0.05/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.05/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.12/0.33 % Computer : n029.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 : 1440 0.12/0.33 % WCLimit : 180 0.12/0.33 % DateTime : Mon Jul 3 11:27:27 EDT 2023 0.12/0.34 % CPUTime : 0.78/1.09 ============================== Prover9 =============================== 0.78/1.09 Prover9 (32) version 2009-11A, November 2009. 0.78/1.09 Process 12912 was started by sandbox2 on n029.cluster.edu, 0.78/1.09 Mon Jul 3 11:27:28 2023 0.78/1.09 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1440 -f /tmp/Prover9_12669_n029.cluster.edu". 0.78/1.09 ============================== end of head =========================== 0.78/1.09 0.78/1.09 ============================== INPUT ================================= 0.78/1.09 0.78/1.09 % Reading from file /tmp/Prover9_12669_n029.cluster.edu 0.78/1.09 0.78/1.09 set(prolog_style_variables). 0.78/1.09 set(auto2). 0.78/1.09 % set(auto2) -> set(auto). 0.78/1.09 % set(auto) -> set(auto_inference). 0.78/1.09 % set(auto) -> set(auto_setup). 0.78/1.09 % set(auto_setup) -> set(predicate_elim). 0.78/1.09 % set(auto_setup) -> assign(eq_defs, unfold). 0.78/1.09 % set(auto) -> set(auto_limits). 0.78/1.09 % set(auto_limits) -> assign(max_weight, "100.000"). 0.78/1.09 % set(auto_limits) -> assign(sos_limit, 20000). 0.78/1.09 % set(auto) -> set(auto_denials). 0.78/1.09 % set(auto) -> set(auto_process). 0.78/1.09 % set(auto2) -> assign(new_constants, 1). 0.78/1.09 % set(auto2) -> assign(fold_denial_max, 3). 0.78/1.09 % set(auto2) -> assign(max_weight, "200.000"). 0.78/1.09 % set(auto2) -> assign(max_hours, 1). 0.78/1.09 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.78/1.09 % set(auto2) -> assign(max_seconds, 0). 0.78/1.09 % set(auto2) -> assign(max_minutes, 5). 0.78/1.09 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.78/1.09 % set(auto2) -> set(sort_initial_sos). 0.78/1.09 % set(auto2) -> assign(sos_limit, -1). 0.78/1.09 % set(auto2) -> assign(lrs_ticks, 3000). 0.78/1.09 % set(auto2) -> assign(max_megs, 400). 0.78/1.09 % set(auto2) -> assign(stats, some). 0.78/1.09 % set(auto2) -> clear(echo_input). 0.78/1.09 % set(auto2) -> set(quiet). 0.78/1.09 % set(auto2) -> clear(print_initial_clauses). 0.78/1.09 % set(auto2) -> clear(print_given). 0.78/1.09 assign(lrs_ticks,-1). 0.78/1.09 assign(sos_limit,10000). 0.78/1.09 assign(order,kbo). 0.78/1.09 set(lex_order_vars). 0.78/1.09 clear(print_given). 0.78/1.09 0.78/1.09 % formulas(sos). % not echoed (43 formulas) 0.78/1.09 0.78/1.09 ============================== end of input ========================== 0.78/1.09 0.78/1.09 % From the command line: assign(max_seconds, 1440). 0.78/1.09 0.78/1.09 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.78/1.09 0.78/1.09 % Formulas that are not ordinary clauses: 0.78/1.09 1 (all X all Y is_a_theorem(implies(X,implies(Y,X)))) <-> implies_1 # label(implies_1) # label(axiom) # label(non_clause). [assumption]. 0.78/1.09 2 (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) <-> cn2 # label(cn2) # label(axiom) # label(non_clause). [assumption]. 0.78/1.09 3 (all X all Y is_a_theorem(implies(and(X,Y),X))) <-> and_1 # label(and_1) # label(axiom) # label(non_clause). [assumption]. 0.78/1.09 4 substitution_of_equivalents <-> (all X all Y (is_a_theorem(equiv(X,Y)) -> X = Y)) # label(substitution_of_equivalents) # label(axiom) # label(non_clause). [assumption]. 0.78/1.09 5 (all X all Y all Z is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))) <-> or_3 # label(or_3) # label(axiom) # label(non_clause). [assumption]. 0.78/1.09 6 and_3 <-> (all X all Y is_a_theorem(implies(X,implies(Y,and(X,Y))))) # label(and_3) # label(axiom) # label(non_clause). [assumption]. 0.78/1.09 7 implies_3 <-> (all X all Y all Z is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))) # label(implies_3) # label(axiom) # label(non_clause). [assumption]. 0.78/1.09 8 (all X all Y is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))) <-> implies_2 # label(implies_2) # label(axiom) # label(non_clause). [assumption]. 0.78/1.09 9 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption]. 0.78/1.09 10 equivalence_2 <-> (all X all Y is_a_theorem(implies(equiv(X,Y),implies(Y,X)))) # label(equivalence_2) # label(axiom) # label(non_clause). [assumption]. 0.78/1.09 11 cn1 <-> (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))) # label(cn1) # label(axiom) # label(non_clause). [assumption]. 0.78/1.09 12 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption]. 0.78/1.09 13 r4 <-> (all P all Q all R is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))) # label(r4) # label(axiom) # label(non_clause). [assumption]. 0.78/1.09 14 modus_ponens <-> (all X all Y (is_a_theorem(X) & is_a_theorem(implies(X,Y)) -> is_a_theorem(Y))) # label(modus_ponens) # label(axiom) # label(non_clause). [assumption]. 0.82/1.53 15 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption]. 