TSTP Solution File: LCL467+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL467+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 119.40s 119.68s
% Output : Refutation 119.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : LCL467+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.36 % Computer : n021.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jul 4 09:29:31 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.49/1.05 ============================== Prover9 ===============================
% 0.49/1.05 Prover9 (32) version 2009-11A, November 2009.
% 0.49/1.05 Process 14860 was started by sandbox2 on n021.cluster.edu,
% 0.49/1.05 Mon Jul 4 09:29:32 2022
% 0.49/1.05 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_14705_n021.cluster.edu".
% 0.49/1.05 ============================== end of head ===========================
% 0.49/1.05
% 0.49/1.05 ============================== INPUT =================================
% 0.49/1.05
% 0.49/1.05 % Reading from file /tmp/Prover9_14705_n021.cluster.edu
% 0.49/1.05
% 0.49/1.05 set(prolog_style_variables).
% 0.49/1.05 set(auto2).
% 0.49/1.05 % set(auto2) -> set(auto).
% 0.49/1.05 % set(auto) -> set(auto_inference).
% 0.49/1.05 % set(auto) -> set(auto_setup).
% 0.49/1.05 % set(auto_setup) -> set(predicate_elim).
% 0.49/1.05 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.49/1.05 % set(auto) -> set(auto_limits).
% 0.49/1.05 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.49/1.05 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.49/1.05 % set(auto) -> set(auto_denials).
% 0.49/1.05 % set(auto) -> set(auto_process).
% 0.49/1.05 % set(auto2) -> assign(new_constants, 1).
% 0.49/1.05 % set(auto2) -> assign(fold_denial_max, 3).
% 0.49/1.05 % set(auto2) -> assign(max_weight, "200.000").
% 0.49/1.05 % set(auto2) -> assign(max_hours, 1).
% 0.49/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.49/1.05 % set(auto2) -> assign(max_seconds, 0).
% 0.49/1.05 % set(auto2) -> assign(max_minutes, 5).
% 0.49/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.49/1.05 % set(auto2) -> set(sort_initial_sos).
% 0.49/1.05 % set(auto2) -> assign(sos_limit, -1).
% 0.49/1.05 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.49/1.05 % set(auto2) -> assign(max_megs, 400).
% 0.49/1.05 % set(auto2) -> assign(stats, some).
% 0.49/1.05 % set(auto2) -> clear(echo_input).
% 0.49/1.05 % set(auto2) -> set(quiet).
% 0.49/1.05 % set(auto2) -> clear(print_initial_clauses).
% 0.49/1.05 % set(auto2) -> clear(print_given).
% 0.49/1.05 assign(lrs_ticks,-1).
% 0.49/1.05 assign(sos_limit,10000).
% 0.49/1.05 assign(order,kbo).
% 0.49/1.05 set(lex_order_vars).
% 0.49/1.05 clear(print_given).
% 0.49/1.05
% 0.49/1.05 % formulas(sos). % not echoed (43 formulas)
% 0.49/1.05
% 0.49/1.05 ============================== end of input ==========================
% 0.49/1.05
% 0.49/1.05 % From the command line: assign(max_seconds, 300).
% 0.49/1.05
% 0.49/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.49/1.05
% 0.49/1.05 % Formulas that are not ordinary clauses:
% 0.49/1.05 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].
% 0.49/1.05 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].
% 0.49/1.05 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].
% 0.49/1.05 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.05 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].
% 0.49/1.05 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].
% 0.49/1.05 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.05 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.05 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].
% 0.49/1.05 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.05 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.49/1.05 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].
% 0.49/1.05 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].
% 0.49/1.05 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].
% 1.27/1.54 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].
% 1.27/1.54 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.54 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.54 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].
% 1.27/1.54 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].
% 1.27/1.54 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.54 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.54 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.54 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.54 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.54 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].
% 1.27/1.54 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].
% 1.27/1.54 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].
% 1.27/1.54 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].
% 1.27/1.54 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].
% 1.27/1.54 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].
% 1.27/1.54 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].
% 1.27/1.54
% 1.27/1.54 ============================== end of process non-clausal formulas ===
% 1.27/1.54
% 1.27/1.54 ============================== PROCESS INITIAL CLAUSES ===============
% 1.27/1.54
% 1.27/1.54 ============================== PREDICATE ELIMINATION =================
% 1.27/1.54
% 1.27/1.54 ============================== end predicate elimination =============
% 1.27/1.54
% 1.27/1.54 Auto_denials: (non-Horn, no changes).
% 1.27/1.54
% 1.27/1.54 Term ordering decisions:
% 1.27/1.54
% 1.27/1.54 % Assigning unary symbol not kb_weight 0 and highest precedence (94).
% 1.27/1.54 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.
% 1.27/1.54
% 1.27/1.54 ============================== end of process initial clauses ========
% 1.27/1.54
% 1.27/1.54 ============================== CLAUSES FOR SEARCH ====================
% 1.27/1.54
% 1.27/1.54 ============================== end of clauses for search =============
% 1.27/1.54
% 1.27/1.54 ============================== SEARCH ================================
% 1.27/1.54
% 1.27/1.54 % Starting search at 0.02 seconds.
% 1.27/1.54
% 1.27/1.54 Low Water (keep): wt=43.000, iters=3397
% 1.27/1.54
% 1.27/1.54 Low Water (keep): wt=34.000, iters=3348
% 1.27/1.54
% 1.27/1.54 Low Water (keep): wt=31.000, iters=3345
% 1.27/1.54
% 1.27/1.54 Low Water (keep): wt=30.000, iters=3345
% 1.27/1.54
% 1.27/1.54 Low Water (keep): wt=29.000, iters=3348
% 1.27/1.54
% 1.27/1.54 Low Water (keep): wt=27.000, iters=3389
% 1.27/1.54
% 1.27/1.54 Low Water (keep): wt=25.000, iters=3346
% 1.27/1.54
% 1.27/1.54 Low Water (keep): wt=24.000, iters=3382
% 1.27/1.54
% 1.27/1.54 Low Water (keep): wt=23.000, iters=3359
% 1.27/1.54
% 1.27/1.54 Low Water (keep): wt=22.000, iters=3335
% 119.40/119.68
% 119.40/119.68 Low Water (keep): wt=21.000, iters=3349
% 119.40/119.68
% 119.40/119.68 Low Water (keep): wt=20.000, iters=3345
% 119.40/119.68
% 119.40/119.68 Low Water (keep): wt=19.000, iters=3367
% 119.40/119.68
% 119.40/119.68 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 80 (0.00 of 1.27 sec).
