TSTP Solution File: LCL492+1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : LCL492+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n029.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Sun Jul 17 13:47:11 EDT 2022

% Result   : Theorem 124.61s 124.92s
% Output   : Refutation 124.63s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL492+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command  : tptp2X_and_run_prover9 %d %s
% 0.12/0.34  % Computer : n029.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sat Jul  2 20:49:10 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.42/1.00  ============================== Prover9 ===============================
% 0.42/1.00  Prover9 (32) version 2009-11A, November 2009.
% 0.42/1.00  Process 27444 was started by sandbox2 on n029.cluster.edu,
% 0.42/1.00  Sat Jul  2 20:49:11 2022
% 0.42/1.00  The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_27291_n029.cluster.edu".
% 0.42/1.00  ============================== end of head ===========================
% 0.42/1.00  
% 0.42/1.00  ============================== INPUT =================================
% 0.42/1.00  
% 0.42/1.00  % Reading from file /tmp/Prover9_27291_n029.cluster.edu
% 0.42/1.00  
% 0.42/1.00  set(prolog_style_variables).
% 0.42/1.00  set(auto2).
% 0.42/1.00      % set(auto2) -> set(auto).
% 0.42/1.00      % set(auto) -> set(auto_inference).
% 0.42/1.00      % set(auto) -> set(auto_setup).
% 0.42/1.00      % set(auto_setup) -> set(predicate_elim).
% 0.42/1.00      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/1.00      % set(auto) -> set(auto_limits).
% 0.42/1.00      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/1.00      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/1.00      % set(auto) -> set(auto_denials).
% 0.42/1.00      % set(auto) -> set(auto_process).
% 0.42/1.00      % set(auto2) -> assign(new_constants, 1).
% 0.42/1.00      % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/1.00      % set(auto2) -> assign(max_weight, "200.000").
% 0.42/1.00      % set(auto2) -> assign(max_hours, 1).
% 0.42/1.00      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/1.00      % set(auto2) -> assign(max_seconds, 0).
% 0.42/1.00      % set(auto2) -> assign(max_minutes, 5).
% 0.42/1.00      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/1.00      % set(auto2) -> set(sort_initial_sos).
% 0.42/1.00      % set(auto2) -> assign(sos_limit, -1).
% 0.42/1.00      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/1.00      % set(auto2) -> assign(max_megs, 400).
% 0.42/1.00      % set(auto2) -> assign(stats, some).
% 0.42/1.00      % set(auto2) -> clear(echo_input).
% 0.42/1.00      % set(auto2) -> set(quiet).
% 0.42/1.00      % set(auto2) -> clear(print_initial_clauses).
% 0.42/1.00      % set(auto2) -> clear(print_given).
% 0.42/1.00  assign(lrs_ticks,-1).
% 0.42/1.00  assign(sos_limit,10000).
% 0.42/1.00  assign(order,kbo).
% 0.42/1.00  set(lex_order_vars).
% 0.42/1.00  clear(print_given).
% 0.42/1.00  
% 0.42/1.00  % formulas(sos).  % not echoed (45 formulas)
% 0.42/1.00  
% 0.42/1.00  ============================== end of input ==========================
% 0.42/1.00  
% 0.42/1.00  % From the command line: assign(max_seconds, 300).
% 0.42/1.00  
% 0.42/1.00  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/1.00  
% 0.42/1.00  % Formulas that are not ordinary clauses:
% 0.42/1.00  1 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].
% 0.42/1.00  2 substitution_of_equivalents <-> (all X all Y (is_a_theorem(equiv(X,Y)) -> X = Y)) # label(substitution_of_equivalents) # label(axiom) # label(non_clause).  [assumption].
% 0.42/1.00  3 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].
% 0.42/1.00  4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause).  [assumption].
% 0.42/1.00  5 implies_2 <-> (all X all Y is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))) # label(implies_2) # label(axiom) # label(non_clause).  [assumption].
% 0.42/1.00  6 implies_3 <-> (all X all Y all Z is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))) # label(implies_3) # label(axiom) # label(non_clause).  [assumption].
% 0.42/1.00  7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause).  [assumption].
% 0.42/1.00  8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause).  [assumption].
% 0.42/1.00  9 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].
% 0.42/1.00  10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause).  [assumption].
% 0.42/1.00  11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause).  [assumption].
% 0.42/1.00  12 or_3 <-> (all X all Y all Z is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))) # label(or_3) # label(axiom) # label(non_clause).  [assumption].
% 0.42/1.00  13 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].
% 0.42/1.00  14 equivalence_2 <-> (all X all Y is_a_theorem(implies(equiv(X,Y),implies(Y,X)))) # label(equivalence_2) # label(axiom) # label(non_clause).  [assumption].
% 1.52/1.83  15 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].
% 1.52/1.83  16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause).  [assumption].
% 1.52/1.83  17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause).  [assumption].
% 1.52/1.83  18 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].
% 1.52/1.83  19 cn1 <-> (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))) # label(cn1) # label(axiom) # label(non_clause).  [assumption].
% 1.52/1.83  20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause).  [assumption].
% 1.52/1.83  21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause).  [assumption].
% 1.52/1.83  22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause).  [assumption].
% 1.52/1.83  23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause).  [assumption].
% 1.52/1.83  24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause).  [assumption].
% 1.52/1.83  25 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].
% 1.52/1.83  26 r5 <-> (all P all Q all R is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))) # label(r5) # label(axiom) # label(non_clause).  [assumption].
% 1.52/1.83  27 op_or -> (all X all Y or(X,Y) = not(and(not(X),not(Y)))) # label(op_or) # label(axiom) # label(non_clause).  [assumption].
% 1.52/1.83  28 op_and -> (all X all Y and(X,Y) = not(or(not(X),not(Y)))) # label(op_and) # label(axiom) # label(non_clause).  [assumption].
% 1.52/1.83  29 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].
% 1.52/1.83  30 op_implies_or -> (all X all Y implies(X,Y) = or(not(X),Y)) # label(op_implies_or) # label(axiom) # label(non_clause).  [assumption].
% 1.52/1.83  31 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].
% 1.52/1.83  
% 1.52/1.83  ============================== end of process non-clausal formulas ===
% 1.52/1.83  
% 1.52/1.83  ============================== PROCESS INITIAL CLAUSES ===============
% 1.52/1.83  
% 1.52/1.83  ============================== PREDICATE ELIMINATION =================
% 1.52/1.83  
% 1.52/1.83  ============================== end predicate elimination =============
% 1.52/1.83  
% 1.52/1.83  Auto_denials:  (non-Horn, no changes).
% 1.52/1.83  
% 1.52/1.83  Term ordering decisions:
% 1.52/1.83  
% 1.52/1.83  % Assigning unary symbol not kb_weight 0 and highest precedence (93).
% 1.52/1.83  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.
% 1.52/1.83  
% 1.52/1.83  ============================== end of process initial clauses ========
% 1.52/1.83  
% 1.52/1.83  ============================== CLAUSES FOR SEARCH ====================
% 1.52/1.83  
% 1.52/1.83  ============================== end of clauses for search =============
% 1.52/1.83  
% 1.52/1.83  ============================== SEARCH ================================
% 1.52/1.83  
% 1.52/1.83  % Starting search at 0.02 seconds.
% 1.52/1.83  
% 1.52/1.83  Low Water (keep): wt=33.000, iters=3454
% 1.52/1.83  
% 1.52/1.83  Low Water (keep): wt=31.000, iters=3409
% 1.52/1.83  
% 1.52/1.83  Low Water (keep): wt=25.000, iters=3349
% 1.52/1.83  
% 1.52/1.83  Low Water (keep): wt=22.000, iters=3376
% 1.52/1.83  
% 1.52/1.83  Low Water (keep): wt=21.000, iters=3355
% 1.52/1.83  
% 1.52/1.83  Low Water (keep): wt=20.000, iters=3350
% 1.52/1.83  
% 1.52/1.83  Low Water (keep): wt=19.000, iters=3349
% 1.52/1.83  
% 1.52/1.83  Low Water (keep): wt=18.000, iters=3333
% 1.52/1.83  
% 1.52/1.83  Low Water (keep): wt=17.000, iters=3370
% 1.52/1.83  
% 1.52/1.83  Low Water (keep): wt=16.000, iters=3367
% 124.61/124.92  
% 124.61/124.92  Low Water (keep): wt=15.000, iters=3370
% 124.61/124.92  
% 124.61/124.92  NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 24 (0.00 of 1.02 sec).
% 124.61/124.92  
% 124.61/124.92  Low Water (keep): wt=14.000, iters=3333
% 124.61/124.92  
% 124.61/124.92  Low Water (displace): id=14816, wt=62.000
% 124.61/124.92  
% 124.61/124.92  Low Water (displace): id=14431, wt=60.000
% 124.61/124.92  
% 124.61/124.92  Low Water (displace): id=14823, wt=59.000
% 124.61/124.92  
% 124.61/124.92  Low Water (displace): id=14438, wt=57.000
% 124.61/124.92  
% 124.61/124.92  Low Water (displace): id=14825, wt=56.000
% 124.61/124.92  
% 124.61/124.92  Low Water (displace): id=14440, wt=54.000
% 124.61/124.92  
% 124.61/124.92  Low Water (displace): id=14813, wt=50.000
% 124.61/124.92  
% 124.61/124.92  Low Water (displace): id=14428, wt=48.000
% 124.61/124.92  
% 124.61/124.92  Low Water (displace): id=14835, wt=44.000
% 124.61/124.92  
% 124.61/124.92  Low Water (displace): id=14450, wt=42.000
% 124.61/124.92  
% 124.61/124.92  Low Water (displace): id=14818, wt=41.000
% 124.61/124.92  
% 124.61/124.92  Low Water (displace): id=13922, wt=40.000
% 124.61/124.92  
% 124.61/124.92  Low Water (displace): id=14433, wt=39.000
% 124.61/124.92  
% 124.61/124.92  Low Water (displace): id=14836, wt=38.000
% 124.61/124.92  
% 124.61/124.92  Low Water (displace): id=14451, wt=36.000
% 124.61/124.92  
% 124.61/124.92  Low Water (displace): id=14888, wt=35.000
% 124.61/124.92  
% 124.61/124.92  Low Water (displace): id=13597, wt=34.000
% 124.61/124.92  
% 124.61/124.92  Low Water (displace): id=15119, wt=33.000
% 124.61/124.92  
% 124.61/124.92  Low Water (displace): id=15283, wt=32.000
% 124.61/124.92  
% 124.61/124.92  Low Water (displace): id=15257, wt=30.000
% 124.61/124.92  
% 124.61/124.92  Low Water (displace): id=15660, wt=29.000
% 124.61/124.92  
% 124.61/124.92  Low Water (displace): id=15611, wt=28.000
% 124.61/124.92  
% 124.61/124.92  Low Water (displace): id=15661, wt=27.000
% 124.61/124.92  
% 124.61/124.92  Low Water (displace): id=15692, wt=26.000
% 124.61/124.92  
% 124.61/124.92  Low Water (displace): id=13750, wt=25.000
% 124.61/124.92  
% 124.61/124.92  Low Water (displace): id=16081, wt=24.000
% 124.61/124.92  
% 124.61/124.92  Low Water (displace): id=16116, wt=13.000
% 124.61/124.92  
% 124.61/124.92  Low Water (displace): id=17416, wt=11.000
% 124.61/124.92  
% 124.61/124.92  Low Water (keep): wt=13.000, iters=3340
% 124.61/124.92  
% 124.61/124.92  Low Water (displace): id=33342, wt=9.000
% 124.61/124.92  
% 124.61/124.92  Low Water (keep): wt=12.000, iters=3333
% 124.61/124.92  
% 124.61/124.92  Low Water (keep): wt=11.000, iters=3339
% 124.61/124.92  
% 124.61/124.92  Low Water (keep): wt=10.000, iters=3334
% 124.61/124.92  
% 124.61/124.92  ============================== PROOF =================================
% 124.61/124.92  % SZS status Theorem
% 124.61/124.92  % SZS output start Refutation
% 124.61/124.92  
% 124.61/124.92  % Proof 1 at 118.30 (+ 5.62) seconds.
% 124.61/124.92  % Length of proof is 510.
% 124.61/124.92  % Level of proof is 88.
% 124.61/124.92  % Maximum clause weight is 23.000.
