TSTP Solution File: LCL468+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL468+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n008.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 13:47:02 EDT 2022
% Result : Theorem 124.24s 124.60s
% Output : Refutation 124.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LCL468+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 4 05:07:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.43/1.01 ============================== Prover9 ===============================
% 0.43/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.01 Process 25579 was started by sandbox on n008.cluster.edu,
% 0.43/1.01 Mon Jul 4 05:07:08 2022
% 0.43/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_25426_n008.cluster.edu".
% 0.43/1.01 ============================== end of head ===========================
% 0.43/1.01
% 0.43/1.01 ============================== INPUT =================================
% 0.43/1.01
% 0.43/1.01 % Reading from file /tmp/Prover9_25426_n008.cluster.edu
% 0.43/1.01
% 0.43/1.01 set(prolog_style_variables).
% 0.43/1.01 set(auto2).
% 0.43/1.01 % set(auto2) -> set(auto).
% 0.43/1.01 % set(auto) -> set(auto_inference).
% 0.43/1.01 % set(auto) -> set(auto_setup).
% 0.43/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.01 % set(auto) -> set(auto_limits).
% 0.43/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.01 % set(auto) -> set(auto_denials).
% 0.43/1.01 % set(auto) -> set(auto_process).
% 0.43/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.01 % set(auto2) -> assign(stats, some).
% 0.43/1.01 % set(auto2) -> clear(echo_input).
% 0.43/1.01 % set(auto2) -> set(quiet).
% 0.43/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.01 % set(auto2) -> clear(print_given).
% 0.43/1.01 assign(lrs_ticks,-1).
% 0.43/1.01 assign(sos_limit,10000).
% 0.43/1.01 assign(order,kbo).
% 0.43/1.01 set(lex_order_vars).
% 0.43/1.01 clear(print_given).
% 0.43/1.01
% 0.43/1.01 % formulas(sos). % not echoed (43 formulas)
% 0.43/1.01
% 0.43/1.01 ============================== end of input ==========================
% 0.43/1.01
% 0.43/1.01 % From the command line: assign(max_seconds, 300).
% 0.43/1.01
% 0.43/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.01
% 0.43/1.01 % Formulas that are not ordinary clauses:
% 0.43/1.01 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].
% 0.43/1.01 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].
% 0.43/1.01 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].
% 0.43/1.01 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 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].
% 0.43/1.01 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].
% 0.43/1.01 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 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].
% 0.43/1.01 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 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].
% 0.43/1.01 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].
% 0.43/1.01 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].
% 1.27/1.59 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].
% 1.27/1.59 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.59 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.59 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].
% 1.27/1.59 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].
% 1.27/1.59 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.59 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.59 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.59 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.59 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.59 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].
% 1.27/1.59 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].
% 1.27/1.59 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].
% 1.27/1.59 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].
% 1.27/1.59 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].
% 1.27/1.59 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].
% 1.27/1.59 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].
% 1.27/1.59
% 1.27/1.59 ============================== end of process non-clausal formulas ===
% 1.27/1.59
% 1.27/1.59 ============================== PROCESS INITIAL CLAUSES ===============
% 1.27/1.59
% 1.27/1.59 ============================== PREDICATE ELIMINATION =================
% 1.27/1.59
% 1.27/1.59 ============================== end predicate elimination =============
% 1.27/1.59
% 1.27/1.59 Auto_denials: (non-Horn, no changes).
% 1.27/1.59
% 1.27/1.59 Term ordering decisions:
% 1.27/1.59
% 1.27/1.59 % Assigning unary symbol not kb_weight 0 and highest precedence (94).
% 1.27/1.59 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.
% 1.27/1.59
% 1.27/1.59 ============================== end of process initial clauses ========
% 1.27/1.59
% 1.27/1.59 ============================== CLAUSES FOR SEARCH ====================
% 1.27/1.59
% 1.27/1.59 ============================== end of clauses for search =============
% 1.27/1.59
% 1.27/1.59 ============================== SEARCH ================================
% 1.27/1.59
% 1.27/1.59 % Starting search at 0.02 seconds.
% 1.27/1.59
% 1.27/1.59 Low Water (keep): wt=43.000, iters=3364
% 1.27/1.59
% 1.27/1.59 Low Water (keep): wt=36.000, iters=3364
% 1.27/1.59
% 1.27/1.59 Low Water (keep): wt=33.000, iters=3372
% 1.27/1.59
% 1.27/1.59 Low Water (keep): wt=32.000, iters=3385
% 1.27/1.59
% 1.27/1.59 Low Water (keep): wt=31.000, iters=3382
% 1.27/1.59
% 1.27/1.59 Low Water (keep): wt=27.000, iters=3391
% 1.27/1.59
% 1.27/1.59 Low Water (keep): wt=25.000, iters=3525
% 1.27/1.59
% 1.27/1.59 Low Water (keep): wt=24.000, iters=3591
% 1.27/1.59
% 1.27/1.59 Low Water (keep): wt=23.000, iters=3355
% 1.27/1.59
% 1.27/1.59 Low Water (keep): wt=22.000, iters=3368
% 1.27/1.59
% 124.24/124.60 Low Water (keep): wt=21.000, iters=3341
% 124.24/124.60
% 124.24/124.60 Low Water (keep): wt=20.000, iters=3480
% 124.24/124.60
% 124.24/124.60 Low Water (keep): wt=19.000, iters=3351
% 124.24/124.60
% 124.24/124.60 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 77 (0.00 of 1.34 sec).
% 124.24/124.60
% 124.24/124.60 Low Water (keep): wt=18.000, iters=3353
% 124.24/124.60
% 124.24/124.60 Low Water (displace): id=2042, wt=127.000
% 124.24/124.60
% 124.24/124.60 Low Water (displace): id=2459, wt=111.000
% 124.24/124.60
% 124.24/124.60 Low Water (displace): id=3163, wt=91.000
% 124.24/124.60
% 124.24/124.60 Low Water (displace): id=1532, wt=83.000
% 124.24/124.60
% 124.24/124.60 Low Water (displace): id=3608, wt=79.000
% 124.24/124.60
% 124.24/124.60 Low Water (displace): id=1534, wt=71.000
% 124.24/124.60
% 124.24/124.60 Low Water (displace): id=1533, wt=63.000
% 124.24/124.60
% 124.24/124.60 Low Water (displace): id=9887, wt=45.000
% 124.24/124.60
% 124.24/124.60 Low Water (displace): id=9588, wt=43.000
% 124.24/124.60
% 124.24/124.60 Low Water (displace): id=9587, wt=42.000
% 124.24/124.60
% 124.24/124.60 Low Water (displace): id=9891, wt=41.000
% 124.24/124.60
% 124.24/124.60 Low Water (displace): id=7416, wt=39.000
% 124.24/124.60
% 124.24/124.60 Low Water (displace): id=7414, wt=38.000
% 124.24/124.60
% 124.24/124.60 Low Water (displace): id=9895, wt=37.000
% 124.24/124.60
% 124.24/124.60 Low Water (displace): id=10778, wt=35.000
% 124.24/124.60
% 124.24/124.60 Low Water (displace): id=9582, wt=34.000
% 124.24/124.60
% 124.24/124.60 Low Water (displace): id=10835, wt=33.000
% 124.24/124.60
% 124.24/124.60 Low Water (displace): id=10833, wt=32.000
% 124.24/124.60
% 124.24/124.60 Low Water (displace): id=11023, wt=31.000
% 124.24/124.60
% 124.24/124.60 Low Water (displace): id=11021, wt=30.000
% 124.24/124.60
% 124.24/124.60 Low Water (displace): id=10970, wt=29.000
% 124.24/124.60
% 124.24/124.60 Low Water (displace): id=11232, wt=17.000
% 124.24/124.60
% 124.24/124.60 Low Water (displace): id=11549, wt=15.000
% 124.24/124.60
% 124.24/124.60 Low Water (displace): id=12022, wt=14.000
% 124.24/124.60
% 124.24/124.60 Low Water (keep): wt=17.000, iters=3334
% 124.24/124.60
% 124.24/124.60 Low Water (displace): id=17700, wt=13.000
% 124.24/124.60
% 124.24/124.60 Low Water (keep): wt=16.000, iters=3439
% 124.24/124.60
% 124.24/124.60 Low Water (keep): wt=15.000, iters=4368
% 124.24/124.60
% 124.24/124.60 Low Water (keep): wt=14.000, iters=3404
% 124.24/124.60
% 124.24/124.60 Low Water (displace): id=122132, wt=12.000
% 124.24/124.60
% 124.24/124.60 Low Water (keep): wt=13.000, iters=3333
% 124.24/124.60
% 124.24/124.60 Low Water (displace): id=162473, wt=11.000
% 124.24/124.60
% 124.24/124.60 ============================== PROOF =================================
% 124.24/124.60 % SZS status Theorem
% 124.24/124.60 % SZS output start Refutation
% 124.24/124.60
% 124.24/124.60 % Proof 1 at 116.25 (+ 7.35) seconds.
