TSTP Solution File: LCL480+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL480+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 13:47:07 EDT 2022
% Result : Theorem 99.89s 100.23s
% Output : Refutation 99.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL480+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 3 04:40:07 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.72/1.00 ============================== Prover9 ===============================
% 0.72/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.72/1.00 Process 31903 was started by sandbox on n009.cluster.edu,
% 0.72/1.00 Sun Jul 3 04:40:08 2022
% 0.72/1.00 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_31750_n009.cluster.edu".
% 0.72/1.00 ============================== end of head ===========================
% 0.72/1.00
% 0.72/1.00 ============================== INPUT =================================
% 0.72/1.00
% 0.72/1.00 % Reading from file /tmp/Prover9_31750_n009.cluster.edu
% 0.72/1.00
% 0.72/1.00 set(prolog_style_variables).
% 0.72/1.00 set(auto2).
% 0.72/1.00 % set(auto2) -> set(auto).
% 0.72/1.00 % set(auto) -> set(auto_inference).
% 0.72/1.00 % set(auto) -> set(auto_setup).
% 0.72/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.72/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.72/1.00 % set(auto) -> set(auto_limits).
% 0.72/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.72/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.72/1.00 % set(auto) -> set(auto_denials).
% 0.72/1.00 % set(auto) -> set(auto_process).
% 0.72/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.72/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.72/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.72/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.72/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.72/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.72/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.72/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.72/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.72/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.72/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.72/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.72/1.00 % set(auto2) -> assign(stats, some).
% 0.72/1.00 % set(auto2) -> clear(echo_input).
% 0.72/1.00 % set(auto2) -> set(quiet).
% 0.72/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.72/1.00 % set(auto2) -> clear(print_given).
% 0.72/1.00 assign(lrs_ticks,-1).
% 0.72/1.00 assign(sos_limit,10000).
% 0.72/1.00 assign(order,kbo).
% 0.72/1.00 set(lex_order_vars).
% 0.72/1.00 clear(print_given).
% 0.72/1.00
% 0.72/1.00 % formulas(sos). % not echoed (43 formulas)
% 0.72/1.00
% 0.72/1.00 ============================== end of input ==========================
% 0.72/1.00
% 0.72/1.00 % From the command line: assign(max_seconds, 300).
% 0.72/1.00
% 0.72/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.72/1.00
% 0.72/1.00 % Formulas that are not ordinary clauses:
% 0.72/1.00 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].
% 0.72/1.00 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].
% 0.72/1.00 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].
% 0.72/1.00 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.00 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].
% 0.72/1.00 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].
% 0.72/1.00 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.00 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.00 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].
% 0.72/1.00 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.00 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.00 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].
% 0.72/1.00 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].
% 0.72/1.00 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=47.000, iters=3366
% 1.27/1.54
% 1.27/1.54 Low Water (keep): wt=36.000, iters=3399
% 1.27/1.54
% 1.27/1.54 Low Water (keep): wt=34.000, iters=3411
% 1.27/1.54
% 1.27/1.54 Low Water (keep): wt=32.000, iters=3442
% 1.27/1.54
% 1.27/1.54 Low Water (keep): wt=31.000, iters=3470
% 1.27/1.54
% 1.27/1.54 Low Water (keep): wt=29.000, iters=3335
% 1.27/1.54
% 1.27/1.54 Low Water (keep): wt=26.000, iters=3357
% 1.27/1.54
% 1.27/1.54 Low Water (keep): wt=25.000, iters=3339
% 1.27/1.54
% 1.27/1.54 Low Water (keep): wt=24.000, iters=3415
% 1.27/1.54
% 1.27/1.54 Low Water (keep): wt=23.000, iters=3352
% 1.27/1.54
% 99.89/100.23 Low Water (keep): wt=22.000, iters=3348
% 99.89/100.23
% 99.89/100.23 Low Water (keep): wt=21.000, iters=3342
% 99.89/100.23
% 99.89/100.23 Low Water (keep): wt=20.000, iters=3355
% 99.89/100.23
% 99.89/100.23 Low Water (keep): wt=19.000, iters=3343
% 99.89/100.23
% 99.89/100.23 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 51 (0.00 of 1.23 sec).
% 99.89/100.23
% 99.89/100.23 Low Water (displace): id=1677, wt=111.000
% 99.89/100.23
% 99.89/100.23 Low Water (displace): id=2047, wt=103.000
% 99.89/100.23
% 99.89/100.23 Low Water (displace): id=3601, wt=95.000
% 99.89/100.23
% 99.89/100.23 Low Water (displace): id=3163, wt=83.000
% 99.89/100.23
% 99.89/100.23 Low Water (displace): id=1530, wt=75.000
% 99.89/100.23
% 99.89/100.23 Low Water (displace): id=1532, wt=55.000
% 99.89/100.23
% 99.89/100.23 Low Water (displace): id=9834, wt=45.000
% 99.89/100.23
% 99.89/100.23 Low Water (displace): id=9560, wt=43.000
% 99.89/100.23
% 99.89/100.23 Low Water (displace): id=9559, wt=42.000
% 99.89/100.23
% 99.89/100.23 Low Water (displace): id=9838, wt=41.000
% 99.89/100.23
% 99.89/100.23 Low Water (displace): id=7230, wt=39.000
% 99.89/100.23
% 99.89/100.23 Low Water (displace): id=7228, wt=38.000
% 99.89/100.23
% 99.89/100.23 Low Water (displace): id=9842, wt=37.000
% 99.89/100.23
% 99.89/100.23 Low Water (displace): id=10846, wt=35.000
% 99.89/100.23
% 99.89/100.23 Low Water (displace): id=9554, wt=34.000
% 99.89/100.23
% 99.89/100.23 Low Water (displace): id=10854, wt=33.000
% 99.89/100.23
% 99.89/100.23 Low Water (displace): id=10852, wt=32.000
% 99.89/100.23
% 99.89/100.23 Low Water (displace): id=11045, wt=31.000
% 99.89/100.23
% 99.89/100.23 Low Water (displace): id=11043, wt=30.000
% 99.89/100.23
% 99.89/100.23 Low Water (displace): id=10989, wt=29.000
% 99.89/100.23
% 99.89/100.23 Low Water (displace): id=11325, wt=18.000
% 99.89/100.23
% 99.89/100.23 Low Water (displace): id=11611, wt=17.000
% 99.89/100.23
% 99.89/100.23 Low Water (displace): id=11915, wt=16.000
% 99.89/100.23
% 99.89/100.23 Low Water (displace): id=12038, wt=15.000
% 99.89/100.23
% 99.89/100.23 Low Water (keep): wt=18.000, iters=3333
% 99.89/100.23
% 99.89/100.23 Low Water (displace): id=13866, wt=14.000
% 99.89/100.23
% 99.89/100.23 Low Water (keep): wt=17.000, iters=3337
% 99.89/100.23
% 99.89/100.23 Low Water (displace): id=23376, wt=13.000
% 99.89/100.23
% 99.89/100.23 Low Water (keep): wt=16.000, iters=3339
% 99.89/100.23
% 99.89/100.23 Low Water (keep): wt=15.000, iters=3930
% 99.89/100.23
% 99.89/100.23 Low Water (keep): wt=14.000, iters=3341
% 99.89/100.23
% 99.89/100.23 Low Water (displace): id=117667, wt=12.000
% 99.89/100.23
% 99.89/100.23 Low Water (displace): id=118313, wt=11.000
% 99.89/100.23
% 99.89/100.23 Low Water (keep): wt=13.000, iters=3334
% 99.89/100.23
% 99.89/100.23 ============================== PROOF =================================
% 99.89/100.23 % SZS status Theorem
% 99.89/100.23 % SZS output start Refutation
% 99.89/100.23
% 99.89/100.23 % Proof 1 at 92.55 (+ 6.68) seconds.