% 124.61/124.92  % Given clauses 10824.
% 124.61/124.92  
% 124.61/124.92  1 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].
% 124.61/124.92  2 substitution_of_equivalents <-> (all X all Y (is_a_theorem(equiv(X,Y)) -> X = Y)) # label(substitution_of_equivalents) # label(axiom) # label(non_clause).  [assumption].
% 124.61/124.92  12 or_3 <-> (all X all Y all Z is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))) # label(or_3) # label(axiom) # label(non_clause).  [assumption].
% 124.61/124.92  22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause).  [assumption].
% 124.61/124.92  23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause).  [assumption].
% 124.61/124.92  24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause).  [assumption].
% 124.61/124.92  25 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].
% 124.61/124.92  26 r5 <-> (all P all Q all R is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))) # label(r5) # label(axiom) # label(non_clause).  [assumption].
% 124.61/124.92  27 op_or -> (all X all Y or(X,Y) = not(and(not(X),not(Y)))) # label(op_or) # label(axiom) # label(non_clause).  [assumption].
% 124.61/124.92  28 op_and -> (all X all Y and(X,Y) = not(or(not(X),not(Y)))) # label(op_and) # label(axiom) # label(non_clause).  [assumption].
% 124.61/124.92  29 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].
% 124.61/124.92  30 op_implies_or -> (all X all Y implies(X,Y) = or(not(X),Y)) # label(op_implies_or) # label(axiom) # label(non_clause).  [assumption].
% 124.61/124.92  31 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].
% 124.61/124.92  32 op_implies_or # label(principia_op_implies_or) # label(axiom).  [assumption].
% 124.61/124.92  33 op_and # label(principia_op_and) # label(axiom).  [assumption].
% 124.61/124.92  34 op_equiv # label(principia_op_equiv) # label(axiom).  [assumption].
% 124.61/124.92  35 modus_ponens # label(principia_modus_ponens) # label(axiom).  [assumption].
% 124.61/124.92  36 r1 # label(principia_r1) # label(axiom).  [assumption].
% 124.61/124.92  37 r2 # label(principia_r2) # label(axiom).  [assumption].
% 124.61/124.92  38 r3 # label(principia_r3) # label(axiom).  [assumption].
% 124.61/124.92  39 r4 # label(principia_r4) # label(axiom).  [assumption].
% 124.61/124.92  40 r5 # label(principia_r5) # label(axiom).  [assumption].
% 124.61/124.92  41 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom).  [assumption].
% 124.61/124.92  42 op_or # label(hilbert_op_or) # label(axiom).  [assumption].
% 124.61/124.92  43 op_implies_and # label(hilbert_op_implies_and) # label(axiom).  [assumption].
% 124.61/124.92  44 -or_3 # label(hilbert_or_3) # label(negated_conjecture).  [assumption].
% 124.61/124.92  59 -r1 | is_a_theorem(implies(or(A,A),A)) # label(r1) # label(axiom).  [clausify(22)].
% 124.61/124.92  60 is_a_theorem(implies(or(A,A),A)).  [copy(59),unit_del(a,36)].
% 124.61/124.92  62 -r2 | is_a_theorem(implies(A,or(B,A))) # label(r2) # label(axiom).  [clausify(23)].
% 124.61/124.92  63 is_a_theorem(implies(A,or(B,A))).  [copy(62),unit_del(a,37)].
% 124.61/124.92  65 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom).  [clausify(2)].
% 124.61/124.92  66 -is_a_theorem(equiv(A,B)) | B = A.  [copy(65),unit_del(a,41)].
% 124.61/124.92  71 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom).  [clausify(1)].
% 124.61/124.92  72 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B).  [copy(71),unit_del(a,35)].
% 124.61/124.92  79 -r3 | is_a_theorem(implies(or(A,B),or(B,A))) # label(r3) # label(axiom).  [clausify(24)].
% 124.61/124.92  80 is_a_theorem(implies(or(A,B),or(B,A))).  [copy(79),unit_del(a,38)].
% 124.61/124.92  82 -op_implies_or | or(not(A),B) = implies(A,B) # label(op_implies_or) # label(axiom).  [clausify(30)].
% 124.61/124.92  83 or(not(A),B) = implies(A,B).  [copy(82),unit_del(a,32)].
% 124.61/124.92  84 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom).  [clausify(29)].
% 124.61/124.92  85 not(and(A,not(B))) = implies(A,B).  [copy(84),unit_del(a,43)].
% 124.61/124.92  90 -op_or | or(A,B) = not(and(not(A),not(B))) # label(op_or) # label(axiom).  [clausify(27)].
% 124.61/124.92  91 or(A,B) = implies(not(A),B).  [copy(90),rewrite([85(6)]),unit_del(a,42)].
% 124.61/124.92  92 -op_and | and(A,B) = not(or(not(A),not(B))) # label(op_and) # label(axiom).  [clausify(28)].
% 124.61/124.92  93 not(implies(not(not(A)),not(B))) = and(A,B).  [copy(92),rewrite([91(5)]),flip(b),unit_del(a,33)].
% 124.63/124.92  94 -op_equiv | and(implies(A,B),implies(B,A)) = equiv(A,B) # label(op_equiv) # label(axiom).  [clausify(31)].
% 124.63/124.92  95 and(implies(A,B),implies(B,A)) = equiv(A,B).  [copy(94),unit_del(a,34)].
% 124.63/124.92  102 -r4 | is_a_theorem(implies(or(A,or(B,C)),or(B,or(A,C)))) # label(r4) # label(axiom).  [clausify(25)].
% 124.63/124.92  103 is_a_theorem(implies(implies(not(A),implies(not(B),C)),implies(not(B),implies(not(A),C)))).  [copy(102),rewrite([91(2),91(4),91(6),91(8)]),unit_del(a,39)].
% 124.63/124.92  105 -r5 | is_a_theorem(implies(implies(A,B),implies(or(C,A),or(C,B)))) # label(r5) # label(axiom).  [clausify(26)].
% 124.63/124.92  106 is_a_theorem(implies(implies(A,B),implies(implies(not(C),A),implies(not(C),B)))).  [copy(105),rewrite([91(3),91(5)]),unit_del(a,40)].
% 124.63/124.92  109 or_3 | -is_a_theorem(implies(implies(c24,c26),implies(implies(c25,c26),implies(or(c24,c25),c26)))) # label(or_3) # label(axiom).  [clausify(12)].
% 124.63/124.92  110 -is_a_theorem(implies(implies(c24,c26),implies(implies(c25,c26),implies(implies(not(c24),c25),c26)))).  [copy(109),rewrite([91(10)]),unit_del(a,44)].
% 124.63/124.92  114 implies(not(not(A)),B) = implies(A,B).  [back_rewrite(83),rewrite([91(2)])].
% 124.63/124.92  115 is_a_theorem(implies(implies(not(A),B),implies(not(B),A))).  [back_rewrite(80),rewrite([91(1),91(3)])].
% 124.63/124.92  116 is_a_theorem(implies(A,implies(not(B),A))).  [back_rewrite(63),rewrite([91(1)])].
% 124.63/124.92  117 is_a_theorem(implies(implies(not(A),A),A)).  [back_rewrite(60),rewrite([91(1)])].
% 124.63/124.92  120 not(implies(A,not(B))) = and(A,B).  [back_rewrite(93),rewrite([114(4)])].
% 124.63/124.92  123 not(and(A,implies(B,C))) = implies(A,and(B,not(C))).  [para(85(a,1),85(a,1,1,2))].
% 124.63/124.92  124 -is_a_theorem(implies(not(A),implies(not(B),C))) | is_a_theorem(implies(not(B),implies(not(A),C))).  [resolve(103,a,72,b)].
% 124.63/124.92  127 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(C),A),implies(not(C),B))).  [resolve(106,a,72,b)].
% 124.63/124.92  132 implies(not(implies(A,B)),C) = implies(and(A,not(B)),C).  [para(85(a,1),114(a,1,1,1))].
% 124.63/124.92  134 and(implies(A,not(not(B))),implies(B,A)) = equiv(A,not(not(B))).  [para(114(a,1),95(a,1,2))].
% 124.63/124.92  135 is_a_theorem(implies(implies(not(A),implies(B,C)),implies(B,implies(not(A),C)))).  [para(114(a,1),103(a,1,1,2)),rewrite([114(8)])].
% 124.63/124.92  138 is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))).  [para(114(a,1),106(a,1,2,1)),rewrite([114(5)])].
% 124.63/124.92  139 -is_a_theorem(implies(not(A),B)) | is_a_theorem(implies(not(B),A)).  [resolve(115,a,72,b)].
% 124.63/124.92  143 is_a_theorem(implies(implies(A,B),implies(not(B),not(A)))).  [para(114(a,1),115(a,1,1))].
% 124.63/124.92  149 is_a_theorem(implies(A,implies(B,A))).  [para(114(a,1),116(a,1,2))].
% 124.63/124.92  152 -is_a_theorem(implies(not(A),A)) | is_a_theorem(A).  [resolve(117,a,72,b)].
% 124.63/124.92  156 is_a_theorem(implies(implies(A,not(A)),not(A))).  [para(114(a,1),117(a,1,1))].
% 124.63/124.92  160 and(not(not(A)),B) = and(A,B).  [para(114(a,1),120(a,1,1)),rewrite([120(3)]),flip(a)].
% 124.63/124.92  168 implies(implies(A,B),and(B,not(A))) = not(equiv(A,B)).  [para(95(a,1),123(a,1,1)),flip(a)].
% 124.63/124.92  197 -is_a_theorem(A) | is_a_theorem(implies(B,A)).  [resolve(149,a,72,b)].
% 124.63/124.92  202 is_a_theorem(implies(A,implies(B,not(not(A))))).  [para(114(a,1),149(a,1))].
% 124.63/124.92  203 is_a_theorem(implies(A,implies(B,implies(C,B)))).  [resolve(197,a,149,a)].
% 124.63/124.92  206 is_a_theorem(implies(not(A),implies(not(B),not(B)))).  [resolve(124,a,149,a)].
% 124.63/124.92  209 -is_a_theorem(implies(not(A),implies(B,C))) | is_a_theorem(implies(B,implies(not(A),C))).  [para(114(a,1),124(a,1,2)),rewrite([114(9)])].
% 124.63/124.92  247 -is_a_theorem(A) | is_a_theorem(implies(B,not(not(A)))).  [resolve(202,a,72,b)].
% 124.63/124.92  270 is_a_theorem(implies(implies(not(A),B),implies(not(A),implies(C,B)))).  [resolve(127,a,149,a)].
% 124.63/124.92  271 is_a_theorem(implies(implies(not(A),implies(not(B),B)),implies(not(A),B))).  [resolve(127,a,117,a)].
% 124.63/124.92  389 is_a_theorem(implies(not(A),not(A))).  [resolve(206,a,152,a)].
% 124.63/124.92  430 is_a_theorem(implies(A,not(not(A)))).  [para(114(a,1),389(a,1))].
% 124.63/124.92  432 is_a_theorem(implies(A,implies(B,B))).  [resolve(430,a,247,a),rewrite([120(4),85(3)])].
% 124.63/124.92  458 is_a_theorem(implies(A,A)).  [resolve(432,a,152,a)].
% 124.63/124.92  536 is_a_theorem(implies(A,not(not(implies(B,B))))).  [resolve(458,a,247,a)].
% 124.63/124.92  746 implies(and(A,not(not(B))),C) = implies(and(A,B),C).  [para(120(a,1),132(a,1,1)),flip(a)].
% 124.63/124.92  994 equiv(A,not(not(B))) = equiv(A,B).  [para(134(a,1),160(a,2)),rewrite([120(4),85(3),95(3)]),flip(a)].
% 124.63/124.92  1206 is_a_theorem(implies(implies(A,implies(B,C)),implies(B,implies(A,C)))).  [para(114(a,1),135(a,1,1)),rewrite([114(5)])].
% 124.63/124.92  1295 -is_a_theorem(equiv(A,B)) | not(not(B)) = A.  [para(994(a,1),66(a,1))].
% 124.63/124.92  1310 is_a_theorem(implies(and(A,not(A)),B)).  [resolve(139,a,536,a),rewrite([114(5),132(3)])].
% 124.63/124.92  1315 is_a_theorem(implies(and(A,B),B)).  [resolve(139,a,202,a),rewrite([120(5),746(4)])].
