0.00/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.12/0.33 % Computer : n025.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 180 0.12/0.33 % DateTime : Thu Aug 29 16:59:45 EDT 2019 0.12/0.33 % CPUTime : 0.40/1.00 ============================== Prover9 =============================== 0.40/1.00 Prover9 (32) version 2009-11A, November 2009. 0.40/1.00 Process 15000 was started by sandbox2 on n025.cluster.edu, 0.40/1.00 Thu Aug 29 16:59:46 2019 0.40/1.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 180 -f /tmp/Prover9_14847_n025.cluster.edu". 0.40/1.00 ============================== end of head =========================== 0.40/1.00 0.40/1.00 ============================== INPUT ================================= 0.40/1.00 0.40/1.00 % Reading from file /tmp/Prover9_14847_n025.cluster.edu 0.40/1.00 0.40/1.00 set(prolog_style_variables). 0.40/1.00 set(auto2). 0.40/1.00 % set(auto2) -> set(auto). 0.40/1.00 % set(auto) -> set(auto_inference). 0.40/1.00 % set(auto) -> set(auto_setup). 0.40/1.00 % set(auto_setup) -> set(predicate_elim). 0.40/1.00 % set(auto_setup) -> assign(eq_defs, unfold). 0.40/1.00 % set(auto) -> set(auto_limits). 0.40/1.00 % set(auto_limits) -> assign(max_weight, "100.000"). 0.40/1.00 % set(auto_limits) -> assign(sos_limit, 20000). 0.40/1.00 % set(auto) -> set(auto_denials). 0.40/1.00 % set(auto) -> set(auto_process). 0.40/1.00 % set(auto2) -> assign(new_constants, 1). 0.40/1.00 % set(auto2) -> assign(fold_denial_max, 3). 0.40/1.00 % set(auto2) -> assign(max_weight, "200.000"). 0.40/1.00 % set(auto2) -> assign(max_hours, 1). 0.40/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.40/1.00 % set(auto2) -> assign(max_seconds, 0). 0.40/1.00 % set(auto2) -> assign(max_minutes, 5). 0.40/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.40/1.00 % set(auto2) -> set(sort_initial_sos). 0.40/1.00 % set(auto2) -> assign(sos_limit, -1). 0.40/1.00 % set(auto2) -> assign(lrs_ticks, 3000). 0.40/1.00 % set(auto2) -> assign(max_megs, 400). 0.40/1.00 % set(auto2) -> assign(stats, some). 0.40/1.00 % set(auto2) -> clear(echo_input). 0.40/1.00 % set(auto2) -> set(quiet). 0.40/1.00 % set(auto2) -> clear(print_initial_clauses). 0.40/1.00 % set(auto2) -> clear(print_given). 0.40/1.00 assign(lrs_ticks,-1). 0.40/1.00 assign(sos_limit,10000). 0.40/1.00 assign(order,kbo). 0.40/1.00 set(lex_order_vars). 0.40/1.00 clear(print_given). 0.40/1.00 0.40/1.00 % formulas(sos). % not echoed (43 formulas) 0.40/1.00 0.40/1.00 ============================== end of input ========================== 0.40/1.00 0.40/1.00 % From the command line: assign(max_seconds, 180). 0.40/1.00 0.40/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.40/1.00 0.40/1.00 % Formulas that are not ordinary clauses: 0.40/1.00 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]. 0.40/1.00 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]. 0.40/1.00 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]. 0.40/1.00 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]. 0.40/1.00 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]. 0.40/1.00 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]. 0.40/1.00 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]. 0.40/1.00 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]. 0.40/1.00 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]. 0.40/1.00 10 (all P is_a_theorem(implies(P,and(P,P)))) <-> kn1 # label(kn1) # label(axiom) # label(non_clause). [assumption]. 0.40/1.00 11 (all X all Y is_a_theorem(implies(and(X,Y),X))) <-> and_1 # label(and_1) # label(axiom) # label(non_clause). [assumption]. 0.40/1.00 12 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption]. 0.40/1.00 13 (all P is_a_theorem(implies(implies(not(P),P),P))) <-> cn3 # label(cn3) # label(axiom) # label(non_clause). [assumption]. 1.05/1.36 14 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption]. 1.05/1.36 15 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption]. 1.05/1.36 16 (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) <-> cn2 # label(cn2) # label(axiom) # label(non_clause). [assumption]. 1.05/1.36 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]. 1.05/1.36 18 (all P all Q is_a_theorem(implies(Q,or(P,Q)))) <-> r2 # label(r2) # label(axiom) # label(non_clause). [assumption]. 1.05/1.36 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]. 1.05/1.36 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]. 1.05/1.36 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]. 1.05/1.36 22 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption]. 1.05/1.36 23 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption]. 1.05/1.36 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]. 1.05/1.36 25 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption]. 1.05/1.36 26 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption]. 1.05/1.36 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]. 1.05/1.36 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]. 1.05/1.36 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]. 1.05/1.36 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]. 1.05/1.36 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]. 1.05/1.36 1.05/1.36 ============================== end of process non-clausal formulas === 1.05/1.36 1.05/1.36 ============================== PROCESS INITIAL CLAUSES =============== 1.05/1.36 1.05/1.36 ============================== PREDICATE ELIMINATION ================= 1.05/1.36 1.05/1.36 ============================== end predicate elimination ============= 1.05/1.36 1.05/1.36 Auto_denials: (non-Horn, no changes). 1.05/1.36 1.05/1.36 Term ordering decisions: 1.05/1.36 1.05/1.36 % Assigning unary symbol not kb_weight 0 and highest precedence (94). 1.05/1.36 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. 1.05/1.36 1.05/1.36 ============================== end of process initial clauses ======== 1.05/1.36 1.05/1.36 ============================== CLAUSES FOR SEARCH ==================== 1.05/1.36 1.05/1.36 ============================== end of clauses for search ============= 1.05/1.36 1.05/1.36 ============================== SEARCH ================================ 1.05/1.36 1.05/1.36 % Starting search at 0.01 seconds. 