0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : tptp2X_and_run_prover9 %d %s 0.03/0.25 % Computer : n008.star.cs.uiowa.edu 0.03/0.25 % Model : x86_64 x86_64 0.03/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.25 % Memory : 32218.625MB 0.03/0.25 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.25 % CPULimit : 300 0.03/0.25 % DateTime : Sat Jul 14 06:19:27 CDT 2018 0.03/0.26 % CPUTime : 0.07/0.48 ============================== Prover9 =============================== 0.07/0.48 Prover9 (32) version 2009-11A, November 2009. 0.07/0.48 Process 20045 was started by sandbox on n008.star.cs.uiowa.edu, 0.07/0.48 Sat Jul 14 06:19:27 2018 0.07/0.48 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_20013_n008.star.cs.uiowa.edu". 0.07/0.48 ============================== end of head =========================== 0.07/0.48 0.07/0.48 ============================== INPUT ================================= 0.07/0.48 0.07/0.48 % Reading from file /tmp/Prover9_20013_n008.star.cs.uiowa.edu 0.07/0.48 0.07/0.48 set(prolog_style_variables). 0.07/0.48 set(auto2). 0.07/0.48 % set(auto2) -> set(auto). 0.07/0.48 % set(auto) -> set(auto_inference). 0.07/0.48 % set(auto) -> set(auto_setup). 0.07/0.48 % set(auto_setup) -> set(predicate_elim). 0.07/0.48 % set(auto_setup) -> assign(eq_defs, unfold). 0.07/0.48 % set(auto) -> set(auto_limits). 0.07/0.48 % set(auto_limits) -> assign(max_weight, "100.000"). 0.07/0.48 % set(auto_limits) -> assign(sos_limit, 20000). 0.07/0.48 % set(auto) -> set(auto_denials). 0.07/0.48 % set(auto) -> set(auto_process). 0.07/0.48 % set(auto2) -> assign(new_constants, 1). 0.07/0.48 % set(auto2) -> assign(fold_denial_max, 3). 0.07/0.48 % set(auto2) -> assign(max_weight, "200.000"). 0.07/0.48 % set(auto2) -> assign(max_hours, 1). 0.07/0.48 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.07/0.48 % set(auto2) -> assign(max_seconds, 0). 0.07/0.48 % set(auto2) -> assign(max_minutes, 5). 0.07/0.48 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.07/0.48 % set(auto2) -> set(sort_initial_sos). 0.07/0.48 % set(auto2) -> assign(sos_limit, -1). 0.07/0.48 % set(auto2) -> assign(lrs_ticks, 3000). 0.07/0.48 % set(auto2) -> assign(max_megs, 400). 0.07/0.48 % set(auto2) -> assign(stats, some). 0.07/0.48 % set(auto2) -> clear(echo_input). 0.07/0.48 % set(auto2) -> set(quiet). 0.07/0.48 % set(auto2) -> clear(print_initial_clauses). 0.07/0.48 % set(auto2) -> clear(print_given). 0.07/0.48 assign(lrs_ticks,-1). 0.07/0.48 assign(sos_limit,10000). 0.07/0.48 assign(order,kbo). 0.07/0.48 set(lex_order_vars). 0.07/0.48 clear(print_given). 0.07/0.48 0.07/0.48 % formulas(sos). % not echoed (43 formulas) 0.07/0.48 0.07/0.48 ============================== end of input ========================== 0.07/0.48 0.07/0.48 % From the command line: assign(max_seconds, 300). 0.07/0.48 0.07/0.48 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.07/0.48 0.07/0.48 % Formulas that are not ordinary clauses: 0.07/0.48 1 (all X all Y is_a_theorem(implies(and(X,Y),Y))) <-> and_2 # label(and_2) # label(axiom) # label(non_clause). [assumption]. 0.07/0.48 2 (all X all Y is_a_theorem(implies(equiv(X,Y),implies(Y,X)))) <-> equivalence_2 # label(equivalence_2) # label(axiom) # label(non_clause). [assumption]. 0.07/0.48 3 substitution_of_equivalents <-> (all X all Y (is_a_theorem(equiv(X,Y)) -> Y = X)) # label(substitution_of_equivalents) # label(axiom) # label(non_clause). [assumption]. 0.07/0.48 4 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]. 0.07/0.48 5 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]. 0.07/0.48 6 (all P is_a_theorem(implies(P,and(P,P)))) <-> kn1 # label(kn1) # label(axiom) # label(non_clause). [assumption]. 0.07/0.48 7 (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))) <-> cn1 # label(cn1) # label(axiom) # label(non_clause). [assumption]. 0.07/0.48 8 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]. 0.07/0.48 9 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption]. 0.07/0.48 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption]. 0.07/0.48 11 (all X all Y is_a_theorem(implies(Y,or(X,Y)))) <-> or_2 # label(or_2) # label(axiom) # label(non_clause). [assumption]. 0.07/0.48 12 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]. 0.07/0.48 13 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]. 0.07/0.48 14 (all P is_a_theorem(implies(or(P,P),P))) <-> r1 # label(r1) # label(axiom) # label(non_clause). [assumption]. 0.70/0.95 15 (all X all Y is_a_theorem(implies(X,implies(Y,and(X,Y))))) <-> and_3 # label(and_3) # label(axiom) # label(non_clause). [assumption]. 0.70/0.95 16 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption]. 0.70/0.95 17 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption]. 0.70/0.95 18 (all P is_a_theorem(implies(implies(not(P),P),P))) <-> cn3 # label(cn3) # label(axiom) # label(non_clause). [assumption]. 0.70/0.95 19 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption]. 0.70/0.95 20 (all X all Y is_a_theorem(implies(equiv(X,Y),implies(X,Y)))) <-> equivalence_1 # label(equivalence_1) # label(axiom) # label(non_clause). [assumption]. 0.70/0.95 21 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]. 0.70/0.95 22 (all X all Y is_a_theorem(implies(X,implies(Y,X)))) <-> implies_1 # label(implies_1) # label(axiom) # label(non_clause). [assumption]. 0.70/0.95 23 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]. 0.70/0.95 24 (all P all Q is_a_theorem(implies(and(P,Q),P))) <-> kn2 # label(kn2) # label(axiom) # label(non_clause). [assumption]. 0.70/0.95 25 (all X all Y is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))) <-> equivalence_3 # label(equivalence_3) # label(axiom) # label(non_clause). [assumption]. 0.70/0.95 26 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]. 0.70/0.95 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]. 0.70/0.95 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]. 0.70/0.95 29 op_implies_and -> (all X all Y not(and(X,not(Y))) = implies(X,Y)) # label(op_implies_and) # label(axiom) # label(non_clause). [assumption]. 0.70/0.95 30 op_implies_or -> (all X all Y or(not(X),Y) = implies(X,Y)) # label(op_implies_or) # label(axiom) # label(non_clause). [assumption]. 0.70/0.95 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]. 0.70/0.95 0.70/0.95 ============================== end of process non-clausal formulas === 0.70/0.95 0.70/0.95 ============================== PROCESS INITIAL CLAUSES =============== 0.70/0.95 0.70/0.95 ============================== PREDICATE ELIMINATION ================= 0.70/0.95 0.70/0.95 ============================== end predicate elimination ============= 0.70/0.95 0.70/0.95 Auto_denials: (non-Horn, no changes). 0.70/0.95 0.70/0.95 Term ordering decisions: 0.70/0.95 0.70/0.95 % Assigning unary symbol not kb_weight 0 and highest precedence (94). 0.70/0.95 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. 0.70/0.95 0.70/0.95 ============================== end of process initial clauses ======== 0.70/0.95 0.70/0.95 ============================== CLAUSES FOR SEARCH ==================== 0.70/0.95 0.70/0.95 ============================== end of clauses for search ============= 0.70/0.95 0.70/0.95 ============================== SEARCH ================================ 0.70/0.95 0.70/0.95 % Starting search at 0.01 seconds. 