TSTP Solution File: LCL515+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL515+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n024.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 13:47:18 EDT 2022
% Result : Theorem 66.37s 66.68s
% Output : Refutation 66.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL515+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 3 16:54:30 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.45/1.01 ============================== Prover9 ===============================
% 0.45/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.45/1.01 Process 26341 was started by sandbox on n024.cluster.edu,
% 0.45/1.01 Sun Jul 3 16:54:30 2022
% 0.45/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_26188_n024.cluster.edu".
% 0.45/1.01 ============================== end of head ===========================
% 0.45/1.01
% 0.45/1.01 ============================== INPUT =================================
% 0.45/1.01
% 0.45/1.01 % Reading from file /tmp/Prover9_26188_n024.cluster.edu
% 0.45/1.01
% 0.45/1.01 set(prolog_style_variables).
% 0.45/1.01 set(auto2).
% 0.45/1.01 % set(auto2) -> set(auto).
% 0.45/1.01 % set(auto) -> set(auto_inference).
% 0.45/1.01 % set(auto) -> set(auto_setup).
% 0.45/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.45/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/1.01 % set(auto) -> set(auto_limits).
% 0.45/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/1.01 % set(auto) -> set(auto_denials).
% 0.45/1.01 % set(auto) -> set(auto_process).
% 0.45/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.45/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.45/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.45/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.45/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.45/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.45/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.45/1.01 % set(auto2) -> assign(stats, some).
% 0.45/1.01 % set(auto2) -> clear(echo_input).
% 0.45/1.01 % set(auto2) -> set(quiet).
% 0.45/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.45/1.01 % set(auto2) -> clear(print_given).
% 0.45/1.01 assign(lrs_ticks,-1).
% 0.45/1.01 assign(sos_limit,10000).
% 0.45/1.01 assign(order,kbo).
% 0.45/1.01 set(lex_order_vars).
% 0.45/1.01 clear(print_given).
% 0.45/1.01
% 0.45/1.01 % formulas(sos). % not echoed (43 formulas)
% 0.45/1.01
% 0.45/1.01 ============================== end of input ==========================
% 0.45/1.01
% 0.45/1.01 % From the command line: assign(max_seconds, 300).
% 0.45/1.01
% 0.45/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/1.01
% 0.45/1.01 % Formulas that are not ordinary clauses:
% 0.45/1.01 1 modus_ponens <-> (all X all Y (is_a_theorem(X) & is_a_theorem(implies(X,Y)) -> is_a_theorem(Y))) # label(modus_ponens) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 2 substitution_of_equivalents <-> (all X all Y (is_a_theorem(equiv(X,Y)) -> X = Y)) # label(substitution_of_equivalents) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 3 modus_tollens <-> (all X all Y is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))) # label(modus_tollens) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 5 implies_2 <-> (all X all Y is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))) # label(implies_2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 6 implies_3 <-> (all X all Y all Z is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))) # label(implies_3) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 9 and_3 <-> (all X all Y is_a_theorem(implies(X,implies(Y,and(X,Y))))) # label(and_3) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 12 or_3 <-> (all X all Y all Z is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))) # label(or_3) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 13 equivalence_1 <-> (all X all Y is_a_theorem(implies(equiv(X,Y),implies(X,Y)))) # label(equivalence_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 14 equivalence_2 <-> (all X all Y is_a_theorem(implies(equiv(X,Y),implies(Y,X)))) # label(equivalence_2) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.49 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].
% 1.21/1.49 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.49 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.49 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].
% 1.21/1.49 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].
% 1.21/1.49 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.49 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.49 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.49 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.49 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 1.21/1.49 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].
% 1.21/1.49 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].
% 1.21/1.49 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].
% 1.21/1.49 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].
% 1.21/1.49 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].
% 1.21/1.49 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].
% 1.21/1.49 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].
% 1.21/1.49
% 1.21/1.49 ============================== end of process non-clausal formulas ===
% 1.21/1.49
% 1.21/1.49 ============================== PROCESS INITIAL CLAUSES ===============
% 1.21/1.49
% 1.21/1.49 ============================== PREDICATE ELIMINATION =================
% 1.21/1.49
% 1.21/1.49 ============================== end predicate elimination =============
% 1.21/1.49
% 1.21/1.49 Auto_denials: (non-Horn, no changes).
% 1.21/1.49
% 1.21/1.49 Term ordering decisions:
% 1.21/1.49
% 1.21/1.49 % Assigning unary symbol not kb_weight 0 and highest precedence (94).
% 1.21/1.49 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.
% 1.21/1.49
% 1.21/1.49 ============================== end of process initial clauses ========
% 1.21/1.49
% 1.21/1.49 ============================== CLAUSES FOR SEARCH ====================
% 1.21/1.49
% 1.21/1.49 ============================== end of clauses for search =============
% 1.21/1.49
% 1.21/1.49 ============================== SEARCH ================================
% 1.21/1.49
% 1.21/1.49 % Starting search at 0.02 seconds.