0.82/1.53 16 (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))) <-> kn3 # label(kn3) # label(axiom) # label(non_clause). [assumption]. 0.82/1.53 17 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption]. 0.82/1.53 18 modus_tollens <-> (all X all Y is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))) # label(modus_tollens) # label(axiom) # label(non_clause). [assumption]. 0.82/1.53 19 (all P is_a_theorem(implies(P,and(P,P)))) <-> kn1 # label(kn1) # label(axiom) # label(non_clause). [assumption]. 0.82/1.53 20 (all P is_a_theorem(implies(implies(not(P),P),P))) <-> cn3 # label(cn3) # label(axiom) # label(non_clause). [assumption]. 0.82/1.53 21 (all P all Q is_a_theorem(implies(Q,or(P,Q)))) <-> r2 # label(r2) # label(axiom) # label(non_clause). [assumption]. 0.82/1.53 22 (all X all Y is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))) <-> equivalence_3 # label(equivalence_3) # label(axiom) # label(non_clause). [assumption]. 0.82/1.53 23 r5 <-> (all P all Q all R is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))) # label(r5) # label(axiom) # label(non_clause). [assumption]. 0.82/1.53 24 (all X all Y is_a_theorem(implies(equiv(X,Y),implies(X,Y)))) <-> equivalence_1 # label(equivalence_1) # label(axiom) # label(non_clause). [assumption]. 0.82/1.53 25 (all X all Y is_a_theorem(implies(and(X,Y),Y))) <-> and_2 # label(and_2) # label(axiom) # label(non_clause). [assumption]. 0.82/1.53 26 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption]. 0.82/1.53 27 op_equiv -> (all X all Y equiv(X,Y) = and(implies(X,Y),implies(Y,X))) # label(op_equiv) # label(axiom) # label(non_clause). [assumption]. 0.82/1.53 28 op_implies_and -> (all X all Y implies(X,Y) = not(and(X,not(Y)))) # label(op_implies_and) # label(axiom) # label(non_clause). [assumption]. 0.82/1.53 29 op_and -> (all X all Y not(or(not(X),not(Y))) = and(X,Y)) # label(op_and) # label(axiom) # label(non_clause). [assumption]. 0.82/1.53 30 op_implies_or -> (all X all Y or(not(X),Y) = implies(X,Y)) # label(op_implies_or) # label(axiom) # label(non_clause). [assumption]. 0.82/1.53 31 op_or -> (all X all Y or(X,Y) = not(and(not(X),not(Y)))) # label(op_or) # label(axiom) # label(non_clause). [assumption]. 0.82/1.53 0.82/1.53 ============================== end of process non-clausal formulas === 0.82/1.53 0.82/1.53 ============================== PROCESS INITIAL CLAUSES =============== 0.82/1.53 0.82/1.53 ============================== PREDICATE ELIMINATION ================= 0.82/1.53 0.82/1.53 ============================== end predicate elimination ============= 0.82/1.53 0.82/1.53 Auto_denials: (non-Horn, no changes). 0.82/1.53 0.82/1.53 Term ordering decisions: 0.82/1.53 0.82/1.53 % Assigning unary symbol not kb_weight 0 and highest precedence (94). 0.82/1.53 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. c10=1. c11=1. c12=1. c13=1. c14=1. c15=1. c16=1. c17=1. c18=1. c19=1. c20=1. c21=1. c22=1. c23=1. c24=1. c25=1. c26=1. c27=1. c28=1. c29=1. c30=1. c31=1. c32=1. c33=1. c34=1. c35=1. c36=1. c37=1. c38=1. c39=1. c40=1. c41=1. c42=1. c43=1. c44=1. c45=1. c46=1. c47=1. c48=1. c49=1. c50=1. c51=1. c52=1. c53=1. c54=1. c55=1. implies=1. or=1. and=1. equiv=1. not=0. 0.82/1.53 0.82/1.53 ============================== end of process initial clauses ======== 0.82/1.53 0.82/1.53 ============================== CLAUSES FOR SEARCH ==================== 0.82/1.53 0.82/1.53 ============================== end of clauses for search ============= 0.82/1.53 0.82/1.53 ============================== SEARCH ================================ 0.82/1.53 0.82/1.53 % Starting search at 0.01 seconds. 0.82/1.53 0.82/1.53 Low Water (keep): wt=43.000, iters=3363 0.82/1.53 0.82/1.53 Low Water (keep): wt=40.000, iters=3461 0.82/1.53 0.82/1.53 Low Water (keep): wt=36.000, iters=3339 0.82/1.53 0.82/1.53 Low Water (keep): wt=33.000, iters=3370 0.82/1.53 0.82/1.53 Low Water (keep): wt=32.000, iters=3369 0.82/1.53 0.82/1.53 Low Water (keep): wt=30.000, iters=3333 0.82/1.53 0.82/1.53 Low Water (keep): wt=27.000, iters=3407 0.82/1.53 0.82/1.53 Low Water (keep): wt=25.000, iters=3391 0.82/1.53 0.82/1.53 Low Water (keep): wt=24.000, iters=3454 0.82/1.53 0.82/1.53 Low Water (keep): wt=23.000, iters=3340 174.70/174.99 174.70/174.99 Low Water (keep): wt=22.000, iters=3363 174.70/174.99 174.70/174.99 Low Water (keep): wt=21.000, iters=3344 174.70/174.99 174.70/174.99 Low Water (keep): wt=20.000, iters=3337 174.70/174.99 174.70/174.99 Low Water (keep): wt=19.000, iters=3367 174.70/174.99 174.70/174.99 Low Water (keep): wt=18.000, iters=3362 174.70/174.99 174.70/174.99 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 90 (0.00 of 1.68 sec). 