0.70/0.95 0.70/0.95 Low Water (keep): wt=47.000, iters=3369 0.70/0.95 0.70/0.95 Low Water (keep): wt=40.000, iters=3351 0.70/0.95 0.70/0.95 Low Water (keep): wt=37.000, iters=3348 0.70/0.95 0.70/0.95 Low Water (keep): wt=36.000, iters=3355 0.70/0.95 0.70/0.95 Low Water (keep): wt=35.000, iters=3555 0.70/0.95 0.70/0.95 Low Water (keep): wt=33.000, iters=3451 0.70/0.95 0.70/0.95 Low Water (keep): wt=31.000, iters=3357 0.70/0.95 0.70/0.95 Low Water (keep): wt=27.000, iters=3389 0.70/0.95 0.70/0.95 Low Water (keep): wt=25.000, iters=3359 0.70/0.95 0.70/0.95 Low Water (keep): wt=24.000, iters=3363 162.21/162.45 162.21/162.45 Low Water (keep): wt=23.000, iters=3352 162.21/162.45 162.21/162.45 Low Water (keep): wt=22.000, iters=3351 162.21/162.45 162.21/162.45 Low Water (keep): wt=21.000, iters=3345 162.21/162.45 162.21/162.45 Low Water (keep): wt=20.000, iters=3369 162.21/162.45 162.21/162.45 Low Water (keep): wt=19.000, iters=3337 162.21/162.45 162.21/162.45 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 66 (0.00 of 1.62 sec). 162.21/162.45 162.21/162.45 Low Water (displace): id=2460, wt=159.000 162.21/162.45 162.21/162.45 Low Water (displace): id=2806, wt=127.000 162.21/162.45 162.21/162.45 Low Water (displace): id=3601, wt=107.000 162.21/162.45 162.21/162.45 Low Water (displace): id=1535, wt=103.000 162.21/162.45 162.21/162.45 Low Water (displace): id=1534, wt=99.000 162.21/162.45 162.21/162.45 Low Water (displace): id=1528, wt=95.000 162.21/162.45 162.21/162.45 Low Water (displace): id=1531, wt=87.000 162.21/162.45 162.21/162.45 Low Water (displace): id=1533, wt=79.000 162.21/162.45 162.21/162.45 Low Water (displace): id=9948, wt=45.000 162.21/162.45 162.21/162.45 Low Water (displace): id=9668, wt=43.000 162.21/162.45 162.21/162.45 Low Water (displace): id=9667, wt=42.000 162.21/162.45 162.21/162.45 Low Water (displace): id=9952, wt=41.000 162.21/162.45 162.21/162.45 Low Water (displace): id=7627, wt=39.000 162.21/162.45 162.21/162.45 Low Water (displace): id=7625, wt=38.000 162.21/162.45 162.21/162.45 Low Water (displace): id=9956, wt=37.000 162.21/162.45 162.21/162.45 Low Water (displace): id=10781, wt=35.000 162.21/162.45 162.21/162.45 Low Water (displace): id=9607, wt=34.000 162.21/162.45 162.21/162.45 Low Water (displace): id=10847, wt=33.000 162.21/162.45 162.21/162.45 Low Water (displace): id=10845, wt=32.000 162.21/162.45 162.21/162.45 Low Water (displace): id=11033, wt=31.000 162.21/162.45 162.21/162.45 Low Water (displace): id=11031, wt=30.000 162.21/162.45 162.21/162.45 Low Water (displace): id=10981, wt=29.000 162.21/162.45 162.21/162.45 Low Water (displace): id=11215, wt=28.000 162.21/162.45 162.21/162.45 Low Water (displace): id=10985, wt=27.000 162.21/162.45 162.21/162.45 Low Water (displace): id=11453, wt=25.000 162.21/162.45 162.21/162.45 Low Water (displace): id=11538, wt=18.000 162.21/162.45 162.21/162.45 Low Water (displace): id=11546, wt=17.000 162.21/162.45 162.21/162.45 Low Water (displace): id=11943, wt=15.000 162.21/162.45 162.21/162.45 Low Water (keep): wt=18.000, iters=3336 162.21/162.45 162.21/162.45 Low Water (displace): id=12977, wt=14.000 162.21/162.45 162.21/162.45 Low Water (displace): id=16614, wt=13.000 162.21/162.45 162.21/162.45 Low Water (displace): id=16826, wt=12.000 162.21/162.45 162.21/162.45 Low Water (keep): wt=17.000, iters=3337 162.21/162.45 162.21/162.45 Low Water (keep): wt=16.000, iters=4462 162.21/162.45 162.21/162.45 Low Water (keep): wt=15.000, iters=3854 162.21/162.45 162.21/162.45 Low Water (keep): wt=14.000, iters=3337 162.21/162.45 162.21/162.45 Low Water (keep): wt=13.000, iters=3334 162.21/162.45 162.21/162.45 ============================== PROOF ================================= 162.21/162.45 % SZS status Theorem 162.21/162.45 % SZS output start Refutation 162.21/162.45 162.21/162.45 % Proof 1 at 155.66 (+ 6.32) seconds. 162.21/162.45 % Length of proof is 404. 162.21/162.45 % Level of proof is 110. 162.21/162.45 % Maximum clause weight is 24.000. 162.21/162.45 % Given clauses 9263. 162.21/162.45 162.21/162.45 3 substitution_of_equivalents <-> (all X all Y (is_a_theorem(equiv(X,Y)) -> Y = X)) # label(substitution_of_equivalents) # label(axiom) # label(non_clause). [assumption]. 162.21/162.45 7 (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))) <-> cn1 # label(cn1) # label(axiom) # label(non_clause). [assumption]. 162.21/162.45 9 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption]. 162.21/162.45 12 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]. 162.21/162.45 18 (all P is_a_theorem(implies(implies(not(P),P),P))) <-> cn3 # label(cn3) # label(axiom) # label(non_clause). [assumption]. 162.21/162.45 25 (all X all Y is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))) <-> equivalence_3 # label(equivalence_3) # label(axiom) # label(non_clause). [assumption]. 162.21/162.45 29 op_implies_and -> (all X all Y not(and(X,not(Y))) = implies(X,Y)) # label(op_implies_and) # label(axiom) # label(non_clause). [assumption]. 162.21/162.45 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]. 162.21/162.45 33 cn3 # label(luka_cn3) # label(axiom). [assumption]. 162.21/162.45 34 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption]. 162.21/162.45 35 cn1 # label(luka_cn1) # label(axiom). [assumption]. 162.21/162.45 36 modus_ponens # label(luka_modus_ponens) # label(axiom). [assumption]. 162.21/162.45 37 cn2 # label(luka_cn2) # label(axiom). [assumption]. 162.21/162.45 39 op_equiv # label(luka_op_equiv) # label(axiom). [assumption]. 162.21/162.45 40 op_implies_and # label(hilbert_op_implies_and) # label(axiom). [assumption]. 162.21/162.45 41 -equivalence_3 # label(hilbert_equivalence_3) # label(negated_conjecture). [assumption]. 162.21/162.45 60 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(3)]. 162.21/162.45 61 -is_a_theorem(equiv(A,B)) | B = A. [copy(60),unit_del(a,34)]. 162.21/162.45 62 -cn2 | is_a_theorem(implies(A,implies(not(A),B))) # label(cn2) # label(axiom). [clausify(9)]. 162.21/162.45 63 is_a_theorem(implies(A,implies(not(A),B))). [copy(62),unit_del(a,37)]. 162.21/162.45 65 is_a_theorem(implies(implies(not(A),A),A)) | -cn3 # label(cn3) # label(axiom). [clausify(18)]. 162.21/162.45 66 is_a_theorem(implies(implies(not(A),A),A)). [copy(65),unit_del(b,33)]. 162.21/162.45 69 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(12)]. 162.21/162.45 70 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(69),unit_del(a,36)]. 162.21/162.45 78 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)]. 162.21/162.45 79 not(and(A,not(B))) = implies(A,B). [copy(78),unit_del(a,40)]. 162.21/162.45 88 -op_equiv | equiv(A,B) = and(implies(A,B),implies(B,A)) # label(op_equiv) # label(axiom). [clausify(31)]. 162.21/162.45 89 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(88),flip(b),unit_del(a,39)]. 162.21/162.45 94 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))) | -cn1 # label(cn1) # label(axiom). [clausify(7)]. 162.21/162.45 95 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))). [copy(94),unit_del(b,35)]. 162.21/162.45 102 -is_a_theorem(implies(implies(c52,c53),implies(implies(c53,c52),equiv(c52,c53)))) | equivalence_3 # label(equivalence_3) # label(axiom). [clausify(25)]. 162.21/162.45 103 -is_a_theorem(implies(implies(c52,c53),implies(implies(c53,c52),equiv(c52,c53)))). [copy(102),unit_del(b,41)]. 162.21/162.45 119 -is_a_theorem(implies(not(A),A)) | is_a_theorem(A). [resolve(70,b,66,a)]. 162.21/162.45 120 -is_a_theorem(A) | is_a_theorem(implies(not(A),B)). [resolve(70,b,63,a)]. 