0.04/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.14/0.35 % Computer : n013.cluster.edu 0.14/0.35 % Model : x86_64 x86_64 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.35 % Memory : 8042.1875MB 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.35 % CPULimit : 180 0.14/0.35 % DateTime : Thu Aug 29 15:33:16 EDT 2019 0.14/0.35 % CPUTime : 0.49/1.06 ============================== Prover9 =============================== 0.49/1.06 Prover9 (32) version 2009-11A, November 2009. 0.49/1.06 Process 3296 was started by sandbox on n013.cluster.edu, 0.49/1.06 Thu Aug 29 15:33:17 2019 0.49/1.06 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 180 -f /tmp/Prover9_3140_n013.cluster.edu". 0.49/1.06 ============================== end of head =========================== 0.49/1.06 0.49/1.06 ============================== INPUT ================================= 0.49/1.06 0.49/1.06 % Reading from file /tmp/Prover9_3140_n013.cluster.edu 0.49/1.06 0.49/1.06 set(prolog_style_variables). 0.49/1.06 set(auto2). 0.49/1.06 % set(auto2) -> set(auto). 0.49/1.06 % set(auto) -> set(auto_inference). 0.49/1.06 % set(auto) -> set(auto_setup). 0.49/1.06 % set(auto_setup) -> set(predicate_elim). 0.49/1.06 % set(auto_setup) -> assign(eq_defs, unfold). 0.49/1.06 % set(auto) -> set(auto_limits). 0.49/1.06 % set(auto_limits) -> assign(max_weight, "100.000"). 0.49/1.06 % set(auto_limits) -> assign(sos_limit, 20000). 0.49/1.06 % set(auto) -> set(auto_denials). 0.49/1.06 % set(auto) -> set(auto_process). 0.49/1.06 % set(auto2) -> assign(new_constants, 1). 0.49/1.06 % set(auto2) -> assign(fold_denial_max, 3). 0.49/1.06 % set(auto2) -> assign(max_weight, "200.000"). 0.49/1.06 % set(auto2) -> assign(max_hours, 1). 0.49/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.49/1.06 % set(auto2) -> assign(max_seconds, 0). 0.49/1.06 % set(auto2) -> assign(max_minutes, 5). 0.49/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.49/1.06 % set(auto2) -> set(sort_initial_sos). 0.49/1.06 % set(auto2) -> assign(sos_limit, -1). 0.49/1.06 % set(auto2) -> assign(lrs_ticks, 3000). 0.49/1.06 % set(auto2) -> assign(max_megs, 400). 0.49/1.06 % set(auto2) -> assign(stats, some). 0.49/1.06 % set(auto2) -> clear(echo_input). 0.49/1.06 % set(auto2) -> set(quiet). 0.49/1.06 % set(auto2) -> clear(print_initial_clauses). 0.49/1.06 % set(auto2) -> clear(print_given). 0.49/1.06 assign(lrs_ticks,-1). 0.49/1.06 assign(sos_limit,10000). 0.49/1.06 assign(order,kbo). 0.49/1.06 set(lex_order_vars). 0.49/1.06 clear(print_given). 0.49/1.06 0.49/1.06 % formulas(sos). % not echoed (43 formulas) 0.49/1.06 0.49/1.06 ============================== end of input ========================== 0.49/1.06 0.49/1.06 % From the command line: assign(max_seconds, 180). 0.49/1.06 0.49/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.49/1.06 0.49/1.06 % Formulas that are not ordinary clauses: 0.49/1.06 1 (all X all Y is_a_theorem(implies(X,implies(Y,and(X,Y))))) <-> and_3 # label(and_3) # label(axiom) # label(non_clause). [assumption]. 0.49/1.06 2 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]. 0.49/1.06 3 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]. 0.49/1.06 4 (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]. 0.49/1.06 5 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]. 0.49/1.06 6 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]. 0.49/1.06 7 (all X all Y is_a_theorem(implies(equiv(X,Y),implies(X,Y)))) <-> equivalence_1 # label(equivalence_1) # label(axiom) # label(non_clause). [assumption]. 0.49/1.06 8 (all X all Y is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))) <-> equivalence_3 # label(equivalence_3) # label(axiom) # label(non_clause). [assumption]. 0.49/1.06 9 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]. 0.49/1.06 10 (all P is_a_theorem(implies(P,and(P,P)))) <-> kn1 # label(kn1) # label(axiom) # label(non_clause). [assumption]. 0.49/1.06 11 (all X all Y is_a_theorem(implies(and(X,Y),X))) <-> and_1 # label(and_1) # label(axiom) # label(non_clause). [assumption]. 0.49/1.06 12 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption]. 0.49/1.06 13 (all P is_a_theorem(implies(implies(not(P),P),P))) <-> cn3 # label(cn3) # label(axiom) # label(non_clause). [assumption]. 1.29/1.56 14 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption]. 1.29/1.56 15 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption]. 1.29/1.56 16 (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) <-> cn2 # label(cn2) # label(axiom) # label(non_clause). [assumption]. 1.29/1.56 17 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]. 1.29/1.56 18 (all P all Q is_a_theorem(implies(Q,or(P,Q)))) <-> r2 # label(r2) # label(axiom) # label(non_clause). [assumption]. 1.29/1.56 19 (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]. 