0.06/0.14 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.15 % Command : tptp2X_and_run_prover9 %d %s 0.11/0.35 % Computer : n005.cluster.edu 0.11/0.35 % Model : x86_64 x86_64 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.35 % Memory : 8042.1875MB 0.11/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.35 % CPULimit : 1440 0.11/0.35 % WCLimit : 180 0.11/0.35 % DateTime : Mon Jul 3 10:38:30 EDT 2023 0.11/0.35 % CPUTime : 0.77/1.17 ============================== Prover9 =============================== 0.77/1.17 Prover9 (32) version 2009-11A, November 2009. 0.77/1.17 Process 21982 was started by sandbox on n005.cluster.edu, 0.77/1.17 Mon Jul 3 10:38:31 2023 0.77/1.17 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1440 -f /tmp/Prover9_21829_n005.cluster.edu". 0.77/1.17 ============================== end of head =========================== 0.77/1.17 0.77/1.17 ============================== INPUT ================================= 0.77/1.17 0.77/1.17 % Reading from file /tmp/Prover9_21829_n005.cluster.edu 0.77/1.17 0.77/1.17 set(prolog_style_variables). 0.77/1.17 set(auto2). 0.77/1.17 % set(auto2) -> set(auto). 0.77/1.17 % set(auto) -> set(auto_inference). 0.77/1.17 % set(auto) -> set(auto_setup). 0.77/1.17 % set(auto_setup) -> set(predicate_elim). 0.77/1.17 % set(auto_setup) -> assign(eq_defs, unfold). 0.77/1.17 % set(auto) -> set(auto_limits). 0.77/1.17 % set(auto_limits) -> assign(max_weight, "100.000"). 0.77/1.17 % set(auto_limits) -> assign(sos_limit, 20000). 0.77/1.17 % set(auto) -> set(auto_denials). 0.77/1.17 % set(auto) -> set(auto_process). 0.77/1.17 % set(auto2) -> assign(new_constants, 1). 0.77/1.17 % set(auto2) -> assign(fold_denial_max, 3). 0.77/1.17 % set(auto2) -> assign(max_weight, "200.000"). 0.77/1.17 % set(auto2) -> assign(max_hours, 1). 0.77/1.17 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.77/1.17 % set(auto2) -> assign(max_seconds, 0). 0.77/1.17 % set(auto2) -> assign(max_minutes, 5). 0.77/1.17 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.77/1.17 % set(auto2) -> set(sort_initial_sos). 0.77/1.17 % set(auto2) -> assign(sos_limit, -1). 0.77/1.17 % set(auto2) -> assign(lrs_ticks, 3000). 0.77/1.17 % set(auto2) -> assign(max_megs, 400). 0.77/1.17 % set(auto2) -> assign(stats, some). 0.77/1.17 % set(auto2) -> clear(echo_input). 0.77/1.17 % set(auto2) -> set(quiet). 0.77/1.17 % set(auto2) -> clear(print_initial_clauses). 0.77/1.17 % set(auto2) -> clear(print_given). 0.77/1.17 assign(lrs_ticks,-1). 0.77/1.17 assign(sos_limit,10000). 0.77/1.17 assign(order,kbo). 0.77/1.17 set(lex_order_vars). 0.77/1.17 clear(print_given). 0.77/1.17 0.77/1.17 % formulas(sos). % not echoed (43 formulas) 0.77/1.17 0.77/1.17 ============================== end of input ========================== 0.77/1.17 0.77/1.17 % From the command line: assign(max_seconds, 1440). 0.77/1.17 0.77/1.17 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.77/1.17 0.77/1.17 % Formulas that are not ordinary clauses: 0.77/1.17 1 (all X all Y is_a_theorem(implies(X,implies(Y,X)))) <-> implies_1 # label(implies_1) # label(axiom) # label(non_clause). [assumption]. 0.77/1.17 2 (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) <-> cn2 # label(cn2) # label(axiom) # label(non_clause). [assumption]. 0.77/1.17 3 (all X all Y is_a_theorem(implies(and(X,Y),X))) <-> and_1 # label(and_1) # label(axiom) # label(non_clause). [assumption]. 0.77/1.17 4 substitution_of_equivalents <-> (all X all Y (is_a_theorem(equiv(X,Y)) -> X = Y)) # label(substitution_of_equivalents) # label(axiom) # label(non_clause). [assumption]. 0.77/1.17 5 (all X all Y all Z is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))) <-> or_3 # label(or_3) # label(axiom) # label(non_clause). [assumption]. 0.77/1.17 6 and_3 <-> (all X all Y is_a_theorem(implies(X,implies(Y,and(X,Y))))) # label(and_3) # label(axiom) # label(non_clause). [assumption]. 0.77/1.17 7 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]. 0.77/1.17 8 (all X all Y is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))) <-> implies_2 # label(implies_2) # label(axiom) # label(non_clause). [assumption]. 0.77/1.17 9 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption]. 0.77/1.17 10 equivalence_2 <-> (all X all Y is_a_theorem(implies(equiv(X,Y),implies(Y,X)))) # label(equivalence_2) # label(axiom) # label(non_clause). [assumption]. 0.77/1.17 11 cn1 <-> (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))) # label(cn1) # label(axiom) # label(non_clause). [assumption]. 0.77/1.17 12 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption]. 0.77/1.17 13 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]. 0.77/1.17 14 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]. 1.56/1.95 15 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption]. 