TSTP Solution File: LCL505+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL505+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 13:47:15 EDT 2022
% Result : Theorem 70.85s 71.18s
% Output : Refutation 70.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL505+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 2 20:49:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.44/1.02 ============================== Prover9 ===============================
% 0.44/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.02 Process 2863 was started by sandbox on n011.cluster.edu,
% 0.44/1.02 Sat Jul 2 20:49:35 2022
% 0.44/1.02 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_2707_n011.cluster.edu".
% 0.44/1.02 ============================== end of head ===========================
% 0.44/1.02
% 0.44/1.02 ============================== INPUT =================================
% 0.44/1.02
% 0.44/1.02 % Reading from file /tmp/Prover9_2707_n011.cluster.edu
% 0.44/1.02
% 0.44/1.02 set(prolog_style_variables).
% 0.44/1.02 set(auto2).
% 0.44/1.02 % set(auto2) -> set(auto).
% 0.44/1.02 % set(auto) -> set(auto_inference).
% 0.44/1.02 % set(auto) -> set(auto_setup).
% 0.44/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.02 % set(auto) -> set(auto_limits).
% 0.44/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.02 % set(auto) -> set(auto_denials).
% 0.44/1.02 % set(auto) -> set(auto_process).
% 0.44/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.02 % set(auto2) -> assign(stats, some).
% 0.44/1.02 % set(auto2) -> clear(echo_input).
% 0.44/1.02 % set(auto2) -> set(quiet).
% 0.44/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.02 % set(auto2) -> clear(print_given).
% 0.44/1.02 assign(lrs_ticks,-1).
% 0.44/1.02 assign(sos_limit,10000).
% 0.44/1.02 assign(order,kbo).
% 0.44/1.02 set(lex_order_vars).
% 0.44/1.02 clear(print_given).
% 0.44/1.02
% 0.44/1.02 % formulas(sos). % not echoed (43 formulas)
% 0.44/1.02
% 0.44/1.02 ============================== end of input ==========================
% 0.44/1.02
% 0.44/1.02 % From the command line: assign(max_seconds, 300).
% 0.44/1.02
% 0.44/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.02
% 0.44/1.02 % Formulas that are not ordinary clauses:
% 0.44/1.02 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].
% 0.44/1.02 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].
% 0.44/1.02 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].
% 0.44/1.02 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 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].
% 0.44/1.02 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].
% 0.44/1.02 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 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].
% 0.44/1.02 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 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].
% 0.44/1.02 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].
% 0.44/1.02 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].
% 1.27/1.55 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].
% 1.27/1.55 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.55 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.55 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].
% 1.27/1.55 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].
% 1.27/1.55 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.55 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.55 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.55 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.55 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.55 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].
% 1.27/1.55 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].
% 1.27/1.55 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].
% 1.27/1.55 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].
% 1.27/1.55 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].
% 1.27/1.55 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].
% 1.27/1.55 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].
% 1.27/1.55
% 1.27/1.55 ============================== end of process non-clausal formulas ===
% 1.27/1.55
% 1.27/1.55 ============================== PROCESS INITIAL CLAUSES ===============
% 1.27/1.55
% 1.27/1.55 ============================== PREDICATE ELIMINATION =================
% 1.27/1.55
% 1.27/1.55 ============================== end predicate elimination =============
% 1.27/1.55
% 1.27/1.55 Auto_denials: (non-Horn, no changes).
% 1.27/1.55
% 1.27/1.55 Term ordering decisions:
% 1.27/1.55
% 1.27/1.55 % Assigning unary symbol not kb_weight 0 and highest precedence (93).
% 1.27/1.55 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.
% 1.27/1.55
% 1.27/1.55 ============================== end of process initial clauses ========
% 1.27/1.55
% 1.27/1.55 ============================== CLAUSES FOR SEARCH ====================
% 1.27/1.55
% 1.27/1.55 ============================== end of clauses for search =============
% 1.27/1.55
% 1.27/1.55 ============================== SEARCH ================================
% 1.27/1.55
% 1.27/1.55 % Starting search at 0.02 seconds.
% 1.27/1.55
% 1.27/1.55 Low Water (keep): wt=38.000, iters=3382
% 1.27/1.55
% 1.27/1.55 Low Water (keep): wt=37.000, iters=3418
% 1.27/1.55
% 1.27/1.55 Low Water (keep): wt=35.000, iters=3529
% 1.27/1.55
% 1.27/1.55 Low Water (keep): wt=33.000, iters=3525
% 1.27/1.55
% 1.27/1.55 Low Water (keep): wt=31.000, iters=3388
% 1.27/1.55
% 1.27/1.55 Low Water (keep): wt=30.000, iters=3427
% 1.27/1.55
% 1.27/1.55 Low Water (keep): wt=28.000, iters=3372
% 1.27/1.55
% 1.27/1.55 Low Water (keep): wt=27.000, iters=3481
% 1.27/1.55
% 1.27/1.55 Low Water (keep): wt=26.000, iters=3562
% 1.27/1.55
% 1.27/1.55 Low Water (keep): wt=25.000, iters=3344
% 1.27/1.55
% 1.27/1.55 Low Water (keep): wt=24.000, iters=3484
% 70.85/71.18
% 70.85/71.18 Low Water (keep): wt=23.000, iters=3370
% 70.85/71.18
% 70.85/71.18 Low Water (keep): wt=22.000, iters=3402
% 70.85/71.18
% 70.85/71.18 Low Water (keep): wt=21.000, iters=3402
% 70.85/71.18
% 70.85/71.18 Low Water (keep): wt=20.000, iters=3354
% 70.85/71.18
% 70.85/71.18 Low Water (keep): wt=19.000, iters=3388
% 70.85/71.18
% 70.85/71.18 Low Water (keep): wt=18.000, iters=3334
% 70.85/71.18
% 70.85/71.18 Low Water (keep): wt=17.000, iters=3353
% 70.85/71.18
% 70.85/71.18 Low Water (displace): id=1928, wt=59.000
% 70.85/71.18
% 70.85/71.18 Low Water (displace): id=1927, wt=57.000
% 70.85/71.18
% 70.85/71.18 Low Water (displace): id=3236, wt=55.000
% 70.85/71.18
% 70.85/71.18 Low Water (displace): id=3235, wt=53.000
% 70.85/71.18
% 70.85/71.18 Low Water (displace): id=1955, wt=46.000
% 70.85/71.18
% 70.85/71.18 Low Water (displace): id=3275, wt=44.000
% 70.85/71.18
% 70.85/71.18 Low Water (displace): id=2762, wt=43.000
% 70.85/71.18
% 70.85/71.18 Low Water (displace): id=1960, wt=42.000
% 70.85/71.18
% 70.85/71.18 Low Water (displace): id=2761, wt=41.000
% 70.85/71.18
% 70.85/71.18 Low Water (displace): id=3280, wt=40.000
% 70.85/71.18
% 70.85/71.18 Low Water (displace): id=10576, wt=16.000
% 70.85/71.18
% 70.85/71.18 Low Water (displace): id=10590, wt=15.000
% 70.85/71.18
% 70.85/71.18 Low Water (displace): id=11338, wt=13.000
% 70.85/71.18
% 70.85/71.18 Low Water (displace): id=11596, wt=11.000
% 70.85/71.18
% 70.85/71.18 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 147 (0.00 of 1.10 sec).