1.29/1.56 20 (all X all Y is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))) <-> modus_tollens # label(modus_tollens) # label(axiom) # label(non_clause). [assumption]. 1.29/1.56 21 equivalence_2 <-> (all X all Y is_a_theorem(implies(equiv(X,Y),implies(Y,X)))) # label(equivalence_2) # label(axiom) # label(non_clause). [assumption]. 1.29/1.56 22 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption]. 1.29/1.56 23 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption]. 1.29/1.56 24 (all P all Q all R is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))) <-> r4 # label(r4) # label(axiom) # label(non_clause). [assumption]. 1.29/1.56 25 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption]. 1.29/1.56 26 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption]. 1.29/1.56 27 op_and -> (all X all Y not(or(not(X),not(Y))) = and(X,Y)) # label(op_and) # label(axiom) # label(non_clause). [assumption]. 1.29/1.56 28 op_or -> (all X all Y or(X,Y) = not(and(not(X),not(Y)))) # label(op_or) # label(axiom) # label(non_clause). [assumption]. 1.29/1.56 29 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]. 1.29/1.56 30 op_implies_or -> (all X all Y implies(X,Y) = or(not(X),Y)) # label(op_implies_or) # label(axiom) # label(non_clause). [assumption]. 1.29/1.56 31 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]. 1.29/1.56 1.29/1.56 ============================== end of process non-clausal formulas === 1.29/1.56 1.29/1.56 ============================== PROCESS INITIAL CLAUSES =============== 1.29/1.56 1.29/1.56 ============================== PREDICATE ELIMINATION ================= 1.29/1.56 1.29/1.56 ============================== end predicate elimination ============= 1.29/1.56 1.29/1.56 Auto_denials: (non-Horn, no changes). 1.29/1.56 1.29/1.56 Term ordering decisions: 1.29/1.56 1.29/1.56 % Assigning unary symbol not kb_weight 0 and highest precedence (93). 1.29/1.56 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. 1.29/1.56 1.29/1.56 ============================== end of process initial clauses ======== 1.29/1.56 1.29/1.56 ============================== CLAUSES FOR SEARCH ==================== 1.29/1.56 1.29/1.56 ============================== end of clauses for search ============= 1.29/1.56 1.29/1.56 ============================== SEARCH ================================ 1.29/1.56 1.29/1.56 % Starting search at 0.02 seconds. 1.29/1.56 1.29/1.56 Low Water (keep): wt=38.000, iters=3382 1.29/1.56 1.29/1.56 Low Water (keep): wt=37.000, iters=3418 1.29/1.56 1.29/1.56 Low Water (keep): wt=35.000, iters=3529 1.29/1.56 1.29/1.56 Low Water (keep): wt=33.000, iters=3525 1.29/1.56 1.29/1.56 Low Water (keep): wt=31.000, iters=3388 1.29/1.56 1.29/1.56 Low Water (keep): wt=30.000, iters=3427 1.29/1.56 1.29/1.56 Low Water (keep): wt=28.000, iters=3372 1.29/1.56 1.29/1.56 Low Water (keep): wt=27.000, iters=3481 1.29/1.56 1.29/1.56 Low Water (keep): wt=26.000, iters=3562 1.29/1.56 1.29/1.56 Low Water (keep): wt=25.000, iters=3344 1.29/1.56 1.29/1.56 Low Water (keep): wt=24.000, iters=3484 75.82/76.08 75.82/76.08 Low Water (keep): wt=23.000, iters=3370 75.82/76.08 75.82/76.08 Low Water (keep): wt=22.000, iters=3402 75.82/76.08 75.82/76.08 Low Water (keep): wt=21.000, iters=3402 75.82/76.08 75.82/76.08 Low Water (keep): wt=20.000, iters=3354 75.82/76.08 75.82/76.08 Low Water (keep): wt=19.000, iters=3388 75.82/76.08 75.82/76.08 Low Water (keep): wt=18.000, iters=3334 75.82/76.08 75.82/76.08 Low Water (keep): wt=17.000, iters=3353 75.82/76.08 75.82/76.08 Low Water (displace): id=1926, wt=59.000 75.82/76.08 75.82/76.08 Low Water (displace): id=1925, wt=57.000 75.82/76.08 75.82/76.08 Low Water (displace): id=3234, wt=55.000 75.82/76.08 75.82/76.08 Low Water (displace): id=3233, wt=53.000 75.82/76.08 75.82/76.08 Low Water (displace): id=1953, wt=46.000 75.82/76.08 75.82/76.08 Low Water (displace): id=3273, wt=44.000 75.82/76.08 75.82/76.08 Low Water (displace): id=2760, wt=43.000 75.82/76.08 75.82/76.08 Low Water (displace): id=1958, wt=42.000 75.82/76.08 75.82/76.08 Low Water (displace): id=2759, wt=41.000 75.82/76.08 75.82/76.08 Low Water (displace): id=3278, wt=40.000 75.82/76.08 75.82/76.08 Low Water (displace): id=10574, wt=16.000 75.82/76.08 75.82/76.08 Low Water (displace): id=10588, wt=15.000 75.82/76.08 75.82/76.08 Low Water (displace): id=11336, wt=13.000 75.82/76.08 75.82/76.08 Low Water (displace): id=11594, wt=11.000 75.82/76.08 75.82/76.08 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 147 (0.00 of 1.10 sec). 