1.56/1.95 16 (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))) <-> kn3 # label(kn3) # label(axiom) # label(non_clause). [assumption]. 1.56/1.95 17 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption]. 1.56/1.95 18 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]. 1.56/1.95 19 (all P is_a_theorem(implies(P,and(P,P)))) <-> kn1 # label(kn1) # label(axiom) # label(non_clause). [assumption]. 1.56/1.95 20 (all P is_a_theorem(implies(implies(not(P),P),P))) <-> cn3 # label(cn3) # label(axiom) # label(non_clause). [assumption]. 1.56/1.95 21 (all P all Q is_a_theorem(implies(Q,or(P,Q)))) <-> r2 # label(r2) # label(axiom) # label(non_clause). [assumption]. 1.56/1.95 22 (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]. 1.56/1.95 23 r5 <-> (all P all Q all R is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))) # label(r5) # label(axiom) # label(non_clause). [assumption]. 1.56/1.95 24 (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]. 1.56/1.95 25 (all X all Y is_a_theorem(implies(and(X,Y),Y))) <-> and_2 # label(and_2) # label(axiom) # label(non_clause). [assumption]. 1.56/1.95 26 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption]. 1.56/1.95 27 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]. 1.56/1.95 28 op_implies_and -> (all X all Y implies(X,Y) = not(and(X,not(Y)))) # label(op_implies_and) # label(axiom) # label(non_clause). [assumption]. 1.56/1.95 29 op_and -> (all X all Y not(or(not(X),not(Y))) = and(X,Y)) # label(op_and) # label(axiom) # label(non_clause). [assumption]. 1.56/1.95 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]. 1.56/1.95 31 op_or -> (all X all Y or(X,Y) = not(and(not(X),not(Y)))) # label(op_or) # label(axiom) # label(non_clause). [assumption]. 1.56/1.95 1.56/1.95 ============================== end of process non-clausal formulas === 1.56/1.95 1.56/1.95 ============================== PROCESS INITIAL CLAUSES =============== 1.56/1.95 1.56/1.95 ============================== PREDICATE ELIMINATION ================= 1.56/1.95 1.56/1.95 ============================== end predicate elimination ============= 1.56/1.95 1.56/1.95 Auto_denials: (non-Horn, no changes). 1.56/1.95 1.56/1.95 Term ordering decisions: 1.56/1.95 1.56/1.95 % Assigning unary symbol not kb_weight 0 and highest precedence (93). 1.56/1.95 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. 1.56/1.95 1.56/1.95 ============================== end of process initial clauses ======== 1.56/1.95 1.56/1.95 ============================== CLAUSES FOR SEARCH ==================== 1.56/1.95 1.56/1.95 ============================== end of clauses for search ============= 1.56/1.95 1.56/1.95 ============================== SEARCH ================================ 1.56/1.95 1.56/1.95 % Starting search at 0.02 seconds. 1.56/1.95 1.56/1.95 Low Water (keep): wt=39.000, iters=3358 1.56/1.95 1.56/1.95 Low Water (keep): wt=35.000, iters=3339 1.56/1.95 1.56/1.95 Low Water (keep): wt=33.000, iters=3405 1.56/1.95 1.56/1.95 Low Water (keep): wt=31.000, iters=3444 1.56/1.95 1.56/1.95 Low Water (keep): wt=30.000, iters=3373 1.56/1.95 1.56/1.95 Low Water (keep): wt=29.000, iters=3623 1.56/1.95 1.56/1.95 Low Water (keep): wt=28.000, iters=3483 1.56/1.95 1.56/1.95 Low Water (keep): wt=26.000, iters=3337 1.56/1.95 1.56/1.95 Low Water (keep): wt=25.000, iters=3379 1.56/1.95 1.56/1.95 Low Water (keep): wt=24.000, iters=3594 135.11/135.57 135.11/135.57 Low Water (keep): wt=23.000, iters=3478 135.11/135.57 135.11/135.57 Low Water (keep): wt=22.000, iters=3458 135.11/135.57 135.11/135.57 Low Water (keep): wt=21.000, iters=3376 135.11/135.57 135.11/135.57 Low Water (keep): wt=20.000, iters=3396 135.11/135.57 135.11/135.57 Low Water (keep): wt=19.000, iters=3363 135.11/135.57 135.11/135.57 Low Water (keep): wt=18.000, iters=3341 135.11/135.57 135.11/135.57 Low Water (keep): wt=17.000, iters=3352 135.11/135.57 135.11/135.57 Low Water (displace): id=2344, wt=59.000 135.11/135.57 135.11/135.57 Low Water (displace): id=2343, wt=57.000 135.11/135.57 135.11/135.57 Low Water (displace): id=2374, wt=56.000 135.11/135.57 135.11/135.57 Low Water (displace): id=1953, wt=55.000 135.11/135.57 135.11/135.57 Low Water (displace): id=1980, wt=54.000 135.11/135.57 135.11/135.57 Low Water (displace): id=1952, wt=53.000 135.11/135.57 135.11/135.57 Low Water (displace): id=3313, wt=48.000 135.11/135.57 135.11/135.57 Low Water (displace): id=2376, wt=46.000 135.11/135.57 135.11/135.57 Low Water (displace): id=2948, wt=45.000 135.11/135.57 135.11/135.57 Low Water (displace): id=1982, wt=44.000 135.11/135.57 135.11/135.57 Low Water (displace): id=3275, wt=43.000 135.11/135.57 135.11/135.57 Low Water (displace): id=2381, wt=42.000 135.11/135.57 135.11/135.57 Low Water (displace): id=3274, wt=41.000 135.11/135.57 135.11/135.57 Low Water (displace): id=2373, wt=40.000 135.11/135.57 135.11/135.57 Low Water (displace): id=10629, wt=16.000 135.11/135.57 135.11/135.57 Low Water (displace): id=10699, wt=15.000 135.11/135.57 135.11/135.57 Low Water (displace): id=11306, wt=14.000 135.11/135.57 135.11/135.57 Low Water (displace): id=11548, wt=13.000 135.11/135.57 135.11/135.57 Low Water (displace): id=11555, wt=11.000 135.11/135.57 135.11/135.57 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 144 (0.00 of 2.06 sec). 