% 1.21/1.49
% 1.21/1.49 Low Water (keep): wt=38.000, iters=3382
% 1.21/1.49
% 1.21/1.49 Low Water (keep): wt=37.000, iters=3418
% 1.21/1.49
% 1.21/1.49 Low Water (keep): wt=35.000, iters=3529
% 1.21/1.49
% 1.21/1.49 Low Water (keep): wt=33.000, iters=3525
% 1.21/1.49
% 1.21/1.49 Low Water (keep): wt=31.000, iters=3388
% 1.21/1.49
% 1.21/1.49 Low Water (keep): wt=30.000, iters=3427
% 1.21/1.49
% 1.21/1.49 Low Water (keep): wt=28.000, iters=3372
% 1.21/1.49
% 1.21/1.49 Low Water (keep): wt=27.000, iters=3481
% 1.21/1.49
% 1.21/1.49 Low Water (keep): wt=26.000, iters=3562
% 1.21/1.49
% 1.21/1.49 Low Water (keep): wt=25.000, iters=3344
% 1.21/1.49
% 66.37/66.68 Low Water (keep): wt=24.000, iters=3484
% 66.37/66.68
% 66.37/66.68 Low Water (keep): wt=23.000, iters=3370
% 66.37/66.68
% 66.37/66.68 Low Water (keep): wt=22.000, iters=3402
% 66.37/66.68
% 66.37/66.68 Low Water (keep): wt=21.000, iters=3402
% 66.37/66.68
% 66.37/66.68 Low Water (keep): wt=20.000, iters=3354
% 66.37/66.68
% 66.37/66.68 Low Water (keep): wt=19.000, iters=3388
% 66.37/66.68
% 66.37/66.68 Low Water (keep): wt=18.000, iters=3334
% 66.37/66.68
% 66.37/66.68 Low Water (keep): wt=17.000, iters=3353
% 66.37/66.68
% 66.37/66.68 Low Water (displace): id=1929, wt=59.000
% 66.37/66.68
% 66.37/66.68 Low Water (displace): id=1928, wt=57.000
% 66.37/66.68
% 66.37/66.68 Low Water (displace): id=3237, wt=55.000
% 66.37/66.68
% 66.37/66.68 Low Water (displace): id=3236, wt=53.000
% 66.37/66.68
% 66.37/66.68 Low Water (displace): id=1956, wt=46.000
% 66.37/66.68
% 66.37/66.68 Low Water (displace): id=3276, wt=44.000
% 66.37/66.68
% 66.37/66.68 Low Water (displace): id=2763, wt=43.000
% 66.37/66.68
% 66.37/66.68 Low Water (displace): id=1961, wt=42.000
% 66.37/66.68
% 66.37/66.68 Low Water (displace): id=2762, wt=41.000
% 66.37/66.68
% 66.37/66.68 Low Water (displace): id=3281, wt=40.000
% 66.37/66.68
% 66.37/66.68 Low Water (displace): id=10577, wt=16.000
% 66.37/66.68
% 66.37/66.68 Low Water (displace): id=10591, wt=15.000
% 66.37/66.68
% 66.37/66.68 Low Water (displace): id=11339, wt=13.000
% 66.37/66.68
% 66.37/66.68 Low Water (displace): id=11597, wt=11.000
% 66.37/66.68
% 66.37/66.68 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 146 (0.00 of 1.01 sec).
% 66.37/66.68
% 66.37/66.68 Low Water (keep): wt=16.000, iters=3336
% 66.37/66.68
% 66.37/66.68 Low Water (keep): wt=15.000, iters=3334
% 66.37/66.68
% 66.37/66.68 Low Water (keep): wt=14.000, iters=3337
% 66.37/66.68
% 66.37/66.68 Low Water (keep): wt=13.000, iters=3373
% 66.37/66.68
% 66.37/66.68 Low Water (displace): id=54452, wt=10.000
% 66.37/66.68
% 66.37/66.68 Low Water (displace): id=55959, wt=9.000
% 66.37/66.68
% 66.37/66.68 Low Water (displace): id=57834, wt=8.000
% 66.37/66.68
% 66.37/66.68 Low Water (displace): id=98499, wt=7.000
% 66.37/66.68
% 66.37/66.68 Low Water (keep): wt=12.000, iters=3334
% 66.37/66.68
% 66.37/66.68 Low Water (keep): wt=11.000, iters=4159
% 66.37/66.68
% 66.37/66.68 Low Water (keep): wt=10.000, iters=3334
% 66.37/66.68
% 66.37/66.68 ============================== PROOF =================================
% 66.37/66.68 % SZS status Theorem
% 66.37/66.68 % SZS output start Refutation
% 66.37/66.68
% 66.37/66.68 % Proof 1 at 60.79 (+ 4.87) seconds.
% 66.37/66.68 % Length of proof is 268.
% 66.37/66.68 % Level of proof is 84.
% 66.37/66.68 % Maximum clause weight is 18.000.
% 66.37/66.68 % Given clauses 6816.
% 66.37/66.68
% 66.37/66.68 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].
% 66.37/66.68 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].
% 66.37/66.68 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].
% 66.37/66.68 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 66.37/66.68 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 66.37/66.68 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].
% 66.37/66.68 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].
% 66.37/66.68 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].
% 66.37/66.68 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].
% 66.37/66.68 33 op_implies_and # label(rosser_op_implies_and) # label(axiom). [assumption].
% 66.37/66.68 34 op_equiv # label(rosser_op_equiv) # label(axiom). [assumption].
% 66.37/66.68 35 modus_ponens # label(rosser_modus_ponens) # label(axiom). [assumption].
% 66.37/66.68 36 kn1 # label(rosser_kn1) # label(axiom). [assumption].
% 66.37/66.68 37 kn2 # label(rosser_kn2) # label(axiom). [assumption].
% 66.37/66.68 38 kn3 # label(rosser_kn3) # label(axiom). [assumption].
% 66.37/66.68 39 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption].
% 66.37/66.68 41 -cn1 # label(luka_cn1) # label(negated_conjecture). [assumption].
% 66.37/66.68 52 -kn1 | is_a_theorem(implies(A,and(A,A))) # label(kn1) # label(axiom). [clausify(16)].
% 66.37/66.68 53 is_a_theorem(implies(A,and(A,A))). [copy(52),unit_del(a,36)].
% 66.37/66.68 55 -kn2 | is_a_theorem(implies(and(A,B),A)) # label(kn2) # label(axiom). [clausify(17)].
% 66.37/66.68 56 is_a_theorem(implies(and(A,B),A)). [copy(55),unit_del(a,37)].
% 66.37/66.68 62 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(2)].
% 66.37/66.68 63 -is_a_theorem(equiv(A,B)) | B = A. [copy(62),unit_del(a,39)].
% 66.37/66.68 68 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 66.37/66.68 69 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(68),unit_del(a,35)].
% 66.37/66.68 79 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 66.37/66.68 80 not(and(A,not(B))) = implies(A,B). [copy(79),unit_del(a,33)].
% 66.37/66.68 89 -op_equiv | and(implies(A,B),implies(B,A)) = equiv(A,B) # label(op_equiv) # label(axiom). [clausify(31)].
% 66.37/66.68 90 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(89),unit_del(a,34)].
% 66.37/66.68 91 -implies_3 | is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))) # label(implies_3) # label(axiom). [clausify(6)].
% 66.37/66.68 92 implies_3 | -is_a_theorem(implies(implies(c11,c12),implies(implies(c12,c13),implies(c11,c13)))) # label(implies_3) # label(axiom). [clausify(6)].