% 124.63/124.92  1317 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(B),not(A))).  [para(114(a,1),139(a,1))].
% 124.63/124.92  1456 is_a_theorem(implies(A,implies(and(B,C),C))).  [resolve(1315,a,197,a)].
% 124.63/124.92  1458 is_a_theorem(implies(implies(not(A),and(B,C)),implies(not(A),C))).  [resolve(1315,a,127,a)].
% 124.63/124.92  1526 -is_a_theorem(and(A,implies(implies(c24,c26),implies(implies(c25,c26),implies(implies(not(c24),c25),c26))))).  [ur(72,b,1315,a,c,110,a)].
% 124.63/124.92  1578 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(C,A),implies(C,B))).  [resolve(138,a,72,b)].
% 124.63/124.92  2852 is_a_theorem(implies(implies(A,not(B)),implies(B,not(A)))).  [para(114(a,1),143(a,1,2))].
% 124.63/124.92  6402 is_a_theorem(implies(A,and(A,A))).  [resolve(1317,a,156,a),rewrite([120(5),114(4)])].
% 124.63/124.92  6419 -is_a_theorem(A) | is_a_theorem(and(A,A)).  [resolve(6402,a,72,b)].
% 124.63/124.92  6553 is_a_theorem(equiv(A,A)).  [resolve(6419,a,458,a),rewrite([95(3)])].
% 124.63/124.92  6699 not(not(A)) = A.  [resolve(6553,a,1295,a)].
% 124.63/124.92  6767 not(and(A,B)) = implies(A,not(B)).  [para(6699(a,1),85(a,1,1,2))].
% 124.63/124.92  6768 not(implies(A,B)) = and(A,not(B)).  [para(85(a,1),6699(a,1,1))].
% 124.63/124.92  6923 implies(implies(not(A),B),and(B,A)) = not(equiv(not(A),B)).  [para(6699(a,1),168(a,1,2,2))].
% 124.63/124.92  8629 is_a_theorem(implies(and(A,B),and(B,A))).  [resolve(2852,a,1317,a),rewrite([6768(3),6699(2),6768(4),6699(3)])].
% 124.63/124.92  8631 -is_a_theorem(implies(A,not(B))) | is_a_theorem(implies(B,not(A))).  [resolve(2852,a,72,b)].
% 124.63/124.92  8803 is_a_theorem(implies(A,implies(and(B,C),and(C,B)))).  [resolve(8629,a,197,a)].
% 124.63/124.92  8886 is_a_theorem(implies(equiv(A,B),equiv(B,A))).  [para(95(a,1),8629(a,1,1)),rewrite([95(4)])].
% 124.63/124.92  8889 is_a_theorem(implies(A,implies(equiv(B,C),equiv(C,B)))).  [resolve(8886,a,197,a)].
% 124.63/124.92  10555 is_a_theorem(implies(and(A,B),implies(not(C),and(B,A)))).  [resolve(209,a,8803,a)].
% 124.63/124.92  10558 is_a_theorem(implies(and(A,B),implies(not(C),B))).  [resolve(209,a,1456,a)].
% 124.63/124.92  10562 is_a_theorem(implies(A,implies(not(B),implies(C,A)))).  [resolve(209,a,203,a)].
% 124.63/124.92  10563 -is_a_theorem(implies(A,implies(B,C))) | is_a_theorem(implies(B,implies(A,C))).  [para(6699(a,1),209(a,1,1)),rewrite([6699(5)])].
% 124.63/124.92  10794 is_a_theorem(implies(and(A,B),implies(C,B))).  [para(6699(a,1),10558(a,1,2,1))].
% 124.63/124.92  10837 is_a_theorem(implies(A,implies(and(B,C),implies(D,C)))).  [resolve(10794,a,197,a)].
% 124.63/124.92  10913 is_a_theorem(implies(A,implies(B,implies(C,A)))).  [para(6699(a,1),10562(a,1,2,1))].
% 124.63/124.92  10918 is_a_theorem(implies(A,implies(B,implies(C,implies(D,B))))).  [resolve(10913,a,197,a)].
% 124.63/124.92  12327 is_a_theorem(implies(and(A,B),implies(C,and(B,A)))).  [para(6699(a,1),10555(a,1,2,1))].
% 124.63/124.92  12338 is_a_theorem(implies(and(not(A),B),not(equiv(A,B)))).  [para(168(a,1),12327(a,1,2))].
% 124.63/124.92  12362 is_a_theorem(implies(equiv(A,B),implies(not(A),not(B)))).  [resolve(12338,a,8631,a),rewrite([6767(4)])].
% 124.63/124.92  12381 is_a_theorem(implies(equiv(not(A),B),implies(A,not(B)))).  [para(6699(a,1),12362(a,1,2,1))].
% 124.63/124.92  12382 is_a_theorem(implies(equiv(A,not(B)),implies(not(A),B))).  [para(6699(a,1),12362(a,1,2,2))].
% 124.63/124.92  12428 is_a_theorem(implies(equiv(not(A),not(B)),implies(A,B))).  [para(6699(a,1),12381(a,1,2,2))].
% 124.63/124.92  12844 is_a_theorem(implies(implies(A,B),implies(A,implies(C,B)))).  [para(6699(a,1),270(a,1,1,1)),rewrite([6699(3)])].
% 124.63/124.92  12874 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(A,implies(C,B))).  [resolve(12844,a,72,b)].
% 124.63/124.92  13382 is_a_theorem(implies(implies(A,implies(not(B),B)),implies(A,B))).  [para(6699(a,1),271(a,1,1,1)),rewrite([6699(5)])].
% 124.63/124.92  14131 -is_a_theorem(implies(A,implies(not(B),B))) | is_a_theorem(implies(A,B)).  [resolve(13382,a,72,b)].
% 124.63/124.92  15608 is_a_theorem(implies(implies(not(A),and(B,A)),A)).  [resolve(1458,a,14131,a)].
% 124.63/124.92  15627 is_a_theorem(implies(implies(A,and(B,C)),implies(A,C))).  [para(6699(a,1),1458(a,1,1,1)),rewrite([6699(4)])].
% 124.63/124.92  15670 is_a_theorem(implies(A,and(A,implies(B,A)))).  [resolve(15608,a,8631,a),rewrite([6699(2),6768(4),6767(3),6699(2)])].
% 124.63/124.92  15962 -is_a_theorem(implies(A,and(B,C))) | is_a_theorem(implies(A,C)).  [resolve(15627,a,72,b)].
% 124.63/124.92  16102 is_a_theorem(implies(and(A,B),A)).  [resolve(15962,a,8629,a)].
% 124.63/124.92  16139 is_a_theorem(implies(and(A,B),implies(C,A))).  [resolve(16102,a,12874,a)].
% 124.63/124.92  16143 is_a_theorem(implies(A,implies(not(A),not(B)))).  [resolve(16102,a,8631,a),rewrite([6767(3)])].
% 124.63/124.92  16459 is_a_theorem(implies(equiv(A,B),implies(A,B))).  [para(95(a,1),16102(a,1,1))].
% 124.63/124.92  16791 is_a_theorem(implies(and(A,not(B)),implies(B,not(C)))).  [resolve(16139,a,1317,a),rewrite([6768(2),6767(4)])].
% 124.63/124.92  16834 is_a_theorem(implies(A,implies(not(A),B))).  [para(6699(a,1),16143(a,1,2,2))].
% 124.63/124.92  16885 is_a_theorem(implies(A,implies(B,implies(not(A),C)))).  [resolve(16834,a,12874,a)].
% 124.63/124.92  16918 is_a_theorem(implies(not(A),implies(A,B))).  [para(6699(a,1),16834(a,1,2,1))].
% 124.63/124.92  17111 -is_a_theorem(not(A)) | is_a_theorem(implies(A,B)).  [resolve(16918,a,72,b)].
% 124.63/124.92  18071 is_a_theorem(implies(A,implies(B,implies(C,implies(not(B),D))))).  [resolve(16885,a,197,a)].
% 124.63/124.92  29244 is_a_theorem(implies(implies(A,B),implies(A,implies(not(B),C)))).  [resolve(1578,a,16834,a)].
% 124.63/124.92  29256 is_a_theorem(implies(implies(A,and(B,C)),implies(A,B))).  [resolve(1578,a,16102,a)].
% 124.63/124.92  29361 is_a_theorem(implies(implies(A,B),implies(A,and(B,B)))).  [resolve(1578,a,6402,a)].
% 124.63/124.92  29418 is_a_theorem(implies(implies(not(A),and(A,B)),A)).  [resolve(29256,a,14131,a)].
% 124.63/124.92  29430 -is_a_theorem(implies(A,and(B,C))) | is_a_theorem(implies(A,B)).  [resolve(29256,a,72,b)].
% 124.63/124.92  29489 is_a_theorem(implies(not(equiv(A,B)),implies(implies(A,B),B))).  [para(168(a,1),29256(a,1,1))].
% 124.63/124.92  29520 is_a_theorem(implies(A,and(A,implies(not(A),not(B))))).  [resolve(29418,a,8631,a),rewrite([6699(2),6768(4),6767(3)])].
% 124.63/124.92  29674 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(A,and(B,B))).  [resolve(29361,a,72,b)].
% 124.63/124.92  30026 is_a_theorem(implies(A,and(A,implies(not(A),B)))).  [para(6699(a,1),29520(a,1,2,2,2))].
% 124.63/124.92  30812 is_a_theorem(not(equiv(A,not(A)))).  [resolve(29674,a,156,a),rewrite([168(6)])].
% 124.63/124.92  30819 is_a_theorem(not(equiv(not(A),A))).  [resolve(29674,a,117,a),rewrite([6923(4)])].
% 124.63/124.92  30834 is_a_theorem(implies(equiv(A,not(A)),B)).  [resolve(30812,a,17111,a)].
% 124.63/124.92  30984 is_a_theorem(implies(equiv(not(A),A),B)).  [resolve(30819,a,17111,a)].
% 124.63/124.92  31056 is_a_theorem(implies(implies(A,equiv(B,not(B))),implies(A,C))).  [resolve(30834,a,1578,a)].
% 124.63/124.92  35523 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(A,implies(not(B),C))).  [resolve(29244,a,72,b)].
% 124.63/124.92  44186 is_a_theorem(implies(implies(not(A),equiv(B,not(B))),A)).  [resolve(31056,a,14131,a)].
% 124.63/124.92  44276 -is_a_theorem(implies(not(A),equiv(B,not(B)))) | is_a_theorem(A).  [resolve(44186,a,72,b)].
% 124.63/124.92  44442 -is_a_theorem(implies(A,equiv(B,not(B)))) | is_a_theorem(not(A)).  [para(6699(a,1),44276(a,1,1))].
% 124.63/124.92  45268 -is_a_theorem(implies(A,equiv(not(B),B))) | is_a_theorem(not(A)).  [para(6699(a,1),44442(a,1,2,2))].
% 124.63/124.92  47959 is_a_theorem(implies(and(A,not(B)),implies(and(B,C),D))).  [resolve(35523,a,16791,a),rewrite([6768(5),6699(4)])].
% 124.63/124.92  98317 is_a_theorem(implies(implies(A,B),implies(not(equiv(A,B)),B))).  [resolve(10563,a,29489,a)].
% 124.63/124.92  98385 is_a_theorem(implies(A,implies(equiv(A,B),B))).  [resolve(10563,a,16459,a)].
% 124.63/124.92  98404 is_a_theorem(implies(A,implies(implies(A,B),implies(C,B)))).  [resolve(10563,a,12844,a)].
% 124.63/124.92  98408 is_a_theorem(implies(A,implies(equiv(not(A),not(B)),B))).  [resolve(10563,a,12428,a)].
% 124.63/124.92  98434 is_a_theorem(implies(A,implies(implies(B,not(A)),not(B)))).  [resolve(10563,a,2852,a)].
% 124.63/124.92  98444 is_a_theorem(implies(A,implies(implies(A,B),B))).  [resolve(10563,a,458,a)].
% 124.63/124.92  98547 is_a_theorem(implies(A,implies(B,implies(equiv(B,C),C)))).  [resolve(98385,a,197,a)].
% 124.63/124.92  98721 -is_a_theorem(A) | is_a_theorem(implies(implies(A,B),B)).  [resolve(98444,a,72,b)].