135.11/135.57 135.11/135.57 Low Water (keep): wt=16.000, iters=3337 135.11/135.57 135.11/135.57 Low Water (keep): wt=15.000, iters=3339 135.11/135.57 135.11/135.57 Low Water (displace): id=18564, wt=10.000 135.11/135.57 135.11/135.57 Low Water (keep): wt=14.000, iters=3339 135.11/135.57 135.11/135.57 Low Water (keep): wt=13.000, iters=3335 135.11/135.57 135.11/135.57 Low Water (displace): id=50178, wt=9.000 135.11/135.57 135.11/135.57 Low Water (keep): wt=12.000, iters=3369 135.11/135.57 135.11/135.57 Low Water (displace): id=121714, wt=8.000 135.11/135.57 135.11/135.57 Low Water (keep): wt=11.000, iters=4078 135.11/135.57 135.11/135.57 Low Water (keep): wt=10.000, iters=3334 135.11/135.57 135.11/135.57 ============================== PROOF ================================= 135.11/135.57 % SZS status Theorem 135.11/135.57 % SZS output start Refutation 135.11/135.57 135.11/135.57 % Proof 1 at 125.50 (+ 8.82) seconds. 135.11/135.57 % Length of proof is 252. 135.11/135.57 % Level of proof is 86. 135.11/135.57 % Maximum clause weight is 18.000. 135.11/135.57 % Given clauses 7555. 135.11/135.57 135.11/135.57 4 substitution_of_equivalents <-> (all X all Y (is_a_theorem(equiv(X,Y)) -> X = Y)) # label(substitution_of_equivalents) # label(axiom) # label(non_clause). [assumption]. 135.11/135.57 7 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]. 135.11/135.57 11 cn1 <-> (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))) # label(cn1) # label(axiom) # label(non_clause). [assumption]. 135.11/135.57 14 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]. 135.11/135.57 15 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption]. 135.11/135.57 16 (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))) <-> kn3 # label(kn3) # label(axiom) # label(non_clause). [assumption]. 135.11/135.57 19 (all P is_a_theorem(implies(P,and(P,P)))) <-> kn1 # label(kn1) # label(axiom) # label(non_clause). [assumption]. 135.11/135.57 27 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]. 135.11/135.57 28 op_implies_and -> (all X all Y implies(X,Y) = not(and(X,not(Y)))) # label(op_implies_and) # label(axiom) # label(non_clause). [assumption]. 135.11/135.57 32 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption]. 135.11/135.57 33 op_implies_and # label(rosser_op_implies_and) # label(axiom). [assumption]. 135.11/135.57 34 op_equiv # label(rosser_op_equiv) # label(axiom). [assumption]. 135.11/135.57 35 modus_ponens # label(rosser_modus_ponens) # label(axiom). [assumption]. 135.11/135.57 36 kn1 # label(rosser_kn1) # label(axiom). [assumption]. 135.11/135.57 38 kn2 # label(rosser_kn2) # label(axiom). [assumption]. 135.11/135.57 39 kn3 # label(rosser_kn3) # label(axiom). [assumption]. 135.11/135.57 40 -implies_3 # label(hilbert_implies_3) # label(negated_conjecture). [assumption]. 135.11/135.57 49 -kn2 | is_a_theorem(implies(and(A,B),A)) # label(kn2) # label(axiom). [clausify(15)]. 135.11/135.57 50 is_a_theorem(implies(and(A,B),A)). [copy(49),unit_del(a,38)]. 135.11/135.57 52 is_a_theorem(implies(A,and(A,A))) | -kn1 # label(kn1) # label(axiom). [clausify(19)]. 135.11/135.57 53 is_a_theorem(implies(A,and(A,A))). [copy(52),unit_del(b,36)]. 135.11/135.57 62 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(4)]. 135.11/135.57 63 -is_a_theorem(equiv(A,B)) | B = A. [copy(62),unit_del(a,32)]. 135.11/135.57 70 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(14)]. 135.11/135.57 71 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(70),unit_del(a,35)]. 135.11/135.57 77 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(28)]. 135.11/135.57 78 not(and(A,not(B))) = implies(A,B). [copy(77),unit_del(a,33)]. 135.11/135.57 87 -op_equiv | equiv(A,B) = and(implies(A,B),implies(B,A)) # label(op_equiv) # label(axiom). [clausify(27)]. 135.11/135.57 88 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(87),flip(b),unit_del(a,34)]. 135.11/135.57 89 implies_3 | -is_a_theorem(implies(implies(c14,c15),implies(implies(c15,c16),implies(c14,c16)))) # label(implies_3) # label(axiom). [clausify(7)]. 135.11/135.57 90 -is_a_theorem(implies(implies(c14,c15),implies(implies(c15,c16),implies(c14,c16)))). [copy(89),unit_del(a,40)]. 135.11/135.57 91 -cn1 | is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))) # label(cn1) # label(axiom). [clausify(11)]. 