TSTP Solution File: LCL474+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL474+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.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 13:47:05 EDT 2022
% Result : Theorem 110.96s 111.31s
% Output : Refutation 110.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL474+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jul 4 07:51:07 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.41/0.99 ============================== Prover9 ===============================
% 0.41/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.41/0.99 Process 15572 was started by sandbox on n009.cluster.edu,
% 0.41/0.99 Mon Jul 4 07:51:08 2022
% 0.41/0.99 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_15419_n009.cluster.edu".
% 0.41/0.99 ============================== end of head ===========================
% 0.41/0.99
% 0.41/0.99 ============================== INPUT =================================
% 0.41/0.99
% 0.41/0.99 % Reading from file /tmp/Prover9_15419_n009.cluster.edu
% 0.41/0.99
% 0.41/0.99 set(prolog_style_variables).
% 0.41/0.99 set(auto2).
% 0.41/0.99 % set(auto2) -> set(auto).
% 0.41/0.99 % set(auto) -> set(auto_inference).
% 0.41/0.99 % set(auto) -> set(auto_setup).
% 0.41/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.41/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.41/0.99 % set(auto) -> set(auto_limits).
% 0.41/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.41/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.41/0.99 % set(auto) -> set(auto_denials).
% 0.41/0.99 % set(auto) -> set(auto_process).
% 0.41/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.41/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.41/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.41/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.41/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.41/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.41/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.41/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.41/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.41/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.41/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.41/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.41/0.99 % set(auto2) -> assign(stats, some).
% 0.41/0.99 % set(auto2) -> clear(echo_input).
% 0.41/0.99 % set(auto2) -> set(quiet).
% 0.41/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.41/0.99 % set(auto2) -> clear(print_given).
% 0.41/0.99 assign(lrs_ticks,-1).
% 0.41/0.99 assign(sos_limit,10000).
% 0.41/0.99 assign(order,kbo).
% 0.41/0.99 set(lex_order_vars).
% 0.41/0.99 clear(print_given).
% 0.41/0.99
% 0.41/0.99 % formulas(sos). % not echoed (43 formulas)
% 0.41/0.99
% 0.41/0.99 ============================== end of input ==========================
% 0.41/0.99
% 0.41/0.99 % From the command line: assign(max_seconds, 300).
% 0.41/0.99
% 0.41/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.41/0.99
% 0.41/0.99 % Formulas that are not ordinary clauses:
% 0.41/0.99 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].
% 0.41/0.99 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].
% 0.41/0.99 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].
% 0.41/0.99 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 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].
% 0.41/0.99 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].
% 0.41/0.99 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 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].
% 0.41/0.99 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 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].
% 0.41/0.99 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].
% 0.41/0.99 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].
% 1.27/1.60 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].
% 1.27/1.60 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.60 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.60 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].
% 1.27/1.60 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].
% 1.27/1.60 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.60 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.60 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.60 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.60 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.60 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].
% 1.27/1.60 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].
% 1.27/1.60 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].
% 1.27/1.60 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].
% 1.27/1.60 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].
% 1.27/1.60 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].
% 1.27/1.60 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].
% 1.27/1.60
% 1.27/1.60 ============================== end of process non-clausal formulas ===
% 1.27/1.60
% 1.27/1.60 ============================== PROCESS INITIAL CLAUSES ===============
% 1.27/1.60
% 1.27/1.60 ============================== PREDICATE ELIMINATION =================
% 1.27/1.60
% 1.27/1.60 ============================== end predicate elimination =============
% 1.27/1.60
% 1.27/1.60 Auto_denials: (non-Horn, no changes).
% 1.27/1.60
% 1.27/1.60 Term ordering decisions:
% 1.27/1.60
% 1.27/1.60 % Assigning unary symbol not kb_weight 0 and highest precedence (94).
% 1.27/1.60 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.
% 1.27/1.60
% 1.27/1.60 ============================== end of process initial clauses ========
% 1.27/1.60
% 1.27/1.60 ============================== CLAUSES FOR SEARCH ====================
% 1.27/1.60
% 1.27/1.60 ============================== end of clauses for search =============
% 1.27/1.60
% 1.27/1.60 ============================== SEARCH ================================
% 1.27/1.60
% 1.27/1.60 % Starting search at 0.02 seconds.
% 1.27/1.60
% 1.27/1.60 Low Water (keep): wt=47.000, iters=3369
% 1.27/1.60
% 1.27/1.60 Low Water (keep): wt=40.000, iters=3351
% 1.27/1.60
% 1.27/1.60 Low Water (keep): wt=37.000, iters=3348
% 1.27/1.60
% 1.27/1.60 Low Water (keep): wt=36.000, iters=3355
% 1.27/1.60
% 1.27/1.60 Low Water (keep): wt=35.000, iters=3555
% 1.27/1.60
% 1.27/1.60 Low Water (keep): wt=33.000, iters=3451
% 1.27/1.60
% 1.27/1.60 Low Water (keep): wt=31.000, iters=3357
% 1.27/1.60
% 1.27/1.60 Low Water (keep): wt=27.000, iters=3389
% 1.27/1.60
% 1.27/1.60 Low Water (keep): wt=25.000, iters=3359
% 1.27/1.60
% 1.27/1.60 Low Water (keep): wt=24.000, iters=3363
% 1.27/1.60
% 110.96/111.30 Low Water (keep): wt=23.000, iters=3352
% 110.96/111.30
% 110.96/111.30 Low Water (keep): wt=22.000, iters=3351
% 110.96/111.30
% 110.96/111.30 Low Water (keep): wt=21.000, iters=3345
% 110.96/111.30
% 110.96/111.30 Low Water (keep): wt=20.000, iters=3369
% 110.96/111.30
% 110.96/111.30 Low Water (keep): wt=19.000, iters=3337
% 110.96/111.30
% 110.96/111.30 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 65 (0.00 of 1.35 sec).
% 110.96/111.30
% 110.96/111.30 Low Water (displace): id=2463, wt=159.000
% 110.96/111.30
% 110.96/111.30 Low Water (displace): id=2809, wt=127.000
% 110.96/111.30
% 110.96/111.30 Low Water (displace): id=3604, wt=107.000
% 110.96/111.30
% 110.96/111.30 Low Water (displace): id=1538, wt=103.000
% 110.96/111.30
% 110.96/111.30 Low Water (displace): id=1536, wt=99.000
% 110.96/111.30
% 110.96/111.30 Low Water (displace): id=1531, wt=95.000
% 110.96/111.30
% 110.96/111.30 Low Water (displace): id=1534, wt=87.000
% 110.96/111.30
% 110.96/111.30 Low Water (displace): id=1537, wt=79.000
% 110.96/111.30
% 110.96/111.30 Low Water (displace): id=9951, wt=45.000
% 110.96/111.30
% 110.96/111.30 Low Water (displace): id=9671, wt=43.000
% 110.96/111.30
% 110.96/111.30 Low Water (displace): id=9670, wt=42.000
% 110.96/111.30
% 110.96/111.30 Low Water (displace): id=9955, wt=41.000
% 110.96/111.30
% 110.96/111.30 Low Water (displace): id=7630, wt=39.000
% 110.96/111.30
% 110.96/111.30 Low Water (displace): id=7628, wt=38.000
% 110.96/111.30
% 110.96/111.30 Low Water (displace): id=9959, wt=37.000
% 110.96/111.30
% 110.96/111.30 Low Water (displace): id=10784, wt=35.000
% 110.96/111.30
% 110.96/111.30 Low Water (displace): id=9610, wt=34.000
% 110.96/111.30
% 110.96/111.30 Low Water (displace): id=10850, wt=33.000
% 110.96/111.31
% 110.96/111.31 Low Water (displace): id=10848, wt=32.000
% 110.96/111.31
% 110.96/111.31 Low Water (displace): id=11036, wt=31.000
% 110.96/111.31
% 110.96/111.31 Low Water (displace): id=11034, wt=30.000
% 110.96/111.31
% 110.96/111.31 Low Water (displace): id=10984, wt=29.000
% 110.96/111.31
% 110.96/111.31 Low Water (displace): id=11218, wt=28.000
% 110.96/111.31
% 110.96/111.31 Low Water (displace): id=10988, wt=27.000
% 110.96/111.31
% 110.96/111.31 Low Water (displace): id=11456, wt=25.000
% 110.96/111.31
% 110.96/111.31 Low Water (displace): id=11541, wt=18.000
% 110.96/111.31
% 110.96/111.31 Low Water (displace): id=11549, wt=17.000
% 110.96/111.31
% 110.96/111.31 Low Water (displace): id=11946, wt=15.000
% 110.96/111.31
% 110.96/111.31 Low Water (keep): wt=18.000, iters=3336
% 110.96/111.31
% 110.96/111.31 Low Water (displace): id=12980, wt=14.000
% 110.96/111.31
% 110.96/111.31 Low Water (displace): id=16617, wt=13.000
% 110.96/111.31
% 110.96/111.31 Low Water (displace): id=16829, wt=12.000
% 110.96/111.31
% 110.96/111.31 Low Water (keep): wt=17.000, iters=3337
% 110.96/111.31
% 110.96/111.31 Low Water (keep): wt=16.000, iters=4462
% 110.96/111.31
% 110.96/111.31 Low Water (keep): wt=15.000, iters=3854
% 110.96/111.31
% 110.96/111.31 Low Water (keep): wt=14.000, iters=3337
% 110.96/111.31
% 110.96/111.31 Low Water (keep): wt=13.000, iters=3334
% 110.96/111.31
% 110.96/111.31 ============================== PROOF =================================
% 110.96/111.31 % SZS status Theorem
% 110.96/111.31 % SZS output start Refutation
% 110.96/111.31
% 110.96/111.31 % Proof 1 at 103.69 (+ 6.61) seconds.
