0.05/0.10	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.05/0.11	% Command  : tptp2X_and_run_prover9 %d %s
0.10/0.31	% Computer : n018.cluster.edu
0.10/0.31	% Model    : x86_64 x86_64
0.10/0.31	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.10/0.31	% Memory   : 8042.1875MB
0.10/0.31	% OS       : Linux 3.10.0-693.el7.x86_64
0.10/0.31	% CPULimit : 960
0.10/0.31	% WCLimit  : 120
0.10/0.31	% DateTime : Tue Aug  9 05:30:45 EDT 2022
0.10/0.31	% CPUTime  : 
0.35/1.01	============================== Prover9 ===============================
0.35/1.01	Prover9 (32) version 2009-11A, November 2009.
0.35/1.01	Process 26771 was started by sandbox2 on n018.cluster.edu,
0.35/1.01	Tue Aug  9 05:30:46 2022
0.35/1.01	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_26615_n018.cluster.edu".
0.35/1.01	============================== end of head ===========================
0.35/1.01	
0.35/1.01	============================== INPUT =================================
0.35/1.01	
0.35/1.01	% Reading from file /tmp/Prover9_26615_n018.cluster.edu
0.35/1.01	
0.35/1.01	set(prolog_style_variables).
0.35/1.01	set(auto2).
0.35/1.01	    % set(auto2) -> set(auto).
0.35/1.01	    % set(auto) -> set(auto_inference).
0.35/1.01	    % set(auto) -> set(auto_setup).
0.35/1.01	    % set(auto_setup) -> set(predicate_elim).
0.35/1.01	    % set(auto_setup) -> assign(eq_defs, unfold).
0.35/1.01	    % set(auto) -> set(auto_limits).
0.35/1.01	    % set(auto_limits) -> assign(max_weight, "100.000").
0.35/1.01	    % set(auto_limits) -> assign(sos_limit, 20000).
0.35/1.01	    % set(auto) -> set(auto_denials).
0.35/1.01	    % set(auto) -> set(auto_process).
0.35/1.01	    % set(auto2) -> assign(new_constants, 1).
0.35/1.01	    % set(auto2) -> assign(fold_denial_max, 3).
0.35/1.01	    % set(auto2) -> assign(max_weight, "200.000").
0.35/1.01	    % set(auto2) -> assign(max_hours, 1).
0.35/1.01	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.35/1.01	    % set(auto2) -> assign(max_seconds, 0).
0.35/1.01	    % set(auto2) -> assign(max_minutes, 5).
0.35/1.01	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.35/1.01	    % set(auto2) -> set(sort_initial_sos).
0.35/1.01	    % set(auto2) -> assign(sos_limit, -1).
0.35/1.01	    % set(auto2) -> assign(lrs_ticks, 3000).
0.35/1.01	    % set(auto2) -> assign(max_megs, 400).
0.35/1.01	    % set(auto2) -> assign(stats, some).
0.35/1.01	    % set(auto2) -> clear(echo_input).
0.35/1.01	    % set(auto2) -> set(quiet).
0.35/1.01	    % set(auto2) -> clear(print_initial_clauses).
0.35/1.01	    % set(auto2) -> clear(print_given).
0.35/1.01	assign(lrs_ticks,-1).
0.35/1.01	assign(sos_limit,10000).
0.35/1.01	assign(order,kbo).
0.35/1.01	set(lex_order_vars).
0.35/1.01	clear(print_given).
0.35/1.01	
0.35/1.01	% formulas(sos).  % not echoed (45 formulas)
0.35/1.01	
0.35/1.01	============================== end of input ==========================
0.35/1.01	
0.35/1.01	% From the command line: assign(max_seconds, 960).
0.35/1.01	
0.35/1.01	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.35/1.01	
0.35/1.01	% Formulas that are not ordinary clauses:
0.35/1.01	1 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause).  [assumption].
0.35/1.01	2 modus_tollens <-> (all X all Y is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))) # label(modus_tollens) # label(axiom) # label(non_clause).  [assumption].
0.35/1.01	3 (all X all Y is_a_theorem(implies(and(X,Y),Y))) <-> and_2 # label(and_2) # label(axiom) # label(non_clause).  [assumption].
0.35/1.01	4 (all X all Y all Z is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))) <-> or_3 # label(or_3) # label(axiom) # label(non_clause).  [assumption].
0.35/1.01	5 and_3 <-> (all X all Y is_a_theorem(implies(X,implies(Y,and(X,Y))))) # label(and_3) # label(axiom) # label(non_clause).  [assumption].
0.35/1.01	6 equivalence_3 <-> (all X all Y is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))) # label(equivalence_3) # label(axiom) # label(non_clause).  [assumption].
0.35/1.01	7 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause).  [assumption].
0.35/1.01	8 kn3 <-> (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))) # label(kn3) # label(axiom) # label(non_clause).  [assumption].
0.35/1.01	9 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause).  [assumption].
0.35/1.01	10 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause).  [assumption].
0.35/1.01	11 (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))) <-> cn1 # label(cn1) # label(axiom) # label(non_clause).  [assumption].
0.35/1.01	12 equivalence_1 <-> (all X all Y is_a_theorem(implies(equiv(X,Y),implies(X,Y)))) # label(equivalence_1) # label(axiom) # label(non_clause).  [assumption].
0.35/1.01	13 substitution_of_equivalents <-> (all X all Y (is_a_theorem(equiv(X,Y)) -> Y = X)) # label(substitution_of_equivalents) # label(axiom) # label(non_clause).  [assumption].
0.35/1.01	14 (all P all Q all R is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))) <-> r5 # label(r5) # label(axiom) # label(non_clause).  [assumption].
2.13/2.40	15 (all P all Q is_a_theorem(implies(Q,or(P,Q)))) <-> r2 # label(r2) # label(axiom) # label(non_clause).  [assumption].