162.21/162.45 121 is_a_theorem(implies(and(A,not(B)),implies(implies(A,B),C))). [para(79(a,1),63(a,1,2,1))]. 162.21/162.45 122 is_a_theorem(implies(implies(implies(A,B),and(A,not(B))),and(A,not(B)))). [para(79(a,1),66(a,1,1,1))]. 162.21/162.45 123 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(79(a,1),79(a,1,1,2))]. 162.21/162.45 124 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(B,C),implies(A,C))). [resolve(95,a,70,b)]. 162.21/162.45 127 -is_a_theorem(implies(implies(implies(not(A),A),A),implies(implies(c52,c53),implies(implies(c53,c52),equiv(c52,c53))))). [ur(70,a,66,a,c,103,a)]. 162.21/162.45 129 -is_a_theorem(implies(implies(A,B),and(A,not(B)))) | is_a_theorem(and(A,not(B))). [para(79(a,1),119(a,1,1))]. 162.21/162.45 131 -is_a_theorem(implies(implies(c52,c53),implies(not(implies(implies(c53,c52),equiv(c52,c53))),implies(implies(c53,c52),equiv(c52,c53))))). [ur(70,b,95,a,c,127,a)]. 162.21/162.45 225 is_a_theorem(implies(implies(implies(implies(A,B),C),D),implies(and(A,not(B)),D))). [resolve(124,a,121,a)]. 162.21/162.45 226 is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))). [resolve(124,a,95,a)]. 162.21/162.45 227 is_a_theorem(implies(implies(A,B),implies(implies(not(A),A),B))). [resolve(124,a,66,a)]. 162.21/162.45 228 is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C))). [resolve(124,a,63,a)]. 162.21/162.45 229 is_a_theorem(implies(implies(implies(implies(not(A),A),B),C),implies(implies(A,B),C))). [resolve(227,a,124,a)]. 162.21/162.45 231 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(A),A),B)). [resolve(227,a,70,b)]. 162.21/162.45 241 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(not(A),D),B),C))). [resolve(228,a,124,a)]. 162.21/162.45 243 -is_a_theorem(implies(implies(not(A),B),C)) | is_a_theorem(implies(A,C)). [resolve(228,a,70,b)]. 162.21/162.45 245 -is_a_theorem(implies(implies(not(implies(c52,c53)),A),implies(not(implies(implies(c53,c52),equiv(c52,c53))),implies(implies(c53,c52),equiv(c52,c53))))). [ur(70,b,228,a,c,131,a)]. 162.21/162.45 256 implies(implies(A,B),and(B,not(A))) = not(equiv(A,B)). [para(89(a,1),123(a,1,1)),flip(a)]. 162.21/162.45 345 is_a_theorem(implies(A,implies(implies(B,C),implies(not(A),C)))). [resolve(243,a,95,a)]. 162.21/162.45 346 is_a_theorem(implies(A,A)). [resolve(243,a,66,a)]. 162.21/162.45 348 -is_a_theorem(implies(implies(implies(A,B),C),D)) | is_a_theorem(implies(and(A,not(B)),D)). [para(79(a,1),243(a,1,1,1))]. 162.21/162.45 410 is_a_theorem(implies(not(implies(A,A)),B)). [resolve(346,a,120,a)]. 162.21/162.45 430 is_a_theorem(implies(implies(A,B),implies(not(implies(C,C)),B))). [resolve(410,a,124,a)]. 162.21/162.45 623 is_a_theorem(implies(implies(not(A),A),implies(implies(B,C),implies(not(A),C)))). [resolve(345,a,231,a)]. 162.21/162.45 624 is_a_theorem(implies(implies(implies(implies(A,B),implies(not(C),B)),D),implies(C,D))). [resolve(345,a,124,a)]. 162.21/162.45 653 is_a_theorem(implies(A,implies(not(implies(B,B)),C))). [resolve(430,a,243,a)]. 162.21/162.45 751 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),implies(D,C))). [resolve(653,a,124,a)]. 162.21/162.45 1021 is_a_theorem(implies(not(equiv(A,A)),and(A,not(A)))). [para(256(a,1),122(a,1,1))]. 162.21/162.45 1205 is_a_theorem(implies(implies(and(A,not(A)),B),implies(not(equiv(A,A)),B))). [resolve(1021,a,124,a)]. 162.21/162.45 2284 -is_a_theorem(implies(implies(not(implies(A,A)),B),C)) | is_a_theorem(implies(D,C)). [resolve(751,a,70,b)]. 162.21/162.45 3019 is_a_theorem(implies(A,implies(B,B))). [resolve(2284,a,66,a)]. 162.21/162.45 3026 is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))). [resolve(3019,a,124,a)]. 162.21/162.45 3373 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(D,D),B),C))). [resolve(3026,a,124,a)]. 162.21/162.45 3375 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(implies(C,B)). [resolve(3026,a,70,b)]. 162.21/162.45 3447 is_a_theorem(implies(A,implies(B,implies(C,C)))). [resolve(3375,a,3026,a)]. 162.21/162.45 3449 is_a_theorem(implies(A,implies(B,implies(not(B),C)))). [resolve(3375,a,228,a)]. 162.21/162.45 3450 is_a_theorem(implies(A,implies(implies(not(B),B),B))). [resolve(3375,a,227,a)]. 162.21/162.45 3456 is_a_theorem(implies(implies(implies(A,implies(B,B)),C),implies(D,C))). [resolve(3447,a,124,a)]. 162.21/162.45 3530 is_a_theorem(implies(implies(implies(A,implies(not(A),B)),C),implies(D,C))). [resolve(3449,a,124,a)]. 162.21/162.45 3826 is_a_theorem(implies(implies(implies(implies(not(A),A),A),B),implies(C,B))). [resolve(3450,a,124,a)]. 162.21/162.45 5455 -is_a_theorem(implies(implies(implies(not(A),A),A),B)) | is_a_theorem(implies(C,B)). [resolve(3826,a,70,b)]. 162.21/162.45 6743 -is_a_theorem(implies(not(A),A)) | is_a_theorem(implies(implies(B,C),implies(not(A),C))). [resolve(623,a,70,b)]. 162.21/162.45 7287 -is_a_theorem(implies(and(A,not(A)),B)) | is_a_theorem(implies(not(equiv(A,A)),B)). [resolve(1205,a,70,b)]. 162.21/162.45 7603 is_a_theorem(implies(A,implies(implies(implies(B,B),C),C))). [resolve(3373,a,5455,a)]. 162.21/162.45 7613 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(implies(D,D),B),C)). [resolve(3373,a,70,b)]. 162.21/162.45 7667 is_a_theorem(implies(implies(implies(implies(implies(A,A),B),B),C),implies(D,C))). [resolve(7603,a,124,a)]. 162.21/162.45 7669 is_a_theorem(implies(implies(implies(A,A),B),B)). [resolve(7603,a,119,a)]. 162.21/162.45 7716 is_a_theorem(implies(implies(A,B),implies(implies(implies(C,C),A),B))). [resolve(7669,a,124,a)]. 162.21/162.45 7717 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(B). [resolve(7669,a,70,b)]. 162.21/162.45 7959 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(C,C),A),B)). [resolve(7716,a,70,b)]. 162.21/162.45 8452 is_a_theorem(implies(implies(implies(A,A),implies(implies(B,B),C)),implies(D,C))). [resolve(7959,a,3026,a)]. 162.21/162.45 9994 is_a_theorem(implies(implies(implies(A,A),B),implies(implies(B,C),implies(D,C)))). [resolve(7613,a,95,a)]. 162.21/162.45 10060 -is_a_theorem(implies(implies(implies(implies(A,A),B),B),C)) | is_a_theorem(implies(D,C)). [resolve(7667,a,70,b)]. 162.21/162.45 10522 -is_a_theorem(implies(implies(A,A),implies(implies(B,B),C))) | is_a_theorem(implies(D,C)). [resolve(8452,a,70,b)]. 162.21/162.45 10776 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(implies(implies(B,C),implies(D,C))). [resolve(9994,a,70,b)]. 162.21/162.45 11426 is_a_theorem(implies(A,implies(and(B,not(B)),C))). [resolve(225,a,10060,a)]. 162.21/162.45 11458 is_a_theorem(implies(and(A,not(A)),B)). [resolve(11426,a,7717,a)]. 162.21/162.45 11514 is_a_theorem(implies(not(equiv(A,A)),B)). [back_unit_del(7287),unit_del(a,11458)]. 162.21/162.45 11643 is_a_theorem(implies(implies(A,B),implies(not(equiv(C,C)),B))). [resolve(11514,a,6743,a)]. 162.21/162.45 12656 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),C),implies(D,C))). [resolve(11643,a,10776,a)]. 162.21/162.45 13133 is_a_theorem(implies(A,implies(B,equiv(C,C)))). [resolve(12656,a,5455,a)]. 162.21/162.45 13177 is_a_theorem(implies(A,equiv(B,B))). [resolve(13133,a,10522,a)]. 162.21/162.45 13254 is_a_theorem(implies(implies(equiv(A,A),B),implies(C,B))). [resolve(13177,a,10776,a)]. 162.21/162.45 13565 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(equiv(D,D),B),C))). [resolve(13254,a,124,a)]. 162.21/162.45 13825 -is_a_theorem(implies(implies(implies(not(A),A),B),C)) | is_a_theorem(implies(implies(A,B),C)). [resolve(229,a,70,b)]. 