1.05/1.36 1.05/1.36 Low Water (keep): wt=91.000, iters=3423 1.05/1.36 1.05/1.36 Low Water (keep): wt=45.000, iters=3385 1.05/1.36 1.05/1.36 Low Water (keep): wt=38.000, iters=3483 1.05/1.36 1.05/1.36 Low Water (keep): wt=33.000, iters=3369 1.05/1.36 1.05/1.36 Low Water (keep): wt=32.000, iters=3381 1.05/1.36 1.05/1.36 Low Water (keep): wt=31.000, iters=3380 1.05/1.36 1.05/1.36 Low Water (keep): wt=26.000, iters=3371 1.05/1.36 1.05/1.36 Low Water (keep): wt=25.000, iters=3501 1.05/1.36 1.05/1.36 Low Water (keep): wt=24.000, iters=3571 1.05/1.36 1.05/1.36 Low Water (keep): wt=23.000, iters=3360 122.24/122.61 122.24/122.61 Low Water (keep): wt=22.000, iters=3335 122.24/122.61 122.24/122.61 Low Water (keep): wt=21.000, iters=3336 122.24/122.61 122.24/122.61 Low Water (keep): wt=20.000, iters=3487 122.24/122.61 122.24/122.61 Low Water (keep): wt=19.000, iters=3336 122.24/122.61 122.24/122.61 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 75 (0.00 of 1.12 sec). 122.24/122.61 122.24/122.61 Low Water (keep): wt=18.000, iters=3351 122.24/122.61 122.24/122.61 Low Water (displace): id=2098, wt=127.000 122.24/122.61 122.24/122.61 Low Water (displace): id=2522, wt=111.000 122.24/122.61 122.24/122.61 Low Water (displace): id=3240, wt=91.000 122.24/122.61 122.24/122.61 Low Water (displace): id=1991, wt=83.000 122.24/122.61 122.24/122.61 Low Water (displace): id=1986, wt=79.000 122.24/122.61 122.24/122.61 Low Water (displace): id=1993, wt=71.000 122.24/122.61 122.24/122.61 Low Water (displace): id=1992, wt=63.000 122.24/122.61 122.24/122.61 Low Water (displace): id=9912, wt=45.000 122.24/122.61 122.24/122.61 Low Water (displace): id=9427, wt=43.000 122.24/122.61 122.24/122.61 Low Water (displace): id=9426, wt=42.000 122.24/122.61 122.24/122.61 Low Water (displace): id=9914, wt=41.000 122.24/122.61 122.24/122.61 Low Water (displace): id=8262, wt=39.000 122.24/122.61 122.24/122.61 Low Water (displace): id=8260, wt=38.000 122.24/122.61 122.24/122.61 Low Water (displace): id=9920, wt=37.000 122.24/122.61 122.24/122.61 Low Water (displace): id=10781, wt=35.000 122.24/122.61 122.24/122.61 Low Water (displace): id=9625, wt=34.000 122.24/122.61 122.24/122.61 Low Water (displace): id=10860, wt=33.000 122.24/122.61 122.24/122.61 Low Water (displace): id=10858, wt=32.000 122.24/122.61 122.24/122.61 Low Water (displace): id=11047, wt=31.000 122.24/122.61 122.24/122.61 Low Water (displace): id=11045, wt=30.000 122.24/122.61 122.24/122.61 Low Water (displace): id=10997, wt=29.000 122.24/122.61 122.24/122.61 Low Water (displace): id=11224, wt=24.000 122.24/122.61 122.24/122.61 Low Water (displace): id=11227, wt=23.000 122.24/122.61 122.24/122.61 Low Water (displace): id=11228, wt=22.000 122.24/122.61 122.24/122.61 Low Water (displace): id=11374, wt=21.000 122.24/122.61 122.24/122.61 Low Water (displace): id=11377, wt=17.000 122.24/122.61 122.24/122.61 Low Water (displace): id=11755, wt=16.000 122.24/122.61 122.24/122.61 Low Water (displace): id=11793, wt=15.000 122.24/122.61 122.24/122.61 Low Water (displace): id=12125, wt=13.000 122.24/122.61 122.24/122.61 Low Water (keep): wt=17.000, iters=3333 122.24/122.61 122.24/122.61 Low Water (keep): wt=16.000, iters=3417 122.24/122.61 122.24/122.61 Low Water (keep): wt=15.000, iters=4323 122.24/122.61 122.24/122.61 Low Water (keep): wt=14.000, iters=3399 122.24/122.61 122.24/122.61 Low Water (displace): id=123160, wt=12.000 122.24/122.61 122.24/122.61 Low Water (keep): wt=13.000, iters=3333 122.24/122.61 122.24/122.61 Low Water (displace): id=168024, wt=11.000 122.24/122.61 122.24/122.61 ============================== PROOF ================================= 122.24/122.61 % SZS status Theorem 122.24/122.61 % SZS output start Refutation 122.24/122.61 122.24/122.61 % Proof 1 at 114.58 (+ 7.03) seconds. 122.24/122.61 % Length of proof is 356. 122.24/122.61 % Level of proof is 100. 122.24/122.61 % Maximum clause weight is 19.000. 122.24/122.61 % Given clauses 9356. 122.24/122.61 122.24/122.61 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]. 122.24/122.61 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]. 122.24/122.61 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]. 122.24/122.61 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]. 122.24/122.61 13 (all P is_a_theorem(implies(implies(not(P),P),P))) <-> cn3 # label(cn3) # label(axiom) # label(non_clause). [assumption]. 122.24/122.61 16 (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) <-> cn2 # label(cn2) # label(axiom) # label(non_clause). [assumption]. 122.24/122.61 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]. 122.24/122.61 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]. 122.24/122.61 32 modus_ponens # label(luka_modus_ponens) # label(axiom). [assumption]. 122.24/122.61 34 cn3 # label(luka_cn3) # label(axiom). [assumption]. 122.24/122.61 35 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption]. 122.24/122.61 36 op_equiv # label(luka_op_equiv) # label(axiom). [assumption]. 122.24/122.61 37 cn1 # label(luka_cn1) # label(axiom). [assumption]. 122.24/122.61 38 cn2 # label(luka_cn2) # label(axiom). [assumption]. 122.24/122.61 40 op_implies_and # label(hilbert_op_implies_and) # label(axiom). [assumption]. 122.24/122.61 41 -and_3 # label(hilbert_and_3) # label(negated_conjecture). [assumption]. 122.24/122.61 60 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(3)]. 122.24/122.61 61 -is_a_theorem(equiv(A,B)) | B = A. [copy(60),unit_del(a,35)]. 122.24/122.61 62 is_a_theorem(implies(implies(not(A),A),A)) | -cn3 # label(cn3) # label(axiom). [clausify(13)]. 122.24/122.61 63 is_a_theorem(implies(implies(not(A),A),A)). [copy(62),unit_del(b,34)]. 122.24/122.61 64 is_a_theorem(implies(A,implies(not(A),B))) | -cn2 # label(cn2) # label(axiom). [clausify(16)]. 122.24/122.61 65 is_a_theorem(implies(A,implies(not(A),B))). [copy(64),unit_del(b,38)]. 122.24/122.61 66 -is_a_theorem(implies(c1,implies(c2,and(c1,c2)))) | and_3 # label(and_3) # label(axiom). [clausify(1)]. 122.24/122.61 67 -is_a_theorem(implies(c1,implies(c2,and(c1,c2)))). [copy(66),unit_del(b,41)]. 122.24/122.61 70 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(9)]. 122.24/122.61 71 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(70),unit_del(a,32)]. 122.24/122.61 77 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(31)]. 122.24/122.61 78 not(and(A,not(B))) = implies(A,B). [copy(77),unit_del(a,40)]. 122.24/122.61 86 -op_equiv | equiv(A,B) = and(implies(A,B),implies(B,A)) # label(op_equiv) # label(axiom). [clausify(29)]. 122.24/122.61 87 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(86),flip(b),unit_del(a,36)]. 122.24/122.61 94 -cn1 | is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))) # label(cn1) # label(axiom). [clausify(6)]. 