2.13/2.40	16 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause).  [assumption].
2.13/2.40	17 (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) <-> cn2 # label(cn2) # label(axiom) # label(non_clause).  [assumption].
2.13/2.40	18 (all X all Y is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))) <-> implies_2 # label(implies_2) # label(axiom) # label(non_clause).  [assumption].
2.13/2.40	19 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause).  [assumption].
2.13/2.40	20 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause).  [assumption].
2.13/2.40	21 r4 <-> (all P all Q all R is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))) # label(r4) # label(axiom) # label(non_clause).  [assumption].
2.13/2.40	22 (all P is_a_theorem(implies(P,and(P,P)))) <-> kn1 # label(kn1) # label(axiom) # label(non_clause).  [assumption].
2.13/2.40	23 (all X all Y is_a_theorem(implies(equiv(X,Y),implies(Y,X)))) <-> equivalence_2 # label(equivalence_2) # label(axiom) # label(non_clause).  [assumption].
2.13/2.40	24 modus_ponens <-> (all X all Y (is_a_theorem(X) & is_a_theorem(implies(X,Y)) -> is_a_theorem(Y))) # label(modus_ponens) # label(axiom) # label(non_clause).  [assumption].
2.13/2.40	25 (all X all Y is_a_theorem(implies(X,implies(Y,X)))) <-> implies_1 # label(implies_1) # label(axiom) # label(non_clause).  [assumption].
2.13/2.40	26 (all X all Y all Z is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))) <-> implies_3 # label(implies_3) # label(axiom) # label(non_clause).  [assumption].
2.13/2.40	27 op_implies_and -> (all X all Y implies(X,Y) = not(and(X,not(Y)))) # label(op_implies_and) # label(axiom) # label(non_clause).  [assumption].
2.13/2.40	28 op_implies_or -> (all X all Y or(not(X),Y) = implies(X,Y)) # label(op_implies_or) # label(axiom) # label(non_clause).  [assumption].
2.13/2.40	29 op_equiv -> (all X all Y equiv(X,Y) = and(implies(X,Y),implies(Y,X))) # label(op_equiv) # label(axiom) # label(non_clause).  [assumption].
2.13/2.40	30 op_or -> (all X all Y not(and(not(X),not(Y))) = or(X,Y)) # label(op_or) # label(axiom) # label(non_clause).  [assumption].
2.13/2.40	31 op_and -> (all X all Y and(X,Y) = not(or(not(X),not(Y)))) # label(op_and) # label(axiom) # label(non_clause).  [assumption].
2.13/2.40	
2.13/2.40	============================== end of process non-clausal formulas ===
2.13/2.40	
2.13/2.40	============================== PROCESS INITIAL CLAUSES ===============
2.13/2.40	
2.13/2.40	============================== PREDICATE ELIMINATION =================
2.13/2.40	
2.13/2.40	============================== end predicate elimination =============
2.13/2.40	
2.13/2.40	Auto_denials:  (non-Horn, no changes).
2.13/2.40	
2.13/2.40	Term ordering decisions:
2.13/2.40	
2.13/2.40	% Assigning unary symbol not kb_weight 0 and highest precedence (93).
2.13/2.40	Function symbol KB weights:  c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. c10=1. c11=1. c12=1. c13=1. c14=1. c15=1. c16=1. c17=1. c18=1. c19=1. c20=1. c21=1. c22=1. c23=1. c24=1. c25=1. c26=1. c27=1. c28=1. c29=1. c30=1. c31=1. c32=1. c33=1. c34=1. c35=1. c36=1. c37=1. c38=1. c39=1. c40=1. c41=1. c42=1. c43=1. c44=1. c45=1. c46=1. c47=1. c48=1. c49=1. c50=1. c51=1. c52=1. c53=1. c54=1. c55=1. implies=1. or=1. and=1. equiv=1. not=0.
2.13/2.40	
2.13/2.40	============================== end of process initial clauses ========
2.13/2.40	
2.13/2.40	============================== CLAUSES FOR SEARCH ====================
2.13/2.40	
2.13/2.40	============================== end of clauses for search =============
2.13/2.40	
2.13/2.40	============================== SEARCH ================================
2.13/2.40	
2.13/2.40	% Starting search at 0.02 seconds.
2.13/2.40	
2.13/2.40	Low Water (keep): wt=35.000, iters=3405
2.13/2.40	
2.13/2.40	Low Water (keep): wt=32.000, iters=3355
2.13/2.40	
2.13/2.40	Low Water (keep): wt=30.000, iters=3389
2.13/2.40	
2.13/2.40	Low Water (keep): wt=29.000, iters=3363
2.13/2.40	
2.13/2.40	Low Water (keep): wt=28.000, iters=3402
2.13/2.40	
2.13/2.40	Low Water (keep): wt=23.000, iters=3334
2.13/2.40	
2.13/2.40	Low Water (keep): wt=22.000, iters=3363
2.13/2.40	
2.13/2.40	Low Water (keep): wt=21.000, iters=3458
2.13/2.40	
2.13/2.40	Low Water (keep): wt=20.000, iters=3352
2.13/2.40	
2.13/2.40	Low Water (keep): wt=19.000, iters=3508
60.76/61.48	
60.76/61.48	Low Water (keep): wt=18.000, iters=3337
60.76/61.48	
60.76/61.48	Low Water (keep): wt=17.000, iters=3337
60.76/61.48	
60.76/61.48	Low Water (keep): wt=16.000, iters=3435
60.76/61.48	
60.76/61.48	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 22 (0.00 of 1.90 sec).