% 99.89/100.23 % Length of proof is 339.
% 99.89/100.23 % Level of proof is 96.
% 99.89/100.23 % Maximum clause weight is 19.000.
% 99.89/100.23 % Given clauses 8706.
% 99.89/100.23
% 99.89/100.23 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].
% 99.89/100.23 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].
% 99.89/100.23 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 99.89/100.23 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].
% 99.89/100.23 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 99.89/100.23 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 99.89/100.23 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].
% 99.89/100.23 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].
% 99.89/100.23 34 op_equiv # label(luka_op_equiv) # label(axiom). [assumption].
% 99.89/100.23 35 modus_ponens # label(luka_modus_ponens) # label(axiom). [assumption].
% 99.89/100.23 36 cn1 # label(luka_cn1) # label(axiom). [assumption].
% 99.89/100.23 37 cn2 # label(luka_cn2) # label(axiom). [assumption].
% 99.89/100.23 38 cn3 # label(luka_cn3) # label(axiom). [assumption].
% 99.89/100.23 39 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption].
% 99.89/100.23 40 op_implies_and # label(rosser_op_implies_and) # label(axiom). [assumption].
% 99.89/100.23 41 -kn1 # label(rosser_kn1) # label(negated_conjecture). [assumption].
% 99.89/100.23 52 kn1 | -is_a_theorem(implies(c33,and(c33,c33))) # label(kn1) # label(axiom). [clausify(16)].
% 99.89/100.23 53 -is_a_theorem(implies(c33,and(c33,c33))). [copy(52),unit_del(a,41)].
% 99.89/100.23 60 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(2)].
% 99.89/100.23 61 -is_a_theorem(equiv(A,B)) | B = A. [copy(60),unit_del(a,39)].
% 99.89/100.23 62 -cn2 | is_a_theorem(implies(A,implies(not(A),B))) # label(cn2) # label(axiom). [clausify(20)].
% 99.89/100.23 63 is_a_theorem(implies(A,implies(not(A),B))). [copy(62),unit_del(a,37)].
% 99.89/100.23 65 -cn3 | is_a_theorem(implies(implies(not(A),A),A)) # label(cn3) # label(axiom). [clausify(21)].
% 99.89/100.23 66 is_a_theorem(implies(implies(not(A),A),A)). [copy(65),unit_del(a,38)].
% 99.89/100.23 68 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 99.89/100.23 69 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(68),unit_del(a,35)].
% 99.89/100.23 79 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 99.89/100.23 80 not(and(A,not(B))) = implies(A,B). [copy(79),unit_del(a,40)].
% 99.89/100.23 89 -op_equiv | and(implies(A,B),implies(B,A)) = equiv(A,B) # label(op_equiv) # label(axiom). [clausify(31)].
% 99.89/100.23 90 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(89),unit_del(a,34)].
% 99.89/100.23 95 -cn1 | is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))) # label(cn1) # label(axiom). [clausify(19)].
% 99.89/100.23 96 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))). [copy(95),unit_del(a,36)].
% 99.89/100.23 122 -is_a_theorem(implies(not(A),A)) | is_a_theorem(A). [resolve(69,b,66,a)].
% 99.89/100.23 123 -is_a_theorem(A) | is_a_theorem(implies(not(A),B)). [resolve(69,b,63,a)].
% 99.89/100.23 127 is_a_theorem(implies(and(A,not(B)),implies(implies(A,B),C))). [para(80(a,1),63(a,1,2,1))].
% 99.89/100.23 128 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))].
% 99.89/100.23 129 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(80(a,1),80(a,1,1,2))].
% 99.89/100.23 130 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(B,C),implies(A,C))). [resolve(96,a,69,b)].
% 99.89/100.23 226 is_a_theorem(implies(implies(implies(implies(A,B),C),D),implies(and(A,not(B)),D))). [resolve(130,a,127,a)].
% 99.89/100.23 227 is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))). [resolve(130,a,96,a)].
% 99.89/100.23 228 is_a_theorem(implies(implies(A,B),implies(implies(not(A),A),B))). [resolve(130,a,66,a)].
% 99.89/100.23 229 is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C))). [resolve(130,a,63,a)].
% 99.89/100.23 230 is_a_theorem(implies(implies(implies(implies(not(A),A),B),C),implies(implies(A,B),C))). [resolve(228,a,130,a)].
% 99.89/100.23 232 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(A),A),B)). [resolve(228,a,69,b)].
% 99.89/100.23 242 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(not(A),D),B),C))). [resolve(229,a,130,a)].
% 99.89/100.23 244 -is_a_theorem(implies(implies(not(A),B),C)) | is_a_theorem(implies(A,C)). [resolve(229,a,69,b)].
% 99.89/100.23 257 implies(implies(A,B),and(B,not(A))) = not(equiv(A,B)). [para(90(a,1),129(a,1,1)),flip(a)].
% 99.89/100.23 258 -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))].
% 99.89/100.23 348 is_a_theorem(implies(A,implies(implies(B,C),implies(not(A),C)))). [resolve(244,a,96,a)].
% 99.89/100.23 349 is_a_theorem(implies(A,A)). [resolve(244,a,66,a)].
% 99.89/100.23 351 -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))].
% 99.89/100.23 414 is_a_theorem(implies(not(implies(A,A)),B)). [resolve(349,a,123,a)].
% 99.89/100.23 434 is_a_theorem(implies(implies(A,B),implies(not(implies(C,C)),B))). [resolve(414,a,130,a)].
% 99.89/100.23 610 is_a_theorem(implies(implies(not(A),A),implies(implies(B,C),implies(not(A),C)))). [resolve(348,a,232,a)].
% 99.89/100.23 611 is_a_theorem(implies(implies(implies(implies(A,B),implies(not(C),B)),D),implies(C,D))). [resolve(348,a,130,a)].
% 99.89/100.23 639 is_a_theorem(implies(A,implies(not(implies(B,B)),C))). [resolve(434,a,244,a)].
% 99.89/100.23 752 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),implies(D,C))). [resolve(639,a,130,a)].
% 99.89/100.23 1019 is_a_theorem(implies(not(equiv(A,A)),and(A,not(A)))). [para(257(a,1),128(a,1,1))].
% 99.89/100.23 1202 is_a_theorem(implies(implies(and(A,not(A)),B),implies(not(equiv(A,A)),B))). [resolve(1019,a,130,a)].
% 99.89/100.23 2287 -is_a_theorem(implies(implies(not(implies(A,A)),B),C)) | is_a_theorem(implies(D,C)). [resolve(752,a,69,b)].
% 99.89/100.23 3024 is_a_theorem(implies(A,implies(B,B))). [resolve(2287,a,66,a)].
% 99.89/100.23 3031 is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))). [resolve(3024,a,130,a)].
% 99.89/100.23 3374 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(D,D),B),C))). [resolve(3031,a,130,a)].
% 99.89/100.23 3376 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(implies(C,B)). [resolve(3031,a,69,b)].
% 99.89/100.23 3447 is_a_theorem(implies(A,implies(B,implies(C,C)))). [resolve(3376,a,3031,a)].
% 99.89/100.23 3449 is_a_theorem(implies(A,implies(B,implies(not(B),C)))). [resolve(3376,a,229,a)].
% 99.89/100.23 3450 is_a_theorem(implies(A,implies(implies(not(B),B),B))). [resolve(3376,a,228,a)].