135.11/135.57 92 cn1 | -is_a_theorem(implies(implies(c23,c24),implies(implies(c24,c25),implies(c23,c25)))) # label(cn1) # label(axiom). [clausify(11)]. 135.11/135.57 107 is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))) | -kn3 # label(kn3) # label(axiom). [clausify(16)]. 135.11/135.57 108 is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))). [copy(107),unit_del(b,39)]. 135.11/135.57 124 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(78(a,1),78(a,1,1,2))]. 135.11/135.57 131 -cn1. [ur(91,b,90,a)]. 135.11/135.57 132 -is_a_theorem(implies(implies(c23,c24),implies(implies(c24,c25),implies(c23,c25)))). [back_unit_del(92),unit_del(a,131)]. 135.11/135.57 133 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(and(B,C)),not(and(C,A)))). [resolve(108,a,71,b)]. 135.11/135.57 135 is_a_theorem(implies(implies(A,B),implies(implies(B,C),not(and(not(C),A))))). [para(78(a,1),108(a,1,2,1))]. 135.11/135.57 138 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(C,and(B,not(A))),not(equiv(B,A))))). [para(88(a,1),108(a,1,2,2,1)),rewrite([124(5)])]. 135.11/135.57 168 implies(implies(A,B),and(B,not(A))) = not(equiv(A,B)). [para(88(a,1),124(a,1,1)),flip(a)]. 135.11/135.57 265 is_a_theorem(implies(not(and(and(A,A),B)),not(and(B,A)))). [resolve(133,a,53,a)]. 135.11/135.57 270 -is_a_theorem(not(and(and(A,A),B))) | is_a_theorem(not(and(B,A))). [resolve(265,a,71,b)]. 135.11/135.57 363 -is_a_theorem(implies(and(A,A),B)) | is_a_theorem(not(and(not(B),A))). [para(78(a,1),270(a,1))]. 135.11/135.57 485 is_a_theorem(not(and(not(A),A))). [resolve(363,a,50,a)]. 135.11/135.57 512 is_a_theorem(not(and(implies(A,B),and(A,not(B))))). [para(78(a,1),485(a,1,1,1))]. 135.11/135.57 513 is_a_theorem(implies(not(not(A)),A)). [para(78(a,1),485(a,1))]. 135.11/135.57 516 is_a_theorem(implies(not(and(A,B)),implies(B,not(A)))). [resolve(513,a,133,a),rewrite([78(6)])]. 135.11/135.57 518 -is_a_theorem(not(not(A))) | is_a_theorem(A). [resolve(513,a,71,b)]. 135.11/135.57 763 -is_a_theorem(not(and(A,B))) | is_a_theorem(implies(B,not(A))). [resolve(516,a,71,b)]. 135.11/135.57 791 is_a_theorem(implies(implies(A,B),implies(not(B),not(A)))). [para(78(a,1),516(a,1,1))]. 135.11/135.57 1272 is_a_theorem(implies(and(A,not(B)),not(implies(A,B)))). [resolve(763,a,512,a)]. 135.11/135.57 1273 is_a_theorem(implies(A,not(not(A)))). [resolve(763,a,485,a)]. 135.11/135.57 1274 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(B),not(A))). [para(78(a,1),763(a,1))]. 135.11/135.57 1436 is_a_theorem(not(and(not(not(not(and(A,A)))),A))). [resolve(1273,a,363,a)]. 135.11/135.57 1439 -is_a_theorem(A) | is_a_theorem(not(not(A))). [resolve(1273,a,71,b)]. 135.11/135.57 1480 is_a_theorem(not(not(implies(A,not(not(A)))))). [resolve(1439,a,1273,a)]. 135.11/135.57 1490 is_a_theorem(not(not(not(and(not(A),A))))). [resolve(1439,a,485,a)]. 135.11/135.57 1504 is_a_theorem(not(not(implies(A,and(A,A))))). [resolve(1439,a,53,a)]. 135.11/135.57 3569 -is_a_theorem(and(A,not(B))) | is_a_theorem(not(implies(A,B))). [resolve(1272,a,71,b)]. 135.11/135.57 3989 is_a_theorem(implies(not(implies(A,not(B))),not(not(and(B,A))))). [resolve(1274,a,516,a)]. 135.11/135.57 4001 is_a_theorem(implies(not(and(A,A)),not(A))). [resolve(1274,a,53,a)]. 135.11/135.57 4002 is_a_theorem(implies(not(A),not(and(A,B)))). [resolve(1274,a,50,a)]. 135.11/135.57 4006 is_a_theorem(implies(not(not(A)),not(not(and(A,A))))). [resolve(4001,a,1274,a)]. 135.11/135.57 4009 -is_a_theorem(not(and(A,A))) | is_a_theorem(not(A)). [resolve(4001,a,71,b)]. 135.11/135.57 4105 -is_a_theorem(not(A)) | is_a_theorem(not(and(A,B))). [resolve(4002,a,71,b)]. 135.11/135.57 4171 is_a_theorem(implies(not(A),implies(A,B))). [para(78(a,1),4002(a,1,2))]. 135.11/135.57 4410 is_a_theorem(implies(not(and(implies(A,B),C)),implies(C,A))). [resolve(4171,a,133,a),rewrite([78(6)])]. 135.11/135.57 4412 -is_a_theorem(not(A)) | is_a_theorem(implies(A,B)). [resolve(4171,a,71,b)]. 135.11/135.57 4496 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(and(A,not(B)),C)). [para(78(a,1),4412(a,1))]. 135.11/135.57 4576 -is_a_theorem(implies(not(A),A)) | is_a_theorem(not(not(A))). [para(78(a,1),4009(a,1))]. 135.11/135.57 4820 is_a_theorem(not(and(not(implies(A,and(A,A))),B))). [resolve(4105,a,1504,a)]. 135.11/135.57 4824 is_a_theorem(not(and(not(implies(A,not(not(A)))),B))). [resolve(4105,a,1480,a)]. 135.11/135.57 4829 is_a_theorem(not(and(and(not(A),A),B))). [resolve(4105,a,485,a)]. 135.11/135.57 4833 is_a_theorem(not(and(and(and(not(A),A),B),C))). [resolve(4829,a,4105,a)]. 135.11/135.57 4837 is_a_theorem(implies(A,not(and(not(B),B)))). [resolve(4829,a,763,a)]. 135.11/135.57 6711 is_a_theorem(implies(A,not(not(not(not(and(A,A))))))). [resolve(1436,a,763,a)]. 135.11/135.57 8306 is_a_theorem(implies(not(not(not(and(A,A)))),not(not(not(A))))). [resolve(4006,a,1274,a)]. 135.11/135.57 8309 -is_a_theorem(not(not(A))) | is_a_theorem(not(not(and(A,A)))). [resolve(4006,a,71,b)]. 