% 70.85/71.18
% 70.85/71.18 Low Water (keep): wt=16.000, iters=3336
% 70.85/71.18
% 70.85/71.18 Low Water (keep): wt=15.000, iters=3334
% 70.85/71.18
% 70.85/71.18 Low Water (keep): wt=14.000, iters=3337
% 70.85/71.18
% 70.85/71.18 Low Water (keep): wt=13.000, iters=3373
% 70.85/71.18
% 70.85/71.18 Low Water (displace): id=54451, wt=10.000
% 70.85/71.18
% 70.85/71.18 Low Water (displace): id=55958, wt=9.000
% 70.85/71.18
% 70.85/71.18 Low Water (displace): id=57833, wt=8.000
% 70.85/71.18
% 70.85/71.18 Low Water (displace): id=98498, wt=7.000
% 70.85/71.18
% 70.85/71.18 Low Water (keep): wt=12.000, iters=3334
% 70.85/71.18
% 70.85/71.18 Low Water (keep): wt=11.000, iters=4159
% 70.85/71.18
% 70.85/71.18 Low Water (keep): wt=10.000, iters=3334
% 70.85/71.18
% 70.85/71.18 ============================== PROOF =================================
% 70.85/71.18 % SZS status Theorem
% 70.85/71.18 % SZS output start Refutation
% 70.85/71.18
% 70.85/71.18 % Proof 1 at 64.81 (+ 5.35) seconds.
% 70.85/71.18 % Length of proof is 268.
% 70.85/71.18 % Level of proof is 84.
% 70.85/71.18 % Maximum clause weight is 18.000.
% 70.85/71.18 % Given clauses 6814.
% 70.85/71.18
% 70.85/71.18 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].
% 70.85/71.18 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].
% 70.85/71.18 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].
% 70.85/71.18 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 70.85/71.18 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 70.85/71.18 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].
% 70.85/71.18 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].
% 70.85/71.18 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].
% 70.85/71.18 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].
% 70.85/71.18 33 op_implies_and # label(rosser_op_implies_and) # label(axiom). [assumption].
% 70.85/71.18 34 op_equiv # label(rosser_op_equiv) # label(axiom). [assumption].
% 70.85/71.18 35 modus_ponens # label(rosser_modus_ponens) # label(axiom). [assumption].
% 70.85/71.18 36 kn1 # label(rosser_kn1) # label(axiom). [assumption].
% 70.85/71.18 37 kn2 # label(rosser_kn2) # label(axiom). [assumption].
% 70.85/71.18 38 kn3 # label(rosser_kn3) # label(axiom). [assumption].
% 70.85/71.18 39 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption].
% 70.85/71.18 40 -implies_3 # label(hilbert_implies_3) # label(negated_conjecture). [assumption].
% 70.85/71.18 51 -kn1 | is_a_theorem(implies(A,and(A,A))) # label(kn1) # label(axiom). [clausify(16)].
% 70.85/71.18 52 is_a_theorem(implies(A,and(A,A))). [copy(51),unit_del(a,36)].
% 70.85/71.18 54 -kn2 | is_a_theorem(implies(and(A,B),A)) # label(kn2) # label(axiom). [clausify(17)].
% 70.85/71.18 55 is_a_theorem(implies(and(A,B),A)). [copy(54),unit_del(a,37)].
% 70.85/71.18 61 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(2)].
% 70.85/71.18 62 -is_a_theorem(equiv(A,B)) | B = A. [copy(61),unit_del(a,39)].
% 70.85/71.18 67 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 70.85/71.18 68 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(67),unit_del(a,35)].
% 70.85/71.18 78 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 70.85/71.18 79 not(and(A,not(B))) = implies(A,B). [copy(78),unit_del(a,33)].
% 70.85/71.18 88 -op_equiv | and(implies(A,B),implies(B,A)) = equiv(A,B) # label(op_equiv) # label(axiom). [clausify(31)].
% 70.85/71.18 89 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(88),unit_del(a,34)].
% 70.85/71.18 90 implies_3 | -is_a_theorem(implies(implies(c11,c12),implies(implies(c12,c13),implies(c11,c13)))) # label(implies_3) # label(axiom). [clausify(6)].
% 70.85/71.18 91 -is_a_theorem(implies(implies(c11,c12),implies(implies(c12,c13),implies(c11,c13)))). [copy(90),unit_del(a,40)].
% 70.85/71.18 94 -cn1 | is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))) # label(cn1) # label(axiom). [clausify(19)].
% 70.85/71.18 95 cn1 | -is_a_theorem(implies(implies(c39,c40),implies(implies(c40,c41),implies(c39,c41)))) # label(cn1) # label(axiom). [clausify(19)].
% 70.85/71.18 108 -kn3 | is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))) # label(kn3) # label(axiom). [clausify(18)].
% 70.85/71.18 109 is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))). [copy(108),unit_del(a,38)].
% 70.85/71.18 124 -is_a_theorem(A) | is_a_theorem(and(A,A)). [resolve(68,b,52,a)].