162.21/162.45 14825 is_a_theorem(implies(A,implies(implies(implies(not(implies(B,B)),C),D),D))). [resolve(241,a,10060,a)]. 162.21/162.45 14832 is_a_theorem(implies(A,implies(implies(implies(not(not(B)),C),B),B))). [resolve(241,a,5455,a)]. 162.21/162.45 14873 is_a_theorem(implies(implies(implies(not(not(A)),B),A),A)). [resolve(14832,a,7717,a)]. 162.21/162.45 14903 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(not(A)),C),A),B))). [resolve(14873,a,124,a)]. 162.21/162.45 14904 -is_a_theorem(implies(implies(not(not(A)),B),A)) | is_a_theorem(A). [resolve(14873,a,70,b)]. 162.21/162.45 14919 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),C)). [resolve(14825,a,14904,a)]. 162.21/162.45 14964 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(implies(C,C)),D),A),B))). [resolve(14919,a,124,a)]. 162.21/162.45 14965 -is_a_theorem(implies(implies(not(implies(A,A)),B),C)) | is_a_theorem(C). [resolve(14919,a,70,b)]. 162.21/162.45 14989 -is_a_theorem(not(equiv(not(implies(A,A)),B))) | is_a_theorem(and(B,not(not(implies(A,A))))). [para(256(a,1),14965(a,1))]. 162.21/162.45 15014 -is_a_theorem(implies(not(implies(implies(c53,c52),equiv(c52,c53))),not(implies(c52,c53)))). [ur(124,b,245,a)]. 162.21/162.45 15240 is_a_theorem(implies(A,implies(implies(equiv(B,B),C),C))). [resolve(13565,a,10060,a)]. 162.21/162.45 15256 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(equiv(D,D),B),C)). [resolve(13565,a,70,b)]. 162.21/162.45 15261 is_a_theorem(implies(implies(equiv(A,A),B),B)). [resolve(15240,a,14965,a)]. 162.21/162.45 15263 is_a_theorem(implies(implies(implies(implies(equiv(A,A),B),B),C),implies(D,C))). [resolve(15240,a,10776,a)]. 162.21/162.45 15319 -is_a_theorem(implies(equiv(A,A),B)) | is_a_theorem(B). [resolve(15261,a,70,b)]. 162.21/162.45 18580 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(not(A)),C),A),B)). [resolve(14903,a,70,b)]. 162.21/162.45 18654 is_a_theorem(implies(implies(equiv(A,A),B),implies(implies(B,C),implies(D,C)))). [resolve(15256,a,9994,a)]. 162.21/162.45 18738 -is_a_theorem(implies(implies(implies(equiv(A,A),B),B),C)) | is_a_theorem(implies(D,C)). [resolve(15263,a,70,b)]. 162.21/162.45 20826 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),and(A,not(A))),C)). [resolve(18580,a,11458,a),rewrite([79(3)])]. 162.21/162.45 21008 -is_a_theorem(implies(equiv(A,A),B)) | is_a_theorem(implies(implies(B,C),implies(D,C))). [resolve(18654,a,70,b)]. 162.21/162.45 21056 is_a_theorem(implies(A,implies(implies(implies(not(equiv(B,B)),C),D),D))). [resolve(18738,a,241,a)]. 162.21/162.45 21085 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),C),C)). [resolve(21056,a,15319,a)]. 162.21/162.45 21127 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(equiv(C,C)),D),A),B))). [resolve(21085,a,124,a)]. 162.21/162.45 23102 is_a_theorem(implies(and(not(equiv(A,A)),not(B)),C)). [resolve(348,a,21085,a)]. 162.21/162.45 23104 is_a_theorem(implies(and(not(implies(A,A)),not(B)),C)). [resolve(348,a,20826,a)]. 162.21/162.45 23112 is_a_theorem(implies(and(not(not(A)),not(B)),A)). [resolve(348,a,14873,a)]. 162.21/162.45 23122 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),implies(C,D))). [resolve(348,a,7667,a)]. 162.21/162.45 23124 is_a_theorem(implies(and(implies(not(A),A),not(A)),implies(B,C))). [resolve(348,a,3826,a)]. 162.21/162.45 23125 is_a_theorem(implies(and(A,not(implies(not(A),B))),implies(C,D))). [resolve(348,a,3530,a)]. 162.21/162.45 23126 is_a_theorem(implies(and(A,not(implies(B,B))),implies(C,D))). [resolve(348,a,3456,a)]. 162.21/162.45 23134 is_a_theorem(implies(and(A,not(B)),implies(implies(implies(not(A),C),B),D))). [resolve(348,a,241,a)]. 162.21/162.45 23137 is_a_theorem(implies(and(implies(A,B),not(implies(C,B))),implies(implies(C,A),D))). [resolve(348,a,226,a)]. 162.21/162.45 23162 is_a_theorem(implies(implies(implies(not(not(A)),B),and(not(not(A)),not(B))),A)). [resolve(23112,a,231,a),rewrite([79(5)])]. 162.21/162.45 23163 is_a_theorem(implies(implies(A,B),implies(and(not(not(A)),not(C)),B))). [resolve(23112,a,124,a)]. 162.21/162.45 23578 is_a_theorem(implies(implies(implies(A,A),and(not(equiv(B,B)),not(C))),D)). [resolve(23102,a,7959,a)]. 162.21/162.45 23622 is_a_theorem(implies(implies(implies(A,A),and(not(implies(B,B)),not(C))),D)). [resolve(23104,a,7959,a)]. 162.21/162.45 24063 is_a_theorem(implies(implies(implies(A,B),C),implies(and(D,not(implies(E,E))),C))). [resolve(23126,a,124,a)]. 162.21/162.45 24323 is_a_theorem(implies(and(implies(not(A),A),not(A)),not(equiv(B,C)))). [para(256(a,1),23124(a,1,2))]. 162.21/162.45 24376 is_a_theorem(implies(and(A,not(implies(not(A),B))),not(equiv(C,D)))). [para(256(a,1),23125(a,1,2))]. 162.21/162.45 24656 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),not(equiv(C,D)))). [para(256(a,1),23122(a,1,2))]. 162.21/162.45 25027 is_a_theorem(implies(and(not(not(not(implies(A,A)))),not(B)),C)). [resolve(23163,a,14965,a)]. 162.21/162.45 25031 is_a_theorem(implies(implies(implies(and(not(not(A)),not(B)),A),C),implies(D,C))). [resolve(23163,a,10776,a)]. 162.21/162.45 25058 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(and(not(not(A)),not(C)),B)). [resolve(23163,a,70,b)]. 162.21/162.45 25146 is_a_theorem(implies(implies(implies(A,A),and(not(not(not(implies(B,B)))),not(C))),D)). [resolve(25027,a,7959,a)]. 162.21/162.45 27670 is_a_theorem(implies(and(A,implies(B,not(A))),implies(not(equiv(not(A),B)),C))). [para(256(a,1),23134(a,1,2,1)),rewrite([79(4)])]. 162.21/162.45 28120 is_a_theorem(and(implies(A,A),implies(not(equiv(B,B)),C))). [resolve(23578,a,129,a),rewrite([79(6)])]. 162.21/162.45 28398 is_a_theorem(and(implies(A,A),implies(not(implies(B,B)),C))). [resolve(23622,a,129,a),rewrite([79(6)])]. 162.21/162.45 31252 -is_a_theorem(implies(implies(implies(A,B),implies(not(C),B)),D)) | is_a_theorem(implies(C,D)). [resolve(624,a,70,b)]. 162.21/162.45 45290 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(implies(C,C)),D),A),B)). [resolve(14964,a,70,b)]. 162.21/162.45 53659 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(equiv(C,C)),D),A),B)). [resolve(21127,a,70,b)]. 162.21/162.45 55696 is_a_theorem(implies(and(implies(A,B),not(implies(C,B))),not(equiv(C,A)))). [para(256(a,1),23137(a,1,2))]. 162.21/162.45 55957 is_a_theorem(implies(implies(not(A),and(not(not(A)),not(not(A)))),A)). [resolve(23162,a,13825,a)]. 162.21/162.45 56034 -is_a_theorem(implies(not(A),and(not(not(A)),not(not(A))))) | is_a_theorem(A). [resolve(55957,a,70,b)]. 162.21/162.45 57146 is_a_theorem(implies(A,implies(and(B,not(implies(C,C))),D))). [resolve(24063,a,18738,a)]. 162.21/162.45 57187 is_a_theorem(implies(implies(implies(and(A,not(implies(B,B))),C),D),implies(E,D))). [resolve(57146,a,21008,a)]. 162.21/162.45 61319 -is_a_theorem(and(A,implies(B,not(A)))) | is_a_theorem(implies(not(equiv(not(A),B)),C)). [resolve(27670,a,70,b)]. 162.21/162.45 62187 is_a_theorem(implies(A,implies(B,implies(not(A),C)))). [resolve(31252,a,25031,a)]. 162.21/162.45 62196 is_a_theorem(implies(A,implies(implies(implies(not(A),B),C),implies(D,C)))). [resolve(31252,a,9994,a)]. 162.21/162.45 62275 is_a_theorem(implies(implies(implies(A,implies(not(B),C)),D),implies(B,D))). [resolve(62187,a,124,a)]. 162.21/162.45 66955 is_a_theorem(implies(A,implies(B,implies(C,implies(not(B),D))))). [resolve(62275,a,3375,a)]. 162.21/162.45 91526 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),and(not(not(C)),not(D))),C)). [resolve(45290,a,23112,a)]. 