60.76/61.48	
60.76/61.48	Low Water (keep): wt=15.000, iters=3340
60.76/61.48	
60.76/61.48	Low Water (displace): id=8068, wt=40.000
60.76/61.48	
60.76/61.48	Low Water (displace): id=8066, wt=38.000
60.76/61.48	
60.76/61.48	Low Water (displace): id=15164, wt=36.000
60.76/61.48	
60.76/61.48	Low Water (displace): id=15656, wt=35.000
60.76/61.48	
60.76/61.48	Low Water (displace): id=12419, wt=34.000
60.76/61.48	
60.76/61.48	Low Water (displace): id=15141, wt=33.000
60.76/61.48	
60.76/61.48	Low Water (displace): id=15723, wt=32.000
60.76/61.48	
60.76/61.48	Low Water (displace): id=15852, wt=14.000
60.76/61.48	
60.76/61.48	Low Water (displace): id=17695, wt=13.000
60.76/61.48	
60.76/61.48	Low Water (displace): id=17807, wt=11.000
60.76/61.48	
60.76/61.48	Low Water (keep): wt=14.000, iters=3351
60.76/61.48	
60.76/61.48	Low Water (displace): id=20506, wt=10.000
60.76/61.48	
60.76/61.48	Low Water (keep): wt=13.000, iters=3334
60.76/61.48	
60.76/61.48	Low Water (keep): wt=12.000, iters=3610
60.76/61.48	
60.76/61.48	Low Water (keep): wt=11.000, iters=3333
60.76/61.48	
60.76/61.48	============================== PROOF =================================
60.76/61.48	% SZS status Theorem
60.76/61.48	% SZS output start Refutation
60.76/61.48	
60.76/61.48	% Proof 1 at 57.09 (+ 3.03) seconds.
60.76/61.48	% Length of proof is 216.
60.76/61.48	% Level of proof is 39.
60.76/61.48	% Maximum clause weight is 29.000.
60.76/61.48	% Given clauses 4062.
60.76/61.48	
60.76/61.48	6 equivalence_3 <-> (all X all Y is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))) # label(equivalence_3) # label(axiom) # label(non_clause).  [assumption].
60.76/61.48	13 substitution_of_equivalents <-> (all X all Y (is_a_theorem(equiv(X,Y)) -> Y = X)) # label(substitution_of_equivalents) # label(axiom) # label(non_clause).  [assumption].
60.76/61.48	14 (all P all Q all R is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))) <-> r5 # label(r5) # label(axiom) # label(non_clause).  [assumption].
60.76/61.48	15 (all P all Q is_a_theorem(implies(Q,or(P,Q)))) <-> r2 # label(r2) # label(axiom) # label(non_clause).  [assumption].
60.76/61.48	19 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause).  [assumption].
60.76/61.48	20 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause).  [assumption].
60.76/61.48	21 r4 <-> (all P all Q all R is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))) # label(r4) # label(axiom) # label(non_clause).  [assumption].
60.76/61.48	24 modus_ponens <-> (all X all Y (is_a_theorem(X) & is_a_theorem(implies(X,Y)) -> is_a_theorem(Y))) # label(modus_ponens) # label(axiom) # label(non_clause).  [assumption].
60.76/61.48	27 op_implies_and -> (all X all Y implies(X,Y) = not(and(X,not(Y)))) # label(op_implies_and) # label(axiom) # label(non_clause).  [assumption].
60.76/61.48	28 op_implies_or -> (all X all Y or(not(X),Y) = implies(X,Y)) # label(op_implies_or) # label(axiom) # label(non_clause).  [assumption].
60.76/61.48	29 op_equiv -> (all X all Y equiv(X,Y) = and(implies(X,Y),implies(Y,X))) # label(op_equiv) # label(axiom) # label(non_clause).  [assumption].
60.76/61.48	30 op_or -> (all X all Y not(and(not(X),not(Y))) = or(X,Y)) # label(op_or) # label(axiom) # label(non_clause).  [assumption].
60.76/61.48	31 op_and -> (all X all Y and(X,Y) = not(or(not(X),not(Y)))) # label(op_and) # label(axiom) # label(non_clause).  [assumption].
60.76/61.48	32 r4 # label(principia_r4) # label(axiom).  [assumption].
60.76/61.48	33 r3 # label(principia_r3) # label(axiom).  [assumption].
60.76/61.48	34 op_implies_or # label(principia_op_implies_or) # label(axiom).  [assumption].
60.76/61.48	35 modus_ponens # label(principia_modus_ponens) # label(axiom).  [assumption].
60.76/61.48	36 r1 # label(principia_r1) # label(axiom).  [assumption].
60.76/61.48	37 op_and # label(principia_op_and) # label(axiom).  [assumption].
60.76/61.48	38 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom).  [assumption].
60.76/61.48	39 r5 # label(principia_r5) # label(axiom).  [assumption].
60.76/61.48	40 op_equiv # label(principia_op_equiv) # label(axiom).  [assumption].
60.76/61.48	41 r2 # label(principia_r2) # label(axiom).  [assumption].
60.76/61.48	42 op_or # label(hilbert_op_or) # label(axiom).  [assumption].
60.76/61.48	43 op_implies_and # label(hilbert_op_implies_and) # label(axiom).  [assumption].
60.76/61.48	44 -equivalence_3 # label(hilbert_equivalence_3) # label(negated_conjecture).  [assumption].
60.76/61.48	53 is_a_theorem(implies(A,or(B,A))) | -r2 # label(r2) # label(axiom).  [clausify(15)].
60.76/61.48	54 is_a_theorem(implies(A,or(B,A))).  [copy(53),unit_del(b,41)].
60.76/61.49	57 -r1 | is_a_theorem(implies(or(A,A),A)) # label(r1) # label(axiom).  [clausify(19)].
60.76/61.49	58 is_a_theorem(implies(or(A,A),A)).  [copy(57),unit_del(a,36)].
60.76/61.49	66 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom).  [clausify(13)].
60.76/61.49	67 -is_a_theorem(equiv(A,B)) | B = A.  [copy(66),unit_del(a,38)].