174.70/174.99 174.70/174.99 Low Water (displace): id=3599, wt=127.000 174.70/174.99 174.70/174.99 Low Water (displace): id=2048, wt=111.000 174.70/174.99 174.70/174.99 Low Water (displace): id=2461, wt=103.000 174.70/174.99 174.70/174.99 Low Water (displace): id=1681, wt=91.000 174.70/174.99 174.70/174.99 Low Water (displace): id=3158, wt=83.000 174.70/174.99 174.70/174.99 Low Water (displace): id=1536, wt=71.000 174.70/174.99 174.70/174.99 Low Water (displace): id=1535, wt=63.000 174.70/174.99 174.70/174.99 Low Water (displace): id=10016, wt=45.000 174.70/174.99 174.70/174.99 Low Water (displace): id=9672, wt=43.000 174.70/174.99 174.70/174.99 Low Water (displace): id=9671, wt=42.000 174.70/174.99 174.70/174.99 Low Water (displace): id=10020, wt=41.000 174.70/174.99 174.70/174.99 Low Water (displace): id=7668, wt=39.000 174.70/174.99 174.70/174.99 Low Water (displace): id=7666, wt=38.000 174.70/174.99 174.70/174.99 Low Water (displace): id=10024, wt=37.000 174.70/174.99 174.70/174.99 Low Water (displace): id=10738, wt=35.000 174.70/174.99 174.70/174.99 Low Water (displace): id=9666, wt=34.000 174.70/174.99 174.70/174.99 Low Water (displace): id=10811, wt=17.000 174.70/174.99 174.70/174.99 Low Water (displace): id=11527, wt=16.000 174.70/174.99 174.70/174.99 Low Water (displace): id=11534, wt=15.000 174.70/174.99 174.70/174.99 Low Water (keep): wt=17.000, iters=3335 174.70/174.99 174.70/174.99 Low Water (displace): id=12938, wt=14.000 174.70/174.99 174.70/174.99 Low Water (displace): id=12965, wt=13.000 174.70/174.99 174.70/174.99 Low Water (keep): wt=16.000, iters=3333 174.70/174.99 174.70/174.99 Low Water (keep): wt=15.000, iters=4003 174.70/174.99 174.70/174.99 Low Water (keep): wt=14.000, iters=3362 174.70/174.99 174.70/174.99 Low Water (keep): wt=13.000, iters=3333 174.70/174.99 174.70/174.99 Low Water (displace): id=130242, wt=12.000 174.70/174.99 174.70/174.99 Low Water (displace): id=132878, wt=11.000 174.70/174.99 174.70/174.99 ============================== PROOF ================================= 174.70/174.99 % SZS status Theorem 174.70/174.99 % SZS output start Refutation 174.70/174.99 174.70/174.99 % Proof 1 at 164.54 (+ 9.36) seconds. 174.70/174.99 % Length of proof is 340. 174.70/174.99 % Level of proof is 100. 174.70/174.99 % Maximum clause weight is 19.000. 174.70/174.99 % Given clauses 8920. 174.70/174.99 174.70/174.99 2 (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) <-> cn2 # label(cn2) # label(axiom) # label(non_clause). [assumption]. 174.70/174.99 4 substitution_of_equivalents <-> (all X all Y (is_a_theorem(equiv(X,Y)) -> X = Y)) # label(substitution_of_equivalents) # label(axiom) # label(non_clause). [assumption]. 174.70/174.99 11 cn1 <-> (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))) # label(cn1) # label(axiom) # label(non_clause). [assumption]. 174.70/174.99 14 modus_ponens <-> (all X all Y (is_a_theorem(X) & is_a_theorem(implies(X,Y)) -> is_a_theorem(Y))) # label(modus_ponens) # label(axiom) # label(non_clause). [assumption]. 174.70/174.99 20 (all P is_a_theorem(implies(implies(not(P),P),P))) <-> cn3 # label(cn3) # label(axiom) # label(non_clause). [assumption]. 174.70/174.99 24 (all X all Y is_a_theorem(implies(equiv(X,Y),implies(X,Y)))) <-> equivalence_1 # label(equivalence_1) # label(axiom) # label(non_clause). [assumption]. 174.70/174.99 27 op_equiv -> (all X all Y equiv(X,Y) = and(implies(X,Y),implies(Y,X))) # label(op_equiv) # label(axiom) # label(non_clause). [assumption]. 174.70/174.99 28 op_implies_and -> (all X all Y implies(X,Y) = not(and(X,not(Y)))) # label(op_implies_and) # label(axiom) # label(non_clause). [assumption]. 174.70/174.99 32 cn3 # label(luka_cn3) # label(axiom). [assumption]. 174.70/174.99 33 cn1 # label(luka_cn1) # label(axiom). [assumption]. 174.70/174.99 34 modus_ponens # label(luka_modus_ponens) # label(axiom). [assumption]. 174.70/174.99 36 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption]. 174.70/174.99 37 op_equiv # label(luka_op_equiv) # label(axiom). [assumption]. 174.70/174.99 38 cn2 # label(luka_cn2) # label(axiom). [assumption]. 174.70/174.99 40 op_implies_and # label(hilbert_op_implies_and) # label(axiom). [assumption]. 174.70/174.99 41 -equivalence_1 # label(hilbert_equivalence_1) # label(negated_conjecture). [assumption]. 174.70/174.99 60 is_a_theorem(implies(A,implies(not(A),B))) | -cn2 # label(cn2) # label(axiom). [clausify(2)]. 174.70/174.99 61 is_a_theorem(implies(A,implies(not(A),B))). [copy(60),unit_del(b,38)]. 174.70/174.99 62 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(4)]. 174.70/174.99 63 -is_a_theorem(equiv(A,B)) | B = A. [copy(62),unit_del(a,36)]. 174.70/174.99 64 is_a_theorem(implies(implies(not(A),A),A)) | -cn3 # label(cn3) # label(axiom). [clausify(20)]. 174.70/174.99 65 is_a_theorem(implies(implies(not(A),A),A)). [copy(64),unit_del(b,32)]. 174.70/174.99 70 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(14)]. 174.70/174.99 71 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(70),unit_del(a,34)]. 174.70/174.99 74 -is_a_theorem(implies(equiv(c50,c51),implies(c50,c51))) | equivalence_1 # label(equivalence_1) # label(axiom). [clausify(24)]. 