135.11/135.57 9170 is_a_theorem(not(and(A,and(not(B),B)))). [resolve(4833,a,270,a)]. 135.11/135.57 9521 -is_a_theorem(A) | is_a_theorem(not(not(not(not(and(A,A)))))). [resolve(6711,a,71,b)]. 135.11/135.57 9678 is_a_theorem(not(implies(not(and(not(A),A)),and(not(A),A)))). [resolve(8309,a,1490,a),rewrite([78(8)])]. 135.11/135.57 10939 -is_a_theorem(not(and(implies(A,B),C))) | is_a_theorem(implies(C,A)). [resolve(4410,a,71,b)]. 135.11/135.57 10949 is_a_theorem(implies(implies(implies(A,B),C),implies(not(C),A))). [para(78(a,1),4410(a,1,1))]. 135.11/135.57 10950 is_a_theorem(implies(not(equiv(A,B)),implies(implies(B,A),A))). [para(88(a,1),4410(a,1,1,1))]. 135.11/135.57 12806 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(not(C),A)). [para(78(a,1),10939(a,1))]. 135.11/135.57 13419 is_a_theorem(implies(not(implies(not(A),B)),implies(B,C))). [resolve(12806,a,10949,a)]. 135.11/135.57 13428 is_a_theorem(implies(not(implies(not(A),not(B))),B)). [resolve(12806,a,791,a)]. 135.11/135.57 14056 is_a_theorem(not(not(implies(not(A),not(A))))). [resolve(13419,a,4576,a)]. 135.11/135.57 14084 is_a_theorem(implies(not(A),not(A))). [resolve(14056,a,518,a)]. 135.11/135.57 14117 is_a_theorem(implies(not(and(not(A),B)),implies(B,A))). [resolve(14084,a,133,a),rewrite([78(6)])]. 135.11/135.57 15693 -is_a_theorem(not(and(not(A),B))) | is_a_theorem(implies(B,A)). [resolve(14117,a,71,b)]. 135.11/135.57 15712 is_a_theorem(implies(implies(not(A),B),implies(not(B),A))). [para(78(a,1),14117(a,1,1))]. 135.11/135.57 15715 is_a_theorem(implies(not(equiv(A,B)),not(equiv(B,A)))). [para(168(a,1),14117(a,1,2)),rewrite([78(3),88(3)])]. 135.11/135.57 16111 is_a_theorem(implies(A,implies(B,not(not(B))))). [resolve(15693,a,4824,a)]. 135.11/135.57 16113 is_a_theorem(implies(A,implies(B,and(B,B)))). [resolve(15693,a,4820,a)]. 135.11/135.57 16118 is_a_theorem(implies(A,not(not(and(A,A))))). [resolve(15693,a,1436,a)]. 135.11/135.57 16120 is_a_theorem(implies(A,A)). [resolve(15693,a,485,a)]. 135.11/135.57 16124 -is_a_theorem(implies(not(A),B)) | is_a_theorem(implies(not(B),A)). [para(78(a,1),15693(a,1))]. 135.11/135.57 16144 is_a_theorem(not(not(not(not(equiv(A,A)))))). [resolve(16120,a,9521,a),rewrite([88(3)])]. 135.11/135.57 16145 is_a_theorem(implies(and(A,not(A)),B)). [resolve(16120,a,4496,a)]. 135.11/135.57 16150 is_a_theorem(implies(not(and(A,B)),not(and(B,A)))). [resolve(16120,a,133,a)]. 135.11/135.57 17599 is_a_theorem(implies(not(A),implies(B,B))). [resolve(16145,a,1274,a),rewrite([78(4)])]. 135.11/135.57 18039 is_a_theorem(implies(not(and(implies(A,A),B)),implies(B,C))). [resolve(17599,a,133,a),rewrite([78(6)])]. 135.11/135.57 18358 is_a_theorem(implies(not(A),not(implies(not(A),A)))). [para(78(a,1),16118(a,1,2,1))]. 135.11/135.57 18502 is_a_theorem(not(not(not(not(not(not(equiv(A,A)))))))). [resolve(16144,a,1439,a)]. 135.11/135.57 20011 -is_a_theorem(not(A)) | is_a_theorem(not(implies(not(A),A))). [resolve(18358,a,71,b)]. 135.11/135.57 20585 is_a_theorem(implies(not(implies(not(A),B)),not(B))). [resolve(15712,a,12806,a)]. 135.11/135.57 20728 -is_a_theorem(not(equiv(A,B))) | is_a_theorem(not(equiv(B,A))). [resolve(15715,a,71,b)]. 135.11/135.57 20810 is_a_theorem(implies(not(not(A)),implies(not(B),A))). [resolve(16124,a,20585,a)]. 135.11/135.57 20812 is_a_theorem(implies(not(implies(A,B)),and(not(B),A))). [resolve(16124,a,14117,a)]. 135.11/135.57 20818 is_a_theorem(implies(not(implies(implies(A,B),B)),equiv(B,A))). [resolve(16124,a,10950,a)]. 135.11/135.57 20823 is_a_theorem(implies(not(implies(A,B)),and(implies(B,C),A))). [resolve(16124,a,4410,a)]. 135.11/135.57 21630 is_a_theorem(implies(not(implies(not(A),B)),not(not(not(B))))). [resolve(20810,a,1274,a)]. 135.11/135.57 21931 is_a_theorem(implies(not(not(and(A,B))),and(B,A))). [resolve(16150,a,16124,a)]. 135.11/135.57 21942 -is_a_theorem(not(and(A,B))) | is_a_theorem(not(and(B,A))). [resolve(16150,a,71,b)]. 135.11/135.57 23371 -is_a_theorem(not(implies(A,B))) | is_a_theorem(and(not(B),A)). [resolve(20812,a,71,b)]. 135.11/135.57 24419 -is_a_theorem(not(not(and(A,B)))) | is_a_theorem(and(B,A)). [resolve(21931,a,71,b)]. 135.11/135.57 24484 -is_a_theorem(implies(A,B)) | is_a_theorem(not(and(not(B),A))). [para(78(a,1),21942(a,1))]. 135.11/135.57 38224 is_a_theorem(implies(not(implies(A,B)),and(implies(C,C),A))). [resolve(18039,a,24484,a),rewrite([78(7)])]. 135.11/135.57 40818 -is_a_theorem(not(implies(implies(A,B),B))) | is_a_theorem(equiv(B,A)). [resolve(20818,a,71,b)]. 135.11/135.57 40964 -is_a_theorem(not(implies(A,B))) | is_a_theorem(and(implies(B,C),A)). [resolve(20823,a,71,b)]. 135.11/135.57 41455 is_a_theorem(implies(not(not(not(not(A)))),implies(not(B),A))). [resolve(21630,a,24484,a),rewrite([78(9)])]. 135.11/135.57 53788 -is_a_theorem(not(implies(A,B))) | is_a_theorem(and(implies(C,C),A)). [resolve(38224,a,71,b)]. 