75.82/76.08 75.82/76.08 Low Water (keep): wt=16.000, iters=3336 75.82/76.08 75.82/76.08 Low Water (keep): wt=15.000, iters=3334 75.82/76.08 75.82/76.08 Low Water (keep): wt=14.000, iters=3337 75.82/76.08 75.82/76.08 Low Water (keep): wt=13.000, iters=3373 75.82/76.08 75.82/76.08 Low Water (displace): id=54449, wt=10.000 75.82/76.08 75.82/76.08 Low Water (displace): id=55956, wt=9.000 75.82/76.08 75.82/76.08 Low Water (displace): id=57831, wt=8.000 75.82/76.08 75.82/76.08 Low Water (displace): id=98496, wt=7.000 75.82/76.08 75.82/76.08 Low Water (keep): wt=12.000, iters=3334 75.82/76.08 75.82/76.08 Low Water (keep): wt=11.000, iters=4159 75.82/76.08 75.82/76.08 Low Water (keep): wt=10.000, iters=3334 75.82/76.08 75.82/76.08 ============================== PROOF ================================= 75.82/76.08 % SZS status Theorem 75.82/76.08 % SZS output start Refutation 75.82/76.08 75.82/76.08 % Proof 1 at 69.90 (+ 5.13) seconds. 75.82/76.08 % Length of proof is 268. 75.82/76.08 % Level of proof is 84. 75.82/76.08 % Maximum clause weight is 18.000. 75.82/76.08 % Given clauses 6807. 75.82/76.08 75.82/76.08 3 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]. 75.82/76.08 4 (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]. 75.82/76.08 5 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]. 75.82/76.08 6 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]. 75.82/76.08 9 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]. 75.82/76.08 10 (all P is_a_theorem(implies(P,and(P,P)))) <-> kn1 # label(kn1) # label(axiom) # label(non_clause). [assumption]. 75.82/76.08 26 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption]. 75.82/76.08 29 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]. 75.82/76.08 31 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]. 75.82/76.08 32 op_implies_and # label(rosser_op_implies_and) # label(axiom). [assumption]. 75.82/76.08 33 kn1 # label(rosser_kn1) # label(axiom). [assumption]. 75.82/76.08 34 kn3 # label(rosser_kn3) # label(axiom). [assumption]. 75.82/76.08 35 op_equiv # label(rosser_op_equiv) # label(axiom). [assumption]. 75.82/76.08 37 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption]. 75.82/76.08 38 kn2 # label(rosser_kn2) # label(axiom). [assumption]. 75.82/76.08 39 modus_ponens # label(rosser_modus_ponens) # label(axiom). [assumption]. 75.82/76.08 40 -implies_3 # label(hilbert_implies_3) # label(negated_conjecture). [assumption]. 75.82/76.08 41 is_a_theorem(implies(A,and(A,A))) | -kn1 # label(kn1) # label(axiom). [clausify(10)]. 75.82/76.08 42 is_a_theorem(implies(A,and(A,A))). [copy(41),unit_del(b,33)]. 75.82/76.08 57 -kn2 | is_a_theorem(implies(and(A,B),A)) # label(kn2) # label(axiom). [clausify(26)]. 75.82/76.08 58 is_a_theorem(implies(and(A,B),A)). [copy(57),unit_del(a,38)]. 75.82/76.08 60 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(3)]. 75.82/76.08 61 -is_a_theorem(equiv(A,B)) | B = A. [copy(60),unit_del(a,37)]. 75.82/76.08 70 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(9)]. 75.82/76.08 71 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(70),unit_del(a,39)]. 75.82/76.08 77 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(31)]. 75.82/76.08 78 not(and(A,not(B))) = implies(A,B). [copy(77),unit_del(a,32)]. 75.82/76.08 86 -op_equiv | equiv(A,B) = and(implies(A,B),implies(B,A)) # label(op_equiv) # label(axiom). [clausify(29)]. 75.82/76.08 87 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(86),flip(b),unit_del(a,35)]. 75.82/76.08 92 implies_3 | -is_a_theorem(implies(implies(c11,c12),implies(implies(c12,c13),implies(c11,c13)))) # label(implies_3) # label(axiom). [clausify(5)]. 75.82/76.08 93 -is_a_theorem(implies(implies(c11,c12),implies(implies(c12,c13),implies(c11,c13)))). [copy(92),unit_del(a,40)]. 75.82/76.08 94 -cn1 | is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))) # label(cn1) # label(axiom). [clausify(6)]. 75.82/76.08 95 cn1 | -is_a_theorem(implies(implies(c14,c15),implies(implies(c15,c16),implies(c14,c16)))) # label(cn1) # label(axiom). [clausify(6)]. 75.82/76.08 102 is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))) | -kn3 # label(kn3) # label(axiom). [clausify(4)]. 75.82/76.08 103 is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))). [copy(102),unit_del(b,34)]. 75.82/76.08 122 -is_a_theorem(A) | is_a_theorem(and(A,A)). [resolve(71,b,42,a)]. 75.82/76.08 123 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(78(a,1),78(a,1,1,2))]. 75.82/76.08 124 is_a_theorem(implies(implies(A,A),equiv(A,A))). [para(87(a,1),42(a,1,2))]. 75.82/76.08 130 -cn1. [ur(94,b,93,a)]. 75.82/76.08 131 -is_a_theorem(implies(implies(c14,c15),implies(implies(c15,c16),implies(c14,c16)))). [back_unit_del(95),unit_del(a,130)]. 75.82/76.08 132 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(and(B,C)),not(and(C,A)))). [resolve(103,a,71,b)]. 75.82/76.08 134 is_a_theorem(implies(implies(A,B),implies(implies(B,C),not(and(not(C),A))))). [para(78(a,1),103(a,1,2,1))]. 75.82/76.08 137 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(C,and(B,not(A))),not(equiv(B,A))))). [para(87(a,1),103(a,1,2,2,1)),rewrite([123(5)])]. 