================== end of clauses for search =============
0.85/1.24	
0.85/1.24	============================== SEARCH ================================
0.85/1.24	
0.85/1.24	% Starting search at 0.01 seconds.
0.85/1.24	
0.85/1.24	============================== PROOF =================================
0.85/1.24	% SZS status Theorem
0.85/1.24	% SZS output start Refutation
0.85/1.24	
0.85/1.24	% Proof 1 at 0.12 (+ 0.00) seconds.
0.85/1.24	% Length of proof is 58.
0.85/1.24	% Level of proof is 10.
0.85/1.24	% Maximum clause weight is 9.000.
0.85/1.24	% Given clauses 267.
0.85/1.24	
0.85/1.24	2 (all B phi(B) = lazy_impl(true,B)) # label(lazy_impl_axiom3) # label(axiom) # label(non_clause).  [assumption].
0.85/1.24	9 (all B (bool(B) -> and1(false,B) = false)) # label(and1_axiom3) # label(axiom) # label(non_clause).  [assumption].
0.85/1.24	12 (all X (-bool(X) <-> prop(X) = false)) # label(prop_false) # label(axiom) # label(non_clause).  [assumption].
0.85/1.24	16 (exists P (-(exists P1 forallprefers(f7(P1),f7(P))) & false2 = phi(f7(P)))) # label(def_false2) # label(axiom) # label(non_clause).  [assumption].
0.85/1.24	20 (all X all Y (forallprefers(X,Y) <-> -d(X) & d(Y) | Y = true & X = false | d(Y) & d(X) & -bool(X) & bool(Y))) # label(def_forallprefers) # label(axiom) # label(non_clause).  [assumption].
0.85/1.24	21 (all X (phi(X) = err & -d(X) | d(X) & phi(X) = X)) # label(def_phi) # label(axiom) # label(non_clause).  [assumption].
0.85/1.24	22 (all B true = lazy_impl(false,B)) # label(lazy_impl_axiom2) # label(axiom) # label(non_clause).  [assumption].
0.85/1.24	28 (all P lazy_impl(prop(P),P) = f7(P)) # label(def_f7) # label(axiom) # label(non_clause).  [assumption].
0.85/1.24	30 (all B false = lazy_and1(false,B)) # label(lazy_and1_axiom2) # label(axiom) # label(non_clause).  [assumption].
0.85/1.24	36 (all X (false = X | X = true <-> bool(X))) # label(def_bool) # label(axiom) # label(non_clause).  [assumption].
0.85/1.24	39 (all X (bool(X) <-> true = prop(X))) # label(prop_true) # label(axiom) # label(non_clause).  [assumption].
0.85/1.24	40 d(true) # label(false_true_err_in_d_AndLHS) # label(axiom).  [assumption].
0.85/1.24	41 d(false) # label(false_true_err_in_d_AndRHS_AndLHS) # label(axiom).  [assumption].
0.85/1.24	43 false = false1 # label(def_false1) # label(axiom).  [assumption].
0.85/1.24	44 false1 = false.  [copy(43),flip(a)].
0.85/1.24	48 phi(f7(c1)) = false2 # label(def_false2) # label(axiom).  [clausify(16)].
0.85/1.24	49 lazy_impl(false,A) = true # label(lazy_impl_axiom2) # label(axiom).  [clausify(22)].
0.85/1.24	50 lazy_and1(false,A) = false # label(lazy_and1_axiom2) # label(axiom).  [clausify(30)].
0.85/1.24	51 lazy_impl(true,A) = phi(A) # label(lazy_impl_axiom3) # label(axiom).  [clausify(2)].
0.85/1.24	53 bool(A) | prop(A) = false # label(prop_false) # label(axiom).  [clausify(12)].
0.85/1.24	58 f7(A) = lazy_impl(prop(A),A) # label(def_f7) # label(axiom).  [clausify(28)].
0.85/1.24	64 phi(A) = err | phi(A) = A # label(def_phi) # label(axiom).  [clausify(21)].
0.85/1.24	85 err != true # label(distinct_false_true_err_AndRHS_AndLHS) # label(axiom).  [assumption].
0.85/1.24	88 false2 != false1 # label(false1_false2) # label(negated_conjecture).  [assumption].
0.85/1.24	89 false2 != false.  [copy(88),rewrite([44(2)])].
0.85/1.24	90 -forallprefers(f7(A),f7(c1)) # label(def_false2) # label(axiom).  [clausify(16)].
0.85/1.24	91 -forallprefers(lazy_impl(prop(A),A),lazy_impl(prop(c1),c1)).  [copy(90),rewrite([58(1),58(4)])].
0.85/1.24	103 A != false | bool(A) # label(def_bool) # label(axiom).  [clausify(36)].