% 66.37/66.68 95 cn1 | -is_a_theorem(implies(implies(c39,c40),implies(implies(c40,c41),implies(c39,c41)))) # label(cn1) # label(axiom). [clausify(19)].
% 66.37/66.68 96 -is_a_theorem(implies(implies(c39,c40),implies(implies(c40,c41),implies(c39,c41)))). [copy(95),unit_del(a,41)].
% 66.37/66.68 109 -kn3 | is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))) # label(kn3) # label(axiom). [clausify(18)].
% 66.37/66.68 110 is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))). [copy(109),unit_del(a,38)].
% 66.37/66.68 125 -is_a_theorem(A) | is_a_theorem(and(A,A)). [resolve(69,b,53,a)].
% 66.37/66.68 126 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(80(a,1),80(a,1,1,2))].
% 66.37/66.68 127 is_a_theorem(implies(implies(A,A),equiv(A,A))). [para(90(a,1),53(a,1,2))].
% 66.37/66.68 130 -implies_3. [ur(91,b,96,a)].
% 66.37/66.68 134 -is_a_theorem(implies(implies(c11,c12),implies(implies(c12,c13),implies(c11,c13)))). [back_unit_del(92),unit_del(a,130)].
% 66.37/66.68 135 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(and(B,C)),not(and(C,A)))). [resolve(110,a,69,b)].
% 66.37/66.68 137 is_a_theorem(implies(implies(A,B),implies(implies(B,C),not(and(not(C),A))))). [para(80(a,1),110(a,1,2,1))].
% 66.37/66.68 140 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(C,and(B,not(A))),not(equiv(B,A))))). [para(90(a,1),110(a,1,2,2,1)),rewrite([126(5)])].
% 66.37/66.68 159 -is_a_theorem(implies(A,A)) | is_a_theorem(equiv(A,A)). [resolve(127,a,69,b)].
% 66.37/66.68 170 implies(implies(A,B),and(B,not(A))) = not(equiv(A,B)). [para(90(a,1),126(a,1,1)),flip(a)].
% 66.37/66.68 256 -is_a_theorem(implies(A,B)) | -is_a_theorem(not(equiv(A,B))) | is_a_theorem(and(B,not(A))). [para(170(a,1),69(b,1))].
% 66.37/66.68 268 is_a_theorem(implies(not(and(and(A,A),B)),not(and(B,A)))). [resolve(135,a,53,a)].
% 66.37/66.68 291 -is_a_theorem(not(and(and(A,A),B))) | is_a_theorem(not(and(B,A))). [resolve(268,a,69,b)].
% 66.37/66.68 389 -is_a_theorem(implies(and(A,A),B)) | is_a_theorem(not(and(not(B),A))). [para(80(a,1),291(a,1))].
% 66.37/66.68 671 is_a_theorem(not(and(not(A),A))). [resolve(389,a,56,a)].
% 66.37/66.68 675 is_a_theorem(and(not(and(not(A),A)),not(and(not(A),A)))). [resolve(671,a,125,a)].
% 66.37/66.68 703 is_a_theorem(not(and(implies(A,B),and(A,not(B))))). [para(80(a,1),671(a,1,1,1))].
% 66.37/66.68 704 is_a_theorem(implies(not(not(A)),A)). [para(80(a,1),671(a,1))].
% 66.37/66.68 707 is_a_theorem(implies(not(and(A,B)),implies(B,not(A)))). [resolve(704,a,135,a),rewrite([80(6)])].
% 66.37/66.68 709 -is_a_theorem(not(not(A))) | is_a_theorem(A). [resolve(704,a,69,b)].
% 66.37/66.68 998 -is_a_theorem(not(and(A,B))) | is_a_theorem(implies(B,not(A))). [resolve(707,a,69,b)].
% 66.37/66.68 1030 is_a_theorem(implies(implies(A,B),implies(not(B),not(A)))). [para(80(a,1),707(a,1,1))].
% 66.37/66.68 1580 is_a_theorem(implies(and(A,not(B)),not(implies(A,B)))). [resolve(998,a,703,a)].
% 66.37/66.68 1581 is_a_theorem(implies(A,not(not(A)))). [resolve(998,a,671,a)].
% 66.37/66.68 1585 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(B),not(A))). [para(80(a,1),998(a,1))].
% 66.37/66.68 1754 is_a_theorem(not(and(not(not(not(and(A,A)))),A))). [resolve(1581,a,389,a)].
% 66.37/66.68 1756 is_a_theorem(implies(not(and(not(not(A)),B)),not(and(B,A)))). [resolve(1581,a,135,a)].
% 66.37/66.68 1758 -is_a_theorem(A) | is_a_theorem(not(not(A))). [resolve(1581,a,69,b)].
% 66.37/66.68 1804 is_a_theorem(not(not(implies(A,not(not(A)))))). [resolve(1758,a,1581,a)].
% 66.37/66.68 1831 is_a_theorem(not(not(implies(and(A,B),A)))). [resolve(1758,a,56,a)].
% 66.37/66.68 1832 is_a_theorem(not(not(implies(A,and(A,A))))). [resolve(1758,a,53,a)].
% 66.37/66.68 4000 -is_a_theorem(and(A,not(B))) | is_a_theorem(not(implies(A,B))). [resolve(1580,a,69,b)].
% 66.37/66.68 4536 is_a_theorem(implies(not(A),not(and(A,B)))). [resolve(1585,a,56,a)].
% 66.37/66.68 4537 is_a_theorem(implies(not(and(A,A)),not(A))). [resolve(1585,a,53,a)].
% 66.37/66.68 4781 -is_a_theorem(not(A)) | is_a_theorem(not(and(A,B))). [resolve(4536,a,69,b)].
% 66.37/66.68 4853 is_a_theorem(implies(not(A),implies(A,B))). [para(80(a,1),4536(a,1,2))].
% 66.37/66.68 4860 is_a_theorem(implies(not(and(implies(A,B),C)),implies(C,A))). [resolve(4853,a,135,a),rewrite([80(6)])].
% 66.37/66.68 4862 -is_a_theorem(not(A)) | is_a_theorem(implies(A,B)). [resolve(4853,a,69,b)].
% 66.37/66.68 4951 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(and(A,not(B)),C)). [para(80(a,1),4862(a,1))].
