0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : tptp2X_and_run_prover9 %d %s 0.02/0.23 % Computer : n004.star.cs.uiowa.edu 0.02/0.23 % Model : x86_64 x86_64 0.02/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.02/0.23 % Memory : 32218.625MB 0.02/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.02/0.23 % CPULimit : 300 0.02/0.23 % DateTime : Sat Jul 14 06:08:54 CDT 2018 0.02/0.23 % CPUTime : 0.07/0.45 ============================== Prover9 =============================== 0.07/0.45 Prover9 (32) version 2009-11A, November 2009. 0.07/0.45 Process 29902 was started by sandbox2 on n004.star.cs.uiowa.edu, 0.07/0.45 Sat Jul 14 06:08:55 2018 0.07/0.45 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_29870_n004.star.cs.uiowa.edu". 0.07/0.45 ============================== end of head =========================== 0.07/0.45 0.07/0.45 ============================== INPUT ================================= 0.07/0.45 0.07/0.45 % Reading from file /tmp/Prover9_29870_n004.star.cs.uiowa.edu 0.07/0.45 0.07/0.45 set(prolog_style_variables). 0.07/0.45 set(auto2). 0.07/0.45 % set(auto2) -> set(auto). 0.07/0.45 % set(auto) -> set(auto_inference). 0.07/0.45 % set(auto) -> set(auto_setup). 0.07/0.45 % set(auto_setup) -> set(predicate_elim). 0.07/0.45 % set(auto_setup) -> assign(eq_defs, unfold). 0.07/0.45 % set(auto) -> set(auto_limits). 0.07/0.45 % set(auto_limits) -> assign(max_weight, "100.000"). 0.07/0.45 % set(auto_limits) -> assign(sos_limit, 20000). 0.07/0.45 % set(auto) -> set(auto_denials). 0.07/0.45 % set(auto) -> set(auto_process). 0.07/0.45 % set(auto2) -> assign(new_constants, 1). 0.07/0.45 % set(auto2) -> assign(fold_denial_max, 3). 0.07/0.45 % set(auto2) -> assign(max_weight, "200.000"). 0.07/0.45 % set(auto2) -> assign(max_hours, 1). 0.07/0.45 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.07/0.45 % set(auto2) -> assign(max_seconds, 0). 0.07/0.45 % set(auto2) -> assign(max_minutes, 5). 0.07/0.45 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.07/0.45 % set(auto2) -> set(sort_initial_sos). 0.07/0.45 % set(auto2) -> assign(sos_limit, -1). 0.07/0.45 % set(auto2) -> assign(lrs_ticks, 3000). 0.07/0.45 % set(auto2) -> assign(max_megs, 400). 0.07/0.45 % set(auto2) -> assign(stats, some). 0.07/0.45 % set(auto2) -> clear(echo_input). 0.07/0.45 % set(auto2) -> set(quiet). 0.07/0.45 % set(auto2) -> clear(print_initial_clauses). 0.07/0.45 % set(auto2) -> clear(print_given). 0.07/0.45 assign(lrs_ticks,-1). 0.07/0.45 assign(sos_limit,10000). 0.07/0.45 assign(order,kbo). 0.07/0.45 set(lex_order_vars). 0.07/0.45 clear(print_given). 0.07/0.45 0.07/0.45 % formulas(sos). % not echoed (45 formulas) 0.07/0.45 0.07/0.45 ============================== end of input ========================== 0.07/0.45 0.07/0.45 % From the command line: assign(max_seconds, 300). 0.07/0.45 0.07/0.45 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.07/0.45 0.07/0.45 % Formulas that are not ordinary clauses: 0.07/0.45 1 (all X all Y is_a_theorem(implies(and(X,Y),Y))) <-> and_2 # label(and_2) # label(axiom) # label(non_clause). [assumption]. 0.07/0.45 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]. 0.07/0.45 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]. 0.07/0.45 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]. 0.07/0.45 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]. 0.07/0.45 6 (all P is_a_theorem(implies(P,and(P,P)))) <-> kn1 # label(kn1) # label(axiom) # label(non_clause). [assumption]. 0.07/0.45 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]. 0.07/0.45 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]. 0.07/0.45 9 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption]. 0.07/0.45 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption]. 0.07/0.45 11 (all X all Y is_a_theorem(implies(Y,or(X,Y)))) <-> or_2 # label(or_2) # label(axiom) # label(non_clause). [assumption]. 0.07/0.45 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]. 0.07/0.45 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]. 0.07/0.45 14 (all P is_a_theorem(implies(or(P,P),P))) <-> r1 # label(r1) # label(axiom) # label(non_clause). [assumption]. 1.19/1.41 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]. 1.19/1.41 16 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption]. 1.19/1.41 17 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption]. 1.19/1.41 18 (all P is_a_theorem(implies(implies(not(P),P),P))) <-> cn3 # label(cn3) # label(axiom) # label(non_clause). [assumption]. 1.19/1.41 19 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption]. 1.19/1.41 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]. 1.19/1.41 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]. 1.19/1.41 22 (all X all Y is_a_theorem(implies(X,implies(Y,X)))) <-> implies_1 # label(implies_1) # label(axiom) # label(non_clause). [assumption]. 1.19/1.41 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]. 1.19/1.41 24 (all P all Q is_a_theorem(implies(and(P,Q),P))) <-> kn2 # label(kn2) # label(axiom) # label(non_clause). [assumption]. 1.19/1.41 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]. 1.19/1.41 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]. 1.19/1.41 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]. 1.19/1.41 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]. 1.19/1.41 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]. 1.19/1.41 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]. 1.19/1.41 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]. 1.19/1.41 1.19/1.41 ============================== end of process non-clausal formulas === 1.19/1.41 1.19/1.41 ============================== PROCESS INITIAL CLAUSES =============== 1.19/1.41 1.19/1.41 ============================== PREDICATE ELIMINATION ================= 1.19/1.41 1.19/1.41 ============================== end predicate elimination ============= 1.19/1.41 1.19/1.41 Auto_denials: (non-Horn, no changes). 1.19/1.41 1.19/1.41 Term ordering decisions: 1.19/1.41 1.19/1.41 % Assigning unary symbol not kb_weight 0 and highest precedence (93). 1.19/1.41 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. 1.19/1.41 1.19/1.41 ============================== end of process initial clauses ======== 1.19/1.41 1.19/1.41 ============================== CLAUSES FOR SEARCH ==================== 1.19/1.41 1.19/1.41 ============================== end of clauses for search ============= 1.19/1.41 1.19/1.41 ============================== SEARCH ================================ 1.19/1.41 1.19/1.41 % Starting search at 0.01 seconds. 1.19/1.41 1.19/1.41 Low Water (keep): wt=33.000, iters=3457 1.19/1.41 1.19/1.41 Low Water (keep): wt=31.000, iters=3412 1.19/1.41 1.19/1.41 Low Water (keep): wt=25.000, iters=3353 1.19/1.41 1.19/1.41 Low Water (keep): wt=22.000, iters=3370 1.19/1.41 1.19/1.41 Low Water (keep): wt=21.000, iters=3405 1.19/1.41 1.19/1.41 Low Water (keep): wt=20.000, iters=3360 1.19/1.41 1.19/1.41 Low Water (keep): wt=19.000, iters=3344 1.19/1.41 1.19/1.41 Low Water (keep): wt=18.000, iters=3342 1.19/1.41 1.19/1.41 Low Water (keep): wt=17.000, iters=3372 1.19/1.41 1.19/1.41 Low Water (keep): wt=16.000, iters=3339 218.54/218.75 218.54/218.75 Low Water (keep): wt=15.000, iters=3363 218.54/218.75 218.54/218.75 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 23 (0.00 of 1.25 sec). 218.54/218.75 218.54/218.75 Low Water (keep): wt=14.000, iters=3344 218.54/218.75 218.54/218.75 Low Water (displace): id=14476, wt=60.000 218.54/218.75 218.54/218.75 Low Water (displace): id=14484, wt=57.000 218.54/218.75 218.54/218.75 Low Water (displace): id=14486, wt=54.000 218.54/218.75 218.54/218.75 Low Water (displace): id=13827, wt=44.000 218.54/218.75 218.54/218.75 Low Water (displace): id=14496, wt=42.000 218.54/218.75 218.54/218.75 Low Water (displace): id=13833, wt=40.000 218.54/218.75 218.54/218.75 Low Water (displace): id=14478, wt=39.000 218.54/218.75 218.54/218.75 Low Water (displace): id=11871, wt=38.000 218.54/218.75 218.54/218.75 Low Water (displace): id=14497, wt=36.000 218.54/218.75 218.54/218.75 Low Water (displace): id=11446, wt=34.000 218.54/218.75 218.54/218.75 Low Water (displace): id=14474, wt=33.000 218.54/218.75 218.54/218.75 Low Water (displace): id=15117, wt=13.000 218.54/218.75 218.54/218.75 Low Water (displace): id=16667, wt=12.000 218.54/218.75 218.54/218.75 Low Water (keep): wt=13.000, iters=3352 218.54/218.75 218.54/218.75 Low Water (displace): id=17277, wt=9.000 218.54/218.75 218.54/218.75 Low Water (displace): id=21206, wt=8.000 218.54/218.75 218.54/218.75 Low Water (keep): wt=12.000, iters=3470 218.54/218.75 218.54/218.75 Low Water (keep): wt=11.000, iters=3357 218.54/218.75 218.54/218.75 Low Water (keep): wt=10.000, iters=3538 218.54/218.75 218.54/218.75 ============================== PROOF ================================= 218.54/218.75 % SZS status Theorem 218.54/218.75 % SZS output start Refutation 218.54/218.75 218.54/218.75 % Proof 1 at 211.95 (+ 6.35) seconds. 