122.24/122.61 95 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))). [copy(94),unit_del(a,37)]. 122.24/122.61 120 -is_a_theorem(A) | is_a_theorem(implies(not(A),B)). [resolve(71,b,65,a)]. 122.24/122.61 121 -is_a_theorem(implies(not(A),A)) | is_a_theorem(A). [resolve(71,b,63,a)]. 122.24/122.61 125 is_a_theorem(implies(implies(implies(A,B),and(A,not(B))),and(A,not(B)))). [para(78(a,1),63(a,1,1,1))]. 122.24/122.61 126 is_a_theorem(implies(and(A,not(B)),implies(implies(A,B),C))). [para(78(a,1),65(a,1,2,1))]. 122.24/122.61 127 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(78(a,1),78(a,1,1,2))]. 122.24/122.61 128 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(B,C),implies(A,C))). [resolve(95,a,71,b)]. 122.24/122.61 223 is_a_theorem(implies(implies(implies(implies(A,B),C),D),implies(and(A,not(B)),D))). [resolve(128,a,126,a)]. 122.24/122.61 225 is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))). [resolve(128,a,95,a)]. 122.24/122.61 226 is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C))). [resolve(128,a,65,a)]. 122.24/122.61 227 is_a_theorem(implies(implies(A,B),implies(implies(not(A),A),B))). [resolve(128,a,63,a)]. 122.24/122.61 228 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(not(A),D),B),C))). [resolve(226,a,128,a)]. 122.24/122.61 230 -is_a_theorem(implies(implies(not(A),B),C)) | is_a_theorem(implies(A,C)). [resolve(226,a,71,b)]. 122.24/122.61 243 is_a_theorem(implies(implies(implies(implies(not(A),A),B),C),implies(implies(A,B),C))). [resolve(227,a,128,a)]. 122.24/122.61 245 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(A),A),B)). [resolve(227,a,71,b)]. 122.24/122.61 255 implies(implies(A,B),and(B,not(A))) = not(equiv(A,B)). [para(87(a,1),127(a,1,1)),flip(a)]. 122.24/122.61 258 -is_a_theorem(implies(implies(A,and(B,not(C))),and(A,implies(B,C)))) | is_a_theorem(and(A,implies(B,C))). [para(127(a,1),121(a,1,1))]. 122.24/122.61 316 is_a_theorem(implies(A,implies(implies(B,C),implies(not(A),C)))). [resolve(230,a,95,a)]. 122.24/122.61 318 is_a_theorem(implies(A,A)). [resolve(230,a,63,a)]. 122.24/122.61 319 -is_a_theorem(implies(implies(implies(A,B),C),D)) | is_a_theorem(implies(and(A,not(B)),D)). [para(78(a,1),230(a,1,1,1))]. 122.24/122.61 321 is_a_theorem(implies(not(implies(A,A)),B)). [resolve(318,a,120,a)]. 122.24/122.61 335 is_a_theorem(implies(implies(A,B),implies(not(implies(C,C)),B))). [resolve(321,a,128,a)]. 122.24/122.61 630 is_a_theorem(implies(implies(not(A),A),implies(implies(B,C),implies(not(A),C)))). [resolve(316,a,245,a)]. 122.24/122.61 632 is_a_theorem(implies(implies(implies(implies(A,B),implies(not(C),B)),D),implies(C,D))). [resolve(316,a,128,a)]. 122.24/122.61 661 is_a_theorem(implies(A,implies(not(implies(B,B)),C))). [resolve(335,a,230,a)]. 122.24/122.61 781 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),implies(D,C))). [resolve(661,a,128,a)]. 122.24/122.61 1055 is_a_theorem(implies(not(equiv(A,A)),and(A,not(A)))). [para(255(a,1),125(a,1,1))]. 122.24/122.61 1244 is_a_theorem(implies(implies(and(A,not(A)),B),implies(not(equiv(A,A)),B))). [resolve(1055,a,128,a)]. 122.24/122.61 2281 -is_a_theorem(implies(implies(not(implies(A,A)),B),C)) | is_a_theorem(implies(D,C)). [resolve(781,a,71,b)]. 122.24/122.61 3026 is_a_theorem(implies(A,implies(B,B))). [resolve(2281,a,63,a)]. 122.24/122.61 3033 is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))). [resolve(3026,a,128,a)]. 122.24/122.61 3171 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(D,D),B),C))). [resolve(3033,a,128,a)]. 122.24/122.61 3173 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(implies(C,B)). [resolve(3033,a,71,b)]. 122.24/122.61 3455 is_a_theorem(implies(A,implies(B,implies(C,C)))). [resolve(3173,a,3033,a)]. 122.24/122.61 3457 is_a_theorem(implies(A,implies(implies(not(B),B),B))). [resolve(3173,a,227,a)]. 122.24/122.61 3458 is_a_theorem(implies(A,implies(B,implies(not(B),C)))). [resolve(3173,a,226,a)]. 122.24/122.61 3464 is_a_theorem(implies(implies(implies(A,implies(B,B)),C),implies(D,C))). [resolve(3455,a,128,a)]. 122.24/122.61 3538 is_a_theorem(implies(implies(implies(implies(not(A),A),A),B),implies(C,B))). [resolve(3457,a,128,a)]. 122.24/122.61 3614 is_a_theorem(implies(implies(implies(A,implies(not(A),B)),C),implies(D,C))). [resolve(3458,a,128,a)]. 122.24/122.61 5205 -is_a_theorem(implies(implies(implies(not(A),A),A),B)) | is_a_theorem(implies(C,B)). [resolve(3538,a,71,b)]. 122.24/122.61 6563 -is_a_theorem(implies(not(A),A)) | is_a_theorem(implies(implies(B,C),implies(not(A),C))). [resolve(630,a,71,b)]. 122.24/122.61 7226 -is_a_theorem(implies(and(A,not(A)),B)) | is_a_theorem(implies(not(equiv(A,A)),B)). [resolve(1244,a,71,b)]. 122.24/122.61 7655 is_a_theorem(implies(A,implies(implies(implies(B,B),C),C))). [resolve(3171,a,5205,a)]. 122.24/122.61 7664 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(implies(D,D),B),C)). [resolve(3171,a,71,b)]. 122.24/122.61 7682 is_a_theorem(implies(implies(implies(implies(implies(A,A),B),B),C),implies(D,C))). [resolve(7655,a,128,a)]. 122.24/122.61 7683 is_a_theorem(implies(implies(implies(A,A),B),B)). [resolve(7655,a,121,a)]. 122.24/122.61 7739 is_a_theorem(implies(implies(A,B),implies(implies(implies(C,C),A),B))). [resolve(7683,a,128,a)]. 122.24/122.61 7740 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(B). [resolve(7683,a,71,b)]. 122.24/122.61 7924 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(C,C),A),B)). [resolve(7739,a,71,b)]. 122.24/122.61 8411 is_a_theorem(implies(implies(implies(A,A),implies(implies(B,B),C)),implies(D,C))). [resolve(7924,a,3033,a)]. 122.24/122.61 9961 is_a_theorem(implies(implies(implies(A,A),B),implies(implies(B,C),implies(D,C)))). [resolve(7664,a,95,a)]. 122.24/122.61 10030 -is_a_theorem(implies(implies(implies(implies(A,A),B),B),C)) | is_a_theorem(implies(D,C)). [resolve(7682,a,71,b)]. 122.24/122.61 10559 -is_a_theorem(implies(implies(A,A),implies(implies(B,B),C))) | is_a_theorem(implies(D,C)). [resolve(8411,a,71,b)]. 122.24/122.61 10796 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(implies(implies(B,C),implies(D,C))). [resolve(9961,a,71,b)]. 122.24/122.61 11392 is_a_theorem(implies(A,implies(and(B,not(B)),C))). [resolve(223,a,10030,a)]. 122.24/122.61 11420 is_a_theorem(implies(and(A,not(A)),B)). [resolve(11392,a,7740,a)]. 122.24/122.61 11471 is_a_theorem(implies(not(equiv(A,A)),B)). [back_unit_del(7226),unit_del(a,11420)]. 