% 119.40/119.68
% 119.40/119.68 Low Water (displace): id=1673, wt=111.000
% 119.40/119.68
% 119.40/119.68 Low Water (displace): id=2040, wt=103.000
% 119.40/119.68
% 119.40/119.68 Low Water (displace): id=3155, wt=83.000
% 119.40/119.68
% 119.40/119.68 Low Water (displace): id=3594, wt=79.000
% 119.40/119.68
% 119.40/119.68 Low Water (displace): id=1526, wt=75.000
% 119.40/119.68
% 119.40/119.68 Low Water (displace): id=1528, wt=55.000
% 119.40/119.68
% 119.40/119.68 Low Water (displace): id=9470, wt=45.000
% 119.40/119.68
% 119.40/119.68 Low Water (displace): id=9163, wt=43.000
% 119.40/119.68
% 119.40/119.68 Low Water (displace): id=9162, wt=42.000
% 119.40/119.68
% 119.40/119.68 Low Water (displace): id=9474, wt=41.000
% 119.40/119.68
% 119.40/119.68 Low Water (displace): id=7186, wt=39.000
% 119.40/119.68
% 119.40/119.68 Low Water (displace): id=7184, wt=38.000
% 119.40/119.68
% 119.40/119.68 Low Water (displace): id=9478, wt=37.000
% 119.40/119.68
% 119.40/119.68 Low Water (displace): id=10494, wt=35.000
% 119.40/119.68
% 119.40/119.68 Low Water (displace): id=9157, wt=34.000
% 119.40/119.68
% 119.40/119.68 Low Water (displace): id=10690, wt=33.000
% 119.40/119.68
% 119.40/119.68 Low Water (displace): id=10913, wt=18.000
% 119.40/119.68
% 119.40/119.68 Low Water (keep): wt=18.000, iters=3407
% 119.40/119.68
% 119.40/119.68 Low Water (displace): id=11512, wt=16.000
% 119.40/119.68
% 119.40/119.68 Low Water (displace): id=12000, wt=15.000
% 119.40/119.68
% 119.40/119.68 Low Water (keep): wt=17.000, iters=3339
% 119.40/119.68
% 119.40/119.68 Low Water (displace): id=13392, wt=14.000
% 119.40/119.68
% 119.40/119.68 Low Water (displace): id=13398, wt=13.000
% 119.40/119.68
% 119.40/119.68 Low Water (keep): wt=16.000, iters=3337
% 119.40/119.68
% 119.40/119.68 Low Water (keep): wt=15.000, iters=3943
% 119.40/119.68
% 119.40/119.68 Low Water (keep): wt=14.000, iters=3345
% 119.40/119.68
% 119.40/119.68 Low Water (displace): id=117700, wt=12.000
% 119.40/119.68
% 119.40/119.68 Low Water (displace): id=117956, wt=11.000
% 119.40/119.68
% 119.40/119.68 Low Water (displace): id=118411, wt=10.000
% 119.40/119.68
% 119.40/119.68 Low Water (keep): wt=13.000, iters=3334
% 119.40/119.68
% 119.40/119.68 ============================== PROOF =================================
% 119.40/119.68 % SZS status Theorem
% 119.40/119.68 % SZS output start Refutation
% 119.40/119.68
% 119.40/119.68 % Proof 1 at 111.30 (+ 7.34) seconds.
% 119.40/119.68 % Length of proof is 347.
% 119.40/119.68 % Level of proof is 98.
% 119.40/119.68 % Maximum clause weight is 19.000.
% 119.40/119.68 % Given clauses 8697.
% 119.40/119.68
% 119.40/119.68 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].
% 119.40/119.68 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].
% 119.40/119.68 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 119.40/119.68 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].
% 119.40/119.68 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 119.40/119.68 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 119.40/119.68 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].
% 119.40/119.68 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].
% 119.40/119.68 34 op_equiv # label(luka_op_equiv) # label(axiom). [assumption].
% 119.40/119.68 35 modus_ponens # label(luka_modus_ponens) # label(axiom). [assumption].
% 119.40/119.68 36 cn1 # label(luka_cn1) # label(axiom). [assumption].
% 119.40/119.68 37 cn2 # label(luka_cn2) # label(axiom). [assumption].
% 119.40/119.68 38 cn3 # label(luka_cn3) # label(axiom). [assumption].
% 119.40/119.68 39 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption].
% 119.40/119.68 40 op_implies_and # label(hilbert_op_implies_and) # label(axiom). [assumption].
% 119.40/119.68 41 -and_2 # label(hilbert_and_2) # label(negated_conjecture). [assumption].
% 119.40/119.68 46 and_2 | -is_a_theorem(implies(and(c16,c17),c17)) # label(and_2) # label(axiom). [clausify(8)].
% 119.40/119.68 47 -is_a_theorem(implies(and(c16,c17),c17)). [copy(46),unit_del(a,41)].
% 119.40/119.68 60 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(2)].
% 119.40/119.68 61 -is_a_theorem(equiv(A,B)) | B = A. [copy(60),unit_del(a,39)].
% 119.40/119.68 62 -cn2 | is_a_theorem(implies(A,implies(not(A),B))) # label(cn2) # label(axiom). [clausify(20)].
% 119.40/119.68 63 is_a_theorem(implies(A,implies(not(A),B))). [copy(62),unit_del(a,37)].
% 119.40/119.68 65 -cn3 | is_a_theorem(implies(implies(not(A),A),A)) # label(cn3) # label(axiom). [clausify(21)].
% 119.40/119.68 66 is_a_theorem(implies(implies(not(A),A),A)). [copy(65),unit_del(a,38)].
% 119.40/119.68 68 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 119.40/119.68 69 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(68),unit_del(a,35)].
% 119.40/119.68 79 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 119.40/119.68 80 not(and(A,not(B))) = implies(A,B). [copy(79),unit_del(a,40)].
% 119.40/119.68 89 -op_equiv | and(implies(A,B),implies(B,A)) = equiv(A,B) # label(op_equiv) # label(axiom). [clausify(31)].
% 119.40/119.68 90 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(89),unit_del(a,34)].
% 119.40/119.68 95 -cn1 | is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))) # label(cn1) # label(axiom). [clausify(19)].
% 119.40/119.68 96 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))). [copy(95),unit_del(a,36)].
% 119.40/119.68 122 -is_a_theorem(implies(not(A),A)) | is_a_theorem(A). [resolve(69,b,66,a)].
% 119.40/119.68 123 -is_a_theorem(A) | is_a_theorem(implies(not(A),B)). [resolve(69,b,63,a)].
% 119.40/119.68 127 is_a_theorem(implies(and(A,not(B)),implies(implies(A,B),C))). [para(80(a,1),63(a,1,2,1))].
% 119.40/119.68 128 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))].
% 119.40/119.68 129 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(80(a,1),80(a,1,1,2))].
% 119.40/119.68 130 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(B,C),implies(A,C))). [resolve(96,a,69,b)].
% 119.40/119.68 226 is_a_theorem(implies(implies(implies(implies(A,B),C),D),implies(and(A,not(B)),D))). [resolve(130,a,127,a)].
% 119.40/119.68 227 is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))). [resolve(130,a,96,a)].
% 119.40/119.68 228 is_a_theorem(implies(implies(A,B),implies(implies(not(A),A),B))). [resolve(130,a,66,a)].
% 119.40/119.68 229 is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C))). [resolve(130,a,63,a)].
% 119.40/119.68 230 is_a_theorem(implies(implies(implies(implies(not(A),A),B),C),implies(implies(A,B),C))). [resolve(228,a,130,a)].
% 119.40/119.68 232 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(A),A),B)). [resolve(228,a,69,b)].
% 119.40/119.68 242 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(not(A),D),B),C))). [resolve(229,a,130,a)].
% 119.40/119.68 244 -is_a_theorem(implies(implies(not(A),B),C)) | is_a_theorem(implies(A,C)). [resolve(229,a,69,b)].
% 119.40/119.68 257 implies(implies(A,B),and(B,not(A))) = not(equiv(A,B)). [para(90(a,1),129(a,1,1)),flip(a)].
% 119.40/119.68 258 -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))].
% 119.40/119.68 346 is_a_theorem(implies(A,implies(implies(B,C),implies(not(A),C)))). [resolve(244,a,96,a)].
% 119.40/119.68 347 is_a_theorem(implies(A,A)). [resolve(244,a,66,a)].
% 119.40/119.68 349 -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))].
% 119.40/119.68 413 is_a_theorem(implies(not(implies(A,A)),B)). [resolve(347,a,123,a)].
% 119.40/119.68 433 is_a_theorem(implies(implies(A,B),implies(not(implies(C,C)),B))). [resolve(413,a,130,a)].
% 119.40/119.68 610 is_a_theorem(implies(implies(not(A),A),implies(implies(B,C),implies(not(A),C)))). [resolve(346,a,232,a)].
% 119.40/119.68 611 is_a_theorem(implies(implies(implies(implies(A,B),implies(not(C),B)),D),implies(C,D))). [resolve(346,a,130,a)].
% 119.40/119.68 639 is_a_theorem(implies(A,implies(not(implies(B,B)),C))). [resolve(433,a,244,a)].
% 119.40/119.68 754 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),implies(D,C))). [resolve(639,a,130,a)].
% 119.40/119.68 1024 is_a_theorem(implies(not(equiv(A,A)),and(A,not(A)))). [para(257(a,1),128(a,1,1))].
% 119.40/119.68 1204 is_a_theorem(implies(implies(and(A,not(A)),B),implies(not(equiv(A,A)),B))). [resolve(1024,a,130,a)].