% 124.24/124.60 % Length of proof is 353.
% 124.24/124.60 % Level of proof is 100.
% 124.24/124.60 % Maximum clause weight is 19.000.
% 124.24/124.60 % Given clauses 9536.
% 124.24/124.60
% 124.24/124.60 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].
% 124.24/124.60 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].
% 124.24/124.60 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].
% 124.24/124.60 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].
% 124.24/124.60 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 124.24/124.60 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 124.24/124.60 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].
% 124.24/124.60 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].
% 124.24/124.60 34 op_equiv # label(luka_op_equiv) # label(axiom). [assumption].
% 124.24/124.60 35 modus_ponens # label(luka_modus_ponens) # label(axiom). [assumption].
% 124.24/124.60 36 cn1 # label(luka_cn1) # label(axiom). [assumption].
% 124.24/124.60 37 cn2 # label(luka_cn2) # label(axiom). [assumption].
% 124.24/124.60 38 cn3 # label(luka_cn3) # label(axiom). [assumption].
% 124.24/124.60 39 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption].
% 124.24/124.60 40 op_implies_and # label(hilbert_op_implies_and) # label(axiom). [assumption].
% 124.24/124.60 41 -and_3 # label(hilbert_and_3) # label(negated_conjecture). [assumption].
% 124.24/124.60 60 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(2)].
% 124.24/124.60 61 -is_a_theorem(equiv(A,B)) | B = A. [copy(60),unit_del(a,39)].
% 124.24/124.60 62 -cn2 | is_a_theorem(implies(A,implies(not(A),B))) # label(cn2) # label(axiom). [clausify(20)].
% 124.24/124.60 63 is_a_theorem(implies(A,implies(not(A),B))). [copy(62),unit_del(a,37)].
% 124.24/124.60 65 -cn3 | is_a_theorem(implies(implies(not(A),A),A)) # label(cn3) # label(axiom). [clausify(21)].
% 124.24/124.60 66 is_a_theorem(implies(implies(not(A),A),A)). [copy(65),unit_del(a,38)].
% 124.24/124.60 68 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 124.24/124.60 69 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(68),unit_del(a,35)].
% 124.24/124.60 70 and_3 | -is_a_theorem(implies(c18,implies(c19,and(c18,c19)))) # label(and_3) # label(axiom). [clausify(9)].
% 124.24/124.60 71 -is_a_theorem(implies(c18,implies(c19,and(c18,c19)))). [copy(70),unit_del(a,41)].
% 124.24/124.60 79 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 124.24/124.60 80 not(and(A,not(B))) = implies(A,B). [copy(79),unit_del(a,40)].
% 124.24/124.60 89 -op_equiv | and(implies(A,B),implies(B,A)) = equiv(A,B) # label(op_equiv) # label(axiom). [clausify(31)].
% 124.24/124.60 90 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(89),unit_del(a,34)].
% 124.24/124.60 95 -cn1 | is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))) # label(cn1) # label(axiom). [clausify(19)].
% 124.24/124.60 96 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))). [copy(95),unit_del(a,36)].
% 124.24/124.60 122 -is_a_theorem(implies(not(A),A)) | is_a_theorem(A). [resolve(69,b,66,a)].
% 124.24/124.60 123 -is_a_theorem(A) | is_a_theorem(implies(not(A),B)). [resolve(69,b,63,a)].
% 124.24/124.60 127 is_a_theorem(implies(and(A,not(B)),implies(implies(A,B),C))). [para(80(a,1),63(a,1,2,1))].
% 124.24/124.60 128 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))].
% 124.24/124.60 129 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(80(a,1),80(a,1,1,2))].
% 124.24/124.60 130 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(B,C),implies(A,C))). [resolve(96,a,69,b)].
% 124.24/124.60 226 is_a_theorem(implies(implies(implies(implies(A,B),C),D),implies(and(A,not(B)),D))). [resolve(130,a,127,a)].
% 124.24/124.60 227 is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))). [resolve(130,a,96,a)].
% 124.24/124.60 228 is_a_theorem(implies(implies(A,B),implies(implies(not(A),A),B))). [resolve(130,a,66,a)].
% 124.24/124.60 229 is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C))). [resolve(130,a,63,a)].
% 124.24/124.60 230 is_a_theorem(implies(implies(implies(implies(not(A),A),B),C),implies(implies(A,B),C))). [resolve(228,a,130,a)].
% 124.24/124.60 232 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(A),A),B)). [resolve(228,a,69,b)].
% 124.24/124.60 242 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(not(A),D),B),C))). [resolve(229,a,130,a)].
% 124.24/124.60 244 -is_a_theorem(implies(implies(not(A),B),C)) | is_a_theorem(implies(A,C)). [resolve(229,a,69,b)].
% 124.24/124.60 257 implies(implies(A,B),and(B,not(A))) = not(equiv(A,B)). [para(90(a,1),129(a,1,1)),flip(a)].
% 124.24/124.60 258 -is_a_theorem(implies(implies(A,and(B,not(C))),and(A,implies(B,C)))) | is_a_theorem(and(A,implies(B,C))). [para(129(a,1),122(a,1,1))].
% 124.24/124.60 347 is_a_theorem(implies(A,implies(implies(B,C),implies(not(A),C)))). [resolve(244,a,96,a)].
% 124.24/124.60 348 is_a_theorem(implies(A,A)). [resolve(244,a,66,a)].
% 124.24/124.60 350 -is_a_theorem(implies(implies(implies(A,B),C),D)) | is_a_theorem(implies(and(A,not(B)),D)). [para(80(a,1),244(a,1,1,1))].
% 124.24/124.60 413 is_a_theorem(implies(not(implies(A,A)),B)). [resolve(348,a,123,a)].
% 124.24/124.60 433 is_a_theorem(implies(implies(A,B),implies(not(implies(C,C)),B))). [resolve(413,a,130,a)].
% 124.24/124.60 609 is_a_theorem(implies(implies(not(A),A),implies(implies(B,C),implies(not(A),C)))). [resolve(347,a,232,a)].
% 124.24/124.60 610 is_a_theorem(implies(implies(implies(implies(A,B),implies(not(C),B)),D),implies(C,D))). [resolve(347,a,130,a)].
% 124.24/124.60 638 is_a_theorem(implies(A,implies(not(implies(B,B)),C))). [resolve(433,a,244,a)].
% 124.24/124.60 753 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),implies(D,C))). [resolve(638,a,130,a)].
% 124.24/124.60 1022 is_a_theorem(implies(not(equiv(A,A)),and(A,not(A)))). [para(257(a,1),128(a,1,1))].
% 124.24/124.60 1205 is_a_theorem(implies(implies(and(A,not(A)),B),implies(not(equiv(A,A)),B))). [resolve(1022,a,130,a)].
% 124.24/124.60 2279 -is_a_theorem(implies(implies(not(implies(A,A)),B),C)) | is_a_theorem(implies(D,C)). [resolve(753,a,69,b)].
% 124.24/124.60 3024 is_a_theorem(implies(A,implies(B,B))). [resolve(2279,a,66,a)].
% 124.24/124.60 3031 is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))). [resolve(3024,a,130,a)].