122.24/122.61 11584 is_a_theorem(implies(implies(A,B),implies(not(equiv(C,C)),B))). [resolve(11471,a,6563,a)]. 122.24/122.61 12571 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),C),implies(D,C))). [resolve(11584,a,10796,a)]. 122.24/122.61 13141 is_a_theorem(implies(A,implies(B,equiv(C,C)))). [resolve(12571,a,5205,a)]. 122.24/122.61 13161 is_a_theorem(implies(A,equiv(B,B))). [resolve(13141,a,10559,a)]. 122.24/122.61 13227 is_a_theorem(implies(implies(equiv(A,A),B),implies(C,B))). [resolve(13161,a,10796,a)]. 122.24/122.61 13535 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(equiv(D,D),B),C))). [resolve(13227,a,128,a)]. 122.24/122.61 13765 is_a_theorem(implies(A,implies(implies(implies(not(implies(B,B)),C),D),D))). [resolve(228,a,10030,a)]. 122.24/122.61 13773 is_a_theorem(implies(A,implies(implies(implies(not(not(B)),C),B),B))). [resolve(228,a,5205,a)]. 122.24/122.61 13782 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(implies(not(A),D),B),C)). [resolve(228,a,71,b)]. 122.24/122.61 13989 is_a_theorem(implies(implies(implies(not(not(A)),B),A),A)). [resolve(13773,a,7740,a)]. 122.24/122.61 14025 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(not(A)),C),A),B))). [resolve(13989,a,128,a)]. 122.24/122.61 14026 -is_a_theorem(implies(implies(not(not(A)),B),A)) | is_a_theorem(A). [resolve(13989,a,71,b)]. 122.24/122.61 14267 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),C)). [resolve(13765,a,14026,a)]. 122.24/122.61 14313 -is_a_theorem(implies(implies(not(implies(A,A)),B),C)) | is_a_theorem(C). [resolve(14267,a,71,b)]. 122.24/122.61 14337 -is_a_theorem(not(equiv(not(implies(A,A)),B))) | is_a_theorem(and(B,not(not(implies(A,A))))). [para(255(a,1),14313(a,1))]. 122.24/122.61 14670 -is_a_theorem(implies(implies(implies(not(A),A),B),C)) | is_a_theorem(implies(implies(A,B),C)). [resolve(243,a,71,b)]. 122.24/122.61 14848 is_a_theorem(implies(A,implies(implies(equiv(B,B),C),C))). [resolve(13535,a,10030,a)]. 122.24/122.61 14864 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(equiv(D,D),B),C)). [resolve(13535,a,71,b)]. 122.24/122.61 14881 is_a_theorem(implies(implies(equiv(A,A),B),B)). [resolve(14848,a,14313,a)]. 122.24/122.61 14883 is_a_theorem(implies(implies(implies(implies(equiv(A,A),B),B),C),implies(D,C))). [resolve(14848,a,10796,a)]. 122.24/122.61 14929 -is_a_theorem(implies(equiv(A,A),B)) | is_a_theorem(B). [resolve(14881,a,71,b)]. 122.24/122.61 17713 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(not(A)),C),A),B)). [resolve(14025,a,71,b)]. 122.24/122.61 17845 is_a_theorem(implies(implies(equiv(A,A),B),implies(implies(B,C),implies(D,C)))). [resolve(14864,a,9961,a)]. 122.24/122.61 17918 -is_a_theorem(implies(implies(implies(equiv(A,A),B),B),C)) | is_a_theorem(implies(D,C)). [resolve(14883,a,71,b)]. 122.24/122.61 20219 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),and(A,not(A))),C)). [resolve(17713,a,11420,a),rewrite([78(3)])]. 122.24/122.61 20409 -is_a_theorem(implies(equiv(A,A),B)) | is_a_theorem(implies(implies(B,C),implies(D,C))). [resolve(17845,a,71,b)]. 122.24/122.61 20456 is_a_theorem(implies(A,implies(implies(implies(not(equiv(B,B)),C),D),D))). [resolve(17918,a,228,a)]. 122.24/122.61 20515 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),C),C)). [resolve(20456,a,14929,a)]. 122.24/122.61 20554 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(equiv(C,C)),D),A),B))). [resolve(20515,a,128,a)]. 122.24/122.61 22533 is_a_theorem(implies(and(not(equiv(A,A)),not(B)),C)). [resolve(319,a,20515,a)]. 122.24/122.61 22535 is_a_theorem(implies(and(not(implies(A,A)),not(B)),C)). [resolve(319,a,20219,a)]. 122.24/122.61 22544 is_a_theorem(implies(and(not(not(A)),not(B)),A)). [resolve(319,a,13989,a)]. 122.24/122.61 22553 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),implies(C,D))). [resolve(319,a,7682,a)]. 122.24/122.61 22555 is_a_theorem(implies(and(A,not(implies(not(A),B))),implies(C,D))). [resolve(319,a,3614,a)]. 122.24/122.61 22556 is_a_theorem(implies(and(implies(not(A),A),not(A)),implies(B,C))). [resolve(319,a,3538,a)]. 122.24/122.61 22557 is_a_theorem(implies(and(A,not(implies(B,B))),implies(C,D))). [resolve(319,a,3464,a)]. 122.24/122.61 22567 is_a_theorem(implies(and(A,not(B)),implies(implies(implies(not(A),C),B),D))). [resolve(319,a,228,a)]. 122.24/122.61 22569 is_a_theorem(implies(and(implies(A,B),not(implies(C,B))),implies(implies(C,A),D))). [resolve(319,a,225,a)]. 122.24/122.61 22587 is_a_theorem(implies(implies(implies(A,A),and(not(not(B)),not(C))),B)). [resolve(22544,a,7924,a)]. 122.24/122.61 22594 is_a_theorem(implies(implies(implies(not(not(A)),B),and(not(not(A)),not(B))),A)). [resolve(22544,a,245,a),rewrite([78(5)])]. 122.24/122.61 22595 is_a_theorem(implies(implies(A,B),implies(and(not(not(A)),not(C)),B))). [resolve(22544,a,128,a)]. 122.24/122.61 23034 is_a_theorem(implies(implies(implies(A,A),and(not(equiv(B,B)),not(C))),D)). [resolve(22533,a,7924,a)]. 122.24/122.61 23074 is_a_theorem(implies(implies(implies(A,A),and(not(implies(B,B)),not(C))),D)). [resolve(22535,a,7924,a)]. 122.24/122.61 23399 is_a_theorem(implies(implies(implies(A,B),C),implies(and(D,not(implies(E,E))),C))). [resolve(22557,a,128,a)]. 122.24/122.61 23594 is_a_theorem(implies(and(A,not(implies(not(A),B))),not(equiv(C,D)))). [para(255(a,1),22555(a,1,2))]. 122.24/122.61 23639 is_a_theorem(implies(and(implies(not(A),A),not(A)),not(equiv(B,C)))). [para(255(a,1),22556(a,1,2))]. 122.24/122.61 23897 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),not(equiv(C,D)))). [para(255(a,1),22553(a,1,2))]. 122.24/122.61 24216 is_a_theorem(implies(and(not(not(not(implies(A,A)))),not(B)),C)). [resolve(22595,a,14313,a)]. 122.24/122.61 24220 is_a_theorem(implies(implies(implies(and(not(not(A)),not(B)),A),C),implies(D,C))). [resolve(22595,a,10796,a)]. 122.24/122.61 24332 is_a_theorem(implies(implies(implies(A,A),and(not(not(not(implies(B,B)))),not(C))),D)). [resolve(24216,a,7924,a)]. 122.24/122.61 26706 is_a_theorem(implies(and(A,implies(B,not(A))),implies(not(equiv(not(A),B)),C))). [para(255(a,1),22567(a,1,2,1)),rewrite([78(4)])]. 122.24/122.61 27007 is_a_theorem(and(implies(A,A),implies(not(equiv(B,B)),C))). [resolve(23034,a,258,a)]. 122.24/122.61 27236 is_a_theorem(and(implies(A,A),implies(not(implies(B,B)),C))). [resolve(23074,a,258,a)]. 122.24/122.61 29736 -is_a_theorem(implies(implies(implies(A,B),implies(not(C),B)),D)) | is_a_theorem(implies(C,D)). [resolve(632,a,71,b)]. 