174.70/174.99 75 -is_a_theorem(implies(equiv(c50,c51),implies(c50,c51))). [copy(74),unit_del(b,41)]. 174.70/174.99 77 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(28)]. 174.70/174.99 78 not(and(A,not(B))) = implies(A,B). [copy(77),unit_del(a,40)]. 174.70/174.99 87 -op_equiv | equiv(A,B) = and(implies(A,B),implies(B,A)) # label(op_equiv) # label(axiom). [clausify(27)]. 174.70/174.99 88 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(87),flip(b),unit_del(a,37)]. 174.70/174.99 91 -cn1 | is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))) # label(cn1) # label(axiom). [clausify(11)]. 174.70/174.99 92 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))). [copy(91),unit_del(a,33)]. 174.70/174.99 121 -is_a_theorem(implies(not(A),A)) | is_a_theorem(A). [resolve(71,b,65,a)]. 174.70/174.99 122 -is_a_theorem(A) | is_a_theorem(implies(not(A),B)). [resolve(71,b,61,a)]. 174.70/174.99 126 is_a_theorem(implies(and(A,not(B)),implies(implies(A,B),C))). [para(78(a,1),61(a,1,2,1))]. 174.70/174.99 127 is_a_theorem(implies(implies(implies(A,B),and(A,not(B))),and(A,not(B)))). [para(78(a,1),65(a,1,1,1))]. 174.70/174.99 128 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(78(a,1),78(a,1,1,2))]. 174.70/174.99 129 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(B,C),implies(A,C))). [resolve(92,a,71,b)]. 174.70/174.99 131 -is_a_theorem(implies(implies(A,B),and(A,not(B)))) | is_a_theorem(and(A,not(B))). [para(78(a,1),121(a,1,1))]. 174.70/174.99 225 is_a_theorem(implies(implies(implies(implies(A,B),C),D),implies(and(A,not(B)),D))). [resolve(129,a,126,a)]. 174.70/174.99 226 is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))). [resolve(129,a,92,a)]. 174.70/174.99 227 is_a_theorem(implies(implies(A,B),implies(implies(not(A),A),B))). [resolve(129,a,65,a)]. 174.70/174.99 228 is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C))). [resolve(129,a,61,a)]. 174.70/174.99 229 is_a_theorem(implies(implies(implies(implies(not(A),A),B),C),implies(implies(A,B),C))). [resolve(227,a,129,a)]. 174.70/174.99 231 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(A),A),B)). [resolve(227,a,71,b)]. 174.70/174.99 241 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(not(A),D),B),C))). [resolve(228,a,129,a)]. 174.70/174.99 243 -is_a_theorem(implies(implies(not(A),B),C)) | is_a_theorem(implies(A,C)). [resolve(228,a,71,b)]. 174.70/174.99 256 implies(implies(A,B),and(B,not(A))) = not(equiv(A,B)). [para(88(a,1),128(a,1,1)),flip(a)]. 174.70/174.99 346 is_a_theorem(implies(A,implies(implies(B,C),implies(not(A),C)))). [resolve(243,a,92,a)]. 174.70/174.99 347 is_a_theorem(implies(A,A)). [resolve(243,a,65,a)]. 174.70/174.99 349 -is_a_theorem(implies(implies(implies(A,B),C),D)) | is_a_theorem(implies(and(A,not(B)),D)). [para(78(a,1),243(a,1,1,1))]. 174.70/174.99 414 is_a_theorem(implies(not(implies(A,A)),B)). [resolve(347,a,122,a)]. 174.70/174.99 434 is_a_theorem(implies(implies(A,B),implies(not(implies(C,C)),B))). [resolve(414,a,129,a)]. 174.70/174.99 609 is_a_theorem(implies(implies(not(A),A),implies(implies(B,C),implies(not(A),C)))). [resolve(346,a,231,a)]. 174.70/174.99 610 is_a_theorem(implies(implies(implies(implies(A,B),implies(not(C),B)),D),implies(C,D))). [resolve(346,a,129,a)]. 174.70/174.99 638 is_a_theorem(implies(A,implies(not(implies(B,B)),C))). [resolve(434,a,243,a)]. 174.70/174.99 755 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),implies(D,C))). [resolve(638,a,129,a)]. 174.70/174.99 1024 is_a_theorem(implies(not(equiv(A,A)),and(A,not(A)))). [para(256(a,1),127(a,1,1))]. 174.70/174.99 1203 is_a_theorem(implies(implies(and(A,not(A)),B),implies(not(equiv(A,A)),B))). [resolve(1024,a,129,a)]. 174.70/174.99 2283 -is_a_theorem(implies(implies(not(implies(A,A)),B),C)) | is_a_theorem(implies(D,C)). [resolve(755,a,71,b)]. 174.70/174.99 3019 is_a_theorem(implies(A,implies(B,B))). [resolve(2283,a,65,a)]. 174.70/174.99 3026 is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))). [resolve(3019,a,129,a)]. 174.70/174.99 3372 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(D,D),B),C))). [resolve(3026,a,129,a)]. 174.70/174.99 3374 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(implies(C,B)). [resolve(3026,a,71,b)]. 174.70/174.99 3447 is_a_theorem(implies(A,implies(B,implies(not(B),C)))). [resolve(3374,a,228,a)]. 174.70/174.99 3448 is_a_theorem(implies(A,implies(implies(not(B),B),B))). [resolve(3374,a,227,a)]. 174.70/174.99 3528 is_a_theorem(implies(implies(implies(A,implies(not(A),B)),C),implies(D,C))). [resolve(3447,a,129,a)]. 174.70/174.99 3828 is_a_theorem(implies(implies(implies(implies(not(A),A),A),B),implies(C,B))). [resolve(3448,a,129,a)]. 174.70/174.99 5536 -is_a_theorem(implies(implies(implies(not(A),A),A),B)) | is_a_theorem(implies(C,B)). [resolve(3828,a,71,b)]. 174.70/174.99 6818 -is_a_theorem(implies(not(A),A)) | is_a_theorem(implies(implies(B,C),implies(not(A),C))). [resolve(609,a,71,b)]. 174.70/174.99 7374 -is_a_theorem(implies(and(A,not(A)),B)) | is_a_theorem(implies(not(equiv(A,A)),B)). [resolve(1203,a,71,b)]. 