% 66.37/66.68 5286 is_a_theorem(implies(not(not(A)),not(not(and(A,A))))). [resolve(4537,a,1585,a)].
% 66.37/66.68 5290 -is_a_theorem(not(and(A,A))) | is_a_theorem(not(A)). [resolve(4537,a,69,b)].
% 66.37/66.68 5362 is_a_theorem(not(and(not(implies(A,and(A,A))),B))). [resolve(4781,a,1832,a)].
% 66.37/66.68 5363 is_a_theorem(not(and(not(implies(and(A,B),A)),C))). [resolve(4781,a,1831,a)].
% 66.37/66.68 5367 is_a_theorem(not(and(not(implies(A,not(not(A)))),B))). [resolve(4781,a,1804,a)].
% 66.37/66.68 5372 is_a_theorem(not(and(and(not(A),A),B))). [resolve(4781,a,671,a)].
% 66.37/66.68 5378 -is_a_theorem(implies(not(A),A)) | is_a_theorem(not(not(A))). [para(80(a,1),5290(a,1))].
% 66.37/66.68 5386 is_a_theorem(implies(A,not(and(not(B),B)))). [resolve(5372,a,998,a)].
% 66.37/66.68 9218 -is_a_theorem(not(not(A))) | is_a_theorem(not(not(and(A,A)))). [resolve(5286,a,69,b)].
% 66.37/66.68 11681 -is_a_theorem(not(and(implies(A,B),C))) | is_a_theorem(implies(C,A)). [resolve(4860,a,69,b)].
% 66.37/66.68 11694 is_a_theorem(implies(implies(implies(A,B),C),implies(not(C),A))). [para(80(a,1),4860(a,1,1))].
% 66.37/66.68 11695 is_a_theorem(implies(not(equiv(A,B)),implies(implies(B,A),A))). [para(90(a,1),4860(a,1,1,1))].
% 66.37/66.68 13974 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(not(C),A)). [para(80(a,1),11681(a,1))].
% 66.37/66.68 14651 is_a_theorem(implies(not(implies(not(A),B)),implies(B,C))). [resolve(13974,a,11694,a)].
% 66.37/66.68 15156 is_a_theorem(not(not(implies(not(A),not(A))))). [resolve(14651,a,5378,a)].
% 66.37/66.68 15186 is_a_theorem(implies(not(A),not(A))). [resolve(15156,a,709,a)].
% 66.37/66.68 15273 is_a_theorem(implies(not(and(not(A),B)),implies(B,A))). [resolve(15186,a,135,a),rewrite([80(6)])].
% 66.37/66.68 16923 -is_a_theorem(not(and(not(A),B))) | is_a_theorem(implies(B,A)). [resolve(15273,a,69,b)].
% 66.37/66.68 16944 is_a_theorem(implies(not(equiv(A,B)),not(equiv(B,A)))). [para(170(a,1),15273(a,1,2)),rewrite([80(3),90(3)])].
% 66.37/66.68 17497 is_a_theorem(implies(A,implies(B,not(not(B))))). [resolve(16923,a,5367,a)].
% 66.37/66.68 17499 is_a_theorem(implies(A,implies(and(B,C),B))). [resolve(16923,a,5363,a)].
% 66.37/66.68 17500 is_a_theorem(implies(A,implies(B,and(B,B)))). [resolve(16923,a,5362,a)].
% 66.37/66.68 17506 is_a_theorem(implies(A,not(not(and(A,A))))). [resolve(16923,a,1754,a)].
% 66.37/66.68 17509 is_a_theorem(implies(A,A)). [resolve(16923,a,671,a)].
% 66.37/66.68 17515 -is_a_theorem(implies(not(A),B)) | is_a_theorem(implies(not(B),A)). [para(80(a,1),16923(a,1))].
% 66.37/66.68 17521 is_a_theorem(equiv(A,A)). [back_unit_del(159),unit_del(a,17509)].
% 66.37/66.68 17530 is_a_theorem(implies(and(A,not(A)),B)). [resolve(17509,a,4951,a)].
% 66.37/66.68 17536 is_a_theorem(implies(not(and(A,B)),not(and(B,A)))). [resolve(17509,a,135,a)].
% 66.37/66.68 17741 is_a_theorem(not(not(equiv(A,A)))). [resolve(17521,a,1758,a)].
% 66.37/66.68 18378 is_a_theorem(not(not(and(equiv(A,A),equiv(A,A))))). [resolve(17741,a,9218,a)].
% 66.37/66.68 18573 is_a_theorem(implies(not(A),implies(B,B))). [resolve(17530,a,1585,a),rewrite([80(4)])].
% 66.37/66.68 19271 is_a_theorem(implies(not(and(implies(A,A),B)),implies(B,C))). [resolve(18573,a,135,a),rewrite([80(6)])].
% 66.37/66.68 19915 -is_a_theorem(A) | is_a_theorem(not(not(and(A,A)))). [resolve(17506,a,69,b)].
% 66.37/66.68 19925 is_a_theorem(implies(not(A),not(implies(not(A),A)))). [para(80(a,1),17506(a,1,2,1))].
% 66.37/66.68 22690 -is_a_theorem(not(A)) | is_a_theorem(not(implies(not(A),A))). [resolve(19925,a,69,b)].
% 66.37/66.68 23993 -is_a_theorem(not(equiv(A,B))) | is_a_theorem(not(equiv(B,A))). [resolve(16944,a,69,b)].
% 66.37/66.68 24094 is_a_theorem(implies(not(implies(implies(A,B),B)),equiv(B,A))). [resolve(17515,a,11695,a)].
% 66.37/66.68 24988 is_a_theorem(implies(not(not(and(A,B))),and(B,A))). [resolve(17536,a,17515,a)].
% 66.37/66.68 25001 -is_a_theorem(not(and(A,B))) | is_a_theorem(not(and(B,A))). [resolve(17536,a,69,b)].
% 66.37/66.68 25002 is_a_theorem(implies(implies(A,B),not(and(not(B),A)))). [para(80(a,1),17536(a,1,1))].
% 66.37/66.68 29570 -is_a_theorem(implies(A,B)) | is_a_theorem(not(and(not(B),A))). [para(80(a,1),25001(a,1))].