122.24/122.61 37009 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),and(not(not(C)),not(D))),C)). [resolve(13782,a,22587,a)]. 122.24/122.61 52102 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(equiv(C,C)),D),A),B)). [resolve(20554,a,71,b)]. 122.24/122.61 54359 is_a_theorem(implies(implies(not(A),and(not(not(A)),not(not(A)))),A)). [resolve(22594,a,14670,a)]. 122.24/122.61 54425 -is_a_theorem(implies(not(A),and(not(not(A)),not(not(A))))) | is_a_theorem(A). [resolve(54359,a,71,b)]. 122.24/122.61 55527 is_a_theorem(implies(A,implies(and(B,not(implies(C,C))),D))). [resolve(23399,a,17918,a)]. 122.24/122.61 55570 is_a_theorem(implies(implies(implies(and(A,not(implies(B,B))),C),D),implies(E,D))). [resolve(55527,a,20409,a)]. 122.24/122.61 59403 -is_a_theorem(and(A,implies(B,not(A)))) | is_a_theorem(implies(not(equiv(not(A),B)),C)). [resolve(26706,a,71,b)]. 122.24/122.61 60337 is_a_theorem(implies(A,implies(B,implies(not(A),C)))). [resolve(29736,a,24220,a)]. 122.24/122.61 60346 is_a_theorem(implies(A,implies(implies(implies(not(A),B),C),implies(D,C)))). [resolve(29736,a,9961,a)]. 122.24/122.61 60426 is_a_theorem(implies(implies(implies(A,implies(not(B),C)),D),implies(B,D))). [resolve(60337,a,128,a)]. 122.24/122.61 65088 is_a_theorem(implies(A,implies(B,implies(C,implies(not(B),D))))). [resolve(60426,a,3173,a)]. 122.24/122.61 110424 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),and(not(implies(C,C)),not(D))),E)). [resolve(52102,a,22535,a)]. 122.24/122.61 112014 is_a_theorem(implies(and(and(A,not(implies(B,B))),not(C)),implies(D,E))). [resolve(55570,a,319,a)]. 122.24/122.61 112154 is_a_theorem(implies(and(and(A,not(implies(B,B))),not(C)),not(equiv(D,E)))). [para(255(a,1),112014(a,1,2))]. 122.24/122.61 114624 is_a_theorem(implies(not(equiv(not(implies(A,A)),not(implies(B,B)))),C)). [resolve(59403,a,27236,a)]. 122.24/122.61 114626 is_a_theorem(implies(not(equiv(not(implies(A,A)),not(equiv(B,B)))),C)). [resolve(59403,a,27007,a)]. 122.24/122.61 114662 is_a_theorem(equiv(not(implies(A,A)),not(implies(B,B)))). [resolve(114624,a,54425,a)]. 122.24/122.61 114759 not(implies(A,A)) = not(implies(B,B)). [resolve(114662,a,61,a)]. 122.24/122.61 114766 not(implies(A,A)) = c_0. [new_symbol(114759)]. 122.24/122.61 114767 is_a_theorem(implies(not(equiv(c_0,not(equiv(A,A)))),B)). [back_rewrite(114626),rewrite([114766(2)])]. 122.24/122.61 114803 is_a_theorem(implies(and(and(A,c_0),not(B)),not(equiv(C,D)))). [back_rewrite(112154),rewrite([114766(2)])]. 122.24/122.61 114837 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),and(c_0,not(C))),D)). [back_rewrite(110424),rewrite([114766(5)])]. 122.24/122.61 115240 is_a_theorem(implies(implies(implies(c_0,A),and(not(not(B)),not(C))),B)). [back_rewrite(37009),rewrite([114766(2)])]. 122.24/122.61 115410 is_a_theorem(implies(implies(implies(A,A),and(not(not(c_0)),not(B))),C)). [back_rewrite(24332),rewrite([114766(3)])]. 122.24/122.62 115594 -is_a_theorem(not(equiv(c_0,A))) | is_a_theorem(and(A,not(c_0))). [back_rewrite(14337),rewrite([114766(2),114766(6)])]. 122.24/122.62 115599 -is_a_theorem(implies(implies(c_0,A),B)) | is_a_theorem(B). [back_rewrite(14313),rewrite([114766(2)])]. 122.24/122.62 116947 is_a_theorem(implies(c_0,A)). [back_rewrite(321),rewrite([114766(2)])]. 122.24/122.62 117420 implies(A,implies(B,B)) = not(and(A,c_0)). [para(114766(a,1),78(a,1,1,2)),flip(a)]. 122.24/122.62 123112 is_a_theorem(equiv(c_0,not(equiv(A,A)))). [resolve(114767,a,54425,a)]. 122.24/122.62 123209 not(equiv(A,A)) = c_0. [resolve(123112,a,61,a)]. 122.24/122.62 123254 is_a_theorem(implies(implies(implies(c_0,A),and(c_0,not(B))),C)). [back_rewrite(114837),rewrite([123209(2)])]. 122.24/122.62 123273 implies(A,equiv(B,B)) = not(and(A,c_0)). [para(123209(a,1),78(a,1,1,2)),flip(a)]. 122.24/122.62 123313 is_a_theorem(implies(and(A,not(implies(not(A),B))),c_0)). [para(123209(a,1),23594(a,1,2))]. 122.24/122.62 123314 is_a_theorem(implies(and(implies(not(A),A),not(A)),c_0)). [para(123209(a,1),23639(a,1,2))]. 122.24/122.62 123319 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),c_0)). [para(123209(a,1),23897(a,1,2))]. 122.24/122.62 127480 -is_a_theorem(implies(not(and(implies(A,A),c_0)),B)) | is_a_theorem(B). [para(117420(a,1),7740(a,1,1))]. 122.24/122.62 129577 is_a_theorem(implies(implies(c_0,A),implies(and(B,not(implies(not(B),C))),A))). [resolve(123313,a,128,a)]. 122.24/122.62 129652 is_a_theorem(implies(implies(c_0,A),implies(and(implies(not(B),B),not(B)),A))). [resolve(123314,a,128,a)]. 122.24/122.62 137843 is_a_theorem(and(implies(c_0,A),implies(c_0,B))). [resolve(123254,a,258,a)]. 122.24/122.62 137878 is_a_theorem(implies(not(equiv(not(implies(c_0,A)),c_0)),B)). [resolve(137843,a,59403,a)]. 122.24/122.62 138061 is_a_theorem(equiv(not(implies(c_0,A)),c_0)). [resolve(137878,a,54425,a)]. 122.24/122.62 138153 not(implies(c_0,A)) = c_0. [resolve(138061,a,61,a),flip(a)]. 122.24/122.62 138157 implies(A,implies(c_0,B)) = not(and(A,c_0)). [para(138153(a,1),78(a,1,1,2)),flip(a)]. 122.24/122.62 139308 is_a_theorem(implies(and(implies(not(and(implies(A,A),c_0)),B),not(B)),c_0)). [para(117420(a,1),123319(a,1,1,1,1))]. 122.24/122.62 143520 is_a_theorem(implies(and(and(A,c_0),not(B)),c_0)). [para(123209(a,1),114803(a,1,2))]. 122.24/122.62 143588 is_a_theorem(implies(implies(c_0,A),implies(and(and(B,c_0),not(C)),A))). [resolve(143520,a,128,a)]. 122.24/122.62 166187 is_a_theorem(implies(not(equiv(c_0,not(not(A)))),A)). [para(255(a,1),115240(a,1,1))]. 122.24/122.62 166258 is_a_theorem(implies(implies(A,B),implies(not(equiv(c_0,not(not(A)))),B))). [resolve(166187,a,128,a)]. 122.24/122.62 167874 is_a_theorem(and(implies(A,A),implies(not(not(c_0)),B))). [resolve(115410,a,258,a)]. 122.24/122.62 167913 is_a_theorem(implies(not(equiv(c_0,not(not(c_0)))),A)). [resolve(167874,a,59403,a),rewrite([114766(2)])]. 122.24/122.62 167981 is_a_theorem(equiv(c_0,not(not(c_0)))). [resolve(167913,a,54425,a)]. 122.24/122.62 168069 not(not(c_0)) = c_0. [resolve(167981,a,61,a)]. 122.24/122.62 168072 not(and(A,c_0)) = implies(A,not(c_0)). [para(168069(a,1),78(a,1,1,2))]. 122.24/122.62 168073 is_a_theorem(not(c_0)). [para(168069(a,1),121(a,1,1)),unit_del(a,116947)]. 122.24/122.62 168080 implies(implies(not(c_0),A),and(A,c_0)) = not(equiv(not(c_0),A)). [para(168069(a,1),255(a,1,2,2))]. 122.24/122.62 168083 is_a_theorem(implies(A,not(c_0))). [para(168069(a,1),3458(a,1,2,2,1)),rewrite([138157(5),168072(5),117420(6),168072(3)])]. 122.24/122.62 168770 is_a_theorem(implies(and(implies(implies(implies(A,A),not(c_0)),B),not(B)),c_0)). [back_rewrite(139308),rewrite([168072(4)])]. 