% 110.96/111.31 % Length of proof is 404.
% 110.96/111.31 % Level of proof is 110.
% 110.96/111.31 % Maximum clause weight is 24.000.
% 110.96/111.31 % Given clauses 9263.
% 110.96/111.31
% 110.96/111.31 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].
% 110.96/111.31 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].
% 110.96/111.31 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].
% 110.96/111.31 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].
% 110.96/111.31 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 110.96/111.31 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 110.96/111.31 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].
% 110.96/111.31 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].
% 110.96/111.31 34 op_equiv # label(luka_op_equiv) # label(axiom). [assumption].
% 110.96/111.31 35 modus_ponens # label(luka_modus_ponens) # label(axiom). [assumption].
% 110.96/111.31 36 cn1 # label(luka_cn1) # label(axiom). [assumption].
% 110.96/111.31 37 cn2 # label(luka_cn2) # label(axiom). [assumption].
% 110.96/111.31 38 cn3 # label(luka_cn3) # label(axiom). [assumption].
% 110.96/111.31 39 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption].
% 110.96/111.31 40 op_implies_and # label(hilbert_op_implies_and) # label(axiom). [assumption].
% 110.96/111.31 41 -equivalence_3 # label(hilbert_equivalence_3) # label(negated_conjecture). [assumption].
% 110.96/111.31 60 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(2)].
% 110.96/111.31 61 -is_a_theorem(equiv(A,B)) | B = A. [copy(60),unit_del(a,39)].
% 110.96/111.31 62 -cn2 | is_a_theorem(implies(A,implies(not(A),B))) # label(cn2) # label(axiom). [clausify(20)].
% 110.96/111.31 63 is_a_theorem(implies(A,implies(not(A),B))). [copy(62),unit_del(a,37)].
% 110.96/111.31 65 -cn3 | is_a_theorem(implies(implies(not(A),A),A)) # label(cn3) # label(axiom). [clausify(21)].
% 110.96/111.31 66 is_a_theorem(implies(implies(not(A),A),A)). [copy(65),unit_del(a,38)].
% 110.96/111.31 68 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 110.96/111.31 69 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(68),unit_del(a,35)].
% 110.96/111.31 79 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 110.96/111.31 80 not(and(A,not(B))) = implies(A,B). [copy(79),unit_del(a,40)].
% 110.96/111.31 89 -op_equiv | and(implies(A,B),implies(B,A)) = equiv(A,B) # label(op_equiv) # label(axiom). [clausify(31)].
% 110.96/111.31 90 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(89),unit_del(a,34)].
% 110.96/111.31 93 equivalence_3 | -is_a_theorem(implies(implies(c31,c32),implies(implies(c32,c31),equiv(c31,c32)))) # label(equivalence_3) # label(axiom). [clausify(15)].
% 110.96/111.31 94 -is_a_theorem(implies(implies(c31,c32),implies(implies(c32,c31),equiv(c31,c32)))). [copy(93),unit_del(a,41)].
% 110.96/111.31 95 -cn1 | is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))) # label(cn1) # label(axiom). [clausify(19)].
% 110.96/111.31 96 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))). [copy(95),unit_del(a,36)].
% 110.96/111.31 122 -is_a_theorem(implies(not(A),A)) | is_a_theorem(A). [resolve(69,b,66,a)].
% 110.96/111.31 123 -is_a_theorem(A) | is_a_theorem(implies(not(A),B)). [resolve(69,b,63,a)].
% 110.96/111.31 124 is_a_theorem(implies(and(A,not(B)),implies(implies(A,B),C))). [para(80(a,1),63(a,1,2,1))].
% 110.96/111.31 125 is_a_theorem(implies(implies(implies(A,B),and(A,not(B))),and(A,not(B)))). [para(80(a,1),66(a,1,1,1))].
% 110.96/111.31 126 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(80(a,1),80(a,1,1,2))].
% 110.96/111.31 128 -is_a_theorem(implies(implies(implies(not(A),A),A),implies(implies(c31,c32),implies(implies(c32,c31),equiv(c31,c32))))). [ur(69,a,66,a,c,94,a)].
% 110.96/111.31 130 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(B,C),implies(A,C))). [resolve(96,a,69,b)].
% 110.96/111.31 132 -is_a_theorem(implies(implies(A,B),and(A,not(B)))) | is_a_theorem(and(A,not(B))). [para(80(a,1),122(a,1,1))].
% 110.96/111.31 134 -is_a_theorem(implies(implies(c31,c32),implies(not(implies(implies(c32,c31),equiv(c31,c32))),implies(implies(c32,c31),equiv(c31,c32))))). [ur(69,b,96,a,c,128,a)].
% 110.96/111.31 228 is_a_theorem(implies(implies(implies(implies(A,B),C),D),implies(and(A,not(B)),D))). [resolve(130,a,124,a)].
% 110.96/111.31 229 is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))). [resolve(130,a,96,a)].
% 110.96/111.31 230 is_a_theorem(implies(implies(A,B),implies(implies(not(A),A),B))). [resolve(130,a,66,a)].
% 110.96/111.31 231 is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C))). [resolve(130,a,63,a)].
% 110.96/111.31 232 is_a_theorem(implies(implies(implies(implies(not(A),A),B),C),implies(implies(A,B),C))). [resolve(230,a,130,a)].
% 110.96/111.31 234 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(A),A),B)). [resolve(230,a,69,b)].
% 110.96/111.31 244 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(not(A),D),B),C))). [resolve(231,a,130,a)].
% 110.96/111.31 246 -is_a_theorem(implies(implies(not(A),B),C)) | is_a_theorem(implies(A,C)). [resolve(231,a,69,b)].
% 110.96/111.31 248 -is_a_theorem(implies(implies(not(implies(c31,c32)),A),implies(not(implies(implies(c32,c31),equiv(c31,c32))),implies(implies(c32,c31),equiv(c31,c32))))). [ur(69,b,231,a,c,134,a)].
% 110.96/111.31 259 implies(implies(A,B),and(B,not(A))) = not(equiv(A,B)). [para(90(a,1),126(a,1,1)),flip(a)].
% 110.96/111.31 348 is_a_theorem(implies(A,implies(implies(B,C),implies(not(A),C)))). [resolve(246,a,96,a)].
% 110.96/111.31 349 is_a_theorem(implies(A,A)). [resolve(246,a,66,a)].
% 110.96/111.31 351 -is_a_theorem(implies(implies(implies(A,B),C),D)) | is_a_theorem(implies(and(A,not(B)),D)). [para(80(a,1),246(a,1,1,1))].
% 110.96/111.31 413 is_a_theorem(implies(not(implies(A,A)),B)). [resolve(349,a,123,a)].
% 110.96/111.31 433 is_a_theorem(implies(implies(A,B),implies(not(implies(C,C)),B))). [resolve(413,a,130,a)].
% 110.96/111.31 626 is_a_theorem(implies(implies(not(A),A),implies(implies(B,C),implies(not(A),C)))). [resolve(348,a,234,a)].
% 110.96/111.31 627 is_a_theorem(implies(implies(implies(implies(A,B),implies(not(C),B)),D),implies(C,D))). [resolve(348,a,130,a)].
% 110.96/111.31 656 is_a_theorem(implies(A,implies(not(implies(B,B)),C))). [resolve(433,a,246,a)].
% 110.96/111.31 754 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),implies(D,C))). [resolve(656,a,130,a)].
% 110.96/111.31 1024 is_a_theorem(implies(not(equiv(A,A)),and(A,not(A)))). [para(259(a,1),125(a,1,1))].
% 110.96/111.31 1208 is_a_theorem(implies(implies(and(A,not(A)),B),implies(not(equiv(A,A)),B))). [resolve(1024,a,130,a)].
% 110.96/111.31 2287 -is_a_theorem(implies(implies(not(implies(A,A)),B),C)) | is_a_theorem(implies(D,C)). [resolve(754,a,69,b)].
% 110.96/111.31 3022 is_a_theorem(implies(A,implies(B,B))). [resolve(2287,a,66,a)].
% 110.96/111.31 3029 is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))). [resolve(3022,a,130,a)].
% 110.96/111.31 3376 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(D,D),B),C))). [resolve(3029,a,130,a)].
% 110.96/111.31 3378 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(implies(C,B)). [resolve(3029,a,69,b)].
% 110.96/111.31 3450 is_a_theorem(implies(A,implies(B,implies(C,C)))). [resolve(3378,a,3029,a)].
% 110.96/111.31 3452 is_a_theorem(implies(A,implies(B,implies(not(B),C)))). [resolve(3378,a,231,a)].
% 110.96/111.31 3453 is_a_theorem(implies(A,implies(implies(not(B),B),B))). [resolve(3378,a,230,a)].
% 110.96/111.31 3459 is_a_theorem(implies(implies(implies(A,implies(B,B)),C),implies(D,C))). [resolve(3450,a,130,a)].