162.21/162.45 112019 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),and(not(implies(C,C)),not(D))),E)). [resolve(53659,a,23104,a)]. 162.21/162.45 113604 is_a_theorem(implies(and(and(A,not(implies(B,B))),not(C)),implies(D,E))). [resolve(57187,a,348,a)]. 162.21/162.45 113751 is_a_theorem(implies(and(and(A,not(implies(B,B))),not(C)),not(equiv(D,E)))). [para(256(a,1),113604(a,1,2))]. 162.21/162.45 116303 is_a_theorem(implies(not(equiv(not(implies(A,A)),not(implies(B,B)))),C)). [resolve(61319,a,28398,a)]. 162.21/162.45 116305 is_a_theorem(implies(not(equiv(not(implies(A,A)),not(equiv(B,B)))),C)). [resolve(61319,a,28120,a)]. 162.21/162.45 116341 is_a_theorem(equiv(not(implies(A,A)),not(implies(B,B)))). [resolve(116303,a,56034,a)]. 162.21/162.45 116439 not(implies(A,A)) = not(implies(B,B)). [resolve(116341,a,61,a)]. 162.21/162.45 116446 not(implies(A,A)) = c_0. [new_symbol(116439)]. 162.21/162.45 116448 is_a_theorem(implies(not(equiv(c_0,not(equiv(A,A)))),B)). [back_rewrite(116305),rewrite([116446(2)])]. 162.21/162.45 116502 is_a_theorem(implies(and(and(A,c_0),not(B)),not(equiv(C,D)))). [back_rewrite(113751),rewrite([116446(2)])]. 162.21/162.45 116537 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),and(c_0,not(C))),D)). [back_rewrite(112019),rewrite([116446(5)])]. 162.21/162.45 116595 is_a_theorem(implies(implies(implies(c_0,A),and(not(not(B)),not(C))),B)). [back_rewrite(91526),rewrite([116446(2)])]. 162.21/162.45 116990 is_a_theorem(implies(implies(implies(A,A),and(not(not(c_0)),not(B))),C)). [back_rewrite(25146),rewrite([116446(3)])]. 162.21/162.45 117165 -is_a_theorem(not(equiv(c_0,A))) | is_a_theorem(and(A,not(c_0))). [back_rewrite(14989),rewrite([116446(2),116446(6)])]. 162.21/162.45 117168 -is_a_theorem(implies(implies(c_0,A),B)) | is_a_theorem(B). [back_rewrite(14965),rewrite([116446(2)])]. 162.21/162.45 119027 is_a_theorem(implies(c_0,A)). [back_rewrite(410),rewrite([116446(2)])]. 162.21/162.45 119253 implies(A,implies(B,B)) = not(and(A,c_0)). [para(116446(a,1),79(a,1,1,2)),flip(a)]. 162.21/162.45 126063 is_a_theorem(equiv(c_0,not(equiv(A,A)))). [resolve(116448,a,56034,a)]. 162.21/162.45 126163 not(equiv(A,A)) = c_0. [resolve(126063,a,61,a)]. 162.21/162.45 126267 is_a_theorem(implies(implies(implies(c_0,A),and(c_0,not(B))),C)). [back_rewrite(116537),rewrite([126163(2)])]. 162.21/162.45 126374 implies(A,equiv(B,B)) = not(and(A,c_0)). [para(126163(a,1),79(a,1,1,2)),flip(a)]. 162.21/162.45 126406 is_a_theorem(implies(and(implies(not(A),A),not(A)),c_0)). [para(126163(a,1),24323(a,1,2))]. 162.21/162.45 126407 is_a_theorem(implies(and(A,not(implies(not(A),B))),c_0)). [para(126163(a,1),24376(a,1,2))]. 162.21/162.45 126413 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),c_0)). [para(126163(a,1),24656(a,1,2))]. 162.21/162.45 130317 -is_a_theorem(implies(not(and(implies(A,A),c_0)),B)) | is_a_theorem(B). [para(119253(a,1),7717(a,1,1))]. 162.21/162.45 132446 is_a_theorem(implies(implies(c_0,A),implies(and(implies(not(B),B),not(B)),A))). [resolve(126406,a,124,a)]. 162.21/162.45 132515 is_a_theorem(implies(implies(c_0,A),implies(and(B,not(implies(not(B),C))),A))). [resolve(126407,a,124,a)]. 162.21/162.45 140990 is_a_theorem(and(implies(c_0,A),implies(c_0,B))). [resolve(126267,a,129,a),rewrite([79(6)])]. 162.21/162.45 141025 is_a_theorem(implies(not(equiv(not(implies(c_0,A)),c_0)),B)). [resolve(140990,a,61319,a)]. 162.21/162.45 141212 is_a_theorem(equiv(not(implies(c_0,A)),c_0)). [resolve(141025,a,56034,a)]. 162.21/162.45 141303 not(implies(c_0,A)) = c_0. [resolve(141212,a,61,a),flip(a)]. 162.21/162.45 141332 implies(A,implies(c_0,B)) = not(and(A,c_0)). [para(141303(a,1),79(a,1,1,2)),flip(a)]. 162.21/162.45 142442 is_a_theorem(implies(and(implies(not(and(implies(A,A),c_0)),B),not(B)),c_0)). [para(119253(a,1),126413(a,1,1,1,1))]. 162.21/162.45 146697 is_a_theorem(implies(and(and(A,c_0),not(B)),c_0)). [para(126163(a,1),116502(a,1,2))]. 162.21/162.45 146764 is_a_theorem(implies(implies(c_0,A),implies(and(and(B,c_0),not(C)),A))). [resolve(146697,a,124,a)]. 162.21/162.45 165402 is_a_theorem(implies(not(equiv(c_0,not(not(A)))),A)). [para(256(a,1),116595(a,1,1))]. 162.21/162.45 165472 is_a_theorem(implies(implies(A,B),implies(not(equiv(c_0,not(not(A)))),B))). [resolve(165402,a,124,a)]. 162.21/162.45 167469 is_a_theorem(and(implies(A,A),implies(not(not(c_0)),B))). [resolve(116990,a,129,a),rewrite([79(7)])]. 162.21/162.45 167507 is_a_theorem(implies(not(equiv(c_0,not(not(c_0)))),A)). [resolve(167469,a,61319,a),rewrite([116446(2)])]. 162.21/162.45 167576 is_a_theorem(equiv(c_0,not(not(c_0)))). [resolve(167507,a,56034,a)]. 162.21/162.45 167668 not(not(c_0)) = c_0. [resolve(167576,a,61,a)]. 162.21/162.45 167672 not(and(A,c_0)) = implies(A,not(c_0)). [para(167668(a,1),79(a,1,1,2))]. 162.21/162.45 167673 is_a_theorem(not(c_0)). [para(167668(a,1),119(a,1,1)),unit_del(a,119027)]. 162.21/162.45 167682 implies(implies(not(c_0),A),and(A,c_0)) = not(equiv(not(c_0),A)). [para(167668(a,1),256(a,1,2,2))]. 162.21/162.45 167686 is_a_theorem(implies(A,not(c_0))). [para(167668(a,1),3449(a,1,2,2,1)),rewrite([141332(5),167672(5),119253(6),167672(3)])]. 162.21/162.45 168341 is_a_theorem(implies(and(implies(implies(implies(A,A),not(c_0)),B),not(B)),c_0)). [back_rewrite(142442),rewrite([167672(4)])]. 162.21/162.45 168498 implies(A,implies(c_0,B)) = implies(A,not(c_0)). [back_rewrite(141332),rewrite([167672(6)])]. 162.21/162.45 168834 -is_a_theorem(implies(implies(implies(A,A),not(c_0)),B)) | is_a_theorem(B). [back_rewrite(130317),rewrite([167672(4)])]. 162.21/162.45 168907 implies(A,equiv(B,B)) = implies(A,not(c_0)). [back_rewrite(126374),rewrite([167672(5)])]. 162.21/162.45 169420 implies(A,implies(B,B)) = implies(A,not(c_0)). [back_rewrite(119253),rewrite([167672(5)])]. 162.21/162.45 169780 is_a_theorem(implies(implies(not(c_0),A),implies(B,A))). [resolve(167686,a,21008,a)]. 162.21/162.45 170867 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(not(c_0),B),C))). [resolve(169780,a,124,a)]. 162.21/162.45 192412 is_a_theorem(implies(and(and(A,c_0),not(B)),C)). [resolve(146764,a,117168,a)]. 162.21/162.45 197923 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(equiv(c_0,not(not(A)))),B)). [resolve(165472,a,70,b)]. 162.21/162.45 210965 is_a_theorem(implies(A,implies(implies(not(c_0),B),B))). [resolve(170867,a,18738,a)]. 162.21/162.45 210972 is_a_theorem(implies(implies(A,B),implies(implies(not(c_0),A),B))). [resolve(170867,a,13825,a)]. 162.21/162.45 210995 is_a_theorem(implies(implies(not(c_0),A),A)). [resolve(210965,a,168834,a)]. 162.21/162.45 211130 -is_a_theorem(implies(not(c_0),A)) | is_a_theorem(A). [resolve(210995,a,70,b)]. 162.21/162.45 214983 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(c_0),A),B)). [resolve(210972,a,70,b)]. 162.21/162.45 216535 is_a_theorem(implies(implies(not(c_0),and(and(A,c_0),not(B))),C)). [resolve(214983,a,192412,a)]. 162.21/162.45 223709 is_a_theorem(and(not(c_0),implies(and(A,c_0),B))). [resolve(216535,a,129,a),rewrite([79(7)])]. 162.21/162.45 223743 is_a_theorem(implies(not(equiv(c_0,and(A,c_0))),B)). [resolve(223709,a,61319,a),rewrite([167668(3)])]. 162.21/162.45 223811 is_a_theorem(equiv(c_0,and(A,c_0))). [resolve(223743,a,56034,a)]. 162.21/162.45 223900 and(A,c_0) = c_0. [resolve(223811,a,61,a)]. 162.21/162.45 223951 implies(implies(not(c_0),A),c_0) = not(equiv(not(c_0),A)). [back_rewrite(167682),rewrite([223900(5)])]. 