122.24/122.62 168932 implies(A,implies(c_0,B)) = implies(A,not(c_0)). [back_rewrite(138157),rewrite([168072(6)])]. 122.24/122.62 169251 -is_a_theorem(implies(implies(implies(A,A),not(c_0)),B)) | is_a_theorem(B). [back_rewrite(127480),rewrite([168072(4)])]. 122.24/122.62 169295 implies(A,equiv(B,B)) = implies(A,not(c_0)). [back_rewrite(123273),rewrite([168072(5)])]. 122.24/122.62 169704 implies(A,implies(B,B)) = implies(A,not(c_0)). [back_rewrite(117420),rewrite([168072(5)])]. 122.24/122.62 170254 is_a_theorem(implies(implies(not(c_0),A),implies(B,A))). [resolve(168083,a,20409,a)]. 122.24/122.62 171307 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(not(c_0),B),C))). [resolve(170254,a,128,a)]. 122.24/122.62 190602 is_a_theorem(implies(and(and(A,c_0),not(B)),C)). [resolve(143588,a,115599,a)]. 122.24/122.62 200226 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(equiv(c_0,not(not(A)))),B)). [resolve(166258,a,71,b)]. 122.24/122.62 213473 is_a_theorem(implies(A,implies(implies(not(c_0),B),B))). [resolve(171307,a,17918,a)]. 122.24/122.62 213479 is_a_theorem(implies(implies(A,B),implies(implies(not(c_0),A),B))). [resolve(171307,a,14670,a)]. 122.24/122.62 213503 is_a_theorem(implies(implies(not(c_0),A),A)). [resolve(213473,a,169251,a)]. 122.24/122.62 213638 -is_a_theorem(implies(not(c_0),A)) | is_a_theorem(A). [resolve(213503,a,71,b)]. 122.24/122.62 217471 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(c_0),A),B)). [resolve(213479,a,71,b)]. 122.24/122.62 218959 is_a_theorem(implies(implies(not(c_0),and(and(A,c_0),not(B))),C)). [resolve(217471,a,190602,a)]. 122.24/122.62 226440 is_a_theorem(and(not(c_0),implies(and(A,c_0),B))). [resolve(218959,a,258,a)]. 122.24/122.62 226476 is_a_theorem(implies(not(equiv(c_0,and(A,c_0))),B)). [resolve(226440,a,59403,a),rewrite([168069(3)])]. 122.24/122.62 226545 is_a_theorem(equiv(c_0,and(A,c_0))). [resolve(226476,a,54425,a)]. 122.24/122.62 226638 and(A,c_0) = c_0. [resolve(226545,a,61,a)]. 122.24/122.62 226685 implies(implies(not(c_0),A),c_0) = not(equiv(not(c_0),A)). [back_rewrite(168080),rewrite([226638(5)])]. 122.24/122.62 226686 implies(A,not(c_0)) = not(c_0). [back_rewrite(168072),rewrite([226638(2)]),flip(a)]. 122.24/122.62 226707 implies(A,implies(B,B)) = not(c_0). [back_rewrite(169704),rewrite([226686(5)])]. 122.24/122.62 226716 implies(A,equiv(B,B)) = not(c_0). [back_rewrite(169295),rewrite([226686(5)])]. 122.24/122.62 226737 implies(A,implies(c_0,B)) = not(c_0). [back_rewrite(168932),rewrite([226686(6)])]. 122.24/122.62 226746 is_a_theorem(implies(and(implies(not(c_0),A),not(A)),c_0)). [back_rewrite(168770),rewrite([226686(4)])]. 122.24/122.62 226756 and(not(c_0),implies(not(c_0),A)) = equiv(A,not(c_0)). [para(226686(a,1),87(a,1,1))]. 122.24/122.62 226757 and(implies(not(c_0),A),not(c_0)) = equiv(not(c_0),A). [para(226686(a,1),87(a,1,2))]. 122.24/122.62 229268 is_a_theorem(implies(implies(c_0,A),implies(and(implies(not(c_0),B),not(B)),A))). [resolve(226746,a,128,a)]. 122.24/122.62 229758 implies(not(c_0),c_0) = c_0. [para(123209(a,1),226685(a,2)),rewrite([226686(5)])]. 122.24/122.62 229780 not(equiv(not(c_0),implies(A,A))) = c_0. [para(226707(a,1),226685(a,1,1)),rewrite([229758(4)]),flip(a)]. 122.24/122.62 229781 not(equiv(not(c_0),equiv(A,A))) = c_0. [para(226716(a,1),226685(a,1,1)),rewrite([229758(4)]),flip(a)]. 122.24/122.62 229782 not(equiv(not(c_0),implies(c_0,A))) = c_0. [para(226737(a,1),226685(a,1,1)),rewrite([229758(4)]),flip(a)]. 122.24/122.62 229785 is_a_theorem(implies(implies(not(c_0),A),implies(implies(A,c_0),c_0))). [para(229758(a,1),95(a,1,2,2))]. 122.24/122.62 229810 is_a_theorem(implies(and(implies(A,c_0),not(c_0)),implies(implies(not(c_0),A),B))). [para(229758(a,1),22569(a,1,1,2,1))]. 122.24/122.62 229815 is_a_theorem(implies(A,implies(implies(implies(not(A),B),c_0),c_0))). [para(229758(a,1),60346(a,1,2,2))]. 122.24/122.62 229882 implies(A,equiv(not(c_0),implies(B,B))) = not(c_0). [para(229780(a,1),78(a,1,1,2)),rewrite([226638(2)]),flip(a)]. 122.24/122.62 229883 is_a_theorem(equiv(not(c_0),implies(A,A))). [para(229780(a,1),121(a,1,1)),rewrite([229882(6)]),unit_del(a,168073)]. 122.24/122.62 229933 implies(A,A) = not(c_0). [resolve(229883,a,61,a)]. 122.24/122.62 230993 equiv(A,A) = and(not(c_0),not(c_0)). [para(229933(a,1),87(a,1,1)),rewrite([229933(3)]),flip(a)]. 122.24/122.62 230994 is_a_theorem(implies(implies(A,B),implies(not(c_0),implies(A,B)))). [para(229933(a,1),95(a,1,2,1))]. 122.24/122.62 230995 implies(A,and(B,not(B))) = implies(A,c_0). [para(229933(a,1),127(a,1,1,2)),rewrite([78(4)]),flip(a)]. 122.24/122.62 231039 implies(A,equiv(not(c_0),equiv(B,B))) = not(c_0). [para(229781(a,1),78(a,1,1,2)),rewrite([226638(2)]),flip(a)]. 122.24/122.62 231040 is_a_theorem(equiv(not(c_0),equiv(A,A))). [para(229781(a,1),121(a,1,1)),rewrite([231039(6)]),unit_del(a,168073)]. 122.24/122.62 231112 equiv(A,A) = not(c_0). [resolve(231040,a,61,a)]. 122.24/122.62 231306 and(not(c_0),not(c_0)) = not(c_0). [back_rewrite(230993),rewrite([231112(1)]),flip(a)]. 122.24/122.62 231325 implies(A,equiv(not(c_0),implies(c_0,B))) = not(c_0). [para(229782(a,1),78(a,1,1,2)),rewrite([226638(2)]),flip(a)]. 122.24/122.62 231326 is_a_theorem(equiv(not(c_0),implies(c_0,A))). [para(229782(a,1),121(a,1,1)),rewrite([231325(7)]),unit_del(a,168073)]. 122.24/122.62 231478 implies(c_0,A) = not(c_0). [resolve(231326,a,61,a)]. 122.24/122.62 231699 is_a_theorem(implies(not(c_0),implies(and(implies(not(c_0),A),not(A)),B))). [back_rewrite(229268),rewrite([231478(2)])]. 122.24/122.62 231702 is_a_theorem(implies(not(c_0),implies(and(implies(not(A),A),not(A)),B))). [back_rewrite(129652),rewrite([231478(2)])]. 122.24/122.62 231703 is_a_theorem(implies(not(c_0),implies(and(A,not(implies(not(A),B))),C))). [back_rewrite(129577),rewrite([231478(2)])]. 122.24/122.62 231707 and(implies(A,c_0),not(c_0)) = equiv(A,c_0). [para(231478(a,1),87(a,1,2))]. 122.24/122.62 231708 is_a_theorem(implies(implies(A,c_0),implies(not(c_0),implies(A,B)))). [para(231478(a,1),95(a,1,2,1))]. 122.24/122.62 231709 implies(A,and(c_0,not(B))) = implies(A,c_0). [para(231478(a,1),127(a,1,1,2)),rewrite([78(4)]),flip(a)]. 122.24/122.62 231712 implies(not(c_0),and(A,not(c_0))) = not(equiv(c_0,A)). [para(231478(a,1),255(a,1,1))]. 122.24/122.62 231754 is_a_theorem(implies(and(A,not(c_0)),implies(not(equiv(not(A),c_0)),B))). [para(231478(a,1),26706(a,1,1,2))]. 