218.54/218.75 % Length of proof is 535. 218.54/218.75 % Level of proof is 74. 218.54/218.75 % Maximum clause weight is 16.000. 218.54/218.75 % Given clauses 11237. 218.54/218.75 218.54/218.75 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]. 218.54/218.75 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]. 218.54/218.75 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]. 218.54/218.75 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]. 218.54/218.75 14 (all P is_a_theorem(implies(or(P,P),P))) <-> r1 # label(r1) # label(axiom) # label(non_clause). [assumption]. 218.54/218.75 16 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption]. 218.54/218.75 19 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption]. 218.54/218.75 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]. 218.54/218.75 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]. 218.54/218.75 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]. 218.54/218.75 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]. 218.54/218.75 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]. 218.54/218.75 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]. 218.54/218.75 32 r4 # label(principia_r4) # label(axiom). [assumption]. 218.54/218.75 33 op_equiv # label(principia_op_equiv) # label(axiom). [assumption]. 218.54/218.75 34 r2 # label(principia_r2) # label(axiom). [assumption]. 218.54/218.75 35 r1 # label(principia_r1) # label(axiom). [assumption]. 218.54/218.75 36 r3 # label(principia_r3) # label(axiom). [assumption]. 218.54/218.75 37 modus_ponens # label(principia_modus_ponens) # label(axiom). [assumption]. 218.54/218.75 38 r5 # label(principia_r5) # label(axiom). [assumption]. 218.54/218.75 39 op_implies_or # label(principia_op_implies_or) # label(axiom). [assumption]. 218.54/218.75 40 op_and # label(principia_op_and) # label(axiom). [assumption]. 218.54/218.75 41 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption]. 218.54/218.75 42 op_implies_and # label(hilbert_op_implies_and) # label(axiom). [assumption]. 218.54/218.75 43 op_or # label(hilbert_op_or) # label(axiom). [assumption]. 218.54/218.75 44 -or_3 # label(hilbert_or_3) # label(negated_conjecture). [assumption]. 218.54/218.75 53 is_a_theorem(implies(or(A,A),A)) | -r1 # label(r1) # label(axiom). [clausify(14)]. 218.54/218.75 54 is_a_theorem(implies(or(A,A),A)). [copy(53),unit_del(b,35)]. 218.54/218.75 55 -r2 | is_a_theorem(implies(A,or(B,A))) # label(r2) # label(axiom). [clausify(16)]. 218.54/218.75 56 is_a_theorem(implies(A,or(B,A))). [copy(55),unit_del(a,34)]. 218.54/218.75 64 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(3)]. 218.54/218.75 65 -is_a_theorem(equiv(A,B)) | B = A. [copy(64),unit_del(a,41)]. 218.54/218.75 72 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(12)]. 218.54/218.75 73 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(72),unit_del(a,37)]. 218.54/218.75 76 -r3 | is_a_theorem(implies(or(A,B),or(B,A))) # label(r3) # label(axiom). [clausify(19)]. 218.54/218.75 77 is_a_theorem(implies(or(A,B),or(B,A))). [copy(76),unit_del(a,36)]. 218.54/218.75 81 -op_implies_or | or(not(A),B) = implies(A,B) # label(op_implies_or) # label(axiom). [clausify(30)]. 218.54/218.75 82 or(not(A),B) = implies(A,B). [copy(81),unit_del(a,39)]. 218.54/218.75 83 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)]. 218.54/218.75 84 not(and(A,not(B))) = implies(A,B). [copy(83),unit_del(a,42)]. 218.54/218.75 89 -op_or | or(A,B) = not(and(not(A),not(B))) # label(op_or) # label(axiom). [clausify(27)]. 218.54/218.75 90 or(A,B) = implies(not(A),B). [copy(89),rewrite([84(6)]),unit_del(a,43)]. 218.54/218.75 91 -op_and | not(or(not(A),not(B))) = and(A,B) # label(op_and) # label(axiom). [clausify(28)]. 218.54/218.75 92 not(implies(not(not(A)),not(B))) = and(A,B). [copy(91),rewrite([90(4)]),unit_del(a,40)]. 218.54/218.75 93 -op_equiv | equiv(A,B) = and(implies(A,B),implies(B,A)) # label(op_equiv) # label(axiom). [clausify(31)]. 218.54/218.75 94 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(93),flip(b),unit_del(a,33)]. 218.54/218.75 95 -r5 | is_a_theorem(implies(implies(A,B),implies(or(C,A),or(C,B)))) # label(r5) # label(axiom). [clausify(5)]. 218.54/218.75 96 is_a_theorem(implies(implies(A,B),implies(implies(not(C),A),implies(not(C),B)))). [copy(95),rewrite([90(3),90(5)]),unit_del(a,38)]. 218.54/218.75 100 -r4 | is_a_theorem(implies(or(A,or(B,C)),or(B,or(A,C)))) # label(r4) # label(axiom). [clausify(8)]. 218.54/218.75 101 is_a_theorem(implies(implies(not(A),implies(not(B),C)),implies(not(B),implies(not(A),C)))). [copy(100),rewrite([90(2),90(4),90(6),90(8)]),unit_del(a,32)]. 218.54/218.75 110 or_3 | -is_a_theorem(implies(implies(c43,c45),implies(implies(c44,c45),implies(or(c43,c44),c45)))) # label(or_3) # label(axiom). [clausify(21)]. 218.54/218.75 111 -is_a_theorem(implies(implies(c43,c45),implies(implies(c44,c45),implies(implies(not(c43),c44),c45)))). [copy(110),rewrite([90(10)]),unit_del(a,44)]. 218.54/218.75 113 implies(not(not(A)),B) = implies(A,B). [back_rewrite(82),rewrite([90(2)])]. 218.54/218.75 114 is_a_theorem(implies(implies(not(A),B),implies(not(B),A))). [back_rewrite(77),rewrite([90(1),90(3)])]. 218.54/218.75 115 is_a_theorem(implies(A,implies(not(B),A))). [back_rewrite(56),rewrite([90(1)])]. 218.54/218.75 116 is_a_theorem(implies(implies(not(A),A),A)). [back_rewrite(54),rewrite([90(1)])]. 218.54/218.75 119 not(implies(A,not(B))) = and(A,B). [back_rewrite(92),rewrite([113(4)])]. 218.54/218.75 122 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(84(a,1),84(a,1,1,2))]. 218.54/218.75 123 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(C),A),implies(not(C),B))). [resolve(96,a,73,b)]. 218.54/218.75 125 -is_a_theorem(implies(not(A),implies(not(B),C))) | is_a_theorem(implies(not(B),implies(not(A),C))). [resolve(101,a,73,b)]. 218.54/218.75 131 implies(not(implies(A,B)),C) = implies(and(A,not(B)),C). [para(84(a,1),113(a,1,1,1))]. 218.54/218.75 133 and(implies(A,not(not(B))),implies(B,A)) = equiv(A,not(not(B))). [para(113(a,1),94(a,1,2))]. 218.54/218.75 135 is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))). [para(113(a,1),96(a,1,2,1)),rewrite([113(5)])]. 218.54/218.75 136 is_a_theorem(implies(implies(not(A),implies(B,C)),implies(B,implies(not(A),C)))). [para(113(a,1),101(a,1,1,2)),rewrite([113(8)])]. 218.54/218.75 138 -is_a_theorem(implies(not(A),B)) | is_a_theorem(implies(not(B),A)). [resolve(114,a,73,b)]. 218.54/218.75 140 is_a_theorem(implies(implies(implies(A,B),C),implies(not(C),and(A,not(B))))). [para(84(a,1),114(a,1,1,1))]. 218.54/218.75 142 is_a_theorem(implies(implies(A,B),implies(not(B),not(A)))). [para(113(a,1),114(a,1,1))]. 218.54/218.75 143 is_a_theorem(implies(implies(not(A),not(B)),implies(B,A))). [para(113(a,1),114(a,1,2))]. 218.54/218.75 148 is_a_theorem(implies(A,implies(B,A))). [para(113(a,1),115(a,1,2))]. 218.54/218.75 151 -is_a_theorem(implies(not(A),A)) | is_a_theorem(A). [resolve(116,a,73,b)]. 218.54/218.75 155 is_a_theorem(implies(implies(A,not(A)),not(A))). [para(113(a,1),116(a,1,1))]. 218.54/218.75 159 and(not(not(A)),B) = and(A,B). [para(113(a,1),119(a,1,1)),rewrite([119(3)]),flip(a)]. 218.54/218.75 167 implies(implies(A,B),and(B,not(A))) = not(equiv(A,B)). [para(94(a,1),122(a,1,1)),flip(a)]. 218.54/218.75 196 -is_a_theorem(A) | is_a_theorem(implies(B,A)). [resolve(148,a,73,b)]. 218.54/218.75 201 is_a_theorem(implies(A,implies(B,not(not(A))))). [para(113(a,1),148(a,1))]. 218.54/218.75 204 is_a_theorem(implies(A,implies(implies(not(B),C),implies(not(C),B)))). [resolve(196,a,114,a)]. 218.54/218.75 205 is_a_theorem(implies(implies(not(A),B),implies(not(A),implies(C,B)))). [resolve(123,a,148,a)]. 218.54/218.75 206 is_a_theorem(implies(implies(not(A),implies(not(B),B)),implies(not(A),B))). [resolve(123,a,116,a)]. 218.54/218.75 247 -is_a_theorem(A) | is_a_theorem(implies(B,not(not(A)))). [resolve(201,a,73,b)]. 218.54/218.75 270 is_a_theorem(implies(not(A),implies(not(B),not(B)))). [resolve(125,a,148,a)]. 218.54/218.75 273 -is_a_theorem(implies(not(A),implies(B,C))) | is_a_theorem(implies(B,implies(not(A),C))). [para(113(a,1),125(a,1,2)),rewrite([113(9)])]. 218.54/218.75 274 -is_a_theorem(implies(A,implies(not(B),C))) | is_a_theorem(implies(not(B),implies(A,C))). [para(113(a,1),125(a,1)),rewrite([113(8)])]. 218.54/218.75 391 is_a_theorem(implies(not(A),not(A))). [resolve(270,a,151,a)]. 218.54/218.75 413 is_a_theorem(implies(A,not(and(not(B),B)))). [resolve(391,a,247,a),rewrite([119(4)])]. 218.54/218.75 432 is_a_theorem(implies(A,not(not(A)))). [para(113(a,1),391(a,1))]. 218.54/218.75 434 is_a_theorem(implies(A,implies(B,B))). [resolve(432,a,247,a),rewrite([119(4),84(3)])]. 218.54/218.75 460 is_a_theorem(implies(A,A)). [resolve(434,a,151,a)]. 218.54/218.75 747 implies(and(A,not(not(B))),C) = implies(and(A,B),C). [para(119(a,1),131(a,1,1)),flip(a)]. 