% 119.40/119.68 2277 -is_a_theorem(implies(implies(not(implies(A,A)),B),C)) | is_a_theorem(implies(D,C)). [resolve(754,a,69,b)].
% 119.40/119.68 3016 is_a_theorem(implies(A,implies(B,B))). [resolve(2277,a,66,a)].
% 119.40/119.68 3023 is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))). [resolve(3016,a,130,a)].
% 119.40/119.68 3367 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(D,D),B),C))). [resolve(3023,a,130,a)].
% 119.40/119.68 3369 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(implies(C,B)). [resolve(3023,a,69,b)].
% 119.40/119.68 3440 is_a_theorem(implies(A,implies(B,implies(C,C)))). [resolve(3369,a,3023,a)].
% 119.40/119.68 3442 is_a_theorem(implies(A,implies(B,implies(not(B),C)))). [resolve(3369,a,229,a)].
% 119.40/119.68 3443 is_a_theorem(implies(A,implies(implies(not(B),B),B))). [resolve(3369,a,228,a)].
% 119.40/119.68 3449 is_a_theorem(implies(implies(implies(A,implies(B,B)),C),implies(D,C))). [resolve(3440,a,130,a)].
% 119.40/119.68 3523 is_a_theorem(implies(implies(implies(A,implies(not(A),B)),C),implies(D,C))). [resolve(3442,a,130,a)].
% 119.40/119.68 3819 is_a_theorem(implies(implies(implies(implies(not(A),A),A),B),implies(C,B))). [resolve(3443,a,130,a)].
% 119.40/119.68 5382 -is_a_theorem(implies(implies(implies(not(A),A),A),B)) | is_a_theorem(implies(C,B)). [resolve(3819,a,69,b)].
% 119.40/119.68 6232 -is_a_theorem(implies(not(A),A)) | is_a_theorem(implies(implies(B,C),implies(not(A),C))). [resolve(610,a,69,b)].
% 119.40/119.68 6964 -is_a_theorem(implies(and(A,not(A)),B)) | is_a_theorem(implies(not(equiv(A,A)),B)). [resolve(1204,a,69,b)].
% 119.40/119.68 7352 is_a_theorem(implies(A,implies(implies(implies(B,B),C),C))). [resolve(3367,a,5382,a)].
% 119.40/119.68 7362 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(implies(D,D),B),C)). [resolve(3367,a,69,b)].
% 119.40/119.68 7416 is_a_theorem(implies(implies(implies(implies(implies(A,A),B),B),C),implies(D,C))). [resolve(7352,a,130,a)].
% 119.40/119.68 7418 is_a_theorem(implies(implies(implies(A,A),B),B)). [resolve(7352,a,122,a)].
% 119.40/119.68 7473 is_a_theorem(implies(implies(A,B),implies(implies(implies(C,C),A),B))). [resolve(7418,a,130,a)].
% 119.40/119.68 7474 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(B). [resolve(7418,a,69,b)].
% 119.40/119.68 7717 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(C,C),A),B)). [resolve(7473,a,69,b)].
% 119.40/119.68 8196 is_a_theorem(implies(implies(implies(A,A),implies(implies(B,B),C)),implies(D,C))). [resolve(7717,a,3023,a)].
% 119.40/119.68 9538 is_a_theorem(implies(implies(implies(A,A),B),implies(implies(B,C),implies(D,C)))). [resolve(7362,a,96,a)].
% 119.40/119.68 9609 -is_a_theorem(implies(implies(implies(implies(A,A),B),B),C)) | is_a_theorem(implies(D,C)). [resolve(7416,a,69,b)].
% 119.40/119.68 10171 -is_a_theorem(implies(implies(A,A),implies(implies(B,B),C))) | is_a_theorem(implies(D,C)). [resolve(8196,a,69,b)].
% 119.40/119.68 10436 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(implies(implies(B,C),implies(D,C))). [resolve(9538,a,69,b)].
% 119.40/119.68 11064 is_a_theorem(implies(A,implies(and(B,not(B)),C))). [resolve(226,a,9609,a)].
% 119.40/119.68 11094 is_a_theorem(implies(and(A,not(A)),B)). [resolve(11064,a,7474,a)].
% 119.40/119.68 11165 is_a_theorem(implies(not(equiv(A,A)),B)). [back_unit_del(6964),unit_del(a,11094)].
% 119.40/119.68 11326 is_a_theorem(implies(implies(A,B),implies(not(equiv(C,C)),B))). [resolve(11165,a,6232,a)].
% 119.40/119.68 12331 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),C),implies(D,C))). [resolve(11326,a,10436,a)].
% 119.40/119.68 12825 is_a_theorem(implies(A,implies(B,equiv(C,C)))). [resolve(12331,a,5382,a)].
% 119.40/119.68 12862 is_a_theorem(implies(A,equiv(B,B))). [resolve(12825,a,10171,a)].
% 119.40/119.68 12959 is_a_theorem(implies(implies(equiv(A,A),B),implies(C,B))). [resolve(12862,a,10436,a)].
% 119.40/119.68 13352 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(equiv(D,D),B),C))). [resolve(12959,a,130,a)].
% 119.40/119.68 13745 -is_a_theorem(implies(implies(implies(not(A),A),B),C)) | is_a_theorem(implies(implies(A,B),C)). [resolve(230,a,69,b)].
% 119.40/119.68 14391 is_a_theorem(implies(A,implies(implies(implies(not(implies(B,B)),C),D),D))). [resolve(242,a,9609,a)].
% 119.40/119.68 14398 is_a_theorem(implies(A,implies(implies(implies(not(not(B)),C),B),B))). [resolve(242,a,5382,a)].
% 119.40/119.68 14408 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(implies(not(A),D),B),C)). [resolve(242,a,69,b)].
% 119.40/119.68 14457 is_a_theorem(implies(implies(implies(not(not(A)),B),A),A)). [resolve(14398,a,7474,a)].
% 119.40/119.68 14481 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(not(A)),C),A),B))). [resolve(14457,a,130,a)].
% 119.40/119.68 14482 -is_a_theorem(implies(implies(not(not(A)),B),A)) | is_a_theorem(A). [resolve(14457,a,69,b)].
% 119.40/119.68 14500 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),C)). [resolve(14391,a,14482,a)].
% 119.40/119.68 14572 -is_a_theorem(implies(implies(not(implies(A,A)),B),C)) | is_a_theorem(C). [resolve(14500,a,69,b)].
% 119.40/119.68 14594 -is_a_theorem(not(equiv(not(implies(A,A)),B))) | is_a_theorem(and(B,not(not(implies(A,A))))). [para(257(a,1),14572(a,1))].
% 119.40/119.68 14679 is_a_theorem(implies(A,implies(implies(equiv(B,B),C),C))). [resolve(13352,a,9609,a)].
% 119.40/119.68 14695 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(equiv(D,D),B),C)). [resolve(13352,a,69,b)].
% 119.40/119.68 14705 is_a_theorem(implies(implies(equiv(A,A),B),B)). [resolve(14679,a,14572,a)].
% 119.40/119.68 14707 is_a_theorem(implies(implies(implies(implies(equiv(A,A),B),B),C),implies(D,C))). [resolve(14679,a,10436,a)].
% 119.40/119.68 14763 -is_a_theorem(implies(equiv(A,A),B)) | is_a_theorem(B). [resolve(14705,a,69,b)].
% 119.40/119.68 17418 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(not(A)),C),A),B)). [resolve(14481,a,69,b)].
% 119.40/119.68 17496 is_a_theorem(implies(implies(equiv(A,A),B),implies(implies(B,C),implies(D,C)))). [resolve(14695,a,9538,a)].
% 119.40/119.68 17576 -is_a_theorem(implies(implies(implies(equiv(A,A),B),B),C)) | is_a_theorem(implies(D,C)). [resolve(14707,a,69,b)].
% 119.40/119.68 19746 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),and(A,not(A))),C)). [resolve(17418,a,11094,a),rewrite([80(3)])].