% 66.37/66.68 29576 is_a_theorem(implies(not(not(and(not(A),B))),B)). [resolve(25002,a,13974,a)].
% 66.37/66.68 29826 is_a_theorem(implies(not(A),not(and(not(B),A)))). [resolve(29576,a,17515,a)].
% 66.37/66.68 32891 is_a_theorem(implies(not(implies(A,B)),and(implies(B,C),A))). [resolve(29570,a,4860,a),rewrite([80(7)])].
% 66.37/66.68 39547 is_a_theorem(implies(not(implies(A,B)),and(implies(C,C),A))). [resolve(19271,a,29570,a),rewrite([80(7)])].
% 66.37/66.68 44239 -is_a_theorem(not(implies(implies(A,B),B))) | is_a_theorem(equiv(B,A)). [resolve(24094,a,69,b)].
% 66.37/66.68 50376 -is_a_theorem(not(implies(A,B))) | is_a_theorem(and(implies(B,C),A)). [resolve(32891,a,69,b)].
% 66.37/66.68 53958 -is_a_theorem(not(implies(A,B))) | is_a_theorem(and(implies(C,C),A)). [resolve(39547,a,69,b)].
% 66.37/66.68 76071 is_a_theorem(implies(not(not(and(A,B))),and(not(not(B)),A))). [resolve(1756,a,29570,a),rewrite([80(9)])].
% 66.37/66.68 76089 -is_a_theorem(not(and(not(not(A)),B))) | is_a_theorem(not(and(B,A))). [resolve(1756,a,69,b)].
% 66.37/66.68 81862 -is_a_theorem(not(not(and(A,B)))) | is_a_theorem(and(not(not(B)),A)). [resolve(76071,a,69,b)].
% 66.37/66.68 81914 -is_a_theorem(implies(not(not(A)),B)) | is_a_theorem(not(and(not(B),A))). [para(80(a,1),76089(a,1))].
% 66.37/66.68 88912 is_a_theorem(and(not(not(equiv(A,A))),equiv(A,A))). [resolve(81862,a,18378,a)].
% 66.37/66.68 92844 is_a_theorem(not(and(not(implies(not(A),B)),B))). [resolve(81914,a,29826,a),rewrite([80(4)])].
% 66.37/66.68 92872 is_a_theorem(not(and(not(and(A,B)),and(B,A)))). [resolve(81914,a,24988,a)].
% 66.37/66.68 92956 is_a_theorem(implies(A,implies(not(B),A))). [resolve(92844,a,25001,a),rewrite([80(5)])].
% 66.37/66.68 102999 is_a_theorem(implies(and(A,B),and(B,A))). [resolve(92872,a,25001,a),rewrite([80(5)])].
% 66.37/66.68 103016 is_a_theorem(implies(and(A,B),not(not(and(B,A))))). [resolve(92872,a,998,a)].
% 66.37/66.68 103064 -is_a_theorem(and(A,B)) | is_a_theorem(and(B,A)). [resolve(102999,a,69,b)].
% 66.37/66.68 103559 is_a_theorem(and(equiv(A,A),not(not(equiv(A,A))))). [resolve(103064,a,88912,a)].
% 66.37/66.68 108992 -is_a_theorem(and(A,B)) | is_a_theorem(not(not(and(B,A)))). [resolve(103016,a,69,b)].
% 66.37/66.68 109003 is_a_theorem(implies(and(not(A),B),not(implies(B,A)))). [para(80(a,1),103016(a,1,2,1))].
% 66.37/66.68 109420 is_a_theorem(not(implies(equiv(A,A),not(equiv(A,A))))). [resolve(103559,a,4000,a)].
% 66.37/66.68 113668 is_a_theorem(not(implies(not(and(not(A),A)),and(not(A),A)))). [resolve(108992,a,675,a),rewrite([80(8)])].
% 66.37/66.68 113726 -is_a_theorem(and(not(A),B)) | is_a_theorem(not(implies(B,A))). [resolve(109003,a,69,b)].
% 66.37/66.68 113958 is_a_theorem(and(implies(A,A),equiv(B,B))). [resolve(109420,a,53958,a)].
% 66.37/66.68 114037 is_a_theorem(not(not(and(implies(A,A),equiv(B,B))))). [resolve(113958,a,1758,a)].
% 66.37/66.68 114724 is_a_theorem(and(not(not(equiv(A,A))),implies(B,B))). [resolve(114037,a,81862,a)].
% 66.37/66.68 114991 is_a_theorem(not(implies(implies(A,A),not(equiv(B,B))))). [resolve(114724,a,113726,a)].
% 66.37/66.68 115070 is_a_theorem(and(implies(not(equiv(A,A)),B),implies(C,C))). [resolve(114991,a,50376,a)].
% 66.37/66.68 118410 is_a_theorem(and(implies(A,A),implies(not(equiv(B,B)),C))). [resolve(115070,a,103064,a)].
% 66.37/66.68 129843 is_a_theorem(and(implies(A,A),not(and(not(B),B)))). [resolve(113668,a,53958,a)].
% 66.37/66.68 129932 is_a_theorem(not(implies(implies(A,A),and(not(B),B)))). [resolve(129843,a,4000,a)].
% 66.37/66.68 129938 is_a_theorem(and(implies(A,A),implies(not(not(B)),B))). [para(80(a,1),129843(a,1,2))].
% 66.37/66.68 130125 is_a_theorem(and(implies(and(not(A),A),B),implies(C,C))). [resolve(129932,a,50376,a)].
% 66.37/66.68 130153 is_a_theorem(not(implies(implies(not(not(A)),A),and(B,not(B))))). [resolve(129938,a,108992,a),rewrite([126(6)])].
% 66.37/66.68 130555 is_a_theorem(not(implies(implies(and(not(A),A),B),and(C,not(C))))). [resolve(130125,a,1758,a),rewrite([126(6)])].
% 66.37/66.68 136525 is_a_theorem(equiv(and(A,not(A)),not(implies(A,A)))). [resolve(130153,a,44239,a),rewrite([80(5)])].
% 66.37/66.68 136608 not(implies(A,A)) = and(A,not(A)). [resolve(136525,a,63,a)].
% 66.37/66.68 136636 not(and(A,and(B,not(B)))) = implies(A,implies(B,B)). [para(136608(a,1),80(a,1,1,2))].