218.54/218.75 995 equiv(A,not(not(B))) = equiv(A,B). [para(133(a,1),159(a,2)),rewrite([119(4),84(3),94(3)]),flip(a)]. 218.54/218.75 1289 -is_a_theorem(equiv(A,B)) | not(not(B)) = A. [para(995(a,1),65(a,1))]. 218.54/218.75 1306 is_a_theorem(implies(and(not(A),A),B)). [resolve(138,a,413,a),rewrite([113(5)])]. 218.54/218.75 1309 is_a_theorem(implies(and(A,B),B)). [resolve(138,a,201,a),rewrite([119(5),747(4)])]. 218.54/218.75 1311 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(B),not(A))). [para(113(a,1),138(a,1))]. 218.54/218.75 1322 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(C,A),implies(C,B))). [resolve(135,a,73,b)]. 218.54/218.75 1567 is_a_theorem(implies(equiv(A,B),implies(B,A))). [para(94(a,1),1309(a,1,1))]. 218.54/218.75 1623 is_a_theorem(implies(implies(A,implies(B,C)),implies(B,implies(A,C)))). [para(113(a,1),136(a,1,1)),rewrite([113(5)])]. 218.54/218.75 2852 is_a_theorem(implies(implies(A,not(B)),implies(B,not(A)))). [para(113(a,1),142(a,1,2))]. 218.54/218.75 3153 -is_a_theorem(implies(not(A),not(B))) | is_a_theorem(implies(B,A)). [resolve(143,a,73,b)]. 218.54/218.75 6415 is_a_theorem(implies(A,and(A,A))). [resolve(1311,a,155,a),rewrite([119(5),113(4)])]. 218.54/218.75 6432 -is_a_theorem(A) | is_a_theorem(and(A,A)). [resolve(6415,a,73,b)]. 218.54/218.75 6565 is_a_theorem(equiv(A,A)). [resolve(6432,a,460,a),rewrite([94(3)])]. 218.54/218.75 6727 not(not(A)) = A. [resolve(6565,a,1289,a)]. 218.54/218.75 6728 is_a_theorem(implies(A,equiv(B,B))). [resolve(6565,a,247,a),rewrite([6727(3)])]. 218.54/218.75 6793 not(and(A,B)) = implies(A,not(B)). [para(6727(a,1),84(a,1,1,2))]. 218.54/218.75 6794 not(implies(A,B)) = and(A,not(B)). [para(84(a,1),6727(a,1,1))]. 218.54/218.75 6810 is_a_theorem(implies(not(equiv(A,A)),B)). [resolve(6728,a,138,a)]. 218.54/218.75 6941 is_a_theorem(implies(not(equiv(A,B)),not(equiv(B,A)))). [para(167(a,1),140(a,1,1)),rewrite([6793(5),6727(4),167(6)])]. 218.54/218.75 6945 implies(implies(not(A),B),and(B,A)) = not(equiv(not(A),B)). [para(6727(a,1),167(a,1,2,2))]. 218.54/218.75 8690 is_a_theorem(implies(and(A,B),and(B,A))). [resolve(2852,a,1311,a),rewrite([6794(3),6727(2),6794(4),6727(3)])]. 218.54/218.75 8692 -is_a_theorem(implies(A,not(B))) | is_a_theorem(implies(B,not(A))). [resolve(2852,a,73,b)]. 218.54/218.75 8865 is_a_theorem(implies(A,implies(and(B,C),and(C,B)))). [resolve(8690,a,196,a)]. 218.54/218.75 8946 is_a_theorem(implies(equiv(A,B),equiv(B,A))). [para(94(a,1),8690(a,1,1)),rewrite([94(4)])]. 218.54/218.75 8949 is_a_theorem(implies(A,implies(equiv(B,C),equiv(C,B)))). [resolve(8946,a,196,a)]. 218.54/218.75 10959 is_a_theorem(implies(implies(A,B),implies(A,implies(C,B)))). [para(6727(a,1),205(a,1,1,1)),rewrite([6727(3)])]. 218.54/218.75 10999 is_a_theorem(implies(and(A,and(B,not(C))),and(A,not(C)))). [resolve(10959,a,1311,a),rewrite([6794(3),6794(2),6794(5)])]. 218.54/218.75 11001 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(A,implies(C,B))). [resolve(10959,a,73,b)]. 218.54/218.75 11022 is_a_theorem(implies(and(A,B),implies(C,and(B,A)))). [resolve(11001,a,8690,a)]. 218.54/218.75 11027 is_a_theorem(implies(and(A,B),implies(C,B))). [resolve(11001,a,1309,a)]. 218.54/218.75 11101 is_a_theorem(implies(A,implies(and(B,C),implies(D,C)))). [resolve(11027,a,196,a)]. 218.54/218.75 11160 is_a_theorem(implies(implies(A,implies(not(B),B)),implies(A,B))). [para(6727(a,1),206(a,1,1,1)),rewrite([6727(5)])]. 218.54/218.75 12117 is_a_theorem(implies(and(not(A),B),not(equiv(A,B)))). [para(167(a,1),11022(a,1,2))]. 218.54/218.75 12869 is_a_theorem(implies(equiv(A,B),implies(not(A),not(B)))). [resolve(12117,a,8692,a),rewrite([6793(4)])]. 218.54/218.75 13337 is_a_theorem(implies(equiv(not(A),B),implies(A,not(B)))). [para(6727(a,1),12869(a,1,2,1))]. 218.54/218.75 13398 is_a_theorem(implies(equiv(not(A),not(B)),implies(A,B))). [para(6727(a,1),13337(a,1,2,2))]. 218.54/218.75 13796 -is_a_theorem(implies(A,implies(not(B),B))) | is_a_theorem(implies(A,B)). [resolve(11160,a,73,b)]. 218.54/218.75 14245 is_a_theorem(implies(implies(and(A,not(B)),B),implies(A,B))). [resolve(13796,a,10959,a),rewrite([6794(2)])]. 218.54/218.75 14294 -is_a_theorem(implies(A,implies(B,C))) | is_a_theorem(implies(B,implies(A,C))). [para(6727(a,1),273(a,1,1)),rewrite([6727(5)])]. 218.54/218.75 14558 is_a_theorem(implies(not(A),implies(equiv(A,not(B)),B))). [resolve(274,a,13398,a),rewrite([6727(3)])]. 218.54/218.75 14566 is_a_theorem(implies(not(A),implies(implies(not(A),B),implies(C,B)))). [resolve(274,a,10959,a)]. 218.54/218.75 14569 is_a_theorem(implies(not(A),implies(implies(B,A),not(B)))). [resolve(274,a,2852,a),rewrite([6727(3)])]. 218.54/218.75 14570 is_a_theorem(implies(not(A),implies(equiv(B,not(A)),B))). [resolve(274,a,1567,a)]. 218.54/218.75 14572 is_a_theorem(implies(not(A),implies(implies(not(A),B),B))). [resolve(274,a,460,a)]. 218.54/218.75 14579 is_a_theorem(implies(not(A),implies(implies(not(B),A),B))). [resolve(274,a,143,a),rewrite([6727(4)])]. 218.54/218.75 14727 -is_a_theorem(not(A)) | is_a_theorem(implies(equiv(A,not(B)),B)). [resolve(14558,a,73,b)]. 218.54/218.75 15092 is_a_theorem(implies(and(implies(A,B),A),B)). [resolve(14569,a,1311,a),rewrite([6794(4),6727(3),6727(4)])]. 218.54/218.75 15094 -is_a_theorem(not(A)) | is_a_theorem(implies(implies(B,A),not(B))). [resolve(14569,a,73,b)]. 218.54/218.75 15111 is_a_theorem(implies(A,implies(and(implies(B,C),B),C))). [resolve(15092,a,196,a)]. 218.54/218.75 15518 is_a_theorem(implies(A,implies(equiv(B,A),B))). [para(6727(a,1),14570(a,1,1)),rewrite([6727(2)])]. 218.54/218.75 15577 is_a_theorem(implies(and(equiv(A,B),not(A)),not(B))). [resolve(15518,a,1311,a),rewrite([6794(3)])]. 218.54/218.75 16620 is_a_theorem(implies(A,implies(implies(A,B),B))). [para(6727(a,1),14572(a,1,1)),rewrite([6727(2)])]. 218.54/218.75 16631 is_a_theorem(implies(and(implies(A,B),not(B)),not(A))). [resolve(16620,a,1311,a),rewrite([6794(3)])]. 218.54/218.75 16633 -is_a_theorem(A) | is_a_theorem(implies(implies(A,B),B)). [resolve(16620,a,73,b)]. 218.54/218.75 17123 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),C),C)). [resolve(16633,a,6810,a)]. 218.54/218.75 17131 is_a_theorem(implies(implies(implies(A,and(A,A)),B),B)). [resolve(16633,a,6415,a)]. 218.54/218.75 17157 is_a_theorem(implies(implies(implies(and(A,B),B),C),C)). [resolve(16633,a,1309,a)]. 218.54/218.75 17160 is_a_theorem(implies(implies(implies(and(not(A),A),B),C),C)). [resolve(16633,a,1306,a)]. 218.54/218.75 17185 is_a_theorem(implies(implies(implies(A,implies(B,A)),C),C)). [resolve(16633,a,148,a)]. 218.54/218.75 17968 -is_a_theorem(not(A)) | is_a_theorem(implies(implies(not(B),A),B)). [resolve(14579,a,73,b)]. 218.54/218.75 18290 -is_a_theorem(A) | is_a_theorem(implies(equiv(not(A),not(B)),B)). [para(6727(a,1),14727(a,1))]. 218.54/218.75 18455 -is_a_theorem(A) | is_a_theorem(implies(implies(B,not(A)),not(B))). [para(6727(a,1),15094(a,1))]. 218.54/218.75 19524 is_a_theorem(implies(and(implies(A,not(B)),B),not(A))). [para(6727(a,1),16631(a,1,1,2))]. 218.54/218.75 19628 -is_a_theorem(implies(implies(A,and(A,A)),B)) | is_a_theorem(B). [resolve(17131,a,73,b)]. 218.54/218.75 19658 -is_a_theorem(implies(implies(and(A,B),B),C)) | is_a_theorem(C). [resolve(17157,a,73,b)]. 218.54/218.75 19720 -is_a_theorem(implies(implies(A,implies(B,A)),C)) | is_a_theorem(C). [resolve(17185,a,73,b)]. 218.54/218.75 20480 -is_a_theorem(A) | is_a_theorem(implies(implies(not(B),not(A)),B)). [para(6727(a,1),17968(a,1))]. 218.54/218.75 24156 is_a_theorem(implies(implies(A,B),implies(A,and(B,B)))). [resolve(19628,a,135,a)]. 218.54/218.75 24268 is_a_theorem(implies(implies(A,and(B,C)),implies(A,C))). [resolve(19658,a,135,a)]. 218.54/218.75 27078 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(A,and(B,B))). [resolve(24156,a,73,b)]. 218.54/218.75 27407 is_a_theorem(implies(implies(not(A),and(B,A)),A)). [resolve(24268,a,13796,a)]. 218.54/218.75 27419 -is_a_theorem(implies(A,and(B,C))) | is_a_theorem(implies(A,C)). [resolve(24268,a,73,b)]. 218.54/218.75 27477 is_a_theorem(implies(A,and(A,implies(B,A)))). [resolve(27407,a,8692,a),rewrite([6727(2),6794(4),6793(3),6727(2)])]. 218.54/218.75 27524 is_a_theorem(implies(A,implies(B,and(B,implies(C,B))))). [resolve(27477,a,196,a)]. 218.54/218.75 30361 is_a_theorem(not(equiv(A,not(A)))). [resolve(27078,a,155,a),rewrite([167(6)])]. 218.54/218.75 30368 is_a_theorem(not(equiv(not(A),A))). [resolve(27078,a,116,a),rewrite([6945(4)])]. 218.54/218.75 30404 is_a_theorem(implies(A,not(equiv(B,not(B))))). [resolve(30361,a,196,a)]. 218.54/218.75 30469 is_a_theorem(implies(implies(not(A),equiv(not(B),B)),A)). [resolve(30368,a,20480,a),rewrite([6727(5)])]. 218.54/218.75 30476 is_a_theorem(implies(implies(A,equiv(not(B),B)),not(A))). [resolve(30368,a,18455,a),rewrite([6727(4)])]. 218.54/218.75 30481 is_a_theorem(implies(implies(not(equiv(not(A),A)),B),B)). [resolve(30368,a,16633,a)]. 218.54/218.75 30578 is_a_theorem(implies(equiv(A,not(A)),B)). [resolve(30404,a,3153,a)]. 