% 99.89/100.23 3456 is_a_theorem(implies(implies(implies(A,implies(B,B)),C),implies(D,C))). [resolve(3447,a,130,a)].
% 99.89/100.23 3530 is_a_theorem(implies(implies(implies(A,implies(not(A),B)),C),implies(D,C))). [resolve(3449,a,130,a)].
% 99.89/100.23 3823 is_a_theorem(implies(implies(implies(implies(not(A),A),A),B),implies(C,B))). [resolve(3450,a,130,a)].
% 99.89/100.23 5433 -is_a_theorem(implies(implies(implies(not(A),A),A),B)) | is_a_theorem(implies(C,B)). [resolve(3823,a,69,b)].
% 99.89/100.23 6503 -is_a_theorem(implies(not(A),A)) | is_a_theorem(implies(implies(B,C),implies(not(A),C))). [resolve(610,a,69,b)].
% 99.89/100.23 7011 -is_a_theorem(implies(and(A,not(A)),B)) | is_a_theorem(implies(not(equiv(A,A)),B)). [resolve(1202,a,69,b)].
% 99.89/100.23 7378 is_a_theorem(implies(A,implies(implies(implies(B,B),C),C))). [resolve(3374,a,5433,a)].
% 99.89/100.23 7388 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(implies(D,D),B),C)). [resolve(3374,a,69,b)].
% 99.89/100.23 7481 is_a_theorem(implies(implies(implies(implies(implies(A,A),B),B),C),implies(D,C))). [resolve(7378,a,130,a)].
% 99.89/100.23 7483 is_a_theorem(implies(implies(implies(A,A),B),B)). [resolve(7378,a,122,a)].
% 99.89/100.23 7532 is_a_theorem(implies(implies(A,B),implies(implies(implies(C,C),A),B))). [resolve(7483,a,130,a)].
% 99.89/100.23 7533 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(B). [resolve(7483,a,69,b)].
% 99.89/100.23 7735 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(C,C),A),B)). [resolve(7532,a,69,b)].
% 99.89/100.23 8223 is_a_theorem(implies(implies(implies(A,A),implies(implies(B,B),C)),implies(D,C))). [resolve(7735,a,3031,a)].
% 99.89/100.23 9881 is_a_theorem(implies(implies(implies(A,A),B),implies(implies(B,C),implies(D,C)))). [resolve(7388,a,96,a)].
% 99.89/100.23 9975 -is_a_theorem(implies(implies(implies(implies(A,A),B),B),C)) | is_a_theorem(implies(D,C)). [resolve(7481,a,69,b)].
% 99.89/100.23 10480 -is_a_theorem(implies(implies(A,A),implies(implies(B,B),C))) | is_a_theorem(implies(D,C)). [resolve(8223,a,69,b)].
% 99.89/100.23 10786 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(implies(implies(B,C),implies(D,C))). [resolve(9881,a,69,b)].
% 99.89/100.23 11533 is_a_theorem(implies(A,implies(and(B,not(B)),C))). [resolve(226,a,9975,a)].
% 99.89/100.23 11583 is_a_theorem(implies(and(A,not(A)),B)). [resolve(11533,a,7533,a)].
% 99.89/100.23 11642 is_a_theorem(implies(not(equiv(A,A)),B)). [back_unit_del(7011),unit_del(a,11583)].
% 99.89/100.23 11781 is_a_theorem(implies(implies(A,B),implies(not(equiv(C,C)),B))). [resolve(11642,a,6503,a)].
% 99.89/100.23 12733 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),C),implies(D,C))). [resolve(11781,a,10786,a)].
% 99.89/100.23 13232 is_a_theorem(implies(A,implies(B,equiv(C,C)))). [resolve(12733,a,5433,a)].
% 99.89/100.23 13308 is_a_theorem(implies(A,equiv(B,B))). [resolve(13232,a,10480,a)].
% 99.89/100.23 13390 is_a_theorem(implies(implies(equiv(A,A),B),implies(C,B))). [resolve(13308,a,10786,a)].
% 99.89/100.23 13701 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(equiv(D,D),B),C))). [resolve(13390,a,130,a)].
% 99.89/100.23 14208 -is_a_theorem(implies(implies(implies(not(A),A),B),C)) | is_a_theorem(implies(implies(A,B),C)). [resolve(230,a,69,b)].
% 99.89/100.23 14924 is_a_theorem(implies(A,implies(implies(implies(not(implies(B,B)),C),D),D))). [resolve(242,a,9975,a)].
% 99.89/100.23 14931 is_a_theorem(implies(A,implies(implies(implies(not(not(B)),C),B),B))). [resolve(242,a,5433,a)].
% 99.89/100.23 14941 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(implies(not(A),D),B),C)). [resolve(242,a,69,b)].
% 99.89/100.23 14971 is_a_theorem(implies(implies(implies(not(not(A)),B),A),A)). [resolve(14931,a,7533,a)].
% 99.89/100.23 14999 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(not(A)),C),A),B))). [resolve(14971,a,130,a)].
% 99.89/100.23 15000 -is_a_theorem(implies(implies(not(not(A)),B),A)) | is_a_theorem(A). [resolve(14971,a,69,b)].
% 99.89/100.23 15022 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),C)). [resolve(14924,a,15000,a)].
% 99.89/100.23 15106 -is_a_theorem(implies(implies(not(implies(A,A)),B),C)) | is_a_theorem(C). [resolve(15022,a,69,b)].
% 99.89/100.23 15134 -is_a_theorem(not(equiv(not(implies(A,A)),B))) | is_a_theorem(and(B,not(not(implies(A,A))))). [para(257(a,1),15106(a,1))].
% 99.89/100.23 15237 is_a_theorem(implies(A,implies(implies(equiv(B,B),C),C))). [resolve(13701,a,9975,a)].
% 99.89/100.23 15253 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(equiv(D,D),B),C)). [resolve(13701,a,69,b)].
% 99.89/100.23 15263 is_a_theorem(implies(implies(equiv(A,A),B),B)). [resolve(15237,a,15106,a)].
% 99.89/100.23 15265 is_a_theorem(implies(implies(implies(implies(equiv(A,A),B),B),C),implies(D,C))). [resolve(15237,a,10786,a)].
% 99.89/100.23 15327 -is_a_theorem(implies(equiv(A,A),B)) | is_a_theorem(B). [resolve(15263,a,69,b)].
% 99.89/100.23 18056 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(not(A)),C),A),B)). [resolve(14999,a,69,b)].
% 99.89/100.23 18107 is_a_theorem(implies(implies(equiv(A,A),B),implies(implies(B,C),implies(D,C)))). [resolve(15253,a,9881,a)].
% 99.89/100.23 18190 -is_a_theorem(implies(implies(implies(equiv(A,A),B),B),C)) | is_a_theorem(implies(D,C)). [resolve(15265,a,69,b)].
% 99.89/100.23 20170 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),and(A,not(A))),C)). [resolve(18056,a,11583,a),rewrite([80(3)])].
% 99.89/100.23 20358 -is_a_theorem(implies(equiv(A,A),B)) | is_a_theorem(implies(implies(B,C),implies(D,C))). [resolve(18107,a,69,b)].
% 99.89/100.23 20403 is_a_theorem(implies(A,implies(implies(implies(not(equiv(B,B)),C),D),D))). [resolve(18190,a,242,a)].
% 99.89/100.23 20432 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),C),C)). [resolve(20403,a,15327,a)].
% 99.89/100.23 20472 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(equiv(C,C)),D),A),B))). [resolve(20432,a,130,a)].
% 99.89/100.23 22218 is_a_theorem(implies(and(not(equiv(A,A)),not(B)),C)). [resolve(351,a,20432,a)].