% 124.63/124.92  100915 is_a_theorem(implies(implies(not(equiv(not(A),A)),B),B)).  [resolve(98721,a,30819,a)].
% 124.63/124.92  101092 is_a_theorem(implies(implies(implies(and(A,B),A),C),C)).  [resolve(98721,a,16102,a)].
% 124.63/124.92  101222 is_a_theorem(implies(implies(implies(A,and(A,A)),B),B)).  [resolve(98721,a,6402,a)].
% 124.63/124.92  101254 is_a_theorem(implies(implies(implies(and(A,B),B),C),C)).  [resolve(98721,a,1315,a)].
% 124.63/124.92  101288 is_a_theorem(implies(implies(implies(A,implies(B,A)),C),C)).  [resolve(98721,a,149,a)].
% 124.63/124.92  105987 -is_a_theorem(A) | is_a_theorem(implies(equiv(not(A),not(B)),B)).  [resolve(98408,a,72,b)].
% 124.63/124.92  106825 is_a_theorem(implies(and(implies(A,B),A),B)).  [resolve(98434,a,139,a),rewrite([6699(2),6768(4),6699(3)])].
% 124.63/124.92  106965 is_a_theorem(implies(A,implies(and(implies(B,C),B),C))).  [resolve(106825,a,197,a)].
% 124.63/124.92  111026 is_a_theorem(implies(A,and(not(equiv(not(B),B)),A))).  [resolve(100915,a,8631,a),rewrite([6768(6),6699(5)])].
% 124.63/124.92  111335 -is_a_theorem(implies(implies(and(A,B),A),C)) | is_a_theorem(C).  [resolve(101092,a,72,b)].
% 124.63/124.92  111546 -is_a_theorem(implies(implies(A,and(A,A)),B)) | is_a_theorem(B).  [resolve(101222,a,72,b)].
% 124.63/124.92  111652 -is_a_theorem(implies(implies(and(A,B),B),C)) | is_a_theorem(C).  [resolve(101254,a,72,b)].
% 124.63/124.92  111916 -is_a_theorem(implies(implies(A,implies(B,A)),C)) | is_a_theorem(C).  [resolve(101288,a,72,b)].
% 124.63/124.92  140208 -is_a_theorem(A) | is_a_theorem(and(not(equiv(not(B),B)),A)).  [resolve(111026,a,72,b)].
% 124.63/124.92  167377 is_a_theorem(implies(not(equiv(A,implies(B,A))),implies(B,A))).  [resolve(98317,a,111916,a)].
% 124.63/124.92  167378 is_a_theorem(implies(not(equiv(and(A,B),B)),B)).  [resolve(98317,a,111652,a)].
% 124.63/124.92  167380 is_a_theorem(implies(not(equiv(and(A,B),A)),A)).  [resolve(98317,a,111335,a)].
% 124.63/124.92  167488 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(equiv(A,B)),B)).  [resolve(98317,a,72,b)].
% 124.63/124.92  167632 is_a_theorem(implies(not(A),equiv(and(B,A),A))).  [resolve(167378,a,1317,a),rewrite([6699(5)])].
% 124.63/124.92  167784 is_a_theorem(implies(not(A),equiv(and(A,B),A))).  [resolve(167380,a,1317,a),rewrite([6699(5)])].
% 124.63/124.92  167921 -is_a_theorem(not(A)) | is_a_theorem(equiv(and(B,A),A)).  [resolve(167632,a,72,b)].
% 124.63/124.92  168089 -is_a_theorem(not(A)) | is_a_theorem(equiv(and(A,B),A)).  [resolve(167784,a,72,b)].
% 124.63/124.92  168126 -is_a_theorem(A) | is_a_theorem(equiv(and(B,not(A)),not(A))).  [para(6699(a,1),167921(a,1))].
% 124.63/124.92  168180 -is_a_theorem(A) | is_a_theorem(equiv(and(not(A),B),not(A))).  [para(6699(a,1),168089(a,1))].
% 124.63/124.92  204611 is_a_theorem(implies(A,implies(not(equiv(B,implies(A,B))),B))).  [resolve(167377,a,10563,a)].
% 124.63/124.92  207689 is_a_theorem(implies(not(equiv(equiv(not(A),A),B)),B)).  [resolve(167488,a,30984,a)].
% 124.63/124.92  207936 is_a_theorem(implies(not(equiv(and(A,not(A)),B)),B)).  [resolve(167488,a,1310,a)].
% 124.63/124.92  207958 is_a_theorem(implies(not(equiv(implies(not(A),A),A)),A)).  [resolve(167488,a,117,a)].
% 124.63/124.92  208047 is_a_theorem(equiv(equiv(not(A),A),equiv(not(B),B))).  [resolve(207689,a,45268,a),rewrite([6699(7)])].
% 124.63/124.92  208096 is_a_theorem(implies(A,equiv(equiv(not(B),B),not(A)))).  [resolve(207689,a,8631,a),rewrite([6699(6)])].
% 124.63/124.92  208532 is_a_theorem(equiv(and(A,not(A)),equiv(not(B),B))).  [resolve(207936,a,45268,a),rewrite([6699(7)])].
% 124.63/124.92  208683 is_a_theorem(equiv(implies(not(equiv(not(A),A)),equiv(not(A),A)),equiv(not(A),A))).  [resolve(207958,a,45268,a),rewrite([6699(11)])].
% 124.63/124.92  208847 equiv(not(A),A) = equiv(not(B),B).  [resolve(208047,a,66,a)].
% 124.63/124.92  208852 equiv(not(A),A) = c_0.  [new_symbol(208847)].
% 124.63/124.92  208871 is_a_theorem(equiv(implies(not(c_0),c_0),c_0)).  [back_rewrite(208683),rewrite([208852(2),208852(4),208852(6)])].
% 124.63/124.92  208880 is_a_theorem(equiv(and(A,not(A)),c_0)).  [back_rewrite(208532),rewrite([208852(4)])].
% 124.63/124.92  208923 is_a_theorem(implies(A,equiv(c_0,not(A)))).  [back_rewrite(208096),rewrite([208852(2)])].
% 124.63/124.92  209150 -is_a_theorem(A) | is_a_theorem(and(not(c_0),A)).  [back_rewrite(140208),rewrite([208852(3)])].
% 124.63/124.92  209179 is_a_theorem(implies(implies(not(c_0),A),A)).  [back_rewrite(100915),rewrite([208852(2)])].
% 124.63/124.92  209384 is_a_theorem(not(c_0)).  [back_rewrite(30819),rewrite([208852(2)])].
% 124.63/124.92  209546 is_a_theorem(equiv(and(c_0,A),c_0)).  [resolve(209384,a,168180,a),rewrite([6699(3),6699(5)])].
% 124.63/124.92  209547 is_a_theorem(equiv(and(A,c_0),c_0)).  [resolve(209384,a,168126,a),rewrite([6699(3),6699(5)])].
% 124.63/124.92  211418 and(c_0,A) = c_0.  [resolve(209546,a,66,a),flip(a)].
% 124.63/124.92  211481 implies(c_0,not(A)) = not(c_0).  [para(211418(a,1),6767(a,1,1)),flip(a)].
% 124.63/124.92  211633 and(A,c_0) = c_0.  [resolve(209547,a,66,a),flip(a)].
% 124.63/124.92  211673 implies(A,not(c_0)) = not(c_0).  [para(211633(a,1),6767(a,1,1)),flip(a)].
% 124.63/124.92  212473 implies(not(c_0),c_0) = c_0.  [resolve(208871,a,66,a),flip(a)].
% 124.63/124.92  212515 and(not(c_0),not(c_0)) = not(c_0).  [para(212473(a,1),6768(a,1,1)),flip(a)].
% 124.63/124.92  212820 and(A,not(A)) = c_0.  [resolve(208880,a,66,a),flip(a)].
% 124.63/124.92  213024 implies(A,A) = not(c_0).  [para(212820(a,1),6767(a,1,1)),rewrite([6699(4)]),flip(a)].
% 124.63/124.92  214193 is_a_theorem(equiv(c_0,and(A,and(B,not(A))))).  [resolve(208923,a,111916,a),rewrite([6768(4),6768(3)])].
% 124.63/124.92  214194 is_a_theorem(equiv(c_0,and(and(A,B),not(B)))).  [resolve(208923,a,111652,a),rewrite([6768(4)])].
% 124.63/124.92  214195 is_a_theorem(equiv(c_0,and(A,implies(A,not(A))))).  [resolve(208923,a,111546,a),rewrite([6768(4),6767(3)])].
% 124.63/124.92  214196 is_a_theorem(equiv(c_0,and(and(A,B),not(A)))).  [resolve(208923,a,111335,a),rewrite([6768(4)])].
% 124.63/124.92  215580 is_a_theorem(and(not(c_0),implies(A,and(A,implies(not(A),B))))).  [resolve(209150,a,30026,a)].
% 124.63/124.92  215735 is_a_theorem(and(not(c_0),implies(A,and(A,implies(B,A))))).  [resolve(209150,a,15670,a)].
% 124.63/124.92  218625 implies(c_0,A) = not(c_0).  [para(6699(a,1),211481(a,1,2))].
% 124.63/124.92  218631 and(implies(A,c_0),not(c_0)) = equiv(A,c_0).  [para(218625(a,1),95(a,1,2))].
% 124.63/124.92  218638 and(not(c_0),implies(not(c_0),A)) = equiv(A,not(c_0)).  [para(211673(a,1),95(a,1,1))].
% 124.63/124.92  218639 and(implies(not(c_0),A),not(c_0)) = equiv(not(c_0),A).  [para(211673(a,1),95(a,1,2))].
% 124.63/124.92  221427 and(A,and(B,not(A))) = c_0.  [resolve(214193,a,66,a)].
% 124.63/124.92  221430 implies(A,implies(B,A)) = not(c_0).  [para(221427(a,1),6767(a,1,1)),rewrite([6767(5),6699(4)]),flip(a)].
% 124.63/124.92  221463 and(and(A,B),not(B)) = c_0.  [resolve(214194,a,66,a)].
% 124.63/124.92  221467 implies(and(A,B),B) = not(c_0).  [para(221463(a,1),6767(a,1,1)),rewrite([6699(5)]),flip(a)].
% 124.63/124.92  221498 and(A,implies(A,not(A))) = c_0.  [resolve(214195,a,66,a)].
% 124.63/124.92  221501 implies(A,and(A,A)) = not(c_0).  [para(221498(a,1),6767(a,1,1)),rewrite([6768(5),6699(4)]),flip(a)].
% 124.63/124.92  221505 equiv(A,and(A,A)) = not(c_0).  [para(221501(a,1),95(a,1,1)),rewrite([221467(4),212515(5)]),flip(a)].
% 124.63/124.92  221519 and(A,A) = A.  [para(221505(a,1),66(a,1)),unit_del(a,209384)].
% 124.63/124.92  221526 implies(A,not(A)) = not(A).  [para(221519(a,1),6767(a,1,1)),flip(a)].
% 124.63/124.92  221544 implies(not(A),A) = A.  [para(221526(a,1),91(a,2)),rewrite([6699(2),91(1),6699(4)])].
% 124.63/124.92  221545 is_a_theorem(implies(implies(A,not(B)),implies(implies(B,A),not(B)))).  [para(221526(a,1),138(a,1,2,2))].
% 124.63/124.92  221569 is_a_theorem(implies(implies(A,B),implies(implies(not(B),A),B))).  [para(221544(a,1),138(a,1,2,2))].
% 124.63/124.92  221646 and(and(A,B),not(A)) = c_0.  [resolve(214196,a,66,a)].
% 124.63/124.92  221653 implies(and(A,B),A) = not(c_0).  [para(221646(a,1),6767(a,1,1)),rewrite([6699(5)]),flip(a)].
% 124.63/124.92  221690 and(not(c_0),implies(A,and(A,B))) = equiv(and(A,B),A).  [para(221653(a,1),95(a,1,1))].
% 124.63/124.92  221691 and(implies(A,and(A,B)),not(c_0)) = equiv(A,and(A,B)).  [para(221653(a,1),95(a,1,2))].
% 124.63/124.92  221692 implies(equiv(A,B),implies(A,B)) = not(c_0).  [para(95(a,1),221653(a,1,1))].