% 110.96/111.31 3533 is_a_theorem(implies(implies(implies(A,implies(not(A),B)),C),implies(D,C))). [resolve(3452,a,130,a)].
% 110.96/111.31 3829 is_a_theorem(implies(implies(implies(implies(not(A),A),A),B),implies(C,B))). [resolve(3453,a,130,a)].
% 110.96/111.31 5458 -is_a_theorem(implies(implies(implies(not(A),A),A),B)) | is_a_theorem(implies(C,B)). [resolve(3829,a,69,b)].
% 110.96/111.31 6746 -is_a_theorem(implies(not(A),A)) | is_a_theorem(implies(implies(B,C),implies(not(A),C))). [resolve(626,a,69,b)].
% 110.96/111.31 7290 -is_a_theorem(implies(and(A,not(A)),B)) | is_a_theorem(implies(not(equiv(A,A)),B)). [resolve(1208,a,69,b)].
% 110.96/111.31 7606 is_a_theorem(implies(A,implies(implies(implies(B,B),C),C))). [resolve(3376,a,5458,a)].
% 110.96/111.31 7616 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(implies(D,D),B),C)). [resolve(3376,a,69,b)].
% 110.96/111.31 7670 is_a_theorem(implies(implies(implies(implies(implies(A,A),B),B),C),implies(D,C))). [resolve(7606,a,130,a)].
% 110.96/111.31 7672 is_a_theorem(implies(implies(implies(A,A),B),B)). [resolve(7606,a,122,a)].
% 110.96/111.31 7719 is_a_theorem(implies(implies(A,B),implies(implies(implies(C,C),A),B))). [resolve(7672,a,130,a)].
% 110.96/111.31 7720 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(B). [resolve(7672,a,69,b)].
% 110.96/111.31 7962 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(C,C),A),B)). [resolve(7719,a,69,b)].
% 110.96/111.31 8455 is_a_theorem(implies(implies(implies(A,A),implies(implies(B,B),C)),implies(D,C))). [resolve(7962,a,3029,a)].
% 110.96/111.31 9997 is_a_theorem(implies(implies(implies(A,A),B),implies(implies(B,C),implies(D,C)))). [resolve(7616,a,96,a)].
% 110.96/111.31 10063 -is_a_theorem(implies(implies(implies(implies(A,A),B),B),C)) | is_a_theorem(implies(D,C)). [resolve(7670,a,69,b)].
% 110.96/111.31 10525 -is_a_theorem(implies(implies(A,A),implies(implies(B,B),C))) | is_a_theorem(implies(D,C)). [resolve(8455,a,69,b)].
% 110.96/111.31 10779 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(implies(implies(B,C),implies(D,C))). [resolve(9997,a,69,b)].
% 110.96/111.31 11429 is_a_theorem(implies(A,implies(and(B,not(B)),C))). [resolve(228,a,10063,a)].
% 110.96/111.31 11461 is_a_theorem(implies(and(A,not(A)),B)). [resolve(11429,a,7720,a)].
% 110.96/111.31 11517 is_a_theorem(implies(not(equiv(A,A)),B)). [back_unit_del(7290),unit_del(a,11461)].
% 110.96/111.31 11646 is_a_theorem(implies(implies(A,B),implies(not(equiv(C,C)),B))). [resolve(11517,a,6746,a)].
% 110.96/111.31 12659 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),C),implies(D,C))). [resolve(11646,a,10779,a)].
% 110.96/111.31 13136 is_a_theorem(implies(A,implies(B,equiv(C,C)))). [resolve(12659,a,5458,a)].
% 110.96/111.31 13180 is_a_theorem(implies(A,equiv(B,B))). [resolve(13136,a,10525,a)].
% 110.96/111.31 13257 is_a_theorem(implies(implies(equiv(A,A),B),implies(C,B))). [resolve(13180,a,10779,a)].
% 110.96/111.31 13568 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(equiv(D,D),B),C))). [resolve(13257,a,130,a)].
% 110.96/111.31 13828 -is_a_theorem(implies(implies(implies(not(A),A),B),C)) | is_a_theorem(implies(implies(A,B),C)). [resolve(232,a,69,b)].
% 110.96/111.31 14828 is_a_theorem(implies(A,implies(implies(implies(not(implies(B,B)),C),D),D))). [resolve(244,a,10063,a)].
% 110.96/111.31 14835 is_a_theorem(implies(A,implies(implies(implies(not(not(B)),C),B),B))). [resolve(244,a,5458,a)].
% 110.96/111.31 14876 is_a_theorem(implies(implies(implies(not(not(A)),B),A),A)). [resolve(14835,a,7720,a)].
% 110.96/111.31 14906 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(not(A)),C),A),B))). [resolve(14876,a,130,a)].
% 110.96/111.31 14907 -is_a_theorem(implies(implies(not(not(A)),B),A)) | is_a_theorem(A). [resolve(14876,a,69,b)].
% 110.96/111.31 14922 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),C)). [resolve(14828,a,14907,a)].
% 110.96/111.31 14967 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(implies(C,C)),D),A),B))). [resolve(14922,a,130,a)].
% 110.96/111.31 14968 -is_a_theorem(implies(implies(not(implies(A,A)),B),C)) | is_a_theorem(C). [resolve(14922,a,69,b)].
% 110.96/111.31 14992 -is_a_theorem(not(equiv(not(implies(A,A)),B))) | is_a_theorem(and(B,not(not(implies(A,A))))). [para(259(a,1),14968(a,1))].
% 110.96/111.31 15017 -is_a_theorem(implies(not(implies(implies(c32,c31),equiv(c31,c32))),not(implies(c31,c32)))). [ur(130,b,248,a)].
% 110.96/111.31 15243 is_a_theorem(implies(A,implies(implies(equiv(B,B),C),C))). [resolve(13568,a,10063,a)].
% 110.96/111.31 15259 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(equiv(D,D),B),C)). [resolve(13568,a,69,b)].
% 110.96/111.31 15264 is_a_theorem(implies(implies(equiv(A,A),B),B)). [resolve(15243,a,14968,a)].
% 110.96/111.31 15266 is_a_theorem(implies(implies(implies(implies(equiv(A,A),B),B),C),implies(D,C))). [resolve(15243,a,10779,a)].
% 110.96/111.31 15322 -is_a_theorem(implies(equiv(A,A),B)) | is_a_theorem(B). [resolve(15264,a,69,b)].
% 110.96/111.31 18583 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(not(A)),C),A),B)). [resolve(14906,a,69,b)].
% 110.96/111.31 18657 is_a_theorem(implies(implies(equiv(A,A),B),implies(implies(B,C),implies(D,C)))). [resolve(15259,a,9997,a)].
% 110.96/111.31 18741 -is_a_theorem(implies(implies(implies(equiv(A,A),B),B),C)) | is_a_theorem(implies(D,C)). [resolve(15266,a,69,b)].
% 110.96/111.31 20829 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),and(A,not(A))),C)). [resolve(18583,a,11461,a),rewrite([80(3)])].
% 110.96/111.31 21011 -is_a_theorem(implies(equiv(A,A),B)) | is_a_theorem(implies(implies(B,C),implies(D,C))). [resolve(18657,a,69,b)].
% 110.96/111.31 21059 is_a_theorem(implies(A,implies(implies(implies(not(equiv(B,B)),C),D),D))). [resolve(18741,a,244,a)].
% 110.96/111.31 21088 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),C),C)). [resolve(21059,a,15322,a)].
% 110.96/111.31 21130 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(equiv(C,C)),D),A),B))). [resolve(21088,a,130,a)].
% 110.96/111.31 23105 is_a_theorem(implies(and(not(equiv(A,A)),not(B)),C)). [resolve(351,a,21088,a)].
% 110.96/111.31 23107 is_a_theorem(implies(and(not(implies(A,A)),not(B)),C)). [resolve(351,a,20829,a)].
% 110.96/111.31 23115 is_a_theorem(implies(and(not(not(A)),not(B)),A)). [resolve(351,a,14876,a)].
% 110.96/111.31 23125 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),implies(C,D))). [resolve(351,a,7670,a)].
% 110.96/111.31 23127 is_a_theorem(implies(and(implies(not(A),A),not(A)),implies(B,C))). [resolve(351,a,3829,a)].
% 110.96/111.31 23128 is_a_theorem(implies(and(A,not(implies(not(A),B))),implies(C,D))). [resolve(351,a,3533,a)].
% 110.96/111.31 23129 is_a_theorem(implies(and(A,not(implies(B,B))),implies(C,D))). [resolve(351,a,3459,a)].
% 110.96/111.31 23137 is_a_theorem(implies(and(A,not(B)),implies(implies(implies(not(A),C),B),D))). [resolve(351,a,244,a)].
% 110.96/111.31 23140 is_a_theorem(implies(and(implies(A,B),not(implies(C,B))),implies(implies(C,A),D))). [resolve(351,a,229,a)].
% 110.96/111.31 23165 is_a_theorem(implies(implies(implies(not(not(A)),B),and(not(not(A)),not(B))),A)). [resolve(23115,a,234,a),rewrite([80(5)])].
% 110.96/111.31 23166 is_a_theorem(implies(implies(A,B),implies(and(not(not(A)),not(C)),B))). [resolve(23115,a,130,a)].