174.70/174.99 7781 is_a_theorem(implies(A,implies(implies(implies(B,B),C),C))). [resolve(3372,a,5536,a)]. 174.70/174.99 7791 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(implies(D,D),B),C)). [resolve(3372,a,71,b)]. 174.70/174.99 7863 is_a_theorem(implies(implies(implies(implies(implies(A,A),B),B),C),implies(D,C))). [resolve(7781,a,129,a)]. 174.70/174.99 7865 is_a_theorem(implies(implies(implies(A,A),B),B)). [resolve(7781,a,121,a)]. 174.70/174.99 7909 is_a_theorem(implies(implies(A,B),implies(implies(implies(C,C),A),B))). [resolve(7865,a,129,a)]. 174.70/174.99 7910 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(B). [resolve(7865,a,71,b)]. 174.70/174.99 8085 is_a_theorem(implies(A,implies(implies(implies(B,B),not(A)),C))). [resolve(7909,a,243,a)]. 174.70/174.99 8089 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(C,C),A),B)). [resolve(7909,a,71,b)]. 174.70/174.99 8113 is_a_theorem(implies(implies(implies(implies(implies(A,A),not(B)),C),D),implies(B,D))). [resolve(8085,a,129,a)]. 174.70/174.99 8578 is_a_theorem(implies(implies(implies(A,A),implies(implies(B,B),C)),implies(D,C))). [resolve(8089,a,3026,a)]. 174.70/174.99 10084 is_a_theorem(implies(implies(implies(A,A),B),implies(implies(B,C),implies(D,C)))). [resolve(7791,a,92,a)]. 174.70/174.99 10155 -is_a_theorem(implies(implies(implies(implies(A,A),B),B),C)) | is_a_theorem(implies(D,C)). [resolve(7863,a,71,b)]. 174.70/174.99 10706 -is_a_theorem(implies(implies(A,A),implies(implies(B,B),C))) | is_a_theorem(implies(D,C)). [resolve(8578,a,71,b)]. 174.70/174.99 10954 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(implies(implies(B,C),implies(D,C))). [resolve(10084,a,71,b)]. 174.70/174.99 11610 is_a_theorem(implies(A,implies(and(B,not(B)),C))). [resolve(225,a,10155,a)]. 174.70/174.99 11645 is_a_theorem(implies(and(A,not(A)),B)). [resolve(11610,a,7910,a)]. 174.70/174.99 11705 is_a_theorem(implies(not(equiv(A,A)),B)). [back_unit_del(7374),unit_del(a,11645)]. 174.70/174.99 11836 is_a_theorem(implies(implies(A,B),implies(not(equiv(C,C)),B))). [resolve(11705,a,6818,a)]. 174.70/174.99 12765 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),C),implies(D,C))). [resolve(11836,a,10954,a)]. 174.70/174.99 13178 is_a_theorem(implies(A,implies(B,equiv(C,C)))). [resolve(12765,a,5536,a)]. 174.70/174.99 13231 is_a_theorem(implies(implies(implies(A,equiv(B,B)),C),implies(D,C))). [resolve(13178,a,10954,a)]. 174.70/174.99 13234 is_a_theorem(implies(A,equiv(B,B))). [resolve(13178,a,10706,a)]. 174.70/174.99 13313 is_a_theorem(implies(implies(equiv(A,A),B),implies(C,B))). [resolve(13234,a,10954,a)]. 174.70/174.99 13635 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(equiv(D,D),B),C))). [resolve(13313,a,129,a)]. 174.70/174.99 14156 -is_a_theorem(implies(implies(implies(not(A),A),B),C)) | is_a_theorem(implies(implies(A,B),C)). [resolve(229,a,71,b)]. 174.70/174.99 14898 is_a_theorem(implies(A,implies(implies(equiv(B,B),C),C))). [resolve(13635,a,10155,a)]. 174.70/174.99 14914 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(equiv(D,D),B),C)). [resolve(13635,a,71,b)]. 174.70/174.99 14925 is_a_theorem(implies(implies(implies(implies(equiv(A,A),B),B),C),implies(D,C))). [resolve(14898,a,10954,a)]. 174.70/174.99 14937 is_a_theorem(implies(implies(equiv(A,A),B),B)). [resolve(14898,a,7910,a)]. 174.70/174.99 14968 is_a_theorem(implies(A,implies(implies(implies(not(implies(B,B)),C),D),D))). [resolve(241,a,10155,a)]. 174.70/174.99 14975 is_a_theorem(implies(A,implies(implies(implies(not(not(B)),C),B),B))). [resolve(241,a,5536,a)]. 174.70/174.99 14985 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(implies(not(A),D),B),C)). [resolve(241,a,71,b)]. 174.70/174.99 15015 is_a_theorem(implies(implies(A,B),implies(implies(equiv(C,C),A),B))). [resolve(14937,a,129,a)]. 174.70/174.99 15016 -is_a_theorem(implies(equiv(A,A),B)) | is_a_theorem(B). [resolve(14937,a,71,b)]. 174.70/174.99 15184 is_a_theorem(implies(implies(implies(not(not(A)),B),A),A)). [resolve(14975,a,15016,a)]. 174.70/174.99 15222 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(not(A)),C),A),B))). [resolve(15184,a,129,a)]. 174.70/174.99 15223 -is_a_theorem(implies(implies(not(not(A)),B),A)) | is_a_theorem(A). [resolve(15184,a,71,b)]. 174.70/174.99 15367 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(equiv(C,C),A),B)). [resolve(15015,a,71,b)]. 174.70/174.99 16916 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),C)). [resolve(14968,a,15223,a)]. 174.70/174.99 16957 -is_a_theorem(implies(implies(not(implies(A,A)),B),C)) | is_a_theorem(C). [resolve(16916,a,71,b)]. 174.70/174.99 18243 is_a_theorem(implies(implies(equiv(A,A),B),implies(implies(B,C),implies(D,C)))). [resolve(14914,a,10084,a)]. 174.70/174.99 18318 -is_a_theorem(implies(implies(implies(equiv(A,A),B),B),C)) | is_a_theorem(implies(D,C)). [resolve(14925,a,71,b)]. 