% 119.40/119.68 19932 -is_a_theorem(implies(equiv(A,A),B)) | is_a_theorem(implies(implies(B,C),implies(D,C))). [resolve(17496,a,69,b)].
% 119.40/119.68 19979 is_a_theorem(implies(A,implies(implies(implies(not(equiv(B,B)),C),D),D))). [resolve(17576,a,242,a)].
% 119.40/119.68 20013 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),C),C)). [resolve(19979,a,14763,a)].
% 119.40/119.68 20064 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(equiv(C,C)),D),A),B))). [resolve(20013,a,130,a)].
% 119.40/119.68 21888 is_a_theorem(implies(and(not(equiv(A,A)),not(B)),C)). [resolve(349,a,20013,a)].
% 119.40/119.68 21890 is_a_theorem(implies(and(not(implies(A,A)),not(B)),C)). [resolve(349,a,19746,a)].
% 119.40/119.68 21897 is_a_theorem(implies(and(not(not(A)),not(B)),A)). [resolve(349,a,14457,a)].
% 119.40/119.68 21906 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),implies(C,D))). [resolve(349,a,7416,a)].
% 119.40/119.68 21908 is_a_theorem(implies(and(implies(not(A),A),not(A)),implies(B,C))). [resolve(349,a,3819,a)].
% 119.40/119.68 21909 is_a_theorem(implies(and(A,not(implies(not(A),B))),implies(C,D))). [resolve(349,a,3523,a)].
% 119.40/119.68 21910 is_a_theorem(implies(and(A,not(implies(B,B))),implies(C,D))). [resolve(349,a,3449,a)].
% 119.40/119.68 21919 is_a_theorem(implies(and(A,not(B)),implies(implies(implies(not(A),C),B),D))). [resolve(349,a,242,a)].
% 119.40/119.68 21922 is_a_theorem(implies(and(implies(A,B),not(implies(C,B))),implies(implies(C,A),D))). [resolve(349,a,227,a)].
% 119.40/119.68 21968 is_a_theorem(implies(implies(implies(A,A),and(not(not(B)),not(C))),B)). [resolve(21897,a,7717,a)].
% 119.40/119.68 21975 is_a_theorem(implies(implies(implies(not(not(A)),B),and(not(not(A)),not(B))),A)). [resolve(21897,a,232,a),rewrite([80(5)])].
% 119.40/119.68 21976 is_a_theorem(implies(implies(A,B),implies(and(not(not(A)),not(C)),B))). [resolve(21897,a,130,a)].
% 119.40/119.68 22409 is_a_theorem(implies(implies(implies(A,A),and(not(equiv(B,B)),not(C))),D)). [resolve(21888,a,7717,a)].
% 119.40/119.68 22452 is_a_theorem(implies(implies(implies(A,A),and(not(implies(B,B)),not(C))),D)). [resolve(21890,a,7717,a)].
% 119.40/119.68 22842 is_a_theorem(implies(implies(implies(A,B),C),implies(and(D,not(implies(E,E))),C))). [resolve(21910,a,130,a)].
% 119.40/119.68 23111 is_a_theorem(implies(and(implies(not(A),A),not(A)),not(equiv(B,C)))). [para(257(a,1),21908(a,1,2))].
% 119.40/119.68 23140 is_a_theorem(implies(and(A,not(implies(not(A),B))),not(equiv(C,D)))). [para(257(a,1),21909(a,1,2))].
% 119.40/119.68 23413 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),not(equiv(C,D)))). [para(257(a,1),21906(a,1,2))].
% 119.40/119.68 23751 is_a_theorem(implies(and(not(not(not(implies(A,A)))),not(B)),C)). [resolve(21976,a,14572,a)].
% 119.40/119.68 23755 is_a_theorem(implies(implies(implies(and(not(not(A)),not(B)),A),C),implies(D,C))). [resolve(21976,a,10436,a)].
% 119.40/119.68 23898 is_a_theorem(implies(implies(implies(A,A),and(not(not(not(implies(B,B)))),not(C))),D)). [resolve(23751,a,7717,a)].
% 119.40/119.68 26080 is_a_theorem(implies(and(A,implies(B,not(A))),implies(not(equiv(not(A),B)),C))). [para(257(a,1),21919(a,1,2,1)),rewrite([80(4)])].
% 119.40/119.68 26454 is_a_theorem(and(implies(A,A),implies(not(equiv(B,B)),C))). [resolve(22409,a,258,a)].
% 119.40/119.68 26689 is_a_theorem(and(implies(A,A),implies(not(implies(B,B)),C))). [resolve(22452,a,258,a)].
% 119.40/119.68 29180 -is_a_theorem(implies(implies(implies(A,B),implies(not(C),B)),D)) | is_a_theorem(implies(C,D)). [resolve(611,a,69,b)].
% 119.40/119.68 41343 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),and(not(not(C)),not(D))),C)). [resolve(14408,a,21968,a)].
% 119.40/119.68 50693 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(equiv(C,C)),D),A),B)). [resolve(20064,a,69,b)].
% 119.40/119.68 53101 is_a_theorem(implies(implies(not(A),and(not(not(A)),not(not(A)))),A)). [resolve(21975,a,13745,a)].
% 119.40/119.68 53264 -is_a_theorem(implies(not(A),and(not(not(A)),not(not(A))))) | is_a_theorem(A). [resolve(53101,a,69,b)].
% 119.40/119.68 54326 is_a_theorem(implies(A,implies(and(B,not(implies(C,C))),D))). [resolve(22842,a,17576,a)].
% 119.40/119.68 54365 is_a_theorem(implies(implies(implies(and(A,not(implies(B,B))),C),D),implies(E,D))). [resolve(54326,a,19932,a)].
% 119.40/119.68 58263 -is_a_theorem(and(A,implies(B,not(A)))) | is_a_theorem(implies(not(equiv(not(A),B)),C)). [resolve(26080,a,69,b)].
% 119.40/119.68 59070 is_a_theorem(implies(A,implies(B,implies(not(A),C)))). [resolve(29180,a,23755,a)].
% 119.40/119.68 59079 is_a_theorem(implies(A,implies(implies(implies(not(A),B),C),implies(D,C)))). [resolve(29180,a,9538,a)].
% 119.40/119.68 59158 is_a_theorem(implies(implies(implies(A,implies(not(B),C)),D),implies(B,D))). [resolve(59070,a,130,a)].
% 119.40/119.68 63878 is_a_theorem(implies(A,implies(B,implies(C,implies(not(B),D))))). [resolve(59158,a,3369,a)].
% 119.40/119.68 108304 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),and(not(implies(C,C)),not(D))),E)). [resolve(50693,a,21890,a)].
% 119.40/119.68 109924 is_a_theorem(implies(and(and(A,not(implies(B,B))),not(C)),implies(D,E))). [resolve(54365,a,349,a)].
% 119.40/119.68 110070 is_a_theorem(implies(and(and(A,not(implies(B,B))),not(C)),not(equiv(D,E)))). [para(257(a,1),109924(a,1,2))].
% 119.40/119.68 112526 is_a_theorem(implies(not(equiv(not(implies(A,A)),not(implies(B,B)))),C)). [resolve(58263,a,26689,a)].
% 119.40/119.68 112528 is_a_theorem(implies(not(equiv(not(implies(A,A)),not(equiv(B,B)))),C)). [resolve(58263,a,26454,a)].
% 119.40/119.68 112564 is_a_theorem(equiv(not(implies(A,A)),not(implies(B,B)))). [resolve(112526,a,53264,a)].
% 119.40/119.68 112654 not(implies(A,A)) = not(implies(B,B)). [resolve(112564,a,61,a)].
% 119.40/119.68 112662 not(implies(A,A)) = c_0. [new_symbol(112654)].
% 119.40/119.68 112663 is_a_theorem(implies(not(equiv(c_0,not(equiv(A,A)))),B)). [back_rewrite(112528),rewrite([112662(2)])].
% 119.40/119.68 112672 is_a_theorem(implies(and(and(A,c_0),not(B)),not(equiv(C,D)))). [back_rewrite(110070),rewrite([112662(2)])].