% 99.89/100.23 22220 is_a_theorem(implies(and(not(implies(A,A)),not(B)),C)). [resolve(351,a,20170,a)].
% 99.89/100.23 22226 is_a_theorem(implies(and(not(not(A)),not(B)),A)). [resolve(351,a,14971,a)].
% 99.89/100.23 22235 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),implies(C,D))). [resolve(351,a,7481,a)].
% 99.89/100.23 22237 is_a_theorem(implies(and(implies(not(A),A),not(A)),implies(B,C))). [resolve(351,a,3823,a)].
% 99.89/100.23 22238 is_a_theorem(implies(and(A,not(implies(not(A),B))),implies(C,D))). [resolve(351,a,3530,a)].
% 99.89/100.23 22239 is_a_theorem(implies(and(A,not(implies(B,B))),implies(C,D))). [resolve(351,a,3456,a)].
% 99.89/100.23 22248 is_a_theorem(implies(and(A,not(B)),implies(implies(implies(not(A),C),B),D))). [resolve(351,a,242,a)].
% 99.89/100.23 22250 is_a_theorem(implies(and(not(A),not(B)),implies(A,C))). [resolve(351,a,229,a)].
% 99.89/100.23 22251 is_a_theorem(implies(and(implies(A,B),not(implies(C,B))),implies(implies(C,A),D))). [resolve(351,a,227,a)].
% 99.89/100.23 22269 is_a_theorem(implies(implies(implies(A,A),and(not(not(B)),not(C))),B)). [resolve(22226,a,7735,a)].
% 99.89/100.23 22276 is_a_theorem(implies(implies(implies(not(not(A)),B),and(not(not(A)),not(B))),A)). [resolve(22226,a,232,a),rewrite([80(5)])].
% 99.89/100.23 22277 is_a_theorem(implies(implies(A,B),implies(and(not(not(A)),not(C)),B))). [resolve(22226,a,130,a)].
% 99.89/100.23 22643 is_a_theorem(implies(implies(implies(A,A),and(not(equiv(B,B)),not(C))),D)). [resolve(22218,a,7735,a)].
% 99.89/100.23 22684 is_a_theorem(implies(implies(implies(A,A),and(not(implies(B,B)),not(C))),D)). [resolve(22220,a,7735,a)].
% 99.89/100.23 22773 is_a_theorem(implies(implies(implies(A,B),C),implies(and(not(A),not(D)),C))). [resolve(22250,a,130,a)].
% 99.89/100.23 23044 is_a_theorem(implies(implies(implies(A,B),C),implies(and(D,not(implies(E,E))),C))). [resolve(22239,a,130,a)].
% 99.89/100.23 23293 is_a_theorem(implies(and(implies(not(A),A),not(A)),not(equiv(B,C)))). [para(257(a,1),22237(a,1,2))].
% 99.89/100.23 23322 is_a_theorem(implies(and(A,not(implies(not(A),B))),not(equiv(C,D)))). [para(257(a,1),22238(a,1,2))].
% 99.89/100.23 23603 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),not(equiv(C,D)))). [para(257(a,1),22235(a,1,2))].
% 99.89/100.23 24028 is_a_theorem(implies(and(not(not(not(implies(A,A)))),not(B)),C)). [resolve(22277,a,15106,a)].
% 99.89/100.23 24032 is_a_theorem(implies(implies(implies(and(not(not(A)),not(B)),A),C),implies(D,C))). [resolve(22277,a,10786,a)].
% 99.89/100.23 24170 is_a_theorem(implies(implies(implies(A,A),and(not(not(not(implies(B,B)))),not(C))),D)). [resolve(24028,a,7735,a)].
% 99.89/100.23 26458 is_a_theorem(implies(and(A,implies(B,not(A))),implies(not(equiv(not(A),B)),C))). [para(257(a,1),22248(a,1,2,1)),rewrite([80(4)])].
% 99.89/100.23 26930 is_a_theorem(and(implies(A,A),implies(not(equiv(B,B)),C))). [resolve(22643,a,258,a)].
% 99.89/100.23 27238 is_a_theorem(and(implies(A,A),implies(not(implies(B,B)),C))). [resolve(22684,a,258,a)].
% 99.89/100.23 27430 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(and(not(A),not(D)),C)). [resolve(22773,a,69,b)].
% 99.89/100.23 29908 -is_a_theorem(implies(implies(implies(A,B),implies(not(C),B)),D)) | is_a_theorem(implies(C,D)). [resolve(611,a,69,b)].
% 99.89/100.23 36571 is_a_theorem(implies(implies(A,and(not(A),not(A))),and(not(A),not(A)))). [resolve(14208,a,128,a)].
% 99.89/100.23 36616 is_a_theorem(implies(and(not(A),not(B)),and(not(A),not(A)))). [resolve(36571,a,27430,a)].
% 99.89/100.23 37472 is_a_theorem(implies(and(implies(A,B),not(C)),and(implies(A,B),implies(A,B)))). [para(80(a,1),36616(a,1,1,1)),rewrite([80(6),80(7)])].
% 99.89/100.23 41985 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),and(not(not(C)),not(D))),C)). [resolve(14941,a,22269,a)].
% 99.89/100.23 51012 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(equiv(C,C)),D),A),B)). [resolve(20472,a,69,b)].
% 99.89/100.23 53380 is_a_theorem(implies(implies(not(A),and(not(not(A)),not(not(A)))),A)). [resolve(22276,a,14208,a)].
% 99.89/100.23 53500 -is_a_theorem(implies(not(A),and(not(not(A)),not(not(A))))) | is_a_theorem(A). [resolve(53380,a,69,b)].
% 99.89/100.23 54954 is_a_theorem(implies(A,implies(and(B,not(implies(C,C))),D))). [resolve(23044,a,18190,a)].
% 99.89/100.23 54993 is_a_theorem(implies(implies(implies(and(A,not(implies(B,B))),C),D),implies(E,D))). [resolve(54954,a,20358,a)].
% 99.89/100.23 58223 -is_a_theorem(and(A,implies(B,not(A)))) | is_a_theorem(implies(not(equiv(not(A),B)),C)). [resolve(26458,a,69,b)].
% 99.89/100.23 59163 is_a_theorem(implies(A,implies(B,implies(not(A),C)))). [resolve(29908,a,24032,a)].
% 99.89/100.23 59172 is_a_theorem(implies(A,implies(implies(implies(not(A),B),C),implies(D,C)))). [resolve(29908,a,9881,a)].
% 99.89/100.23 59251 is_a_theorem(implies(implies(implies(A,implies(not(B),C)),D),implies(B,D))). [resolve(59163,a,130,a)].
% 99.89/100.23 63839 is_a_theorem(implies(A,implies(B,implies(C,implies(not(B),D))))). [resolve(59251,a,3376,a)].
% 99.89/100.23 108015 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),and(not(implies(C,C)),not(D))),E)). [resolve(51012,a,22220,a)].
% 99.89/100.23 109579 is_a_theorem(implies(and(and(A,not(implies(B,B))),not(C)),implies(D,E))). [resolve(54993,a,351,a)].
% 99.89/100.23 109718 is_a_theorem(implies(and(and(A,not(implies(B,B))),not(C)),not(equiv(D,E)))). [para(257(a,1),109579(a,1,2))].
% 99.89/100.23 112034 is_a_theorem(implies(not(equiv(not(implies(A,A)),not(implies(B,B)))),C)). [resolve(58223,a,27238,a)].
% 99.89/100.23 112036 is_a_theorem(implies(not(equiv(not(implies(A,A)),not(equiv(B,B)))),C)). [resolve(58223,a,26930,a)].