60.76/61.49	74 -r3 | is_a_theorem(implies(or(A,B),or(B,A))) # label(r3) # label(axiom).  [clausify(20)].
60.76/61.49	75 is_a_theorem(implies(or(A,B),or(B,A))).  [copy(74),unit_del(a,33)].
60.76/61.49	79 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom).  [clausify(24)].
60.76/61.49	80 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B).  [copy(79),unit_del(a,35)].
60.76/61.49	81 -op_implies_or | or(not(A),B) = implies(A,B) # label(op_implies_or) # label(axiom).  [clausify(28)].
60.76/61.49	82 or(not(A),B) = implies(A,B).  [copy(81),unit_del(a,34)].
60.76/61.49	83 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom).  [clausify(27)].
60.76/61.49	84 not(and(A,not(B))) = implies(A,B).  [copy(83),unit_del(a,43)].
60.76/61.49	89 -op_or | or(A,B) = not(and(not(A),not(B))) # label(op_or) # label(axiom).  [clausify(30)].
60.76/61.49	90 or(A,B) = implies(not(A),B).  [copy(89),rewrite([84(6)]),unit_del(a,42)].
60.76/61.49	91 -op_and | not(or(not(A),not(B))) = and(A,B) # label(op_and) # label(axiom).  [clausify(31)].
60.76/61.49	92 not(implies(not(not(A)),not(B))) = and(A,B).  [copy(91),rewrite([90(4)]),unit_del(a,37)].
60.76/61.49	93 -op_equiv | equiv(A,B) = and(implies(A,B),implies(B,A)) # label(op_equiv) # label(axiom).  [clausify(29)].
60.76/61.49	94 and(implies(A,B),implies(B,A)) = equiv(A,B).  [copy(93),flip(b),unit_del(a,40)].
60.76/61.49	95 equivalence_3 | -is_a_theorem(implies(implies(c12,c13),implies(implies(c13,c12),equiv(c12,c13)))) # label(equivalence_3) # label(axiom).  [clausify(6)].
60.76/61.49	96 -is_a_theorem(implies(implies(c12,c13),implies(implies(c13,c12),equiv(c12,c13)))).  [copy(95),unit_del(a,44)].
60.76/61.49	100 is_a_theorem(implies(implies(A,B),implies(or(C,A),or(C,B)))) | -r5 # label(r5) # label(axiom).  [clausify(14)].
60.76/61.49	101 is_a_theorem(implies(implies(A,B),implies(implies(not(C),A),implies(not(C),B)))).  [copy(100),rewrite([90(2),90(4)]),unit_del(b,39)].
60.76/61.49	102 -r4 | is_a_theorem(implies(or(A,or(B,C)),or(B,or(A,C)))) # label(r4) # label(axiom).  [clausify(21)].
60.76/61.49	103 is_a_theorem(implies(implies(not(A),implies(not(B),C)),implies(not(B),implies(not(A),C)))).  [copy(102),rewrite([90(2),90(4),90(6),90(8)]),unit_del(a,32)].
60.76/61.49	113 implies(not(not(A)),B) = implies(A,B).  [back_rewrite(82),rewrite([90(2)])].
60.76/61.49	114 is_a_theorem(implies(implies(not(A),B),implies(not(B),A))).  [back_rewrite(75),rewrite([90(1),90(3)])].
60.76/61.49	115 is_a_theorem(implies(implies(not(A),A),A)).  [back_rewrite(58),rewrite([90(1)])].
60.76/61.49	116 is_a_theorem(implies(A,implies(not(B),A))).  [back_rewrite(54),rewrite([90(1)])].
60.76/61.49	119 not(implies(A,not(B))) = and(A,B).  [back_rewrite(92),rewrite([113(4)])].
60.76/61.49	121 not(and(A,implies(B,C))) = implies(A,and(B,not(C))).  [para(84(a,1),84(a,1,1,2))].
60.76/61.49	122 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(C),A),implies(not(C),B))).  [resolve(101,a,80,b)].
60.76/61.49	125 -is_a_theorem(implies(not(A),implies(not(B),C))) | is_a_theorem(implies(not(B),implies(not(A),C))).  [resolve(103,a,80,b)].
60.76/61.49	130 implies(not(implies(A,B)),C) = implies(and(A,not(B)),C).  [para(84(a,1),113(a,1,1,1))].
60.76/61.49	132 and(implies(A,not(not(B))),implies(B,A)) = equiv(A,not(not(B))).  [para(113(a,1),94(a,1,2))].
60.76/61.49	134 is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))).  [para(113(a,1),101(a,1,2,1)),rewrite([113(5)])].
60.76/61.49	137 -is_a_theorem(implies(not(A),B)) | is_a_theorem(implies(not(B),A)).  [resolve(114,a,80,b)].
60.76/61.49	140 is_a_theorem(implies(implies(not(A),and(B,not(C))),implies(implies(B,C),A))).  [para(84(a,1),114(a,1,2,1))].
60.76/61.49	141 is_a_theorem(implies(implies(A,B),implies(not(B),not(A)))).  [para(113(a,1),114(a,1,1))].
60.76/61.49	142 is_a_theorem(implies(implies(not(A),not(B)),implies(B,A))).  [para(113(a,1),114(a,1,2))].
60.76/61.49	144 -is_a_theorem(implies(not(A),A)) | is_a_theorem(A).  [resolve(115,a,80,b)].
60.76/61.49	148 is_a_theorem(implies(implies(A,not(A)),not(A))).  [para(113(a,1),115(a,1,1))].
60.76/61.49	152 is_a_theorem(implies(A,implies(B,A))).  [para(113(a,1),116(a,1,2))].
60.76/61.49	158 and(not(not(A)),B) = and(A,B).  [para(113(a,1),119(a,1,1)),rewrite([119(3)]),flip(a)].
60.76/61.49	165 implies(implies(A,B),and(B,not(A))) = not(equiv(A,B)).  [para(94(a,1),121(a,1,1)),flip(a)].