% 66.37/66.68 162115 is_a_theorem(equiv(and(A,not(A)),and(not(B),B))). [resolve(130555,a,44239,a)].
% 66.37/66.68 162266 and(not(A),A) = and(B,not(B)). [resolve(162115,a,63,a)].
% 66.37/66.68 162273 and(not(A),A) = c_0. [new_symbol(162266)].
% 66.37/66.68 162276 and(A,not(A)) = c_0. [back_rewrite(162266),rewrite([162273(2)]),flip(a)].
% 66.37/66.68 163106 is_a_theorem(implies(A,not(c_0))). [back_rewrite(5386),rewrite([162273(2)])].
% 66.37/66.68 163110 is_a_theorem(not(and(c_0,A))). [back_rewrite(5372),rewrite([162273(2)])].
% 66.37/66.68 163167 is_a_theorem(not(c_0)). [back_rewrite(671),rewrite([162273(2)])].
% 66.37/66.68 163258 implies(A,implies(B,B)) = not(and(A,c_0)). [back_rewrite(136636),rewrite([162276(2)]),flip(a)].
% 66.37/66.68 163269 not(implies(A,A)) = c_0. [back_rewrite(136608),rewrite([162276(4)])].
% 66.37/66.68 164928 is_a_theorem(not(implies(implies(A,not(c_0)),and(A,not(not(c_0)))))). [resolve(163106,a,19915,a),rewrite([126(8)])].
% 66.37/66.68 164937 is_a_theorem(implies(not(and(not(c_0),A)),not(and(A,B)))). [resolve(163106,a,135,a)].
% 66.37/66.68 165105 is_a_theorem(not(implies(not(and(c_0,A)),and(c_0,A)))). [resolve(163110,a,22690,a)].
% 66.37/66.68 165258 implies(not(not(A)),A) = not(c_0). [para(162273(a,1),80(a,1,1)),flip(a)].
% 66.37/66.68 165381 implies(A,A) = not(c_0). [para(162276(a,1),80(a,1,1)),flip(a)].
% 66.37/66.68 165385 not(equiv(A,A)) = implies(not(c_0),c_0). [para(162276(a,1),170(a,1,2)),rewrite([165381(1)]),flip(a)].
% 66.37/66.68 165458 not(not(c_0)) = c_0. [back_rewrite(163269),rewrite([165381(1)])].
% 66.37/66.68 165459 not(and(A,c_0)) = implies(A,not(c_0)). [back_rewrite(163258),rewrite([165381(1)]),flip(a)].
% 66.37/66.68 165698 is_a_theorem(and(not(c_0),implies(not(equiv(A,A)),B))). [back_rewrite(118410),rewrite([165381(1)])].
% 66.37/66.68 165738 -is_a_theorem(not(implies(A,B))) | is_a_theorem(and(not(c_0),A)). [back_rewrite(53958),rewrite([165381(4)])].
% 66.37/66.68 165800 is_a_theorem(not(implies(implies(A,not(c_0)),and(A,c_0)))). [back_rewrite(164928),rewrite([165458(6)])].
% 66.37/66.68 173567 not(equiv(A,A)) = not(equiv(B,B)). [para(165385(a,2),165385(a,2))].
% 66.37/66.68 178328 and(equiv(A,A),not(equiv(B,B))) = c_0. [para(173567(a,1),162276(a,1,2))].
% 66.37/66.68 188838 is_a_theorem(not(implies(implies(not(equiv(A,A)),B),c_0))). [resolve(165698,a,113726,a)].
% 66.37/66.68 189210 is_a_theorem(and(not(c_0),not(and(c_0,A)))). [resolve(165738,a,165105,a)].
% 66.37/66.68 189241 is_a_theorem(not(implies(not(and(c_0,A)),c_0))). [resolve(189210,a,113726,a)].
% 66.37/66.68 189423 is_a_theorem(and(implies(c_0,A),not(and(c_0,B)))). [resolve(189241,a,50376,a)].
% 66.37/66.68 190169 is_a_theorem(not(implies(implies(c_0,A),and(c_0,B)))). [resolve(189423,a,4000,a)].
% 66.37/66.68 190487 is_a_theorem(equiv(and(c_0,A),c_0)). [resolve(190169,a,44239,a)].
% 66.37/66.68 190572 and(c_0,A) = c_0. [resolve(190487,a,63,a),flip(a)].
% 66.37/66.68 190573 implies(c_0,A) = not(c_0). [para(190572(a,1),80(a,1,1)),flip(a)].
% 66.37/66.68 190575 implies(implies(A,c_0),c_0) = not(equiv(A,c_0)). [para(190572(a,1),170(a,1,2))].
% 66.37/66.68 190630 and(not(c_0),implies(A,c_0)) = equiv(c_0,A). [para(190573(a,1),90(a,1,1))].
% 66.37/66.68 190641 -is_a_theorem(not(implies(not(c_0),A))) | is_a_theorem(equiv(A,c_0)). [para(190573(a,1),44239(a,1,1,1))].
% 66.37/66.68 190849 is_a_theorem(and(not(c_0),implies(A,not(c_0)))). [resolve(165800,a,165738,a)].
% 66.37/66.68 190985 is_a_theorem(not(implies(not(c_0),and(A,c_0)))). [resolve(190849,a,1758,a),rewrite([126(7),165458(5)])].
% 66.37/66.68 191211 is_a_theorem(and(implies(and(A,c_0),B),not(c_0))). [resolve(190985,a,50376,a)].
% 66.37/66.68 191775 is_a_theorem(not(implies(implies(and(A,c_0),B),c_0))). [resolve(191211,a,4000,a)].
% 66.37/66.68 192015 is_a_theorem(equiv(c_0,and(A,c_0))). [resolve(191775,a,44239,a)].
% 66.37/66.68 192099 and(A,c_0) = c_0. [resolve(192015,a,63,a)].
% 66.37/66.68 192211 implies(A,not(c_0)) = not(c_0). [back_rewrite(165459),rewrite([192099(2)]),flip(a)].
% 66.37/66.68 192224 and(implies(not(c_0),A),not(c_0)) = equiv(not(c_0),A). [para(192211(a,1),90(a,1,2))].
% 66.37/66.68 196144 implies(equiv(A,A),equiv(B,B)) = not(c_0). [para(178328(a,1),80(a,1,1)),flip(a)].
