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