% 70.85/71.18 125 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(79(a,1),79(a,1,1,2))].
% 70.85/71.18 126 is_a_theorem(implies(implies(A,A),equiv(A,A))). [para(89(a,1),52(a,1,2))].
% 70.85/71.18 132 -cn1. [ur(94,b,91,a)].
% 70.85/71.18 133 -is_a_theorem(implies(implies(c39,c40),implies(implies(c40,c41),implies(c39,c41)))). [back_unit_del(95),unit_del(a,132)].
% 70.85/71.18 134 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(and(B,C)),not(and(C,A)))). [resolve(109,a,68,b)].
% 70.85/71.18 136 is_a_theorem(implies(implies(A,B),implies(implies(B,C),not(and(not(C),A))))). [para(79(a,1),109(a,1,2,1))].
% 70.85/71.18 139 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(C,and(B,not(A))),not(equiv(B,A))))). [para(89(a,1),109(a,1,2,2,1)),rewrite([125(5)])].
% 70.85/71.18 158 -is_a_theorem(implies(A,A)) | is_a_theorem(equiv(A,A)). [resolve(126,a,68,b)].
% 70.85/71.18 169 implies(implies(A,B),and(B,not(A))) = not(equiv(A,B)). [para(89(a,1),125(a,1,1)),flip(a)].
% 70.85/71.18 255 -is_a_theorem(implies(A,B)) | -is_a_theorem(not(equiv(A,B))) | is_a_theorem(and(B,not(A))). [para(169(a,1),68(b,1))].
% 70.85/71.18 267 is_a_theorem(implies(not(and(and(A,A),B)),not(and(B,A)))). [resolve(134,a,52,a)].
% 70.85/71.18 290 -is_a_theorem(not(and(and(A,A),B))) | is_a_theorem(not(and(B,A))). [resolve(267,a,68,b)].
% 70.85/71.18 388 -is_a_theorem(implies(and(A,A),B)) | is_a_theorem(not(and(not(B),A))). [para(79(a,1),290(a,1))].
% 70.85/71.18 670 is_a_theorem(not(and(not(A),A))). [resolve(388,a,55,a)].
% 70.85/71.18 674 is_a_theorem(and(not(and(not(A),A)),not(and(not(A),A)))). [resolve(670,a,124,a)].
% 70.85/71.18 702 is_a_theorem(not(and(implies(A,B),and(A,not(B))))). [para(79(a,1),670(a,1,1,1))].
% 70.85/71.18 703 is_a_theorem(implies(not(not(A)),A)). [para(79(a,1),670(a,1))].
% 70.85/71.18 706 is_a_theorem(implies(not(and(A,B)),implies(B,not(A)))). [resolve(703,a,134,a),rewrite([79(6)])].
% 70.85/71.18 708 -is_a_theorem(not(not(A))) | is_a_theorem(A). [resolve(703,a,68,b)].
% 70.85/71.18 997 -is_a_theorem(not(and(A,B))) | is_a_theorem(implies(B,not(A))). [resolve(706,a,68,b)].
% 70.85/71.18 1029 is_a_theorem(implies(implies(A,B),implies(not(B),not(A)))). [para(79(a,1),706(a,1,1))].
% 70.85/71.18 1579 is_a_theorem(implies(and(A,not(B)),not(implies(A,B)))). [resolve(997,a,702,a)].
% 70.85/71.18 1580 is_a_theorem(implies(A,not(not(A)))). [resolve(997,a,670,a)].
% 70.85/71.18 1584 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(B),not(A))). [para(79(a,1),997(a,1))].
% 70.85/71.18 1753 is_a_theorem(not(and(not(not(not(and(A,A)))),A))). [resolve(1580,a,388,a)].
% 70.85/71.18 1755 is_a_theorem(implies(not(and(not(not(A)),B)),not(and(B,A)))). [resolve(1580,a,134,a)].
% 70.85/71.18 1757 -is_a_theorem(A) | is_a_theorem(not(not(A))). [resolve(1580,a,68,b)].
% 70.85/71.18 1803 is_a_theorem(not(not(implies(A,not(not(A)))))). [resolve(1757,a,1580,a)].
% 70.85/71.18 1830 is_a_theorem(not(not(implies(and(A,B),A)))). [resolve(1757,a,55,a)].
% 70.85/71.18 1831 is_a_theorem(not(not(implies(A,and(A,A))))). [resolve(1757,a,52,a)].
% 70.85/71.18 3999 -is_a_theorem(and(A,not(B))) | is_a_theorem(not(implies(A,B))). [resolve(1579,a,68,b)].
% 70.85/71.18 4535 is_a_theorem(implies(not(A),not(and(A,B)))). [resolve(1584,a,55,a)].
% 70.85/71.18 4536 is_a_theorem(implies(not(and(A,A)),not(A))). [resolve(1584,a,52,a)].
% 70.85/71.18 4780 -is_a_theorem(not(A)) | is_a_theorem(not(and(A,B))). [resolve(4535,a,68,b)].
% 70.85/71.18 4852 is_a_theorem(implies(not(A),implies(A,B))). [para(79(a,1),4535(a,1,2))].
% 70.85/71.18 4859 is_a_theorem(implies(not(and(implies(A,B),C)),implies(C,A))). [resolve(4852,a,134,a),rewrite([79(6)])].
% 70.85/71.18 4861 -is_a_theorem(not(A)) | is_a_theorem(implies(A,B)). [resolve(4852,a,68,b)].
% 70.85/71.18 4950 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(and(A,not(B)),C)). [para(79(a,1),4861(a,1))].
% 70.85/71.18 5285 is_a_theorem(implies(not(not(A)),not(not(and(A,A))))). [resolve(4536,a,1584,a)].
% 70.85/71.18 5289 -is_a_theorem(not(and(A,A))) | is_a_theorem(not(A)). [resolve(4536,a,68,b)].
% 70.85/71.18 5361 is_a_theorem(not(and(not(implies(A,and(A,A))),B))). [resolve(4780,a,1831,a)].
% 70.85/71.18 5362 is_a_theorem(not(and(not(implies(and(A,B),A)),C))). [resolve(4780,a,1830,a)].