% 119.40/119.68 112683 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),and(c_0,not(C))),D)). [back_rewrite(108304),rewrite([112662(5)])].
% 119.40/119.68 113042 is_a_theorem(implies(implies(implies(c_0,A),and(not(not(B)),not(C))),B)). [back_rewrite(41343),rewrite([112662(2)])].
% 119.40/119.68 113202 is_a_theorem(implies(implies(implies(A,A),and(not(not(c_0)),not(B))),C)). [back_rewrite(23898),rewrite([112662(3)])].
% 119.40/119.68 113456 -is_a_theorem(not(equiv(c_0,A))) | is_a_theorem(and(A,not(c_0))). [back_rewrite(14594),rewrite([112662(2),112662(6)])].
% 119.40/119.68 113460 -is_a_theorem(implies(implies(c_0,A),B)) | is_a_theorem(B). [back_rewrite(14572),rewrite([112662(2)])].
% 119.40/119.68 115042 is_a_theorem(implies(c_0,A)). [back_rewrite(413),rewrite([112662(2)])].
% 119.40/119.68 115166 implies(A,implies(B,B)) = not(and(A,c_0)). [para(112662(a,1),80(a,1,1,2)),flip(a)].
% 119.40/119.68 120951 is_a_theorem(equiv(c_0,not(equiv(A,A)))). [resolve(112663,a,53264,a)].
% 119.40/119.68 121062 not(equiv(A,A)) = c_0. [resolve(120951,a,61,a)].
% 119.40/119.68 121138 is_a_theorem(implies(implies(implies(c_0,A),and(c_0,not(B))),C)). [back_rewrite(112683),rewrite([121062(2)])].
% 119.40/119.68 121153 implies(A,equiv(B,B)) = not(and(A,c_0)). [para(121062(a,1),80(a,1,1,2)),flip(a)].
% 119.40/119.68 121188 is_a_theorem(implies(and(implies(not(A),A),not(A)),c_0)). [para(121062(a,1),23111(a,1,2))].
% 119.40/119.68 121189 is_a_theorem(implies(and(A,not(implies(not(A),B))),c_0)). [para(121062(a,1),23140(a,1,2))].
% 119.40/119.68 121196 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),c_0)). [para(121062(a,1),23413(a,1,2))].
% 119.40/119.68 124361 -is_a_theorem(implies(not(and(implies(A,A),c_0)),B)) | is_a_theorem(B). [para(115166(a,1),7474(a,1,1))].
% 119.40/119.68 126419 is_a_theorem(implies(implies(c_0,A),implies(and(implies(not(B),B),not(B)),A))). [resolve(121188,a,130,a)].
% 119.40/119.68 126490 is_a_theorem(implies(implies(c_0,A),implies(and(B,not(implies(not(B),C))),A))). [resolve(121189,a,130,a)].
% 119.40/119.68 134612 is_a_theorem(and(implies(c_0,A),implies(c_0,B))). [resolve(121138,a,258,a)].
% 119.40/119.68 134649 is_a_theorem(implies(not(equiv(not(implies(c_0,A)),c_0)),B)). [resolve(134612,a,58263,a)].
% 119.40/119.68 134848 is_a_theorem(equiv(not(implies(c_0,A)),c_0)). [resolve(134649,a,53264,a)].
% 119.40/119.68 134926 not(implies(c_0,A)) = c_0. [resolve(134848,a,61,a),flip(a)].
% 119.40/119.68 134929 implies(A,implies(c_0,B)) = not(and(A,c_0)). [para(134926(a,1),80(a,1,1,2)),flip(a)].
% 119.40/119.68 135794 is_a_theorem(implies(and(implies(not(and(implies(A,A),c_0)),B),not(B)),c_0)). [para(115166(a,1),121196(a,1,1,1,1))].
% 119.40/119.68 136428 is_a_theorem(implies(and(and(A,c_0),not(B)),c_0)). [para(121062(a,1),112672(a,1,2))].
% 119.40/119.68 136443 is_a_theorem(implies(implies(c_0,A),implies(and(and(B,c_0),not(C)),A))). [resolve(136428,a,130,a)].
% 119.40/119.68 140797 is_a_theorem(implies(not(equiv(c_0,not(not(A)))),A)). [para(257(a,1),113042(a,1,1))].
% 119.40/119.68 140813 is_a_theorem(implies(implies(A,B),implies(not(equiv(c_0,not(not(A)))),B))). [resolve(140797,a,130,a)].
% 119.40/119.68 140880 is_a_theorem(and(implies(A,A),implies(not(not(c_0)),B))). [resolve(113202,a,258,a)].
% 119.40/119.68 140884 is_a_theorem(implies(not(equiv(c_0,not(not(c_0)))),A)). [resolve(140880,a,58263,a),rewrite([112662(2)])].
% 119.40/119.68 140900 is_a_theorem(equiv(c_0,not(not(c_0)))). [resolve(140884,a,53264,a)].
% 119.40/119.68 140929 not(not(c_0)) = c_0. [resolve(140900,a,61,a)].
% 119.40/119.68 140935 not(and(A,c_0)) = implies(A,not(c_0)). [para(140929(a,1),80(a,1,1,2))].
% 119.40/119.68 140936 is_a_theorem(not(c_0)). [para(140929(a,1),122(a,1,1)),unit_del(a,115042)].
% 119.40/119.68 140945 implies(implies(not(c_0),A),and(A,c_0)) = not(equiv(not(c_0),A)). [para(140929(a,1),257(a,1,2,2))].
% 119.40/119.68 140947 is_a_theorem(implies(A,not(c_0))). [para(140929(a,1),3442(a,1,2,2,1)),rewrite([134929(5),140935(5),115166(6),140935(3)])].
% 119.40/119.68 141597 is_a_theorem(implies(and(implies(implies(implies(A,A),not(c_0)),B),not(B)),c_0)). [back_rewrite(135794),rewrite([140935(4)])].
% 119.40/119.68 141761 implies(A,implies(c_0,B)) = implies(A,not(c_0)). [back_rewrite(134929),rewrite([140935(6)])].
% 119.40/119.68 142104 -is_a_theorem(implies(implies(implies(A,A),not(c_0)),B)) | is_a_theorem(B). [back_rewrite(124361),rewrite([140935(4)])].
% 119.40/119.68 142166 implies(A,equiv(B,B)) = implies(A,not(c_0)). [back_rewrite(121153),rewrite([140935(5)])].
% 119.40/119.68 142631 implies(A,implies(B,B)) = implies(A,not(c_0)). [back_rewrite(115166),rewrite([140935(5)])].
% 119.40/119.68 143130 is_a_theorem(implies(implies(not(c_0),A),implies(B,A))). [resolve(140947,a,19932,a)].
% 119.40/119.68 144117 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(not(c_0),B),C))). [resolve(143130,a,130,a)].
% 119.40/119.68 162241 is_a_theorem(implies(and(and(A,c_0),not(B)),C)). [resolve(136443,a,113460,a)].
% 119.40/119.68 173033 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(equiv(c_0,not(not(A)))),B)). [resolve(140813,a,69,b)].
% 119.40/119.68 177144 is_a_theorem(implies(A,implies(implies(not(c_0),B),B))). [resolve(144117,a,17576,a)].
% 119.40/119.68 177145 is_a_theorem(implies(implies(A,B),implies(implies(not(c_0),A),B))). [resolve(144117,a,13745,a)].
% 119.40/119.68 177147 is_a_theorem(implies(and(A,not(B)),implies(implies(not(c_0),B),C))). [resolve(144117,a,349,a)].
% 119.40/119.68 177152 is_a_theorem(implies(implies(not(c_0),A),A)). [resolve(177144,a,142104,a)].
% 119.40/119.68 177190 -is_a_theorem(implies(not(c_0),A)) | is_a_theorem(A). [resolve(177152,a,69,b)].
% 119.40/119.68 177666 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(c_0),A),B)). [resolve(177145,a,69,b)].