174.70/174.99 18510 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(not(A)),C),A),B)). [resolve(15222,a,71,b)]. 174.70/174.99 19831 -is_a_theorem(implies(equiv(A,A),B)) | is_a_theorem(implies(implies(B,C),implies(D,C))). [resolve(18243,a,71,b)]. 174.70/174.99 19937 is_a_theorem(implies(A,implies(implies(implies(not(equiv(B,B)),C),D),D))). [resolve(18318,a,241,a)]. 174.70/174.99 19961 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),C),C)). [resolve(19937,a,16957,a)]. 174.70/174.99 20005 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(equiv(C,C)),D),A),B))). [resolve(19961,a,129,a)]. 174.70/174.99 20006 -is_a_theorem(implies(implies(not(equiv(A,A)),B),C)) | is_a_theorem(C). [resolve(19961,a,71,b)]. 174.70/174.99 20025 -is_a_theorem(not(equiv(not(equiv(A,A)),B))) | is_a_theorem(and(B,not(not(equiv(A,A))))). [para(256(a,1),20006(a,1))]. 174.70/174.99 20627 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),and(A,not(A))),C)). [resolve(18510,a,11645,a),rewrite([78(3)])]. 174.70/174.99 22702 is_a_theorem(implies(and(not(implies(A,A)),not(B)),C)). [resolve(349,a,20627,a)]. 174.70/174.99 22704 is_a_theorem(implies(and(not(equiv(A,A)),not(B)),C)). [resolve(349,a,19961,a)]. 174.70/174.99 22710 is_a_theorem(implies(and(not(not(A)),not(B)),A)). [resolve(349,a,15184,a)]. 174.70/174.99 22714 is_a_theorem(implies(and(A,not(equiv(B,B))),implies(C,D))). [resolve(349,a,13231,a)]. 174.70/174.99 22721 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),implies(C,D))). [resolve(349,a,7863,a)]. 174.70/174.99 22723 is_a_theorem(implies(and(implies(not(A),A),not(A)),implies(B,C))). [resolve(349,a,3828,a)]. 174.70/174.99 22724 is_a_theorem(implies(and(A,not(implies(not(A),B))),implies(C,D))). [resolve(349,a,3528,a)]. 174.70/174.99 22733 is_a_theorem(implies(and(A,not(B)),implies(implies(implies(not(A),C),B),D))). [resolve(349,a,241,a)]. 174.70/174.99 22736 is_a_theorem(implies(and(implies(A,B),not(implies(C,B))),implies(implies(C,A),D))). [resolve(349,a,226,a)]. 174.70/174.99 22767 is_a_theorem(implies(implies(implies(not(not(A)),B),and(not(not(A)),not(B))),A)). [resolve(22710,a,231,a),rewrite([78(5)])]. 174.70/174.99 22768 is_a_theorem(implies(implies(A,B),implies(and(not(not(A)),not(C)),B))). [resolve(22710,a,129,a)]. 174.70/174.99 23084 is_a_theorem(implies(implies(equiv(A,A),and(not(implies(B,B)),not(C))),D)). [resolve(22702,a,15367,a)]. 174.70/174.99 23132 is_a_theorem(implies(implies(implies(A,A),and(not(equiv(B,B)),not(C))),D)). [resolve(22704,a,8089,a)]. 174.70/174.99 23573 is_a_theorem(implies(implies(implies(A,B),C),implies(and(D,not(equiv(E,E))),C))). [resolve(22714,a,129,a)]. 174.70/174.99 23877 is_a_theorem(implies(and(implies(not(A),A),not(A)),not(equiv(B,C)))). [para(256(a,1),22723(a,1,2))]. 174.70/174.99 23906 is_a_theorem(implies(and(A,not(implies(not(A),B))),not(equiv(C,D)))). [para(256(a,1),22724(a,1,2))]. 174.70/174.99 24167 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),not(equiv(C,D)))). [para(256(a,1),22721(a,1,2))]. 174.70/174.99 24557 is_a_theorem(implies(and(not(not(not(equiv(A,A)))),not(B)),C)). [resolve(22768,a,20006,a)]. 174.70/174.99 24569 is_a_theorem(implies(implies(implies(and(not(not(A)),not(B)),A),C),implies(D,C))). [resolve(22768,a,10954,a)]. 174.70/174.99 27107 is_a_theorem(implies(and(A,implies(B,not(A))),implies(not(equiv(not(A),B)),C))). [para(256(a,1),22733(a,1,2,1)),rewrite([78(4)])]. 174.70/174.99 27460 is_a_theorem(and(equiv(A,A),implies(not(implies(B,B)),C))). [resolve(23084,a,131,a),rewrite([78(6)])]. 174.70/174.99 27754 is_a_theorem(and(implies(A,A),implies(not(equiv(B,B)),C))). [resolve(23132,a,131,a),rewrite([78(6)])]. 174.70/174.99 30594 -is_a_theorem(implies(implies(implies(A,B),implies(not(C),B)),D)) | is_a_theorem(implies(C,D)). [resolve(610,a,71,b)]. 174.70/174.99 33436 -is_a_theorem(implies(implies(implies(implies(A,A),not(B)),C),D)) | is_a_theorem(implies(B,D)). [resolve(8113,a,71,b)]. 174.70/174.99 53808 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(equiv(C,C)),D),A),B)). [resolve(20005,a,71,b)]. 174.70/174.99 55935 is_a_theorem(implies(and(implies(A,B),not(implies(C,B))),not(equiv(C,A)))). [para(256(a,1),22736(a,1,2))]. 174.70/174.99 56154 is_a_theorem(implies(implies(not(A),and(not(not(A)),not(not(A)))),A)). [resolve(22767,a,14156,a)]. 174.70/174.99 56220 -is_a_theorem(implies(not(A),and(not(not(A)),not(not(A))))) | is_a_theorem(A). [resolve(56154,a,71,b)]. 174.70/174.99 56453 is_a_theorem(implies(A,implies(and(B,not(equiv(C,C))),D))). [resolve(23573,a,18318,a)]. 174.70/174.99 56497 is_a_theorem(implies(implies(implies(and(A,not(equiv(B,B))),C),D),implies(E,D))). [resolve(56453,a,19831,a)]. 174.70/174.99 61386 -is_a_theorem(and(A,implies(B,not(A)))) | is_a_theorem(implies(not(equiv(not(A),B)),C)). [resolve(27107,a,71,b)]. 174.70/174.99 62361 is_a_theorem(implies(A,implies(B,implies(not(A),C)))). [resolve(30594,a,24569,a)]. 174.70/174.99 62370 is_a_theorem(implies(A,implies(implies(implies(not(A),B),C),implies(D,C)))). [resolve(30594,a,10084,a)]. 