% 70.85/71.18 5366 is_a_theorem(not(and(not(implies(A,not(not(A)))),B))). [resolve(4780,a,1803,a)].
% 70.85/71.18 5371 is_a_theorem(not(and(and(not(A),A),B))). [resolve(4780,a,670,a)].
% 70.85/71.18 5377 -is_a_theorem(implies(not(A),A)) | is_a_theorem(not(not(A))). [para(79(a,1),5289(a,1))].
% 70.85/71.18 5385 is_a_theorem(implies(A,not(and(not(B),B)))). [resolve(5371,a,997,a)].
% 70.85/71.18 9217 -is_a_theorem(not(not(A))) | is_a_theorem(not(not(and(A,A)))). [resolve(5285,a,68,b)].
% 70.85/71.18 11680 -is_a_theorem(not(and(implies(A,B),C))) | is_a_theorem(implies(C,A)). [resolve(4859,a,68,b)].
% 70.85/71.18 11693 is_a_theorem(implies(implies(implies(A,B),C),implies(not(C),A))). [para(79(a,1),4859(a,1,1))].
% 70.85/71.18 11694 is_a_theorem(implies(not(equiv(A,B)),implies(implies(B,A),A))). [para(89(a,1),4859(a,1,1,1))].
% 70.85/71.18 13973 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(not(C),A)). [para(79(a,1),11680(a,1))].
% 70.85/71.18 14650 is_a_theorem(implies(not(implies(not(A),B)),implies(B,C))). [resolve(13973,a,11693,a)].
% 70.85/71.18 15155 is_a_theorem(not(not(implies(not(A),not(A))))). [resolve(14650,a,5377,a)].
% 70.85/71.18 15185 is_a_theorem(implies(not(A),not(A))). [resolve(15155,a,708,a)].
% 70.85/71.18 15272 is_a_theorem(implies(not(and(not(A),B)),implies(B,A))). [resolve(15185,a,134,a),rewrite([79(6)])].
% 70.85/71.18 16922 -is_a_theorem(not(and(not(A),B))) | is_a_theorem(implies(B,A)). [resolve(15272,a,68,b)].
% 70.85/71.18 16943 is_a_theorem(implies(not(equiv(A,B)),not(equiv(B,A)))). [para(169(a,1),15272(a,1,2)),rewrite([79(3),89(3)])].
% 70.85/71.18 17496 is_a_theorem(implies(A,implies(B,not(not(B))))). [resolve(16922,a,5366,a)].
% 70.85/71.18 17498 is_a_theorem(implies(A,implies(and(B,C),B))). [resolve(16922,a,5362,a)].
% 70.85/71.18 17499 is_a_theorem(implies(A,implies(B,and(B,B)))). [resolve(16922,a,5361,a)].
% 70.85/71.18 17505 is_a_theorem(implies(A,not(not(and(A,A))))). [resolve(16922,a,1753,a)].
% 70.85/71.18 17508 is_a_theorem(implies(A,A)). [resolve(16922,a,670,a)].
% 70.85/71.18 17514 -is_a_theorem(implies(not(A),B)) | is_a_theorem(implies(not(B),A)). [para(79(a,1),16922(a,1))].
% 70.85/71.18 17520 is_a_theorem(equiv(A,A)). [back_unit_del(158),unit_del(a,17508)].
% 70.85/71.18 17529 is_a_theorem(implies(and(A,not(A)),B)). [resolve(17508,a,4950,a)].
% 70.85/71.18 17535 is_a_theorem(implies(not(and(A,B)),not(and(B,A)))). [resolve(17508,a,134,a)].
% 70.85/71.18 17740 is_a_theorem(not(not(equiv(A,A)))). [resolve(17520,a,1757,a)].
% 70.85/71.18 18377 is_a_theorem(not(not(and(equiv(A,A),equiv(A,A))))). [resolve(17740,a,9217,a)].
% 70.85/71.18 18572 is_a_theorem(implies(not(A),implies(B,B))). [resolve(17529,a,1584,a),rewrite([79(4)])].
% 70.85/71.18 19270 is_a_theorem(implies(not(and(implies(A,A),B)),implies(B,C))). [resolve(18572,a,134,a),rewrite([79(6)])].
% 70.85/71.18 19914 -is_a_theorem(A) | is_a_theorem(not(not(and(A,A)))). [resolve(17505,a,68,b)].
% 70.85/71.18 19924 is_a_theorem(implies(not(A),not(implies(not(A),A)))). [para(79(a,1),17505(a,1,2,1))].
% 70.85/71.18 22689 -is_a_theorem(not(A)) | is_a_theorem(not(implies(not(A),A))). [resolve(19924,a,68,b)].
% 70.85/71.18 23992 -is_a_theorem(not(equiv(A,B))) | is_a_theorem(not(equiv(B,A))). [resolve(16943,a,68,b)].
% 70.85/71.18 24093 is_a_theorem(implies(not(implies(implies(A,B),B)),equiv(B,A))). [resolve(17514,a,11694,a)].
% 70.85/71.18 24987 is_a_theorem(implies(not(not(and(A,B))),and(B,A))). [resolve(17535,a,17514,a)].
% 70.85/71.18 25000 -is_a_theorem(not(and(A,B))) | is_a_theorem(not(and(B,A))). [resolve(17535,a,68,b)].
% 70.85/71.18 25001 is_a_theorem(implies(implies(A,B),not(and(not(B),A)))). [para(79(a,1),17535(a,1,1))].
% 70.85/71.18 29569 -is_a_theorem(implies(A,B)) | is_a_theorem(not(and(not(B),A))). [para(79(a,1),25000(a,1))].
% 70.85/71.18 29575 is_a_theorem(implies(not(not(and(not(A),B))),B)). [resolve(25001,a,13973,a)].
% 70.85/71.18 29825 is_a_theorem(implies(not(A),not(and(not(B),A)))). [resolve(29575,a,17514,a)].
% 70.85/71.18 32890 is_a_theorem(implies(not(implies(A,B)),and(implies(B,C),A))). [resolve(29569,a,4859,a),rewrite([79(7)])].