% 124.24/124.60 3380 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(D,D),B),C))). [resolve(3031,a,130,a)].
% 124.24/124.60 3382 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(implies(C,B)). [resolve(3031,a,69,b)].
% 124.24/124.60 3454 is_a_theorem(implies(A,implies(B,implies(C,C)))). [resolve(3382,a,3031,a)].
% 124.24/124.60 3456 is_a_theorem(implies(A,implies(B,implies(not(B),C)))). [resolve(3382,a,229,a)].
% 124.24/124.60 3457 is_a_theorem(implies(A,implies(implies(not(B),B),B))). [resolve(3382,a,228,a)].
% 124.24/124.60 3463 is_a_theorem(implies(implies(implies(A,implies(B,B)),C),implies(D,C))). [resolve(3454,a,130,a)].
% 124.24/124.60 3537 is_a_theorem(implies(implies(implies(A,implies(not(A),B)),C),implies(D,C))). [resolve(3456,a,130,a)].
% 124.24/124.60 3832 is_a_theorem(implies(implies(implies(implies(not(A),A),A),B),implies(C,B))). [resolve(3457,a,130,a)].
% 124.24/124.60 5460 -is_a_theorem(implies(implies(implies(not(A),A),A),B)) | is_a_theorem(implies(C,B)). [resolve(3832,a,69,b)].
% 124.24/124.60 6557 -is_a_theorem(implies(not(A),A)) | is_a_theorem(implies(implies(B,C),implies(not(A),C))). [resolve(609,a,69,b)].
% 124.24/124.60 7190 -is_a_theorem(implies(and(A,not(A)),B)) | is_a_theorem(implies(not(equiv(A,A)),B)). [resolve(1205,a,69,b)].
% 124.24/124.60 7577 is_a_theorem(implies(A,implies(implies(implies(B,B),C),C))). [resolve(3380,a,5460,a)].
% 124.24/124.60 7587 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(implies(D,D),B),C)). [resolve(3380,a,69,b)].
% 124.24/124.60 7643 is_a_theorem(implies(implies(implies(implies(implies(A,A),B),B),C),implies(D,C))). [resolve(7577,a,130,a)].
% 124.24/124.60 7645 is_a_theorem(implies(implies(implies(A,A),B),B)). [resolve(7577,a,122,a)].
% 124.24/124.60 7700 is_a_theorem(implies(implies(A,B),implies(implies(implies(C,C),A),B))). [resolve(7645,a,130,a)].
% 124.24/124.60 7701 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(B). [resolve(7645,a,69,b)].
% 124.24/124.60 7898 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(C,C),A),B)). [resolve(7700,a,69,b)].
% 124.24/124.60 8387 is_a_theorem(implies(implies(implies(A,A),implies(implies(B,B),C)),implies(D,C))). [resolve(7898,a,3031,a)].
% 124.24/124.60 9936 is_a_theorem(implies(implies(implies(A,A),B),implies(implies(B,C),implies(D,C)))). [resolve(7587,a,96,a)].
% 124.24/124.60 10006 -is_a_theorem(implies(implies(implies(implies(A,A),B),B),C)) | is_a_theorem(implies(D,C)). [resolve(7643,a,69,b)].
% 124.24/124.60 10534 -is_a_theorem(implies(implies(A,A),implies(implies(B,B),C))) | is_a_theorem(implies(D,C)). [resolve(8387,a,69,b)].
% 124.24/124.60 10772 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(implies(implies(B,C),implies(D,C))). [resolve(9936,a,69,b)].
% 124.24/124.60 11368 is_a_theorem(implies(A,implies(and(B,not(B)),C))). [resolve(226,a,10006,a)].
% 124.24/124.60 11400 is_a_theorem(implies(and(A,not(A)),B)). [resolve(11368,a,7701,a)].
% 124.24/124.60 11451 is_a_theorem(implies(not(equiv(A,A)),B)). [back_unit_del(7190),unit_del(a,11400)].
% 124.24/124.60 11563 is_a_theorem(implies(implies(A,B),implies(not(equiv(C,C)),B))). [resolve(11451,a,6557,a)].
% 124.24/124.60 12551 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),C),implies(D,C))). [resolve(11563,a,10772,a)].
% 124.24/124.60 13109 is_a_theorem(implies(A,implies(B,equiv(C,C)))). [resolve(12551,a,5460,a)].
% 124.24/124.60 13162 is_a_theorem(implies(A,equiv(B,B))). [resolve(13109,a,10534,a)].
% 124.24/124.60 13229 is_a_theorem(implies(implies(equiv(A,A),B),implies(C,B))). [resolve(13162,a,10772,a)].
% 124.24/124.60 13520 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(equiv(D,D),B),C))). [resolve(13229,a,130,a)].
% 124.24/124.60 13892 -is_a_theorem(implies(implies(implies(not(A),A),B),C)) | is_a_theorem(implies(implies(A,B),C)). [resolve(230,a,69,b)].
% 124.24/124.60 14554 is_a_theorem(implies(A,implies(implies(implies(not(implies(B,B)),C),D),D))). [resolve(242,a,10006,a)].
% 124.24/124.60 14561 is_a_theorem(implies(A,implies(implies(implies(not(not(B)),C),B),B))). [resolve(242,a,5460,a)].
% 124.24/124.60 14571 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(implies(not(A),D),B),C)). [resolve(242,a,69,b)].
% 124.24/124.60 14597 is_a_theorem(implies(implies(implies(not(not(A)),B),A),A)). [resolve(14561,a,7701,a)].
% 124.24/124.60 14621 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(not(A)),C),A),B))). [resolve(14597,a,130,a)].
% 124.24/124.60 14622 -is_a_theorem(implies(implies(not(not(A)),B),A)) | is_a_theorem(A). [resolve(14597,a,69,b)].
% 124.24/124.60 14641 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),C)). [resolve(14554,a,14622,a)].
% 124.24/124.61 14693 -is_a_theorem(implies(implies(not(implies(A,A)),B),C)) | is_a_theorem(C). [resolve(14641,a,69,b)].
% 124.24/124.61 14719 -is_a_theorem(not(equiv(not(implies(A,A)),B))) | is_a_theorem(and(B,not(not(implies(A,A))))). [para(257(a,1),14693(a,1))].
% 124.24/124.61 14807 is_a_theorem(implies(A,implies(implies(equiv(B,B),C),C))). [resolve(13520,a,10006,a)].
% 124.24/124.61 14823 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(equiv(D,D),B),C)). [resolve(13520,a,69,b)].
% 124.24/124.61 14830 is_a_theorem(implies(implies(equiv(A,A),B),B)). [resolve(14807,a,14693,a)].
% 124.24/124.61 14832 is_a_theorem(implies(implies(implies(implies(equiv(A,A),B),B),C),implies(D,C))). [resolve(14807,a,10772,a)].
% 124.24/124.61 14887 is_a_theorem(implies(implies(A,B),implies(implies(equiv(C,C),A),B))). [resolve(14830,a,130,a)].
% 124.24/124.61 14888 -is_a_theorem(implies(equiv(A,A),B)) | is_a_theorem(B). [resolve(14830,a,69,b)].
% 124.24/124.61 15064 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(equiv(C,C),A),B)). [resolve(14887,a,69,b)].
% 124.24/124.61 17592 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(not(A)),C),A),B)). [resolve(14621,a,69,b)].
% 124.24/124.61 17670 is_a_theorem(implies(implies(equiv(A,A),B),implies(implies(B,C),implies(D,C)))). [resolve(14823,a,9936,a)].
% 124.24/124.61 17772 -is_a_theorem(implies(implies(implies(equiv(A,A),B),B),C)) | is_a_theorem(implies(D,C)). [resolve(14832,a,69,b)].
% 124.24/124.61 20127 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),and(A,not(A))),C)). [resolve(17592,a,11400,a),rewrite([80(3)])].
% 124.24/124.61 20318 -is_a_theorem(implies(equiv(A,A),B)) | is_a_theorem(implies(implies(B,C),implies(D,C))). [resolve(17670,a,69,b)].