218.54/218.75 30679 is_a_theorem(implies(equiv(not(A),A),B)). [para(6727(a,1),30578(a,1,1,2))]. 218.54/218.75 30708 is_a_theorem(implies(implies(implies(equiv(not(A),A),B),C),C)). [resolve(30679,a,16633,a)]. 218.54/218.75 31040 is_a_theorem(implies(and(A,B),A)). [resolve(27419,a,8690,a)]. 218.54/218.75 31127 is_a_theorem(implies(implies(implies(and(A,B),A),C),C)). [resolve(31040,a,16633,a)]. 218.54/218.75 31131 is_a_theorem(implies(and(implies(not(A),A),B),A)). [resolve(31040,a,13796,a)]. 218.54/218.75 31137 is_a_theorem(implies(A,implies(not(A),not(B)))). [resolve(31040,a,8692,a),rewrite([6793(3)])]. 218.54/218.75 31139 is_a_theorem(implies(not(A),implies(A,not(B)))). [resolve(31040,a,1311,a),rewrite([6793(3)])]. 218.54/218.75 31553 is_a_theorem(implies(equiv(A,B),implies(A,B))). [para(94(a,1),31040(a,1,1))]. 218.54/218.75 31923 is_a_theorem(implies(A,implies(not(A),B))). [para(6727(a,1),31137(a,1,2,2))]. 218.54/218.75 31959 is_a_theorem(implies(implies(implies(A,implies(not(A),B)),C),C)). [resolve(31923,a,16633,a)]. 218.54/218.75 31968 is_a_theorem(implies(A,implies(B,implies(not(A),C)))). [resolve(31923,a,11001,a)]. 218.54/218.75 32477 is_a_theorem(implies(not(A),implies(equiv(not(A),B),B))). [resolve(31553,a,274,a)]. 218.54/218.75 32740 is_a_theorem(implies(and(implies(not(A),A),B),and(A,A))). [resolve(31131,a,27078,a)]. 218.54/218.75 32831 is_a_theorem(implies(and(A,and(B,not(C))),B)). [resolve(31968,a,138,a),rewrite([6727(2),6794(3),6794(2)])]. 218.54/218.75 33343 is_a_theorem(implies(and(A,and(B,C)),B)). [para(6727(a,1),32831(a,1,1,2,2))]. 218.54/218.75 33382 is_a_theorem(implies(A,implies(and(B,and(C,D)),C))). [resolve(33343,a,196,a)]. 218.54/218.75 36173 is_a_theorem(implies(A,and(A,not(equiv(not(B),B))))). [resolve(30469,a,8692,a),rewrite([6727(2),6794(4)])]. 218.54/218.75 36335 -is_a_theorem(implies(A,equiv(not(B),B))) | is_a_theorem(not(A)). [resolve(30476,a,73,b)]. 218.54/218.75 37561 -is_a_theorem(implies(implies(and(A,B),A),C)) | is_a_theorem(C). [resolve(31127,a,73,b)]. 218.54/218.75 39381 is_a_theorem(implies(A,implies(equiv(A,B),B))). [para(6727(a,1),32477(a,1,1)),rewrite([6727(2)])]. 218.54/218.75 39434 is_a_theorem(implies(A,implies(B,implies(equiv(B,C),C)))). [resolve(39381,a,196,a)]. 218.54/218.75 42913 is_a_theorem(implies(implies(A,and(B,C)),implies(A,B))). [resolve(37561,a,135,a)]. 218.54/218.75 50233 -is_a_theorem(implies(A,and(B,C))) | is_a_theorem(implies(A,B)). [resolve(42913,a,73,b)]. 218.54/218.75 50300 is_a_theorem(implies(not(equiv(A,B)),implies(implies(A,B),B))). [para(167(a,1),42913(a,1,1))]. 218.54/218.75 57775 -is_a_theorem(implies(and(A,not(B)),B)) | is_a_theorem(implies(A,B)). [resolve(14245,a,73,b)]. 218.54/218.75 61607 -is_a_theorem(implies(implies(not(equiv(A,A)),B),C)) | is_a_theorem(C). [resolve(17123,a,73,b)]. 218.54/218.75 61683 -is_a_theorem(implies(implies(and(not(A),A),B),C)) | is_a_theorem(C). [resolve(17160,a,73,b)]. 218.54/218.75 67616 -is_a_theorem(implies(implies(equiv(not(A),A),B),C)) | is_a_theorem(C). [resolve(30708,a,73,b)]. 218.54/218.75 68595 is_a_theorem(implies(A,and(implies(B,implies(not(B),C)),A))). [resolve(31959,a,8692,a),rewrite([6794(6),6727(5)])]. 218.54/218.75 82988 is_a_theorem(implies(and(implies(A,B),not(B)),equiv(A,B))). [resolve(50300,a,1311,a),rewrite([6794(3),6727(6)])]. 218.54/218.75 82989 is_a_theorem(implies(implies(A,B),implies(not(equiv(A,B)),B))). [resolve(50300,a,273,a)]. 218.54/218.75 86081 is_a_theorem(implies(implies(not(A),A),and(A,A))). [resolve(57775,a,32740,a)]. 218.54/218.75 101646 is_a_theorem(implies(not(equiv(equiv(not(A),A),B)),B)). [resolve(82989,a,67616,a)]. 218.54/218.75 101653 is_a_theorem(implies(not(equiv(and(not(A),A),B)),B)). [resolve(82989,a,61683,a)]. 218.54/218.75 101654 is_a_theorem(implies(not(equiv(not(equiv(A,A)),B)),B)). [resolve(82989,a,61607,a)]. 218.54/218.75 101676 is_a_theorem(implies(not(equiv(and(A,B),A)),A)). [resolve(82989,a,37561,a)]. 218.54/218.75 101698 is_a_theorem(implies(not(equiv(A,implies(B,A))),implies(B,A))). [resolve(82989,a,19720,a)]. 218.54/218.75 101699 is_a_theorem(implies(not(equiv(and(A,B),B)),B)). [resolve(82989,a,19658,a)]. 218.54/218.75 101816 is_a_theorem(implies(not(A),equiv(and(A,B),A))). [resolve(101676,a,1311,a),rewrite([6727(5)])]. 218.54/218.75 101917 is_a_theorem(implies(not(A),equiv(and(B,A),A))). [resolve(101699,a,1311,a),rewrite([6727(5)])]. 218.54/218.75 102004 -is_a_theorem(not(A)) | is_a_theorem(equiv(and(A,B),A)). [resolve(101816,a,73,b)]. 218.54/218.75 102120 -is_a_theorem(not(A)) | is_a_theorem(equiv(and(B,A),A)). [resolve(101917,a,73,b)]. 218.54/218.75 102156 -is_a_theorem(A) | is_a_theorem(equiv(and(not(A),B),not(A))). [para(6727(a,1),102004(a,1))]. 218.54/218.75 102224 -is_a_theorem(A) | is_a_theorem(equiv(and(B,not(A)),not(A))). [para(6727(a,1),102120(a,1))]. 218.54/218.75 102267 is_a_theorem(equiv(equiv(not(A),A),equiv(not(B),B))). [resolve(101646,a,36335,a),rewrite([6727(7)])]. 218.54/218.75 102313 is_a_theorem(implies(A,equiv(equiv(not(B),B),not(A)))). [resolve(101646,a,8692,a),rewrite([6727(6)])]. 218.54/218.75 102714 is_a_theorem(equiv(and(not(A),A),equiv(not(B),B))). [resolve(101653,a,36335,a),rewrite([6727(7)])]. 218.54/218.75 102822 is_a_theorem(equiv(not(equiv(A,A)),equiv(not(B),B))). [resolve(101654,a,36335,a),rewrite([6727(7)])]. 218.54/218.75 103147 is_a_theorem(equiv(and(equiv(not(A),A),B),equiv(not(A),A))). [resolve(102156,a,86081,a),rewrite([6794(5),6793(4),94(5),6794(8),6793(7),94(8)])]. 218.54/218.75 104002 is_a_theorem(equiv(and(A,equiv(not(B),B)),equiv(not(B),B))). [resolve(102224,a,86081,a),rewrite([6794(5),6793(4),94(5),6794(8),6793(7),94(8)])]. 218.54/218.75 104908 equiv(not(A),A) = equiv(not(B),B). [resolve(102267,a,65,a)]. 218.54/218.75 104913 equiv(not(A),A) = c_0. [new_symbol(104908)]. 218.54/218.75 104915 is_a_theorem(equiv(and(A,c_0),c_0)). [back_rewrite(104002),rewrite([104913(2),104913(4)])]. 218.54/218.75 104916 is_a_theorem(equiv(and(c_0,A),c_0)). [back_rewrite(103147),rewrite([104913(2),104913(4)])]. 218.54/218.75 104917 is_a_theorem(equiv(not(equiv(A,A)),c_0)). [back_rewrite(102822),rewrite([104913(4)])]. 218.54/218.75 104918 is_a_theorem(equiv(and(not(A),A),c_0)). [back_rewrite(102714),rewrite([104913(4)])]. 218.54/218.75 104923 is_a_theorem(implies(A,equiv(c_0,not(A)))). [back_rewrite(102313),rewrite([104913(2)])]. 218.54/218.75 105077 is_a_theorem(implies(A,and(A,not(c_0)))). [back_rewrite(36173),rewrite([104913(2)])]. 218.54/218.75 105181 is_a_theorem(implies(implies(not(c_0),A),A)). [back_rewrite(30481),rewrite([104913(2)])]. 218.54/218.75 105204 is_a_theorem(not(c_0)). [back_rewrite(30368),rewrite([104913(2)])]. 218.54/218.75 106207 and(A,c_0) = c_0. [resolve(104915,a,65,a),flip(a)]. 218.54/218.75 106223 implies(A,not(c_0)) = not(c_0). [para(106207(a,1),6793(a,1,1)),flip(a)]. 218.54/218.75 106304 and(c_0,A) = c_0. [resolve(104916,a,65,a),flip(a)]. 218.54/218.75 106309 implies(c_0,not(A)) = not(c_0). [para(106304(a,1),6793(a,1,1)),flip(a)]. 218.54/218.75 106630 not(equiv(A,A)) = c_0. [resolve(104917,a,65,a),flip(a)]. 218.54/218.75 106858 equiv(A,A) = not(c_0). [para(106630(a,1),6727(a,1,1)),flip(a)]. 218.54/218.75 107817 and(not(A),A) = c_0. [resolve(104918,a,65,a),flip(a)]. 218.54/218.75 107840 and(A,not(A)) = c_0. [para(6727(a,1),107817(a,1,1))]. 218.54/218.75 107971 implies(A,A) = not(c_0). [para(107840(a,1),6793(a,1,1)),rewrite([6727(4)]),flip(a)]. 218.54/218.75 108064 and(not(c_0),not(c_0)) = not(c_0). [para(107971(a,1),94(a,1,1)),rewrite([107971(3),106858(6)])]. 218.54/218.75 108895 is_a_theorem(equiv(c_0,and(and(A,B),not(A)))). [resolve(104923,a,37561,a),rewrite([6794(4)])]. 218.54/218.75 108906 is_a_theorem(equiv(c_0,and(A,and(B,not(A))))). [resolve(104923,a,19720,a),rewrite([6794(4),6794(3)])]. 218.54/218.75 108907 is_a_theorem(equiv(c_0,and(and(A,B),not(B)))). [resolve(104923,a,19658,a),rewrite([6794(4)])]. 218.54/218.75 108908 is_a_theorem(equiv(c_0,and(A,implies(A,not(A))))). [resolve(104923,a,19628,a),rewrite([6794(4),6793(3)])]. 218.54/218.75 108926 -is_a_theorem(A) | is_a_theorem(equiv(c_0,not(A))). [resolve(104923,a,73,b)]. 218.54/218.75 111882 and(implies(not(c_0),A),not(c_0)) = equiv(not(c_0),A). [para(106223(a,1),94(a,1,2))]. 218.54/218.75 111888 implies(c_0,A) = not(c_0). [para(6727(a,1),106309(a,1,2))]. 218.54/218.75 111956 and(implies(A,c_0),not(c_0)) = equiv(A,c_0). [para(111888(a,1),94(a,1,2))]. 218.54/218.75 111969 is_a_theorem(equiv(c_0,and(A,implies(A,c_0)))). [resolve(108926,a,105077,a),rewrite([6794(6),6793(5),6727(4)])]. 218.54/218.75 112243 is_a_theorem(equiv(c_0,and(not(A),and(A,B)))). [resolve(108926,a,31139,a),rewrite([6794(6),6794(5),6727(4)])]. 218.54/218.75 113703 and(A,implies(A,c_0)) = c_0. [resolve(111969,a,65,a)]. 218.54/218.75 113736 implies(A,and(A,not(c_0))) = not(c_0). [para(113703(a,1),6793(a,1,1)),rewrite([6794(5)]),flip(a)]. 218.54/218.75 115520 and(and(A,B),not(A)) = c_0. [resolve(108895,a,65,a)]. 