162.21/162.45 223952 implies(A,not(c_0)) = not(c_0). [back_rewrite(167672),rewrite([223900(2)]),flip(a)]. 162.21/162.45 223974 implies(A,implies(B,B)) = not(c_0). [back_rewrite(169420),rewrite([223952(5)])]. 162.21/162.45 223997 implies(A,equiv(B,B)) = not(c_0). [back_rewrite(168907),rewrite([223952(5)])]. 162.21/162.45 224016 implies(A,implies(c_0,B)) = not(c_0). [back_rewrite(168498),rewrite([223952(6)])]. 162.21/162.45 224017 is_a_theorem(implies(and(implies(not(c_0),A),not(A)),c_0)). [back_rewrite(168341),rewrite([223952(4)])]. 162.21/162.45 224021 and(not(c_0),implies(not(c_0),A)) = equiv(A,not(c_0)). [para(223952(a,1),89(a,1,1))]. 162.21/162.45 224022 and(implies(not(c_0),A),not(c_0)) = equiv(not(c_0),A). [para(223952(a,1),89(a,1,2))]. 162.21/162.45 226549 is_a_theorem(implies(implies(c_0,A),implies(and(implies(not(c_0),B),not(B)),A))). [resolve(224017,a,124,a)]. 162.21/162.45 227056 implies(not(c_0),c_0) = c_0. [para(126163(a,1),223951(a,2)),rewrite([223952(5)])]. 162.21/162.45 227081 not(equiv(not(c_0),implies(A,A))) = c_0. [para(223974(a,1),223951(a,1,1)),rewrite([227056(4)]),flip(a)]. 162.21/162.45 227082 not(equiv(not(c_0),equiv(A,A))) = c_0. [para(223997(a,1),223951(a,1,1)),rewrite([227056(4)]),flip(a)]. 162.21/162.45 227083 not(equiv(not(c_0),implies(c_0,A))) = c_0. [para(224016(a,1),223951(a,1,1)),rewrite([227056(4)]),flip(a)]. 162.21/162.45 227125 is_a_theorem(implies(implies(not(c_0),A),implies(implies(A,c_0),c_0))). [para(227056(a,1),95(a,1,2,2))]. 162.21/162.45 227150 is_a_theorem(implies(and(implies(A,c_0),not(c_0)),implies(implies(not(c_0),A),B))). [para(227056(a,1),23137(a,1,1,2,1))]. 162.21/162.45 227157 is_a_theorem(implies(A,implies(implies(implies(not(A),B),c_0),c_0))). [para(227056(a,1),62196(a,1,2,2))]. 162.21/162.45 227198 implies(A,equiv(not(c_0),implies(B,B))) = not(c_0). [para(227081(a,1),79(a,1,1,2)),rewrite([223900(2)]),flip(a)]. 162.21/162.45 227199 is_a_theorem(equiv(not(c_0),implies(A,A))). [para(227081(a,1),119(a,1,1)),rewrite([227198(6)]),unit_del(a,167673)]. 162.21/162.45 227265 implies(A,A) = not(c_0). [resolve(227199,a,61,a)]. 162.21/162.45 228588 equiv(A,A) = and(not(c_0),not(c_0)). [para(227265(a,1),89(a,1,1)),rewrite([227265(3)]),flip(a)]. 162.21/162.45 228589 is_a_theorem(implies(implies(A,B),implies(not(c_0),implies(A,B)))). [para(227265(a,1),95(a,1,2,1))]. 162.21/162.45 228590 implies(A,and(B,not(B))) = implies(A,c_0). [para(227265(a,1),123(a,1,1,2)),rewrite([79(4)]),flip(a)]. 162.21/162.45 228637 implies(A,equiv(not(c_0),equiv(B,B))) = not(c_0). [para(227082(a,1),79(a,1,1,2)),rewrite([223900(2)]),flip(a)]. 162.21/162.45 228638 is_a_theorem(equiv(not(c_0),equiv(A,A))). [para(227082(a,1),119(a,1,1)),rewrite([228637(6)]),unit_del(a,167673)]. 162.21/162.45 228692 equiv(A,A) = not(c_0). [resolve(228638,a,61,a)]. 162.21/162.45 228911 and(not(c_0),not(c_0)) = not(c_0). [back_rewrite(228588),rewrite([228692(1)]),flip(a)]. 162.21/162.45 229031 implies(A,equiv(not(c_0),implies(c_0,B))) = not(c_0). [para(227083(a,1),79(a,1,1,2)),rewrite([223900(2)]),flip(a)]. 162.21/162.45 229032 is_a_theorem(equiv(not(c_0),implies(c_0,A))). [para(227083(a,1),119(a,1,1)),rewrite([229031(7)]),unit_del(a,167673)]. 162.21/162.45 229082 implies(c_0,A) = not(c_0). [resolve(229032,a,61,a)]. 162.21/162.45 229341 is_a_theorem(implies(not(c_0),implies(and(implies(not(c_0),A),not(A)),B))). [back_rewrite(226549),rewrite([229082(2)])]. 162.21/162.45 229345 is_a_theorem(implies(not(c_0),implies(and(A,not(implies(not(A),B))),C))). [back_rewrite(132515),rewrite([229082(2)])]. 162.21/162.45 229346 is_a_theorem(implies(not(c_0),implies(and(implies(not(A),A),not(A)),B))). [back_rewrite(132446),rewrite([229082(2)])]. 162.21/162.45 229349 and(implies(A,c_0),not(c_0)) = equiv(A,c_0). [para(229082(a,1),89(a,1,2))]. 162.21/162.45 229350 is_a_theorem(implies(implies(A,c_0),implies(not(c_0),implies(A,B)))). [para(229082(a,1),95(a,1,2,1))]. 162.21/162.45 229351 implies(A,and(c_0,not(B))) = implies(A,c_0). [para(229082(a,1),123(a,1,1,2)),rewrite([79(4)]),flip(a)]. 162.21/162.45 229352 implies(not(c_0),and(A,not(c_0))) = not(equiv(c_0,A)). [para(229082(a,1),256(a,1,1))]. 162.21/162.45 229393 is_a_theorem(implies(and(A,not(c_0)),implies(not(equiv(not(A),c_0)),B))). [para(229082(a,1),27670(a,1,1,2))]. 162.21/162.45 229449 is_a_theorem(implies(equiv(A,c_0),implies(implies(not(c_0),A),B))). [back_rewrite(227150),rewrite([229349(5)])]. 162.21/162.45 230016 implies(implies(A,c_0),and(and(B,not(B)),not(A))) = not(equiv(A,and(B,not(B)))). [para(228590(a,1),256(a,1,1))]. 162.21/162.45 230046 implies(and(A,not(A)),c_0) = not(c_0). [para(228590(a,1),227265(a,1))]. 162.21/162.45 230049 equiv(and(A,not(A)),c_0) = not(c_0). [para(230046(a,1),89(a,1,1)),rewrite([228590(6),227265(5),228911(5)]),flip(a)]. 162.21/162.45 230075 and(A,not(A)) = c_0. [para(230049(a,1),61(a,1)),flip(b),unit_del(a,167673)]. 162.21/162.45 230078 implies(implies(A,c_0),c_0) = not(equiv(A,c_0)). [back_rewrite(230016),rewrite([230075(4),229351(6),230075(6)])]. 162.21/162.45 230091 is_a_theorem(implies(A,not(equiv(implies(not(A),B),c_0)))). [back_rewrite(227157),rewrite([230078(6)])]. 162.21/162.45 230102 is_a_theorem(implies(implies(not(c_0),A),not(equiv(A,c_0)))). [back_rewrite(227125),rewrite([230078(7)])]. 162.21/162.45 230781 is_a_theorem(implies(implies(A,implies(B,c_0)),implies(not(equiv(B,c_0)),implies(A,c_0)))). [para(230078(a,1),95(a,1,2,1))]. 162.21/162.45 230909 is_a_theorem(implies(A,implies(not(equiv(not(A),c_0)),implies(B,c_0)))). [para(230078(a,1),62196(a,1,2,1))]. 162.21/162.45 231434 -is_a_theorem(implies(not(c_0),A)) | is_a_theorem(not(equiv(A,c_0))). [resolve(230102,a,70,b)]. 162.21/162.45 231920 is_a_theorem(not(equiv(implies(A,implies(B,implies(not(A),C))),c_0))). [resolve(231434,a,66955,a)]. 162.21/162.45 231941 is_a_theorem(not(equiv(implies(implies(implies(not(not(A)),B),A),A),c_0))). [resolve(231434,a,14832,a)]. 162.21/162.45 231989 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(c_0),implies(A,B))). [resolve(228589,a,70,b)]. 162.21/162.45 232291 is_a_theorem(implies(not(c_0),implies(equiv(A,c_0),implies(implies(not(c_0),A),B)))). [resolve(231989,a,229449,a)]. 162.21/162.45 235876 is_a_theorem(implies(A,implies(not(equiv(not(A),c_0)),c_0))). [para(227056(a,1),230909(a,1,2,2))]. 162.21/162.45 235929 -is_a_theorem(A) | is_a_theorem(implies(not(equiv(not(A),c_0)),c_0)). [resolve(235876,a,70,b)]. 162.21/162.45 238337 is_a_theorem(implies(and(implies(not(c_0),A),not(A)),B)). [resolve(229341,a,211130,a)]. 162.21/162.45 238346 is_a_theorem(implies(not(equiv(c_0,not(implies(implies(not(c_0),A),A)))),B)). [resolve(238337,a,197923,a),rewrite([79(7)])]. 162.21/162.45 238416 is_a_theorem(implies(and(A,not(implies(not(A),B))),C)). [resolve(229345,a,211130,a)]. 162.21/162.45 238425 is_a_theorem(implies(not(equiv(c_0,not(implies(A,implies(not(A),B))))),C)). [resolve(238416,a,197923,a),rewrite([79(6)])]. 162.21/162.45 238472 is_a_theorem(implies(and(implies(not(A),A),not(A)),B)). [resolve(229346,a,211130,a)]. 162.21/162.45 238479 is_a_theorem(implies(implies(not(c_0),and(implies(not(A),A),not(A))),B)). [resolve(238472,a,214983,a)]. 162.21/162.45 239313 is_a_theorem(equiv(c_0,not(implies(implies(not(c_0),A),A)))). [resolve(238346,a,56034,a)]. 162.21/162.45 239328 not(implies(implies(not(c_0),A),A)) = c_0. [resolve(239313,a,61,a)]. 