% 124.24/124.61 20364 is_a_theorem(implies(A,implies(implies(implies(not(equiv(B,B)),C),D),D))). [resolve(17772,a,242,a)].
% 124.24/124.61 20411 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),C),C)). [resolve(20364,a,14888,a)].
% 124.24/124.61 20461 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(equiv(C,C)),D),A),B))). [resolve(20411,a,130,a)].
% 124.24/124.61 22468 is_a_theorem(implies(and(not(equiv(A,A)),not(B)),C)). [resolve(350,a,20411,a)].
% 124.24/124.61 22470 is_a_theorem(implies(and(not(implies(A,A)),not(B)),C)). [resolve(350,a,20127,a)].
% 124.24/124.61 22478 is_a_theorem(implies(and(not(not(A)),not(B)),A)). [resolve(350,a,14597,a)].
% 124.24/124.61 22487 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),implies(C,D))). [resolve(350,a,7643,a)].
% 124.24/124.61 22489 is_a_theorem(implies(and(implies(not(A),A),not(A)),implies(B,C))). [resolve(350,a,3832,a)].
% 124.24/124.61 22490 is_a_theorem(implies(and(A,not(implies(not(A),B))),implies(C,D))). [resolve(350,a,3537,a)].
% 124.24/124.61 22491 is_a_theorem(implies(and(A,not(implies(B,B))),implies(C,D))). [resolve(350,a,3463,a)].
% 124.24/124.61 22500 is_a_theorem(implies(and(A,not(B)),implies(implies(implies(not(A),C),B),D))). [resolve(350,a,242,a)].
% 124.24/124.61 22503 is_a_theorem(implies(and(implies(A,B),not(implies(C,B))),implies(implies(C,A),D))). [resolve(350,a,227,a)].
% 124.24/124.61 22521 is_a_theorem(implies(implies(implies(A,A),and(not(not(B)),not(C))),B)). [resolve(22478,a,7898,a)].
% 124.24/124.61 22528 is_a_theorem(implies(implies(implies(not(not(A)),B),and(not(not(A)),not(B))),A)). [resolve(22478,a,232,a),rewrite([80(5)])].
% 124.24/124.61 22529 is_a_theorem(implies(implies(A,B),implies(and(not(not(A)),not(C)),B))). [resolve(22478,a,130,a)].
% 124.24/124.61 22934 is_a_theorem(implies(implies(implies(A,A),and(not(equiv(B,B)),not(C))),D)). [resolve(22468,a,7898,a)].
% 124.24/124.61 22974 is_a_theorem(implies(implies(implies(A,A),and(not(implies(B,B)),not(C))),D)). [resolve(22470,a,7898,a)].
% 124.24/124.61 23323 is_a_theorem(implies(implies(implies(A,B),C),implies(and(D,not(implies(E,E))),C))). [resolve(22491,a,130,a)].
% 124.24/124.61 23525 is_a_theorem(implies(and(implies(not(A),A),not(A)),not(equiv(B,C)))). [para(257(a,1),22489(a,1,2))].
% 124.24/124.61 23554 is_a_theorem(implies(and(A,not(implies(not(A),B))),not(equiv(C,D)))). [para(257(a,1),22490(a,1,2))].
% 124.24/124.61 23843 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),not(equiv(C,D)))). [para(257(a,1),22487(a,1,2))].
% 124.24/124.61 24224 is_a_theorem(implies(and(not(not(not(implies(A,A)))),not(B)),C)). [resolve(22529,a,14693,a)].
% 124.24/124.61 24228 is_a_theorem(implies(implies(implies(and(not(not(A)),not(B)),A),C),implies(D,C))). [resolve(22529,a,10772,a)].
% 124.24/124.61 26631 is_a_theorem(implies(and(A,implies(B,not(A))),implies(not(equiv(not(A),B)),C))). [para(257(a,1),22500(a,1,2,1)),rewrite([80(4)])].
% 124.24/124.61 27021 is_a_theorem(and(implies(A,A),implies(not(equiv(B,B)),C))). [resolve(22934,a,258,a)].
% 124.24/124.61 27260 is_a_theorem(and(implies(A,A),implies(not(implies(B,B)),C))). [resolve(22974,a,258,a)].
% 124.24/124.61 29853 -is_a_theorem(implies(implies(implies(A,B),implies(not(C),B)),D)) | is_a_theorem(implies(C,D)). [resolve(610,a,69,b)].
% 124.24/124.61 42275 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),and(not(not(C)),not(D))),C)). [resolve(14571,a,22521,a)].
% 124.24/124.61 51701 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(equiv(C,C)),D),A),B)). [resolve(20461,a,69,b)].
% 124.24/124.61 54040 is_a_theorem(implies(implies(not(A),and(not(not(A)),not(not(A)))),A)). [resolve(22528,a,13892,a)].
% 124.24/124.61 54105 -is_a_theorem(implies(not(A),and(not(not(A)),not(not(A))))) | is_a_theorem(A). [resolve(54040,a,69,b)].
% 124.24/124.61 55555 is_a_theorem(implies(A,implies(and(B,not(implies(C,C))),D))). [resolve(23323,a,17772,a)].
% 124.24/124.61 55596 is_a_theorem(implies(implies(implies(and(A,not(implies(B,B))),C),D),implies(E,D))). [resolve(55555,a,20318,a)].
% 124.24/124.61 59497 -is_a_theorem(and(A,implies(B,not(A)))) | is_a_theorem(implies(not(equiv(not(A),B)),C)). [resolve(26631,a,69,b)].
% 124.24/124.61 60326 is_a_theorem(implies(A,implies(B,implies(not(A),C)))). [resolve(29853,a,24228,a)].
% 124.24/124.61 60335 is_a_theorem(implies(A,implies(implies(implies(not(A),B),C),implies(D,C)))). [resolve(29853,a,9936,a)].
% 124.24/124.61 60415 is_a_theorem(implies(implies(implies(A,implies(not(B),C)),D),implies(B,D))). [resolve(60326,a,130,a)].
% 124.24/124.61 65081 is_a_theorem(implies(A,implies(B,implies(C,implies(not(B),D))))). [resolve(60415,a,3382,a)].
% 124.24/124.61 109977 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),and(not(implies(C,C)),not(D))),E)). [resolve(51701,a,22470,a)].
% 124.24/124.61 111566 is_a_theorem(implies(and(and(A,not(implies(B,B))),not(C)),implies(D,E))). [resolve(55596,a,350,a)].
% 124.24/124.61 111714 is_a_theorem(implies(and(and(A,not(implies(B,B))),not(C)),not(equiv(D,E)))). [para(257(a,1),111566(a,1,2))].
% 124.24/124.61 114181 is_a_theorem(implies(not(equiv(not(implies(A,A)),not(implies(B,B)))),C)). [resolve(59497,a,27260,a)].
% 124.24/124.61 114183 is_a_theorem(implies(not(equiv(not(implies(A,A)),not(equiv(B,B)))),C)). [resolve(59497,a,27021,a)].
% 124.24/124.61 114219 is_a_theorem(equiv(not(implies(A,A)),not(implies(B,B)))). [resolve(114181,a,54105,a)].
% 124.24/124.61 114317 not(implies(A,A)) = not(implies(B,B)). [resolve(114219,a,61,a)].
% 124.24/124.61 114324 not(implies(A,A)) = c_0. [new_symbol(114317)].
% 124.24/124.61 114325 is_a_theorem(implies(not(equiv(c_0,not(equiv(A,A)))),B)). [back_rewrite(114183),rewrite([114324(2)])].
% 124.24/124.61 114339 is_a_theorem(implies(and(and(A,c_0),not(B)),not(equiv(C,D)))). [back_rewrite(111714),rewrite([114324(2)])].
% 124.24/124.61 114359 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),and(c_0,not(C))),D)). [back_rewrite(109977),rewrite([114324(5)])].
% 124.24/124.61 114772 is_a_theorem(implies(implies(implies(c_0,A),and(not(not(B)),not(C))),B)). [back_rewrite(42275),rewrite([114324(2)])].
% 124.24/124.61 114961 is_a_theorem(implies(and(not(not(c_0)),not(A)),B)). [back_rewrite(24224),rewrite([114324(2)])].