% 70.85/71.18 39546 is_a_theorem(implies(not(implies(A,B)),and(implies(C,C),A))). [resolve(19270,a,29569,a),rewrite([79(7)])].
% 70.85/71.18 44238 -is_a_theorem(not(implies(implies(A,B),B))) | is_a_theorem(equiv(B,A)). [resolve(24093,a,68,b)].
% 70.85/71.18 50375 -is_a_theorem(not(implies(A,B))) | is_a_theorem(and(implies(B,C),A)). [resolve(32890,a,68,b)].
% 70.85/71.18 53957 -is_a_theorem(not(implies(A,B))) | is_a_theorem(and(implies(C,C),A)). [resolve(39546,a,68,b)].
% 70.85/71.18 76070 is_a_theorem(implies(not(not(and(A,B))),and(not(not(B)),A))). [resolve(1755,a,29569,a),rewrite([79(9)])].
% 70.85/71.18 76088 -is_a_theorem(not(and(not(not(A)),B))) | is_a_theorem(not(and(B,A))). [resolve(1755,a,68,b)].
% 70.85/71.18 81861 -is_a_theorem(not(not(and(A,B)))) | is_a_theorem(and(not(not(B)),A)). [resolve(76070,a,68,b)].
% 70.85/71.18 81913 -is_a_theorem(implies(not(not(A)),B)) | is_a_theorem(not(and(not(B),A))). [para(79(a,1),76088(a,1))].
% 70.85/71.18 88911 is_a_theorem(and(not(not(equiv(A,A))),equiv(A,A))). [resolve(81861,a,18377,a)].
% 70.85/71.18 92843 is_a_theorem(not(and(not(implies(not(A),B)),B))). [resolve(81913,a,29825,a),rewrite([79(4)])].
% 70.85/71.18 92871 is_a_theorem(not(and(not(and(A,B)),and(B,A)))). [resolve(81913,a,24987,a)].
% 70.85/71.18 92955 is_a_theorem(implies(A,implies(not(B),A))). [resolve(92843,a,25000,a),rewrite([79(5)])].
% 70.85/71.18 102998 is_a_theorem(implies(and(A,B),and(B,A))). [resolve(92871,a,25000,a),rewrite([79(5)])].
% 70.85/71.18 103015 is_a_theorem(implies(and(A,B),not(not(and(B,A))))). [resolve(92871,a,997,a)].
% 70.85/71.18 103063 -is_a_theorem(and(A,B)) | is_a_theorem(and(B,A)). [resolve(102998,a,68,b)].
% 70.85/71.18 103558 is_a_theorem(and(equiv(A,A),not(not(equiv(A,A))))). [resolve(103063,a,88911,a)].
% 70.85/71.18 108991 -is_a_theorem(and(A,B)) | is_a_theorem(not(not(and(B,A)))). [resolve(103015,a,68,b)].
% 70.85/71.18 109002 is_a_theorem(implies(and(not(A),B),not(implies(B,A)))). [para(79(a,1),103015(a,1,2,1))].
% 70.85/71.18 109419 is_a_theorem(not(implies(equiv(A,A),not(equiv(A,A))))). [resolve(103558,a,3999,a)].
% 70.85/71.18 113667 is_a_theorem(not(implies(not(and(not(A),A)),and(not(A),A)))). [resolve(108991,a,674,a),rewrite([79(8)])].
% 70.85/71.18 113725 -is_a_theorem(and(not(A),B)) | is_a_theorem(not(implies(B,A))). [resolve(109002,a,68,b)].
% 70.85/71.18 113957 is_a_theorem(and(implies(A,A),equiv(B,B))). [resolve(109419,a,53957,a)].
% 70.85/71.18 114036 is_a_theorem(not(not(and(implies(A,A),equiv(B,B))))). [resolve(113957,a,1757,a)].
% 70.85/71.18 114723 is_a_theorem(and(not(not(equiv(A,A))),implies(B,B))). [resolve(114036,a,81861,a)].
% 70.85/71.18 114990 is_a_theorem(not(implies(implies(A,A),not(equiv(B,B))))). [resolve(114723,a,113725,a)].
% 70.85/71.18 115069 is_a_theorem(and(implies(not(equiv(A,A)),B),implies(C,C))). [resolve(114990,a,50375,a)].
% 70.85/71.18 118409 is_a_theorem(and(implies(A,A),implies(not(equiv(B,B)),C))). [resolve(115069,a,103063,a)].
% 70.85/71.18 129842 is_a_theorem(and(implies(A,A),not(and(not(B),B)))). [resolve(113667,a,53957,a)].
% 70.85/71.18 129931 is_a_theorem(not(implies(implies(A,A),and(not(B),B)))). [resolve(129842,a,3999,a)].
% 70.85/71.18 129937 is_a_theorem(and(implies(A,A),implies(not(not(B)),B))). [para(79(a,1),129842(a,1,2))].
% 70.85/71.18 130124 is_a_theorem(and(implies(and(not(A),A),B),implies(C,C))). [resolve(129931,a,50375,a)].
% 70.85/71.18 130152 is_a_theorem(not(implies(implies(not(not(A)),A),and(B,not(B))))). [resolve(129937,a,108991,a),rewrite([125(6)])].
% 70.85/71.18 130554 is_a_theorem(not(implies(implies(and(not(A),A),B),and(C,not(C))))). [resolve(130124,a,1757,a),rewrite([125(6)])].
% 70.85/71.18 136524 is_a_theorem(equiv(and(A,not(A)),not(implies(A,A)))). [resolve(130152,a,44238,a),rewrite([79(5)])].
% 70.85/71.18 136607 not(implies(A,A)) = and(A,not(A)). [resolve(136524,a,62,a)].
% 70.85/71.18 136635 not(and(A,and(B,not(B)))) = implies(A,implies(B,B)). [para(136607(a,1),79(a,1,1,2))].
% 70.85/71.18 162114 is_a_theorem(equiv(and(A,not(A)),and(not(B),B))). [resolve(130554,a,44238,a)].
% 70.85/71.18 162265 and(not(A),A) = and(B,not(B)). [resolve(162114,a,62,a)].
% 70.85/71.18 162272 and(not(A),A) = c_0. [new_symbol(162265)].