162.21/162.45 239330 implies(A,implies(implies(not(c_0),B),B)) = not(c_0). [para(239328(a,1),79(a,1,1,2)),rewrite([223900(2)]),flip(a)]. 162.21/162.45 239343 equiv(implies(implies(not(c_0),A),A),not(c_0)) = not(c_0). [para(239330(a,1),224021(a,1,2)),rewrite([228911(5)]),flip(a)]. 162.21/162.45 239353 implies(implies(not(c_0),A),A) = not(c_0). [para(239343(a,1),61(a,1)),flip(b),unit_del(a,167673)]. 162.21/162.45 239356 and(implies(A,implies(not(c_0),A)),not(c_0)) = equiv(A,implies(not(c_0),A)). [para(239353(a,1),89(a,1,2))]. 162.21/162.45 239443 is_a_theorem(equiv(c_0,not(implies(A,implies(not(A),B))))). [resolve(238425,a,56034,a)]. 162.21/162.45 239450 not(implies(A,implies(not(A),B))) = c_0. [resolve(239443,a,61,a)]. 162.21/162.45 239452 implies(A,implies(B,implies(not(B),C))) = not(c_0). [para(239450(a,1),79(a,1,1,2)),rewrite([223900(2)]),flip(a)]. 162.21/162.45 239517 equiv(implies(A,implies(not(A),B)),not(c_0)) = not(c_0). [para(239452(a,1),224021(a,1,2)),rewrite([228911(5)]),flip(a)]. 162.21/162.45 239523 implies(A,implies(not(A),B)) = not(c_0). [para(239517(a,1),61(a,1)),flip(b),unit_del(a,167673)]. 162.21/162.45 239527 and(not(c_0),implies(implies(not(A),B),A)) = equiv(A,implies(not(A),B)). [para(239523(a,1),89(a,1,1))]. 162.21/162.45 239528 and(implies(implies(not(A),B),A),not(c_0)) = equiv(implies(not(A),B),A). [para(239523(a,1),89(a,1,2))]. 162.21/162.45 239646 is_a_theorem(equiv(A,implies(not(A),A))). [resolve(238479,a,129,a),rewrite([79(7),239527(6)])]. 162.21/162.45 239699 implies(not(A),A) = A. [resolve(239646,a,61,a)]. 162.21/162.45 239707 implies(implies(A,B),and(A,not(B))) = and(A,not(B)). [para(79(a,1),239699(a,1,1))]. 162.21/162.45 239712 implies(A,and(not(B),not(B))) = not(and(A,B)). [para(239699(a,1),123(a,1,1,2)),flip(a)]. 162.21/162.45 239844 is_a_theorem(implies(A,implies(implies(A,B),implies(C,B)))). [para(239699(a,1),62196(a,1,2,1,1))]. 162.21/162.45 239936 is_a_theorem(implies(A,not(equiv(A,c_0)))). [para(239699(a,1),230091(a,1,2,1,1))]. 162.21/162.45 239938 is_a_theorem(implies(implies(not(A),c_0),implies(not(c_0),A))). [para(239699(a,1),229350(a,1,2,2))]. 162.21/162.45 239942 is_a_theorem(not(equiv(implies(A,implies(B,A)),c_0))). [para(239699(a,1),231920(a,1,1,1,2,2))]. 162.21/162.45 239979 is_a_theorem(implies(and(A,not(c_0)),equiv(not(A),c_0))). [para(239699(a,1),229393(a,1,2))]. 162.21/162.45 240944 -is_a_theorem(A) | is_a_theorem(not(equiv(A,c_0))). [resolve(239936,a,70,b)]. 162.21/162.45 241012 is_a_theorem(not(equiv(implies(A,not(equiv(A,c_0))),c_0))). [resolve(240944,a,239936,a)]. 162.21/162.45 242931 is_a_theorem(implies(A,implies(implies(A,B),B))). [para(239699(a,1),239844(a,1,2,2))]. 162.21/162.45 243593 is_a_theorem(not(equiv(implies(implies(not(A),c_0),implies(not(c_0),A)),c_0))). [resolve(239938,a,240944,a)]. 162.21/162.45 243669 is_a_theorem(implies(not(equiv(A,c_0)),not(equiv(c_0,A)))). [para(229352(a,1),239938(a,1,2)),rewrite([79(4),230078(4)])]. 162.21/162.45 243724 -is_a_theorem(and(A,not(c_0))) | is_a_theorem(equiv(not(A),c_0)). [resolve(239979,a,70,b)]. 162.21/162.45 244505 -is_a_theorem(not(equiv(A,c_0))) | is_a_theorem(not(equiv(c_0,A))). [resolve(243669,a,70,b)]. 162.21/162.45 244699 is_a_theorem(not(equiv(c_0,implies(A,not(equiv(A,c_0)))))). [resolve(244505,a,241012,a)]. 162.21/162.45 244700 is_a_theorem(not(equiv(c_0,implies(A,implies(B,A))))). [resolve(244505,a,239942,a)]. 162.21/162.45 244711 is_a_theorem(not(equiv(c_0,implies(implies(implies(not(not(A)),B),A),A)))). [resolve(244505,a,231941,a)]. 162.21/162.45 244750 is_a_theorem(and(implies(A,implies(B,A)),not(c_0))). [resolve(244700,a,117165,a)]. 162.21/162.45 244766 is_a_theorem(equiv(not(implies(A,implies(B,A))),c_0)). [resolve(244750,a,243724,a)]. 162.21/162.45 244820 not(implies(A,implies(B,A))) = c_0. [resolve(244766,a,61,a),flip(a)]. 162.21/162.45 244822 implies(A,implies(B,implies(C,B))) = not(c_0). [para(244820(a,1),79(a,1,1,2)),rewrite([223900(2)]),flip(a)]. 162.21/162.45 244824 implies(A,implies(B,A)) = not(c_0). [para(244820(a,1),239699(a,1,1)),rewrite([244822(4)]),flip(a)]. 162.21/162.45 244831 equiv(A,implies(not(c_0),A)) = not(c_0). [back_rewrite(239356),rewrite([244824(4),228911(5)]),flip(a)]. 162.21/162.45 244859 and(implies(implies(A,B),B),not(c_0)) = equiv(implies(A,B),B). [para(244824(a,1),89(a,1,2))]. 162.21/162.45 244917 implies(not(c_0),A) = A. [para(244831(a,1),61(a,1)),unit_del(a,167673)]. 162.21/162.45 244965 is_a_theorem(not(equiv(implies(implies(not(A),c_0),A),c_0))). [back_rewrite(243593),rewrite([244917(6)])]. 162.21/162.45 245062 is_a_theorem(implies(equiv(A,c_0),implies(A,B))). [back_rewrite(232291),rewrite([244917(7),244917(7)])]. 162.21/162.45 245112 not(equiv(c_0,A)) = and(A,not(c_0)). [back_rewrite(229352),rewrite([244917(6)]),flip(a)]. 162.21/162.45 245121 equiv(not(c_0),A) = and(A,not(c_0)). [back_rewrite(224022),rewrite([244917(3)]),flip(a)]. 162.21/162.45 245128 is_a_theorem(equiv(implies(implies(not(not(A)),B),A),A)). [back_rewrite(244711),rewrite([245112(8),244859(8)])]. 162.21/162.45 245133 is_a_theorem(and(implies(A,not(equiv(A,c_0))),not(c_0))). [back_rewrite(244699),rewrite([245112(7)])]. 162.21/162.45 245137 -is_a_theorem(not(equiv(A,c_0))) | is_a_theorem(and(A,not(c_0))). [back_rewrite(244505),rewrite([245112(7)])]. 162.21/162.45 247159 is_a_theorem(implies(equiv(not(A),c_0),A)). [para(239699(a,1),245062(a,1,2))]. 162.21/162.45 247170 is_a_theorem(implies(not(equiv(not(implies(equiv(not(A),c_0),A)),c_0)),c_0)). [resolve(247159,a,235929,a)]. 162.21/162.45 248149 not(and(A,and(B,not(c_0)))) = implies(A,equiv(c_0,B)). [para(245112(a,1),79(a,1,1,2))]. 162.21/162.45 248468 implies(and(A,not(c_0)),equiv(c_0,A)) = equiv(c_0,A). [para(245112(a,1),239699(a,1,1))]. 162.21/162.45 248507 -is_a_theorem(and(A,not(c_0))) | not(c_0) = A. [para(245121(a,1),61(a,1)),flip(b)]. 162.21/162.45 249468 implies(implies(not(not(A)),B),A) = A. [resolve(245128,a,61,a),flip(a)]. 162.21/162.45 249561 is_a_theorem(implies(not(not(A)),A)). [para(249468(a,1),242931(a,1,2))]. 162.21/162.45 250052 is_a_theorem(implies(implies(A,c_0),equiv(c_0,A))). [para(245112(a,1),249561(a,1,1,1)),rewrite([79(4)])]. 162.21/162.45 250153 is_a_theorem(implies(A,equiv(c_0,not(A)))). [resolve(250052,a,243,a)]. 162.21/162.45 250263 -is_a_theorem(A) | is_a_theorem(equiv(c_0,not(A))). [resolve(250153,a,70,b)]. 162.21/162.45 250307 is_a_theorem(equiv(c_0,not(implies(not(not(A)),A)))). [resolve(250263,a,249561,a)]. 162.21/162.45 250797 not(implies(not(not(A)),A)) = c_0. [resolve(250307,a,61,a)]. 162.21/162.45 250832 implies(A,implies(not(not(B)),B)) = not(c_0). [para(250797(a,1),79(a,1,1,2)),rewrite([223900(2)]),flip(a)]. 162.21/162.45 250839 implies(not(not(A)),A) = not(c_0). [para(250797(a,1),239699(a,1,1)),rewrite([250832(5)]),flip(a)]. 162.21/162.45 250884 is_a_theorem(implies(not(not(A)),implies(B,A))). [para(250839(a,1),239844(a,1,2,1)),rewrite([244917(6)])]. 162.21/162.45 250914 is_a_theorem(implies(and(not(not(not(not(A)))),not(B)),implies(C,A))). [resolve(250884,a,25058,a)]. 162.21/162.45 251190 implies(A,not(equiv(A,c_0))) = not(c_0). [resolve(245133,a,248507,a),flip(a)]. 162.21/162.45 251218 and(implies(not(equiv(A,c_0)),A),not(c_0)) = equiv(not(equiv(A,c_0)),A). [para(251190(a,1),89(a,1,2))]. 162.21/162.45 251555 is_a_theorem(equiv(implies(not(A),c_0),A)). [resolve(245137,a,244965,a),rewrite([239528(7)])]. 