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
0.13/0.33	% Computer   : n008.cluster.edu
0.13/0.33	% Model      : x86_64 x86_64
0.13/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.33	% Memory     : 8042.1875MB
0.13/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.33	% CPULimit   : 180
0.13/0.33	% DateTime   : Thu Aug 29 10:18:08 EDT 2019
0.13/0.33	% CPUTime    : 
0.77/1.03	============================== Prover9 ===============================
0.77/1.03	Prover9 (32) version 2009-11A, November 2009.
0.77/1.03	Process 20827 was started by sandbox2 on n008.cluster.edu,
0.77/1.03	Thu Aug 29 10:18:09 2019
0.77/1.03	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 180 -f /tmp/Prover9_20674_n008.cluster.edu".
0.77/1.03	============================== end of head ===========================
0.77/1.03	
0.77/1.03	============================== INPUT =================================
0.77/1.03	
0.77/1.03	% Reading from file /tmp/Prover9_20674_n008.cluster.edu
0.77/1.03	
0.77/1.03	set(prolog_style_variables).
0.77/1.03	set(auto2).
0.77/1.03	    % set(auto2) -> set(auto).
0.77/1.03	    % set(auto) -> set(auto_inference).
0.77/1.03	    % set(auto) -> set(auto_setup).
0.77/1.03	    % set(auto_setup) -> set(predicate_elim).
0.77/1.03	    % set(auto_setup) -> assign(eq_defs, unfold).
0.77/1.03	    % set(auto) -> set(auto_limits).
0.77/1.03	    % set(auto_limits) -> assign(max_weight, "100.000").
0.77/1.03	    % set(auto_limits) -> assign(sos_limit, 20000).
0.77/1.03	    % set(auto) -> set(auto_denials).
0.77/1.03	    % set(auto) -> set(auto_process).
0.77/1.03	    % set(auto2) -> assign(new_constants, 1).
0.77/1.03	    % set(auto2) -> assign(fold_denial_max, 3).
0.77/1.03	    % set(auto2) -> assign(max_weight, "200.000").
0.77/1.03	    % set(auto2) -> assign(max_hours, 1).
0.77/1.03	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.77/1.03	    % set(auto2) -> assign(max_seconds, 0).
0.77/1.03	    % set(auto2) -> assign(max_minutes, 5).
0.77/1.03	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.77/1.03	    % set(auto2) -> set(sort_initial_sos).
0.77/1.03	    % set(auto2) -> assign(sos_limit, -1).
0.77/1.03	    % set(auto2) -> assign(lrs_ticks, 3000).
0.77/1.03	    % set(auto2) -> assign(max_megs, 400).
0.77/1.03	    % set(auto2) -> assign(stats, some).
0.77/1.03	    % set(auto2) -> clear(echo_input).
0.77/1.03	    % set(auto2) -> set(quiet).
0.77/1.03	    % set(auto2) -> clear(print_initial_clauses).
0.77/1.03	    % set(auto2) -> clear(print_given).
0.77/1.03	assign(lrs_ticks,-1).
0.77/1.03	assign(sos_limit,10000).
0.77/1.03	assign(order,kbo).
0.77/1.03	set(lex_order_vars).
0.77/1.03	clear(print_given).
0.77/1.03	
0.77/1.03	% formulas(sos).  % not echoed (49 formulas)
0.77/1.03	
0.77/1.03	============================== end of input ==========================
0.77/1.03	
0.77/1.03	% From the command line: assign(max_seconds, 180).
0.77/1.03	
0.77/1.03	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.77/1.03	
0.77/1.03	% Formulas that are not ordinary clauses:
0.77/1.03	1 (all B phi(B) = lazy_and1(true,B)) # label(lazy_and1_axiom3) # label(axiom) # label(non_clause).  [assumption].
0.77/1.03	2 (all B phi(B) = lazy_impl(true,B)) # label(lazy_impl_axiom3) # label(axiom) # label(non_clause).  [assumption].
0.77/1.03	3 (all B (bool(B) -> or1(false,B) = B)) # label(or1_axiom4) # label(axiom) # label(non_clause).  [assumption].