122.24/122.62 231794 is_a_theorem(implies(equiv(A,c_0),implies(implies(not(c_0),A),B))). [back_rewrite(229810),rewrite([231707(5)])]. 122.24/122.62 231804 implies(implies(A,c_0),and(and(B,not(B)),not(A))) = not(equiv(A,and(B,not(B)))). [para(230995(a,1),255(a,1,1))]. 122.24/122.62 231829 implies(and(A,not(A)),c_0) = not(c_0). [para(230995(a,1),229933(a,1))]. 122.24/122.62 232273 equiv(and(A,not(A)),c_0) = not(c_0). [para(231829(a,1),87(a,1,1)),rewrite([230995(6),229933(5),231306(5)]),flip(a)]. 122.24/122.62 232297 and(A,not(A)) = c_0. [para(232273(a,1),61(a,1)),flip(b),unit_del(a,168073)]. 122.24/122.62 232301 implies(implies(A,c_0),c_0) = not(equiv(A,c_0)). [back_rewrite(231804),rewrite([232297(4),231709(6),232297(6)])]. 122.24/122.62 232313 is_a_theorem(implies(A,not(equiv(implies(not(A),B),c_0)))). [back_rewrite(229815),rewrite([232301(6)])]. 122.24/122.62 232324 is_a_theorem(implies(implies(not(c_0),A),not(equiv(A,c_0)))). [back_rewrite(229785),rewrite([232301(7)])]. 122.24/122.62 232776 is_a_theorem(implies(implies(A,implies(B,c_0)),implies(not(equiv(B,c_0)),implies(A,c_0)))). [para(232301(a,1),95(a,1,2,1))]. 122.24/122.62 232912 is_a_theorem(implies(A,implies(not(equiv(not(A),c_0)),implies(B,c_0)))). [para(232301(a,1),60346(a,1,2,1))]. 122.24/122.62 233707 -is_a_theorem(implies(not(c_0),A)) | is_a_theorem(not(equiv(A,c_0))). [resolve(232324,a,71,b)]. 122.24/122.62 234267 is_a_theorem(not(equiv(implies(A,implies(B,implies(not(A),C))),c_0))). [resolve(233707,a,65088,a)]. 122.24/122.62 234374 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(c_0),implies(A,B))). [resolve(230994,a,71,b)]. 122.24/122.62 234633 is_a_theorem(implies(not(c_0),implies(equiv(A,c_0),implies(implies(not(c_0),A),B)))). [resolve(234374,a,231794,a)]. 122.24/122.62 238128 is_a_theorem(implies(A,implies(not(equiv(not(A),c_0)),c_0))). [para(229758(a,1),232912(a,1,2,2))]. 122.24/122.62 238188 -is_a_theorem(A) | is_a_theorem(implies(not(equiv(not(A),c_0)),c_0)). [resolve(238128,a,71,b)]. 122.24/122.62 240604 is_a_theorem(implies(and(implies(not(c_0),A),not(A)),B)). [resolve(231699,a,213638,a)]. 122.24/122.62 240613 is_a_theorem(implies(not(equiv(c_0,not(implies(implies(not(c_0),A),A)))),B)). [resolve(240604,a,200226,a),rewrite([78(7)])]. 122.24/122.62 240668 is_a_theorem(implies(and(implies(not(A),A),not(A)),B)). [resolve(231702,a,213638,a)]. 122.24/122.62 240676 is_a_theorem(implies(not(equiv(c_0,not(implies(implies(not(A),A),A)))),B)). [resolve(240668,a,200226,a),rewrite([78(6)])]. 122.24/122.62 240708 is_a_theorem(implies(and(A,not(implies(not(A),B))),C)). [resolve(231703,a,213638,a)]. 122.24/122.62 240717 is_a_theorem(implies(not(equiv(c_0,not(implies(A,implies(not(A),B))))),C)). [resolve(240708,a,200226,a),rewrite([78(6)])]. 122.24/122.62 241337 is_a_theorem(equiv(c_0,not(implies(implies(not(c_0),A),A)))). [resolve(240613,a,54425,a)]. 122.24/122.62 241342 not(implies(implies(not(c_0),A),A)) = c_0. [resolve(241337,a,61,a)]. 122.24/122.62 241344 implies(A,implies(implies(not(c_0),B),B)) = not(c_0). [para(241342(a,1),78(a,1,1,2)),rewrite([226638(2)]),flip(a)]. 122.24/122.62 241363 equiv(implies(implies(not(c_0),A),A),not(c_0)) = not(c_0). [para(241344(a,1),226756(a,1,2)),rewrite([231306(5)]),flip(a)]. 122.24/122.62 241372 implies(implies(not(c_0),A),A) = not(c_0). [para(241363(a,1),61(a,1)),flip(b),unit_del(a,168073)]. 122.24/122.62 241375 and(implies(A,implies(not(c_0),A)),not(c_0)) = equiv(A,implies(not(c_0),A)). [para(241372(a,1),87(a,1,2))]. 122.24/122.62 241529 is_a_theorem(equiv(c_0,not(implies(implies(not(A),A),A)))). [resolve(240676,a,54425,a)]. 122.24/122.62 241543 not(implies(implies(not(A),A),A)) = c_0. [resolve(241529,a,61,a)]. 122.24/122.62 241606 implies(A,implies(implies(not(B),B),B)) = not(c_0). [para(241543(a,1),78(a,1,1,2)),rewrite([226638(2)]),flip(a)]. 122.24/122.62 241620 equiv(implies(implies(not(A),A),A),not(c_0)) = not(c_0). [para(241606(a,1),226756(a,1,2)),rewrite([231306(5)]),flip(a)]. 122.24/122.62 241626 implies(implies(not(A),A),A) = not(c_0). [para(241620(a,1),61(a,1)),flip(b),unit_del(a,168073)]. 122.24/122.62 241645 and(implies(A,implies(not(A),A)),not(c_0)) = equiv(A,implies(not(A),A)). [para(241626(a,1),87(a,1,2))]. 122.24/122.62 242502 is_a_theorem(equiv(c_0,not(implies(A,implies(not(A),B))))). [resolve(240717,a,54425,a)]. 122.24/122.62 242508 not(implies(A,implies(not(A),B))) = c_0. [resolve(242502,a,61,a)]. 122.24/122.62 242542 implies(A,implies(B,implies(not(B),C))) = not(c_0). [para(242508(a,1),78(a,1,1,2)),rewrite([226638(2)]),flip(a)]. 122.24/122.62 242555 equiv(implies(A,implies(not(A),B)),not(c_0)) = not(c_0). [para(242542(a,1),226756(a,1,2)),rewrite([231306(5)]),flip(a)]. 122.24/122.62 242561 implies(A,implies(not(A),B)) = not(c_0). [para(242555(a,1),61(a,1)),flip(b),unit_del(a,168073)]. 122.24/122.62 242564 equiv(A,implies(not(A),A)) = not(c_0). [back_rewrite(241645),rewrite([242561(3),231306(5)]),flip(a)]. 122.24/122.62 242568 and(implies(implies(not(A),B),A),not(c_0)) = equiv(implies(not(A),B),A). [para(242561(a,1),87(a,1,2))]. 122.24/122.62 242630 implies(not(A),A) = A. [para(242564(a,1),61(a,1)),unit_del(a,168073)]. 122.24/122.62 242792 is_a_theorem(implies(A,implies(implies(A,B),implies(C,B)))). [para(242630(a,1),60346(a,1,2,1,1))]. 122.24/122.62 242896 is_a_theorem(implies(A,not(equiv(A,c_0)))). [para(242630(a,1),232313(a,1,2,1,1))]. 122.24/122.62 242900 is_a_theorem(implies(implies(not(A),c_0),implies(not(c_0),A))). [para(242630(a,1),231708(a,1,2,2))]. 122.24/122.62 242904 is_a_theorem(not(equiv(implies(A,implies(B,A)),c_0))). [para(242630(a,1),234267(a,1,1,1,2,2))]. 122.24/122.62 242948 is_a_theorem(implies(and(A,not(c_0)),equiv(not(A),c_0))). [para(242630(a,1),231754(a,1,2))]. 122.24/122.62 243797 -is_a_theorem(A) | is_a_theorem(not(equiv(A,c_0))). [resolve(242896,a,71,b)]. 122.24/122.62 243852 is_a_theorem(not(equiv(implies(A,not(equiv(A,c_0))),c_0))). [resolve(243797,a,242896,a)]. 122.24/122.62 245759 is_a_theorem(implies(A,implies(implies(A,B),B))). [para(242630(a,1),242792(a,1,2,2))]. 122.24/122.62 245838 is_a_theorem(implies(implies(implies(implies(A,B),B),C),implies(A,C))). [resolve(245759,a,128,a)]. 122.24/122.62 246485 is_a_theorem(not(equiv(implies(implies(not(A),c_0),implies(not(c_0),A)),c_0))). [resolve(242900,a,243797,a)]. 122.24/122.62 246587 is_a_theorem(implies(not(equiv(A,c_0)),not(equiv(c_0,A)))). [para(231712(a,1),242900(a,1,2)),rewrite([78(4),232301(4)])]. 122.24/122.62 246697 -is_a_theorem(and(A,not(c_0))) | is_a_theorem(equiv(not(A),c_0)). [resolve(242948,a,71,b)]. 