% 70.85/71.18 162275 and(A,not(A)) = c_0. [back_rewrite(162265),rewrite([162272(2)]),flip(a)].
% 70.85/71.18 163105 is_a_theorem(implies(A,not(c_0))). [back_rewrite(5385),rewrite([162272(2)])].
% 70.85/71.18 163109 is_a_theorem(not(and(c_0,A))). [back_rewrite(5371),rewrite([162272(2)])].
% 70.85/71.18 163166 is_a_theorem(not(c_0)). [back_rewrite(670),rewrite([162272(2)])].
% 70.85/71.18 163257 implies(A,implies(B,B)) = not(and(A,c_0)). [back_rewrite(136635),rewrite([162275(2)]),flip(a)].
% 70.85/71.18 163268 not(implies(A,A)) = c_0. [back_rewrite(136607),rewrite([162275(4)])].
% 70.85/71.18 164927 is_a_theorem(not(implies(implies(A,not(c_0)),and(A,not(not(c_0)))))). [resolve(163105,a,19914,a),rewrite([125(8)])].
% 70.85/71.18 164936 is_a_theorem(implies(not(and(not(c_0),A)),not(and(A,B)))). [resolve(163105,a,134,a)].
% 70.85/71.18 165104 is_a_theorem(not(implies(not(and(c_0,A)),and(c_0,A)))). [resolve(163109,a,22689,a)].
% 70.85/71.18 165257 implies(not(not(A)),A) = not(c_0). [para(162272(a,1),79(a,1,1)),flip(a)].
% 70.85/71.18 165380 implies(A,A) = not(c_0). [para(162275(a,1),79(a,1,1)),flip(a)].
% 70.85/71.18 165384 not(equiv(A,A)) = implies(not(c_0),c_0). [para(162275(a,1),169(a,1,2)),rewrite([165380(1)]),flip(a)].
% 70.85/71.18 165457 not(not(c_0)) = c_0. [back_rewrite(163268),rewrite([165380(1)])].
% 70.85/71.18 165458 not(and(A,c_0)) = implies(A,not(c_0)). [back_rewrite(163257),rewrite([165380(1)]),flip(a)].
% 70.85/71.18 165697 is_a_theorem(and(not(c_0),implies(not(equiv(A,A)),B))). [back_rewrite(118409),rewrite([165380(1)])].
% 70.85/71.18 165737 -is_a_theorem(not(implies(A,B))) | is_a_theorem(and(not(c_0),A)). [back_rewrite(53957),rewrite([165380(4)])].
% 70.85/71.18 165799 is_a_theorem(not(implies(implies(A,not(c_0)),and(A,c_0)))). [back_rewrite(164927),rewrite([165457(6)])].
% 70.85/71.18 173566 not(equiv(A,A)) = not(equiv(B,B)). [para(165384(a,2),165384(a,2))].
% 70.85/71.18 178327 and(equiv(A,A),not(equiv(B,B))) = c_0. [para(173566(a,1),162275(a,1,2))].
% 70.85/71.18 188837 is_a_theorem(not(implies(implies(not(equiv(A,A)),B),c_0))). [resolve(165697,a,113725,a)].
% 70.85/71.18 189209 is_a_theorem(and(not(c_0),not(and(c_0,A)))). [resolve(165737,a,165104,a)].
% 70.85/71.18 189240 is_a_theorem(not(implies(not(and(c_0,A)),c_0))). [resolve(189209,a,113725,a)].
% 70.85/71.18 189422 is_a_theorem(and(implies(c_0,A),not(and(c_0,B)))). [resolve(189240,a,50375,a)].
% 70.85/71.18 190168 is_a_theorem(not(implies(implies(c_0,A),and(c_0,B)))). [resolve(189422,a,3999,a)].
% 70.85/71.18 190486 is_a_theorem(equiv(and(c_0,A),c_0)). [resolve(190168,a,44238,a)].
% 70.85/71.18 190571 and(c_0,A) = c_0. [resolve(190486,a,62,a),flip(a)].
% 70.85/71.18 190572 implies(c_0,A) = not(c_0). [para(190571(a,1),79(a,1,1)),flip(a)].
% 70.85/71.18 190574 implies(implies(A,c_0),c_0) = not(equiv(A,c_0)). [para(190571(a,1),169(a,1,2))].
% 70.85/71.18 190629 and(not(c_0),implies(A,c_0)) = equiv(c_0,A). [para(190572(a,1),89(a,1,1))].
% 70.85/71.18 190640 -is_a_theorem(not(implies(not(c_0),A))) | is_a_theorem(equiv(A,c_0)). [para(190572(a,1),44238(a,1,1,1))].
% 70.85/71.18 190848 is_a_theorem(and(not(c_0),implies(A,not(c_0)))). [resolve(165799,a,165737,a)].
% 70.85/71.18 190984 is_a_theorem(not(implies(not(c_0),and(A,c_0)))). [resolve(190848,a,1757,a),rewrite([125(7),165457(5)])].
% 70.85/71.18 191210 is_a_theorem(and(implies(and(A,c_0),B),not(c_0))). [resolve(190984,a,50375,a)].
% 70.85/71.18 191774 is_a_theorem(not(implies(implies(and(A,c_0),B),c_0))). [resolve(191210,a,3999,a)].
% 70.85/71.18 192014 is_a_theorem(equiv(c_0,and(A,c_0))). [resolve(191774,a,44238,a)].
% 70.85/71.18 192098 and(A,c_0) = c_0. [resolve(192014,a,62,a)].
% 70.85/71.18 192210 implies(A,not(c_0)) = not(c_0). [back_rewrite(165458),rewrite([192098(2)]),flip(a)].
% 70.85/71.18 192223 and(implies(not(c_0),A),not(c_0)) = equiv(not(c_0),A). [para(192210(a,1),89(a,1,2))].
% 70.85/71.18 196143 implies(equiv(A,A),equiv(B,B)) = not(c_0). [para(178327(a,1),79(a,1,1)),flip(a)].
% 70.85/71.18 196145 not(equiv(equiv(A,A),equiv(B,B))) = implies(not(c_0),c_0). [para(178327(a,1),169(a,1,2)),rewrite([196143(3)]),flip(a)].