0.77/1.03	4 (all B true = lazy_impl(false,B)) # label(lazy_impl_axiom2) # label(axiom) # label(non_clause).  [assumption].
0.77/1.03	5 (all B (bool(B) -> or1(true,B) = true)) # label(or1_axiom3) # label(axiom) # label(non_clause).  [assumption].
0.77/1.03	6 (all P all Q all R f1(P,Q,R) = lazy_impl(prop(R),impl(impl(P,impl(Q,R)),R))) # label(def_f1) # label(axiom) # label(non_clause).  [assumption].
0.77/1.03	7 (exists P (-(exists P1 forallprefers(f7(P1),f7(P))) & phi(f7(P)) = false2)) # label(def_false2) # label(axiom) # label(non_clause).  [assumption].
0.77/1.03	8 (all P exists R (phi(f6(P,R)) = exists2(P) & -(exists R1 forallprefers(f6(P,R1),f6(P,R))))) # label(def_exists2) # label(axiom) # label(non_clause).  [assumption].
0.77/1.03	9 (all B (bool(B) -> impl(true,B) = B)) # label(impl_axiom4) # label(axiom) # label(non_clause).  [assumption].
0.77/1.03	10 (all B (bool(B) -> and1(true,B) = B)) # label(and1_axiom4) # label(axiom) # label(non_clause).  [assumption].
0.77/1.03	11 (all X all Y (-d(X) & d(Y) | Y = false & true = X | d(Y) & -bool(X) & bool(Y) & d(X) <-> existsprefers(X,Y))) # label(def_existsprefers) # label(axiom) # label(non_clause).  [assumption].
0.77/1.03	12 (all A (-bool(A) -> not1(A) = phi(A))) # label(not1_axiom1) # label(axiom) # label(non_clause).  [assumption].
0.77/1.03	13 (all A all B (-bool(B) & bool(A) -> or1(A,B) = phi(B))) # label(or1_axiom2) # label(axiom) # label(non_clause).  [assumption].
0.77/1.03	14 (all A all B (-bool(A) -> phi(A) = impl(A,B))) # label(impl_axiom1) # label(axiom) # label(non_clause).  [assumption].
0.77/1.03	15 (all A all B (-bool(A) -> phi(A) = lazy_and1(A,B))) # label(lazy_and1_axiom1) # label(axiom) # label(non_clause).  [assumption].
0.77/1.03	16 (all B (bool(B) -> and1(false,B) = false)) # label(and1_axiom3) # label(axiom) # label(non_clause).  [assumption].
0.77/1.04	17 (all P all X all R impl(apply(P,X),R) = f4(P,X,R)) # label(def_f4) # label(axiom) # label(non_clause).  [assumption].
0.77/1.04	18 (all P all Q all R lazy_impl(prop(R),impl(lazy_impl(P,impl(Q,R)),R)) = f2(P,Q,R)) # label(def_f2) # label(axiom) # label(non_clause).  [assumption].
0.77/1.04	19 (all X (bool(X) <-> prop(X) = true)) # label(prop_true) # label(axiom) # label(non_clause).  [assumption].
0.77/1.04	20 (all P not2(P) = impl(P,false2)) # label(def_not2) # label(axiom) # label(non_clause).  [assumption].
0.77/1.04	21 (all B false = lazy_and1(false,B)) # label(lazy_and1_axiom2) # label(axiom) # label(non_clause).  [assumption].
0.77/1.04	22 (all X (d(X) & phi(X) = X | -d(X) & err = phi(X))) # label(def_phi) # label(axiom) # label(non_clause).  [assumption].
0.77/1.04	23 (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].
0.77/1.04	24 (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].
0.77/1.04	25 (all A all B (bool(A) & -bool(B) -> phi(B) = and1(A,B))) # label(and1_axiom2) # label(axiom) # label(non_clause).  [assumption].
0.77/1.04	26 (all A all B (-bool(A) -> phi(A) = lazy_impl(A,B))) # label(lazy_impl_axiom1) # label(axiom) # label(non_clause).  [assumption].
0.77/1.04	27 (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].