218.54/218.75 115524 implies(and(A,B),A) = not(c_0). [para(115520(a,1),6793(a,1,1)),rewrite([6727(5)]),flip(a)]. 218.54/218.75 115529 implies(equiv(A,B),implies(A,B)) = not(c_0). [para(94(a,1),115524(a,1,1))]. 218.54/218.75 115543 and(A,and(B,not(A))) = c_0. [resolve(108906,a,65,a)]. 218.54/218.75 115546 implies(A,implies(B,A)) = not(c_0). [para(115543(a,1),6793(a,1,1)),rewrite([6793(5),6727(4)]),flip(a)]. 218.54/218.75 115578 and(and(A,B),not(B)) = c_0. [resolve(108907,a,65,a)]. 218.54/218.75 115582 implies(and(A,B),B) = not(c_0). [para(115578(a,1),6793(a,1,1)),rewrite([6727(5)]),flip(a)]. 218.54/218.75 115591 is_a_theorem(implies(implies(A,B),implies(not(c_0),implies(and(C,A),B)))). [para(115582(a,1),135(a,1,2,1))]. 218.54/218.75 115696 and(A,implies(A,not(A))) = c_0. [resolve(108908,a,65,a)]. 218.54/218.75 115699 implies(A,and(A,A)) = not(c_0). [para(115696(a,1),6793(a,1,1)),rewrite([6794(5),6727(4)]),flip(a)]. 218.54/218.75 115713 equiv(A,and(A,A)) = not(c_0). [para(115699(a,1),94(a,1,1)),rewrite([115524(4),108064(5)]),flip(a)]. 218.54/218.75 115728 and(A,A) = A. [para(115713(a,1),65(a,1)),unit_del(a,105204)]. 218.54/218.75 115738 implies(A,not(A)) = not(A). [para(115728(a,1),6793(a,1,1)),flip(a)]. 218.54/218.75 115753 implies(not(A),A) = A. [para(115738(a,1),90(a,2)),rewrite([6727(2),90(1),6727(4)])]. 218.54/218.75 115754 is_a_theorem(implies(implies(A,not(B)),implies(implies(B,A),not(B)))). [para(115738(a,1),135(a,1,2,2))]. 218.54/218.75 115762 is_a_theorem(implies(implies(A,B),implies(implies(not(B),A),B))). [para(115753(a,1),135(a,1,2,2))]. 218.54/218.75 116710 and(not(A),and(A,B)) = c_0. [resolve(112243,a,65,a)]. 218.54/218.75 116713 and(and(A,not(B)),equiv(A,B)) = c_0. [para(94(a,1),116710(a,1,2)),rewrite([6794(2)])]. 218.54/218.75 117133 equiv(A,and(A,not(c_0))) = not(c_0). [para(113736(a,1),94(a,1,1)),rewrite([115524(6),115728(5)]),flip(a)]. 218.54/218.75 118330 and(A,not(c_0)) = A. [para(117133(a,1),65(a,1)),unit_del(a,105204)]. 218.54/218.75 118336 equiv(A,c_0) = implies(A,c_0). [back_rewrite(111956),rewrite([118330(5)]),flip(a)]. 218.54/218.75 118337 equiv(not(c_0),A) = implies(not(c_0),A). [back_rewrite(111882),rewrite([118330(6)]),flip(a)]. 218.54/218.75 118664 implies(A,c_0) = not(A). [para(118330(a,1),6793(a,1,1)),rewrite([6727(4)]),flip(a)]. 218.54/218.75 118666 equiv(A,c_0) = not(A). [back_rewrite(118336),rewrite([118664(4)])]. 218.54/218.75 119148 -is_a_theorem(not(A)) | c_0 = A. [para(118666(a,1),65(a,1))]. 218.54/218.75 120664 -is_a_theorem(A) | not(A) = c_0. [para(6727(a,1),119148(a,1)),flip(b)]. 218.54/218.75 120665 -is_a_theorem(implies(A,not(B))) | and(A,B) = c_0. [para(6793(a,1),119148(a,1)),flip(b)]. 218.54/218.75 120682 and(implies(not(c_0),A),not(A)) = c_0. [resolve(120664,a,105181,a),rewrite([6794(5)])]. 218.54/218.75 120696 and(and(implies(A,B),not(B)),not(equiv(A,B))) = c_0. [resolve(120664,a,82988,a),rewrite([6794(6)])]. 218.54/218.75 120766 and(not(equiv(A,B)),and(implies(A,B),not(B))) = c_0. [resolve(120664,a,50300,a),rewrite([6794(6),6794(5)])]. 218.54/218.75 120782 and(A,and(equiv(A,B),not(B))) = c_0. [resolve(120664,a,39381,a),rewrite([6794(4),6794(3)])]. 218.54/218.75 120875 and(and(equiv(A,B),not(A)),B) = c_0. [resolve(120664,a,15577,a),rewrite([6794(6),6727(5)])]. 218.54/218.75 120941 -is_a_theorem(implies(not(c_0),A)) | not(c_0) = A. [para(118337(a,1),65(a,1)),flip(b)]. 218.54/218.75 122334 not(equiv(A,implies(not(c_0),A))) = c_0. [para(120682(a,1),167(a,1,2)),rewrite([115546(4),118664(4),6727(3)]),flip(a)]. 218.54/218.75 122589 implies(A,implies(not(A),B)) = not(c_0). [resolve(120941,a,68595,a),rewrite([118330(8)]),flip(a)]. 218.54/218.75 122599 implies(A,implies(equiv(A,B),B)) = not(c_0). [resolve(120941,a,39434,a),flip(a)]. 218.54/218.75 122604 implies(and(A,and(B,C)),B) = not(c_0). [resolve(120941,a,33382,a),flip(a)]. 218.54/218.75 122609 implies(A,and(A,implies(B,A))) = not(c_0). [resolve(120941,a,27524,a),flip(a)]. 218.54/218.75 122613 implies(and(implies(A,B),A),B) = not(c_0). [resolve(120941,a,15111,a),flip(a)]. 218.54/218.75 122615 implies(and(A,B),implies(C,B)) = not(c_0). [resolve(120941,a,11101,a),flip(a)]. 218.54/218.75 122618 implies(equiv(A,B),equiv(B,A)) = not(c_0). [resolve(120941,a,8949,a),flip(a)]. 218.54/218.75 122619 implies(and(A,B),and(B,A)) = not(c_0). [resolve(120941,a,8865,a),flip(a)]. 218.54/218.75 122622 implies(implies(not(A),B),implies(not(B),A)) = not(c_0). [resolve(120941,a,204,a),flip(a)]. 218.54/218.75 122857 is_a_theorem(equiv(implies(not(c_0),A),A)). [para(122334(a,1),6941(a,1,2)),rewrite([118664(7),6727(6)])]. 218.54/218.75 122875 implies(not(c_0),A) = A. [resolve(122857,a,65,a),flip(a)]. 218.54/218.75 122891 -is_a_theorem(A) | not(c_0) = A. [back_rewrite(120941),rewrite([122875(3)])]. 218.54/218.75 122893 is_a_theorem(implies(implies(A,B),implies(and(C,A),B))). [back_rewrite(115591),rewrite([122875(6)])]. 218.54/218.75 123725 and(not(c_0),not(A)) = not(A). [para(122875(a,1),6794(a,1,1)),flip(a)]. 218.54/218.75 123803 implies(implies(A,and(B,C)),implies(A,B)) = not(c_0). [resolve(122891,a,42913,a),flip(a)]. 218.54/218.75 123836 implies(and(implies(A,not(B)),B),not(A)) = not(c_0). [resolve(122891,a,19524,a),flip(a)]. 218.54/218.75 123880 implies(implies(A,implies(B,C)),implies(B,implies(A,C))) = not(c_0). [resolve(122891,a,1623,a),flip(a)]. 218.54/218.75 123889 implies(implies(A,B),implies(implies(C,A),implies(C,B))) = not(c_0). [resolve(122891,a,135,a),flip(a)]. 218.54/218.75 124049 and(not(c_0),A) = A. [para(6727(a,1),123725(a,1,2)),rewrite([6727(5)])]. 218.54/218.75 124156 equiv(A,implies(not(A),B)) = implies(implies(not(A),B),A). [para(122589(a,1),94(a,1,1)),rewrite([124049(6)]),flip(a)]. 218.54/218.75 124490 equiv(implies(A,B),equiv(A,B)) = implies(implies(A,B),equiv(A,B)). [para(115529(a,1),94(a,1,2)),rewrite([118330(6)]),flip(a)]. 218.54/218.75 124837 and(and(A,implies(B,not(C))),equiv(A,and(B,C))) = c_0. [para(6793(a,1),116713(a,1,1,2))]. 218.54/218.75 124839 -is_a_theorem(implies(A,B)) | and(A,not(B)) = c_0. [para(6727(a,1),120665(a,1,2))]. 218.54/218.75 124840 -is_a_theorem(implies(A,implies(B,not(C)))) | and(A,and(B,C)) = c_0. [para(6793(a,1),120665(a,1,2))]. 218.54/218.75 125406 and(A,and(equiv(A,not(B)),B)) = c_0. [para(6727(a,1),120782(a,1,2,2))]. 218.54/218.75 126556 equiv(A,and(B,and(A,C))) = implies(A,and(B,and(A,C))). [para(122604(a,1),94(a,1,2)),rewrite([118330(6)]),flip(a)]. 218.54/218.75 126618 equiv(A,and(A,implies(B,A))) = not(c_0). [para(122609(a,1),94(a,1,1)),rewrite([115524(5),115728(5)]),flip(a)]. 218.54/218.75 126742 equiv(and(A,B),implies(C,B)) = implies(implies(C,B),and(A,B)). [para(122615(a,1),94(a,1,1)),rewrite([124049(6)]),flip(a)]. 218.54/218.75 126854 equiv(equiv(A,B),equiv(B,A)) = not(c_0). [para(122618(a,1),94(a,1,1)),rewrite([122618(5),115728(5)]),flip(a)]. 218.54/218.75 126856 equiv(and(A,B),and(B,A)) = not(c_0). [para(122619(a,1),94(a,1,1)),rewrite([122619(5),115728(5)]),flip(a)]. 218.54/218.75 126858 implies(implies(A,B),implies(and(C,A),B)) = not(c_0). [resolve(122893,a,122891,a),flip(a)]. 218.54/218.75 126864 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(and(C,A),B)). [resolve(122893,a,73,b)]. 218.54/218.75 126869 is_a_theorem(implies(not(equiv(A,B)),implies(and(C,implies(A,B)),and(B,not(A))))). [para(167(a,1),122893(a,1,1))]. 218.54/218.75 127374 and(A,implies(B,A)) = A. [para(126618(a,1),65(a,1)),unit_del(a,105204)]. 218.54/218.75 127481 implies(A,and(B,not(A))) = not(A). [para(127374(a,1),6793(a,1,1)),rewrite([6794(3)]),flip(a)]. 218.54/218.75 127503 implies(not(A),and(B,A)) = A. [para(127481(a,1),90(a,2)),rewrite([6727(2),90(2),6727(5)])]. 218.54/218.75 127504 and(not(A),implies(and(B,not(A)),A)) = equiv(A,and(B,not(A))). [para(127481(a,1),94(a,1,1))]. 218.54/218.75 127505 and(implies(and(A,not(B)),B),not(B)) = equiv(and(A,not(B)),B). [para(127481(a,1),94(a,1,2))]. 218.54/218.75 127522 and(A,implies(and(B,A),not(A))) = equiv(not(A),and(B,A)). [para(127503(a,1),94(a,1,1))]. 218.54/218.75 127523 and(implies(and(A,B),not(B)),B) = equiv(and(A,B),not(B)). [para(127503(a,1),94(a,1,2))]. 218.54/218.75 127524 implies(and(A,not(B)),equiv(B,A)) = implies(A,B). [para(94(a,1),127503(a,1,2)),rewrite([6794(2)])]. 218.54/218.75 127526 implies(implies(A,not(B)),and(C,and(A,B))) = and(A,B). [para(6793(a,1),127503(a,1,1))]. 218.54/218.75 127531 and(and(A,B),B) = and(A,B). [para(127503(a,1),127374(a,1,2))]. 218.54/218.75 127532 implies(and(A,not(B)),B) = implies(A,B). [para(127374(a,1),127503(a,1,2)),rewrite([6794(2)])]. 218.54/218.75 127534 equiv(and(A,not(B)),B) = and(implies(A,B),not(B)). [back_rewrite(127505),rewrite([127532(3)]),flip(a)]. 218.54/218.75 127535 equiv(A,and(B,not(A))) = and(not(A),implies(B,A)). [back_rewrite(127504),rewrite([127532(4)]),flip(a)]. 218.54/218.75 127631 and(equiv(A,B),implies(B,A)) = equiv(A,B). [para(94(a,1),127531(a,1,1)),rewrite([94(6)])]. 218.54/218.75 127632 implies(and(A,B),not(B)) = implies(A,not(B)). [para(127531(a,1),6793(a,1,1)),rewrite([6793(2)]),flip(a)]. 