75.82/76.08 156 -is_a_theorem(implies(A,A)) | is_a_theorem(equiv(A,A)). [resolve(124,a,71,b)]. 75.82/76.08 167 implies(implies(A,B),and(B,not(A))) = not(equiv(A,B)). [para(87(a,1),123(a,1,1)),flip(a)]. 75.82/76.08 253 -is_a_theorem(implies(A,B)) | -is_a_theorem(not(equiv(A,B))) | is_a_theorem(and(B,not(A))). [para(167(a,1),71(b,1))]. 75.82/76.08 265 is_a_theorem(implies(not(and(and(A,A),B)),not(and(B,A)))). [resolve(132,a,42,a)]. 75.82/76.08 288 -is_a_theorem(not(and(and(A,A),B))) | is_a_theorem(not(and(B,A))). [resolve(265,a,71,b)]. 75.82/76.08 386 -is_a_theorem(implies(and(A,A),B)) | is_a_theorem(not(and(not(B),A))). [para(78(a,1),288(a,1))]. 75.82/76.08 668 is_a_theorem(not(and(not(A),A))). [resolve(386,a,58,a)]. 75.82/76.08 672 is_a_theorem(and(not(and(not(A),A)),not(and(not(A),A)))). [resolve(668,a,122,a)]. 75.82/76.08 700 is_a_theorem(not(and(implies(A,B),and(A,not(B))))). [para(78(a,1),668(a,1,1,1))]. 75.82/76.08 701 is_a_theorem(implies(not(not(A)),A)). [para(78(a,1),668(a,1))]. 75.82/76.08 704 is_a_theorem(implies(not(and(A,B)),implies(B,not(A)))). [resolve(701,a,132,a),rewrite([78(6)])]. 75.82/76.08 706 -is_a_theorem(not(not(A))) | is_a_theorem(A). [resolve(701,a,71,b)]. 75.82/76.08 995 -is_a_theorem(not(and(A,B))) | is_a_theorem(implies(B,not(A))). [resolve(704,a,71,b)]. 75.82/76.08 1027 is_a_theorem(implies(implies(A,B),implies(not(B),not(A)))). [para(78(a,1),704(a,1,1))]. 75.82/76.08 1577 is_a_theorem(implies(and(A,not(B)),not(implies(A,B)))). [resolve(995,a,700,a)]. 75.82/76.08 1578 is_a_theorem(implies(A,not(not(A)))). [resolve(995,a,668,a)]. 75.82/76.08 1582 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(B),not(A))). [para(78(a,1),995(a,1))]. 75.82/76.08 1751 is_a_theorem(not(and(not(not(not(and(A,A)))),A))). [resolve(1578,a,386,a)]. 75.82/76.08 1753 is_a_theorem(implies(not(and(not(not(A)),B)),not(and(B,A)))). [resolve(1578,a,132,a)]. 75.82/76.08 1755 -is_a_theorem(A) | is_a_theorem(not(not(A))). [resolve(1578,a,71,b)]. 75.82/76.08 1801 is_a_theorem(not(not(implies(A,not(not(A)))))). [resolve(1755,a,1578,a)]. 75.82/76.08 1828 is_a_theorem(not(not(implies(and(A,B),A)))). [resolve(1755,a,58,a)]. 75.82/76.08 1829 is_a_theorem(not(not(implies(A,and(A,A))))). [resolve(1755,a,42,a)]. 75.82/76.08 3997 -is_a_theorem(and(A,not(B))) | is_a_theorem(not(implies(A,B))). [resolve(1577,a,71,b)]. 75.82/76.08 4533 is_a_theorem(implies(not(A),not(and(A,B)))). [resolve(1582,a,58,a)]. 75.82/76.08 4534 is_a_theorem(implies(not(and(A,A)),not(A))). [resolve(1582,a,42,a)]. 75.82/76.08 4778 -is_a_theorem(not(A)) | is_a_theorem(not(and(A,B))). [resolve(4533,a,71,b)]. 75.82/76.08 4850 is_a_theorem(implies(not(A),implies(A,B))). [para(78(a,1),4533(a,1,2))]. 75.82/76.08 4857 is_a_theorem(implies(not(and(implies(A,B),C)),implies(C,A))). [resolve(4850,a,132,a),rewrite([78(6)])]. 75.82/76.08 4859 -is_a_theorem(not(A)) | is_a_theorem(implies(A,B)). [resolve(4850,a,71,b)]. 75.82/76.08 4948 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(and(A,not(B)),C)). [para(78(a,1),4859(a,1))]. 75.82/76.08 5283 is_a_theorem(implies(not(not(A)),not(not(and(A,A))))). [resolve(4534,a,1582,a)]. 75.82/76.08 5287 -is_a_theorem(not(and(A,A))) | is_a_theorem(not(A)). [resolve(4534,a,71,b)]. 75.82/76.08 5359 is_a_theorem(not(and(not(implies(A,and(A,A))),B))). [resolve(4778,a,1829,a)]. 75.82/76.08 5360 is_a_theorem(not(and(not(implies(and(A,B),A)),C))). [resolve(4778,a,1828,a)]. 75.82/76.08 5364 is_a_theorem(not(and(not(implies(A,not(not(A)))),B))). [resolve(4778,a,1801,a)]. 75.82/76.08 5369 is_a_theorem(not(and(and(not(A),A),B))). [resolve(4778,a,668,a)]. 75.82/76.08 5375 -is_a_theorem(implies(not(A),A)) | is_a_theorem(not(not(A))). [para(78(a,1),5287(a,1))]. 75.82/76.08 5383 is_a_theorem(implies(A,not(and(not(B),B)))). [resolve(5369,a,995,a)]. 75.82/76.08 9215 -is_a_theorem(not(not(A))) | is_a_theorem(not(not(and(A,A)))). [resolve(5283,a,71,b)]. 75.82/76.08 11678 -is_a_theorem(not(and(implies(A,B),C))) | is_a_theorem(implies(C,A)). [resolve(4857,a,71,b)]. 75.82/76.08 11691 is_a_theorem(implies(implies(implies(A,B),C),implies(not(C),A))). [para(78(a,1),4857(a,1,1))]. 75.82/76.08 11692 is_a_theorem(implies(not(equiv(A,B)),implies(implies(B,A),A))). [para(87(a,1),4857(a,1,1,1))]. 75.82/76.08 13971 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(not(C),A)). [para(78(a,1),11678(a,1))]. 75.82/76.08 14648 is_a_theorem(implies(not(implies(not(A),B)),implies(B,C))). [resolve(13971,a,11691,a)]. 75.82/76.08 15153 is_a_theorem(not(not(implies(not(A),not(A))))). [resolve(14648,a,5375,a)]. 75.82/76.08 15183 is_a_theorem(implies(not(A),not(A))). [resolve(15153,a,706,a)]. 75.82/76.08 15270 is_a_theorem(implies(not(and(not(A),B)),implies(B,A))). [resolve(15183,a,132,a),rewrite([78(6)])]. 