174.70/174.99 62461 is_a_theorem(implies(implies(implies(A,implies(not(B),C)),D),implies(B,D))). [resolve(62361,a,129,a)]. 174.70/174.99 67506 is_a_theorem(implies(A,implies(B,implies(C,implies(not(B),D))))). [resolve(62461,a,3374,a)]. 174.70/174.99 74595 is_a_theorem(implies(A,and(implies(B,B),not(not(A))))). [resolve(33436,a,127,a)]. 174.70/174.99 74721 is_a_theorem(implies(implies(and(implies(A,A),not(not(B))),C),implies(B,C))). [resolve(74595,a,129,a)]. 174.70/174.99 113950 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),and(not(not(C)),not(D))),C)). [resolve(53808,a,22710,a)]. 174.70/174.99 114843 is_a_theorem(implies(and(and(A,not(equiv(B,B))),not(C)),implies(D,E))). [resolve(56497,a,349,a)]. 174.70/174.99 115024 is_a_theorem(implies(and(and(A,not(equiv(B,B))),not(C)),not(equiv(D,E)))). [para(256(a,1),114843(a,1,2))]. 174.70/174.99 118427 is_a_theorem(implies(not(equiv(not(implies(A,A)),not(equiv(B,B)))),C)). [resolve(61386,a,27754,a)]. 174.70/174.99 118430 is_a_theorem(implies(not(equiv(not(equiv(A,A)),not(implies(B,B)))),C)). [resolve(61386,a,27460,a)]. 174.70/174.99 118465 is_a_theorem(equiv(not(implies(A,A)),not(equiv(B,B)))). [resolve(118427,a,56220,a)]. 174.70/174.99 118574 not(equiv(A,A)) = not(implies(B,B)). [resolve(118465,a,63,a)]. 174.70/174.99 118584 not(equiv(A,A)) = c_0. [new_symbol(118574)]. 174.70/174.99 118588 not(implies(A,A)) = c_0. [back_rewrite(118574),rewrite([118584(2)]),flip(a)]. 174.70/174.99 118599 is_a_theorem(implies(c_0,A)). [back_rewrite(118430),rewrite([118584(2),118588(3),118584(4)])]. 174.70/174.99 118609 is_a_theorem(implies(and(and(A,c_0),not(B)),not(equiv(C,D)))). [back_rewrite(115024),rewrite([118584(2)])]. 174.70/174.99 118626 is_a_theorem(implies(implies(implies(c_0,A),and(not(not(B)),not(C))),B)). [back_rewrite(113950),rewrite([118584(2)])]. 174.70/174.99 119004 is_a_theorem(implies(and(not(not(c_0)),not(A)),B)). [back_rewrite(24557),rewrite([118584(2)])]. 174.70/174.99 119039 is_a_theorem(implies(implies(implies(A,A),and(c_0,not(B))),C)). [back_rewrite(23132),rewrite([118584(3)])]. 174.70/174.99 119058 -is_a_theorem(not(equiv(c_0,A))) | is_a_theorem(and(A,not(c_0))). [back_rewrite(20025),rewrite([118584(2),118584(6)])]. 174.70/174.99 119063 -is_a_theorem(implies(implies(c_0,A),B)) | is_a_theorem(B). [back_rewrite(20006),rewrite([118584(2)])]. 174.70/174.99 121029 implies(A,equiv(B,B)) = not(and(A,c_0)). [para(118584(a,1),78(a,1,1,2)),flip(a)]. 174.70/174.99 121177 is_a_theorem(implies(and(implies(not(A),A),not(A)),c_0)). [para(118584(a,1),23877(a,1,2))]. 174.70/174.99 121180 is_a_theorem(implies(and(A,not(implies(not(A),B))),c_0)). [para(118584(a,1),23906(a,1,2))]. 174.70/174.99 121202 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),c_0)). [para(118584(a,1),24167(a,1,2))]. 174.70/174.99 122278 implies(A,implies(B,B)) = not(and(A,c_0)). [para(118588(a,1),78(a,1,1,2)),flip(a)]. 174.70/174.99 126299 is_a_theorem(implies(implies(equiv(A,A),and(not(not(c_0)),not(B))),C)). [resolve(119004,a,15367,a)]. 174.70/174.99 130631 -is_a_theorem(implies(not(and(equiv(A,A),c_0)),B)) | is_a_theorem(B). [para(121029(a,1),7910(a,1,1))]. 174.70/174.99 131716 is_a_theorem(implies(implies(c_0,A),implies(and(implies(not(B),B),not(B)),A))). [resolve(121177,a,129,a)]. 174.70/174.99 131788 is_a_theorem(implies(implies(c_0,A),implies(and(B,not(implies(not(B),C))),A))). [resolve(121180,a,129,a)]. 174.70/174.99 137185 is_a_theorem(implies(implies(implies(c_0,A),and(c_0,not(B))),C)). [resolve(119039,a,14985,a),rewrite([118588(2)])]. 174.70/174.99 138411 is_a_theorem(implies(and(implies(not(and(equiv(A,A),c_0)),B),not(B)),c_0)). [para(121029(a,1),121202(a,1,1,1,1))]. 174.70/174.99 143312 is_a_theorem(and(implies(c_0,A),implies(c_0,B))). [resolve(137185,a,131,a),rewrite([78(6)])]. 174.70/174.99 143347 is_a_theorem(implies(not(equiv(not(implies(c_0,A)),c_0)),B)). [resolve(143312,a,61386,a)]. 174.70/174.99 143533 is_a_theorem(equiv(not(implies(c_0,A)),c_0)). [resolve(143347,a,56220,a)]. 174.70/174.99 143627 not(implies(c_0,A)) = c_0. [resolve(143533,a,63,a),flip(a)]. 174.70/174.99 143631 implies(A,implies(c_0,B)) = not(and(A,c_0)). [para(143627(a,1),78(a,1,1,2)),flip(a)]. 174.70/174.99 147089 is_a_theorem(implies(and(and(A,c_0),not(B)),c_0)). [para(118584(a,1),118609(a,1,2))]. 174.70/174.99 147157 is_a_theorem(implies(implies(c_0,A),implies(and(and(B,c_0),not(C)),A))). [resolve(147089,a,129,a)]. 174.70/174.99 166177 is_a_theorem(implies(not(equiv(c_0,not(not(A)))),A)). [para(256(a,1),118626(a,1,1))]. 174.70/174.99 166248 is_a_theorem(implies(implies(A,B),implies(not(equiv(c_0,not(not(A)))),B))). [resolve(166177,a,129,a)]. 174.70/174.99 180868 is_a_theorem(and(equiv(A,A),implies(not(not(c_0)),B))). [resolve(126299,a,131,a),rewrite([78(7)])]. 174.70/174.99 180902 is_a_theorem(implies(not(equiv(c_0,not(not(c_0)))),A)). [resolve(180868,a,61386,a),rewrite([118584(2)])]. 174.70/174.99 180967 is_a_theorem(equiv(c_0,not(not(c_0)))). [resolve(180902,a,56220,a)]. 