218.54/218.75 127649 equiv(and(A,B),not(B)) = and(implies(A,not(B)),B). [back_rewrite(127523),rewrite([127632(3)]),flip(a)]. 218.54/218.75 127650 equiv(not(A),and(B,A)) = and(A,implies(B,not(A))). [back_rewrite(127522),rewrite([127632(3)]),flip(a)]. 218.54/218.75 127652 equiv(A,B) = equiv(B,A). [para(126854(a,1),65(a,1)),unit_del(a,105204)]. 218.54/218.75 127653 and(implies(A,not(B)),B) = and(B,implies(A,not(B))). [back_rewrite(127649),rewrite([127652(3),127650(3)]),flip(a)]. 218.54/218.75 127683 and(implies(A,B),not(B)) = and(not(B),implies(A,B)). [back_rewrite(127534),rewrite([127652(3),127535(3)]),flip(a)]. 218.54/218.75 127684 implies(and(A,not(B)),equiv(A,B)) = implies(A,B). [back_rewrite(127524),rewrite([127652(3)])]. 218.54/218.75 128813 implies(and(A,implies(B,not(A))),not(B)) = not(c_0). [back_rewrite(123836),rewrite([127653(3)])]. 218.54/218.75 128932 and(not(equiv(A,B)),and(not(B),implies(A,B))) = c_0. [back_rewrite(120766),rewrite([127683(5)])]. 218.54/218.75 128933 and(and(not(A),implies(B,A)),not(equiv(B,A))) = c_0. [back_rewrite(120696),rewrite([127683(3)])]. 218.54/218.75 128948 -is_a_theorem(equiv(A,B)) | A = B. [para(127652(a,1),65(a,1))]. 218.54/218.75 129446 and(A,B) = and(B,A). [para(126856(a,1),65(a,1)),unit_del(a,105204)]. 218.54/218.75 129611 and(not(equiv(A,B)),and(not(A),implies(B,A))) = c_0. [back_rewrite(128933),rewrite([127652(4),129446(6)])]. 218.54/218.75 129900 and(implies(A,B),equiv(B,A)) = equiv(B,A). [back_rewrite(127631),rewrite([129446(3)])]. 218.54/218.75 129915 and(A,and(B,A)) = and(B,A). [back_rewrite(127531),rewrite([129446(2)])]. 218.54/218.75 129920 implies(not(A),and(A,B)) = A. [back_rewrite(127503),rewrite([129446(2)])]. 218.54/218.75 129987 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(and(A,C),B)). [back_rewrite(126864),rewrite([129446(3)])]. 218.54/218.75 129992 implies(implies(A,B),implies(and(A,C),B)) = not(c_0). [back_rewrite(126858),rewrite([129446(2)])]. 218.54/218.75 130133 and(A,and(B,equiv(A,not(B)))) = c_0. [back_rewrite(125406),rewrite([129446(3)])]. 218.54/218.75 130343 implies(and(A,implies(A,B)),B) = not(c_0). [back_rewrite(122613),rewrite([129446(2)])]. 218.54/218.75 130388 and(A,and(not(B),equiv(B,A))) = c_0. [back_rewrite(120875),rewrite([129446(3),129446(4)])]. 218.54/218.75 130530 implies(and(A,and(B,not(C))),and(A,not(C))) = not(c_0). [resolve(10999,a,122891,a),flip(a)]. 218.54/218.75 130532 is_a_theorem(implies(equiv(c_0,not(A)),A)). [resolve(10999,a,18290,a),rewrite([130530(6),6727(3)])]. 218.54/218.75 130539 is_a_theorem(implies(and(A,and(B,C)),and(A,C))). [para(6727(a,1),10999(a,1,1,2,2)),rewrite([6727(4)])]. 218.54/218.75 130551 implies(A,not(B)) = implies(B,not(A)). [para(129446(a,1),6793(a,1,1)),rewrite([6793(2)])]. 218.54/218.75 130652 implies(A,implies(B,and(B,A))) = not(c_0). [back_rewrite(128813),rewrite([130551(2),130551(5),6793(4),6794(3),6727(2)])]. 218.54/218.75 130660 implies(A,implies(B,not(A))) = implies(B,not(A)). [back_rewrite(127632),rewrite([130551(3),6793(2)])]. 218.54/218.75 130676 is_a_theorem(implies(implies(A,not(B)),implies(B,and(B,not(A))))). [back_rewrite(115754),rewrite([130551(5),6794(4)])]. 218.54/218.75 130687 implies(equiv(c_0,not(A)),A) = not(c_0). [resolve(130532,a,122891,a),flip(a)]. 218.54/218.75 130689 is_a_theorem(implies(equiv(c_0,implies(A,not(B))),A)). [resolve(130532,a,50233,a),rewrite([6793(3)])]. 218.54/218.75 130926 and(not(A),implies(A,not(B))) = not(A). [para(129920(a,1),6794(a,1,1)),rewrite([6793(4)]),flip(a)]. 218.54/218.75 131361 and(implies(A,not(B)),implies(not(A),B)) = equiv(B,not(A)). [para(130551(a,1),94(a,1,1))]. 218.54/218.75 131378 and(not(c_0),implies(A,equiv(c_0,not(A)))) = equiv(A,equiv(c_0,not(A))). [para(130687(a,1),94(a,1,1)),rewrite([127652(11)])]. 218.54/218.75 131530 is_a_theorem(implies(equiv(c_0,implies(A,B)),A)). [para(6727(a,1),130689(a,1,1,2,2))]. 218.54/218.75 131563 implies(equiv(c_0,implies(A,B)),A) = not(c_0). [resolve(131530,a,122891,a),flip(a)]. 218.54/218.75 132230 implies(implies(A,B),B) = implies(not(B),and(A,not(B))). [para(127532(a,1),167(a,1,1)),rewrite([6793(4),6727(3),127374(3),127652(5),127535(5),6793(6),6794(5)])]. 218.54/218.75 134142 is_a_theorem(implies(and(A,B),and(A,implies(C,B)))). [para(127374(a,1),130539(a,1,1,2))]. 218.54/218.75 134291 is_a_theorem(implies(implies(A,B),implies(A,implies(C,and(B,C))))). [para(130652(a,1),1322(a,1)),rewrite([129446(5)]),unit_del(a,105204)]. 218.54/218.75 134430 and(not(A),implies(A,B)) = not(A). [para(6727(a,1),130926(a,1,2,2))]. 218.54/218.75 134432 and(not(c_0),implies(A,B)) = implies(A,B). [para(115524(a,1),130926(a,1,2)),rewrite([129446(2),6793(3),6727(2),129446(4),129446(6),6793(7),6727(6)])]. 218.54/218.75 134440 equiv(A,equiv(c_0,not(A))) = implies(A,equiv(c_0,not(A))). [back_rewrite(131378),rewrite([134432(7)]),flip(a)]. 218.54/218.75 134442 and(A,implies(not(A),B)) = A. [para(6727(a,1),134430(a,1,1)),rewrite([6727(5)])]. 218.54/218.75 134870 is_a_theorem(implies(A,and(A,implies(B,implies(C,A))))). [para(127374(a,1),134142(a,1,1))]. 218.54/218.75 134871 is_a_theorem(implies(and(A,B),and(B,implies(C,A)))). [para(129446(a,1),134142(a,1,1))]. 218.54/218.75 135410 implies(A,and(A,implies(B,implies(C,A)))) = not(c_0). [resolve(134870,a,122891,a),flip(a)]. 218.54/218.75 135437 is_a_theorem(implies(and(A,B),and(and(A,B),implies(C,B)))). [para(129915(a,1),134871(a,1,1))]. 218.54/218.75 135439 is_a_theorem(implies(A,and(implies(not(A),B),implies(C,A)))). [para(134442(a,1),134871(a,1,1))]. 218.54/218.75 136188 is_a_theorem(implies(A,implies(equiv(c_0,implies(implies(A,B),C)),B))). [para(131563(a,1),14294(a,1)),unit_del(a,105204)]. 218.54/218.75 136223 is_a_theorem(implies(A,implies(implies(A,B),implies(C,B)))). [para(6727(a,1),14566(a,1,1)),rewrite([6727(2)])]. 218.54/218.75 136245 and(A,and(implies(A,B),and(C,not(B)))) = c_0. [resolve(136223,a,124839,a),rewrite([6794(4),6794(3)])]. 218.54/218.75 136253 is_a_theorem(implies(A,implies(B,and(A,implies(C,B))))). [para(127481(a,1),136223(a,1,2,2)),rewrite([130551(5),6794(4),6793(3),6727(2)])]. 218.54/218.75 136281 is_a_theorem(implies(implies(A,B),implies(A,equiv(A,B)))). [para(94(a,1),136253(a,1,2,2))]. 218.54/218.75 136284 is_a_theorem(implies(A,implies(and(B,C),and(A,B)))). [para(129920(a,1),136253(a,1,2,2,2))]. 218.54/218.75 136360 is_a_theorem(implies(and(A,implies(B,C)),implies(B,equiv(B,C)))). [resolve(136281,a,129987,a),rewrite([129446(2)])]. 218.54/218.75 136363 and(implies(A,B),and(A,not(equiv(A,B)))) = c_0. [resolve(136281,a,124839,a),rewrite([6794(4)])]. 218.54/218.75 136394 is_a_theorem(implies(and(and(A,B),implies(A,C)),C)). [resolve(136284,a,138,a),rewrite([129446(3),6794(5),6793(4),6727(3)])]. 218.54/218.75 136571 is_a_theorem(implies(and(and(A,B),implies(B,C)),C)). [para(129446(a,1),136394(a,1,1,1))]. 218.54/218.75 136701 is_a_theorem(implies(and(A,implies(implies(B,A),C)),C)). [para(127374(a,1),136571(a,1,1,1))]. 218.54/218.75 136703 is_a_theorem(implies(and(not(A),implies(implies(A,B),C)),C)). [para(134430(a,1),136571(a,1,1,1))]. 218.54/218.75 136831 implies(and(A,implies(implies(B,A),C)),C) = not(c_0). [resolve(136701,a,122891,a),flip(a)]. 218.54/218.75 137348 is_a_theorem(implies(A,equiv(c_0,not(A)))). [para(118664(a,1),101698(a,1,1,1,2)),rewrite([118664(6),130551(6),6727(5)])]. 218.54/218.75 137375 implies(A,equiv(c_0,not(A))) = not(c_0). [resolve(137348,a,122891,a),flip(a)]. 218.54/218.75 137382 equiv(A,equiv(c_0,not(A))) = not(c_0). [back_rewrite(134440),rewrite([137375(8)])]. 218.54/218.75 137475 equiv(c_0,not(A)) = A. [para(137382(a,1),65(a,1)),unit_del(a,105204)]. 218.54/218.75 137525 equiv(c_0,implies(A,not(B))) = and(A,B). [para(6793(a,1),137475(a,1,2))]. 218.54/218.75 137526 equiv(c_0,and(A,not(B))) = implies(A,B). [para(6794(a,1),137475(a,1,2))]. 218.54/218.75 137703 and(not(c_0),and(A,B)) = and(A,B). [para(137525(a,1),94(a,2)),rewrite([111888(4),118664(6),6794(5),6727(4)])]. 218.54/218.75 137704 equiv(c_0,implies(A,B)) = and(A,not(B)). [para(6727(a,1),137525(a,1,2,2))]. 218.54/218.75 137708 is_a_theorem(implies(A,implies(and(implies(A,B),not(C)),B))). [back_rewrite(136188),rewrite([137704(4)])]. 218.54/218.75 137903 equiv(c_0,equiv(A,B)) = not(equiv(A,B)). [para(167(a,1),137526(a,2)),rewrite([6793(5),6727(4),94(4)])]. 218.54/218.75 138237 is_a_theorem(implies(implies(not(A),and(B,implies(B,A))),A)). [para(130343(a,1),115762(a,1,1)),rewrite([122875(8)])]. 218.54/218.75 138758 -is_a_theorem(implies(A,equiv(B,C))) | is_a_theorem(implies(A,implies(C,B))). [para(129900(a,1),50233(a,1,2))]. 218.54/218.75 139178 implies(not(A),implies(B,A)) = implies(B,A). [para(130660(a,1),90(a,2)),rewrite([6727(2),90(2),6727(5)])]. 218.54/218.75 139224 implies(implies(A,not(B)),A) = A. [para(129920(a,1),139178(a,1,2)),rewrite([6793(2),129920(6)])]. 218.54/218.75 139227 implies(implies(A,B),A) = A. [para(6727(a,1),139224(a,1,1,2))]. 