75.82/76.08 16920 -is_a_theorem(not(and(not(A),B))) | is_a_theorem(implies(B,A)). [resolve(15270,a,71,b)]. 75.82/76.08 16941 is_a_theorem(implies(not(equiv(A,B)),not(equiv(B,A)))). [para(167(a,1),15270(a,1,2)),rewrite([78(3),87(3)])]. 75.82/76.08 17494 is_a_theorem(implies(A,implies(B,not(not(B))))). [resolve(16920,a,5364,a)]. 75.82/76.08 17496 is_a_theorem(implies(A,implies(and(B,C),B))). [resolve(16920,a,5360,a)]. 75.82/76.08 17497 is_a_theorem(implies(A,implies(B,and(B,B)))). [resolve(16920,a,5359,a)]. 75.82/76.08 17503 is_a_theorem(implies(A,not(not(and(A,A))))). [resolve(16920,a,1751,a)]. 75.82/76.08 17506 is_a_theorem(implies(A,A)). [resolve(16920,a,668,a)]. 75.82/76.08 17512 -is_a_theorem(implies(not(A),B)) | is_a_theorem(implies(not(B),A)). [para(78(a,1),16920(a,1))]. 75.82/76.08 17518 is_a_theorem(equiv(A,A)). [back_unit_del(156),unit_del(a,17506)]. 75.82/76.08 17527 is_a_theorem(implies(and(A,not(A)),B)). [resolve(17506,a,4948,a)]. 75.82/76.08 17533 is_a_theorem(implies(not(and(A,B)),not(and(B,A)))). [resolve(17506,a,132,a)]. 75.82/76.08 17738 is_a_theorem(not(not(equiv(A,A)))). [resolve(17518,a,1755,a)]. 75.82/76.08 18375 is_a_theorem(not(not(and(equiv(A,A),equiv(A,A))))). [resolve(17738,a,9215,a)]. 75.82/76.08 18570 is_a_theorem(implies(not(A),implies(B,B))). [resolve(17527,a,1582,a),rewrite([78(4)])]. 75.82/76.08 19268 is_a_theorem(implies(not(and(implies(A,A),B)),implies(B,C))). [resolve(18570,a,132,a),rewrite([78(6)])]. 75.82/76.08 19912 -is_a_theorem(A) | is_a_theorem(not(not(and(A,A)))). [resolve(17503,a,71,b)]. 75.82/76.08 19922 is_a_theorem(implies(not(A),not(implies(not(A),A)))). [para(78(a,1),17503(a,1,2,1))]. 75.82/76.08 22687 -is_a_theorem(not(A)) | is_a_theorem(not(implies(not(A),A))). [resolve(19922,a,71,b)]. 75.82/76.08 23990 -is_a_theorem(not(equiv(A,B))) | is_a_theorem(not(equiv(B,A))). [resolve(16941,a,71,b)]. 75.82/76.08 24091 is_a_theorem(implies(not(implies(implies(A,B),B)),equiv(B,A))). [resolve(17512,a,11692,a)]. 75.82/76.09 24985 is_a_theorem(implies(not(not(and(A,B))),and(B,A))). [resolve(17533,a,17512,a)]. 75.82/76.09 24998 -is_a_theorem(not(and(A,B))) | is_a_theorem(not(and(B,A))). [resolve(17533,a,71,b)]. 75.82/76.09 24999 is_a_theorem(implies(implies(A,B),not(and(not(B),A)))). [para(78(a,1),17533(a,1,1))]. 75.82/76.09 29567 -is_a_theorem(implies(A,B)) | is_a_theorem(not(and(not(B),A))). [para(78(a,1),24998(a,1))]. 75.82/76.09 29573 is_a_theorem(implies(not(not(and(not(A),B))),B)). [resolve(24999,a,13971,a)]. 75.82/76.09 29823 is_a_theorem(implies(not(A),not(and(not(B),A)))). [resolve(29573,a,17512,a)]. 75.82/76.09 32888 is_a_theorem(implies(not(implies(A,B)),and(implies(B,C),A))). [resolve(29567,a,4857,a),rewrite([78(7)])]. 75.82/76.09 39544 is_a_theorem(implies(not(implies(A,B)),and(implies(C,C),A))). [resolve(19268,a,29567,a),rewrite([78(7)])]. 75.82/76.09 44236 -is_a_theorem(not(implies(implies(A,B),B))) | is_a_theorem(equiv(B,A)). [resolve(24091,a,71,b)]. 75.82/76.09 50373 -is_a_theorem(not(implies(A,B))) | is_a_theorem(and(implies(B,C),A)). [resolve(32888,a,71,b)]. 75.82/76.09 53955 -is_a_theorem(not(implies(A,B))) | is_a_theorem(and(implies(C,C),A)). [resolve(39544,a,71,b)]. 75.82/76.09 76068 is_a_theorem(implies(not(not(and(A,B))),and(not(not(B)),A))). [resolve(1753,a,29567,a),rewrite([78(9)])]. 75.82/76.09 76086 -is_a_theorem(not(and(not(not(A)),B))) | is_a_theorem(not(and(B,A))). [resolve(1753,a,71,b)]. 75.82/76.09 81859 -is_a_theorem(not(not(and(A,B)))) | is_a_theorem(and(not(not(B)),A)). [resolve(76068,a,71,b)]. 75.82/76.09 81911 -is_a_theorem(implies(not(not(A)),B)) | is_a_theorem(not(and(not(B),A))). [para(78(a,1),76086(a,1))]. 75.82/76.09 88909 is_a_theorem(and(not(not(equiv(A,A))),equiv(A,A))). [resolve(81859,a,18375,a)]. 75.82/76.09 92841 is_a_theorem(not(and(not(implies(not(A),B)),B))). [resolve(81911,a,29823,a),rewrite([78(4)])]. 75.82/76.09 92869 is_a_theorem(not(and(not(and(A,B)),and(B,A)))). [resolve(81911,a,24985,a)]. 75.82/76.09 92953 is_a_theorem(implies(A,implies(not(B),A))). [resolve(92841,a,24998,a),rewrite([78(5)])]. 75.82/76.09 102996 is_a_theorem(implies(and(A,B),and(B,A))). [resolve(92869,a,24998,a),rewrite([78(5)])]. 75.82/76.09 103013 is_a_theorem(implies(and(A,B),not(not(and(B,A))))). [resolve(92869,a,995,a)]. 75.82/76.09 103061 -is_a_theorem(and(A,B)) | is_a_theorem(and(B,A)). [resolve(102996,a,71,b)]. 75.82/76.09 103556 is_a_theorem(and(equiv(A,A),not(not(equiv(A,A))))). [resolve(103061,a,88909,a)]. 75.82/76.09 108989 -is_a_theorem(and(A,B)) | is_a_theorem(not(not(and(B,A)))). [resolve(103013,a,71,b)]. 75.82/76.09 109000 is_a_theorem(implies(and(not(A),B),not(implies(B,A)))). [para(78(a,1),103013(a,1,2,1))]. 75.82/76.09 109417 is_a_theorem(not(implies(equiv(A,A),not(equiv(A,A))))). [resolve(103556,a,3997,a)]. 