% 99.89/100.23 112072 is_a_theorem(equiv(not(implies(A,A)),not(implies(B,B)))). [resolve(112034,a,53500,a)].
% 99.89/100.23 112160 not(implies(A,A)) = not(implies(B,B)). [resolve(112072,a,61,a)].
% 99.89/100.23 112166 not(implies(A,A)) = c_0. [new_symbol(112160)].
% 99.89/100.23 112168 is_a_theorem(implies(not(equiv(c_0,not(equiv(A,A)))),B)). [back_rewrite(112036),rewrite([112166(2)])].
% 99.89/100.23 112177 is_a_theorem(implies(and(and(A,c_0),not(B)),not(equiv(C,D)))). [back_rewrite(109718),rewrite([112166(2)])].
% 99.89/100.23 112192 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),and(c_0,not(C))),D)). [back_rewrite(108015),rewrite([112166(5)])].
% 99.89/100.23 112629 is_a_theorem(implies(implies(implies(c_0,A),and(not(not(B)),not(C))),B)). [back_rewrite(41985),rewrite([112166(2)])].
% 99.89/100.23 112933 is_a_theorem(implies(implies(implies(A,A),and(not(not(c_0)),not(B))),C)). [back_rewrite(24170),rewrite([112166(3)])].
% 99.89/100.23 113180 -is_a_theorem(not(equiv(c_0,A))) | is_a_theorem(and(A,not(c_0))). [back_rewrite(15134),rewrite([112166(2),112166(6)])].
% 99.89/100.23 113184 -is_a_theorem(implies(implies(c_0,A),B)) | is_a_theorem(B). [back_rewrite(15106),rewrite([112166(2)])].
% 99.89/100.23 114788 is_a_theorem(implies(c_0,A)). [back_rewrite(414),rewrite([112166(2)])].
% 99.89/100.23 114900 implies(A,implies(B,B)) = not(and(A,c_0)). [para(112166(a,1),80(a,1,1,2)),flip(a)].
% 99.89/100.23 120557 is_a_theorem(equiv(c_0,not(equiv(A,A)))). [resolve(112168,a,53500,a)].
% 99.89/100.23 120662 not(equiv(A,A)) = c_0. [resolve(120557,a,61,a)].
% 99.89/100.23 120743 is_a_theorem(implies(implies(implies(c_0,A),and(c_0,not(B))),C)). [back_rewrite(112192),rewrite([120662(2)])].
% 99.89/100.23 120811 implies(A,equiv(B,B)) = not(and(A,c_0)). [para(120662(a,1),80(a,1,1,2)),flip(a)].
% 99.89/100.23 120847 is_a_theorem(implies(and(implies(not(A),A),not(A)),c_0)). [para(120662(a,1),23293(a,1,2))].
% 99.89/100.23 120848 is_a_theorem(implies(and(A,not(implies(not(A),B))),c_0)). [para(120662(a,1),23322(a,1,2))].
% 99.89/100.23 120853 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),c_0)). [para(120662(a,1),23603(a,1,2))].
% 99.89/100.23 123648 -is_a_theorem(implies(not(and(implies(A,A),c_0)),B)) | is_a_theorem(B). [para(114900(a,1),7533(a,1,1))].
% 99.89/100.23 124333 is_a_theorem(implies(implies(c_0,A),implies(and(implies(not(B),B),not(B)),A))). [resolve(120847,a,130,a)].
% 99.89/100.23 124359 is_a_theorem(implies(implies(c_0,A),implies(and(B,not(implies(not(B),C))),A))). [resolve(120848,a,130,a)].
% 99.89/100.23 125304 is_a_theorem(and(implies(c_0,A),implies(c_0,B))). [resolve(120743,a,258,a)].
% 99.89/100.23 125317 is_a_theorem(implies(not(equiv(not(implies(c_0,A)),c_0)),B)). [resolve(125304,a,58223,a)].
% 99.89/100.23 125514 is_a_theorem(equiv(not(implies(c_0,A)),c_0)). [resolve(125317,a,53500,a)].
% 99.89/100.23 125608 not(implies(c_0,A)) = c_0. [resolve(125514,a,61,a),flip(a)].
% 99.89/100.23 125611 implies(A,implies(c_0,B)) = not(and(A,c_0)). [para(125608(a,1),80(a,1,1,2)),flip(a)].
% 99.89/100.23 126325 is_a_theorem(implies(and(implies(not(and(implies(A,A),c_0)),B),not(B)),c_0)). [para(114900(a,1),120853(a,1,1,1,1))].
% 99.89/100.23 126709 is_a_theorem(implies(and(and(A,c_0),not(B)),c_0)). [para(120662(a,1),112177(a,1,2))].
% 99.89/100.23 126724 is_a_theorem(implies(implies(c_0,A),implies(and(and(B,c_0),not(C)),A))). [resolve(126709,a,130,a)].
% 99.89/100.23 128112 is_a_theorem(implies(not(equiv(c_0,not(not(A)))),A)). [para(257(a,1),112629(a,1,1))].
% 99.89/100.23 128128 is_a_theorem(implies(implies(A,B),implies(not(equiv(c_0,not(not(A)))),B))). [resolve(128112,a,130,a)].
% 99.89/100.23 128273 is_a_theorem(and(implies(A,A),implies(not(not(c_0)),B))). [resolve(112933,a,258,a)].
% 99.89/100.23 128275 is_a_theorem(implies(not(equiv(c_0,not(not(c_0)))),A)). [resolve(128273,a,58223,a),rewrite([112166(2)])].
% 99.89/100.23 128290 is_a_theorem(equiv(c_0,not(not(c_0)))). [resolve(128275,a,53500,a)].
% 99.89/100.23 128319 not(not(c_0)) = c_0. [resolve(128290,a,61,a)].
% 99.89/100.23 128327 not(and(A,c_0)) = implies(A,not(c_0)). [para(128319(a,1),80(a,1,1,2))].
% 99.89/100.23 128328 is_a_theorem(not(c_0)). [para(128319(a,1),122(a,1,1)),unit_del(a,114788)].
% 99.89/100.23 128336 implies(implies(not(c_0),A),and(A,c_0)) = not(equiv(not(c_0),A)). [para(128319(a,1),257(a,1,2,2))].
% 99.89/100.23 128339 is_a_theorem(implies(A,not(c_0))). [para(128319(a,1),3449(a,1,2,2,1)),rewrite([125611(5),128327(5),114900(6),128327(3)])].
% 99.89/100.23 128940 is_a_theorem(implies(and(implies(implies(implies(A,A),not(c_0)),B),not(B)),c_0)). [back_rewrite(126325),rewrite([128327(4)])].
% 99.89/100.23 129105 implies(A,implies(c_0,B)) = implies(A,not(c_0)). [back_rewrite(125611),rewrite([128327(6)])].
% 99.89/100.23 129492 -is_a_theorem(implies(implies(implies(A,A),not(c_0)),B)) | is_a_theorem(B). [back_rewrite(123648),rewrite([128327(4)])].
% 99.89/100.23 129558 implies(A,equiv(B,B)) = implies(A,not(c_0)). [back_rewrite(120811),rewrite([128327(5)])].
% 99.89/100.23 129964 implies(A,implies(B,B)) = implies(A,not(c_0)). [back_rewrite(114900),rewrite([128327(5)])].
% 99.89/100.23 130397 is_a_theorem(implies(implies(not(c_0),A),implies(B,A))). [resolve(128339,a,20358,a)].
% 99.89/100.23 130863 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(not(c_0),B),C))). [resolve(130397,a,130,a)].