% 124.63/124.92  221694 is_a_theorem(implies(implies(A,B),implies(not(c_0),implies(and(A,C),B)))).  [para(221653(a,1),138(a,1,2,1))].
% 124.63/124.92  221701 is_a_theorem(equiv(and(A,implies(B,A)),A)).  [back_rewrite(215735),rewrite([221690(6)])].
% 124.63/124.92  221702 is_a_theorem(equiv(and(A,implies(not(A),B)),A)).  [back_rewrite(215580),rewrite([221690(7)])].
% 124.63/124.92  221773 and(A,implies(B,A)) = A.  [resolve(221701,a,66,a),flip(a)].
% 124.63/124.92  221782 implies(A,and(B,not(A))) = not(A).  [para(221773(a,1),6767(a,1,1)),rewrite([6768(3)]),flip(a)].
% 124.63/124.92  221860 and(A,not(c_0)) = A.  [para(213024(a,1),221773(a,1,2))].
% 124.63/124.92  221861 equiv(A,and(A,B)) = implies(A,and(A,B)).  [back_rewrite(221691),rewrite([221860(5)]),flip(a)].
% 124.63/124.92  221863 equiv(not(c_0),A) = implies(not(c_0),A).  [back_rewrite(218639),rewrite([221860(6)]),flip(a)].
% 124.63/124.92  221865 equiv(A,c_0) = implies(A,c_0).  [back_rewrite(218631),rewrite([221860(5)]),flip(a)].
% 124.63/124.92  221959 implies(A,c_0) = not(A).  [para(221860(a,1),6767(a,1,1)),rewrite([6699(4)]),flip(a)].
% 124.63/124.92  221964 equiv(A,c_0) = not(A).  [back_rewrite(221865),rewrite([221959(4)])].
% 124.63/124.92  223887 -is_a_theorem(not(A)) | c_0 = A.  [para(221964(a,1),66(a,1))].
% 124.63/124.92  223888 -is_a_theorem(A) | not(A) = c_0.  [para(6699(a,1),223887(a,1)),flip(b)].
% 124.63/124.92  223889 -is_a_theorem(implies(A,not(B))) | and(A,B) = c_0.  [para(6767(a,1),223887(a,1)),flip(b)].
% 124.63/124.92  223909 and(implies(not(c_0),A),not(A)) = c_0.  [resolve(223888,a,209179,a),rewrite([6768(5)])].
% 124.63/124.92  224025 and(A,and(implies(A,B),and(C,not(B)))) = c_0.  [resolve(223888,a,98404,a),rewrite([6768(5),6768(4),6768(3)])].
% 124.63/124.92  224094 and(and(A,not(B)),and(and(B,C),not(D))) = c_0.  [resolve(223888,a,47959,a),rewrite([6768(6),6768(5)])].
% 124.63/124.92  224316 and(implies(A,B),and(implies(C,A),and(C,not(B)))) = c_0.  [resolve(223888,a,138,a),rewrite([6768(6),6768(5),6768(4)])].
% 124.63/124.92  225889 and(A,implies(not(A),B)) = A.  [resolve(221702,a,66,a),flip(a)].
% 124.63/124.92  226359 and(not(A),implies(A,B)) = not(A).  [para(6699(a,1),225889(a,1,2,1))].
% 124.63/124.92  226363 is_a_theorem(implies(A,and(implies(not(A),B),A))).  [para(225889(a,1),8629(a,1,1))].
% 124.63/124.92  226432 implies(A,implies(not(A),B)) = not(c_0).  [para(225889(a,1),221467(a,1,1))].
% 124.63/124.92  226433 implies(not(A),and(B,A)) = A.  [para(221782(a,1),91(a,2)),rewrite([6699(2),91(2),6699(5)])].
% 124.63/124.92  226448 is_a_theorem(implies(equiv(A,implies(B,not(A))),A)).  [para(221782(a,1),12382(a,1,2)),rewrite([6699(2),6767(2),6699(5)])].
% 124.63/124.92  226521 and(and(A,B),B) = and(A,B).  [para(226433(a,1),221773(a,1,2))].
% 124.63/124.92  226522 implies(and(A,not(B)),B) = implies(A,B).  [para(221773(a,1),226433(a,1,2)),rewrite([6768(2)])].
% 124.63/124.92  226524 implies(and(not(A),not(B)),A) = implies(not(A),B).  [para(225889(a,1),226433(a,1,2)),rewrite([6768(3)])].
% 124.63/124.92  226777 -is_a_theorem(implies(not(c_0),A)) | not(c_0) = A.  [para(221863(a,1),66(a,1)),flip(b)].
% 124.63/124.92  226963 not(equiv(A,implies(not(c_0),A))) = c_0.  [para(223909(a,1),168(a,1,2)),rewrite([221430(4),221959(4),6699(3)]),flip(a)].
% 124.63/124.92  227105 implies(not(A),and(A,not(B))) = A.  [para(226359(a,1),6767(a,1,1)),rewrite([6699(2),6768(3)]),flip(a)].
% 124.63/124.92  227145 implies(not(A),implies(A,B)) = not(c_0).  [para(226359(a,1),221467(a,1,1))].
% 124.63/124.92  227175 is_a_theorem(implies(implies(implies(A,B),A),A)).  [resolve(226363,a,139,a),rewrite([6699(2),6767(4),6699(3)])].
% 124.63/124.92  227462 is_a_theorem(implies(implies(implies(not(A),B),C),implies(not(c_0),implies(A,C)))).  [para(226432(a,1),138(a,1,2,1))].
% 124.63/124.92  227570 is_a_theorem(implies(A,implies(equiv(implies(A,B),implies(C,and(A,not(B)))),B))).  [resolve(226448,a,10563,a),rewrite([6768(3)])].
% 124.63/124.92  227703 implies(and(A,B),not(B)) = implies(A,not(B)).  [para(226521(a,1),6767(a,1,1)),rewrite([6767(2)]),flip(a)].
% 124.63/124.92  227828 implies(and(implies(A,B),A),B) = not(c_0).  [resolve(226777,a,106965,a),flip(a)].
% 124.63/124.92  227833 implies(A,implies(equiv(A,B),B)) = not(c_0).  [resolve(226777,a,98547,a),flip(a)].
% 124.63/124.92  227856 implies(A,implies(B,implies(not(A),C))) = not(c_0).  [resolve(226777,a,18071,a),flip(a)].
% 124.63/124.92  227860 implies(A,implies(B,implies(C,A))) = not(c_0).  [resolve(226777,a,10918,a),flip(a)].
% 124.63/124.92  227861 implies(and(A,B),implies(C,B)) = not(c_0).  [resolve(226777,a,10837,a),flip(a)].
% 124.63/124.92  227866 implies(equiv(A,B),equiv(B,A)) = not(c_0).  [resolve(226777,a,8889,a),flip(a)].
% 124.63/124.92  227867 implies(and(A,B),and(B,A)) = not(c_0).  [resolve(226777,a,8803,a),flip(a)].
% 124.63/124.92  227988 equiv(A,implies(not(c_0),A)) = not(c_0).  [para(226963(a,1),6699(a,1,1)),flip(a)].
% 124.63/124.92  228055 implies(not(A),and(A,B)) = A.  [para(6699(a,1),227105(a,1,2,2))].
% 124.63/124.92  228061 is_a_theorem(implies(implies(not(A),implies(B,and(A,not(C)))),implies(B,A))).  [para(227105(a,1),1206(a,1,2,2))].
% 124.63/124.92  228073 implies(and(A,not(B)),equiv(A,B)) = implies(A,B).  [para(95(a,1),228055(a,1,2)),rewrite([6768(2)])].
% 124.63/124.92  228450 is_a_theorem(implies(implies(implies(A,B),C),implies(not(c_0),implies(not(A),C)))).  [para(227145(a,1),138(a,1,2,1))].
% 124.63/124.92  228580 implies(not(c_0),A) = A.  [para(227988(a,1),66(a,1)),unit_del(a,209384)].
% 124.63/124.92  228582 is_a_theorem(implies(implies(implies(A,B),C),implies(not(A),C))).  [back_rewrite(228450),rewrite([228580(7)])].
% 124.63/124.92  228590 is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C))).  [back_rewrite(227462),rewrite([228580(7)])].
% 124.63/124.92  228611 -is_a_theorem(A) | not(c_0) = A.  [back_rewrite(226777),rewrite([228580(3)])].
% 124.63/124.92  229053 is_a_theorem(implies(implies(A,B),implies(and(A,C),B))).  [back_rewrite(221694),rewrite([228580(6)])].
% 124.63/124.92  229054 equiv(A,not(c_0)) = and(not(c_0),A).  [back_rewrite(218638),rewrite([228580(5)]),flip(a)].
% 124.63/124.92  229358 and(not(c_0),not(A)) = not(A).  [para(228580(a,1),6768(a,1,1)),flip(a)].
% 124.63/124.92  229384 implies(implies(implies(A,B),A),A) = not(c_0).  [resolve(228611,a,227175,a),flip(a)].
% 124.63/124.92  229553 implies(implies(A,and(B,C)),implies(A,B)) = not(c_0).  [resolve(228611,a,29256,a),flip(a)].
% 124.63/124.92  229839 and(not(c_0),A) = A.  [para(6699(a,1),229358(a,1,2)),rewrite([6699(5)])].
% 124.63/124.92  229862 equiv(A,not(c_0)) = A.  [back_rewrite(229054),rewrite([229839(6)])].
% 124.63/124.92  230696 equiv(implies(A,B),equiv(A,B)) = implies(implies(A,B),equiv(A,B)).  [para(221692(a,1),95(a,1,2)),rewrite([221860(6)]),flip(a)].
% 124.63/124.92  231332 -is_a_theorem(implies(A,B)) | and(A,not(B)) = c_0.  [para(6699(a,1),223889(a,1,2))].
% 124.63/124.92  232896 implies(equiv(A,B),and(B,not(A))) = not(equiv(A,B)).  [para(168(a,1),226522(a,2)),rewrite([6767(4),6699(3),95(3)])].
% 124.63/124.92  233289 equiv(A,implies(B,implies(C,A))) = implies(implies(B,implies(C,A)),A).  [para(227860(a,1),95(a,1,1)),rewrite([229839(6)]),flip(a)].
% 124.63/124.92  233293 equiv(and(A,B),implies(C,B)) = implies(implies(C,B),and(A,B)).  [para(227861(a,1),95(a,1,1)),rewrite([229839(6)]),flip(a)].
% 124.63/124.92  233310 equiv(equiv(A,B),equiv(B,A)) = not(c_0).  [para(227866(a,1),95(a,1,1)),rewrite([227866(5),221519(5)]),flip(a)].
% 124.63/124.92  233375 equiv(and(A,B),and(B,A)) = not(c_0).  [para(227867(a,1),95(a,1,1)),rewrite([227867(5),221519(5)]),flip(a)].
% 124.63/124.92  233544 implies(implies(A,B),implies(and(A,C),B)) = not(c_0).  [resolve(229053,a,228611,a),flip(a)].
% 124.63/124.92  233550 is_a_theorem(implies(and(A,B),implies(implies(A,C),C))).  [resolve(229053,a,10563,a)].
% 124.63/124.92  233561 is_a_theorem(implies(and(and(implies(A,B),A),C),B)).  [para(227828(a,1),229053(a,1,1)),rewrite([228580(7)])].
% 124.63/124.92  233565 is_a_theorem(implies(and(A,B),implies(equiv(A,C),C))).  [para(227833(a,1),229053(a,1,1)),rewrite([228580(7)])].
% 124.63/124.92  233581 equiv(A,implies(implies(A,B),A)) = not(c_0).  [para(229384(a,1),95(a,1,2)),rewrite([221430(3),221519(5)]),flip(a)].
% 124.63/124.92  234099 equiv(A,B) = equiv(B,A).  [para(233310(a,1),66(a,1)),unit_del(a,209384)].
% 124.63/124.92  234673 and(A,B) = and(B,A).  [para(233375(a,1),66(a,1)),unit_del(a,209384)].
% 124.63/124.92  234893 is_a_theorem(implies(and(A,and(B,implies(B,C))),C)).  [back_rewrite(233561),rewrite([234673(2),234673(3)])].
% 124.63/124.92  235460 implies(and(A,implies(A,B)),B) = not(c_0).  [back_rewrite(227828),rewrite([234673(2)])].