% 70.85/71.18 196147 is_a_theorem(implies(implies(not(c_0),A),implies(implies(A,c_0),implies(not(c_0),c_0)))). [para(178327(a,1),139(a,1,2,1,2)),rewrite([196143(3),196145(9)])].
% 70.85/71.18 197295 is_a_theorem(equiv(c_0,not(equiv(A,A)))). [resolve(188837,a,44238,a)].
% 70.85/71.18 197383 not(equiv(A,A)) = c_0. [resolve(197295,a,62,a)].
% 70.85/71.18 197396 implies(not(c_0),c_0) = c_0. [back_rewrite(165384),rewrite([197383(2)]),flip(a)].
% 70.85/71.18 197397 is_a_theorem(implies(implies(not(c_0),A),not(equiv(A,c_0)))). [back_rewrite(196147),rewrite([197396(9),190574(7)])].
% 70.85/71.18 197704 equiv(c_0,c_0) = and(not(c_0),not(c_0)). [para(165380(a,1),190629(a,1,2)),flip(a)].
% 70.85/71.18 198070 -is_a_theorem(implies(not(c_0),A)) | is_a_theorem(not(equiv(A,c_0))). [resolve(197397,a,68,b)].
% 70.85/71.18 198245 is_a_theorem(not(equiv(implies(A,and(A,A)),c_0))). [resolve(198070,a,17499,a)].
% 70.85/71.18 198246 is_a_theorem(not(equiv(implies(and(A,B),A),c_0))). [resolve(198070,a,17498,a)].
% 70.85/71.18 198248 is_a_theorem(not(equiv(implies(A,not(not(A))),c_0))). [resolve(198070,a,17496,a)].
% 70.85/71.18 198322 is_a_theorem(not(equiv(c_0,implies(A,and(A,A))))). [resolve(198245,a,23992,a)].
% 70.85/71.18 198402 is_a_theorem(not(equiv(c_0,implies(and(A,B),A)))). [resolve(198246,a,23992,a)].
% 70.85/71.18 198482 is_a_theorem(not(equiv(c_0,implies(A,not(not(A)))))). [resolve(198248,a,23992,a)].
% 70.85/71.18 198607 is_a_theorem(and(implies(A,and(A,A)),not(c_0))). [resolve(198322,a,255,b),rewrite([190572(4)]),unit_del(a,163166)].
% 70.85/71.18 198687 is_a_theorem(and(implies(and(A,B),A),not(c_0))). [resolve(198402,a,255,b),rewrite([190572(4)]),unit_del(a,163166)].
% 70.85/71.18 198768 is_a_theorem(and(implies(A,not(not(A))),not(c_0))). [resolve(198482,a,255,b),rewrite([190572(5)]),unit_del(a,163166)].
% 70.85/71.18 198787 is_a_theorem(not(implies(not(c_0),and(A,not(and(A,A)))))). [resolve(198607,a,108991,a),rewrite([125(6)])].
% 70.85/71.18 198867 is_a_theorem(not(implies(not(c_0),and(and(A,B),not(A))))). [resolve(198687,a,108991,a),rewrite([125(6)])].
% 70.85/71.18 198926 is_a_theorem(not(implies(not(c_0),and(A,not(not(not(A))))))). [resolve(198768,a,108991,a),rewrite([125(7)])].
% 70.85/71.18 205208 is_a_theorem(implies(not(not(and(A,B))),not(not(and(not(c_0),A))))). [resolve(164936,a,1584,a)].
% 70.85/71.18 212308 is_a_theorem(equiv(and(A,not(and(A,A))),c_0)). [resolve(198787,a,190640,a)].
% 70.85/71.18 212440 and(A,not(and(A,A))) = c_0. [resolve(212308,a,62,a),flip(a)].
% 70.85/71.18 212443 implies(A,and(A,A)) = not(c_0). [para(212440(a,1),79(a,1,1)),flip(a)].
% 70.85/71.18 212504 and(not(c_0),implies(and(A,A),A)) = equiv(A,and(A,A)). [para(212443(a,1),89(a,1,1))].
% 70.85/71.18 212627 is_a_theorem(equiv(and(and(A,B),not(A)),c_0)). [resolve(198867,a,190640,a)].
% 70.85/71.18 212760 and(and(A,B),not(A)) = c_0. [resolve(212627,a,62,a),flip(a)].
% 70.85/71.18 212775 implies(and(A,B),A) = not(c_0). [para(212760(a,1),79(a,1,1)),flip(a)].
% 70.85/71.18 212805 equiv(A,and(A,A)) = and(not(c_0),not(c_0)). [back_rewrite(212504),rewrite([212775(4)]),flip(a)].
% 70.85/71.18 212806 and(not(c_0),implies(A,and(A,B))) = equiv(and(A,B),A). [para(212775(a,1),89(a,1,1))].
% 70.85/71.18 212977 is_a_theorem(equiv(and(A,not(not(not(A)))),c_0)). [resolve(198926,a,190640,a)].
% 70.85/71.18 213109 and(A,not(not(not(A)))) = c_0. [resolve(212977,a,62,a),flip(a)].
% 70.85/71.18 213121 not(equiv(not(not(A)),A)) = c_0. [para(213109(a,1),169(a,1,2)),rewrite([165257(3),197396(4)]),flip(a)].
% 70.85/71.18 213176 is_a_theorem(equiv(not(not(A)),A)). [para(213121(a,1),708(a,1,1)),unit_del(a,163166)].
% 70.85/71.18 213226 not(not(A)) = A. [resolve(213176,a,62,a),flip(a)].
% 70.85/71.18 213279 is_a_theorem(implies(and(A,B),and(not(c_0),A))). [back_rewrite(205208),rewrite([213226(3),213226(6)])].
% 70.85/71.18 213545 not(and(A,B)) = implies(A,not(B)). [para(213226(a,1),79(a,1,1,2))].
% 70.85/71.18 213546 not(implies(A,B)) = and(A,not(B)). [para(79(a,1),213226(a,1,1))].
% 70.85/71.18 213639 is_a_theorem(implies(A,implies(B,A))). [para(213226(a,1),92955(a,1,2,1))].