218.54/218.75 139239 and(A,implies(A,implies(A,B))) = equiv(A,implies(A,B)). [para(139227(a,1),94(a,1,1)),rewrite([127652(5)])]. 218.54/218.75 139253 implies(A,implies(A,B)) = implies(A,B). [para(139227(a,1),139227(a,1,1))]. 218.54/218.75 139254 equiv(A,implies(A,B)) = and(A,implies(A,B)). [back_rewrite(139239),rewrite([139253(2)]),flip(a)]. 218.54/218.75 139882 is_a_theorem(implies(implies(implies(A,B),and(A,C)),A)). [resolve(135439,a,138,a),rewrite([6727(2),130551(3),6793(5),6794(4),6727(3)])]. 218.54/218.75 139935 implies(implies(implies(A,B),and(A,C)),A) = not(c_0). [resolve(139882,a,122891,a),flip(a)]. 218.54/218.75 140427 is_a_theorem(implies(not(A),implies(equiv(B,implies(A,C)),B))). [para(122599(a,1),136703(a,1,1,2)),rewrite([118330(4),127652(3)])]. 218.54/218.75 141043 is_a_theorem(implies(A,implies(B,implies(implies(A,not(B)),C)))). [para(130551(a,1),137708(a,1,2,1,1)),rewrite([130551(2),130551(6),6793(5),6727(4)])]. 218.54/218.75 141260 is_a_theorem(implies(A,and(A,implies(B,and(A,B))))). [para(6727(a,1),138237(a,1,1,1)),rewrite([130551(2),130551(6),6794(5),6793(4),6794(3),6727(2)])]. 218.54/218.75 141285 implies(A,and(A,implies(B,and(A,B)))) = not(c_0). [resolve(141260,a,122891,a),flip(a)]. 218.54/218.75 142064 is_a_theorem(implies(equiv(A,implies(B,C)),implies(not(B),A))). [resolve(140427,a,14294,a)]. 218.54/218.75 142164 is_a_theorem(implies(A,implies(B,implies(C,and(A,B))))). [para(130551(a,1),141043(a,1,2,2)),rewrite([6794(3),6727(2)])]. 218.54/218.75 142170 and(A,and(B,and(C,implies(A,not(B))))) = c_0. [resolve(142164,a,124839,a),rewrite([6794(4),6794(3),6793(2)])]. 218.54/218.75 142575 is_a_theorem(implies(equiv(not(A),implies(B,C)),implies(A,B))). [para(130551(a,1),142064(a,1,2)),rewrite([6727(5)])]. 218.54/218.75 143224 is_a_theorem(implies(equiv(A,not(B)),implies(B,implies(A,C)))). [para(139227(a,1),142575(a,1,1,2)),rewrite([127652(2)])]. 218.54/218.75 143611 is_a_theorem(implies(equiv(not(A),not(B)),implies(B,implies(C,A)))). [para(139178(a,1),143224(a,1,2,2))]. 218.54/218.75 144116 equiv(implies(not(A),B),implies(not(B),A)) = not(c_0). [para(122622(a,1),94(a,1,1)),rewrite([122622(7),115728(5),127652(7)]),flip(a)]. 218.54/218.75 145825 implies(implies(A,equiv(A,B)),implies(A,B)) = not(c_0). [para(127684(a,1),129992(a,1,2))]. 218.54/218.75 146015 is_a_theorem(implies(implies(A,B),implies(A,and(B,A)))). [para(6727(a,1),130676(a,1,2,2,2)),rewrite([130551(3),6727(2),129446(2)])]. 218.54/218.75 146022 is_a_theorem(implies(A,implies(implies(A,B),and(A,B)))). [resolve(146015,a,14294,a),rewrite([129446(2)])]. 218.54/218.75 146025 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(A,and(A,B))). [resolve(146015,a,73,b),rewrite([129446(3)])]. 218.54/218.75 146041 and(A,and(implies(A,B),implies(A,not(B)))) = c_0. [resolve(146022,a,124839,a),rewrite([6794(4),6793(3)])]. 218.54/218.75 146060 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))). [para(123889(a,1),14294(a,1)),unit_del(a,105204)]. 218.54/218.75 146551 -is_a_theorem(implies(implies(not(A),B),A)) | implies(not(A),B) = A. [para(124156(a,1),65(a,1))]. 218.54/218.75 146552 equiv(A,implies(B,A)) = implies(not(A),and(B,not(A))). [para(130551(a,1),124156(a,1,2)),rewrite([6727(2),130551(5),6727(4),132230(4)])]. 218.54/218.75 147941 is_a_theorem(implies(A,implies(B,equiv(A,B)))). [para(127374(a,1),136360(a,1,1)),rewrite([127652(1)])]. 218.54/218.75 147956 and(A,and(B,not(equiv(A,B)))) = c_0. [resolve(147941,a,124839,a),rewrite([6794(3)])]. 218.54/218.75 148067 equiv(A,and(A,B)) = implies(A,and(A,B)). [para(115728(a,1),126556(a,1,2,2)),rewrite([129446(1),115728(3),129446(3)])]. 218.54/218.75 148313 -is_a_theorem(implies(A,and(A,B))) | and(A,B) = A. [para(148067(a,1),65(a,1))]. 218.54/218.75 148386 and(and(A,B),implies(C,B)) = and(A,B). [resolve(148313,a,135437,a)]. 218.54/218.75 148389 and(A,implies(B,implies(C,A))) = A. [para(135410(a,1),148313(a,1)),unit_del(a,105204)]. 218.54/218.75 148402 implies(A,and(B,and(C,not(A)))) = not(A). [para(148389(a,1),6793(a,1,1)),rewrite([6794(4),6794(3)]),flip(a)]. 218.54/218.75 148428 and(implies(A,B),and(C,B)) = and(C,B). [para(148386(a,1),129446(a,1)),flip(a)]. 218.54/218.75 148535 implies(not(A),and(B,and(A,C))) = A. [para(148402(a,1),90(a,2)),rewrite([6727(2),129446(1),90(3),6727(6)])]. 218.54/218.75 148550 implies(implies(A,implies(B,not(C))),B) = B. [para(148535(a,1),139178(a,1,2)),rewrite([6793(3),6793(2),148535(8)])]. 218.54/218.75 148555 implies(implies(A,implies(B,C)),B) = B. [para(6727(a,1),148550(a,1,1,2,2))]. 218.54/218.75 148560 implies(implies(A,B),implies(B,C)) = implies(B,C). [para(139227(a,1),148555(a,1,1,2))]. 218.54/218.75 148588 equiv(A,and(B,A)) = implies(A,and(B,A)). [para(115753(a,1),126742(a,1,2)),rewrite([127652(2),115753(4)])]. 218.54/218.75 148691 implies(implies(A,B),implies(C,A)) = implies(C,A). [para(148560(a,1),139227(a,1,1))]. 218.54/218.75 148739 implies(implies(and(A,and(B,C)),D),B) = B. [para(148535(a,1),148691(a,1,2)),rewrite([148535(8)])]. 218.54/218.75 148826 implies(implies(and(A,and(B,C)),D),C) = C. [para(129446(a,1),148739(a,1,1,1,2))]. 218.54/218.75 149675 and(A,implies(B,and(A,B))) = A. [para(141285(a,1),148313(a,1)),unit_del(a,105204)]. 218.54/218.75 149676 implies(A,and(B,implies(A,not(B)))) = not(A). [para(149675(a,1),6793(a,1,1)),rewrite([6794(4),6793(3)]),flip(a)]. 218.54/218.75 149689 and(A,implies(B,not(equiv(A,not(B))))) = A. [para(130133(a,1),149675(a,1,2,2)),rewrite([118664(5),6793(4)])]. 218.54/218.75 149691 and(A,implies(not(B),not(equiv(A,B)))) = A. [para(130388(a,1),149675(a,1,2,2)),rewrite([127652(2),118664(5),6793(4)])]. 218.54/218.75 149725 and(A,implies(implies(A,B),implies(C,B))) = A. [para(136245(a,1),149675(a,1,2,2)),rewrite([118664(6),6793(5),6793(4),6727(3)])]. 218.54/218.75 149728 and(A,implies(B,equiv(A,B))) = A. [para(147956(a,1),149675(a,1,2,2)),rewrite([118664(5),6793(4),6727(3)])]. 218.54/218.75 149731 and(implies(A,B),implies(A,equiv(A,B))) = implies(A,B). [para(136363(a,1),149675(a,1,2,2)),rewrite([118664(6),6793(5),6727(4)])]. 218.54/218.75 149740 implies(A,and(B,not(equiv(A,B)))) = not(A). [para(149728(a,1),6793(a,1,1)),rewrite([6794(4)]),flip(a)]. 218.54/218.75 149839 implies(not(A),and(B,implies(B,A))) = A. [para(149676(a,1),90(a,2)),rewrite([130551(3),6727(2),90(3),6727(6)])]. 218.54/218.75 149846 and(A,and(B,implies(B,A))) = and(B,implies(B,A)). [para(149839(a,1),127374(a,1,2)),rewrite([129446(3)])]. 218.54/218.75 149872 implies(not(A),and(B,implies(implies(C,B),A))) = A. [para(136831(a,1),149839(a,1,2,2)),rewrite([129446(7),137703(7)])]. 218.54/218.75 149962 is_a_theorem(implies(A,equiv(B,not(equiv(A,not(B)))))). [para(149689(a,1),126869(a,1,2,1)),rewrite([129446(10),149740(11),130551(7),6727(6)])]. 218.54/218.75 149971 is_a_theorem(implies(A,implies(not(equiv(A,not(B))),B))). [resolve(149962,a,138758,a)]. 218.54/218.75 149991 is_a_theorem(implies(not(equiv(A,not(B))),implies(A,B))). [resolve(149971,a,14294,a)]. 218.54/218.75 150020 and(and(A,B),not(equiv(A,B))) = c_0. [resolve(149991,a,124840,a),rewrite([6727(2),129446(4)])]. 218.54/218.75 150106 and(and(A,B),equiv(A,B)) = and(A,B). [para(150020(a,1),149675(a,1,2,2)),rewrite([118664(5),6727(4)])]. 218.54/218.75 150175 and(A,implies(equiv(A,B),B)) = A. [para(130551(a,1),149691(a,1,2)),rewrite([6727(3)])]. 218.54/218.75 150209 is_a_theorem(implies(A,equiv(B,equiv(A,B)))). [para(150175(a,1),126869(a,1,2,1)),rewrite([127652(2),149740(7),130551(5),6727(4)])]. 218.54/218.75 150212 is_a_theorem(implies(A,and(A,equiv(B,equiv(A,B))))). [resolve(150209,a,146025,a)]. 218.54/218.75 150230 and(A,equiv(B,equiv(A,B))) = A. [resolve(150212,a,148313,a)]. 218.54/218.75 150247 and(A,equiv(B,equiv(B,A))) = A. [para(150230(a,1),129446(a,2)),rewrite([127652(1),129446(3)])]. 218.54/218.75 150297 and(A,implies(A,and(A,B))) = and(A,B). [para(148067(a,1),150247(a,1,2,2)),rewrite([139254(4),149846(5)])]. 218.54/218.75 150298 and(A,implies(A,and(B,A))) = and(B,A). [para(148588(a,1),150247(a,1,2,2)),rewrite([139254(4),149846(5)])]. 218.54/218.75 150632 and(A,implies(B,implies(C,and(A,B)))) = A. [para(142170(a,1),149675(a,1,2,2)),rewrite([118664(6),6793(5),6793(4),6794(3),6727(2)])]. 218.54/218.75 150970 is_a_theorem(implies(equiv(not(A),and(B,not(C))),implies(C,A))). [para(148560(a,1),143611(a,1,2)),rewrite([6794(3)])]. 218.54/218.75 151036 implies(not(A),B) = implies(not(B),A). [para(144116(a,1),65(a,1)),unit_del(a,105204)]. 218.54/218.75 151052 equiv(A,not(B)) = equiv(B,not(A)). [para(151036(a,1),94(a,1,1)),rewrite([129446(5),131361(5),127652(4)])]. 218.54/218.75 151119 and(A,implies(and(B,implies(A,C)),C)) = A. [para(151036(a,1),150632(a,1,2)),rewrite([6794(4),6793(3),6727(2)])]. 218.54/218.75 151426 implies(not(c_0),implies(A,B)) = implies(A,B). [para(128932(a,1),148826(a,1,1,1)),rewrite([111888(2)])]. 218.54/218.75 151576 and(implies(A,B),implies(A,implies(C,B))) = implies(A,B). [para(149725(a,1),151119(a,1,2,1))]. 