% 99.89/100.23 131434 is_a_theorem(implies(and(and(A,c_0),not(B)),C)). [resolve(126724,a,113184,a)].
% 99.89/100.23 132045 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(equiv(c_0,not(not(A)))),B)). [resolve(128128,a,69,b)].
% 99.89/100.23 132273 is_a_theorem(implies(A,implies(implies(not(c_0),B),B))). [resolve(130863,a,18190,a)].
% 99.89/100.23 132274 is_a_theorem(implies(implies(A,B),implies(implies(not(c_0),A),B))). [resolve(130863,a,14208,a)].
% 99.89/100.23 132280 is_a_theorem(implies(implies(not(c_0),A),A)). [resolve(132273,a,129492,a)].
% 99.89/100.23 132318 -is_a_theorem(implies(not(c_0),A)) | is_a_theorem(A). [resolve(132280,a,69,b)].
% 99.89/100.23 132772 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(c_0),A),B)). [resolve(132274,a,69,b)].
% 99.89/100.23 132916 is_a_theorem(implies(implies(not(c_0),and(and(A,c_0),not(B))),C)). [resolve(132772,a,131434,a)].
% 99.89/100.23 133420 is_a_theorem(and(not(c_0),implies(and(A,c_0),B))). [resolve(132916,a,258,a)].
% 99.89/100.23 133423 is_a_theorem(implies(not(equiv(c_0,and(A,c_0))),B)). [resolve(133420,a,58223,a),rewrite([128319(3)])].
% 99.89/100.23 133435 is_a_theorem(equiv(c_0,and(A,c_0))). [resolve(133423,a,53500,a)].
% 99.89/100.23 133451 and(A,c_0) = c_0. [resolve(133435,a,61,a)].
% 99.89/100.23 133513 implies(implies(not(c_0),A),c_0) = not(equiv(not(c_0),A)). [back_rewrite(128336),rewrite([133451(5)])].
% 99.89/100.23 133514 implies(A,not(c_0)) = not(c_0). [back_rewrite(128327),rewrite([133451(2)]),flip(a)].
% 99.89/100.23 133539 implies(A,implies(B,B)) = not(c_0). [back_rewrite(129964),rewrite([133514(5)])].
% 99.89/100.23 133550 implies(A,equiv(B,B)) = not(c_0). [back_rewrite(129558),rewrite([133514(5)])].
% 99.89/100.23 133579 implies(A,implies(c_0,B)) = not(c_0). [back_rewrite(129105),rewrite([133514(6)])].
% 99.89/100.23 133580 is_a_theorem(implies(and(implies(not(c_0),A),not(A)),c_0)). [back_rewrite(128940),rewrite([133514(4)])].
% 99.89/100.23 133698 and(not(c_0),implies(not(c_0),A)) = equiv(A,not(c_0)). [para(133514(a,1),90(a,1,1))].
% 99.89/100.23 133699 and(implies(not(c_0),A),not(c_0)) = equiv(not(c_0),A). [para(133514(a,1),90(a,1,2))].
% 99.89/100.23 135876 is_a_theorem(implies(implies(c_0,A),implies(and(implies(not(c_0),B),not(B)),A))). [resolve(133580,a,130,a)].
% 99.89/100.23 136274 implies(not(c_0),c_0) = c_0. [para(120662(a,1),133513(a,2)),rewrite([133514(5)])].
% 99.89/100.23 136297 not(equiv(not(c_0),implies(A,A))) = c_0. [para(133539(a,1),133513(a,1,1)),rewrite([136274(4)]),flip(a)].
% 99.89/100.23 136298 not(equiv(not(c_0),equiv(A,A))) = c_0. [para(133550(a,1),133513(a,1,1)),rewrite([136274(4)]),flip(a)].
% 99.89/100.23 136299 not(equiv(not(c_0),implies(c_0,A))) = c_0. [para(133579(a,1),133513(a,1,1)),rewrite([136274(4)]),flip(a)].
% 99.89/100.23 136311 is_a_theorem(implies(implies(not(c_0),A),implies(implies(A,c_0),c_0))). [para(136274(a,1),96(a,1,2,2))].
% 99.89/100.23 136335 is_a_theorem(implies(and(implies(A,c_0),not(c_0)),implies(implies(not(c_0),A),B))). [para(136274(a,1),22251(a,1,1,2,1))].
% 99.89/100.23 136340 is_a_theorem(implies(A,implies(implies(implies(not(A),B),c_0),c_0))). [para(136274(a,1),59172(a,1,2,2))].
% 99.89/100.23 136364 implies(A,equiv(not(c_0),implies(B,B))) = not(c_0). [para(136297(a,1),80(a,1,1,2)),rewrite([133451(2)]),flip(a)].
% 99.89/100.23 136365 is_a_theorem(equiv(not(c_0),implies(A,A))). [para(136297(a,1),122(a,1,1)),rewrite([136364(6)]),unit_del(a,128328)].
% 99.89/100.23 136393 implies(A,A) = not(c_0). [resolve(136365,a,61,a)].
% 99.89/100.23 137844 and(not(c_0),not(c_0)) = equiv(A,A). [para(136393(a,1),90(a,1,1)),rewrite([136393(3)])].
% 99.89/100.23 137845 is_a_theorem(implies(implies(A,B),implies(not(c_0),implies(A,B)))). [para(136393(a,1),96(a,1,2,1))].
% 99.89/100.23 137846 implies(A,and(B,not(B))) = implies(A,c_0). [para(136393(a,1),129(a,1,1,2)),rewrite([80(4)]),flip(a)].
% 99.89/100.23 137901 implies(A,equiv(not(c_0),equiv(B,B))) = not(c_0). [para(136298(a,1),80(a,1,1,2)),rewrite([133451(2)]),flip(a)].
% 99.89/100.23 137902 is_a_theorem(equiv(not(c_0),equiv(A,A))). [para(136298(a,1),122(a,1,1)),rewrite([137901(6)]),unit_del(a,128328)].
% 99.89/100.23 137956 equiv(A,A) = not(c_0). [resolve(137902,a,61,a)].
% 99.89/100.23 138195 and(not(c_0),not(c_0)) = not(c_0). [back_rewrite(137844),rewrite([137956(6)])].
% 99.89/100.23 138312 implies(A,equiv(not(c_0),implies(c_0,B))) = not(c_0). [para(136299(a,1),80(a,1,1,2)),rewrite([133451(2)]),flip(a)].
% 99.89/100.23 138313 is_a_theorem(equiv(not(c_0),implies(c_0,A))). [para(136299(a,1),122(a,1,1)),rewrite([138312(7)]),unit_del(a,128328)].
% 99.89/100.23 138369 implies(c_0,A) = not(c_0). [resolve(138313,a,61,a)].
% 99.89/100.23 138528 is_a_theorem(implies(not(c_0),implies(and(implies(not(c_0),A),not(A)),B))). [back_rewrite(135876),rewrite([138369(2)])].
% 99.89/100.23 138533 is_a_theorem(implies(not(c_0),implies(and(A,not(implies(not(A),B))),C))). [back_rewrite(124359),rewrite([138369(2)])].
% 99.89/100.23 138534 is_a_theorem(implies(not(c_0),implies(and(implies(not(A),A),not(A)),B))). [back_rewrite(124333),rewrite([138369(2)])].
% 99.89/100.23 138537 and(implies(A,c_0),not(c_0)) = equiv(A,c_0). [para(138369(a,1),90(a,1,2))].
% 99.89/100.23 138538 is_a_theorem(implies(implies(A,c_0),implies(not(c_0),implies(A,B)))). [para(138369(a,1),96(a,1,2,1))].