% 110.96/111.31 23581 is_a_theorem(implies(implies(implies(A,A),and(not(equiv(B,B)),not(C))),D)). [resolve(23105,a,7962,a)].
% 110.96/111.31 23625 is_a_theorem(implies(implies(implies(A,A),and(not(implies(B,B)),not(C))),D)). [resolve(23107,a,7962,a)].
% 110.96/111.31 24066 is_a_theorem(implies(implies(implies(A,B),C),implies(and(D,not(implies(E,E))),C))). [resolve(23129,a,130,a)].
% 110.96/111.31 24326 is_a_theorem(implies(and(implies(not(A),A),not(A)),not(equiv(B,C)))). [para(259(a,1),23127(a,1,2))].
% 110.96/111.31 24379 is_a_theorem(implies(and(A,not(implies(not(A),B))),not(equiv(C,D)))). [para(259(a,1),23128(a,1,2))].
% 110.96/111.31 24659 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),not(equiv(C,D)))). [para(259(a,1),23125(a,1,2))].
% 110.96/111.31 25030 is_a_theorem(implies(and(not(not(not(implies(A,A)))),not(B)),C)). [resolve(23166,a,14968,a)].
% 110.96/111.31 25034 is_a_theorem(implies(implies(implies(and(not(not(A)),not(B)),A),C),implies(D,C))). [resolve(23166,a,10779,a)].
% 110.96/111.31 25061 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(and(not(not(A)),not(C)),B)). [resolve(23166,a,69,b)].
% 110.96/111.31 25149 is_a_theorem(implies(implies(implies(A,A),and(not(not(not(implies(B,B)))),not(C))),D)). [resolve(25030,a,7962,a)].
% 110.96/111.31 27673 is_a_theorem(implies(and(A,implies(B,not(A))),implies(not(equiv(not(A),B)),C))). [para(259(a,1),23137(a,1,2,1)),rewrite([80(4)])].
% 110.96/111.31 28123 is_a_theorem(and(implies(A,A),implies(not(equiv(B,B)),C))). [resolve(23581,a,132,a),rewrite([80(6)])].
% 110.96/111.31 28401 is_a_theorem(and(implies(A,A),implies(not(implies(B,B)),C))). [resolve(23625,a,132,a),rewrite([80(6)])].
% 110.96/111.31 31255 -is_a_theorem(implies(implies(implies(A,B),implies(not(C),B)),D)) | is_a_theorem(implies(C,D)). [resolve(627,a,69,b)].
% 110.96/111.31 45293 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(implies(C,C)),D),A),B)). [resolve(14967,a,69,b)].
% 110.96/111.31 53662 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(equiv(C,C)),D),A),B)). [resolve(21130,a,69,b)].
% 110.96/111.31 55699 is_a_theorem(implies(and(implies(A,B),not(implies(C,B))),not(equiv(C,A)))). [para(259(a,1),23140(a,1,2))].
% 110.96/111.31 55960 is_a_theorem(implies(implies(not(A),and(not(not(A)),not(not(A)))),A)). [resolve(23165,a,13828,a)].
% 110.96/111.31 56037 -is_a_theorem(implies(not(A),and(not(not(A)),not(not(A))))) | is_a_theorem(A). [resolve(55960,a,69,b)].
% 110.96/111.31 57149 is_a_theorem(implies(A,implies(and(B,not(implies(C,C))),D))). [resolve(24066,a,18741,a)].
% 110.96/111.31 57190 is_a_theorem(implies(implies(implies(and(A,not(implies(B,B))),C),D),implies(E,D))). [resolve(57149,a,21011,a)].
% 110.96/111.31 61322 -is_a_theorem(and(A,implies(B,not(A)))) | is_a_theorem(implies(not(equiv(not(A),B)),C)). [resolve(27673,a,69,b)].
% 110.96/111.31 62190 is_a_theorem(implies(A,implies(B,implies(not(A),C)))). [resolve(31255,a,25034,a)].
% 110.96/111.31 62199 is_a_theorem(implies(A,implies(implies(implies(not(A),B),C),implies(D,C)))). [resolve(31255,a,9997,a)].
% 110.96/111.31 62278 is_a_theorem(implies(implies(implies(A,implies(not(B),C)),D),implies(B,D))). [resolve(62190,a,130,a)].
% 110.96/111.31 66958 is_a_theorem(implies(A,implies(B,implies(C,implies(not(B),D))))). [resolve(62278,a,3378,a)].
% 110.96/111.31 91529 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),and(not(not(C)),not(D))),C)). [resolve(45293,a,23115,a)].
% 110.96/111.31 112022 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),and(not(implies(C,C)),not(D))),E)). [resolve(53662,a,23107,a)].
% 110.96/111.31 113607 is_a_theorem(implies(and(and(A,not(implies(B,B))),not(C)),implies(D,E))). [resolve(57190,a,351,a)].
% 110.96/111.31 113754 is_a_theorem(implies(and(and(A,not(implies(B,B))),not(C)),not(equiv(D,E)))). [para(259(a,1),113607(a,1,2))].
% 110.96/111.31 116306 is_a_theorem(implies(not(equiv(not(implies(A,A)),not(implies(B,B)))),C)). [resolve(61322,a,28401,a)].
% 110.96/111.31 116308 is_a_theorem(implies(not(equiv(not(implies(A,A)),not(equiv(B,B)))),C)). [resolve(61322,a,28123,a)].
% 110.96/111.31 116344 is_a_theorem(equiv(not(implies(A,A)),not(implies(B,B)))). [resolve(116306,a,56037,a)].
% 110.96/111.31 116442 not(implies(A,A)) = not(implies(B,B)). [resolve(116344,a,61,a)].
% 110.96/111.31 116449 not(implies(A,A)) = c_0. [new_symbol(116442)].
% 110.96/111.31 116451 is_a_theorem(implies(not(equiv(c_0,not(equiv(A,A)))),B)). [back_rewrite(116308),rewrite([116449(2)])].
% 110.96/111.31 116505 is_a_theorem(implies(and(and(A,c_0),not(B)),not(equiv(C,D)))). [back_rewrite(113754),rewrite([116449(2)])].
% 110.96/111.31 116540 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),and(c_0,not(C))),D)). [back_rewrite(112022),rewrite([116449(5)])].
% 110.96/111.31 116598 is_a_theorem(implies(implies(implies(c_0,A),and(not(not(B)),not(C))),B)). [back_rewrite(91529),rewrite([116449(2)])].
% 110.96/111.31 116993 is_a_theorem(implies(implies(implies(A,A),and(not(not(c_0)),not(B))),C)). [back_rewrite(25149),rewrite([116449(3)])].
% 110.96/111.31 117168 -is_a_theorem(not(equiv(c_0,A))) | is_a_theorem(and(A,not(c_0))). [back_rewrite(14992),rewrite([116449(2),116449(6)])].
% 110.96/111.31 117171 -is_a_theorem(implies(implies(c_0,A),B)) | is_a_theorem(B). [back_rewrite(14968),rewrite([116449(2)])].
% 110.96/111.31 119030 is_a_theorem(implies(c_0,A)). [back_rewrite(413),rewrite([116449(2)])].
% 110.96/111.31 119256 implies(A,implies(B,B)) = not(and(A,c_0)). [para(116449(a,1),80(a,1,1,2)),flip(a)].
% 110.96/111.31 126066 is_a_theorem(equiv(c_0,not(equiv(A,A)))). [resolve(116451,a,56037,a)].
% 110.96/111.31 126166 not(equiv(A,A)) = c_0. [resolve(126066,a,61,a)].
% 110.96/111.31 126270 is_a_theorem(implies(implies(implies(c_0,A),and(c_0,not(B))),C)). [back_rewrite(116540),rewrite([126166(2)])].
% 110.96/111.31 126377 implies(A,equiv(B,B)) = not(and(A,c_0)). [para(126166(a,1),80(a,1,1,2)),flip(a)].
% 110.96/111.31 126409 is_a_theorem(implies(and(implies(not(A),A),not(A)),c_0)). [para(126166(a,1),24326(a,1,2))].
% 110.96/111.31 126410 is_a_theorem(implies(and(A,not(implies(not(A),B))),c_0)). [para(126166(a,1),24379(a,1,2))].
% 110.96/111.31 126416 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),c_0)). [para(126166(a,1),24659(a,1,2))].
% 110.96/111.31 130320 -is_a_theorem(implies(not(and(implies(A,A),c_0)),B)) | is_a_theorem(B). [para(119256(a,1),7720(a,1,1))].
% 110.96/111.31 132449 is_a_theorem(implies(implies(c_0,A),implies(and(implies(not(B),B),not(B)),A))). [resolve(126409,a,130,a)].
% 110.96/111.31 132518 is_a_theorem(implies(implies(c_0,A),implies(and(B,not(implies(not(B),C))),A))). [resolve(126410,a,130,a)].
% 110.96/111.31 140993 is_a_theorem(and(implies(c_0,A),implies(c_0,B))). [resolve(126270,a,132,a),rewrite([80(6)])].
% 110.96/111.31 141028 is_a_theorem(implies(not(equiv(not(implies(c_0,A)),c_0)),B)). [resolve(140993,a,61322,a)].
% 110.96/111.31 141215 is_a_theorem(equiv(not(implies(c_0,A)),c_0)). [resolve(141028,a,56037,a)].
% 110.96/111.31 141306 not(implies(c_0,A)) = c_0. [resolve(141215,a,61,a),flip(a)].