0.77/1.04	28 (all X (X = false | true = X <-> bool(X))) # label(def_bool) # label(axiom) # label(non_clause).  [assumption].
0.77/1.04	29 (all A all B (-bool(A) -> and1(A,B) = phi(A))) # label(and1_axiom1) # label(axiom) # label(non_clause).  [assumption].
0.77/1.04	30 (all A all B (-bool(A) -> phi(A) = or1(A,B))) # label(or1_axiom1) # label(axiom) # label(non_clause).  [assumption].
0.77/1.04	31 (all X all Y (d(X) & d(Y) & bool(Y) & -bool(X) | Y = true & X = false | -d(X) & d(Y) <-> forallprefers(X,Y))) # label(def_forallprefers) # label(axiom) # label(non_clause).  [assumption].
0.77/1.04	32 (all P f7(P) = lazy_impl(prop(P),P)) # label(def_f7) # label(axiom) # label(non_clause).  [assumption].
0.77/1.04	33 (all A all B (-bool(B) & bool(A) -> impl(A,B) = phi(B))) # label(impl_axiom2) # label(axiom) # label(non_clause).  [assumption].
0.77/1.04	34 (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].
0.77/1.04	35 (all X (prop(X) = false <-> -bool(X))) # label(prop_false) # label(axiom) # label(non_clause).  [assumption].
0.77/1.04	36 (all B (bool(B) -> true = impl(false,B))) # label(impl_axiom3) # label(axiom) # label(non_clause).  [assumption].
0.77/1.04	37 (all P all Q exists R (phi(f3(P,Q,R)) = or2(P,Q) & -(exists R1 forallprefers(f3(P,Q,R1),f3(P,Q,R))))) # label(def_or2) # label(axiom) # label(non_clause).  [assumption].
0.77/1.04	38 (all P all R exists X (-(exists X1 forallprefers(f4(P,X1,R),f4(P,X,R))) & phi(f4(P,X,R)) = f5(P,R))) # label(def_f5) # label(axiom) # label(non_clause).  [assumption].
0.77/1.04	39 (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].
0.77/1.04	
0.77/1.04	============================== end of process non-clausal formulas ===
0.77/1.04	
0.77/1.04	============================== PROCESS INITIAL CLAUSES ===============
0.77/1.04	
0.77/1.04	============================== PREDICATE ELIMINATION =================
0.77/1.04	
0.77/1.04	============================== end predicate elimination =============
0.77/1.04	
0.77/1.04	Auto_denials:  (non-Horn, no changes).
0.77/1.04	
0.77/1.04	Term ordering decisions:
0.77/1.04	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.
0.77/1.04	
0.77/1.04	============================== end of process initial clauses ========
0.77/1.04	
0.77/1.04	============================== CLAUSES FOR SEARCH ====================
0.77/1.04	
0.77/1.04	============================== end of clauses for search =============
0.89/1.16	
0.89/1.16	============================== SEARCH ================================
0.89/1.16	
0.89/1.16	% Starting search at 0.02 seconds.
0.89/1.16	
0.89/1.16	============================== PROOF =================================
0.89/1.16	% SZS status Theorem
0.89/1.16	% SZS output start Refutation
0.89/1.16	
0.89/1.16	% Proof 1 at 0.14 (+ 0.00) seconds.
0.89/1.16	% Length of proof is 58.
0.89/1.16	% Level of proof is 10.
0.89/1.16	% Maximum clause weight is 9.000.
0.89/1.16	% Given clauses 265.
0.89/1.16	
0.89/1.16	2 (all B phi(B) = lazy_impl(true,B)) # label(lazy_impl_axiom3) # label(axiom) # label(non_clause).  [assumption].
0.89/1.16	4 (all B true = lazy_impl(false,B)) # label(lazy_impl_axiom2) # label(axiom) # label(non_clause).  [assumption].
0.89/1.16	7 (exists P (-(exists P1 forallprefers(f7(P1),f7(P))) & phi(f7(P)) = false2)) # label(def_false2) # label(axiom) # label(non_clause).  [assumption].