% 124.24/124.61 115134 -is_a_theorem(not(equiv(c_0,A))) | is_a_theorem(and(A,not(c_0))). [back_rewrite(14719),rewrite([114324(2),114324(6)])].
% 124.24/124.61 115139 -is_a_theorem(implies(implies(c_0,A),B)) | is_a_theorem(B). [back_rewrite(14693),rewrite([114324(2)])].
% 124.24/124.61 116504 is_a_theorem(implies(c_0,A)). [back_rewrite(413),rewrite([114324(2)])].
% 124.24/124.61 116642 implies(A,implies(B,B)) = not(and(A,c_0)). [para(114324(a,1),80(a,1,1,2)),flip(a)].
% 124.24/124.61 121680 is_a_theorem(implies(implies(equiv(A,A),and(not(not(c_0)),not(B))),C)). [resolve(114961,a,15064,a)].
% 124.24/124.61 122524 is_a_theorem(equiv(c_0,not(equiv(A,A)))). [resolve(114325,a,54105,a)].
% 124.24/124.61 122621 not(equiv(A,A)) = c_0. [resolve(122524,a,61,a)].
% 124.24/124.61 122673 is_a_theorem(implies(implies(implies(c_0,A),and(c_0,not(B))),C)). [back_rewrite(114359),rewrite([122621(2)])].
% 124.24/124.61 122700 implies(A,equiv(B,B)) = not(and(A,c_0)). [para(122621(a,1),80(a,1,1,2)),flip(a)].
% 124.24/124.61 122739 is_a_theorem(implies(and(implies(not(A),A),not(A)),c_0)). [para(122621(a,1),23525(a,1,2))].
% 124.24/124.61 122740 is_a_theorem(implies(and(A,not(implies(not(A),B))),c_0)). [para(122621(a,1),23554(a,1,2))].
% 124.24/124.61 122746 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),c_0)). [para(122621(a,1),23843(a,1,2))].
% 124.24/124.61 126899 -is_a_theorem(implies(not(and(implies(A,A),c_0)),B)) | is_a_theorem(B). [para(116642(a,1),7701(a,1,1))].
% 124.24/124.61 128970 is_a_theorem(implies(implies(c_0,A),implies(and(implies(not(B),B),not(B)),A))). [resolve(122739,a,130,a)].
% 124.24/124.61 129041 is_a_theorem(implies(implies(c_0,A),implies(and(B,not(implies(not(B),C))),A))). [resolve(122740,a,130,a)].
% 124.24/124.61 137342 is_a_theorem(and(implies(c_0,A),implies(c_0,B))). [resolve(122673,a,258,a)].
% 124.24/124.61 137377 is_a_theorem(implies(not(equiv(not(implies(c_0,A)),c_0)),B)). [resolve(137342,a,59497,a)].
% 124.24/124.61 137560 is_a_theorem(equiv(not(implies(c_0,A)),c_0)). [resolve(137377,a,54105,a)].
% 124.24/124.61 137652 not(implies(c_0,A)) = c_0. [resolve(137560,a,61,a),flip(a)].
% 124.24/124.61 137654 implies(A,implies(c_0,B)) = not(and(A,c_0)). [para(137652(a,1),80(a,1,1,2)),flip(a)].
% 124.24/124.61 138781 is_a_theorem(implies(and(implies(not(and(implies(A,A),c_0)),B),not(B)),c_0)). [para(116642(a,1),122746(a,1,1,1,1))].
% 124.24/124.61 143081 is_a_theorem(implies(and(and(A,c_0),not(B)),c_0)). [para(122621(a,1),114339(a,1,2))].
% 124.24/124.61 143149 is_a_theorem(implies(implies(c_0,A),implies(and(and(B,c_0),not(C)),A))). [resolve(143081,a,130,a)].
% 124.24/124.61 166535 is_a_theorem(implies(not(equiv(c_0,not(not(A)))),A)). [para(257(a,1),114772(a,1,1))].
% 124.24/124.61 166606 is_a_theorem(implies(implies(A,B),implies(not(equiv(c_0,not(not(A)))),B))). [resolve(166535,a,130,a)].
% 124.24/124.61 177563 is_a_theorem(and(equiv(A,A),implies(not(not(c_0)),B))). [resolve(121680,a,258,a)].
% 124.24/124.61 177608 is_a_theorem(implies(not(equiv(c_0,not(not(c_0)))),A)). [resolve(177563,a,59497,a),rewrite([122621(2)])].
% 124.24/124.61 177673 is_a_theorem(equiv(c_0,not(not(c_0)))). [resolve(177608,a,54105,a)].
% 124.24/124.61 177767 not(not(c_0)) = c_0. [resolve(177673,a,61,a)].
% 124.24/124.61 177769 not(and(A,c_0)) = implies(A,not(c_0)). [para(177767(a,1),80(a,1,1,2))].
% 124.24/124.61 177770 is_a_theorem(not(c_0)). [para(177767(a,1),122(a,1,1)),unit_del(a,116504)].
% 124.24/124.61 177778 implies(implies(not(c_0),A),and(A,c_0)) = not(equiv(not(c_0),A)). [para(177767(a,1),257(a,1,2,2))].
% 124.24/124.61 177780 is_a_theorem(implies(A,not(c_0))). [para(177767(a,1),3456(a,1,2,2,1)),rewrite([137654(5),177769(5),116642(6),177769(3)])].
% 124.24/124.61 178471 is_a_theorem(implies(and(implies(implies(implies(A,A),not(c_0)),B),not(B)),c_0)). [back_rewrite(138781),rewrite([177769(4)])].
% 124.24/124.61 178628 implies(A,implies(c_0,B)) = implies(A,not(c_0)). [back_rewrite(137654),rewrite([177769(6)])].
% 124.24/124.61 178949 -is_a_theorem(implies(implies(implies(A,A),not(c_0)),B)) | is_a_theorem(B). [back_rewrite(126899),rewrite([177769(4)])].
% 124.24/124.61 178998 implies(A,equiv(B,B)) = implies(A,not(c_0)). [back_rewrite(122700),rewrite([177769(5)])].
% 124.24/124.61 179416 implies(A,implies(B,B)) = implies(A,not(c_0)). [back_rewrite(116642),rewrite([177769(5)])].
% 124.24/124.61 180011 is_a_theorem(implies(implies(not(c_0),A),implies(B,A))). [resolve(177780,a,20318,a)].
% 124.24/124.61 181014 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(not(c_0),B),C))). [resolve(180011,a,130,a)].
% 124.24/124.61 193054 is_a_theorem(implies(and(and(A,c_0),not(B)),C)). [resolve(143149,a,115139,a)].
% 124.24/124.61 204358 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(equiv(c_0,not(not(A)))),B)). [resolve(166606,a,69,b)].
% 124.24/124.61 219330 is_a_theorem(implies(A,implies(implies(not(c_0),B),B))). [resolve(181014,a,17772,a)].
% 124.24/124.61 219337 is_a_theorem(implies(implies(A,B),implies(implies(not(c_0),A),B))). [resolve(181014,a,13892,a)].
% 124.24/124.61 219361 is_a_theorem(implies(implies(not(c_0),A),A)). [resolve(219330,a,178949,a)].
% 124.24/124.61 219496 -is_a_theorem(implies(not(c_0),A)) | is_a_theorem(A). [resolve(219361,a,69,b)].
% 124.24/124.61 223394 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(c_0),A),B)). [resolve(219337,a,69,b)].
% 124.24/124.61 224888 is_a_theorem(implies(implies(not(c_0),and(and(A,c_0),not(B))),C)). [resolve(223394,a,193054,a)].
% 124.24/124.61 232661 is_a_theorem(and(not(c_0),implies(and(A,c_0),B))). [resolve(224888,a,258,a)].
% 124.24/124.61 232697 is_a_theorem(implies(not(equiv(c_0,and(A,c_0))),B)). [resolve(232661,a,59497,a),rewrite([177767(3)])].
% 124.24/124.61 232766 is_a_theorem(equiv(c_0,and(A,c_0))). [resolve(232697,a,54105,a)].