60.76/61.49	194 -is_a_theorem(A) | is_a_theorem(implies(B,A)).  [resolve(152,a,80,b)].
60.76/61.49	199 is_a_theorem(implies(A,implies(B,not(not(A))))).  [para(113(a,1),152(a,1))].
60.76/61.49	204 is_a_theorem(implies(implies(not(A),implies(not(B),B)),implies(not(A),B))).  [resolve(122,a,115,a)].
60.76/61.49	245 -is_a_theorem(A) | is_a_theorem(implies(B,not(not(A)))).  [resolve(199,a,80,b)].
60.76/61.49	346 is_a_theorem(implies(not(A),implies(not(B),not(B)))).  [resolve(125,a,152,a)].
60.76/61.49	349 -is_a_theorem(implies(not(A),implies(B,C))) | is_a_theorem(implies(B,implies(not(A),C))).  [para(113(a,1),125(a,1,2)),rewrite([113(9)])].
60.76/61.49	350 -is_a_theorem(implies(A,implies(not(B),C))) | is_a_theorem(implies(not(B),implies(A,C))).  [para(113(a,1),125(a,1)),rewrite([113(8)])].
60.76/61.49	401 is_a_theorem(implies(not(A),not(A))).  [resolve(346,a,144,a)].
60.76/61.49	442 is_a_theorem(implies(A,not(not(A)))).  [para(113(a,1),401(a,1))].
60.76/61.49	444 is_a_theorem(implies(A,implies(B,B))).  [resolve(442,a,245,a),rewrite([119(4),84(3)])].
60.76/61.49	470 is_a_theorem(implies(A,A)).  [resolve(444,a,144,a)].
60.76/61.49	759 implies(and(A,not(not(B))),C) = implies(and(A,B),C).  [para(119(a,1),130(a,1,1)),flip(a)].
60.76/61.49	1040 equiv(A,not(not(B))) = equiv(A,B).  [para(132(a,1),158(a,2)),rewrite([119(4),84(3),94(3)]),flip(a)].
60.76/61.49	1340 -is_a_theorem(equiv(A,B)) | not(not(B)) = A.  [para(1040(a,1),67(a,1))].
60.76/61.49	1360 is_a_theorem(implies(and(A,B),B)).  [resolve(137,a,199,a),rewrite([119(5),759(4)])].
60.76/61.49	1362 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(B),not(A))).  [para(113(a,1),137(a,1))].
60.76/61.49	1373 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(C,A),implies(C,B))).  [resolve(134,a,80,b)].
60.76/61.49	2522 -is_a_theorem(implies(and(implies(c13,c12),not(equiv(c12,c13))),and(c12,not(c13)))).  [ur(80,b,140,a,c,96,a),rewrite([130(13)])].
60.76/61.49	2850 is_a_theorem(implies(implies(A,not(B)),implies(B,not(A)))).  [para(113(a,1),141(a,1,2))].
60.76/61.49	3149 -is_a_theorem(implies(not(A),not(B))) | is_a_theorem(implies(B,A)).  [resolve(142,a,80,b)].
60.76/61.49	6720 is_a_theorem(implies(A,and(A,A))).  [resolve(1362,a,148,a),rewrite([119(5),113(4)])].
60.76/61.49	6737 -is_a_theorem(A) | is_a_theorem(and(A,A)).  [resolve(6720,a,80,b)].
60.76/61.49	6866 is_a_theorem(equiv(A,A)).  [resolve(6737,a,470,a),rewrite([94(3)])].
60.76/61.49	7053 not(not(A)) = A.  [resolve(6866,a,1340,a)].
60.76/61.49	7118 not(and(A,B)) = implies(A,not(B)).  [para(7053(a,1),84(a,1,1,2))].
60.76/61.49	7119 not(implies(A,B)) = and(A,not(B)).  [para(84(a,1),7053(a,1,1))].
60.76/61.49	7245 implies(implies(not(A),B),and(B,A)) = not(equiv(not(A),B)).  [para(7053(a,1),165(a,1,2,2))].
60.76/61.49	8916 is_a_theorem(implies(and(A,B),and(B,A))).  [resolve(2850,a,1362,a),rewrite([7119(3),7053(2),7119(4),7053(3)])].
60.76/61.49	8918 -is_a_theorem(implies(A,not(B))) | is_a_theorem(implies(B,not(A))).  [resolve(2850,a,80,b)].
60.76/61.49	9184 is_a_theorem(implies(A,implies(and(B,C),and(C,B)))).  [resolve(8916,a,194,a)].
60.76/61.49	12168 is_a_theorem(implies(implies(A,implies(not(B),B)),implies(A,B))).  [para(7053(a,1),204(a,1,1,1)),rewrite([7053(5)])].
60.76/61.49	14576 -is_a_theorem(implies(A,implies(not(B),B))) | is_a_theorem(implies(A,B)).  [resolve(12168,a,80,b)].
60.76/61.49	16649 is_a_theorem(implies(implies(A,B),implies(A,and(B,B)))).  [resolve(1373,a,6720,a)].
60.76/61.49	16662 is_a_theorem(implies(implies(A,and(B,C)),implies(A,C))).  [resolve(1373,a,1360,a)].
60.76/61.49	16699 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(A,and(B,B))).  [resolve(16649,a,80,b)].
60.76/61.49	16708 is_a_theorem(implies(implies(not(A),and(B,A)),A)).  [resolve(16662,a,14576,a)].
60.76/61.49	16720 -is_a_theorem(implies(A,and(B,C))) | is_a_theorem(implies(A,C)).  [resolve(16662,a,80,b)].
60.76/61.49	16752 is_a_theorem(implies(A,and(A,implies(B,A)))).  [resolve(16708,a,8918,a),rewrite([7053(2),7119(4),7118(3),7053(2)])].