% 124.63/124.92  235489 and(A,and(B,A)) = and(B,A).  [back_rewrite(226521),rewrite([234673(2)])].
% 124.63/124.92  235717 implies(A,not(B)) = implies(B,not(A)).  [para(234673(a,1),6767(a,1,1)),rewrite([6767(2)])].
% 124.63/124.92  235844 implies(A,implies(B,not(A))) = implies(B,not(A)).  [back_rewrite(227703),rewrite([235717(3),6767(2)])].
% 124.63/124.92  235856 is_a_theorem(implies(implies(A,not(B)),implies(B,and(B,not(A))))).  [back_rewrite(221545),rewrite([235717(5),6768(4)])].
% 124.63/124.92  236563 and(implies(A,not(B)),implies(not(A),B)) = equiv(B,not(A)).  [para(235717(a,1),95(a,1,1))].
% 124.63/124.92  236655 implies(and(A,B),implies(implies(A,C),C)) = not(c_0).  [resolve(233550,a,228611,a),flip(a)].
% 124.63/124.92  236657 is_a_theorem(implies(equiv(c_0,not(A)),A)).  [resolve(233550,a,105987,a),rewrite([236655(4),6699(3)])].
% 124.63/124.92  236667 is_a_theorem(implies(and(A,B),implies(implies(B,C),C))).  [para(234673(a,1),233550(a,1,1))].
% 124.63/124.92  236671 implies(equiv(c_0,not(A)),A) = not(c_0).  [resolve(236657,a,228611,a),flip(a)].
% 124.63/124.92  236674 is_a_theorem(implies(equiv(c_0,implies(A,not(B))),A)).  [resolve(236657,a,29430,a),rewrite([6767(3)])].
% 124.63/124.92  236943 and(not(c_0),implies(A,equiv(c_0,not(A)))) = equiv(A,equiv(c_0,not(A))).  [para(236671(a,1),95(a,1,1)),rewrite([234099(11)])].
% 124.63/124.92  237125 is_a_theorem(implies(equiv(c_0,implies(A,B)),A)).  [para(6699(a,1),236674(a,1,1,2,2))].
% 124.63/124.92  237129 implies(equiv(c_0,implies(A,B)),A) = not(c_0).  [resolve(237125,a,228611,a),flip(a)].
% 124.63/124.92  237857 is_a_theorem(implies(and(A,B),implies(equiv(B,C),C))).  [para(234673(a,1),233565(a,1,1))].
% 124.63/124.92  237949 implies(implies(A,B),A) = A.  [para(233581(a,1),66(a,1)),unit_del(a,209384)].
% 124.63/124.92  237951 and(A,implies(A,implies(A,B))) = equiv(A,implies(A,B)).  [para(237949(a,1),95(a,1,1)),rewrite([234099(5)])].
% 124.63/124.92  237963 implies(implies(A,not(B)),B) = B.  [para(235717(a,1),237949(a,1,1))].
% 124.63/124.92  237966 implies(A,implies(A,B)) = implies(A,B).  [para(237949(a,1),237949(a,1,1))].
% 124.63/124.92  237979 equiv(A,implies(A,B)) = and(A,implies(A,B)).  [back_rewrite(237951),rewrite([237966(2)]),flip(a)].
% 124.63/124.92  238743 -is_a_theorem(and(A,and(B,implies(B,C)))) | is_a_theorem(C).  [resolve(234893,a,72,b)].
% 124.63/124.92  240124 is_a_theorem(implies(A,implies(implies(implies(B,A),C),C))).  [para(221773(a,1),236667(a,1,1))].
% 124.63/124.92  240127 is_a_theorem(implies(and(A,B),implies(C,and(B,C)))).  [para(235717(a,1),236667(a,1,2,1)),rewrite([235717(3),235717(5),6768(4),6699(3)])].
% 124.63/124.92  240296 and(not(c_0),not(equiv(c_0,implies(A,B)))) = not(equiv(c_0,implies(A,B))).  [para(237129(a,1),226359(a,1,2)),rewrite([234673(7)])].
% 124.63/124.92  240496 is_a_theorem(implies(not(A),implies(equiv(B,implies(A,C)),B))).  [para(226359(a,1),237857(a,1,1)),rewrite([234099(3)])].
% 124.63/124.92  240690 is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))).  [resolve(240124,a,10563,a)].
% 124.63/124.92  240695 is_a_theorem(implies(A,implies(B,and(B,implies(C,A))))).  [para(235717(a,1),240124(a,1,2,1)),rewrite([6768(2),235717(5),6768(4),6767(3),6699(2)])].
% 124.63/124.92  240707 is_a_theorem(implies(A,implies(and(B,C),and(A,C)))).  [resolve(240127,a,10563,a),rewrite([234673(2)])].
% 124.63/124.92  241183 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(B,C)).  [resolve(240690,a,72,b)].
% 124.63/124.92  241215 is_a_theorem(implies(A,and(implies(B,A),implies(C,A)))).  [para(221782(a,1),240690(a,1,2)),rewrite([235717(6),6768(5),6767(4),6699(3)])].
% 124.63/124.92  241262 is_a_theorem(implies(A,implies(B,and(A,implies(C,B))))).  [resolve(240695,a,10563,a)].
% 124.63/124.92  241294 is_a_theorem(implies(and(and(A,B),implies(B,C)),C)).  [resolve(240707,a,139,a),rewrite([234673(3),6768(5),6767(4),6699(3)])].
% 124.63/124.92  241641 and(A,implies(implies(B,A),and(C,not(A)))) = c_0.  [resolve(241215,a,231332,a),rewrite([6767(4),6768(3)])].
% 124.63/124.92  241697 and(A,and(B,implies(A,and(C,not(B))))) = c_0.  [resolve(241262,a,231332,a),rewrite([6768(4),6767(3),6768(2)])].
% 124.63/124.92  241705 is_a_theorem(implies(implies(A,B),implies(A,equiv(A,B)))).  [para(95(a,1),241262(a,1,2,2))].
% 124.63/124.92  241858 is_a_theorem(implies(and(A,implies(implies(B,A),C)),C)).  [para(221773(a,1),241294(a,1,1,1))].
% 124.63/124.92  241862 is_a_theorem(implies(A,implies(and(B,C),and(C,A)))).  [para(235717(a,1),241294(a,1,1,2)),rewrite([235717(3),235717(6),6767(5),6768(4),6699(3)])].
% 124.63/124.92  242209 is_a_theorem(implies(A,implies(B,equiv(A,B)))).  [resolve(241705,a,241183,a),rewrite([234099(1)])].
% 124.63/124.92  242250 and(A,and(B,not(equiv(A,B)))) = c_0.  [resolve(242209,a,231332,a),rewrite([6768(3)])].
% 124.63/124.92  242453 implies(and(A,implies(implies(B,A),C)),C) = not(c_0).  [resolve(241858,a,228611,a),flip(a)].
% 124.63/124.92  243228 is_a_theorem(implies(A,equiv(c_0,not(A)))).  [para(221959(a,1),204611(a,1,2,1,1,2)),rewrite([221959(6),6699(5)])].
% 124.63/124.92  243264 implies(A,equiv(c_0,not(A))) = not(c_0).  [resolve(243228,a,228611,a),flip(a)].
% 124.63/124.92  243272 equiv(A,equiv(c_0,not(A))) = not(c_0).  [back_rewrite(236943),rewrite([243264(6),221519(5)]),flip(a)].
% 124.63/124.92  243437 equiv(c_0,not(A)) = A.  [para(243272(a,1),66(a,1)),unit_del(a,209384)].
% 124.63/124.92  243447 equiv(c_0,implies(A,not(B))) = and(A,B).  [para(6767(a,1),243437(a,1,2))].
% 124.63/124.92  243685 and(not(c_0),and(A,B)) = and(A,B).  [para(243447(a,1),95(a,2)),rewrite([218625(4),221959(6),6768(5),6699(4)])].
% 124.63/124.92  243686 equiv(c_0,implies(A,B)) = and(A,not(B)).  [para(6699(a,1),243447(a,1,2,2))].
% 124.63/124.92  243762 and(not(c_0),implies(A,B)) = implies(A,B).  [back_rewrite(240296),rewrite([243686(5),6767(5),6699(4),243686(7),6767(7),6699(6)])].
% 124.63/124.92  244401 is_a_theorem(implies(implies(not(A),and(B,implies(B,A))),A)).  [para(235460(a,1),221569(a,1,1)),rewrite([228580(8)])].
% 124.63/124.92  244633 -is_a_theorem(implies(A,and(A,B))) | and(A,B) = A.  [para(221861(a,1),66(a,1))].
% 124.63/124.92  244643 equiv(not(c_0),implies(A,B)) = implies(A,B).  [para(243762(a,1),221861(a,1,2)),rewrite([243762(10),228580(8)])].
% 124.63/124.92  244655 -is_a_theorem(implies(A,B)) | implies(A,B) = not(c_0).  [para(244643(a,1),66(a,1))].
% 124.63/124.92  244829 is_a_theorem(implies(implies(implies(A,B),and(A,C)),A)).  [para(221782(a,1),228582(a,1,2)),rewrite([6699(3),234673(2),6699(5)])].
% 124.63/124.92  244845 implies(implies(implies(A,B),and(A,C)),A) = not(c_0).  [resolve(244829,a,244655,a)].
% 124.63/124.92  244922 is_a_theorem(implies(implies(implies(and(A,B),C),B),B)).  [para(237963(a,1),228590(a,1,2)),rewrite([6768(3),6699(2)])].
% 124.63/124.92  244945 is_a_theorem(implies(A,and(A,implies(and(B,not(A)),C)))).  [para(235717(a,1),244922(a,1,1)),rewrite([6768(4),235717(7),6768(6),6767(5),6699(4)])].
% 124.63/124.92  245436 implies(not(A),implies(B,A)) = implies(B,A).  [para(235844(a,1),91(a,2)),rewrite([6699(2),91(2),6699(5)])].
% 124.63/124.92  245442 equiv(not(A),implies(B,A)) = and(not(A),implies(B,A)).  [para(245436(a,1),95(a,1,1)),rewrite([235717(4),6768(3),221782(4),234673(3)]),flip(a)].
% 124.63/124.92  245443 implies(implies(A,B),B) = implies(not(B),and(A,not(B))).  [para(245436(a,1),168(a,1,1)),rewrite([6699(4),234673(3),221773(3),245442(5),6767(6),6768(5)])].
% 124.63/124.92  245699 is_a_theorem(implies(equiv(A,implies(B,C)),implies(not(B),A))).  [resolve(240496,a,10563,a)].
% 124.63/124.92  246527 is_a_theorem(implies(A,and(A,implies(B,and(A,B))))).  [para(6699(a,1),244401(a,1,1,1)),rewrite([235717(2),235717(6),6768(5),6767(4),6768(3),6699(2)])].
% 124.63/124.92  246531 implies(A,and(A,implies(B,and(A,B)))) = not(c_0).  [resolve(246527,a,244655,a)].
% 124.63/124.92  246679 and(A,implies(and(B,not(A)),C)) = A.  [resolve(244945,a,244633,a)].
% 124.63/124.92  246692 and(not(A),implies(and(A,B),C)) = not(A).  [para(6699(a,1),246679(a,1,2,1,2)),rewrite([234673(2)])].
% 124.63/124.92  246711 and(A,implies(B,implies(C,A))) = A.  [para(235717(a,1),246679(a,1,2)),rewrite([6767(3),6699(2)])].
% 124.63/124.92  246738 implies(A,and(B,and(C,not(A)))) = not(A).  [para(246711(a,1),6767(a,1,1)),rewrite([6768(4),6768(3)]),flip(a)].
% 124.63/124.92  246751 and(and(A,B),implies(C,A)) = and(A,B).  [para(228055(a,1),246711(a,1,2,2))].
% 124.63/124.92  247025 is_a_theorem(implies(equiv(not(A),implies(B,C)),implies(A,B))).  [para(235717(a,1),245699(a,1,2)),rewrite([6699(5)])].
% 124.63/124.92  247759 implies(not(A),and(and(A,B),not(C))) = A.  [para(246692(a,1),6767(a,1,1)),rewrite([6699(2),6768(4)]),flip(a)].
% 124.63/124.92  247812 implies(not(A),and(B,and(A,C))) = A.  [para(246738(a,1),91(a,2)),rewrite([6699(2),234673(1),91(3),6699(6)])].