% 70.85/71.18 213780 equiv(A,A) = not(c_0). [para(197383(a,1),213226(a,1,1)),flip(a)].
% 70.85/71.18 214206 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(not(C),not(A))))). [back_rewrite(136),rewrite([213545(5)])].
% 70.85/71.18 214626 and(not(c_0),not(c_0)) = not(c_0). [back_rewrite(197704),rewrite([213780(3)]),flip(a)].
% 70.85/71.18 214638 equiv(A,and(A,A)) = not(c_0). [back_rewrite(212805),rewrite([214626(7)])].
% 70.85/71.18 218422 and(A,A) = A. [para(214638(a,1),62(a,1)),unit_del(a,163166)].
% 70.85/71.18 219159 is_a_theorem(implies(A,and(not(c_0),A))). [para(218422(a,1),213279(a,1,1))].
% 70.85/71.18 219168 is_a_theorem(implies(implies(not(c_0),A),A)). [resolve(219159,a,17514,a),rewrite([213545(5),213226(4)])].
% 70.85/71.18 219170 -is_a_theorem(A) | is_a_theorem(and(not(c_0),A)). [resolve(219159,a,68,b)].
% 70.85/71.18 219193 is_a_theorem(implies(implies(A,c_0),equiv(c_0,A))). [para(190629(a,1),219159(a,1,2))].
% 70.85/71.18 219437 is_a_theorem(and(not(c_0),implies(implies(not(c_0),A),A))). [resolve(219170,a,219168,a)].
% 70.85/71.18 219615 is_a_theorem(implies(not(equiv(c_0,A)),A)). [resolve(219193,a,13973,a)].
% 70.85/71.18 219633 is_a_theorem(implies(not(A),equiv(c_0,A))). [resolve(219615,a,17514,a)].
% 70.85/71.18 219929 -is_a_theorem(not(A)) | is_a_theorem(equiv(c_0,A)). [resolve(219633,a,68,b)].
% 70.85/71.18 219971 -is_a_theorem(A) | is_a_theorem(equiv(c_0,not(A))). [para(213226(a,1),219929(a,1))].
% 70.85/71.18 220031 is_a_theorem(equiv(c_0,and(A,and(B,not(A))))). [resolve(219971,a,213639,a),rewrite([213546(4),213546(3)])].
% 70.85/71.18 221768 and(A,and(B,not(A))) = c_0. [resolve(220031,a,62,a)].
% 70.85/71.18 221780 implies(A,implies(B,A)) = not(c_0). [para(221768(a,1),213545(a,1,1)),rewrite([213545(5),213226(4)]),flip(a)].
% 70.85/71.18 221792 and(not(c_0),implies(implies(A,B),B)) = equiv(B,implies(A,B)). [para(221780(a,1),89(a,1,1))].
% 70.85/71.18 221804 is_a_theorem(equiv(A,implies(not(c_0),A))). [back_rewrite(219437),rewrite([221792(7)])].
% 70.85/71.18 221815 implies(not(c_0),A) = A. [resolve(221804,a,62,a)].
% 70.85/71.18 221885 equiv(not(c_0),A) = and(A,not(c_0)). [back_rewrite(192223),rewrite([221815(3)]),flip(a)].
% 70.85/71.18 221939 is_a_theorem(implies(implies(A,c_0),not(A))). [para(221815(a,1),1029(a,1,2))].
% 70.85/71.18 224310 is_a_theorem(implies(A,and(A,not(c_0)))). [resolve(221939,a,1584,a),rewrite([213226(2),213546(3)])].
% 70.85/71.18 225443 is_a_theorem(equiv(and(A,not(c_0)),A)). [resolve(224310,a,219170,a),rewrite([212806(7)])].
% 70.85/71.18 225518 and(A,not(c_0)) = A. [resolve(225443,a,62,a),flip(a)].
% 70.85/71.18 225525 equiv(not(c_0),A) = A. [back_rewrite(221885),rewrite([225518(6)])].
% 70.85/71.18 226170 -is_a_theorem(A) | not(c_0) = A. [para(225525(a,1),62(a,1)),flip(b)].
% 70.85/71.18 226751 implies(and(A,B),and(B,A)) = not(c_0). [resolve(226170,a,102998,a),flip(a)].
% 70.85/71.18 227567 equiv(and(A,B),and(B,A)) = not(c_0). [para(226751(a,1),89(a,1,1)),rewrite([226751(5),218422(5)]),flip(a)].
% 70.85/71.18 230369 and(A,B) = and(B,A). [para(227567(a,1),62(a,1)),unit_del(a,163166)].
% 70.85/71.18 232032 implies(A,not(B)) = implies(B,not(A)). [para(230369(a,1),213545(a,1,1)),rewrite([213545(2)])].
% 70.85/71.18 232369 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))). [back_rewrite(214206),rewrite([232032(5),213226(4)])].
% 70.85/71.18 232370 $F. [resolve(232369,a,133,a)].
% 70.85/71.18
% 70.85/71.18 % SZS output end Refutation
% 70.85/71.18 ============================== end of proof ==========================
% 70.85/71.18
% 70.85/71.18 ============================== STATISTICS ============================
% 70.85/71.18
% 70.85/71.18 Given=6814. Generated=9830478. Kept=232319. proofs=1.
% 70.85/71.18 Usable=267. Sos=1448. Demods=162. Limbo=337, Disabled=230338. Hints=0.
% 70.85/71.18 Megabytes=146.04.
% 70.85/71.18 User_CPU=64.81, System_CPU=5.35, Wall_clock=71.
% 70.85/71.18
% 70.85/71.18 ============================== end of statistics =====================
% 70.85/71.18
% 70.85/71.18 ============================== end of search =========================
% 70.85/71.18
% 70.85/71.18 THEOREM PROVED
% 70.85/71.18 % SZS status Theorem
% 70.85/71.18
% 70.85/71.18 Exiting with 1 proof.
% 70.85/71.18
% 70.85/71.18 Process 2863 exit (max_proofs) Sat Jul 2 20:50:46 2022
% 70.85/71.18 Prover9 interrupted
%------------------------------------------------------------------------------