% 110.96/111.31 141335 implies(A,implies(c_0,B)) = not(and(A,c_0)). [para(141306(a,1),80(a,1,1,2)),flip(a)].
% 110.96/111.31 142445 is_a_theorem(implies(and(implies(not(and(implies(A,A),c_0)),B),not(B)),c_0)). [para(119256(a,1),126416(a,1,1,1,1))].
% 110.96/111.31 146700 is_a_theorem(implies(and(and(A,c_0),not(B)),c_0)). [para(126166(a,1),116505(a,1,2))].
% 110.96/111.31 146767 is_a_theorem(implies(implies(c_0,A),implies(and(and(B,c_0),not(C)),A))). [resolve(146700,a,130,a)].
% 110.96/111.31 165405 is_a_theorem(implies(not(equiv(c_0,not(not(A)))),A)). [para(259(a,1),116598(a,1,1))].
% 110.96/111.31 165475 is_a_theorem(implies(implies(A,B),implies(not(equiv(c_0,not(not(A)))),B))). [resolve(165405,a,130,a)].
% 110.96/111.31 167472 is_a_theorem(and(implies(A,A),implies(not(not(c_0)),B))). [resolve(116993,a,132,a),rewrite([80(7)])].
% 110.96/111.31 167510 is_a_theorem(implies(not(equiv(c_0,not(not(c_0)))),A)). [resolve(167472,a,61322,a),rewrite([116449(2)])].
% 110.96/111.31 167579 is_a_theorem(equiv(c_0,not(not(c_0)))). [resolve(167510,a,56037,a)].
% 110.96/111.31 167671 not(not(c_0)) = c_0. [resolve(167579,a,61,a)].
% 110.96/111.31 167675 not(and(A,c_0)) = implies(A,not(c_0)). [para(167671(a,1),80(a,1,1,2))].
% 110.96/111.31 167676 is_a_theorem(not(c_0)). [para(167671(a,1),122(a,1,1)),unit_del(a,119030)].
% 110.96/111.31 167685 implies(implies(not(c_0),A),and(A,c_0)) = not(equiv(not(c_0),A)). [para(167671(a,1),259(a,1,2,2))].
% 110.96/111.31 167689 is_a_theorem(implies(A,not(c_0))). [para(167671(a,1),3452(a,1,2,2,1)),rewrite([141335(5),167675(5),119256(6),167675(3)])].
% 110.96/111.31 168344 is_a_theorem(implies(and(implies(implies(implies(A,A),not(c_0)),B),not(B)),c_0)). [back_rewrite(142445),rewrite([167675(4)])].
% 110.96/111.31 168501 implies(A,implies(c_0,B)) = implies(A,not(c_0)). [back_rewrite(141335),rewrite([167675(6)])].
% 110.96/111.31 168837 -is_a_theorem(implies(implies(implies(A,A),not(c_0)),B)) | is_a_theorem(B). [back_rewrite(130320),rewrite([167675(4)])].
% 110.96/111.31 168910 implies(A,equiv(B,B)) = implies(A,not(c_0)). [back_rewrite(126377),rewrite([167675(5)])].
% 110.96/111.31 169423 implies(A,implies(B,B)) = implies(A,not(c_0)). [back_rewrite(119256),rewrite([167675(5)])].
% 110.96/111.31 169783 is_a_theorem(implies(implies(not(c_0),A),implies(B,A))). [resolve(167689,a,21011,a)].
% 110.96/111.31 170870 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(not(c_0),B),C))). [resolve(169783,a,130,a)].
% 110.96/111.31 192415 is_a_theorem(implies(and(and(A,c_0),not(B)),C)). [resolve(146767,a,117171,a)].
% 110.96/111.31 197926 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(equiv(c_0,not(not(A)))),B)). [resolve(165475,a,69,b)].
% 110.96/111.31 210968 is_a_theorem(implies(A,implies(implies(not(c_0),B),B))). [resolve(170870,a,18741,a)].
% 110.96/111.31 210975 is_a_theorem(implies(implies(A,B),implies(implies(not(c_0),A),B))). [resolve(170870,a,13828,a)].
% 110.96/111.31 210998 is_a_theorem(implies(implies(not(c_0),A),A)). [resolve(210968,a,168837,a)].
% 110.96/111.31 211133 -is_a_theorem(implies(not(c_0),A)) | is_a_theorem(A). [resolve(210998,a,69,b)].
% 110.96/111.31 214986 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(c_0),A),B)). [resolve(210975,a,69,b)].
% 110.96/111.31 216538 is_a_theorem(implies(implies(not(c_0),and(and(A,c_0),not(B))),C)). [resolve(214986,a,192415,a)].
% 110.96/111.31 223712 is_a_theorem(and(not(c_0),implies(and(A,c_0),B))). [resolve(216538,a,132,a),rewrite([80(7)])].
% 110.96/111.31 223746 is_a_theorem(implies(not(equiv(c_0,and(A,c_0))),B)). [resolve(223712,a,61322,a),rewrite([167671(3)])].
% 110.96/111.31 223814 is_a_theorem(equiv(c_0,and(A,c_0))). [resolve(223746,a,56037,a)].
% 110.96/111.31 223903 and(A,c_0) = c_0. [resolve(223814,a,61,a)].
% 110.96/111.31 223954 implies(implies(not(c_0),A),c_0) = not(equiv(not(c_0),A)). [back_rewrite(167685),rewrite([223903(5)])].
% 110.96/111.31 223955 implies(A,not(c_0)) = not(c_0). [back_rewrite(167675),rewrite([223903(2)]),flip(a)].
% 110.96/111.31 223977 implies(A,implies(B,B)) = not(c_0). [back_rewrite(169423),rewrite([223955(5)])].
% 110.96/111.31 224000 implies(A,equiv(B,B)) = not(c_0). [back_rewrite(168910),rewrite([223955(5)])].
% 110.96/111.31 224019 implies(A,implies(c_0,B)) = not(c_0). [back_rewrite(168501),rewrite([223955(6)])].
% 110.96/111.31 224020 is_a_theorem(implies(and(implies(not(c_0),A),not(A)),c_0)). [back_rewrite(168344),rewrite([223955(4)])].
% 110.96/111.31 224024 and(not(c_0),implies(not(c_0),A)) = equiv(A,not(c_0)). [para(223955(a,1),90(a,1,1))].
% 110.96/111.31 224025 and(implies(not(c_0),A),not(c_0)) = equiv(not(c_0),A). [para(223955(a,1),90(a,1,2))].
% 110.96/111.31 226552 is_a_theorem(implies(implies(c_0,A),implies(and(implies(not(c_0),B),not(B)),A))). [resolve(224020,a,130,a)].
% 110.96/111.31 227059 implies(not(c_0),c_0) = c_0. [para(126166(a,1),223954(a,2)),rewrite([223955(5)])].
% 110.96/111.31 227084 not(equiv(not(c_0),implies(A,A))) = c_0. [para(223977(a,1),223954(a,1,1)),rewrite([227059(4)]),flip(a)].
% 110.96/111.31 227085 not(equiv(not(c_0),equiv(A,A))) = c_0. [para(224000(a,1),223954(a,1,1)),rewrite([227059(4)]),flip(a)].
% 110.96/111.31 227086 not(equiv(not(c_0),implies(c_0,A))) = c_0. [para(224019(a,1),223954(a,1,1)),rewrite([227059(4)]),flip(a)].
% 110.96/111.31 227128 is_a_theorem(implies(implies(not(c_0),A),implies(implies(A,c_0),c_0))). [para(227059(a,1),96(a,1,2,2))].
% 110.96/111.31 227153 is_a_theorem(implies(and(implies(A,c_0),not(c_0)),implies(implies(not(c_0),A),B))). [para(227059(a,1),23140(a,1,1,2,1))].
% 110.96/111.31 227160 is_a_theorem(implies(A,implies(implies(implies(not(A),B),c_0),c_0))). [para(227059(a,1),62199(a,1,2,2))].
% 110.96/111.31 227201 implies(A,equiv(not(c_0),implies(B,B))) = not(c_0). [para(227084(a,1),80(a,1,1,2)),rewrite([223903(2)]),flip(a)].
% 110.96/111.31 227202 is_a_theorem(equiv(not(c_0),implies(A,A))). [para(227084(a,1),122(a,1,1)),rewrite([227201(6)]),unit_del(a,167676)].
% 110.96/111.31 227268 implies(A,A) = not(c_0). [resolve(227202,a,61,a)].
% 110.96/111.31 228591 and(not(c_0),not(c_0)) = equiv(A,A). [para(227268(a,1),90(a,1,1)),rewrite([227268(3)])].
% 110.96/111.31 228592 is_a_theorem(implies(implies(A,B),implies(not(c_0),implies(A,B)))). [para(227268(a,1),96(a,1,2,1))].
% 110.96/111.31 228593 implies(A,and(B,not(B))) = implies(A,c_0). [para(227268(a,1),126(a,1,1,2)),rewrite([80(4)]),flip(a)].
% 110.96/111.31 228640 implies(A,equiv(not(c_0),equiv(B,B))) = not(c_0). [para(227085(a,1),80(a,1,1,2)),rewrite([223903(2)]),flip(a)].