0.85/1.24	104 false != A | bool(A).  [copy(103),flip(a)].
0.85/1.24	105 A != true | bool(A) # label(def_bool) # label(axiom).  [clausify(36)].
0.85/1.24	106 true != A | bool(A).  [copy(105),flip(a)].
0.85/1.24	107 -d(A) | phi(A) = A # label(def_phi) # label(axiom).  [clausify(21)].
0.85/1.24	108 -bool(A) | prop(A) = true # label(prop_true) # label(axiom).  [clausify(39)].
0.85/1.24	109 bool(A) | prop(A) != true # label(prop_true) # label(axiom).  [clausify(39)].
0.85/1.24	112 -bool(A) | and1(false,A) = false # label(and1_axiom3) # label(axiom).  [clausify(9)].
0.85/1.24	126 A = false | A = true | -bool(A) # label(def_bool) # label(axiom).  [clausify(36)].
0.85/1.24	127 false = A | true = A | -bool(A).  [copy(126),flip(a),flip(b)].
0.85/1.24	130 forallprefers(A,B) | B != true | A != false # label(def_forallprefers) # label(axiom).  [clausify(20)].
0.85/1.24	131 forallprefers(A,B) | true != B | false != A.  [copy(130),flip(b),flip(c)].
0.85/1.24	154 phi(lazy_impl(prop(c1),c1)) = false2.  [back_rewrite(48),rewrite([58(2)])].
0.85/1.24	178 bool(false).  [resolve(104,a,50,a(flip)),rewrite([50(2)])].
0.85/1.24	180 bool(true).  [resolve(106,a,49,a(flip)),rewrite([49(2)])].
0.85/1.24	181 phi(false) = false.  [resolve(107,a,41,a)].
0.85/1.24	182 phi(true) = true.  [resolve(107,a,40,a)].
0.85/1.24	189 prop(A) = true | prop(A) = false.  [resolve(108,a,53,a)].
0.85/1.24	250 forallprefers(A,true) | false != A.  [resolve(131,b,64,b(flip)),rewrite([182(2),182(6)]),flip(c),unit_del(c,85)].
0.85/1.24	314 prop(false) = true.  [resolve(178,a,108,a)].
0.85/1.24	325 and1(false,true) = false.  [resolve(180,a,112,a)].
0.85/1.24	339 -forallprefers(false,lazy_impl(prop(c1),c1)).  [para(314(a,1),91(a,1,1)),rewrite([51(3),181(2)])].
0.85/1.24	440 forallprefers(false,true).  [resolve(250,b,325,a(flip)),rewrite([325(3)])].
0.85/1.24	502 prop(c1) = true.  [para(189(b,1),339(a,2,1)),rewrite([49(8)]),unit_del(b,440)].
0.85/1.24	539 -forallprefers(false,phi(c1)).  [back_rewrite(339),rewrite([502(3),51(4)])].
0.85/1.24	541 phi(phi(c1)) = false2.  [back_rewrite(154),rewrite([502(2),51(3)])].
0.85/1.24	562 bool(c1).  [resolve(502,a,109,b)].
0.85/1.24	574 c1 = false | c1 = true.  [resolve(562,a,127,c),flip(a),flip(b)].
0.85/1.24	584 phi(c1) = err | -forallprefers(false,c1).  [para(64(b,1),539(a,2))].
0.85/1.24	1156 c1 = true.  [para(574(a,1),541(a,1,1,1)),rewrite([181(5),181(5)]),flip(b),unit_del(b,89)].
0.85/1.24	1187 $F.  [back_rewrite(584),rewrite([1156(1),182(2),1156(5)]),flip(a),unit_del(a,85),unit_del(b,440)].
0.85/1.24	
0.85/1.24	% SZS output end Refutation
0.85/1.24	============================== end of proof ==========================
0.85/1.24	
0.85/1.24	============================== STATISTICS ============================
0.85/1.24	
0.85/1.24	Given=267. Generated=2420. Kept=1111. proofs=1.
0.85/1.24	Usable=224. Sos=680. Demods=153. Limbo=31, Disabled=254. Hints=0.
0.85/1.24	Megabytes=1.98.
0.85/1.24	User_CPU=0.12, System_CPU=0.00, Wall_clock=1.
0.85/1.24	
0.85/1.24	============================== end of statistics =====================
0.85/1.24	
0.85/1.24	============================== end of search =========================
0.85/1.24	
0.85/1.24	THEOREM PROVED
0.85/1.24	% SZS status Theorem
0.85/1.24	
0.85/1.24	Exiting with 1 proof.
0.85/1.24	
0.85/1.24	Process 21092 exit (max_proofs) Thu Jul  2 07:53:04 2020
0.85/1.24	Prover9 interrupted
0.85/1.24	EOF