0.89/1.16	16 (all B (bool(B) -> and1(false,B) = false)) # label(and1_axiom3) # label(axiom) # label(non_clause).  [assumption].
0.89/1.16	19 (all X (bool(X) <-> prop(X) = true)) # label(prop_true) # label(axiom) # label(non_clause).  [assumption].
0.89/1.16	21 (all B false = lazy_and1(false,B)) # label(lazy_and1_axiom2) # label(axiom) # label(non_clause).  [assumption].
0.89/1.16	22 (all X (d(X) & phi(X) = X | -d(X) & err = phi(X))) # label(def_phi) # label(axiom) # label(non_clause).  [assumption].
0.89/1.16	28 (all X (X = false | true = X <-> bool(X))) # label(def_bool) # label(axiom) # label(non_clause).  [assumption].
0.89/1.16	31 (all X all Y (d(X) & d(Y) & bool(Y) & -bool(X) | Y = true & X = false | -d(X) & d(Y) <-> forallprefers(X,Y))) # label(def_forallprefers) # label(axiom) # label(non_clause).  [assumption].
0.89/1.16	32 (all P f7(P) = lazy_impl(prop(P),P)) # label(def_f7) # label(axiom) # label(non_clause).  [assumption].
0.89/1.16	35 (all X (prop(X) = false <-> -bool(X))) # label(prop_false) # label(axiom) # label(non_clause).  [assumption].
0.89/1.16	40 d(true) # label(false_true_err_in_d_AndLHS) # label(axiom).  [assumption].
0.89/1.16	42 d(false) # label(false_true_err_in_d_AndRHS_AndRHS) # label(axiom).  [assumption].
0.89/1.16	43 false1 = false # label(def_false1) # label(axiom).  [assumption].
0.89/1.16	47 lazy_impl(false,A) = true # label(lazy_impl_axiom2) # label(axiom).  [clausify(4)].
0.89/1.16	48 phi(f7(c1)) = false2 # label(def_false2) # label(axiom).  [clausify(7)].
0.89/1.16	49 lazy_and1(false,A) = false # label(lazy_and1_axiom2) # label(axiom).  [clausify(21)].
0.89/1.16	51 lazy_impl(true,A) = phi(A) # label(lazy_impl_axiom3) # label(axiom).  [clausify(2)].
0.89/1.16	55 prop(A) = false | bool(A) # label(prop_false) # label(axiom).  [clausify(35)].
0.89/1.16	57 f7(A) = lazy_impl(prop(A),A) # label(def_f7) # label(axiom).  [clausify(32)].
0.89/1.16	62 phi(A) = A | phi(A) = err # label(def_phi) # label(axiom).  [clausify(22)].
0.89/1.16	83 true != err # label(distinct_false_true_err_AndRHS_AndLHS) # label(axiom).  [assumption].
0.89/1.16	84 err != true.  [copy(83),flip(a)].
0.89/1.16	86 false1 != false2 # label(false1_false2) # label(negated_conjecture).  [assumption].
0.89/1.16	87 false2 != false.  [copy(86),rewrite([43(1)]),flip(a)].
0.89/1.16	88 -forallprefers(f7(A),f7(c1)) # label(def_false2) # label(axiom).  [clausify(7)].
0.89/1.16	89 -forallprefers(lazy_impl(prop(A),A),lazy_impl(prop(c1),c1)).  [copy(88),rewrite([57(1),57(4)])].
0.89/1.16	101 A != false | bool(A) # label(def_bool) # label(axiom).  [clausify(28)].
0.89/1.16	102 false != A | bool(A).  [copy(101),flip(a)].
0.89/1.16	103 A != true | bool(A) # label(def_bool) # label(axiom).  [clausify(28)].
0.89/1.16	104 true != A | bool(A).  [copy(103),flip(a)].
0.89/1.16	105 -bool(A) | prop(A) = true # label(prop_true) # label(axiom).  [clausify(19)].
0.89/1.16	106 bool(A) | prop(A) != true # label(prop_true) # label(axiom).  [clausify(19)].
0.89/1.16	107 phi(A) = A | -d(A) # label(def_phi) # label(axiom).  [clausify(22)].