218.54/218.75 152480 and(A,implies(implies(A,B),and(A,B))) = A. [para(146041(a,1),149675(a,1,2,2)),rewrite([118664(6),6793(5),6794(4),6727(3)])]. 218.54/218.75 152488 implies(implies(A,B),and(A,B)) = A. [para(152480(a,1),150298(a,1,2,2)),rewrite([139935(7),129446(6),134432(6),152480(7)])]. 218.54/218.75 152492 implies(A,equiv(A,B)) = implies(A,B). [para(145825(a,1),152480(a,1,2,1)),rewrite([129446(8),149731(8),151426(6),129446(4),149731(4)]),flip(a)]. 218.54/218.75 152495 implies(implies(A,B),equiv(B,A)) = implies(B,A). [para(94(a,1),152488(a,1,2)),rewrite([148560(3)])]. 218.54/218.75 152528 implies(A,and(A,B)) = implies(A,B). [para(152488(a,1),152488(a,1,1)),rewrite([148428(3)])]. 218.54/218.75 152531 and(A,implies(A,B)) = and(A,B). [back_rewrite(150297),rewrite([152528(2)])]. 218.54/218.75 152532 -is_a_theorem(implies(A,B)) | and(A,B) = A. [back_rewrite(148313),rewrite([152528(2)])]. 218.54/218.75 152577 implies(not(A),and(B,not(A))) = implies(not(A),B). [para(152528(a,1),90(a,2)),rewrite([129446(2),90(3)])]. 218.54/218.75 152578 implies(implies(A,B),equiv(A,B)) = implies(B,A). [para(94(a,1),152528(a,1,2)),rewrite([148560(6)])]. 218.54/218.75 152591 is_a_theorem(implies(implies(A,B),implies(A,implies(C,and(A,B))))). [para(152528(a,1),134291(a,1,1)),rewrite([129446(3),152528(4)])]. 218.54/218.75 152622 equiv(A,implies(B,A)) = implies(not(A),B). [back_rewrite(146552),rewrite([152577(6)])]. 218.54/218.75 152625 implies(implies(A,B),B) = implies(not(A),B). [back_rewrite(132230),rewrite([152577(6),151036(4)])]. 218.54/218.75 152626 equiv(implies(A,B),equiv(A,B)) = implies(B,A). [back_rewrite(124490),rewrite([152578(6)])]. 218.54/218.75 152634 and(A,equiv(A,B)) = and(A,B). [para(152492(a,1),152531(a,1,2)),rewrite([152531(2)]),flip(a)]. 218.54/218.75 152684 -is_a_theorem(implies(A,not(B))) | and(B,not(A)) = B. [para(130551(a,1),152532(a,1))]. 218.54/218.75 152724 and(not(A),implies(B,A)) = and(not(A),not(B)). [para(129611(a,1),127526(a,1,2)),rewrite([6794(3),152577(4),118664(4),6794(3)]),flip(a)]. 218.54/218.75 152867 -is_a_theorem(implies(not(A),B)) | implies(B,A) = A. [para(152622(a,1),65(a,1))]. 218.54/218.75 152869 implies(implies(not(A),B),A) = implies(B,A). [para(130551(a,1),152622(a,2)),rewrite([151036(2),124156(3),6727(5)])]. 218.54/218.75 152880 implies(not(A),equiv(A,B)) = implies(B,A). [para(152492(a,1),152622(a,1,2)),rewrite([127652(3),152626(3),151036(4)]),flip(a)]. 218.54/218.75 152881 -is_a_theorem(implies(A,B)) | implies(not(B),A) = B. [back_rewrite(146551),rewrite([152869(3)])]. 218.54/218.75 152887 implies(A,and(B,A)) = implies(A,B). [para(152625(a,1),6793(a,2)),rewrite([129446(3),6793(4),6794(3),6727(2),130551(5),6727(4)])]. 218.54/218.75 152928 equiv(A,and(B,A)) = implies(A,B). [para(152887(a,1),94(a,1,2)),rewrite([115582(2),134432(4),127652(3)]),flip(a)]. 218.54/218.75 152933 implies(equiv(A,B),and(A,B)) = implies(equiv(A,B),A). [para(152634(a,1),152887(a,1,2))]. 218.54/218.75 152935 equiv(and(A,B),equiv(A,B)) = implies(equiv(A,B),A). [para(150106(a,1),152928(a,1,2)),rewrite([127652(3),152933(6)])]. 218.54/218.75 152979 -is_a_theorem(implies(A,B)) | implies(not(A),B) = B. [para(130551(a,1),152867(a,1)),rewrite([6727(2)])]. 218.54/218.75 153004 and(implies(A,B),implies(not(B),A)) = B. [para(152869(a,1),152531(a,1,2)),rewrite([129446(4),129446(7),134442(7)])]. 218.54/218.75 153031 implies(A,equiv(B,A)) = implies(A,B). [para(152880(a,1),152625(a,1,1)),rewrite([127652(2),152578(3),6727(3),127652(2)]),flip(a)]. 218.54/218.75 153033 implies(equiv(A,B),B) = implies(not(A),B). [para(152880(a,1),152869(a,1,1)),rewrite([152625(2),127652(3)]),flip(a)]. 218.54/218.75 153042 equiv(A,equiv(B,A)) = B. [para(153031(a,1),94(a,1,2)),rewrite([153033(2),129446(4),153004(4),127652(2)]),flip(a)]. 218.54/218.75 153206 equiv(not(A),equiv(A,not(B))) = B. [para(151052(a,1),153042(a,1,2))]. 218.54/218.75 153219 implies(equiv(A,B),A) = implies(not(A),B). [para(153042(a,1),152880(a,1,2)),rewrite([127652(3)]),flip(a)]. 218.54/218.75 153222 equiv(and(A,B),equiv(A,B)) = implies(not(A),B). [back_rewrite(152935),rewrite([153219(5)])]. 218.54/218.76 153271 equiv(not(A),equiv(A,B)) = not(B). [para(6727(a,1),153206(a,1,2,2))]. 218.54/218.76 153433 not(equiv(A,B)) = equiv(A,not(B)). [para(153042(a,1),153271(a,1,2)),rewrite([127652(2),151052(2),127652(3)]),flip(a)]. 218.54/218.76 153659 equiv(c_0,equiv(A,B)) = equiv(A,not(B)). [back_rewrite(137903),rewrite([153433(5)])]. 218.54/218.76 155087 implies(and(A,not(B)),implies(A,and(B,C))) = implies(A,B). [para(123803(a,1),152881(a,1)),rewrite([6794(5)]),unit_del(a,105204)]. 218.54/218.76 155974 -is_a_theorem(implies(A,B)) | -is_a_theorem(implies(B,A)) | is_a_theorem(equiv(A,B)). [para(152495(a,1),73(b,1)),rewrite([127652(5)])]. 218.54/218.76 156043 -is_a_theorem(implies(A,B)) | and(B,A) = A. [para(152625(a,1),152684(a,1)),rewrite([130551(3),6727(2),6794(5),6727(4),129915(4)])]. 218.54/218.76 156525 is_a_theorem(implies(implies(A,B),implies(A,and(B,implies(C,A))))). [para(127481(a,1),146060(a,1,2,2)),rewrite([130551(6),6794(5),6793(4),6727(3)])]. 218.54/218.76 158334 is_a_theorem(implies(not(A),implies(equiv(not(B),and(A,C)),B))). [resolve(150970,a,274,a),rewrite([6727(4),129446(3)])]. 218.54/218.76 158728 is_a_theorem(implies(implies(A,implies(implies(B,A),C)),implies(A,C))). [para(149872(a,1),152591(a,1,2,2))]. 218.54/218.76 158865 implies(not(A),implies(B,not(C))) = implies(and(B,C),A). [para(124837(a,1),153222(a,1,1)),rewrite([153659(8),153433(6),6793(5),153222(7),6793(8),6794(7),6727(6),152578(9)])]. 218.54/218.76 159118 is_a_theorem(equiv(implies(A,implies(B,C)),implies(B,implies(A,C)))). [para(123880(a,1),155974(a,1)),rewrite([123880(8),127652(11)]),merge(b),unit_del(a,105204)]. 218.54/218.76 159256 implies(A,and(B,implies(C,A))) = implies(A,B). [resolve(156525,a,152979,a),rewrite([6794(2),155087(6)]),flip(a)]. 218.54/218.76 159260 implies(and(A,B),and(A,C)) = implies(and(A,B),C). [para(129920(a,1),159256(a,1,2,2)),rewrite([129446(2)])]. 218.54/218.76 159964 implies(A,implies(implies(B,A),C)) = implies(A,C). [resolve(158728,a,156043,a),rewrite([151576(5)]),flip(a)]. 218.54/218.76 159972 implies(A,equiv(B,implies(C,A))) = implies(A,B). [para(152492(a,1),159964(a,1,2)),rewrite([159964(3),127652(3)]),flip(a)]. 218.54/218.76 159986 implies(equiv(A,and(B,C)),B) = implies(not(B),A). [para(159972(a,1),151036(a,1)),rewrite([130551(4),153433(6),6794(5),6727(4)]),flip(a)]. 218.54/218.76 160111 implies(A,implies(B,C)) = implies(B,implies(A,C)). [resolve(159118,a,128948,a)]. 218.54/218.76 160156 implies(and(A,B),C) = implies(A,implies(B,C)). [back_rewrite(158865),rewrite([160111(4),130551(3),6727(2)]),flip(a)]. 218.54/218.76 160409 implies(A,implies(B,and(A,C))) = implies(A,implies(B,C)). [back_rewrite(159260),rewrite([160156(3),160156(5)])]. 218.54/218.76 160924 -is_a_theorem(and(A,B)) | -is_a_theorem(implies(A,implies(B,C))) | is_a_theorem(C). [para(160156(a,1),73(b,1))]. 218.54/218.76 161244 implies(not(A),implies(implies(B,A),C)) = implies(not(A),implies(not(B),C)). [para(152724(a,1),160156(a,1,1)),rewrite([160156(4)]),flip(a)]. 218.54/218.76 164095 and(not(A),equiv(B,and(A,C))) = and(not(A),not(B)). [para(159986(a,1),6794(a,1,1)),rewrite([6794(3),129446(7)]),flip(a)]. 218.54/218.76 164112 implies(not(A),and(B,and(C,A))) = A. [para(148402(a,1),159986(a,2)),rewrite([6727(2),159986(5),6727(6)])]. 218.54/218.76 164176 and(A,and(B,C)) = and(B,and(A,C)). [para(164112(a,1),153004(a,1,1)),rewrite([129446(1),6793(3),6793(2),160111(3),130551(5),6794(4),6794(3),6727(2),152528(3),152531(3),129446(3)])]. 218.54/218.76 167101 -is_a_theorem(not(A)). [ur(160924,b,158334,a,c,111,a),rewrite([6794(16),6794(15),6794(14),129446(14),164176(15),164176(16),164095(19),6793(17),6793(16),6793(15),6794(14),161244(17),160409(15),130551(11),6794(10),152528(11),160111(10),130551(9),6727(8),160111(9),160111(8),151036(7),115546(8),106223(5),118330(4)])]. 218.54/218.76 167102 $F. [resolve(167101,a,105204,a)]. 218.54/218.76 218.54/218.76 % SZS output end Refutation 218.54/218.76 ============================== end of proof ========================== 218.54/218.76 218.54/218.76 ============================== STATISTICS ============================ 218.54/218.76 218.54/218.76 Given=11237. Generated=11872328. Kept=167052. proofs=1. 218.54/218.76 Usable=2332. Sos=7042. Demods=1276. Limbo=486, Disabled=157265. Hints=0. 218.54/218.76 Megabytes=89.14. 218.54/218.76 User_CPU=211.96, System_CPU=6.35, Wall_clock=218. 218.54/218.76 218.54/218.76 ============================== end of statistics ===================== 218.54/218.76 218.54/218.76 ============================== end of search ========================= 218.54/218.76 218.54/218.76 THEOREM PROVED 218.54/218.76 % SZS status Theorem 218.54/218.76 218.54/218.76 Exiting with 1 proof. 218.54/218.76 218.54/218.76 Process 29902 exit (max_proofs) Sat Jul 14 06:12:33 2018 218.54/218.76 Prover9 interrupted 218.54/218.77 EOF