75.82/76.09 113665 is_a_theorem(not(implies(not(and(not(A),A)),and(not(A),A)))). [resolve(108989,a,672,a),rewrite([78(8)])]. 75.82/76.09 113723 -is_a_theorem(and(not(A),B)) | is_a_theorem(not(implies(B,A))). [resolve(109000,a,71,b)]. 75.82/76.09 113955 is_a_theorem(and(implies(A,A),equiv(B,B))). [resolve(109417,a,53955,a)]. 75.82/76.09 114034 is_a_theorem(not(not(and(implies(A,A),equiv(B,B))))). [resolve(113955,a,1755,a)]. 75.82/76.09 114721 is_a_theorem(and(not(not(equiv(A,A))),implies(B,B))). [resolve(114034,a,81859,a)]. 75.82/76.09 114988 is_a_theorem(not(implies(implies(A,A),not(equiv(B,B))))). [resolve(114721,a,113723,a)]. 75.82/76.09 115067 is_a_theorem(and(implies(not(equiv(A,A)),B),implies(C,C))). [resolve(114988,a,50373,a)]. 75.82/76.09 118407 is_a_theorem(and(implies(A,A),implies(not(equiv(B,B)),C))). [resolve(115067,a,103061,a)]. 75.82/76.09 129840 is_a_theorem(and(implies(A,A),not(and(not(B),B)))). [resolve(113665,a,53955,a)]. 75.82/76.09 129929 is_a_theorem(not(implies(implies(A,A),and(not(B),B)))). [resolve(129840,a,3997,a)]. 75.82/76.09 129935 is_a_theorem(and(implies(A,A),implies(not(not(B)),B))). [para(78(a,1),129840(a,1,2))]. 75.82/76.09 130122 is_a_theorem(and(implies(and(not(A),A),B),implies(C,C))). [resolve(129929,a,50373,a)]. 75.82/76.09 130150 is_a_theorem(not(implies(implies(not(not(A)),A),and(B,not(B))))). [resolve(129935,a,108989,a),rewrite([123(6)])]. 75.82/76.09 130552 is_a_theorem(not(implies(implies(and(not(A),A),B),and(C,not(C))))). [resolve(130122,a,1755,a),rewrite([123(6)])]. 75.82/76.09 136522 is_a_theorem(equiv(and(A,not(A)),not(implies(A,A)))). [resolve(130150,a,44236,a),rewrite([78(5)])]. 75.82/76.09 136605 not(implies(A,A)) = and(A,not(A)). [resolve(136522,a,61,a)]. 75.82/76.09 136633 not(and(A,and(B,not(B)))) = implies(A,implies(B,B)). [para(136605(a,1),78(a,1,1,2))]. 75.82/76.09 162112 is_a_theorem(equiv(and(A,not(A)),and(not(B),B))). [resolve(130552,a,44236,a)]. 75.82/76.09 162263 and(not(A),A) = and(B,not(B)). [resolve(162112,a,61,a)]. 75.82/76.09 162270 and(not(A),A) = c_0. [new_symbol(162263)]. 75.82/76.09 162273 and(A,not(A)) = c_0. [back_rewrite(162263),rewrite([162270(2)]),flip(a)]. 75.82/76.09 163103 is_a_theorem(implies(A,not(c_0))). [back_rewrite(5383),rewrite([162270(2)])]. 75.82/76.09 163107 is_a_theorem(not(and(c_0,A))). [back_rewrite(5369),rewrite([162270(2)])]. 75.82/76.09 163164 is_a_theorem(not(c_0)). [back_rewrite(668),rewrite([162270(2)])]. 75.82/76.09 163255 implies(A,implies(B,B)) = not(and(A,c_0)). [back_rewrite(136633),rewrite([162273(2)]),flip(a)]. 75.82/76.09 163266 not(implies(A,A)) = c_0. [back_rewrite(136605),rewrite([162273(4)])]. 75.82/76.09 164925 is_a_theorem(not(implies(implies(A,not(c_0)),and(A,not(not(c_0)))))). [resolve(163103,a,19912,a),rewrite([123(8)])]. 75.82/76.09 164934 is_a_theorem(implies(not(and(not(c_0),A)),not(and(A,B)))). [resolve(163103,a,132,a)]. 75.82/76.09 165102 is_a_theorem(not(implies(not(and(c_0,A)),and(c_0,A)))). [resolve(163107,a,22687,a)]. 75.82/76.09 165255 implies(not(not(A)),A) = not(c_0). [para(162270(a,1),78(a,1,1)),flip(a)]. 75.82/76.09 165378 implies(A,A) = not(c_0). [para(162273(a,1),78(a,1,1)),flip(a)]. 75.82/76.09 165382 not(equiv(A,A)) = implies(not(c_0),c_0). [para(162273(a,1),167(a,1,2)),rewrite([165378(1)]),flip(a)]. 75.82/76.09 165455 not(not(c_0)) = c_0. [back_rewrite(163266),rewrite([165378(1)])]. 75.82/76.09 165456 not(and(A,c_0)) = implies(A,not(c_0)). [back_rewrite(163255),rewrite([165378(1)]),flip(a)]. 75.82/76.09 165695 is_a_theorem(and(not(c_0),implies(not(equiv(A,A)),B))). [back_rewrite(118407),rewrite([165378(1)])]. 75.82/76.09 165735 -is_a_theorem(not(implies(A,B))) | is_a_theorem(and(not(c_0),A)). [back_rewrite(53955),rewrite([165378(4)])]. 75.82/76.09 165797 is_a_theorem(not(implies(implies(A,not(c_0)),and(A,c_0)))). [back_rewrite(164925),rewrite([165455(6)])]. 75.82/76.09 166769 equiv(A,A) = and(not(c_0),not(c_0)). [para(165378(a,1),87(a,1,1)),rewrite([165378(3)]),flip(a)]. 75.82/76.09 173564 not(equiv(A,A)) = not(equiv(B,B)). [para(165382(a,2),165382(a,2))]. 75.82/76.09 178325 and(equiv(A,A),not(equiv(B,B))) = c_0. [para(173564(a,1),162273(a,1,2))]. 75.82/76.09 188835 is_a_theorem(not(implies(implies(not(equiv(A,A)),B),c_0))). [resolve(165695,a,113723,a)]. 75.82/76.09 189207 is_a_theorem(and(not(c_0),not(and(c_0,A)))). [resolve(165735,a,165102,a)]. 75.82/76.09 189238 is_a_theorem(not(implies(not(and(c_0,A)),c_0))). [resolve(189207,a,113723,a)]. 75.82/76.09 189420 is_a_theorem(and(implies(c_0,A),not(and(c_0,B)))). [resolve(189238,a,50373,a)]. 75.82/76.09 190166 is_a_theorem(not(implies(implies(c_0,A),and(c_0,B)))). [resolve(189420,a,3997,a)]. 75.82/76.09 190484 is_a_theorem(equiv(and(c_0,A),c_0)). [resolve(190166,a,44236,a)]. 75.82/76.09 190569 and(c_0,A) = c_0. [resolve(190484,a,61,a),flip(a)]. 