% 110.96/111.31 228641 is_a_theorem(equiv(not(c_0),equiv(A,A))). [para(227085(a,1),122(a,1,1)),rewrite([228640(6)]),unit_del(a,167676)].
% 110.96/111.31 228695 equiv(A,A) = not(c_0). [resolve(228641,a,61,a)].
% 110.96/111.31 228914 and(not(c_0),not(c_0)) = not(c_0). [back_rewrite(228591),rewrite([228695(6)])].
% 110.96/111.31 229034 implies(A,equiv(not(c_0),implies(c_0,B))) = not(c_0). [para(227086(a,1),80(a,1,1,2)),rewrite([223903(2)]),flip(a)].
% 110.96/111.31 229035 is_a_theorem(equiv(not(c_0),implies(c_0,A))). [para(227086(a,1),122(a,1,1)),rewrite([229034(7)]),unit_del(a,167676)].
% 110.96/111.31 229085 implies(c_0,A) = not(c_0). [resolve(229035,a,61,a)].
% 110.96/111.31 229344 is_a_theorem(implies(not(c_0),implies(and(implies(not(c_0),A),not(A)),B))). [back_rewrite(226552),rewrite([229085(2)])].
% 110.96/111.31 229348 is_a_theorem(implies(not(c_0),implies(and(A,not(implies(not(A),B))),C))). [back_rewrite(132518),rewrite([229085(2)])].
% 110.96/111.31 229349 is_a_theorem(implies(not(c_0),implies(and(implies(not(A),A),not(A)),B))). [back_rewrite(132449),rewrite([229085(2)])].
% 110.96/111.31 229352 and(implies(A,c_0),not(c_0)) = equiv(A,c_0). [para(229085(a,1),90(a,1,2))].
% 110.96/111.31 229353 is_a_theorem(implies(implies(A,c_0),implies(not(c_0),implies(A,B)))). [para(229085(a,1),96(a,1,2,1))].
% 110.96/111.31 229354 implies(A,and(c_0,not(B))) = implies(A,c_0). [para(229085(a,1),126(a,1,1,2)),rewrite([80(4)]),flip(a)].
% 110.96/111.31 229355 implies(not(c_0),and(A,not(c_0))) = not(equiv(c_0,A)). [para(229085(a,1),259(a,1,1))].
% 110.96/111.31 229396 is_a_theorem(implies(and(A,not(c_0)),implies(not(equiv(not(A),c_0)),B))). [para(229085(a,1),27673(a,1,1,2))].
% 110.96/111.31 229452 is_a_theorem(implies(equiv(A,c_0),implies(implies(not(c_0),A),B))). [back_rewrite(227153),rewrite([229352(5)])].
% 110.96/111.31 230019 implies(implies(A,c_0),and(and(B,not(B)),not(A))) = not(equiv(A,and(B,not(B)))). [para(228593(a,1),259(a,1,1))].
% 110.96/111.31 230049 implies(and(A,not(A)),c_0) = not(c_0). [para(228593(a,1),227268(a,1))].
% 110.96/111.31 230052 equiv(and(A,not(A)),c_0) = not(c_0). [para(230049(a,1),90(a,1,1)),rewrite([228593(6),227268(5),228914(5)]),flip(a)].
% 110.96/111.31 230078 and(A,not(A)) = c_0. [para(230052(a,1),61(a,1)),flip(b),unit_del(a,167676)].
% 110.96/111.31 230081 implies(implies(A,c_0),c_0) = not(equiv(A,c_0)). [back_rewrite(230019),rewrite([230078(4),229354(6),230078(6)])].
% 110.96/111.31 230094 is_a_theorem(implies(A,not(equiv(implies(not(A),B),c_0)))). [back_rewrite(227160),rewrite([230081(6)])].
% 110.96/111.31 230105 is_a_theorem(implies(implies(not(c_0),A),not(equiv(A,c_0)))). [back_rewrite(227128),rewrite([230081(7)])].
% 110.96/111.31 230784 is_a_theorem(implies(implies(A,implies(B,c_0)),implies(not(equiv(B,c_0)),implies(A,c_0)))). [para(230081(a,1),96(a,1,2,1))].
% 110.96/111.31 230912 is_a_theorem(implies(A,implies(not(equiv(not(A),c_0)),implies(B,c_0)))). [para(230081(a,1),62199(a,1,2,1))].
% 110.96/111.31 231437 -is_a_theorem(implies(not(c_0),A)) | is_a_theorem(not(equiv(A,c_0))). [resolve(230105,a,69,b)].
% 110.96/111.31 231923 is_a_theorem(not(equiv(implies(A,implies(B,implies(not(A),C))),c_0))). [resolve(231437,a,66958,a)].
% 110.96/111.31 231944 is_a_theorem(not(equiv(implies(implies(implies(not(not(A)),B),A),A),c_0))). [resolve(231437,a,14835,a)].
% 110.96/111.31 231992 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(c_0),implies(A,B))). [resolve(228592,a,69,b)].
% 110.96/111.31 232294 is_a_theorem(implies(not(c_0),implies(equiv(A,c_0),implies(implies(not(c_0),A),B)))). [resolve(231992,a,229452,a)].
% 110.96/111.31 235879 is_a_theorem(implies(A,implies(not(equiv(not(A),c_0)),c_0))). [para(227059(a,1),230912(a,1,2,2))].
% 110.96/111.31 235932 -is_a_theorem(A) | is_a_theorem(implies(not(equiv(not(A),c_0)),c_0)). [resolve(235879,a,69,b)].
% 110.96/111.31 238340 is_a_theorem(implies(and(implies(not(c_0),A),not(A)),B)). [resolve(229344,a,211133,a)].
% 110.96/111.31 238349 is_a_theorem(implies(not(equiv(c_0,not(implies(implies(not(c_0),A),A)))),B)). [resolve(238340,a,197926,a),rewrite([80(7)])].
% 110.96/111.31 238419 is_a_theorem(implies(and(A,not(implies(not(A),B))),C)). [resolve(229348,a,211133,a)].
% 110.96/111.31 238428 is_a_theorem(implies(not(equiv(c_0,not(implies(A,implies(not(A),B))))),C)). [resolve(238419,a,197926,a),rewrite([80(6)])].
% 110.96/111.31 238475 is_a_theorem(implies(and(implies(not(A),A),not(A)),B)). [resolve(229349,a,211133,a)].
% 110.96/111.31 238482 is_a_theorem(implies(implies(not(c_0),and(implies(not(A),A),not(A))),B)). [resolve(238475,a,214986,a)].
% 110.96/111.31 239316 is_a_theorem(equiv(c_0,not(implies(implies(not(c_0),A),A)))). [resolve(238349,a,56037,a)].
% 110.96/111.31 239331 not(implies(implies(not(c_0),A),A)) = c_0. [resolve(239316,a,61,a)].
% 110.96/111.31 239333 implies(A,implies(implies(not(c_0),B),B)) = not(c_0). [para(239331(a,1),80(a,1,1,2)),rewrite([223903(2)]),flip(a)].
% 110.96/111.31 239346 equiv(implies(implies(not(c_0),A),A),not(c_0)) = not(c_0). [para(239333(a,1),224024(a,1,2)),rewrite([228914(5)]),flip(a)].
% 110.96/111.31 239356 implies(implies(not(c_0),A),A) = not(c_0). [para(239346(a,1),61(a,1)),flip(b),unit_del(a,167676)].
% 110.96/111.31 239359 and(implies(A,implies(not(c_0),A)),not(c_0)) = equiv(A,implies(not(c_0),A)). [para(239356(a,1),90(a,1,2))].
% 110.96/111.31 239446 is_a_theorem(equiv(c_0,not(implies(A,implies(not(A),B))))). [resolve(238428,a,56037,a)].
% 110.96/111.31 239453 not(implies(A,implies(not(A),B))) = c_0. [resolve(239446,a,61,a)].
% 110.96/111.31 239455 implies(A,implies(B,implies(not(B),C))) = not(c_0). [para(239453(a,1),80(a,1,1,2)),rewrite([223903(2)]),flip(a)].
% 110.96/111.31 239520 equiv(implies(A,implies(not(A),B)),not(c_0)) = not(c_0). [para(239455(a,1),224024(a,1,2)),rewrite([228914(5)]),flip(a)].
% 110.96/111.31 239526 implies(A,implies(not(A),B)) = not(c_0). [para(239520(a,1),61(a,1)),flip(b),unit_del(a,167676)].
% 110.96/111.31 239530 and(not(c_0),implies(implies(not(A),B),A)) = equiv(A,implies(not(A),B)). [para(239526(a,1),90(a,1,1))].
% 110.96/111.31 239531 and(implies(implies(not(A),B),A),not(c_0)) = equiv(implies(not(A),B),A). [para(239526(a,1),90(a,1,2))].
% 110.96/111.31 239649 is_a_theorem(equiv(A,implies(not(A),A))). [resolve(238482,a,132,a),rewrite([80(7),239530(6)])].
% 110.96/111.31 239702 implies(not(A),A) = A. [resolve(239649,a,61,a)].
% 110.96/111.31 239710 implies(implies(A,B),and(A,not(B))) = and(A,not(B)). [para(80(a,1),239702(a,1,1))].
% 110.96/111.31 239715 implies(A,and(not(B),not(B))) = not(and(A,B)). [para(239702(a,1),126(a,1,1,2)),flip(a)].