60.76/61.49	17104 is_a_theorem(not(equiv(A,not(A)))).  [resolve(16699,a,148,a),rewrite([165(6)])].
60.76/61.49	17111 is_a_theorem(not(equiv(not(A),A))).  [resolve(16699,a,115,a),rewrite([7245(4)])].
60.76/61.49	17139 is_a_theorem(implies(A,not(equiv(B,not(B))))).  [resolve(17104,a,194,a)].
60.76/61.49	17294 is_a_theorem(implies(equiv(A,not(A)),B)).  [resolve(17139,a,3149,a)].
60.76/61.49	17360 is_a_theorem(implies(equiv(not(A),A),B)).  [para(7053(a,1),17294(a,1,1,2))].
60.76/61.49	17735 is_a_theorem(implies(and(A,B),A)).  [resolve(16720,a,8916,a)].
60.76/61.49	17778 is_a_theorem(implies(implies(A,and(B,C)),implies(A,B))).  [resolve(17735,a,1373,a)].
60.76/61.49	20795 is_a_theorem(implies(not(equiv(A,B)),implies(implies(A,B),B))).  [para(165(a,1),17778(a,1,1))].
60.76/61.49	24159 is_a_theorem(implies(not(A),implies(implies(not(A),B),B))).  [resolve(350,a,470,a)].
60.76/61.49	24166 is_a_theorem(implies(not(A),implies(implies(not(B),A),B))).  [resolve(350,a,142,a),rewrite([7053(4)])].
60.76/61.49	29111 is_a_theorem(implies(A,implies(implies(A,B),B))).  [para(7053(a,1),24159(a,1,1)),rewrite([7053(2)])].
60.76/61.49	29139 -is_a_theorem(A) | is_a_theorem(implies(implies(A,B),B)).  [resolve(29111,a,80,b)].
60.76/61.49	29294 is_a_theorem(implies(implies(implies(and(A,B),A),C),C)).  [resolve(29139,a,17735,a)].
60.76/61.49	29296 is_a_theorem(implies(implies(implies(equiv(not(A),A),B),C),C)).  [resolve(29139,a,17360,a)].
60.76/61.49	29436 is_a_theorem(implies(implies(equiv(A,A),B),B)).  [resolve(29139,a,6866,a)].
60.76/61.49	29438 is_a_theorem(implies(implies(implies(A,and(A,A)),B),B)).  [resolve(29139,a,6720,a)].
60.76/61.49	29464 is_a_theorem(implies(implies(implies(and(A,B),B),C),C)).  [resolve(29139,a,1360,a)].
60.76/61.49	29471 is_a_theorem(implies(implies(implies(A,A),B),B)).  [resolve(29139,a,470,a)].
60.76/61.49	29492 is_a_theorem(implies(implies(implies(A,implies(B,A)),C),C)).  [resolve(29139,a,152,a)].
60.76/61.49	29532 -is_a_theorem(implies(equiv(A,A),B)) | is_a_theorem(B).  [resolve(29436,a,80,b)].
60.76/61.49	29609 is_a_theorem(implies(A,and(implies(B,B),A))).  [resolve(29471,a,8918,a),rewrite([7119(4),7053(3)])].
60.76/61.49	29614 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(B).  [resolve(29471,a,80,b)].
60.76/61.49	29841 -is_a_theorem(A) | is_a_theorem(and(implies(B,B),A)).  [resolve(29609,a,80,b)].
60.76/61.49	30428 is_a_theorem(and(implies(A,A),implies(B,and(B,implies(C,B))))).  [resolve(29841,a,16752,a)].
60.76/61.49	30778 is_a_theorem(implies(A,implies(implies(not(B),not(A)),B))).  [para(7053(a,1),24166(a,1,1))].
60.76/61.49	34282 -is_a_theorem(implies(implies(and(A,B),A),C)) | is_a_theorem(C).  [resolve(29294,a,80,b)].
60.76/61.49	34438 -is_a_theorem(implies(implies(A,and(A,A)),B)) | is_a_theorem(B).  [resolve(29438,a,80,b)].
60.76/61.49	34472 -is_a_theorem(implies(implies(and(A,B),B),C)) | is_a_theorem(C).  [resolve(29464,a,80,b)].
60.76/61.49	34540 -is_a_theorem(implies(implies(A,implies(B,A)),C)) | is_a_theorem(C).  [resolve(29492,a,80,b)].
60.76/61.49	35929 is_a_theorem(implies(implies(not(A),and(B,not(B))),A)).  [resolve(30778,a,29614,a),rewrite([7119(3)])].
60.76/61.49	35930 is_a_theorem(implies(implies(not(A),not(equiv(B,B))),A)).  [resolve(30778,a,29532,a)].
60.76/61.49	46268 -is_a_theorem(implies(not(A),and(B,not(B)))) | is_a_theorem(A).  [resolve(35929,a,80,b)].
60.76/61.49	46320 -is_a_theorem(implies(not(A),not(equiv(B,B)))) | is_a_theorem(A).  [resolve(35930,a,80,b)].
60.76/61.49	53149 -is_a_theorem(implies(not(A),and(not(B),B))) | is_a_theorem(A).  [para(7053(a,1),46268(a,1,2,2))].
60.76/61.49	64479 is_a_theorem(implies(implies(A,B),implies(not(equiv(A,B)),B))).  [resolve(20795,a,349,a)].
60.76/61.49	74884 -is_a_theorem(implies(implies(equiv(not(A),A),B),C)) | is_a_theorem(C).  [resolve(29296,a,80,b)].
60.76/61.49	92374 is_a_theorem(implies(not(equiv(A,implies(B,A))),implies(B,A))).  [resolve(64479,a,34540,a)].
60.76/61.49	92375 is_a_theorem(implies(not(equiv(and(A,B),B)),B)).  [resolve(64479,a,34472,a)].