% 119.40/119.68 177851 is_a_theorem(implies(implies(not(c_0),and(and(A,c_0),not(B))),C)). [resolve(177666,a,162241,a)].
% 119.40/119.68 178353 is_a_theorem(and(not(c_0),implies(and(A,c_0),B))). [resolve(177851,a,258,a)].
% 119.40/119.68 178356 is_a_theorem(implies(not(equiv(c_0,and(A,c_0))),B)). [resolve(178353,a,58263,a),rewrite([140929(3)])].
% 119.40/119.68 178368 is_a_theorem(equiv(c_0,and(A,c_0))). [resolve(178356,a,53264,a)].
% 119.40/119.68 178384 and(A,c_0) = c_0. [resolve(178368,a,61,a)].
% 119.40/119.68 178443 implies(implies(not(c_0),A),c_0) = not(equiv(not(c_0),A)). [back_rewrite(140945),rewrite([178384(5)])].
% 119.40/119.68 178444 implies(A,not(c_0)) = not(c_0). [back_rewrite(140935),rewrite([178384(2)]),flip(a)].
% 119.40/119.68 178462 implies(A,implies(B,B)) = not(c_0). [back_rewrite(142631),rewrite([178444(5)])].
% 119.40/119.68 178473 implies(A,equiv(B,B)) = not(c_0). [back_rewrite(142166),rewrite([178444(5)])].
% 119.40/119.68 178501 implies(A,implies(c_0,B)) = not(c_0). [back_rewrite(141761),rewrite([178444(6)])].
% 119.40/119.68 178502 is_a_theorem(implies(and(implies(not(c_0),A),not(A)),c_0)). [back_rewrite(141597),rewrite([178444(4)])].
% 119.40/119.68 178569 and(not(c_0),implies(not(c_0),A)) = equiv(A,not(c_0)). [para(178444(a,1),90(a,1,1))].
% 119.40/119.68 178570 and(implies(not(c_0),A),not(c_0)) = equiv(not(c_0),A). [para(178444(a,1),90(a,1,2))].
% 119.40/119.68 180915 is_a_theorem(implies(implies(c_0,A),implies(and(implies(not(c_0),B),not(B)),A))). [resolve(178502,a,130,a)].
% 119.40/119.68 181432 implies(not(c_0),c_0) = c_0. [para(121062(a,1),178443(a,2)),rewrite([178444(5)])].
% 119.40/119.68 181456 not(equiv(not(c_0),implies(A,A))) = c_0. [para(178462(a,1),178443(a,1,1)),rewrite([181432(4)]),flip(a)].
% 119.40/119.68 181457 not(equiv(not(c_0),equiv(A,A))) = c_0. [para(178473(a,1),178443(a,1,1)),rewrite([181432(4)]),flip(a)].
% 119.40/119.68 181458 not(equiv(not(c_0),implies(c_0,A))) = c_0. [para(178501(a,1),178443(a,1,1)),rewrite([181432(4)]),flip(a)].
% 119.40/119.68 181461 is_a_theorem(implies(implies(not(c_0),A),implies(implies(A,c_0),c_0))). [para(181432(a,1),96(a,1,2,2))].
% 119.40/119.68 181486 is_a_theorem(implies(and(implies(A,c_0),not(c_0)),implies(implies(not(c_0),A),B))). [para(181432(a,1),21922(a,1,1,2,1))].
% 119.40/119.68 181491 is_a_theorem(implies(A,implies(implies(implies(not(A),B),c_0),c_0))). [para(181432(a,1),59079(a,1,2,2))].
% 119.40/119.68 181526 implies(A,equiv(not(c_0),implies(B,B))) = not(c_0). [para(181456(a,1),80(a,1,1,2)),rewrite([178384(2)]),flip(a)].
% 119.40/119.68 181527 is_a_theorem(equiv(not(c_0),implies(A,A))). [para(181456(a,1),122(a,1,1)),rewrite([181526(6)]),unit_del(a,140936)].
% 119.40/119.68 181577 implies(A,A) = not(c_0). [resolve(181527,a,61,a)].
% 119.40/119.68 182881 and(not(c_0),not(c_0)) = equiv(A,A). [para(181577(a,1),90(a,1,1)),rewrite([181577(3)])].
% 119.40/119.68 182882 is_a_theorem(implies(implies(A,B),implies(not(c_0),implies(A,B)))). [para(181577(a,1),96(a,1,2,1))].
% 119.40/119.68 182883 implies(A,and(B,not(B))) = implies(A,c_0). [para(181577(a,1),129(a,1,1,2)),rewrite([80(4)]),flip(a)].
% 119.40/119.68 182928 implies(A,equiv(not(c_0),equiv(B,B))) = not(c_0). [para(181457(a,1),80(a,1,1,2)),rewrite([178384(2)]),flip(a)].
% 119.40/119.68 182929 is_a_theorem(equiv(not(c_0),equiv(A,A))). [para(181457(a,1),122(a,1,1)),rewrite([182928(6)]),unit_del(a,140936)].
% 119.40/119.68 183011 equiv(A,A) = not(c_0). [resolve(182929,a,61,a)].
% 119.40/119.68 183271 and(not(c_0),not(c_0)) = not(c_0). [back_rewrite(182881),rewrite([183011(6)])].
% 119.40/119.68 183320 implies(A,equiv(not(c_0),implies(c_0,B))) = not(c_0). [para(181458(a,1),80(a,1,1,2)),rewrite([178384(2)]),flip(a)].
% 119.40/119.68 183321 is_a_theorem(equiv(not(c_0),implies(c_0,A))). [para(181458(a,1),122(a,1,1)),rewrite([183320(7)]),unit_del(a,140936)].
% 119.40/119.68 183453 implies(c_0,A) = not(c_0). [resolve(183321,a,61,a)].
% 119.40/119.68 183604 is_a_theorem(implies(not(c_0),implies(and(implies(not(c_0),A),not(A)),B))). [back_rewrite(180915),rewrite([183453(2)])].
% 119.40/119.68 183611 is_a_theorem(implies(not(c_0),implies(and(A,not(implies(not(A),B))),C))). [back_rewrite(126490),rewrite([183453(2)])].
% 119.40/119.68 183612 is_a_theorem(implies(not(c_0),implies(and(implies(not(A),A),not(A)),B))). [back_rewrite(126419),rewrite([183453(2)])].
% 119.40/119.68 183615 and(implies(A,c_0),not(c_0)) = equiv(A,c_0). [para(183453(a,1),90(a,1,2))].
% 119.40/119.68 183616 is_a_theorem(implies(implies(A,c_0),implies(not(c_0),implies(A,B)))). [para(183453(a,1),96(a,1,2,1))].
% 119.40/119.68 183617 implies(A,and(c_0,not(B))) = implies(A,c_0). [para(183453(a,1),129(a,1,1,2)),rewrite([80(4)]),flip(a)].
% 119.40/119.68 183619 implies(not(c_0),and(A,not(c_0))) = not(equiv(c_0,A)). [para(183453(a,1),257(a,1,1))].
% 119.40/119.68 183689 is_a_theorem(implies(and(A,not(c_0)),implies(not(equiv(not(A),c_0)),B))). [para(183453(a,1),26080(a,1,1,2))].
% 119.40/119.68 183741 is_a_theorem(implies(equiv(A,c_0),implies(implies(not(c_0),A),B))). [back_rewrite(181486),rewrite([183615(5)])].
% 119.40/119.68 183750 implies(implies(A,c_0),and(and(B,not(B)),not(A))) = not(equiv(A,and(B,not(B)))). [para(182883(a,1),257(a,1,1))].
% 119.40/119.68 183778 implies(and(A,not(A)),c_0) = not(c_0). [para(182883(a,1),181577(a,1))].
% 119.40/119.68 184178 equiv(and(A,not(A)),c_0) = not(c_0). [para(183778(a,1),90(a,1,1)),rewrite([182883(6),181577(5),183271(5)]),flip(a)].
% 119.40/119.68 184203 and(A,not(A)) = c_0. [para(184178(a,1),61(a,1)),flip(b),unit_del(a,140936)].