135.11/135.57 75532 -is_a_theorem(not(implies(A,not(B)))) | is_a_theorem(not(not(and(B,A)))). [resolve(3989,a,71,b)]. 135.11/135.57 81667 is_a_theorem(implies(not(not(not(not(A)))),not(not(and(A,A))))). [resolve(8306,a,24484,a),rewrite([78(10)])]. 135.11/135.57 84705 is_a_theorem(and(implies(A,A),not(and(not(B),B)))). [resolve(9678,a,53788,a)]. 135.11/135.57 84827 is_a_theorem(not(implies(implies(A,A),and(not(B),B)))). [resolve(84705,a,3569,a)]. 135.11/135.57 84937 is_a_theorem(and(not(and(not(A),A)),implies(B,B))). [resolve(84827,a,23371,a)]. 135.11/135.57 85150 is_a_theorem(not(implies(not(and(not(A),A)),and(B,not(B))))). [resolve(84937,a,1439,a),rewrite([124(6)])]. 135.11/135.57 85154 is_a_theorem(and(implies(not(not(A)),A),implies(B,B))). [para(78(a,1),84937(a,1,1))]. 135.11/135.57 85292 is_a_theorem(not(implies(implies(not(not(A)),A),and(B,not(B))))). [resolve(85154,a,1439,a),rewrite([124(6)])]. 135.11/135.57 103688 -is_a_theorem(not(not(not(not(A))))) | is_a_theorem(not(not(and(A,A)))). [resolve(81667,a,71,b)]. 135.11/135.57 105665 is_a_theorem(and(implies(and(A,not(A)),B),not(and(not(C),C)))). [resolve(85150,a,40964,a)]. 135.11/135.57 105787 is_a_theorem(equiv(and(A,not(A)),not(implies(A,A)))). [resolve(85292,a,40818,a),rewrite([78(5)])]. 135.11/135.57 105859 not(implies(A,A)) = and(A,not(A)). [resolve(105787,a,63,a)]. 135.11/135.57 108926 is_a_theorem(not(implies(not(not(equiv(A,A))),not(equiv(A,A))))). [resolve(103688,a,18502,a),rewrite([78(8)])]. 135.11/135.57 114571 is_a_theorem(and(implies(A,A),not(not(equiv(B,B))))). [resolve(108926,a,53788,a)]. 135.11/135.57 114758 is_a_theorem(not(implies(implies(A,A),not(equiv(B,B))))). [resolve(114571,a,3569,a)]. 135.11/135.57 115216 is_a_theorem(and(implies(not(equiv(A,A)),B),implies(C,C))). [resolve(114758,a,40964,a)]. 135.11/135.57 135420 is_a_theorem(not(implies(implies(and(A,not(A)),B),and(not(C),C)))). [resolve(105665,a,3569,a)]. 135.11/135.57 141661 is_a_theorem(equiv(and(not(A),A),and(B,not(B)))). [resolve(135420,a,40818,a)]. 135.11/135.57 141742 and(not(A),A) = and(B,not(B)). [resolve(141661,a,63,a),flip(a)]. 135.11/135.57 141749 and(not(A),A) = c_0. [new_symbol(141742)]. 135.11/135.57 141751 and(A,not(A)) = c_0. [back_rewrite(141742),rewrite([141749(2)]),flip(a)]. 135.11/135.57 142276 is_a_theorem(not(and(A,c_0))). [back_rewrite(9170),rewrite([141749(2)])]. 135.11/135.57 142455 is_a_theorem(implies(A,not(c_0))). [back_rewrite(4837),rewrite([141749(2)])]. 135.11/135.57 142459 is_a_theorem(not(and(c_0,A))). [back_rewrite(4829),rewrite([141749(2)])]. 135.11/135.57 142517 is_a_theorem(not(c_0)). [back_rewrite(485),rewrite([141749(2)])]. 135.11/135.57 142618 not(implies(A,A)) = c_0. [back_rewrite(105859),rewrite([141751(4)])]. 135.11/135.57 143733 is_a_theorem(not(implies(not(and(A,c_0)),and(A,c_0)))). [resolve(142276,a,20011,a)]. 135.11/135.57 143822 is_a_theorem(implies(not(and(not(c_0),A)),not(and(A,B)))). [resolve(142455,a,133,a)]. 135.11/135.57 143904 is_a_theorem(not(implies(not(and(c_0,A)),and(c_0,A)))). [resolve(142459,a,20011,a)]. 135.11/135.57 144111 implies(not(not(A)),A) = not(c_0). [para(141749(a,1),78(a,1,1)),flip(a)]. 135.11/135.57 144153 implies(A,A) = not(c_0). [para(141751(a,1),78(a,1,1)),flip(a)]. 135.11/135.57 144157 not(equiv(A,A)) = implies(not(c_0),c_0). [para(141751(a,1),168(a,1,2)),rewrite([144153(1)]),flip(a)]. 135.11/135.57 144265 not(not(c_0)) = c_0. [back_rewrite(142618),rewrite([144153(1)])]. 135.11/135.57 144370 is_a_theorem(and(implies(not(equiv(A,A)),B),not(c_0))). [back_rewrite(115216),rewrite([144153(4)])]. 135.11/135.57 144459 -is_a_theorem(not(implies(A,B))) | is_a_theorem(and(not(c_0),A)). [back_rewrite(53788),rewrite([144153(4)])]. 135.11/135.57 144512 not(and(A,c_0)) = implies(A,not(c_0)). [para(144265(a,1),78(a,1,1,2))]. 135.11/135.57 144529 -is_a_theorem(not(implies(A,c_0))) | is_a_theorem(not(not(and(not(c_0),A)))). [para(144265(a,1),75532(a,1,1,2))]. 135.11/135.57 144556 is_a_theorem(not(implies(implies(A,not(c_0)),and(A,c_0)))). [back_rewrite(143733),rewrite([144512(3)])]. 135.11/135.57 151787 not(equiv(A,A)) = not(equiv(B,B)). [para(144157(a,2),144157(a,2))]. 135.11/135.57 154792 and(equiv(A,A),not(equiv(B,B))) = c_0. [para(151787(a,1),141751(a,1,2))]. 135.11/135.57 159331 is_a_theorem(not(implies(implies(not(equiv(A,A)),B),c_0))). [resolve(144370,a,3569,a)]. 135.11/135.57 159575 is_a_theorem(and(not(c_0),not(and(c_0,A)))). [resolve(144459,a,143904,a)]. 135.11/135.57 159621 is_a_theorem(not(implies(not(c_0),and(c_0,A)))). [resolve(159575,a,3569,a)]. 135.11/135.57 159724 is_a_theorem(and(implies(and(c_0,A),B),not(c_0))). [resolve(159621,a,40964,a)]. 135.11/135.57 160165 is_a_theorem(not(implies(implies(and(c_0,A),B),c_0))). [resolve(159724,a,3569,a)]. 