% 66.37/66.68 196146 not(equiv(equiv(A,A),equiv(B,B))) = implies(not(c_0),c_0). [para(178328(a,1),170(a,1,2)),rewrite([196144(3)]),flip(a)].
% 66.37/66.68 196148 is_a_theorem(implies(implies(not(c_0),A),implies(implies(A,c_0),implies(not(c_0),c_0)))). [para(178328(a,1),140(a,1,2,1,2)),rewrite([196144(3),196146(9)])].
% 66.37/66.68 197296 is_a_theorem(equiv(c_0,not(equiv(A,A)))). [resolve(188838,a,44239,a)].
% 66.37/66.68 197384 not(equiv(A,A)) = c_0. [resolve(197296,a,63,a)].
% 66.37/66.68 197397 implies(not(c_0),c_0) = c_0. [back_rewrite(165385),rewrite([197384(2)]),flip(a)].
% 66.37/66.68 197398 is_a_theorem(implies(implies(not(c_0),A),not(equiv(A,c_0)))). [back_rewrite(196148),rewrite([197397(9),190575(7)])].
% 66.37/66.68 197705 equiv(c_0,c_0) = and(not(c_0),not(c_0)). [para(165381(a,1),190630(a,1,2)),flip(a)].
% 66.37/66.68 198071 -is_a_theorem(implies(not(c_0),A)) | is_a_theorem(not(equiv(A,c_0))). [resolve(197398,a,69,b)].
% 66.37/66.68 198246 is_a_theorem(not(equiv(implies(A,and(A,A)),c_0))). [resolve(198071,a,17500,a)].
% 66.37/66.68 198247 is_a_theorem(not(equiv(implies(and(A,B),A),c_0))). [resolve(198071,a,17499,a)].
% 66.37/66.68 198249 is_a_theorem(not(equiv(implies(A,not(not(A))),c_0))). [resolve(198071,a,17497,a)].
% 66.37/66.68 198323 is_a_theorem(not(equiv(c_0,implies(A,and(A,A))))). [resolve(198246,a,23993,a)].
% 66.37/66.68 198403 is_a_theorem(not(equiv(c_0,implies(and(A,B),A)))). [resolve(198247,a,23993,a)].
% 66.37/66.68 198483 is_a_theorem(not(equiv(c_0,implies(A,not(not(A)))))). [resolve(198249,a,23993,a)].
% 66.37/66.68 198608 is_a_theorem(and(implies(A,and(A,A)),not(c_0))). [resolve(198323,a,256,b),rewrite([190573(4)]),unit_del(a,163167)].
% 66.37/66.68 198688 is_a_theorem(and(implies(and(A,B),A),not(c_0))). [resolve(198403,a,256,b),rewrite([190573(4)]),unit_del(a,163167)].
% 66.37/66.68 198769 is_a_theorem(and(implies(A,not(not(A))),not(c_0))). [resolve(198483,a,256,b),rewrite([190573(5)]),unit_del(a,163167)].
% 66.37/66.68 198788 is_a_theorem(not(implies(not(c_0),and(A,not(and(A,A)))))). [resolve(198608,a,108992,a),rewrite([126(6)])].
% 66.37/66.68 198868 is_a_theorem(not(implies(not(c_0),and(and(A,B),not(A))))). [resolve(198688,a,108992,a),rewrite([126(6)])].
% 66.37/66.68 198927 is_a_theorem(not(implies(not(c_0),and(A,not(not(not(A))))))). [resolve(198769,a,108992,a),rewrite([126(7)])].
% 66.37/66.68 205209 is_a_theorem(implies(not(not(and(A,B))),not(not(and(not(c_0),A))))). [resolve(164937,a,1585,a)].
% 66.37/66.68 212309 is_a_theorem(equiv(and(A,not(and(A,A))),c_0)). [resolve(198788,a,190641,a)].
% 66.37/66.68 212441 and(A,not(and(A,A))) = c_0. [resolve(212309,a,63,a),flip(a)].
% 66.37/66.68 212444 implies(A,and(A,A)) = not(c_0). [para(212441(a,1),80(a,1,1)),flip(a)].
% 66.37/66.68 212505 and(not(c_0),implies(and(A,A),A)) = equiv(A,and(A,A)). [para(212444(a,1),90(a,1,1))].
% 66.37/66.68 212628 is_a_theorem(equiv(and(and(A,B),not(A)),c_0)). [resolve(198868,a,190641,a)].
% 66.37/66.68 212761 and(and(A,B),not(A)) = c_0. [resolve(212628,a,63,a),flip(a)].
% 66.37/66.68 212776 implies(and(A,B),A) = not(c_0). [para(212761(a,1),80(a,1,1)),flip(a)].
% 66.37/66.68 212806 equiv(A,and(A,A)) = and(not(c_0),not(c_0)). [back_rewrite(212505),rewrite([212776(4)]),flip(a)].
% 66.37/66.68 212807 and(not(c_0),implies(A,and(A,B))) = equiv(and(A,B),A). [para(212776(a,1),90(a,1,1))].
% 66.37/66.68 212978 is_a_theorem(equiv(and(A,not(not(not(A)))),c_0)). [resolve(198927,a,190641,a)].
% 66.37/66.68 213110 and(A,not(not(not(A)))) = c_0. [resolve(212978,a,63,a),flip(a)].
% 66.37/66.68 213122 not(equiv(not(not(A)),A)) = c_0. [para(213110(a,1),170(a,1,2)),rewrite([165258(3),197397(4)]),flip(a)].
% 66.37/66.68 213177 is_a_theorem(equiv(not(not(A)),A)). [para(213122(a,1),709(a,1,1)),unit_del(a,163167)].
% 66.37/66.68 213227 not(not(A)) = A. [resolve(213177,a,63,a),flip(a)].
% 66.37/66.68 213280 is_a_theorem(implies(and(A,B),and(not(c_0),A))). [back_rewrite(205209),rewrite([213227(3),213227(6)])].
% 66.37/66.68 213546 not(and(A,B)) = implies(A,not(B)). [para(213227(a,1),80(a,1,1,2))].
% 66.37/66.68 213547 not(implies(A,B)) = and(A,not(B)). [para(80(a,1),213227(a,1,1))].