60.76/61.49	92377 is_a_theorem(implies(not(equiv(and(A,B),A)),A)).  [resolve(64479,a,34282,a)].
60.76/61.49	92505 is_a_theorem(implies(not(A),equiv(and(B,A),A))).  [resolve(92375,a,1362,a),rewrite([7053(5)])].
60.76/61.49	92692 is_a_theorem(implies(not(A),equiv(and(A,B),A))).  [resolve(92377,a,1362,a),rewrite([7053(5)])].
60.76/61.49	92773 -is_a_theorem(not(A)) | is_a_theorem(equiv(and(B,A),A)).  [resolve(92505,a,80,b)].
60.76/61.49	92852 -is_a_theorem(not(A)) | is_a_theorem(equiv(and(A,B),A)).  [resolve(92692,a,80,b)].
60.76/61.49	92920 is_a_theorem(equiv(and(A,equiv(not(B),B)),equiv(not(B),B))).  [resolve(92773,a,17111,a)].
60.76/61.49	92953 -is_a_theorem(A) | is_a_theorem(equiv(and(not(A),B),not(A))).  [para(7053(a,1),92852(a,1))].
60.76/61.49	94612 is_a_theorem(equiv(and(equiv(not(A),A),B),equiv(not(A),A))).  [resolve(92953,a,17111,a),rewrite([7053(4),7053(7)])].
60.76/61.49	100599 is_a_theorem(implies(not(equiv(equiv(not(A),A),B)),B)).  [resolve(74884,a,64479,a)].
60.76/61.49	100681 is_a_theorem(equiv(equiv(not(A),A),and(not(B),B))).  [resolve(100599,a,53149,a)].
60.76/61.49	100690 is_a_theorem(equiv(equiv(not(A),A),not(equiv(B,B)))).  [resolve(100599,a,46320,a)].
60.76/61.49	100748 is_a_theorem(implies(A,equiv(equiv(not(B),B),not(A)))).  [resolve(100599,a,8918,a),rewrite([7053(6)])].
60.76/61.49	100849 equiv(not(A),A) = and(not(B),B).  [resolve(100681,a,67,a),flip(a)].
60.76/61.49	100855 equiv(not(A),A) = c_0.  [new_symbol(100849)].
60.76/61.49	100857 and(not(A),A) = c_0.  [back_rewrite(100849),rewrite([100855(2)]),flip(a)].
60.76/61.49	100861 is_a_theorem(implies(A,equiv(c_0,not(A)))).  [back_rewrite(100748),rewrite([100855(2)])].
60.76/61.49	100868 is_a_theorem(equiv(c_0,not(equiv(A,A)))).  [back_rewrite(100690),rewrite([100855(2)])].
60.76/61.49	100871 is_a_theorem(equiv(and(c_0,A),c_0)).  [back_rewrite(94612),rewrite([100855(2),100855(4)])].
60.76/61.49	100872 is_a_theorem(equiv(and(A,c_0),c_0)).  [back_rewrite(92920),rewrite([100855(2),100855(4)])].
60.76/61.49	101307 is_a_theorem(not(c_0)).  [back_rewrite(17111),rewrite([100855(2)])].
60.76/61.49	102669 and(A,not(A)) = c_0.  [para(7053(a,1),100857(a,1,1))].
60.76/61.49	102856 and(c_0,A) = c_0.  [resolve(100871,a,67,a),flip(a)].
60.76/61.49	102886 implies(c_0,not(A)) = not(c_0).  [para(102856(a,1),7118(a,1,1)),flip(a)].
60.76/61.49	102968 and(A,c_0) = c_0.  [resolve(100872,a,67,a),flip(a)].
60.76/61.49	102973 implies(A,not(c_0)) = not(c_0).  [para(102968(a,1),7118(a,1,1)),flip(a)].
60.76/61.49	103255 implies(A,A) = not(c_0).  [para(102669(a,1),7118(a,1,1)),rewrite([7053(4)]),flip(a)].
60.76/61.49	103525 is_a_theorem(and(not(c_0),implies(A,and(A,implies(B,A))))).  [back_rewrite(30428),rewrite([103255(1)])].
60.76/61.49	103930 equiv(A,A) = and(not(c_0),not(c_0)).  [para(103255(a,1),94(a,1,1)),rewrite([103255(3)]),flip(a)].
60.76/61.49	104126 is_a_theorem(equiv(c_0,and(and(A,B),not(B)))).  [resolve(100861,a,34472,a),rewrite([7119(4)])].
60.76/61.49	104127 is_a_theorem(equiv(c_0,and(A,implies(A,not(A))))).  [resolve(100861,a,34438,a),rewrite([7119(4),7118(3)])].
60.76/61.49	104129 is_a_theorem(equiv(c_0,and(and(A,B),not(A)))).  [resolve(100861,a,34282,a),rewrite([7119(4)])].
60.76/61.49	104274 not(equiv(A,A)) = c_0.  [resolve(100868,a,67,a)].
60.76/61.49	104315 equiv(A,A) = not(c_0).  [para(104274(a,1),7053(a,1,1)),flip(a)].
60.76/61.49	104359 and(not(c_0),not(c_0)) = not(c_0).  [back_rewrite(103930),rewrite([104315(1)]),flip(a)].
60.76/61.49	107595 implies(c_0,A) = not(c_0).  [para(7053(a,1),102886(a,1,2))].
60.76/61.49	107601 and(implies(A,c_0),not(c_0)) = equiv(A,c_0).  [para(107595(a,1),94(a,1,2))].
60.76/61.49	107608 and(implies(not(c_0),A),not(c_0)) = equiv(not(c_0),A).  [para(102973(a,1),94(a,1,2))].
60.76/61.49	111177 and(and(A,B),not(B)) = c_0.  [resolve(104126,a,67,a)].
60.76/61.49	111182 implies(and(A,B),B) = not(c_0).  [para(111177(a,1),7118(a,1,1)),rewrite([7053(5)]),flip(a)].