% 124.63/124.92  247855 implies(implies(A,implies(B,not(C))),B) = B.  [para(247812(a,1),245436(a,1,2)),rewrite([6767(3),6767(2),247812(8)])].
% 124.63/124.92  247860 implies(implies(A,implies(B,C)),B) = B.  [para(6699(a,1),247855(a,1,1,2,2))].
% 124.63/124.92  247862 implies(implies(A,implies(B,not(C))),C) = C.  [para(235717(a,1),247855(a,1,1,2))].
% 124.63/124.92  247890 implies(A,implies(B,implies(A,C))) = implies(B,implies(A,C)).  [para(247860(a,1),237949(a,1,1))].
% 124.63/124.92  247891 implies(implies(A,B),implies(B,C)) = implies(B,C).  [para(237949(a,1),247860(a,1,1,2))].
% 124.63/124.92  247935 and(and(A,B),implies(C,B)) = and(A,B).  [para(234673(a,1),246751(a,1,1)),rewrite([234673(4)])].
% 124.63/124.92  248078 is_a_theorem(implies(A,implies(equiv(not(A),implies(B,C)),B))).  [resolve(247025,a,10563,a)].
% 124.63/124.92  248107 is_a_theorem(implies(equiv(and(A,and(B,C)),implies(C,D)),C)).  [para(247862(a,1),247025(a,1,2)),rewrite([6768(4),6768(3),6699(2)])].
% 124.63/124.92  248234 implies(implies(and(A,B),C),A) = A.  [para(247759(a,1),245436(a,1,2)),rewrite([6767(4),6699(3),247759(8)])].
% 124.63/124.92  248262 implies(implies(and(A,B),C),B) = B.  [para(234673(a,1),248234(a,1,1,1))].
% 124.63/124.92  248277 implies(implies(A,B),implies(C,A)) = implies(C,A).  [para(221773(a,1),248262(a,1,1,1))].
% 124.63/124.92  248456 and(implies(A,B),and(C,B)) = and(C,B).  [para(247935(a,1),234673(a,1)),flip(a)].
% 124.63/124.92  248598 is_a_theorem(implies(A,implies(equiv(B,not(A)),implies(B,C)))).  [para(237949(a,1),248078(a,1,2,1,2)),rewrite([234099(2)])].
% 124.63/124.92  248854 implies(implies(and(A,and(B,C)),D),B) = B.  [para(247812(a,1),248277(a,1,2)),rewrite([247812(8)])].
% 124.63/124.92  249515 is_a_theorem(implies(A,implies(equiv(not(A),not(B)),implies(C,B)))).  [para(245436(a,1),248598(a,1,2,2)),rewrite([234099(3)])].
% 124.63/124.92  249825 implies(not(A),B) = implies(not(B),A).  [para(234673(a,1),226524(a,1,1)),rewrite([226522(4)])].
% 124.63/124.92  249918 equiv(A,not(B)) = equiv(B,not(A)).  [para(249825(a,1),95(a,1,1)),rewrite([234673(5),236563(5),234099(4)])].
% 124.63/124.92  249972 is_a_theorem(implies(A,implies(equiv(A,B),implies(C,B)))).  [back_rewrite(249515),rewrite([249918(3),6699(2),234099(1)])].
% 124.63/124.92  250119 implies(not(c_0),and(A,B)) = and(A,B).  [para(224094(a,1),248854(a,1,1,1)),rewrite([218625(2)])].
% 124.63/124.92  250241 and(A,and(equiv(A,B),and(C,not(B)))) = c_0.  [resolve(249972,a,231332,a),rewrite([6768(4),6768(3)])].
% 124.63/124.92  250453 implies(not(c_0),implies(A,B)) = implies(A,B).  [para(243762(a,1),250119(a,1,2)),rewrite([243762(8)])].
% 124.63/124.92  250812 and(implies(A,B),and(and(A,C),not(B))) = c_0.  [para(221467(a,1),224316(a,1,2,1)),rewrite([234673(4),243685(7)])].
% 124.63/124.92  251016 -is_a_theorem(and(A,implies(B,and(C,D)))) | is_a_theorem(implies(B,C)).  [para(229553(a,1),238743(a,1,2,2)),rewrite([234673(5),243762(5)])].
% 124.63/124.92  251525 implies(implies(A,equiv(A,B)),implies(A,B)) = not(c_0).  [para(228073(a,1),233544(a,1,2))].
% 124.63/124.92  251803 is_a_theorem(implies(implies(A,B),implies(A,and(B,A)))).  [para(6699(a,1),235856(a,1,2,2,2)),rewrite([235717(3),6699(2),234673(2)])].
% 124.63/124.92  251811 is_a_theorem(implies(A,implies(implies(A,B),and(A,B)))).  [resolve(251803,a,10563,a),rewrite([234673(2)])].
% 124.63/124.92  251812 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(A,and(A,B))).  [resolve(251803,a,72,b),rewrite([234673(3)])].
% 124.63/124.92  251816 is_a_theorem(implies(A,and(A,implies(equiv(A,B),B)))).  [para(227833(a,1),251803(a,1,1)),rewrite([234673(5),250453(7)])].
% 124.63/124.92  251960 and(A,and(implies(A,B),implies(A,not(B)))) = c_0.  [resolve(251811,a,231332,a),rewrite([6768(4),6767(3)])].
% 124.63/124.92  251966 is_a_theorem(implies(and(implies(A,B),implies(not(B),A)),B)).  [para(249825(a,1),251811(a,1)),rewrite([234673(4),6768(6),6767(5),6699(4),234673(4)])].
% 124.63/124.92  251976 and(A,implies(equiv(A,B),B)) = A.  [resolve(251816,a,244633,a)].
% 124.63/124.92  252000 is_a_theorem(implies(A,implies(B,and(A,implies(equiv(B,C),C))))).  [para(251976(a,1),241862(a,1,2,1)),rewrite([234673(3)])].
% 124.63/124.92  253022 is_a_theorem(implies(implies(and(A,implies(B,C)),B),implies(A,B))).  [para(249825(a,1),228061(a,1,1)),rewrite([6768(4),6767(3),6699(2)])].
% 124.63/124.92  255061 and(A,implies(B,and(A,B))) = A.  [para(246531(a,1),244633(a,1)),unit_del(a,209384)].
% 124.63/124.92  255063 implies(A,and(B,implies(A,not(B)))) = not(A).  [para(255061(a,1),6767(a,1,1)),rewrite([6768(4),6767(3)]),flip(a)].
% 124.63/124.92  255084 and(A,implies(B,equiv(A,B))) = A.  [para(242250(a,1),255061(a,1,2,2)),rewrite([221959(5),6767(4),6699(3)])].
% 124.63/124.92  255091 and(A,implies(implies(A,B),implies(C,B))) = A.  [para(224025(a,1),255061(a,1,2,2)),rewrite([221959(6),6767(5),6767(4),6699(3)])].
% 124.63/124.92  255107 and(A,and(implies(B,A),implies(C,A))) = A.  [para(241641(a,1),255061(a,1,2,2)),rewrite([221959(6),6768(5),6767(4),6699(3)])].
% 124.63/124.92  255108 and(A,implies(B,and(A,implies(C,B)))) = A.  [para(241697(a,1),255061(a,1,2,2)),rewrite([221959(6),6767(5),6768(4),6767(3),6699(2)])].
% 124.63/124.92  255164 implies(A,and(B,not(equiv(A,B)))) = not(A).  [para(255084(a,1),6767(a,1,1)),rewrite([6768(4)]),flip(a)].
% 124.63/124.92  255348 implies(not(A),and(B,implies(B,A))) = A.  [para(255063(a,1),91(a,2)),rewrite([235717(3),6699(2),91(3),6699(6)])].
% 124.63/124.92  255360 and(A,and(B,implies(B,A))) = and(B,implies(B,A)).  [para(255348(a,1),221773(a,1,2)),rewrite([234673(3)])].
% 124.63/124.92  255382 implies(not(A),and(B,implies(implies(C,B),A))) = A.  [para(242453(a,1),255348(a,1,2,2)),rewrite([234673(7),243685(7)])].
% 124.63/124.92  255570 and(A,implies(implies(A,and(B,C)),B)) = A.  [para(228055(a,1),255091(a,1,2,2))].
% 124.63/124.92  255665 and(implies(A,B),implies(A,equiv(A,B))) = implies(A,B).  [para(95(a,1),255108(a,1,2,2))].
% 124.63/124.92  255668 and(A,implies(implies(A,and(B,C)),C)) = A.  [para(249825(a,1),255108(a,1,2)),rewrite([6767(4),6768(3),6699(2)])].
% 124.63/124.92  255886 implies(implies(A,equiv(B,not(A))),B) = B.  [para(255164(a,1),249825(a,1)),rewrite([6699(2),234099(2),249918(2),6767(5),6699(4)]),flip(a)].
% 124.63/124.92  255894 implies(implies(not(A),equiv(B,A)),B) = B.  [para(249825(a,1),255886(a,1,1)),rewrite([6699(2),249825(3)])].
% 124.63/124.92  256745 implies(implies(A,implies(equiv(B,A),B)),B) = B.  [para(227833(a,1),233289(a,1,2)),rewrite([229862(3),234099(1)]),flip(a)].
% 124.63/124.92  256760 implies(A,implies(equiv(B,A),B)) = not(c_0).  [para(256745(a,1),237949(a,1,1)),rewrite([227860(4)]),flip(a)].
% 124.63/124.92  256767 equiv(A,and(B,A)) = implies(A,and(B,A)).  [para(221544(a,1),233293(a,1,2)),rewrite([234099(2),221544(4)])].
% 124.63/124.92  256769 equiv(A,implies(B,A)) = implies(not(A),and(B,not(A))).  [para(221773(a,1),256767(a,1,2)),rewrite([234099(2),221773(5),245443(4)])].
% 124.63/124.92  256805 and(A,implies(equiv(A,B),implies(C,B))) = A.  [para(250241(a,1),255061(a,1,2,2)),rewrite([221959(6),6767(5),6767(4),6699(3)])].
% 124.63/124.92  256807 and(A,implies(equiv(A,and(B,C)),B)) = A.  [para(228055(a,1),256805(a,1,2,2))].
% 124.63/124.92  256823 and(A,implies(equiv(A,and(B,C)),C)) = A.  [para(234673(a,1),256807(a,1,2,1,2))].
% 124.63/124.92  257028 and(implies(A,B),implies(and(A,C),B)) = implies(A,B).  [para(250812(a,1),255061(a,1,2,2)),rewrite([221959(6),6767(5),6699(4)])].
% 124.63/124.92  257106 -is_a_theorem(A) | is_a_theorem(implies(implies(A,and(B,and(C,D))),C)).  [para(255570(a,1),251016(a,1)),rewrite([234673(3)])].
% 124.63/124.92  257622 and(A,implies(implies(A,B),and(A,B))) = A.  [para(251960(a,1),255061(a,1,2,2)),rewrite([221959(6),6767(5),6768(4),6699(3)])].
% 124.63/124.92  257626 implies(A,equiv(A,B)) = implies(A,B).  [para(251525(a,1),257622(a,1,2,1)),rewrite([234673(8),255665(8),250453(6),234673(4),255665(4)]),flip(a)].
% 124.63/124.92  257636 and(A,not(equiv(A,B))) = and(A,not(B)).  [para(257626(a,1),6768(a,1,1)),rewrite([6768(2)]),flip(a)].
% 124.63/124.92  257719 is_a_theorem(implies(A,equiv(B,equiv(B,A)))).  [para(95(a,1),252000(a,1,2,2)),rewrite([234099(1),257626(2),234099(2),247891(5)])].
% 124.63/124.92  257725 is_a_theorem(implies(A,and(A,equiv(B,equiv(A,B))))).  [resolve(257719,a,251812,a),rewrite([234099(1)])].
% 124.63/124.92  257753 and(A,equiv(B,equiv(A,B))) = A.  [resolve(257725,a,244633,a)].
% 124.63/124.92  257770 and(A,equiv(B,equiv(B,A))) = A.  [para(257753(a,1),234673(a,2)),rewrite([234099(1),234673(3)])].
% 124.63/124.92  257818 and(A,implies(A,and(A,B))) = and(A,B).  [para(221861(a,1),257770(a,1,2,2)),rewrite([237979(4),255360(5)])].