162.21/162.45 251620 implies(not(A),c_0) = A. [resolve(251555,a,61,a),flip(a)]. 162.21/162.45 251675 is_a_theorem(equiv(not(implies(equiv(not(A),c_0),A)),c_0)). [back_rewrite(247170),rewrite([251620(10)])]. 162.21/162.45 251794 implies(implies(A,B),c_0) = and(A,not(B)). [para(79(a,1),251620(a,1,1))]. 162.21/162.45 251795 equiv(not(A),c_0) = and(A,not(c_0)). [para(251620(a,1),89(a,1,1)),rewrite([229082(3)]),flip(a)]. 162.21/162.45 251799 implies(A,and(not(B),not(c_0))) = not(and(A,B)). [para(251620(a,1),123(a,1,1,2)),flip(a)]. 162.21/162.45 251816 is_a_theorem(implies(and(A,not(implies(B,c_0))),implies(implies(B,not(A)),C))). [para(251620(a,1),23137(a,1,1,1))]. 162.21/162.45 251818 is_a_theorem(implies(and(A,not(implies(B,c_0))),not(equiv(B,not(A))))). [para(251620(a,1),55696(a,1,1,1))]. 162.21/162.45 251851 implies(and(A,not(c_0)),c_0) = equiv(c_0,A). [para(245112(a,1),251620(a,1,1))]. 162.21/162.45 252064 not(equiv(A,c_0)) = and(A,not(c_0)). [back_rewrite(230078),rewrite([251794(4)]),flip(a)]. 162.21/162.45 252157 is_a_theorem(and(implies(and(A,not(c_0)),A),not(c_0))). [back_rewrite(251675),rewrite([251795(3),251795(7)])]. 162.21/162.45 253411 and(implies(and(A,not(c_0)),A),not(c_0)) = equiv(and(A,not(c_0)),A). [back_rewrite(251218),rewrite([252064(3),252064(10)])]. 162.21/162.45 253836 is_a_theorem(implies(implies(A,implies(B,c_0)),implies(and(B,not(c_0)),implies(A,c_0)))). [back_rewrite(230781),rewrite([252064(6)])]. 162.21/162.45 253852 is_a_theorem(equiv(and(A,not(c_0)),A)). [back_rewrite(252157),rewrite([253411(7)])]. 162.21/162.45 254914 and(A,not(c_0)) = A. [resolve(253852,a,61,a),flip(a)]. 162.21/162.45 254927 is_a_theorem(implies(implies(A,implies(B,c_0)),implies(B,implies(A,c_0)))). [back_rewrite(253836),rewrite([254914(6)])]. 162.21/162.45 255055 equiv(c_0,A) = implies(A,c_0). [back_rewrite(251851),rewrite([254914(3)]),flip(a)]. 162.21/162.45 255067 not(and(A,B)) = implies(A,not(B)). [back_rewrite(251799),rewrite([254914(4)]),flip(a)]. 162.21/162.45 255087 -is_a_theorem(A) | not(c_0) = A. [back_rewrite(248507),rewrite([254914(3)])]. 162.21/162.45 255107 implies(A,implies(A,c_0)) = implies(A,c_0). [back_rewrite(248468),rewrite([254914(3),255055(2),255055(5)])]. 162.21/162.45 255292 implies(A,implies(B,c_0)) = implies(A,not(B)). [back_rewrite(248149),rewrite([254914(3),255067(2),255055(4)]),flip(a)]. 162.21/162.45 255368 equiv(not(c_0),A) = A. [back_rewrite(245121),rewrite([254914(6)])]. 162.21/162.45 255369 not(implies(A,c_0)) = A. [back_rewrite(245112),rewrite([255055(2),254914(6)])]. 162.21/162.45 255680 implies(A,and(not(B),not(B))) = implies(A,not(B)). [back_rewrite(239712),rewrite([255067(6)])]. 162.21/162.45 255681 implies(A,not(implies(B,C))) = implies(A,and(B,not(C))). [back_rewrite(123),rewrite([255067(3)])]. 162.21/162.45 255706 implies(A,not(A)) = implies(A,c_0). [back_rewrite(255107),rewrite([255292(3)])]. 162.21/162.45 255715 is_a_theorem(implies(implies(A,not(B)),implies(B,not(A)))). [back_rewrite(254927),rewrite([255292(3),255292(5)])]. 162.21/162.45 255763 is_a_theorem(implies(and(A,B),not(equiv(B,not(A))))). [back_rewrite(251818),rewrite([255369(3)])]. 162.21/162.45 255764 is_a_theorem(implies(and(A,B),implies(implies(B,not(A)),C))). [back_rewrite(251816),rewrite([255369(3)])]. 162.21/162.45 256196 -is_a_theorem(implies(not(implies(implies(c53,c52),equiv(c52,c53))),and(c52,not(c53)))). [back_rewrite(15014),rewrite([255681(13)])]. 162.21/162.45 257877 implies(A,implies(implies(A,B),B)) = not(c_0). [resolve(255087,a,242931,a),flip(a)]. 162.21/162.45 258021 implies(A,c_0) = not(A). [para(255368(a,1),256(a,2,1)),rewrite([244917(3),167668(3),223900(2)])]. 162.21/162.45 258032 implies(A,not(A)) = not(A). [back_rewrite(255706),rewrite([258021(4)])]. 162.21/162.45 258083 not(not(A)) = A. [back_rewrite(255369),rewrite([258021(2)])]. 162.21/162.45 258213 not(implies(A,B)) = and(A,not(B)). [back_rewrite(251794),rewrite([258021(3)])]. 162.21/162.45 258316 is_a_theorem(implies(and(A,not(B)),implies(C,A))). [back_rewrite(250914),rewrite([258083(2),258083(2)])]. 162.21/162.45 258642 -is_a_theorem(implies(and(implies(c53,c52),not(equiv(c52,c53))),and(c52,not(c53)))). [back_rewrite(256196),rewrite([258213(8)])]. 162.21/162.45 259281 and(not(A),not(A)) = not(A). [para(239699(a,1),239707(a,1,1)),rewrite([255680(4),258032(2)]),flip(a)]. 162.21/162.45 259305 and(A,A) = A. [para(258083(a,1),259281(a,1,1)),rewrite([258083(2),258083(3)])]. 162.21/162.45 259385 is_a_theorem(implies(and(A,B),implies(C,A))). [para(258083(a,1),258316(a,1,1,2))]. 162.21/162.45 259419 implies(and(A,B),implies(C,A)) = not(c_0). [resolve(259385,a,255087,a),flip(a)]. 162.21/162.45 260497 is_a_theorem(implies(implies(A,B),implies(not(B),not(A)))). [para(258083(a,1),255715(a,1,1,2))]. 162.21/162.45 260539 is_a_theorem(implies(equiv(A,B),not(equiv(implies(B,A),and(A,not(B)))))). [para(89(a,1),255763(a,1,1)),rewrite([258213(4)])]. 162.21/162.45 261395 equiv(implies(A,B),and(B,C)) = implies(implies(A,B),and(B,C)). [para(259419(a,1),89(a,1,2)),rewrite([254914(6)]),flip(a)]. 162.21/162.45 261400 is_a_theorem(implies(equiv(A,B),equiv(B,A))). [back_rewrite(260539),rewrite([261395(5),256(5),258083(4)])]. 162.21/162.45 261405 implies(equiv(A,B),equiv(B,A)) = not(c_0). [resolve(261400,a,255087,a),flip(a)]. 162.21/162.45 262186 is_a_theorem(implies(and(implies(A,B),not(B)),not(A))). [para(257877(a,1),260497(a,1,1)),rewrite([258213(5),244917(8)])]. 162.21/162.45 262937 equiv(equiv(A,B),equiv(B,A)) = not(c_0). [para(261405(a,1),89(a,1,1)),rewrite([261405(5),259305(5)]),flip(a)]. 162.21/162.45 263527 is_a_theorem(implies(and(not(equiv(A,B)),implies(B,A)),and(A,not(B)))). [para(256(a,1),262186(a,1,1,1)),rewrite([255067(5),258083(4),258213(6)])]. 162.21/162.45 265492 equiv(A,B) = equiv(B,A). [para(262937(a,1),61(a,1)),unit_del(a,167673)]. 162.21/162.45 268231 is_a_theorem(implies(and(A,B),and(B,A))). [para(258021(a,1),255764(a,1,2)),rewrite([258213(4),258083(3)])]. 162.21/162.45 268242 implies(and(A,B),and(B,A)) = not(c_0). [resolve(268231,a,255087,a),flip(a)]. 162.21/162.45 268620 equiv(and(A,B),and(B,A)) = not(c_0). [para(268242(a,1),89(a,1,1)),rewrite([268242(5),259305(5),265492(5)]),flip(a)]. 162.21/162.45 268943 and(A,B) = and(B,A). [para(268620(a,1),61(a,1)),unit_del(a,167673)]. 162.21/162.45 269528 is_a_theorem(implies(and(implies(A,B),not(equiv(B,A))),and(B,not(A)))). [back_rewrite(263527),rewrite([268943(4)])]. 162.21/162.45 269529 $F. [resolve(269528,a,258642,a)]. 162.21/162.45 162.21/162.45 % SZS output end Refutation 162.21/162.45 ============================== end of proof ========================== 162.21/162.45 162.21/162.45 ============================== STATISTICS ============================ 162.21/162.45 162.21/162.45 Given=9263. Generated=12963639. Kept=269479. proofs=1. 162.21/162.45 Usable=563. Sos=4791. Demods=523. Limbo=585, Disabled=263611. Hints=0. 162.21/162.45 Megabytes=184.47. 162.21/162.45 User_CPU=155.66, System_CPU=6.32, Wall_clock=162. 162.21/162.45 162.21/162.45 ============================== end of statistics ===================== 162.21/162.45 162.21/162.45 ============================== end of search ========================= 162.21/162.46 162.21/162.46 THEOREM PROVED 162.21/162.46 % SZS status Theorem 162.21/162.46 162.21/162.46 Exiting with 1 proof. 162.21/162.46 162.21/162.46 Process 20045 exit (max_proofs) Sat Jul 14 06:22:09 2018 162.21/162.46 Prover9 interrupted 162.21/162.46 EOF