% 110.96/111.31 239847 is_a_theorem(implies(A,implies(implies(A,B),implies(C,B)))). [para(239702(a,1),62199(a,1,2,1,1))].
% 110.96/111.31 239939 is_a_theorem(implies(A,not(equiv(A,c_0)))). [para(239702(a,1),230094(a,1,2,1,1))].
% 110.96/111.31 239941 is_a_theorem(implies(implies(not(A),c_0),implies(not(c_0),A))). [para(239702(a,1),229353(a,1,2,2))].
% 110.96/111.31 239945 is_a_theorem(not(equiv(implies(A,implies(B,A)),c_0))). [para(239702(a,1),231923(a,1,1,1,2,2))].
% 110.96/111.31 239982 is_a_theorem(implies(and(A,not(c_0)),equiv(not(A),c_0))). [para(239702(a,1),229396(a,1,2))].
% 110.96/111.31 240947 -is_a_theorem(A) | is_a_theorem(not(equiv(A,c_0))). [resolve(239939,a,69,b)].
% 110.96/111.31 241015 is_a_theorem(not(equiv(implies(A,not(equiv(A,c_0))),c_0))). [resolve(240947,a,239939,a)].
% 110.96/111.31 242934 is_a_theorem(implies(A,implies(implies(A,B),B))). [para(239702(a,1),239847(a,1,2,2))].
% 110.96/111.31 243596 is_a_theorem(not(equiv(implies(implies(not(A),c_0),implies(not(c_0),A)),c_0))). [resolve(239941,a,240947,a)].
% 110.96/111.31 243672 is_a_theorem(implies(not(equiv(A,c_0)),not(equiv(c_0,A)))). [para(229355(a,1),239941(a,1,2)),rewrite([80(4),230081(4)])].
% 110.96/111.31 243727 -is_a_theorem(and(A,not(c_0))) | is_a_theorem(equiv(not(A),c_0)). [resolve(239982,a,69,b)].
% 110.96/111.31 244508 -is_a_theorem(not(equiv(A,c_0))) | is_a_theorem(not(equiv(c_0,A))). [resolve(243672,a,69,b)].
% 110.96/111.31 244702 is_a_theorem(not(equiv(c_0,implies(A,not(equiv(A,c_0)))))). [resolve(244508,a,241015,a)].
% 110.96/111.31 244703 is_a_theorem(not(equiv(c_0,implies(A,implies(B,A))))). [resolve(244508,a,239945,a)].
% 110.96/111.31 244714 is_a_theorem(not(equiv(c_0,implies(implies(implies(not(not(A)),B),A),A)))). [resolve(244508,a,231944,a)].
% 110.96/111.31 244753 is_a_theorem(and(implies(A,implies(B,A)),not(c_0))). [resolve(244703,a,117168,a)].
% 110.96/111.31 244769 is_a_theorem(equiv(not(implies(A,implies(B,A))),c_0)). [resolve(244753,a,243727,a)].
% 110.96/111.31 244823 not(implies(A,implies(B,A))) = c_0. [resolve(244769,a,61,a),flip(a)].
% 110.96/111.31 244825 implies(A,implies(B,implies(C,B))) = not(c_0). [para(244823(a,1),80(a,1,1,2)),rewrite([223903(2)]),flip(a)].
% 110.96/111.31 244827 implies(A,implies(B,A)) = not(c_0). [para(244823(a,1),239702(a,1,1)),rewrite([244825(4)]),flip(a)].
% 110.96/111.31 244834 equiv(A,implies(not(c_0),A)) = not(c_0). [back_rewrite(239359),rewrite([244827(4),228914(5)]),flip(a)].
% 110.96/111.31 244862 and(implies(implies(A,B),B),not(c_0)) = equiv(implies(A,B),B). [para(244827(a,1),90(a,1,2))].
% 110.96/111.31 244920 implies(not(c_0),A) = A. [para(244834(a,1),61(a,1)),unit_del(a,167676)].
% 110.96/111.31 244968 is_a_theorem(not(equiv(implies(implies(not(A),c_0),A),c_0))). [back_rewrite(243596),rewrite([244920(6)])].
% 110.96/111.31 245065 is_a_theorem(implies(equiv(A,c_0),implies(A,B))). [back_rewrite(232294),rewrite([244920(7),244920(7)])].
% 110.96/111.31 245115 not(equiv(c_0,A)) = and(A,not(c_0)). [back_rewrite(229355),rewrite([244920(6)]),flip(a)].
% 110.96/111.31 245124 equiv(not(c_0),A) = and(A,not(c_0)). [back_rewrite(224025),rewrite([244920(3)]),flip(a)].
% 110.96/111.31 245131 is_a_theorem(equiv(implies(implies(not(not(A)),B),A),A)). [back_rewrite(244714),rewrite([245115(8),244862(8)])].
% 110.96/111.31 245136 is_a_theorem(and(implies(A,not(equiv(A,c_0))),not(c_0))). [back_rewrite(244702),rewrite([245115(7)])].
% 110.96/111.31 245140 -is_a_theorem(not(equiv(A,c_0))) | is_a_theorem(and(A,not(c_0))). [back_rewrite(244508),rewrite([245115(7)])].
% 110.96/111.31 247162 is_a_theorem(implies(equiv(not(A),c_0),A)). [para(239702(a,1),245065(a,1,2))].
% 110.96/111.31 247173 is_a_theorem(implies(not(equiv(not(implies(equiv(not(A),c_0),A)),c_0)),c_0)). [resolve(247162,a,235932,a)].
% 110.96/111.31 248152 not(and(A,and(B,not(c_0)))) = implies(A,equiv(c_0,B)). [para(245115(a,1),80(a,1,1,2))].
% 110.96/111.31 248471 implies(and(A,not(c_0)),equiv(c_0,A)) = equiv(c_0,A). [para(245115(a,1),239702(a,1,1))].
% 110.96/111.31 248510 -is_a_theorem(and(A,not(c_0))) | not(c_0) = A. [para(245124(a,1),61(a,1)),flip(b)].
% 110.96/111.31 249471 implies(implies(not(not(A)),B),A) = A. [resolve(245131,a,61,a),flip(a)].
% 110.96/111.31 249564 is_a_theorem(implies(not(not(A)),A)). [para(249471(a,1),242934(a,1,2))].
% 110.96/111.31 250055 is_a_theorem(implies(implies(A,c_0),equiv(c_0,A))). [para(245115(a,1),249564(a,1,1,1)),rewrite([80(4)])].
% 110.96/111.31 250156 is_a_theorem(implies(A,equiv(c_0,not(A)))). [resolve(250055,a,246,a)].
% 110.96/111.31 250266 -is_a_theorem(A) | is_a_theorem(equiv(c_0,not(A))). [resolve(250156,a,69,b)].
% 110.96/111.31 250310 is_a_theorem(equiv(c_0,not(implies(not(not(A)),A)))). [resolve(250266,a,249564,a)].
% 110.96/111.31 250800 not(implies(not(not(A)),A)) = c_0. [resolve(250310,a,61,a)].
% 110.96/111.31 250835 implies(A,implies(not(not(B)),B)) = not(c_0). [para(250800(a,1),80(a,1,1,2)),rewrite([223903(2)]),flip(a)].
% 110.96/111.31 250842 implies(not(not(A)),A) = not(c_0). [para(250800(a,1),239702(a,1,1)),rewrite([250835(5)]),flip(a)].
% 110.96/111.31 250887 is_a_theorem(implies(not(not(A)),implies(B,A))). [para(250842(a,1),239847(a,1,2,1)),rewrite([244920(6)])].
% 110.96/111.31 250917 is_a_theorem(implies(and(not(not(not(not(A)))),not(B)),implies(C,A))). [resolve(250887,a,25061,a)].
% 110.96/111.31 251193 implies(A,not(equiv(A,c_0))) = not(c_0). [resolve(245136,a,248510,a),flip(a)].
% 110.96/111.31 251221 and(implies(not(equiv(A,c_0)),A),not(c_0)) = equiv(not(equiv(A,c_0)),A). [para(251193(a,1),90(a,1,2))].
% 110.96/111.31 251558 is_a_theorem(equiv(implies(not(A),c_0),A)). [resolve(245140,a,244968,a),rewrite([239531(7)])].
% 110.96/111.31 251623 implies(not(A),c_0) = A. [resolve(251558,a,61,a),flip(a)].
% 110.96/111.31 251678 is_a_theorem(equiv(not(implies(equiv(not(A),c_0),A)),c_0)). [back_rewrite(247173),rewrite([251623(10)])].
% 110.96/111.31 251797 implies(implies(A,B),c_0) = and(A,not(B)). [para(80(a,1),251623(a,1,1))].
% 110.96/111.31 251798 equiv(not(A),c_0) = and(A,not(c_0)). [para(251623(a,1),90(a,1,1)),rewrite([229085(3)]),flip(a)].
% 110.96/111.31 251802 implies(A,and(not(B),not(c_0))) = not(and(A,B)). [para(251623(a,1),126(a,1,1,2)),flip(a)].
% 110.96/111.31 251819 is_a_theorem(implies(and(A,not(implies(B,c_0))),implies(implies(B,not(A)),C))). [para(251623(a,1),23140(a,1,1,1))].
% 110.96/111.31 251821 is_a_theorem(implies(and(A,not(implies(B,c_0))),not(equiv(B,not(A))))). [para(251623(a,1),55699(a,1,1,1))].