% 124.63/124.92  257820 and(A,implies(A,and(B,A))) = and(B,A).  [para(256767(a,1),257770(a,1,2,2)),rewrite([237979(4),255360(5)])].
% 124.63/124.92  257968 implies(implies(A,B),and(A,B)) = A.  [para(257622(a,1),257820(a,1,2,2)),rewrite([244845(7),234673(6),243762(6),257622(7)])].
% 124.63/124.92  257984 implies(A,and(A,B)) = implies(A,B).  [para(257968(a,1),257968(a,1,1)),rewrite([248456(3)])].
% 124.63/124.92  257986 and(A,implies(A,B)) = and(A,B).  [back_rewrite(257818),rewrite([257984(2)])].
% 124.63/124.92  257990 -is_a_theorem(implies(A,B)) | and(A,B) = A.  [back_rewrite(244633),rewrite([257984(2)])].
% 124.63/124.92  258033 implies(not(A),and(B,not(A))) = implies(not(A),B).  [para(257984(a,1),91(a,2)),rewrite([234673(2),91(3)])].
% 124.63/124.92  258034 implies(implies(A,B),equiv(A,B)) = implies(B,A).  [para(95(a,1),257984(a,1,2)),rewrite([247891(6)])].
% 124.63/124.92  258069 implies(A,not(equiv(A,B))) = implies(A,not(B)).  [para(257636(a,1),257984(a,1,2)),rewrite([257984(3)]),flip(a)].
% 124.63/124.92  258070 equiv(A,implies(B,A)) = implies(not(A),B).  [back_rewrite(256769),rewrite([258033(6)])].
% 124.63/124.92  258076 implies(implies(A,B),B) = implies(not(A),B).  [back_rewrite(245443),rewrite([258033(6),249825(4)])].
% 124.63/124.92  258079 equiv(implies(A,B),equiv(A,B)) = implies(B,A).  [back_rewrite(230696),rewrite([258034(6)])].
% 124.63/124.92  258088 and(A,equiv(A,B)) = and(A,B).  [para(257626(a,1),257986(a,1,2)),rewrite([257986(2)]),flip(a)].
% 124.63/124.92  258098 and(implies(A,B),implies(not(A),B)) = B.  [resolve(257990,a,251966,a),rewrite([249825(3),234673(5),255107(5),249825(3)]),flip(a)].
% 124.63/124.92  258127 -is_a_theorem(implies(A,not(B))) | and(B,not(A)) = B.  [para(235717(a,1),257990(a,1))].
% 124.63/124.92  258207 -is_a_theorem(implies(not(A),B)) | implies(B,A) = A.  [para(258070(a,1),66(a,1))].
% 124.63/124.92  258208 and(not(A),implies(B,A)) = and(not(A),not(B)).  [para(258070(a,1),168(a,2,1)),rewrite([221430(2),234673(5),250119(6),6768(6)])].
% 124.63/124.92  258222 implies(not(A),equiv(A,B)) = implies(B,A).  [para(257626(a,1),258070(a,1,2)),rewrite([234099(3),258079(3),249825(4)]),flip(a)].
% 124.63/124.92  258248 implies(A,and(B,A)) = implies(A,B).  [para(258076(a,1),6767(a,2)),rewrite([234673(3),6767(4),6768(3),6699(2),235717(5),6699(4)])].
% 124.63/124.92  258286 implies(implies(A,B),and(B,A)) = A.  [para(255894(a,1),258248(a,2)),rewrite([234099(2),258222(3),234099(3),258222(4),257986(3),234673(2)])].
% 124.63/124.92  258312 and(A,implies(equiv(B,A),B)) = A.  [para(256760(a,1),258286(a,1,1)),rewrite([234673(5),250119(6)])].
% 124.63/124.92  258346 and(implies(A,B),implies(not(B),A)) = B.  [para(258098(a,1),234673(a,1)),rewrite([249825(2),234673(4)]),flip(a)].
% 124.63/124.92  258347 and(implies(A,not(B)),implies(B,A)) = not(B).  [para(235717(a,1),258098(a,1,2)),rewrite([6699(4)])].
% 124.63/124.92  258380 -is_a_theorem(implies(A,B)) | implies(not(A),B) = B.  [para(235717(a,1),258207(a,1)),rewrite([6699(2)])].
% 124.63/124.92  258415 equiv(not(A),equiv(A,B)) = not(B).  [para(258222(a,1),95(a,1,2)),rewrite([235717(3),258069(3),258347(4),234099(4)]),flip(a)].
% 124.63/124.92  258440 and(not(A),equiv(A,B)) = and(not(A),not(B)).  [para(258222(a,1),257986(a,1,2)),rewrite([258208(3)]),flip(a)].
% 124.63/124.92  258462 implies(not(A),and(B,A)) = A.  [para(258415(a,1),232896(a,2,1)),rewrite([258415(3),6699(4),234673(3),258088(3),6699(5)])].
% 124.63/124.92  258473 not(equiv(A,B)) = equiv(A,not(B)).  [para(258415(a,1),258415(a,1,2)),rewrite([6699(2)]),flip(a)].
% 124.63/124.92  258805 implies(and(A,implies(B,and(C,not(A)))),B) = implies(A,and(B,implies(C,A))).  [para(255108(a,1),258462(a,1,2)),rewrite([6768(4),6767(3),6768(2)])].
% 124.63/124.92  258811 implies(and(not(A),implies(B,and(C,A))),B) = implies(implies(B,and(C,A)),A).  [para(255668(a,1),258462(a,1,2)),rewrite([6768(4),234673(4)])].
% 124.63/124.92  258822 implies(and(not(A),equiv(B,and(C,A))),B) = implies(equiv(B,and(C,A)),A).  [para(256823(a,1),258462(a,1,2)),rewrite([6768(4),234673(4)])].
% 124.63/124.92  258826 implies(equiv(A,B),A) = implies(not(A),B).  [para(258312(a,1),258462(a,1,2)),rewrite([6768(3),234673(3),258440(3),226522(4)]),flip(a)].
% 124.63/124.92  259803 implies(and(A,not(B)),implies(A,and(B,C))) = implies(A,B).  [para(229553(a,1),258346(a,1,1)),rewrite([6768(4),243762(8)])].
% 124.63/124.92  260010 implies(equiv(and(A,and(B,C)),and(C,not(D))),C) = C.  [resolve(258380,a,248107,a),rewrite([258473(5),6768(4)])].
% 124.63/124.92  260317 -is_a_theorem(implies(A,B)) | and(B,A) = A.  [para(258076(a,1),258127(a,1)),rewrite([235717(3),6699(2),6768(5),6699(4),235489(4)])].
% 124.63/124.92  260612 implies(and(A,implies(B,C)),B) = implies(A,B).  [resolve(253022,a,260317,a),rewrite([257028(5)]),flip(a)].
% 124.63/124.92  260615 implies(implies(A,and(B,C)),B) = implies(not(B),A).  [back_rewrite(258811),rewrite([234673(2),260612(5),234673(3)]),flip(a)].
% 124.63/124.92  260616 implies(A,and(B,implies(C,A))) = implies(A,B).  [back_rewrite(258805),rewrite([260612(5)]),flip(a)].
% 124.63/124.92  260620 implies(and(A,B),implies(B,C)) = implies(A,implies(B,C)).  [para(237949(a,1),260612(a,1,1,2))].
% 124.63/124.92  260646 and(A,and(B,implies(C,A))) = and(A,B).  [para(260616(a,1),257986(a,1,2)),rewrite([257986(2)]),flip(a)].
% 124.63/124.92  261715 and(A,implies(implies(B,A),C)) = and(A,C).  [para(255382(a,1),221773(a,1,2)),rewrite([234673(4),260646(4),234673(1)]),flip(a)].
% 124.63/124.92  261737 implies(A,implies(implies(B,A),C)) = implies(A,C).  [para(261715(a,1),257984(a,1,2)),rewrite([257984(2)]),flip(a)].
% 124.63/124.92  261781 implies(and(A,B),implies(A,C)) = implies(and(A,B),C).  [para(228055(a,1),261737(a,1,2,1))].
% 124.63/124.92  261788 implies(A,implies(implies(not(A),B),C)) = implies(A,C).  [para(226524(a,1),261737(a,1,2,1))].
% 124.63/124.92  261808 implies(and(A,B),C) = implies(A,implies(B,C)).  [para(258286(a,1),261737(a,1,2,1)),rewrite([260620(3)]),flip(a)].
% 124.63/124.92  261826 implies(not(A),implies(B,and(A,C))) = implies(B,A).  [back_rewrite(259803),rewrite([261808(5),247890(5)])].
% 124.63/124.92  261879 implies(A,implies(B,C)) = implies(B,implies(A,C)).  [back_rewrite(261781),rewrite([261808(3),247890(3),261808(4)])].
% 124.63/124.92  261946 implies(equiv(A,and(B,C)),B) = implies(not(B),A).  [back_rewrite(258822),rewrite([234673(2),261808(5),258826(4),261826(5),249825(2),234673(3)]),flip(a)].
% 124.63/124.92  262203 implies(not(A),and(B,and(C,A))) = A.  [back_rewrite(260010),rewrite([261946(6)])].
% 124.63/124.92  262250 and(A,and(B,C)) = and(B,and(A,C)).  [para(262203(a,1),258346(a,1,1)),rewrite([234673(1),6767(3),6767(2),261879(3),235717(5),6768(4),6768(3),6699(2),257984(3),257986(3),234673(3)])].
% 124.63/124.92  264155 implies(A,implies(implies(A,B),C)) = implies(A,implies(B,C)).  [para(257986(a,1),261808(a,1,1)),rewrite([261808(2)]),flip(a)].
% 124.63/124.92  264301 -is_a_theorem(and(A,implies(not(c25),implies(implies(c24,c26),implies(implies(not(c24),c25),c26))))).  [para(261879(a,1),1526(a,1,2,2)),rewrite([258076(12),261879(12),261879(13)])].
% 124.63/124.92  266381 is_a_theorem(implies(implies(implies(A,implies(equiv(implies(A,B),implies(C,and(A,not(B)))),B)),and(D,and(E,F))),E)).  [resolve(257106,a,227570,a)].
% 124.63/124.92  268273 implies(implies(A,and(B,and(C,D))),C) = implies(not(A),C).  [para(262250(a,1),260615(a,1,1,2)),rewrite([249825(6)])].
% 124.63/124.92  268307 is_a_theorem(implies(A,implies(not(B),implies(equiv(implies(A,B),implies(C,and(A,not(B)))),D)))).  [back_rewrite(266381),rewrite([268273(11),6768(8),6768(7),234673(7),261808(9),261808(8)])].
% 124.63/124.92  269036 implies(implies(A,B),implies(implies(not(A),C),B)) = implies(C,implies(not(A),B)).  [para(261788(a,1),258076(a,1,1)),rewrite([264155(10),261879(8)])].
% 124.63/124.92  269070 -is_a_theorem(A).  [back_rewrite(264301),rewrite([269036(12),261879(9),261879(8),227856(9),221860(3)])].
% 124.63/124.92  269071 $F.  [resolve(269070,a,268307,a)].
% 124.63/124.92  
% 124.63/124.92  % SZS output end Refutation
% 124.63/124.92  ============================== end of proof ==========================
% 124.63/124.92  
% 124.63/124.92  ============================== STATISTICS ============================
% 124.63/124.92  
% 124.63/124.92  Given=10824. Generated=10842644. Kept=269020. proofs=1.
% 124.63/124.92  Usable=1688. Sos=7994. Demods=1384. Limbo=34, Disabled=259377. Hints=0.
% 124.63/124.92  Megabytes=159.37.
% 124.63/124.92  User_CPU=118.30, System_CPU=5.62, Wall_clock=124.
% 124.63/124.92  
% 124.63/124.92  ============================== end of statistics =====================
% 124.63/124.92  
% 124.63/124.92  ============================== end of search =========================
% 124.63/124.92  
% 124.63/124.92  THEOREM PROVED
% 124.63/124.92  % SZS status Theorem
% 124.63/124.92  
% 124.63/124.92  Exiting with 1 proof.
% 124.63/124.92  
% 124.63/124.92  Process 27444 exit (max_proofs) Sat Jul  2 20:51:15 2022
% 124.63/124.92  Prover9 interrupted
%------------------------------------------------------------------------------