60.76/61.49	111241 and(A,implies(A,not(A))) = c_0.  [resolve(104127,a,67,a)].
60.76/61.49	111244 implies(A,and(A,A)) = not(c_0).  [para(111241(a,1),7118(a,1,1)),rewrite([7119(5),7053(4)]),flip(a)].
60.76/61.49	111287 equiv(A,and(A,A)) = not(c_0).  [para(111244(a,1),94(a,1,1)),rewrite([111182(4),104359(5)]),flip(a)].
60.76/61.49	111289 and(A,A) = A.  [para(111287(a,1),67(a,1)),unit_del(a,101307)].
60.76/61.49	111403 and(and(A,B),not(A)) = c_0.  [resolve(104129,a,67,a)].
60.76/61.49	111410 implies(and(A,B),A) = not(c_0).  [para(111403(a,1),7118(a,1,1)),rewrite([7053(5)]),flip(a)].
60.76/61.49	111490 and(not(c_0),implies(A,and(A,B))) = equiv(and(A,B),A).  [para(111410(a,1),94(a,1,1))].
60.76/61.49	111501 is_a_theorem(equiv(and(A,implies(B,A)),A)).  [back_rewrite(103525),rewrite([111490(6)])].
60.76/61.49	111552 and(A,implies(B,A)) = A.  [resolve(111501,a,67,a),flip(a)].
60.76/61.49	111559 is_a_theorem(implies(A,and(implies(B,A),A))).  [para(111552(a,1),8916(a,1,1))].
60.76/61.49	111604 and(A,not(c_0)) = A.  [para(103255(a,1),111552(a,1,2))].
60.76/61.49	111607 equiv(not(c_0),A) = implies(not(c_0),A).  [back_rewrite(107608),rewrite([111604(6)]),flip(a)].
60.76/61.49	111609 equiv(A,c_0) = implies(A,c_0).  [back_rewrite(107601),rewrite([111604(5)]),flip(a)].
60.76/61.49	111762 implies(A,c_0) = not(A).  [para(111604(a,1),7118(a,1,1)),rewrite([7053(4)]),flip(a)].
60.76/61.49	111768 equiv(A,c_0) = not(A).  [back_rewrite(111609),rewrite([111762(4)])].
60.76/61.49	113674 -is_a_theorem(not(A)) | c_0 = A.  [para(111768(a,1),67(a,1))].
60.76/61.49	113675 -is_a_theorem(A) | not(A) = c_0.  [para(7053(a,1),113674(a,1)),flip(b)].
60.76/61.49	113762 and(A,and(implies(A,B),not(B))) = c_0.  [resolve(113675,a,29111,a),rewrite([7119(4),7119(3)])].
60.76/61.49	114913 is_a_theorem(implies(implies(implies(A,not(B)),B),B)).  [resolve(111559,a,137,a),rewrite([7118(5),7053(4)])].
60.76/61.49	116416 -is_a_theorem(implies(not(c_0),A)) | not(c_0) = A.  [para(111607(a,1),67(a,1)),flip(b)].
60.76/61.49	116818 -is_a_theorem(implies(implies(A,not(B)),B)) | is_a_theorem(B).  [resolve(114913,a,80,b)].
60.76/61.49	117648 implies(and(A,B),and(B,A)) = not(c_0).  [resolve(116416,a,9184,a),flip(a)].
60.76/61.49	120076 -is_a_theorem(implies(implies(A,and(and(implies(c13,c12),not(equiv(c12,c13))),implies(c12,c13))),implies(and(implies(c13,c12),not(equiv(c12,c13))),and(c12,not(c13))))).  [ur(116818,b,2522,a),rewrite([7119(14),7118(13),7053(12)])].
60.76/61.49	121792 and(implies(A,B),and(not(equiv(A,B)),implies(B,A))) = c_0.  [para(165(a,1),113762(a,1,2,1)),rewrite([7118(6),7053(5)])].
60.76/61.49	123457 equiv(and(A,B),and(B,A)) = not(c_0).  [para(117648(a,1),94(a,1,1)),rewrite([117648(5),111289(5)]),flip(a)].
60.76/61.49	125596 and(A,B) = and(B,A).  [para(123457(a,1),67(a,1)),unit_del(a,101307)].
60.76/61.49	126090 and(implies(A,B),and(implies(B,A),not(equiv(A,B)))) = c_0.  [back_rewrite(121792),rewrite([125596(5)])].
60.76/61.49	126325 -is_a_theorem(implies(not(A),implies(and(implies(c13,c12),not(equiv(c12,c13))),and(c12,not(c13))))).  [back_rewrite(120076),rewrite([125596(12),126090(12),111762(2)])].
60.76/61.49	126326 $F.  [resolve(126325,a,92374,a)].
60.76/61.49	
60.76/61.49	% SZS output end Refutation
60.76/61.49	============================== end of proof ==========================
60.76/61.49	
60.76/61.49	============================== STATISTICS ============================
60.76/61.49	
60.76/61.49	Given=4062. Generated=3241121. Kept=126274. proofs=1.
60.76/61.49	Usable=631. Sos=1841. Demods=444. Limbo=729, Disabled=123146. Hints=0.
60.76/61.49	Megabytes=70.09.
60.76/61.49	User_CPU=57.09, System_CPU=3.03, Wall_clock=61.
60.76/61.49	
60.76/61.49	============================== end of statistics =====================
60.76/61.49	
60.76/61.49	============================== end of search =========================
60.76/61.49	
60.76/61.49	THEOREM PROVED
60.76/61.49	% SZS status Theorem
60.76/61.49	
60.76/61.49	Exiting with 1 proof.
60.76/61.49	
60.76/61.49	Process 26771 exit (max_proofs) Tue Aug  9 05:31:47 2022
60.76/61.49	Prover9 interrupted
60.76/61.49	EOF