0.89/1.16	113 -bool(A) | and1(false,A) = false # label(and1_axiom3) # label(axiom).  [clausify(16)].
0.89/1.16	120 A = false | A = true | -bool(A) # label(def_bool) # label(axiom).  [clausify(28)].
0.89/1.16	121 false = A | true = A | -bool(A).  [copy(120),flip(a),flip(b)].
0.89/1.16	128 A != true | B != false | forallprefers(B,A) # label(def_forallprefers) # label(axiom).  [clausify(31)].
0.89/1.16	129 true != A | false != B | forallprefers(B,A).  [copy(128),flip(a),flip(b)].
0.89/1.16	151 phi(lazy_impl(prop(c1),c1)) = false2.  [back_rewrite(48),rewrite([57(2)])].
0.89/1.16	175 bool(false).  [resolve(102,a,49,a(flip)),rewrite([49(2)])].
0.89/1.16	177 bool(true).  [resolve(104,a,47,a(flip)),rewrite([47(2)])].
0.89/1.16	184 prop(A) = true | prop(A) = false.  [resolve(105,a,55,b)].
0.89/1.16	185 phi(false) = false.  [resolve(107,b,42,a)].
0.89/1.16	186 phi(true) = true.  [resolve(107,b,40,a)].
0.89/1.16	247 false != A | forallprefers(A,true).  [resolve(129,a,62,a(flip)),rewrite([186(4),186(6)]),flip(c),unit_del(c,84)].
0.89/1.16	311 prop(false) = true.  [resolve(175,a,105,a)].
0.89/1.16	318 and1(false,true) = false.  [resolve(177,a,113,a)].
0.89/1.16	334 -forallprefers(false,lazy_impl(prop(c1),c1)).  [para(311(a,1),89(a,1,1)),rewrite([51(3),185(2)])].
0.89/1.16	446 forallprefers(false,true).  [resolve(247,a,318,a(flip)),rewrite([318(3)])].
0.89/1.16	508 prop(c1) = true.  [para(184(b,1),334(a,2,1)),rewrite([47(8)]),unit_del(b,446)].
0.89/1.16	546 -forallprefers(false,phi(c1)).  [back_rewrite(334),rewrite([508(3),51(4)])].
0.89/1.16	548 phi(phi(c1)) = false2.  [back_rewrite(151),rewrite([508(2),51(3)])].
0.89/1.16	567 bool(c1).  [resolve(508,a,106,b)].
0.89/1.16	579 c1 = false | c1 = true.  [resolve(567,a,121,c),flip(a),flip(b)].
0.89/1.16	596 phi(c1) = err | -forallprefers(false,c1).  [para(62(a,1),546(a,2))].
0.89/1.16	1150 c1 = true.  [para(579(a,1),548(a,1,1,1)),rewrite([185(5),185(5)]),flip(b),unit_del(b,87)].
0.89/1.16	1168 $F.  [back_rewrite(596),rewrite([1150(1),186(2),1150(5)]),flip(a),unit_del(a,84),unit_del(b,446)].
0.89/1.16	
0.89/1.16	% SZS output end Refutation
0.89/1.16	============================== end of proof ==========================
0.89/1.16	
0.89/1.16	============================== STATISTICS ============================
0.89/1.16	
0.89/1.16	Given=265. Generated=2410. Kept=1095. proofs=1.
0.89/1.16	Usable=224. Sos=683. Demods=144. Limbo=18, Disabled=248. Hints=0.
0.89/1.16	Megabytes=2.05.
0.89/1.16	User_CPU=0.14, System_CPU=0.00, Wall_clock=0.
0.89/1.16	
0.89/1.16	============================== end of statistics =====================
0.89/1.16	
0.89/1.16	============================== end of search =========================
0.89/1.16	
0.89/1.16	THEOREM PROVED
0.89/1.16	% SZS status Theorem
0.89/1.16	
0.89/1.16	Exiting with 1 proof.
0.89/1.16	
0.89/1.16	Process 20827 exit (max_proofs) Thu Aug 29 10:18:09 2019
0.89/1.16	Prover9 interrupted
0.89/1.16	EOF