% 99.89/100.23 138539 implies(A,and(c_0,not(B))) = implies(A,c_0). [para(138369(a,1),129(a,1,1,2)),rewrite([80(4)]),flip(a)].
% 99.89/100.23 138542 implies(not(c_0),and(A,not(c_0))) = not(equiv(c_0,A)). [para(138369(a,1),257(a,1,1))].
% 99.89/100.23 138616 is_a_theorem(implies(and(A,not(c_0)),implies(not(equiv(not(A),c_0)),B))). [para(138369(a,1),26458(a,1,1,2))].
% 99.89/100.23 138666 is_a_theorem(implies(equiv(A,c_0),implies(implies(not(c_0),A),B))). [back_rewrite(136335),rewrite([138537(5)])].
% 99.89/100.23 139685 implies(implies(A,c_0),and(and(B,not(B)),not(A))) = not(equiv(A,and(B,not(B)))). [para(137846(a,1),257(a,1,1))].
% 99.89/100.23 139714 implies(and(A,not(A)),c_0) = not(c_0). [para(137846(a,1),136393(a,1))].
% 99.89/100.23 139717 equiv(and(A,not(A)),c_0) = not(c_0). [para(139714(a,1),90(a,1,1)),rewrite([137846(6),136393(5),138195(5)]),flip(a)].
% 99.89/100.23 139744 and(A,not(A)) = c_0. [para(139717(a,1),61(a,1)),flip(b),unit_del(a,128328)].
% 99.89/100.23 139748 implies(implies(A,c_0),c_0) = not(equiv(A,c_0)). [back_rewrite(139685),rewrite([139744(4),138539(6),139744(6)])].
% 99.89/100.23 139755 is_a_theorem(implies(A,not(equiv(implies(not(A),B),c_0)))). [back_rewrite(136340),rewrite([139748(6)])].
% 99.89/100.23 139766 is_a_theorem(implies(implies(not(c_0),A),not(equiv(A,c_0)))). [back_rewrite(136311),rewrite([139748(7)])].
% 99.89/100.23 140850 is_a_theorem(implies(A,implies(not(equiv(not(A),c_0)),implies(B,c_0)))). [para(139748(a,1),59172(a,1,2,1))].
% 99.89/100.23 141338 -is_a_theorem(implies(not(c_0),A)) | is_a_theorem(not(equiv(A,c_0))). [resolve(139766,a,69,b)].
% 99.89/100.23 141913 is_a_theorem(not(equiv(implies(A,implies(B,implies(not(A),C))),c_0))). [resolve(141338,a,63839,a)].
% 99.89/100.23 141982 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(c_0),implies(A,B))). [resolve(137845,a,69,b)].
% 99.89/100.23 142250 is_a_theorem(implies(not(c_0),implies(equiv(A,c_0),implies(implies(not(c_0),A),B)))). [resolve(141982,a,138666,a)].
% 99.89/100.23 145558 is_a_theorem(implies(A,implies(not(equiv(not(A),c_0)),c_0))). [para(136274(a,1),140850(a,1,2,2))].
% 99.89/100.23 145610 -is_a_theorem(A) | is_a_theorem(implies(not(equiv(not(A),c_0)),c_0)). [resolve(145558,a,69,b)].
% 99.89/100.23 147853 is_a_theorem(implies(and(implies(not(c_0),A),not(A)),B)). [resolve(138528,a,132318,a)].
% 99.89/100.23 147862 is_a_theorem(implies(not(equiv(c_0,not(implies(implies(not(c_0),A),A)))),B)). [resolve(147853,a,132045,a),rewrite([80(7)])].
% 99.89/100.23 147925 is_a_theorem(implies(and(A,not(implies(not(A),B))),C)). [resolve(138533,a,132318,a)].
% 99.89/100.23 147934 is_a_theorem(implies(not(equiv(c_0,not(implies(A,implies(not(A),B))))),C)). [resolve(147925,a,132045,a),rewrite([80(6)])].
% 99.89/100.23 147974 is_a_theorem(implies(and(implies(not(A),A),not(A)),B)). [resolve(138534,a,132318,a)].
% 99.89/100.23 147981 is_a_theorem(implies(implies(not(c_0),and(implies(not(A),A),not(A))),B)). [resolve(147974,a,132772,a)].
% 99.89/100.23 148897 is_a_theorem(equiv(c_0,not(implies(implies(not(c_0),A),A)))). [resolve(147862,a,53500,a)].
% 99.89/100.23 148913 not(implies(implies(not(c_0),A),A)) = c_0. [resolve(148897,a,61,a)].
% 99.89/100.23 148915 implies(A,implies(implies(not(c_0),B),B)) = not(c_0). [para(148913(a,1),80(a,1,1,2)),rewrite([133451(2)]),flip(a)].
% 99.89/100.23 148928 equiv(implies(implies(not(c_0),A),A),not(c_0)) = not(c_0). [para(148915(a,1),133698(a,1,2)),rewrite([138195(5)]),flip(a)].
% 99.89/100.23 148944 implies(implies(not(c_0),A),A) = not(c_0). [para(148928(a,1),61(a,1)),flip(b),unit_del(a,128328)].
% 99.89/100.23 148947 and(implies(A,implies(not(c_0),A)),not(c_0)) = equiv(A,implies(not(c_0),A)). [para(148944(a,1),90(a,1,2))].
% 99.89/100.23 149051 is_a_theorem(equiv(c_0,not(implies(A,implies(not(A),B))))). [resolve(147934,a,53500,a)].
% 99.89/100.23 149059 not(implies(A,implies(not(A),B))) = c_0. [resolve(149051,a,61,a)].
% 99.89/100.23 149061 implies(A,implies(B,implies(not(B),C))) = not(c_0). [para(149059(a,1),80(a,1,1,2)),rewrite([133451(2)]),flip(a)].
% 99.89/100.23 149084 equiv(implies(A,implies(not(A),B)),not(c_0)) = not(c_0). [para(149061(a,1),133698(a,1,2)),rewrite([138195(5)]),flip(a)].
% 99.89/100.23 149090 implies(A,implies(not(A),B)) = not(c_0). [para(149084(a,1),61(a,1)),flip(b),unit_del(a,128328)].
% 99.89/100.23 149094 and(not(c_0),implies(implies(not(A),B),A)) = equiv(A,implies(not(A),B)). [para(149090(a,1),90(a,1,1))].
% 99.89/100.23 149095 and(implies(implies(not(A),B),A),not(c_0)) = equiv(implies(not(A),B),A). [para(149090(a,1),90(a,1,2))].
% 99.89/100.23 149215 is_a_theorem(equiv(A,implies(not(A),A))). [resolve(147981,a,258,a),rewrite([149094(6)])].
% 99.89/100.23 149272 implies(not(A),A) = A. [resolve(149215,a,61,a)].
% 99.89/100.23 149516 is_a_theorem(implies(and(A,not(B)),and(A,A))). [para(149272(a,1),37472(a,1,1,1)),rewrite([149272(4),149272(4)])].
% 99.89/100.23 149563 is_a_theorem(implies(A,not(equiv(A,c_0)))). [para(149272(a,1),139755(a,1,2,1,1))].
% 99.89/100.23 149565 is_a_theorem(implies(implies(not(A),c_0),implies(not(c_0),A))). [para(149272(a,1),138538(a,1,2,2))].
% 99.89/100.23 149581 is_a_theorem(not(equiv(implies(A,implies(B,A)),c_0))). [para(149272(a,1),141913(a,1,1,1,2,2))].