135.11/135.57 160480 is_a_theorem(equiv(c_0,and(c_0,A))). [resolve(160165,a,40818,a)]. 135.11/135.57 160546 and(c_0,A) = c_0. [resolve(160480,a,63,a)]. 135.11/135.57 160547 implies(c_0,A) = not(c_0). [para(160546(a,1),78(a,1,1)),flip(a)]. 135.11/135.57 160549 implies(implies(A,c_0),c_0) = not(equiv(A,c_0)). [para(160546(a,1),168(a,1,2))]. 135.11/135.57 160593 implies(not(c_0),and(A,not(c_0))) = not(equiv(c_0,A)). [para(160547(a,1),168(a,1,1))]. 135.11/135.57 160601 -is_a_theorem(not(implies(not(c_0),A))) | is_a_theorem(equiv(A,c_0)). [para(160547(a,1),40818(a,1,1,1))]. 135.11/135.57 160779 is_a_theorem(and(not(c_0),implies(A,not(c_0)))). [resolve(144556,a,144459,a)]. 135.11/135.57 160878 is_a_theorem(not(implies(not(c_0),and(A,c_0)))). [resolve(160779,a,1439,a),rewrite([124(7),144265(5)])]. 135.11/135.57 160914 is_a_theorem(and(implies(and(A,c_0),B),not(c_0))). [resolve(160878,a,40964,a)]. 135.11/135.57 161438 is_a_theorem(not(implies(implies(and(A,c_0),B),c_0))). [resolve(160914,a,3569,a)]. 135.11/135.57 161716 is_a_theorem(equiv(c_0,and(A,c_0))). [resolve(161438,a,40818,a)]. 135.11/135.57 161767 and(A,c_0) = c_0. [resolve(161716,a,63,a)]. 135.11/135.57 162016 implies(A,not(c_0)) = not(c_0). [back_rewrite(144512),rewrite([161767(2)]),flip(a)]. 135.11/135.57 162031 and(not(c_0),implies(not(c_0),A)) = equiv(A,not(c_0)). [para(162016(a,1),88(a,1,1))]. 135.11/135.57 162034 implies(not(c_0),and(not(c_0),not(A))) = not(equiv(A,not(c_0))). [para(162016(a,1),168(a,1,1))]. 135.11/135.57 165484 implies(equiv(A,A),equiv(B,B)) = not(c_0). [para(154792(a,1),78(a,1,1)),flip(a)]. 135.11/135.57 165486 not(equiv(equiv(A,A),equiv(B,B))) = implies(not(c_0),c_0). [para(154792(a,1),168(a,1,2)),rewrite([165484(3)]),flip(a)]. 135.11/135.57 165488 is_a_theorem(implies(implies(not(c_0),A),implies(implies(A,c_0),implies(not(c_0),c_0)))). [para(154792(a,1),138(a,1,2,1,2)),rewrite([165484(3),165486(9)])]. 135.11/135.57 166347 is_a_theorem(equiv(c_0,not(equiv(A,A)))). [resolve(159331,a,40818,a)]. 135.11/135.57 166417 not(equiv(A,A)) = c_0. [resolve(166347,a,63,a)]. 135.11/135.57 166437 implies(not(c_0),c_0) = c_0. [back_rewrite(144157),rewrite([166417(2)]),flip(a)]. 135.11/135.57 166438 is_a_theorem(implies(implies(not(c_0),A),not(equiv(A,c_0)))). [back_rewrite(165488),rewrite([166437(9),160549(7)])]. 135.11/135.57 167139 -is_a_theorem(implies(not(c_0),A)) | is_a_theorem(not(equiv(A,c_0))). [resolve(166438,a,71,b)]. 135.11/135.57 167348 is_a_theorem(not(equiv(implies(A,and(A,A)),c_0))). [resolve(167139,a,16113,a)]. 135.11/135.57 167350 is_a_theorem(not(equiv(implies(A,not(not(A))),c_0))). [resolve(167139,a,16111,a)]. 135.11/135.57 167503 is_a_theorem(not(equiv(c_0,implies(A,and(A,A))))). [resolve(167348,a,20728,a)]. 135.11/135.57 167569 is_a_theorem(not(equiv(c_0,implies(A,not(not(A)))))). [resolve(167350,a,20728,a)]. 135.11/135.57 169701 is_a_theorem(implies(not(not(and(A,B))),and(not(c_0),A))). [resolve(143822,a,24484,a),rewrite([78(9)])]. 135.11/135.57 177424 is_a_theorem(not(not(implies(not(not(and(A,B))),and(not(c_0),A))))). [resolve(169701,a,1439,a)]. 135.11/135.57 177429 -is_a_theorem(not(not(and(A,B)))) | is_a_theorem(and(not(c_0),A)). [resolve(169701,a,71,b)]. 135.11/135.57 188656 -is_a_theorem(not(equiv(c_0,A))) | is_a_theorem(and(A,not(c_0))). [para(160593(a,1),71(b,1)),unit_del(a,142517)]. 135.11/135.57 188729 is_a_theorem(and(implies(A,not(not(A))),not(c_0))). [resolve(188656,a,167569,a)]. 135.11/135.57 188730 is_a_theorem(and(implies(A,and(A,A)),not(c_0))). [resolve(188656,a,167503,a)]. 135.11/135.57 188900 is_a_theorem(not(implies(implies(A,not(not(A))),c_0))). [resolve(188729,a,3569,a)]. 135.11/135.57 188942 is_a_theorem(not(implies(implies(A,and(A,A)),c_0))). [resolve(188730,a,3569,a)]. 135.11/135.57 188989 is_a_theorem(not(implies(not(c_0),and(A,not(not(not(A))))))). [resolve(188900,a,144529,a),rewrite([124(7)])]. 135.11/135.57 189048 is_a_theorem(and(not(c_0),implies(A,and(A,A)))). [resolve(188942,a,144459,a)]. 135.11/135.57 192957 is_a_theorem(equiv(and(A,not(not(not(A)))),c_0)). [resolve(188989,a,160601,a)]. 135.11/135.57 193067 and(A,not(not(not(A)))) = c_0. [resolve(192957,a,63,a),flip(a)]. 135.11/135.57 193075 not(equiv(not(not(A)),A)) = c_0. [para(193067(a,1),168(a,1,2)),rewrite([144111(3),166437(4)]),flip(a)]. 135.11/135.57 193108 is_a_theorem(equiv(not(not(A)),A)). [para(193075(a,1),518(a,1,1)),unit_del(a,142517)]. 135.11/135.57 193185 not(not(A)) = A. [resolve(193108,a,63,a),flip(a)]. 135.11/135.57 193230 -is_a_theorem(and(A,B)) | is_a_theorem(and(not(c_0),A)). [back_rewrite(177429),rewrite([193185(3)])]. 135.11/135.57 193231 is_a_theorem(implies(and(A,B),and(not(c_0),A))). [back_rewrite(177424),rewrite([193185(3),193185(7)])]. 135.11/135.57 193431 is_a_theorem(implies(A,implies(not(B),A))). [back_rewrite(41455),rewrite([193185(2),193185(2)])]. 