122.24/122.62 247407 -is_a_theorem(not(equiv(A,c_0))) | is_a_theorem(not(equiv(c_0,A))). [resolve(246587,a,71,b)]. 122.24/122.62 247676 is_a_theorem(not(equiv(c_0,implies(A,not(equiv(A,c_0)))))). [resolve(247407,a,243852,a)]. 122.24/122.62 247677 is_a_theorem(not(equiv(c_0,implies(A,implies(B,A))))). [resolve(247407,a,242904,a)]. 122.24/122.62 247722 is_a_theorem(and(implies(A,implies(B,A)),not(c_0))). [resolve(247677,a,115594,a)]. 122.24/122.62 247739 is_a_theorem(equiv(not(implies(A,implies(B,A))),c_0)). [resolve(247722,a,246697,a)]. 122.24/122.62 247849 not(implies(A,implies(B,A))) = c_0. [resolve(247739,a,61,a),flip(a)]. 122.24/122.62 247851 implies(A,implies(B,implies(C,B))) = not(c_0). [para(247849(a,1),78(a,1,1,2)),rewrite([226638(2)]),flip(a)]. 122.24/122.62 247854 implies(A,implies(B,A)) = not(c_0). [para(247849(a,1),242630(a,1,1)),rewrite([247851(4)]),flip(a)]. 122.24/122.62 247858 equiv(A,implies(not(c_0),A)) = not(c_0). [back_rewrite(241375),rewrite([247854(4),231306(5)]),flip(a)]. 122.24/122.62 247884 implies(not(c_0),A) = A. [para(247858(a,1),61(a,1)),unit_del(a,168073)]. 122.24/122.62 247910 is_a_theorem(not(equiv(implies(implies(not(A),c_0),A),c_0))). [back_rewrite(246485),rewrite([247884(6)])]. 122.24/122.62 247968 is_a_theorem(implies(equiv(A,c_0),implies(A,B))). [back_rewrite(234633),rewrite([247884(7),247884(7)])]. 122.24/122.62 248013 not(equiv(c_0,A)) = and(A,not(c_0)). [back_rewrite(231712),rewrite([247884(6)]),flip(a)]. 122.24/122.62 248022 equiv(not(c_0),A) = and(A,not(c_0)). [back_rewrite(226757),rewrite([247884(3)]),flip(a)]. 122.24/122.62 248036 is_a_theorem(and(implies(A,not(equiv(A,c_0))),not(c_0))). [back_rewrite(247676),rewrite([248013(7)])]. 122.24/122.62 248043 -is_a_theorem(not(equiv(A,c_0))) | is_a_theorem(and(A,not(c_0))). [back_rewrite(247407),rewrite([248013(7)])]. 122.24/122.62 249747 is_a_theorem(implies(equiv(not(A),c_0),A)). [para(242630(a,1),247968(a,1,2))]. 122.24/122.62 249865 is_a_theorem(implies(not(equiv(not(implies(equiv(not(A),c_0),A)),c_0)),c_0)). [resolve(249747,a,238188,a)]. 122.24/122.62 250676 not(and(A,and(B,not(c_0)))) = implies(A,equiv(c_0,B)). [para(248013(a,1),78(a,1,1,2))]. 122.24/122.62 251052 -is_a_theorem(and(A,not(c_0))) | not(c_0) = A. [para(248022(a,1),61(a,1)),flip(b)]. 122.24/122.62 253757 implies(A,not(equiv(A,c_0))) = not(c_0). [resolve(248036,a,251052,a),flip(a)]. 122.24/122.62 253761 and(implies(not(equiv(A,c_0)),A),not(c_0)) = equiv(not(equiv(A,c_0)),A). [para(253757(a,1),87(a,1,2))]. 122.24/122.62 254116 is_a_theorem(equiv(implies(not(A),c_0),A)). [resolve(248043,a,247910,a),rewrite([242568(7)])]. 122.24/122.62 254156 implies(not(A),c_0) = A. [resolve(254116,a,61,a),flip(a)]. 122.24/122.62 254204 is_a_theorem(equiv(not(implies(equiv(not(A),c_0),A)),c_0)). [back_rewrite(249865),rewrite([254156(10)])]. 122.24/122.62 254324 implies(implies(A,B),c_0) = and(A,not(B)). [para(78(a,1),254156(a,1,1))]. 122.24/122.62 254325 equiv(not(A),c_0) = and(A,not(c_0)). [para(254156(a,1),87(a,1,1)),rewrite([231478(3)]),flip(a)]. 122.24/122.62 254329 implies(A,and(not(B),not(c_0))) = not(and(A,B)). [para(254156(a,1),127(a,1,1,2)),flip(a)]. 122.24/122.62 254374 implies(and(A,not(c_0)),c_0) = equiv(c_0,A). [para(248013(a,1),254156(a,1,1))]. 122.24/122.62 254441 not(equiv(A,c_0)) = and(A,not(c_0)). [back_rewrite(232301),rewrite([254324(4)]),flip(a)]. 122.24/122.62 254570 is_a_theorem(and(implies(and(A,not(c_0)),A),not(c_0))). [back_rewrite(254204),rewrite([254325(3),254325(7)])]. 122.24/122.62 255925 and(implies(and(A,not(c_0)),A),not(c_0)) = equiv(and(A,not(c_0)),A). [back_rewrite(253761),rewrite([254441(3),254441(10)])]. 122.24/122.62 256313 is_a_theorem(implies(implies(A,implies(B,c_0)),implies(and(B,not(c_0)),implies(A,c_0)))). [back_rewrite(232776),rewrite([254441(6)])]. 122.24/122.62 256327 is_a_theorem(equiv(and(A,not(c_0)),A)). [back_rewrite(254570),rewrite([255925(7)])]. 122.24/122.62 257387 and(A,not(c_0)) = A. [resolve(256327,a,61,a),flip(a)]. 122.24/122.62 257402 is_a_theorem(implies(implies(A,implies(B,c_0)),implies(B,implies(A,c_0)))). [back_rewrite(256313),rewrite([257387(6)])]. 122.24/122.62 257526 equiv(c_0,A) = implies(A,c_0). [back_rewrite(254374),rewrite([257387(3)]),flip(a)]. 122.24/122.62 257536 not(and(A,B)) = implies(A,not(B)). [back_rewrite(254329),rewrite([257387(4)]),flip(a)]. 122.24/122.62 257766 implies(A,implies(B,c_0)) = implies(A,not(B)). [back_rewrite(250676),rewrite([257387(3),257536(2),257526(4)]),flip(a)]. 122.24/122.62 257817 equiv(not(c_0),A) = A. [back_rewrite(248022),rewrite([257387(6)])]. 122.24/122.62 257818 not(implies(A,c_0)) = A. [back_rewrite(248013),rewrite([257526(2),257387(6)])]. 122.24/122.62 258348 is_a_theorem(implies(implies(A,not(B)),implies(B,not(A)))). [back_rewrite(257402),rewrite([257766(3),257766(5)])]. 122.24/122.62 260223 implies(A,c_0) = not(A). [para(257817(a,1),255(a,2,1)),rewrite([247884(3),168069(3),226638(2)])]. 122.24/122.62 260274 not(not(A)) = A. [back_rewrite(257818),rewrite([260223(2)])]. 122.24/122.62 262709 is_a_theorem(implies(implies(not(A),not(B)),implies(B,A))). [para(260274(a,1),258348(a,1,2,2))]. 122.24/122.62 264498 is_a_theorem(implies(implies(implies(A,not(B)),not(C)),implies(C,and(A,B)))). [para(257536(a,1),262709(a,1,1,1))]. 122.24/122.62 269631 -is_a_theorem(implies(implies(implies(c1,A),A),implies(c2,and(c1,c2)))). [ur(71,b,245838,a,c,67,a)]. 122.24/122.62 269632 $F. [resolve(269631,a,264498,a)]. 122.24/122.62 122.24/122.62 % SZS output end Refutation 122.24/122.62 ============================== end of proof ========================== 122.24/122.62 122.24/122.62 ============================== STATISTICS ============================ 122.24/122.62 122.24/122.62 Given=9356. Generated=13634406. Kept=269584. proofs=1. 122.24/122.62 Usable=600. Sos=7009. Demods=530. Limbo=54, Disabled=261992. Hints=0. 122.24/122.62 Megabytes=183.78. 122.24/122.62 User_CPU=114.59, System_CPU=7.03, Wall_clock=122. 122.24/122.62 122.24/122.62 ============================== end of statistics ===================== 122.24/122.62 122.24/122.62 ============================== end of search ========================= 122.24/122.62 122.24/122.62 THEOREM PROVED 122.24/122.62 % SZS status Theorem 122.24/122.62 122.24/122.62 Exiting with 1 proof. 122.24/122.62 122.24/122.62 Process 15000 exit (max_proofs) Thu Aug 29 17:01:48 2019 122.24/122.62 Prover9 interrupted 122.34/122.62 EOF