% 66.37/66.68 213640 is_a_theorem(implies(A,implies(B,A))). [para(213227(a,1),92956(a,1,2,1))].
% 66.37/66.68 213781 equiv(A,A) = not(c_0). [para(197384(a,1),213227(a,1,1)),flip(a)].
% 66.37/66.68 214207 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(not(C),not(A))))). [back_rewrite(137),rewrite([213546(5)])].
% 66.37/66.68 214627 and(not(c_0),not(c_0)) = not(c_0). [back_rewrite(197705),rewrite([213781(3)]),flip(a)].
% 66.37/66.68 214639 equiv(A,and(A,A)) = not(c_0). [back_rewrite(212806),rewrite([214627(7)])].
% 66.37/66.68 218423 and(A,A) = A. [para(214639(a,1),63(a,1)),unit_del(a,163167)].
% 66.37/66.68 219160 is_a_theorem(implies(A,and(not(c_0),A))). [para(218423(a,1),213280(a,1,1))].
% 66.37/66.68 219169 is_a_theorem(implies(implies(not(c_0),A),A)). [resolve(219160,a,17515,a),rewrite([213546(5),213227(4)])].
% 66.37/66.68 219171 -is_a_theorem(A) | is_a_theorem(and(not(c_0),A)). [resolve(219160,a,69,b)].
% 66.37/66.68 219194 is_a_theorem(implies(implies(A,c_0),equiv(c_0,A))). [para(190630(a,1),219160(a,1,2))].
% 66.37/66.68 219438 is_a_theorem(and(not(c_0),implies(implies(not(c_0),A),A))). [resolve(219171,a,219169,a)].
% 66.37/66.68 219616 is_a_theorem(implies(not(equiv(c_0,A)),A)). [resolve(219194,a,13974,a)].
% 66.37/66.68 219634 is_a_theorem(implies(not(A),equiv(c_0,A))). [resolve(219616,a,17515,a)].
% 66.37/66.68 219930 -is_a_theorem(not(A)) | is_a_theorem(equiv(c_0,A)). [resolve(219634,a,69,b)].
% 66.37/66.68 219972 -is_a_theorem(A) | is_a_theorem(equiv(c_0,not(A))). [para(213227(a,1),219930(a,1))].
% 66.37/66.68 220032 is_a_theorem(equiv(c_0,and(A,and(B,not(A))))). [resolve(219972,a,213640,a),rewrite([213547(4),213547(3)])].
% 66.37/66.68 221769 and(A,and(B,not(A))) = c_0. [resolve(220032,a,63,a)].
% 66.37/66.68 221781 implies(A,implies(B,A)) = not(c_0). [para(221769(a,1),213546(a,1,1)),rewrite([213546(5),213227(4)]),flip(a)].
% 66.37/66.68 221793 and(not(c_0),implies(implies(A,B),B)) = equiv(B,implies(A,B)). [para(221781(a,1),90(a,1,1))].
% 66.37/66.68 221805 is_a_theorem(equiv(A,implies(not(c_0),A))). [back_rewrite(219438),rewrite([221793(7)])].
% 66.37/66.68 221816 implies(not(c_0),A) = A. [resolve(221805,a,63,a)].
% 66.37/66.68 221886 equiv(not(c_0),A) = and(A,not(c_0)). [back_rewrite(192224),rewrite([221816(3)]),flip(a)].
% 66.37/66.68 221940 is_a_theorem(implies(implies(A,c_0),not(A))). [para(221816(a,1),1030(a,1,2))].
% 66.37/66.68 224311 is_a_theorem(implies(A,and(A,not(c_0)))). [resolve(221940,a,1585,a),rewrite([213227(2),213547(3)])].
% 66.37/66.68 225444 is_a_theorem(equiv(and(A,not(c_0)),A)). [resolve(224311,a,219171,a),rewrite([212807(7)])].
% 66.37/66.68 225519 and(A,not(c_0)) = A. [resolve(225444,a,63,a),flip(a)].
% 66.37/66.68 225526 equiv(not(c_0),A) = A. [back_rewrite(221886),rewrite([225519(6)])].
% 66.37/66.68 226171 -is_a_theorem(A) | not(c_0) = A. [para(225526(a,1),63(a,1)),flip(b)].
% 66.37/66.68 226752 implies(and(A,B),and(B,A)) = not(c_0). [resolve(226171,a,102999,a),flip(a)].
% 66.37/66.68 227568 equiv(and(A,B),and(B,A)) = not(c_0). [para(226752(a,1),90(a,1,1)),rewrite([226752(5),218423(5)]),flip(a)].
% 66.37/66.68 230370 and(A,B) = and(B,A). [para(227568(a,1),63(a,1)),unit_del(a,163167)].
% 66.37/66.68 232033 implies(A,not(B)) = implies(B,not(A)). [para(230370(a,1),213546(a,1,1)),rewrite([213546(2)])].
% 66.37/66.68 232370 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))). [back_rewrite(214207),rewrite([232033(5),213227(4)])].
% 66.37/66.68 232371 $F. [resolve(232370,a,134,a)].
% 66.37/66.68
% 66.37/66.68 % SZS output end Refutation
% 66.37/66.68 ============================== end of proof ==========================
% 66.37/66.68
% 66.37/66.68 ============================== STATISTICS ============================
% 66.37/66.68
% 66.37/66.68 Given=6816. Generated=9830478. Kept=232320. proofs=1.
% 66.37/66.68 Usable=268. Sos=1448. Demods=162. Limbo=337, Disabled=230338. Hints=0.
% 66.37/66.68 Megabytes=146.04.
% 66.37/66.68 User_CPU=60.79, System_CPU=4.87, Wall_clock=66.
% 66.37/66.68
% 66.37/66.68 ============================== end of statistics =====================
% 66.37/66.68
% 66.37/66.68 ============================== end of search =========================
% 66.37/66.68
% 66.37/66.68 THEOREM PROVED
% 66.37/66.68 % SZS status Theorem
% 66.37/66.68
% 66.37/66.68 Exiting with 1 proof.
% 66.37/66.68
% 66.37/66.68 Process 26341 exit (max_proofs) Sun Jul 3 16:55:36 2022
% 66.37/66.68 Prover9 interrupted
%------------------------------------------------------------------------------