% 124.24/124.61 232858 and(A,c_0) = c_0. [resolve(232766,a,61,a)].
% 124.24/124.61 232898 implies(implies(not(c_0),A),c_0) = not(equiv(not(c_0),A)). [back_rewrite(177778),rewrite([232858(5)])].
% 124.24/124.61 232899 implies(A,not(c_0)) = not(c_0). [back_rewrite(177769),rewrite([232858(2)]),flip(a)].
% 124.24/124.61 232924 implies(A,implies(B,B)) = not(c_0). [back_rewrite(179416),rewrite([232899(5)])].
% 124.24/124.61 232933 implies(A,equiv(B,B)) = not(c_0). [back_rewrite(178998),rewrite([232899(5)])].
% 124.24/124.61 232952 implies(A,implies(c_0,B)) = not(c_0). [back_rewrite(178628),rewrite([232899(6)])].
% 124.24/124.61 232960 is_a_theorem(implies(and(implies(not(c_0),A),not(A)),c_0)). [back_rewrite(178471),rewrite([232899(4)])].
% 124.24/124.61 232972 and(not(c_0),implies(not(c_0),A)) = equiv(A,not(c_0)). [para(232899(a,1),90(a,1,1))].
% 124.24/124.61 232973 and(implies(not(c_0),A),not(c_0)) = equiv(not(c_0),A). [para(232899(a,1),90(a,1,2))].
% 124.24/124.61 235526 is_a_theorem(implies(implies(c_0,A),implies(and(implies(not(c_0),B),not(B)),A))). [resolve(232960,a,130,a)].
% 124.24/124.61 235997 implies(not(c_0),c_0) = c_0. [para(122621(a,1),232898(a,2)),rewrite([232899(5)])].
% 124.24/124.61 236020 not(equiv(not(c_0),implies(A,A))) = c_0. [para(232924(a,1),232898(a,1,1)),rewrite([235997(4)]),flip(a)].
% 124.24/124.61 236021 not(equiv(not(c_0),equiv(A,A))) = c_0. [para(232933(a,1),232898(a,1,1)),rewrite([235997(4)]),flip(a)].
% 124.24/124.61 236022 not(equiv(not(c_0),implies(c_0,A))) = c_0. [para(232952(a,1),232898(a,1,1)),rewrite([235997(4)]),flip(a)].
% 124.24/124.61 236025 is_a_theorem(implies(implies(not(c_0),A),implies(implies(A,c_0),c_0))). [para(235997(a,1),96(a,1,2,2))].
% 124.24/124.61 236050 is_a_theorem(implies(and(implies(A,c_0),not(c_0)),implies(implies(not(c_0),A),B))). [para(235997(a,1),22503(a,1,1,2,1))].
% 124.24/124.61 236055 is_a_theorem(implies(A,implies(implies(implies(not(A),B),c_0),c_0))). [para(235997(a,1),60335(a,1,2,2))].
% 124.24/124.61 236129 implies(A,equiv(not(c_0),implies(B,B))) = not(c_0). [para(236020(a,1),80(a,1,1,2)),rewrite([232858(2)]),flip(a)].
% 124.24/124.61 236130 is_a_theorem(equiv(not(c_0),implies(A,A))). [para(236020(a,1),122(a,1,1)),rewrite([236129(6)]),unit_del(a,177770)].
% 124.24/124.61 236177 implies(A,A) = not(c_0). [resolve(236130,a,61,a)].
% 124.24/124.61 237227 and(not(c_0),not(c_0)) = equiv(A,A). [para(236177(a,1),90(a,1,1)),rewrite([236177(3)])].
% 124.24/124.61 237228 is_a_theorem(implies(implies(A,B),implies(not(c_0),implies(A,B)))). [para(236177(a,1),96(a,1,2,1))].
% 124.24/124.61 237229 implies(A,and(B,not(B))) = implies(A,c_0). [para(236177(a,1),129(a,1,1,2)),rewrite([80(4)]),flip(a)].
% 124.24/124.61 237273 implies(A,equiv(not(c_0),equiv(B,B))) = not(c_0). [para(236021(a,1),80(a,1,1,2)),rewrite([232858(2)]),flip(a)].
% 124.24/124.61 237274 is_a_theorem(equiv(not(c_0),equiv(A,A))). [para(236021(a,1),122(a,1,1)),rewrite([237273(6)]),unit_del(a,177770)].
% 124.24/124.61 237346 equiv(A,A) = not(c_0). [resolve(237274,a,61,a)].
% 124.24/124.61 237553 and(not(c_0),not(c_0)) = not(c_0). [back_rewrite(237227),rewrite([237346(6)])].
% 124.24/124.61 237597 implies(A,equiv(not(c_0),implies(c_0,B))) = not(c_0). [para(236022(a,1),80(a,1,1,2)),rewrite([232858(2)]),flip(a)].
% 124.24/124.61 237598 is_a_theorem(equiv(not(c_0),implies(c_0,A))). [para(236022(a,1),122(a,1,1)),rewrite([237597(7)]),unit_del(a,177770)].
% 124.24/124.61 237749 implies(c_0,A) = not(c_0). [resolve(237598,a,61,a)].
% 124.24/124.61 237973 is_a_theorem(implies(not(c_0),implies(and(implies(not(c_0),A),not(A)),B))). [back_rewrite(235526),rewrite([237749(2)])].
% 124.24/124.61 237976 is_a_theorem(implies(not(c_0),implies(and(A,not(implies(not(A),B))),C))). [back_rewrite(129041),rewrite([237749(2)])].
% 124.24/124.61 237977 is_a_theorem(implies(not(c_0),implies(and(implies(not(A),A),not(A)),B))). [back_rewrite(128970),rewrite([237749(2)])].
% 124.24/124.61 237981 and(implies(A,c_0),not(c_0)) = equiv(A,c_0). [para(237749(a,1),90(a,1,2))].
% 124.24/124.61 237982 is_a_theorem(implies(implies(A,c_0),implies(not(c_0),implies(A,B)))). [para(237749(a,1),96(a,1,2,1))].
% 124.24/124.61 237983 implies(A,and(c_0,not(B))) = implies(A,c_0). [para(237749(a,1),129(a,1,1,2)),rewrite([80(4)]),flip(a)].
% 124.24/124.61 237985 implies(not(c_0),and(A,not(c_0))) = not(equiv(c_0,A)). [para(237749(a,1),257(a,1,1))].
% 124.24/124.61 238030 is_a_theorem(implies(and(A,not(c_0)),implies(not(equiv(not(A),c_0)),B))). [para(237749(a,1),26631(a,1,1,2))].
% 124.24/124.61 238069 is_a_theorem(implies(equiv(A,c_0),implies(implies(not(c_0),A),B))). [back_rewrite(236050),rewrite([237981(5)])].
% 124.24/124.61 238078 implies(implies(A,c_0),and(and(B,not(B)),not(A))) = not(equiv(A,and(B,not(B)))). [para(237229(a,1),257(a,1,1))].
% 124.24/124.61 238103 implies(and(A,not(A)),c_0) = not(c_0). [para(237229(a,1),236177(a,1))].
% 124.24/124.61 238522 equiv(and(A,not(A)),c_0) = not(c_0). [para(238103(a,1),90(a,1,1)),rewrite([237229(6),236177(5),237553(5)]),flip(a)].
% 124.24/124.61 238546 and(A,not(A)) = c_0. [para(238522(a,1),61(a,1)),flip(b),unit_del(a,177770)].
% 124.24/124.61 238550 implies(implies(A,c_0),c_0) = not(equiv(A,c_0)). [back_rewrite(238078),rewrite([238546(4),237983(6),238546(6)])].
% 124.24/124.61 238562 is_a_theorem(implies(A,not(equiv(implies(not(A),B),c_0)))). [back_rewrite(236055),rewrite([238550(6)])].
% 124.24/124.61 238573 is_a_theorem(implies(implies(not(c_0),A),not(equiv(A,c_0)))). [back_rewrite(236025),rewrite([238550(7)])].