% 99.89/100.23 149625 is_a_theorem(implies(and(A,not(c_0)),equiv(not(A),c_0))). [para(149272(a,1),138616(a,1,2))].
% 99.89/100.23 150761 -is_a_theorem(A) | is_a_theorem(not(equiv(A,c_0))). [resolve(149563,a,69,b)].
% 99.89/100.23 150798 is_a_theorem(not(equiv(implies(A,not(equiv(A,c_0))),c_0))). [resolve(150761,a,149563,a)].
% 99.89/100.23 153842 is_a_theorem(not(equiv(implies(implies(not(A),c_0),implies(not(c_0),A)),c_0))). [resolve(149565,a,150761,a)].
% 99.89/100.23 153920 is_a_theorem(implies(not(equiv(A,c_0)),not(equiv(c_0,A)))). [para(138542(a,1),149565(a,1,2)),rewrite([80(4),139748(4)])].
% 99.89/100.23 154242 -is_a_theorem(and(A,not(c_0))) | is_a_theorem(equiv(not(A),c_0)). [resolve(149625,a,69,b)].
% 99.89/100.23 155109 -is_a_theorem(not(equiv(A,c_0))) | is_a_theorem(not(equiv(c_0,A))). [resolve(153920,a,69,b)].
% 99.89/100.23 155319 is_a_theorem(not(equiv(c_0,implies(A,not(equiv(A,c_0)))))). [resolve(155109,a,150798,a)].
% 99.89/100.23 155320 is_a_theorem(not(equiv(c_0,implies(A,implies(B,A))))). [resolve(155109,a,149581,a)].
% 99.89/100.23 155381 is_a_theorem(and(implies(A,implies(B,A)),not(c_0))). [resolve(155320,a,113180,a)].
% 99.89/100.23 155397 is_a_theorem(equiv(not(implies(A,implies(B,A))),c_0)). [resolve(155381,a,154242,a)].
% 99.89/100.23 155451 not(implies(A,implies(B,A))) = c_0. [resolve(155397,a,61,a),flip(a)].
% 99.89/100.23 155453 implies(A,implies(B,implies(C,B))) = not(c_0). [para(155451(a,1),80(a,1,1,2)),rewrite([133451(2)]),flip(a)].
% 99.89/100.23 155456 implies(A,implies(B,A)) = not(c_0). [para(155451(a,1),149272(a,1,1)),rewrite([155453(4)]),flip(a)].
% 99.89/100.23 155459 equiv(A,implies(not(c_0),A)) = not(c_0). [back_rewrite(148947),rewrite([155456(4),138195(5)]),flip(a)].
% 99.89/100.23 155507 implies(not(c_0),A) = A. [para(155459(a,1),61(a,1)),unit_del(a,128328)].
% 99.89/100.23 155538 is_a_theorem(not(equiv(implies(implies(not(A),c_0),A),c_0))). [back_rewrite(153842),rewrite([155507(6)])].
% 99.89/100.23 155613 is_a_theorem(implies(equiv(A,c_0),implies(A,B))). [back_rewrite(142250),rewrite([155507(7),155507(7)])].
% 99.89/100.23 155658 not(equiv(c_0,A)) = and(A,not(c_0)). [back_rewrite(138542),rewrite([155507(6)]),flip(a)].
% 99.89/100.23 155666 equiv(not(c_0),A) = and(A,not(c_0)). [back_rewrite(133699),rewrite([155507(3)]),flip(a)].
% 99.89/100.23 155679 is_a_theorem(and(implies(A,not(equiv(A,c_0))),not(c_0))). [back_rewrite(155319),rewrite([155658(7)])].
% 99.89/100.23 155685 -is_a_theorem(not(equiv(A,c_0))) | is_a_theorem(and(A,not(c_0))). [back_rewrite(155109),rewrite([155658(7)])].
% 99.89/100.23 157520 is_a_theorem(implies(equiv(not(A),c_0),A)). [para(149272(a,1),155613(a,1,2))].
% 99.89/100.23 157531 is_a_theorem(implies(not(equiv(not(implies(equiv(not(A),c_0),A)),c_0)),c_0)). [resolve(157520,a,145610,a)].
% 99.89/100.23 158752 -is_a_theorem(and(A,not(c_0))) | not(c_0) = A. [para(155666(a,1),61(a,1)),flip(b)].
% 99.89/100.23 161494 implies(A,not(equiv(A,c_0))) = not(c_0). [resolve(155679,a,158752,a),flip(a)].
% 99.89/100.23 161538 and(implies(not(equiv(A,c_0)),A),not(c_0)) = equiv(not(equiv(A,c_0)),A). [para(161494(a,1),90(a,1,2))].
% 99.89/100.23 161886 is_a_theorem(equiv(implies(not(A),c_0),A)). [resolve(155685,a,155538,a),rewrite([149095(7)])].
% 99.89/100.23 161974 implies(not(A),c_0) = A. [resolve(161886,a,61,a),flip(a)].
% 99.89/100.23 162027 is_a_theorem(equiv(not(implies(equiv(not(A),c_0),A)),c_0)). [back_rewrite(157531),rewrite([161974(10)])].
% 99.89/100.23 162143 implies(implies(A,B),c_0) = and(A,not(B)). [para(80(a,1),161974(a,1,1))].
% 99.89/100.23 162144 equiv(not(A),c_0) = and(A,not(c_0)). [para(161974(a,1),90(a,1,1)),rewrite([138369(3)]),flip(a)].
% 99.89/100.23 162312 not(equiv(A,c_0)) = and(A,not(c_0)). [back_rewrite(139748),rewrite([162143(4)]),flip(a)].
% 99.89/100.23 162403 is_a_theorem(and(implies(and(A,not(c_0)),A),not(c_0))). [back_rewrite(162027),rewrite([162144(3),162144(7)])].
% 99.89/100.23 163659 and(implies(and(A,not(c_0)),A),not(c_0)) = equiv(and(A,not(c_0)),A). [back_rewrite(161538),rewrite([162312(3),162312(10)])].
% 99.89/100.23 164068 is_a_theorem(equiv(and(A,not(c_0)),A)). [back_rewrite(162403),rewrite([163659(7)])].
% 99.89/100.23 165488 and(A,not(c_0)) = A. [resolve(164068,a,61,a),flip(a)].
% 99.89/100.23 167967 is_a_theorem(implies(A,and(A,A))). [para(165488(a,1),149516(a,1,1))].
% 99.89/100.23 167968 $F. [resolve(167967,a,53,a)].
% 99.89/100.23
% 99.89/100.23 % SZS output end Refutation
% 99.89/100.23 ============================== end of proof ==========================
% 99.89/100.23
% 99.89/100.23 ============================== STATISTICS ============================
% 99.89/100.23
% 99.89/100.23 Given=8706. Generated=13374128. Kept=167917. proofs=1.
% 99.89/100.23 Usable=703. Sos=4586. Demods=76. Limbo=72, Disabled=162627. Hints=0.
% 99.89/100.23 Megabytes=110.16.
% 99.89/100.23 User_CPU=92.56, System_CPU=6.68, Wall_clock=99.
% 99.89/100.23
% 99.89/100.23 ============================== end of statistics =====================
% 99.89/100.23
% 99.89/100.23 ============================== end of search =========================
% 99.89/100.23
% 99.89/100.23 THEOREM PROVED
% 99.89/100.23 % SZS status Theorem
% 99.89/100.23
% 99.89/100.23 Exiting with 1 proof.
% 99.89/100.23
% 99.89/100.23 Process 31903 exit (max_proofs) Sun Jul 3 04:41:47 2022
% 99.89/100.23 Prover9 interrupted
%------------------------------------------------------------------------------