% 110.96/111.31 251854 implies(and(A,not(c_0)),c_0) = equiv(c_0,A). [para(245115(a,1),251623(a,1,1))].
% 110.96/111.31 252067 not(equiv(A,c_0)) = and(A,not(c_0)). [back_rewrite(230081),rewrite([251797(4)]),flip(a)].
% 110.96/111.31 252160 is_a_theorem(and(implies(and(A,not(c_0)),A),not(c_0))). [back_rewrite(251678),rewrite([251798(3),251798(7)])].
% 110.96/111.31 253414 and(implies(and(A,not(c_0)),A),not(c_0)) = equiv(and(A,not(c_0)),A). [back_rewrite(251221),rewrite([252067(3),252067(10)])].
% 110.96/111.31 253839 is_a_theorem(implies(implies(A,implies(B,c_0)),implies(and(B,not(c_0)),implies(A,c_0)))). [back_rewrite(230784),rewrite([252067(6)])].
% 110.96/111.31 253855 is_a_theorem(equiv(and(A,not(c_0)),A)). [back_rewrite(252160),rewrite([253414(7)])].
% 110.96/111.31 254917 and(A,not(c_0)) = A. [resolve(253855,a,61,a),flip(a)].
% 110.96/111.31 254930 is_a_theorem(implies(implies(A,implies(B,c_0)),implies(B,implies(A,c_0)))). [back_rewrite(253839),rewrite([254917(6)])].
% 110.96/111.31 255058 equiv(c_0,A) = implies(A,c_0). [back_rewrite(251854),rewrite([254917(3)]),flip(a)].
% 110.96/111.31 255070 not(and(A,B)) = implies(A,not(B)). [back_rewrite(251802),rewrite([254917(4)]),flip(a)].
% 110.96/111.31 255090 -is_a_theorem(A) | not(c_0) = A. [back_rewrite(248510),rewrite([254917(3)])].
% 110.96/111.31 255110 implies(A,implies(A,c_0)) = implies(A,c_0). [back_rewrite(248471),rewrite([254917(3),255058(2),255058(5)])].
% 110.96/111.31 255295 implies(A,implies(B,c_0)) = implies(A,not(B)). [back_rewrite(248152),rewrite([254917(3),255070(2),255058(4)]),flip(a)].
% 110.96/111.31 255371 equiv(not(c_0),A) = A. [back_rewrite(245124),rewrite([254917(6)])].
% 110.96/111.31 255372 not(implies(A,c_0)) = A. [back_rewrite(245115),rewrite([255058(2),254917(6)])].
% 110.96/111.31 255683 implies(A,and(not(B),not(B))) = implies(A,not(B)). [back_rewrite(239715),rewrite([255070(6)])].
% 110.96/111.31 255684 implies(A,not(implies(B,C))) = implies(A,and(B,not(C))). [back_rewrite(126),rewrite([255070(3)])].
% 110.96/111.31 255709 implies(A,not(A)) = implies(A,c_0). [back_rewrite(255110),rewrite([255295(3)])].
% 110.96/111.31 255718 is_a_theorem(implies(implies(A,not(B)),implies(B,not(A)))). [back_rewrite(254930),rewrite([255295(3),255295(5)])].
% 110.96/111.31 255766 is_a_theorem(implies(and(A,B),not(equiv(B,not(A))))). [back_rewrite(251821),rewrite([255372(3)])].
% 110.96/111.31 255767 is_a_theorem(implies(and(A,B),implies(implies(B,not(A)),C))). [back_rewrite(251819),rewrite([255372(3)])].
% 110.96/111.31 256199 -is_a_theorem(implies(not(implies(implies(c32,c31),equiv(c31,c32))),and(c31,not(c32)))). [back_rewrite(15017),rewrite([255684(13)])].
% 110.96/111.31 257880 implies(A,implies(implies(A,B),B)) = not(c_0). [resolve(255090,a,242934,a),flip(a)].
% 110.96/111.31 258024 implies(A,c_0) = not(A). [para(255371(a,1),259(a,2,1)),rewrite([244920(3),167671(3),223903(2)])].
% 110.96/111.31 258035 implies(A,not(A)) = not(A). [back_rewrite(255709),rewrite([258024(4)])].
% 110.96/111.31 258086 not(not(A)) = A. [back_rewrite(255372),rewrite([258024(2)])].
% 110.96/111.31 258216 not(implies(A,B)) = and(A,not(B)). [back_rewrite(251797),rewrite([258024(3)])].
% 110.96/111.31 258319 is_a_theorem(implies(and(A,not(B)),implies(C,A))). [back_rewrite(250917),rewrite([258086(2),258086(2)])].
% 110.96/111.31 258645 -is_a_theorem(implies(and(implies(c32,c31),not(equiv(c31,c32))),and(c31,not(c32)))). [back_rewrite(256199),rewrite([258216(8)])].
% 110.96/111.31 259284 and(not(A),not(A)) = not(A). [para(239702(a,1),239710(a,1,1)),rewrite([255683(4),258035(2)]),flip(a)].
% 110.96/111.31 259308 and(A,A) = A. [para(258086(a,1),259284(a,1,1)),rewrite([258086(2),258086(3)])].
% 110.96/111.31 259388 is_a_theorem(implies(and(A,B),implies(C,A))). [para(258086(a,1),258319(a,1,1,2))].
% 110.96/111.31 259422 implies(and(A,B),implies(C,A)) = not(c_0). [resolve(259388,a,255090,a),flip(a)].
% 110.96/111.31 260500 is_a_theorem(implies(implies(A,B),implies(not(B),not(A)))). [para(258086(a,1),255718(a,1,1,2))].
% 110.96/111.31 260542 is_a_theorem(implies(equiv(A,B),not(equiv(implies(B,A),and(A,not(B)))))). [para(90(a,1),255766(a,1,1)),rewrite([258216(4)])].
% 110.96/111.31 261398 equiv(implies(A,B),and(B,C)) = implies(implies(A,B),and(B,C)). [para(259422(a,1),90(a,1,2)),rewrite([254917(6)]),flip(a)].
% 110.96/111.31 261403 is_a_theorem(implies(equiv(A,B),equiv(B,A))). [back_rewrite(260542),rewrite([261398(5),259(5),258086(4)])].
% 110.96/111.31 261408 implies(equiv(A,B),equiv(B,A)) = not(c_0). [resolve(261403,a,255090,a),flip(a)].
% 110.96/111.31 262189 is_a_theorem(implies(and(implies(A,B),not(B)),not(A))). [para(257880(a,1),260500(a,1,1)),rewrite([258216(5),244920(8)])].
% 110.96/111.31 262940 equiv(equiv(A,B),equiv(B,A)) = not(c_0). [para(261408(a,1),90(a,1,1)),rewrite([261408(5),259308(5)]),flip(a)].
% 110.96/111.31 263530 is_a_theorem(implies(and(not(equiv(A,B)),implies(B,A)),and(A,not(B)))). [para(259(a,1),262189(a,1,1,1)),rewrite([255070(5),258086(4),258216(6)])].
% 110.96/111.31 265495 equiv(A,B) = equiv(B,A). [para(262940(a,1),61(a,1)),unit_del(a,167676)].
% 110.96/111.31 268234 is_a_theorem(implies(and(A,B),and(B,A))). [para(258024(a,1),255767(a,1,2)),rewrite([258216(4),258086(3)])].
% 110.96/111.31 268245 implies(and(A,B),and(B,A)) = not(c_0). [resolve(268234,a,255090,a),flip(a)].
% 110.96/111.31 268623 equiv(and(A,B),and(B,A)) = not(c_0). [para(268245(a,1),90(a,1,1)),rewrite([268245(5),259308(5),265495(5)]),flip(a)].
% 110.96/111.31 268946 and(A,B) = and(B,A). [para(268623(a,1),61(a,1)),unit_del(a,167676)].
% 110.96/111.31 269531 is_a_theorem(implies(and(implies(A,B),not(equiv(B,A))),and(B,not(A)))). [back_rewrite(263530),rewrite([268946(4)])].
% 110.96/111.31 269532 $F. [resolve(269531,a,258645,a)].
% 110.96/111.31
% 110.96/111.31 % SZS output end Refutation
% 110.96/111.31 ============================== end of proof ==========================
% 110.96/111.31
% 110.96/111.31 ============================== STATISTICS ============================
% 110.96/111.31
% 110.96/111.31 Given=9263. Generated=12963640. Kept=269481. proofs=1.
% 110.96/111.31 Usable=563. Sos=4791. Demods=523. Limbo=585, Disabled=263613. Hints=0.
% 110.96/111.31 Megabytes=184.47.
% 110.96/111.31 User_CPU=103.70, System_CPU=6.61, Wall_clock=110.
% 110.96/111.31
% 110.96/111.31 ============================== end of statistics =====================
% 110.96/111.31
% 110.96/111.31 ============================== end of search =========================
% 110.96/111.31
% 110.96/111.31 THEOREM PROVED
% 110.96/111.31 % SZS status Theorem
% 110.96/111.31
% 110.96/111.31 Exiting with 1 proof.
% 110.96/111.31
% 110.96/111.31 Process 15572 exit (max_proofs) Mon Jul 4 07:52:58 2022
% 110.96/111.31 Prover9 interrupted
%------------------------------------------------------------------------------