75.82/76.09 190570 implies(c_0,A) = not(c_0). [para(190569(a,1),78(a,1,1)),flip(a)]. 75.82/76.09 190572 implies(implies(A,c_0),c_0) = not(equiv(A,c_0)). [para(190569(a,1),167(a,1,2))]. 75.82/76.09 190627 and(not(c_0),implies(A,c_0)) = equiv(c_0,A). [para(190570(a,1),87(a,1,1))]. 75.82/76.09 190638 -is_a_theorem(not(implies(not(c_0),A))) | is_a_theorem(equiv(A,c_0)). [para(190570(a,1),44236(a,1,1,1))]. 75.82/76.09 190846 is_a_theorem(and(not(c_0),implies(A,not(c_0)))). [resolve(165797,a,165735,a)]. 75.82/76.09 190982 is_a_theorem(not(implies(not(c_0),and(A,c_0)))). [resolve(190846,a,1755,a),rewrite([123(7),165455(5)])]. 75.82/76.09 191208 is_a_theorem(and(implies(and(A,c_0),B),not(c_0))). [resolve(190982,a,50373,a)]. 75.82/76.09 191772 is_a_theorem(not(implies(implies(and(A,c_0),B),c_0))). [resolve(191208,a,3997,a)]. 75.82/76.09 192012 is_a_theorem(equiv(c_0,and(A,c_0))). [resolve(191772,a,44236,a)]. 75.82/76.09 192096 and(A,c_0) = c_0. [resolve(192012,a,61,a)]. 75.82/76.09 192208 implies(A,not(c_0)) = not(c_0). [back_rewrite(165456),rewrite([192096(2)]),flip(a)]. 75.82/76.09 192221 and(implies(not(c_0),A),not(c_0)) = equiv(not(c_0),A). [para(192208(a,1),87(a,1,2))]. 75.82/76.09 196141 implies(equiv(A,A),equiv(B,B)) = not(c_0). [para(178325(a,1),78(a,1,1)),flip(a)]. 75.82/76.09 196143 not(equiv(equiv(A,A),equiv(B,B))) = implies(not(c_0),c_0). [para(178325(a,1),167(a,1,2)),rewrite([196141(3)]),flip(a)]. 75.82/76.09 196145 is_a_theorem(implies(implies(not(c_0),A),implies(implies(A,c_0),implies(not(c_0),c_0)))). [para(178325(a,1),137(a,1,2,1,2)),rewrite([196141(3),196143(9)])]. 75.82/76.09 197293 is_a_theorem(equiv(c_0,not(equiv(A,A)))). [resolve(188835,a,44236,a)]. 75.82/76.09 197381 not(equiv(A,A)) = c_0. [resolve(197293,a,61,a)]. 75.82/76.09 197394 implies(not(c_0),c_0) = c_0. [back_rewrite(165382),rewrite([197381(2)]),flip(a)]. 75.82/76.09 197395 is_a_theorem(implies(implies(not(c_0),A),not(equiv(A,c_0)))). [back_rewrite(196145),rewrite([197394(9),190572(7)])]. 75.82/76.09 198027 -is_a_theorem(implies(not(c_0),A)) | is_a_theorem(not(equiv(A,c_0))). [resolve(197395,a,71,b)]. 75.82/76.09 198194 is_a_theorem(not(equiv(implies(A,and(A,A)),c_0))). [resolve(198027,a,17497,a)]. 75.82/76.09 198195 is_a_theorem(not(equiv(implies(and(A,B),A),c_0))). [resolve(198027,a,17496,a)]. 75.82/76.09 198197 is_a_theorem(not(equiv(implies(A,not(not(A))),c_0))). [resolve(198027,a,17494,a)]. 75.82/76.09 198279 is_a_theorem(not(equiv(c_0,implies(A,and(A,A))))). [resolve(198194,a,23990,a)]. 75.82/76.09 198359 is_a_theorem(not(equiv(c_0,implies(and(A,B),A)))). [resolve(198195,a,23990,a)]. 75.82/76.09 198439 is_a_theorem(not(equiv(c_0,implies(A,not(not(A)))))). [resolve(198197,a,23990,a)]. 75.82/76.09 198537 is_a_theorem(and(implies(A,and(A,A)),not(c_0))). [resolve(198279,a,253,b),rewrite([190570(4)]),unit_del(a,163164)]. 75.82/76.09 198644 is_a_theorem(and(implies(and(A,B),A),not(c_0))). [resolve(198359,a,253,b),rewrite([190570(4)]),unit_del(a,163164)]. 75.82/76.09 198725 is_a_theorem(and(implies(A,not(not(A))),not(c_0))). [resolve(198439,a,253,b),rewrite([190570(5)]),unit_del(a,163164)]. 75.82/76.09 198744 is_a_theorem(not(implies(not(c_0),and(A,not(and(A,A)))))). [resolve(198537,a,108989,a),rewrite([123(6)])]. 75.82/76.09 198802 is_a_theorem(not(implies(not(c_0),and(and(A,B),not(A))))). [resolve(198644,a,108989,a),rewrite([123(6)])]. 75.82/76.09 198883 is_a_theorem(not(implies(not(c_0),and(A,not(not(not(A))))))). [resolve(198725,a,108989,a),rewrite([123(7)])]. 75.82/76.09 205197 is_a_theorem(implies(not(not(and(A,B))),not(not(and(not(c_0),A))))). [resolve(164934,a,1582,a)]. 75.82/76.09 212304 is_a_theorem(equiv(and(A,not(and(A,A))),c_0)). [resolve(198744,a,190638,a)]. 75.82/76.09 212436 and(A,not(and(A,A))) = c_0. [resolve(212304,a,61,a),flip(a)]. 75.82/76.09 212439 implies(A,and(A,A)) = not(c_0). [para(212436(a,1),78(a,1,1)),flip(a)]. 75.82/76.09 212474 and(not(c_0),implies(and(A,A),A)) = equiv(A,and(A,A)). [para(212439(a,1),87(a,1,1))]. 75.82/76.09 212623 is_a_theorem(equiv(and(and(A,B),not(A)),c_0)). [resolve(198802,a,190638,a)]. 75.82/76.09 212756 and(and(A,B),not(A)) = c_0. [resolve(212623,a,61,a),flip(a)]. 75.82/76.09 212764 implies(and(A,B),A) = not(c_0). [para(212756(a,1),78(a,1,1)),flip(a)]. 75.82/76.09 212794 equiv(A,and(A,A)) = and(not(c_0),not(c_0)). [back_rewrite(212474),rewrite([212764(4)]),flip(a)]. 75.82/76.09 212795 and(not(c_0),implies(A,and(A,B))) = equiv(and(A,B),A). [para(212764(a,1),87(a,1,1))]. 75.82/76.09 212966 is_a_theorem(equiv(and(A,not(not(not(A)))),c_0)). [resolve(198883,a,190638,a)]. 75.82/76.09 213098 and(A,not(not(not(A)))) = c_0. [resolve(212966,a,61,a),flip(a)]. 75.82/76.09 213105 not(equiv(not(not(A)),A)) = c_0. [para(213098(a,1),167(a,1,2)),rewrite([165255(3),197394(4)]),flip(a)]. 