% 119.40/119.68 184206 implies(implies(A,c_0),c_0) = not(equiv(A,c_0)). [back_rewrite(183750),rewrite([184203(4),183617(6),184203(6)])].
% 119.40/119.68 184216 is_a_theorem(implies(A,not(equiv(implies(not(A),B),c_0)))). [back_rewrite(181491),rewrite([184206(6)])].
% 119.40/119.68 184228 is_a_theorem(implies(implies(not(c_0),A),not(equiv(A,c_0)))). [back_rewrite(181461),rewrite([184206(7)])].
% 119.40/119.68 184886 equiv(c_0,implies(A,c_0)) = and(not(c_0),not(equiv(A,c_0))). [para(184206(a,1),90(a,1,2)),rewrite([183453(4)]),flip(a)].
% 119.40/119.68 185031 is_a_theorem(implies(A,implies(not(equiv(not(A),c_0)),implies(B,c_0)))). [para(184206(a,1),59079(a,1,2,1))].
% 119.40/119.68 185452 -is_a_theorem(implies(not(c_0),A)) | is_a_theorem(not(equiv(A,c_0))). [resolve(184228,a,69,b)].
% 119.40/119.68 185951 is_a_theorem(not(equiv(implies(A,implies(B,implies(not(A),C))),c_0))). [resolve(185452,a,63878,a)].
% 119.40/119.68 186092 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(c_0),implies(A,B))). [resolve(182882,a,69,b)].
% 119.40/119.68 186320 is_a_theorem(implies(not(c_0),implies(equiv(A,c_0),implies(implies(not(c_0),A),B)))). [resolve(186092,a,183741,a)].
% 119.40/119.68 189596 is_a_theorem(implies(and(A,implies(B,c_0)),implies(not(equiv(c_0,B)),C))). [para(183619(a,1),177147(a,1,2,1)),rewrite([80(4)])].
% 119.40/119.68 189780 is_a_theorem(implies(A,implies(not(equiv(not(A),c_0)),c_0))). [para(181432(a,1),185031(a,1,2,2))].
% 119.40/119.68 189876 -is_a_theorem(A) | is_a_theorem(implies(not(equiv(not(A),c_0)),c_0)). [resolve(189780,a,69,b)].
% 119.40/119.68 192102 is_a_theorem(implies(and(implies(not(c_0),A),not(A)),B)). [resolve(183604,a,177190,a)].
% 119.40/119.68 192111 is_a_theorem(implies(not(equiv(c_0,not(implies(implies(not(c_0),A),A)))),B)). [resolve(192102,a,173033,a),rewrite([80(7)])].
% 119.40/119.68 192186 is_a_theorem(implies(and(A,not(implies(not(A),B))),C)). [resolve(183611,a,177190,a)].
% 119.40/119.68 192195 is_a_theorem(implies(not(equiv(c_0,not(implies(A,implies(not(A),B))))),C)). [resolve(192186,a,173033,a),rewrite([80(6)])].
% 119.40/119.68 192243 is_a_theorem(implies(and(implies(not(A),A),not(A)),B)). [resolve(183612,a,177190,a)].
% 119.40/119.68 192250 is_a_theorem(implies(implies(not(c_0),and(implies(not(A),A),not(A))),B)). [resolve(192243,a,177666,a)].
% 119.40/119.68 193034 is_a_theorem(equiv(c_0,not(implies(implies(not(c_0),A),A)))). [resolve(192111,a,53264,a)].
% 119.40/119.68 193040 not(implies(implies(not(c_0),A),A)) = c_0. [resolve(193034,a,61,a)].
% 119.40/119.68 193042 implies(A,implies(implies(not(c_0),B),B)) = not(c_0). [para(193040(a,1),80(a,1,1,2)),rewrite([178384(2)]),flip(a)].
% 119.40/119.68 193067 equiv(implies(implies(not(c_0),A),A),not(c_0)) = not(c_0). [para(193042(a,1),178569(a,1,2)),rewrite([183271(5)]),flip(a)].
% 119.40/119.68 193078 implies(implies(not(c_0),A),A) = not(c_0). [para(193067(a,1),61(a,1)),flip(b),unit_del(a,140936)].
% 119.40/119.68 193081 and(implies(A,implies(not(c_0),A)),not(c_0)) = equiv(A,implies(not(c_0),A)). [para(193078(a,1),90(a,1,2))].
% 119.40/119.68 193181 is_a_theorem(equiv(c_0,not(implies(A,implies(not(A),B))))). [resolve(192195,a,53264,a)].
% 119.40/119.68 193197 not(implies(A,implies(not(A),B))) = c_0. [resolve(193181,a,61,a)].
% 119.40/119.68 193199 implies(A,implies(B,implies(not(B),C))) = not(c_0). [para(193197(a,1),80(a,1,1,2)),rewrite([178384(2)]),flip(a)].
% 119.40/119.68 193215 equiv(implies(A,implies(not(A),B)),not(c_0)) = not(c_0). [para(193199(a,1),178569(a,1,2)),rewrite([183271(5)]),flip(a)].
% 119.40/119.68 193224 implies(A,implies(not(A),B)) = not(c_0). [para(193215(a,1),61(a,1)),flip(b),unit_del(a,140936)].
% 119.40/119.68 193237 and(not(c_0),implies(implies(not(A),B),A)) = equiv(A,implies(not(A),B)). [para(193224(a,1),90(a,1,1))].
% 119.40/119.68 193238 and(implies(implies(not(A),B),A),not(c_0)) = equiv(implies(not(A),B),A). [para(193224(a,1),90(a,1,2))].
% 119.40/119.68 193328 is_a_theorem(equiv(A,implies(not(A),A))). [resolve(192250,a,258,a),rewrite([193237(6)])].
% 119.40/119.68 193364 implies(not(A),A) = A. [resolve(193328,a,61,a)].
% 119.40/119.68 193707 is_a_theorem(implies(A,not(equiv(A,c_0)))). [para(193364(a,1),184216(a,1,2,1,1))].
% 119.40/119.68 193711 is_a_theorem(implies(implies(not(A),c_0),implies(not(c_0),A))). [para(193364(a,1),183616(a,1,2,2))].
% 119.40/119.68 193726 is_a_theorem(not(equiv(implies(A,implies(B,A)),c_0))). [para(193364(a,1),185951(a,1,1,1,2,2))].
% 119.40/119.68 193769 is_a_theorem(implies(and(A,not(c_0)),equiv(not(A),c_0))). [para(193364(a,1),183689(a,1,2))].
% 119.40/119.68 193782 is_a_theorem(implies(and(A,implies(B,c_0)),equiv(c_0,B))). [para(193364(a,1),189596(a,1,2))].
% 119.40/119.68 195059 -is_a_theorem(A) | is_a_theorem(not(equiv(A,c_0))). [resolve(193707,a,69,b)].
% 119.40/119.68 195210 is_a_theorem(not(equiv(implies(A,not(equiv(A,c_0))),c_0))). [resolve(195059,a,193707,a)].
% 119.40/119.68 197918 is_a_theorem(not(equiv(implies(implies(not(A),c_0),implies(not(c_0),A)),c_0))). [resolve(193711,a,195059,a)].
% 119.40/119.68 197987 is_a_theorem(implies(not(equiv(A,c_0)),not(equiv(c_0,A)))). [para(183619(a,1),193711(a,1,2)),rewrite([80(4),184206(4)])].
% 119.40/119.68 198113 -is_a_theorem(and(A,not(c_0))) | is_a_theorem(equiv(not(A),c_0)). [resolve(193769,a,69,b)].
% 119.40/119.68 198194 is_a_theorem(implies(and(A,not(equiv(B,c_0))),and(not(c_0),not(equiv(B,c_0))))). [para(184206(a,1),193782(a,1,1,2)),rewrite([184886(8)])].
% 119.40/119.68 198838 -is_a_theorem(not(equiv(A,c_0))) | is_a_theorem(not(equiv(c_0,A))). [resolve(197987,a,69,b)].