135.11/135.57 193452 -is_a_theorem(and(A,B)) | is_a_theorem(and(B,A)). [back_rewrite(24419),rewrite([193185(3)])]. 135.11/135.57 193463 is_a_theorem(implies(and(A,B),and(B,A))). [back_rewrite(21931),rewrite([193185(3)])]. 135.11/135.57 193519 not(and(A,B)) = implies(A,not(B)). [para(193185(a,1),78(a,1,1,2))]. 135.11/135.57 193520 not(implies(A,B)) = and(A,not(B)). [para(78(a,1),193185(a,1,1))]. 135.11/135.57 193546 is_a_theorem(implies(and(A,B),B)). [para(193185(a,1),13428(a,1,1,1,1)),rewrite([193520(3),193185(2)])]. 135.11/135.57 193983 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(not(C),not(A))))). [back_rewrite(135),rewrite([193519(5)])]. 135.11/135.57 194109 -is_a_theorem(and(not(c_0),not(A))) | is_a_theorem(equiv(A,c_0)). [back_rewrite(160601),rewrite([193520(4)])]. 135.11/135.57 197935 is_a_theorem(implies(A,implies(B,A))). [para(193185(a,1),193431(a,1,2,1))]. 135.11/135.57 197943 -is_a_theorem(A) | is_a_theorem(implies(B,A)). [resolve(197935,a,71,b)]. 135.11/135.57 198026 is_a_theorem(implies(A,implies(and(B,C),C))). [resolve(197943,a,193546,a)]. 135.11/135.57 198742 is_a_theorem(not(equiv(implies(and(A,B),B),c_0))). [resolve(198026,a,167139,a)]. 135.11/135.57 200652 is_a_theorem(not(equiv(c_0,implies(and(A,B),B)))). [resolve(198742,a,20728,a)]. 135.11/135.57 201000 is_a_theorem(and(implies(and(A,B),B),not(c_0))). [resolve(200652,a,188656,a)]. 135.11/135.57 201392 is_a_theorem(and(not(c_0),implies(and(A,B),B))). [resolve(201000,a,193452,a)]. 135.11/135.57 201820 -is_a_theorem(and(not(c_0),A)) | is_a_theorem(equiv(not(A),c_0)). [para(193185(a,1),194109(a,1,2))]. 135.11/135.57 202373 is_a_theorem(equiv(and(and(A,B),not(B)),c_0)). [resolve(201820,a,201392,a),rewrite([193520(3)])]. 135.11/135.57 202398 and(and(A,B),not(B)) = c_0. [resolve(202373,a,63,a),flip(a)]. 135.11/135.57 202413 implies(and(A,B),B) = not(c_0). [para(202398(a,1),193519(a,1,1)),rewrite([193185(5)]),flip(a)]. 135.11/135.57 202632 and(not(c_0),implies(A,and(B,A))) = equiv(and(B,A),A). [para(202413(a,1),88(a,1,1))]. 135.11/135.57 202643 is_a_theorem(equiv(and(A,A),A)). [back_rewrite(189048),rewrite([202632(5)])]. 135.11/135.57 202659 and(A,A) = A. [resolve(202643,a,63,a),flip(a)]. 135.11/135.57 202725 -is_a_theorem(A) | is_a_theorem(and(not(c_0),A)). [para(202659(a,1),193230(a,1))]. 135.11/135.57 202726 is_a_theorem(implies(A,and(not(c_0),A))). [para(202659(a,1),193231(a,1,1))]. 135.11/135.57 202900 is_a_theorem(equiv(and(not(c_0),A),A)). [resolve(202726,a,202725,a),rewrite([202632(7)])]. 135.11/135.57 203371 and(not(c_0),A) = A. [resolve(202900,a,63,a),flip(a)]. 135.11/135.57 203572 not(equiv(A,not(c_0))) = implies(not(c_0),not(A)). [back_rewrite(162034),rewrite([203371(6)]),flip(a)]. 135.11/135.57 203573 equiv(A,not(c_0)) = implies(not(c_0),A). [back_rewrite(162031),rewrite([203371(6)]),flip(a)]. 135.11/135.57 203578 implies(not(c_0),not(A)) = not(A). [back_rewrite(203572),rewrite([203573(3),193520(4),203371(4)]),flip(a)]. 135.11/135.57 208285 implies(not(c_0),A) = A. [para(193185(a,1),203578(a,1,2)),rewrite([193185(5)])]. 135.11/135.57 208292 equiv(A,not(c_0)) = A. [back_rewrite(203573),rewrite([208285(6)])]. 135.11/135.57 208330 -is_a_theorem(A) | not(c_0) = A. [para(208292(a,1),63(a,1))]. 135.11/135.57 208367 implies(and(A,B),and(B,A)) = not(c_0). [resolve(208330,a,193463,a),flip(a)]. 135.11/135.57 210810 equiv(and(A,B),and(B,A)) = not(c_0). [para(208367(a,1),88(a,1,1)),rewrite([208367(5),202659(5)]),flip(a)]. 135.11/135.57 211123 and(A,B) = and(B,A). [para(210810(a,1),63(a,1)),unit_del(a,142517)]. 135.11/135.57 211629 implies(A,not(B)) = implies(B,not(A)). [para(211123(a,1),193519(a,1,1)),rewrite([193519(2)])]. 135.11/135.57 211675 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))). [back_rewrite(193983),rewrite([211629(5),193185(4)])]. 135.11/135.57 211676 $F. [resolve(211675,a,132,a)]. 135.11/135.57 135.11/135.57 % SZS output end Refutation 135.11/135.57 ============================== end of proof ========================== 135.11/135.57 135.11/135.57 ============================== STATISTICS ============================ 135.11/135.57 135.11/135.57 Given=7555. Generated=10962266. Kept=211627. proofs=1. 135.11/135.57 Usable=271. Sos=844. Demods=140. Limbo=46, Disabled=210537. Hints=0. 135.11/135.57 Megabytes=141.14. 135.11/135.57 User_CPU=125.51, System_CPU=8.82, Wall_clock=134. 135.11/135.57 135.11/135.57 ============================== end of statistics ===================== 135.11/135.57 135.11/135.57 ============================== end of search ========================= 135.11/135.57 135.11/135.57 THEOREM PROVED 135.11/135.57 % SZS status Theorem 135.11/135.57 135.11/135.57 Exiting with 1 proof. 135.11/135.57 135.11/135.57 Process 21982 exit (max_proofs) Mon Jul 3 10:40:45 2023 135.11/135.57 Prover9 interrupted 135.11/135.58 EOF