% 124.24/124.61 239030 is_a_theorem(implies(implies(A,implies(B,c_0)),implies(not(equiv(B,c_0)),implies(A,c_0)))). [para(238550(a,1),96(a,1,2,1))].
% 124.24/124.61 239167 is_a_theorem(implies(A,implies(not(equiv(not(A),c_0)),implies(B,c_0)))). [para(238550(a,1),60335(a,1,2,1))].
% 124.24/124.61 239976 -is_a_theorem(implies(not(c_0),A)) | is_a_theorem(not(equiv(A,c_0))). [resolve(238573,a,69,b)].
% 124.24/124.61 240533 is_a_theorem(not(equiv(implies(A,implies(B,implies(not(A),C))),c_0))). [resolve(239976,a,65081,a)].
% 124.24/124.61 240640 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(c_0),implies(A,B))). [resolve(237228,a,69,b)].
% 124.24/124.61 240898 is_a_theorem(implies(not(c_0),implies(equiv(A,c_0),implies(implies(not(c_0),A),B)))). [resolve(240640,a,238069,a)].
% 124.24/124.61 244407 is_a_theorem(implies(A,implies(not(equiv(not(A),c_0)),c_0))). [para(235997(a,1),239167(a,1,2,2))].
% 124.24/124.61 244470 -is_a_theorem(A) | is_a_theorem(implies(not(equiv(not(A),c_0)),c_0)). [resolve(244407,a,69,b)].
% 124.24/124.61 246860 is_a_theorem(implies(and(implies(not(c_0),A),not(A)),B)). [resolve(237973,a,219496,a)].
% 124.24/124.61 246891 is_a_theorem(implies(not(equiv(c_0,not(implies(implies(not(c_0),A),A)))),B)). [resolve(246860,a,204358,a),rewrite([80(7)])].
% 124.24/124.61 246944 is_a_theorem(implies(and(A,not(implies(not(A),B))),C)). [resolve(237976,a,219496,a)].
% 124.24/124.61 246962 is_a_theorem(implies(not(equiv(c_0,not(implies(A,implies(not(A),B))))),C)). [resolve(246944,a,204358,a),rewrite([80(6)])].
% 124.24/124.61 246994 is_a_theorem(implies(and(implies(not(A),A),not(A)),B)). [resolve(237977,a,219496,a)].
% 124.24/124.61 247001 is_a_theorem(implies(implies(not(c_0),and(implies(not(A),A),not(A))),B)). [resolve(246994,a,223394,a)].
% 124.24/124.61 247621 is_a_theorem(equiv(c_0,not(implies(implies(not(c_0),A),A)))). [resolve(246891,a,54105,a)].
% 124.24/124.61 247626 not(implies(implies(not(c_0),A),A)) = c_0. [resolve(247621,a,61,a)].
% 124.24/124.61 247628 implies(A,implies(implies(not(c_0),B),B)) = not(c_0). [para(247626(a,1),80(a,1,1,2)),rewrite([232858(2)]),flip(a)].
% 124.24/124.61 247639 equiv(implies(implies(not(c_0),A),A),not(c_0)) = not(c_0). [para(247628(a,1),232972(a,1,2)),rewrite([237553(5)]),flip(a)].
% 124.24/124.61 247661 implies(implies(not(c_0),A),A) = not(c_0). [para(247639(a,1),61(a,1)),flip(b),unit_del(a,177770)].
% 124.24/124.61 247664 and(implies(A,implies(not(c_0),A)),not(c_0)) = equiv(A,implies(not(c_0),A)). [para(247661(a,1),90(a,1,2))].
% 124.24/124.61 247818 is_a_theorem(equiv(c_0,not(implies(A,implies(not(A),B))))). [resolve(246962,a,54105,a)].
% 124.24/124.61 247827 not(implies(A,implies(not(A),B))) = c_0. [resolve(247818,a,61,a)].
% 124.24/124.61 247893 implies(A,implies(B,implies(not(B),C))) = not(c_0). [para(247827(a,1),80(a,1,1,2)),rewrite([232858(2)]),flip(a)].
% 124.24/124.61 247909 equiv(implies(A,implies(not(A),B)),not(c_0)) = not(c_0). [para(247893(a,1),232972(a,1,2)),rewrite([237553(5)]),flip(a)].
% 124.24/124.61 247915 implies(A,implies(not(A),B)) = not(c_0). [para(247909(a,1),61(a,1)),flip(b),unit_del(a,177770)].
% 124.24/124.61 247918 and(not(c_0),implies(implies(not(A),B),A)) = equiv(A,implies(not(A),B)). [para(247915(a,1),90(a,1,1))].
% 124.24/124.61 247919 and(implies(implies(not(A),B),A),not(c_0)) = equiv(implies(not(A),B),A). [para(247915(a,1),90(a,1,2))].
% 124.24/124.61 248039 is_a_theorem(equiv(A,implies(not(A),A))). [resolve(247001,a,258,a),rewrite([247918(6)])].
% 124.24/124.61 248075 implies(not(A),A) = A. [resolve(248039,a,61,a)].
% 124.24/124.61 248298 is_a_theorem(implies(A,implies(implies(A,B),implies(C,B)))). [para(248075(a,1),60335(a,1,2,1,1))].
% 124.24/124.61 248421 is_a_theorem(implies(A,not(equiv(A,c_0)))). [para(248075(a,1),238562(a,1,2,1,1))].
% 124.24/124.61 248425 is_a_theorem(implies(implies(not(A),c_0),implies(not(c_0),A))). [para(248075(a,1),237982(a,1,2,2))].
% 124.24/124.61 248432 is_a_theorem(not(equiv(implies(A,implies(B,A)),c_0))). [para(248075(a,1),240533(a,1,1,1,2,2))].
% 124.24/124.61 248476 is_a_theorem(implies(and(A,not(c_0)),equiv(not(A),c_0))). [para(248075(a,1),238030(a,1,2))].
% 124.24/124.61 249713 -is_a_theorem(A) | is_a_theorem(not(equiv(A,c_0))). [resolve(248421,a,69,b)].
% 124.24/124.61 249758 is_a_theorem(not(equiv(implies(A,not(equiv(A,c_0))),c_0))). [resolve(249713,a,248421,a)].
% 124.24/124.61 251863 is_a_theorem(implies(A,implies(implies(A,B),B))). [para(248075(a,1),248298(a,1,2,2))].
% 124.24/124.61 251912 is_a_theorem(implies(implies(implies(implies(A,B),B),C),implies(A,C))). [resolve(251863,a,130,a)].
% 124.24/124.61 252605 is_a_theorem(not(equiv(implies(implies(not(A),c_0),implies(not(c_0),A)),c_0))). [resolve(248425,a,249713,a)].
% 124.24/124.61 252707 is_a_theorem(implies(not(equiv(A,c_0)),not(equiv(c_0,A)))). [para(237985(a,1),248425(a,1,2)),rewrite([80(4),238550(4)])].
% 124.24/124.61 252820 -is_a_theorem(and(A,not(c_0))) | is_a_theorem(equiv(not(A),c_0)). [resolve(248476,a,69,b)].
% 124.24/124.61 253494 -is_a_theorem(not(equiv(A,c_0))) | is_a_theorem(not(equiv(c_0,A))). [resolve(252707,a,69,b)].
% 124.24/124.61 253761 is_a_theorem(not(equiv(c_0,implies(A,not(equiv(A,c_0)))))). [resolve(253494,a,249758,a)].
% 124.24/124.61 253762 is_a_theorem(not(equiv(c_0,implies(A,implies(B,A))))). [resolve(253494,a,248432,a)].
% 124.24/124.61 253805 is_a_theorem(and(implies(A,implies(B,A)),not(c_0))). [resolve(253762,a,115134,a)].
% 124.24/124.61 253822 is_a_theorem(equiv(not(implies(A,implies(B,A))),c_0)). [resolve(253805,a,252820,a)].
% 124.24/124.61 253877 not(implies(A,implies(B,A))) = c_0. [resolve(253822,a,61,a),flip(a)].
% 124.24/124.61 253899 implies(A,implies(B,implies(C,B))) = not(c_0). [para(253877(a,1),80(a,1,1,2)),rewrite([232858(2)]),flip(a)].