% 119.40/119.68 199454 is_a_theorem(not(equiv(c_0,implies(A,not(equiv(A,c_0)))))). [resolve(198838,a,195210,a)].
% 119.40/119.68 199455 is_a_theorem(not(equiv(c_0,implies(A,implies(B,A))))). [resolve(198838,a,193726,a)].
% 119.40/119.68 199498 is_a_theorem(and(implies(A,implies(B,A)),not(c_0))). [resolve(199455,a,113456,a)].
% 119.40/119.68 199511 is_a_theorem(equiv(not(implies(A,implies(B,A))),c_0)). [resolve(199498,a,198113,a)].
% 119.40/119.68 199597 not(implies(A,implies(B,A))) = c_0. [resolve(199511,a,61,a),flip(a)].
% 119.40/119.68 199599 implies(A,implies(B,implies(C,B))) = not(c_0). [para(199597(a,1),80(a,1,1,2)),rewrite([178384(2)]),flip(a)].
% 119.40/119.68 199602 implies(A,implies(B,A)) = not(c_0). [para(199597(a,1),193364(a,1,1)),rewrite([199599(4)]),flip(a)].
% 119.40/119.68 199607 equiv(A,implies(not(c_0),A)) = not(c_0). [back_rewrite(193081),rewrite([199602(4),183271(5)]),flip(a)].
% 119.40/119.68 199634 implies(not(c_0),A) = A. [para(199607(a,1),61(a,1)),unit_del(a,140936)].
% 119.40/119.68 199663 is_a_theorem(not(equiv(implies(implies(not(A),c_0),A),c_0))). [back_rewrite(197918),rewrite([199634(6)])].
% 119.40/119.68 199739 is_a_theorem(implies(equiv(A,c_0),implies(A,B))). [back_rewrite(186320),rewrite([199634(7),199634(7)])].
% 119.40/119.68 199787 not(equiv(c_0,A)) = and(A,not(c_0)). [back_rewrite(183619),rewrite([199634(6)]),flip(a)].
% 119.40/119.68 199797 equiv(not(c_0),A) = and(A,not(c_0)). [back_rewrite(178570),rewrite([199634(3)]),flip(a)].
% 119.40/119.68 199810 is_a_theorem(and(implies(A,not(equiv(A,c_0))),not(c_0))). [back_rewrite(199454),rewrite([199787(7)])].
% 119.40/119.68 199816 -is_a_theorem(not(equiv(A,c_0))) | is_a_theorem(and(A,not(c_0))). [back_rewrite(198838),rewrite([199787(7)])].
% 119.40/119.68 200987 implies(A,and(not(c_0),not(B))) = not(and(A,B)). [para(199634(a,1),129(a,1,1,2)),flip(a)].
% 119.40/119.68 201033 is_a_theorem(not(and(and(A,not(equiv(B,c_0))),equiv(B,c_0)))). [back_rewrite(198194),rewrite([200987(11)])].
% 119.40/119.68 201522 is_a_theorem(implies(equiv(not(A),c_0),A)). [para(193364(a,1),199739(a,1,2))].
% 119.40/119.68 201707 is_a_theorem(implies(not(equiv(not(implies(equiv(not(A),c_0),A)),c_0)),c_0)). [resolve(201522,a,189876,a)].
% 119.40/119.68 202834 -is_a_theorem(and(A,not(c_0))) | not(c_0) = A. [para(199797(a,1),61(a,1)),flip(b)].
% 119.40/119.68 205428 implies(A,not(equiv(A,c_0))) = not(c_0). [resolve(199810,a,202834,a),flip(a)].
% 119.40/119.68 205432 and(implies(not(equiv(A,c_0)),A),not(c_0)) = equiv(not(equiv(A,c_0)),A). [para(205428(a,1),90(a,1,2))].
% 119.40/119.68 205791 is_a_theorem(equiv(implies(not(A),c_0),A)). [resolve(199816,a,199663,a),rewrite([193238(7)])].
% 119.40/119.68 205830 implies(not(A),c_0) = A. [resolve(205791,a,61,a),flip(a)].
% 119.40/119.68 205893 is_a_theorem(equiv(not(implies(equiv(not(A),c_0),A)),c_0)). [back_rewrite(201707),rewrite([205830(10)])].
% 119.40/119.68 206020 implies(implies(A,B),c_0) = and(A,not(B)). [para(80(a,1),205830(a,1,1))].
% 119.40/119.68 206021 equiv(not(A),c_0) = and(A,not(c_0)). [para(205830(a,1),90(a,1,1)),rewrite([183453(3)]),flip(a)].
% 119.40/119.68 206025 implies(A,and(not(B),not(c_0))) = not(and(A,B)). [para(205830(a,1),129(a,1,1,2)),flip(a)].
% 119.40/119.68 206071 implies(and(A,not(c_0)),c_0) = equiv(c_0,A). [para(199787(a,1),205830(a,1,1))].
% 119.40/119.68 206168 not(equiv(A,c_0)) = and(A,not(c_0)). [back_rewrite(184206),rewrite([206020(4)]),flip(a)].
% 119.40/119.68 206328 is_a_theorem(and(implies(and(A,not(c_0)),A),not(c_0))). [back_rewrite(205893),rewrite([206021(3),206021(7)])].
% 119.40/119.68 207616 and(implies(and(A,not(c_0)),A),not(c_0)) = equiv(and(A,not(c_0)),A). [back_rewrite(205432),rewrite([206168(3),206168(10)])].
% 119.40/119.68 207676 is_a_theorem(not(and(and(A,and(B,not(c_0))),equiv(B,c_0)))). [back_rewrite(201033),rewrite([206168(3)])].
% 119.40/119.68 208048 is_a_theorem(equiv(and(A,not(c_0)),A)). [back_rewrite(206328),rewrite([207616(7)])].
% 119.40/119.68 209149 and(A,not(c_0)) = A. [resolve(208048,a,61,a),flip(a)].
% 119.40/119.68 209204 is_a_theorem(not(and(and(A,B),equiv(B,c_0)))). [back_rewrite(207676),rewrite([209149(3)])].
% 119.40/119.68 209322 equiv(c_0,A) = implies(A,c_0). [back_rewrite(206071),rewrite([209149(3)]),flip(a)].
% 119.40/119.68 209332 not(and(A,B)) = implies(A,not(B)). [back_rewrite(206025),rewrite([209149(4)]),flip(a)].
% 119.40/119.68 209626 not(implies(A,c_0)) = A. [back_rewrite(199787),rewrite([209322(2),209149(6)])].
% 119.40/119.68 209634 equiv(A,c_0) = implies(A,c_0). [back_rewrite(183615),rewrite([209149(5)]),flip(a)].
% 119.40/119.68 209773 is_a_theorem(implies(and(A,B),B)). [back_rewrite(209204),rewrite([209634(3),209332(5),209626(4)])].
% 119.40/119.68 209774 $F. [resolve(209773,a,47,a)].
% 119.40/119.68
% 119.40/119.68 % SZS output end Refutation
% 119.40/119.68 ============================== end of proof ==========================
% 119.40/119.68
% 119.40/119.68 ============================== STATISTICS ============================
% 119.40/119.68
% 119.40/119.68 Given=8697. Generated=13591550. Kept=209723. proofs=1.
% 119.40/119.68 Usable=801. Sos=5129. Demods=88. Limbo=441, Disabled=203423. Hints=0.
% 119.40/119.68 Megabytes=143.02.
% 119.40/119.68 User_CPU=111.30, System_CPU=7.34, Wall_clock=119.
% 119.40/119.68
% 119.40/119.68 ============================== end of statistics =====================
% 119.40/119.68
% 119.40/119.68 ============================== end of search =========================
% 119.40/119.68
% 119.40/119.68 THEOREM PROVED
% 119.40/119.68 % SZS status Theorem
% 119.40/119.68
% 119.40/119.68 Exiting with 1 proof.
% 119.40/119.68
% 119.40/119.68 Process 14860 exit (max_proofs) Mon Jul 4 09:31:31 2022
% 119.40/119.68 Prover9 interrupted
%------------------------------------------------------------------------------