75.82/76.09 213175 is_a_theorem(equiv(not(not(A)),A)). [para(213105(a,1),706(a,1,1)),unit_del(a,163164)]. 75.82/76.09 213225 not(not(A)) = A. [resolve(213175,a,61,a),flip(a)]. 75.82/76.09 213278 is_a_theorem(implies(and(A,B),and(not(c_0),A))). [back_rewrite(205197),rewrite([213225(3),213225(6)])]. 75.82/76.09 213476 not(and(A,B)) = implies(A,not(B)). [para(213225(a,1),78(a,1,1,2))]. 75.82/76.09 213477 not(implies(A,B)) = and(A,not(B)). [para(78(a,1),213225(a,1,1))]. 75.82/76.09 213570 is_a_theorem(implies(A,implies(B,A))). [para(213225(a,1),92953(a,1,2,1))]. 75.82/76.09 213711 equiv(A,A) = not(c_0). [para(197381(a,1),213225(a,1,1)),flip(a)]. 75.82/76.09 214154 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(not(C),not(A))))). [back_rewrite(134),rewrite([213476(5)])]. 75.82/76.09 214564 and(not(c_0),not(c_0)) = not(c_0). [back_rewrite(166769),rewrite([213711(1)]),flip(a)]. 75.82/76.09 214574 equiv(A,and(A,A)) = not(c_0). [back_rewrite(212794),rewrite([214564(7)])]. 75.82/76.09 218376 and(A,A) = A. [para(214574(a,1),61(a,1)),unit_del(a,163164)]. 75.82/76.09 219109 is_a_theorem(implies(A,and(not(c_0),A))). [para(218376(a,1),213278(a,1,1))]. 75.82/76.09 219118 is_a_theorem(implies(implies(not(c_0),A),A)). [resolve(219109,a,17512,a),rewrite([213476(5),213225(4)])]. 75.82/76.09 219120 -is_a_theorem(A) | is_a_theorem(and(not(c_0),A)). [resolve(219109,a,71,b)]. 75.82/76.09 219143 is_a_theorem(implies(implies(A,c_0),equiv(c_0,A))). [para(190627(a,1),219109(a,1,2))]. 75.82/76.09 219403 is_a_theorem(and(not(c_0),implies(implies(not(c_0),A),A))). [resolve(219120,a,219118,a)]. 75.82/76.09 219572 is_a_theorem(implies(not(equiv(c_0,A)),A)). [resolve(219143,a,13971,a)]. 75.82/76.09 219598 is_a_theorem(implies(not(A),equiv(c_0,A))). [resolve(219572,a,17512,a)]. 75.82/76.09 219894 -is_a_theorem(not(A)) | is_a_theorem(equiv(c_0,A)). [resolve(219598,a,71,b)]. 75.82/76.09 219926 -is_a_theorem(A) | is_a_theorem(equiv(c_0,not(A))). [para(213225(a,1),219894(a,1))]. 75.82/76.09 220009 is_a_theorem(equiv(c_0,and(A,and(B,not(A))))). [resolve(219926,a,213570,a),rewrite([213477(4),213477(3)])]. 75.82/76.09 221741 and(A,and(B,not(A))) = c_0. [resolve(220009,a,61,a)]. 75.82/76.09 221753 implies(A,implies(B,A)) = not(c_0). [para(221741(a,1),213476(a,1,1)),rewrite([213476(5),213225(4)]),flip(a)]. 75.82/76.09 221761 and(not(c_0),implies(implies(A,B),B)) = equiv(B,implies(A,B)). [para(221753(a,1),87(a,1,1))]. 75.82/76.09 221773 is_a_theorem(equiv(A,implies(not(c_0),A))). [back_rewrite(219403),rewrite([221761(7)])]. 75.82/76.09 221788 implies(not(c_0),A) = A. [resolve(221773,a,61,a)]. 75.82/76.09 221858 equiv(not(c_0),A) = and(A,not(c_0)). [back_rewrite(192221),rewrite([221788(3)]),flip(a)]. 75.82/76.09 221910 is_a_theorem(implies(implies(A,c_0),not(A))). [para(221788(a,1),1027(a,1,2))]. 75.82/76.09 223845 is_a_theorem(implies(A,and(A,not(c_0)))). [resolve(221910,a,1582,a),rewrite([213225(2),213477(3)])]. 75.82/76.09 224945 is_a_theorem(equiv(and(A,not(c_0)),A)). [resolve(223845,a,219120,a),rewrite([212795(7)])]. 75.82/76.09 225022 and(A,not(c_0)) = A. [resolve(224945,a,61,a),flip(a)]. 75.82/76.09 225029 equiv(not(c_0),A) = A. [back_rewrite(221858),rewrite([225022(6)])]. 75.82/76.09 226107 -is_a_theorem(A) | not(c_0) = A. [para(225029(a,1),61(a,1)),flip(b)]. 75.82/76.09 226653 implies(and(A,B),and(B,A)) = not(c_0). [resolve(226107,a,102996,a),flip(a)]. 75.82/76.09 227446 equiv(and(A,B),and(B,A)) = not(c_0). [para(226653(a,1),87(a,1,1)),rewrite([226653(5),218376(5)]),flip(a)]. 75.82/76.09 230281 and(A,B) = and(B,A). [para(227446(a,1),61(a,1)),unit_del(a,163164)]. 75.82/76.09 231928 implies(A,not(B)) = implies(B,not(A)). [para(230281(a,1),213476(a,1,1)),rewrite([213476(2)])]. 75.82/76.09 232267 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))). [back_rewrite(214154),rewrite([231928(5),213225(4)])]. 75.82/76.09 232268 $F. [resolve(232267,a,131,a)]. 75.82/76.09 75.82/76.09 % SZS output end Refutation 75.82/76.09 ============================== end of proof ========================== 75.82/76.09 75.82/76.09 ============================== STATISTICS ============================ 75.82/76.09 75.82/76.09 Given=6807. Generated=9825310. Kept=232220. proofs=1. 75.82/76.09 Usable=262. Sos=1436. Demods=162. Limbo=339, Disabled=230254. Hints=0. 75.82/76.09 Megabytes=145.99. 75.82/76.09 User_CPU=69.90, System_CPU=5.13, Wall_clock=75. 75.82/76.09 75.82/76.09 ============================== end of statistics ===================== 75.82/76.09 75.82/76.09 ============================== end of search ========================= 75.82/76.09 75.82/76.09 THEOREM PROVED 75.82/76.09 % SZS status Theorem 75.82/76.09 75.82/76.09 Exiting with 1 proof. 75.82/76.09 75.82/76.09 Process 3296 exit (max_proofs) Thu Aug 29 15:34:32 2019 75.82/76.09 Prover9 interrupted 75.82/76.09 EOF