% 124.24/124.61 253902 implies(A,implies(B,A)) = not(c_0). [para(253877(a,1),248075(a,1,1)),rewrite([253899(4)]),flip(a)].
% 124.24/124.61 253904 equiv(A,implies(not(c_0),A)) = not(c_0). [back_rewrite(247664),rewrite([253902(4),237553(5)]),flip(a)].
% 124.24/124.61 253929 implies(not(c_0),A) = A. [para(253904(a,1),61(a,1)),unit_del(a,177770)].
% 124.24/124.61 253954 is_a_theorem(not(equiv(implies(implies(not(A),c_0),A),c_0))). [back_rewrite(252605),rewrite([253929(6)])].
% 124.24/124.61 254021 is_a_theorem(implies(equiv(A,c_0),implies(A,B))). [back_rewrite(240898),rewrite([253929(7),253929(7)])].
% 124.24/124.61 254075 not(equiv(c_0,A)) = and(A,not(c_0)). [back_rewrite(237985),rewrite([253929(6)]),flip(a)].
% 124.24/124.61 254081 equiv(not(c_0),A) = and(A,not(c_0)). [back_rewrite(232973),rewrite([253929(3)]),flip(a)].
% 124.24/124.61 254094 is_a_theorem(and(implies(A,not(equiv(A,c_0))),not(c_0))). [back_rewrite(253761),rewrite([254075(7)])].
% 124.24/124.61 254101 -is_a_theorem(not(equiv(A,c_0))) | is_a_theorem(and(A,not(c_0))). [back_rewrite(253494),rewrite([254075(7)])].
% 124.24/124.61 255729 is_a_theorem(implies(equiv(not(A),c_0),A)). [para(248075(a,1),254021(a,1,2))].
% 124.24/124.61 255740 is_a_theorem(implies(not(equiv(not(implies(equiv(not(A),c_0),A)),c_0)),c_0)). [resolve(255729,a,244470,a)].
% 124.24/124.61 256685 not(and(A,and(B,not(c_0)))) = implies(A,equiv(c_0,B)). [para(254075(a,1),80(a,1,1,2))].
% 124.24/124.61 257014 -is_a_theorem(and(A,not(c_0))) | not(c_0) = A. [para(254081(a,1),61(a,1)),flip(b)].
% 124.24/124.61 259760 implies(A,not(equiv(A,c_0))) = not(c_0). [resolve(254094,a,257014,a),flip(a)].
% 124.24/124.61 259764 and(implies(not(equiv(A,c_0)),A),not(c_0)) = equiv(not(equiv(A,c_0)),A). [para(259760(a,1),90(a,1,2))].
% 124.24/124.61 260116 is_a_theorem(equiv(implies(not(A),c_0),A)). [resolve(254101,a,253954,a),rewrite([247919(7)])].
% 124.24/124.61 260155 implies(not(A),c_0) = A. [resolve(260116,a,61,a),flip(a)].
% 124.24/124.61 260202 is_a_theorem(equiv(not(implies(equiv(not(A),c_0),A)),c_0)). [back_rewrite(255740),rewrite([260155(10)])].
% 124.24/124.61 260307 implies(implies(A,B),c_0) = and(A,not(B)). [para(80(a,1),260155(a,1,1))].
% 124.24/124.61 260308 equiv(not(A),c_0) = and(A,not(c_0)). [para(260155(a,1),90(a,1,1)),rewrite([237749(3)]),flip(a)].
% 124.24/124.61 260312 implies(A,and(not(B),not(c_0))) = not(and(A,B)). [para(260155(a,1),129(a,1,1,2)),flip(a)].
% 124.24/124.61 260357 implies(and(A,not(c_0)),c_0) = equiv(c_0,A). [para(254075(a,1),260155(a,1,1))].
% 124.24/124.61 260420 not(equiv(A,c_0)) = and(A,not(c_0)). [back_rewrite(238550),rewrite([260307(4)]),flip(a)].
% 124.24/124.61 260547 is_a_theorem(and(implies(and(A,not(c_0)),A),not(c_0))). [back_rewrite(260202),rewrite([260308(3),260308(7)])].
% 124.24/124.61 261833 and(implies(and(A,not(c_0)),A),not(c_0)) = equiv(and(A,not(c_0)),A). [back_rewrite(259764),rewrite([260420(3),260420(10)])].
% 124.24/124.61 262275 is_a_theorem(implies(implies(A,implies(B,c_0)),implies(and(B,not(c_0)),implies(A,c_0)))). [back_rewrite(239030),rewrite([260420(6)])].
% 124.24/124.61 262289 is_a_theorem(equiv(and(A,not(c_0)),A)). [back_rewrite(260547),rewrite([261833(7)])].
% 124.24/124.61 263248 and(A,not(c_0)) = A. [resolve(262289,a,61,a),flip(a)].
% 124.24/124.61 263263 is_a_theorem(implies(implies(A,implies(B,c_0)),implies(B,implies(A,c_0)))). [back_rewrite(262275),rewrite([263248(6)])].
% 124.24/124.61 263387 equiv(c_0,A) = implies(A,c_0). [back_rewrite(260357),rewrite([263248(3)]),flip(a)].
% 124.24/124.61 263397 not(and(A,B)) = implies(A,not(B)). [back_rewrite(260312),rewrite([263248(4)]),flip(a)].
% 124.24/124.61 263619 implies(A,implies(B,c_0)) = implies(A,not(B)). [back_rewrite(256685),rewrite([263248(3),263397(2),263387(4)]),flip(a)].
% 124.24/124.61 263675 equiv(not(c_0),A) = A. [back_rewrite(254081),rewrite([263248(6)])].
% 124.24/124.61 263676 not(implies(A,c_0)) = A. [back_rewrite(254075),rewrite([263387(2),263248(6)])].
% 124.24/124.61 264170 is_a_theorem(implies(implies(A,not(B)),implies(B,not(A)))). [back_rewrite(263263),rewrite([263619(3),263619(5)])].
% 124.24/124.61 266301 implies(A,c_0) = not(A). [para(263675(a,1),257(a,2,1)),rewrite([253929(3),177767(3),232858(2)])].
% 124.24/124.61 266355 not(not(A)) = A. [back_rewrite(263676),rewrite([266301(2)])].
% 124.24/124.61 268767 is_a_theorem(implies(implies(not(A),not(B)),implies(B,A))). [para(266355(a,1),264170(a,1,2,2))].
% 124.24/124.61 270510 is_a_theorem(implies(implies(implies(A,not(B)),not(C)),implies(C,and(A,B)))). [para(263397(a,1),268767(a,1,1,1))].
% 124.24/124.61 275323 -is_a_theorem(implies(implies(implies(c18,A),A),implies(c19,and(c18,c19)))). [ur(69,b,251912,a,c,71,a)].
% 124.24/124.61 275324 $F. [resolve(275323,a,270510,a)].
% 124.24/124.61
% 124.24/124.61 % SZS output end Refutation
% 124.24/124.61 ============================== end of proof ==========================
% 124.24/124.61
% 124.24/124.61 ============================== STATISTICS ============================
% 124.24/124.61
% 124.24/124.61 Given=9536. Generated=14338205. Kept=275273. proofs=1.
% 124.24/124.61 Usable=567. Sos=6678. Demods=510. Limbo=50, Disabled=268049. Hints=0.
% 124.24/124.61 Megabytes=188.15.
% 124.24/124.61 User_CPU=116.25, System_CPU=7.36, Wall_clock=124.
% 124.24/124.61
% 124.24/124.61 ============================== end of statistics =====================
% 124.24/124.61
% 124.24/124.61 ============================== end of search =========================
% 124.24/124.61
% 124.24/124.61 THEOREM PROVED
% 124.24/124.61 % SZS status Theorem
% 124.24/124.61
% 124.24/124.61 Exiting with 1 proof.
% 124.24/124.61
% 124.24/124.61 Process 25579 exit (max_proofs) Mon Jul 4 05:09:12 2022
% 124.24/124.61 Prover9 interrupted
%------------------------------------------------------------------------------