174.70/174.99 181062 not(not(c_0)) = c_0. [resolve(180967,a,63,a)]. 174.70/174.99 181095 not(and(A,c_0)) = implies(A,not(c_0)). [para(181062(a,1),78(a,1,1,2))]. 174.70/174.99 181096 is_a_theorem(not(c_0)). [para(181062(a,1),121(a,1,1)),unit_del(a,118599)]. 174.70/174.99 181104 implies(implies(not(c_0),A),and(A,c_0)) = not(equiv(not(c_0),A)). [para(181062(a,1),256(a,1,2,2))]. 174.70/174.99 181106 is_a_theorem(implies(A,not(c_0))). [para(181062(a,1),3447(a,1,2,2,1)),rewrite([143631(5),181095(5),122278(6),181095(3)])]. 174.70/174.99 181863 implies(A,implies(c_0,B)) = implies(A,not(c_0)). [back_rewrite(143631),rewrite([181095(6)])]. 174.70/174.99 181916 is_a_theorem(implies(and(implies(implies(equiv(A,A),not(c_0)),B),not(B)),c_0)). [back_rewrite(138411),rewrite([181095(4)])]. 174.70/174.99 182137 -is_a_theorem(implies(implies(equiv(A,A),not(c_0)),B)) | is_a_theorem(B). [back_rewrite(130631),rewrite([181095(4)])]. 174.70/174.99 182291 implies(A,implies(B,B)) = implies(A,not(c_0)). [back_rewrite(122278),rewrite([181095(5)])]. 174.70/174.99 182635 implies(A,equiv(B,B)) = implies(A,not(c_0)). [back_rewrite(121029),rewrite([181095(5)])]. 174.70/174.99 183255 is_a_theorem(implies(implies(not(c_0),A),implies(B,A))). [resolve(181106,a,19831,a)]. 174.70/174.99 184327 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(not(c_0),B),C))). [resolve(183255,a,129,a)]. 174.70/174.99 197118 is_a_theorem(implies(and(and(A,c_0),not(B)),C)). [resolve(147157,a,119063,a)]. 174.70/174.99 203092 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(equiv(c_0,not(not(A)))),B)). [resolve(166248,a,71,b)]. 174.70/174.99 222477 is_a_theorem(implies(A,implies(implies(not(c_0),B),B))). [resolve(184327,a,18318,a)]. 174.70/174.99 222483 is_a_theorem(implies(implies(A,B),implies(implies(not(c_0),A),B))). [resolve(184327,a,14156,a)]. 174.70/174.99 222509 is_a_theorem(implies(implies(not(c_0),A),A)). [resolve(222477,a,182137,a)]. 174.70/174.99 222643 -is_a_theorem(implies(not(c_0),A)) | is_a_theorem(A). [resolve(222509,a,71,b)]. 174.70/174.99 226513 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(c_0),A),B)). [resolve(222483,a,71,b)]. 174.70/174.99 227983 is_a_theorem(implies(implies(not(c_0),and(and(A,c_0),not(B))),C)). [resolve(226513,a,197118,a)]. 174.70/174.99 235671 is_a_theorem(and(not(c_0),implies(and(A,c_0),B))). [resolve(227983,a,131,a),rewrite([78(7)])]. 174.70/174.99 235706 is_a_theorem(implies(not(equiv(c_0,and(A,c_0))),B)). [resolve(235671,a,61386,a),rewrite([181062(3)])]. 174.70/174.99 235776 is_a_theorem(equiv(c_0,and(A,c_0))). [resolve(235706,a,56220,a)]. 174.70/174.99 235868 and(A,c_0) = c_0. [resolve(235776,a,63,a)]. 174.70/174.99 235909 implies(implies(not(c_0),A),c_0) = not(equiv(not(c_0),A)). [back_rewrite(181104),rewrite([235868(5)])]. 174.70/174.99 235910 implies(A,not(c_0)) = not(c_0). [back_rewrite(181095),rewrite([235868(2)]),flip(a)]. 174.70/174.99 235938 implies(A,equiv(B,B)) = not(c_0). [back_rewrite(182635),rewrite([235910(5)])]. 174.70/174.99 235945 implies(A,implies(B,B)) = not(c_0). [back_rewrite(182291),rewrite([235910(5)])]. 174.70/174.99 235957 is_a_theorem(implies(and(implies(not(c_0),A),not(A)),c_0)). [back_rewrite(181916),rewrite([235910(4)])]. 174.70/174.99 235959 implies(A,implies(c_0,B)) = not(c_0). [back_rewrite(181863),rewrite([235910(6)])]. 174.70/174.99 236065 and(not(c_0),implies(not(c_0),A)) = equiv(A,not(c_0)). [para(235910(a,1),88(a,1,1))]. 174.70/174.99 236066 and(implies(not(c_0),A),not(c_0)) = equiv(not(c_0),A). [para(235910(a,1),88(a,1,2))]. 174.70/174.99 236277 is_a_theorem(implies(implies(and(not(c_0),not(not(A))),B),implies(A,B))). [para(235910(a,1),74721(a,1,1,1,1))]. 174.70/174.99 239052 is_a_theorem(implies(implies(c_0,A),implies(and(implies(not(c_0),B),not(B)),A))). [resolve(235957,a,129,a)]. 174.70/174.99 245241 implies(not(c_0),c_0) = c_0. [para(118584(a,1),235909(a,2)),rewrite([235910(5)])]. 174.70/174.99 245274 not(equiv(not(c_0),equiv(A,A))) = c_0. [para(235938(a,1),235909(a,1,1)),rewrite([245241(4)]),flip(a)]. 174.70/174.99 245275 not(equiv(not(c_0),implies(A,A))) = c_0. [para(235945(a,1),235909(a,1,1)),rewrite([245241(4)]),flip(a)]. 174.70/174.99 245276 not(equiv(not(c_0),implies(c_0,A))) = c_0. [para(235959(a,1),235909(a,1,1)),rewrite([245241(4)]),flip(a)]. 174.70/174.99 245300 is_a_theorem(implies(implies(not(c_0),A),implies(implies(A,c_0),c_0))). [para(245241(a,1),92(a,1,2,2))]. 174.70/174.99 245325 is_a_theorem(implies(and(implies(A,c_0),not(c_0)),implies(implies(not(c_0),A),B))). [para(245241(a,1),22736(a,1,1,2,1))]. 174.70/174.99 245331 is_a_theorem(implies(A,implies(implies(implies(not(A),B),c_0),c_0))). [para(245241(a,1),62370(a,1,2,2))]. 174.70/174.99 245354 implies(A,equiv(not(c_0),equiv(B,B))) = not(c_0). [para(245274(a,1),78(a,1,1,2)),rewrite([235868(2)]),flip(a)]. 174.70/174.99 245355 is_a_theorem(equiv(not(c_0),equiv(A,A))). [para(245274(a,1),121(a,1,1)),rewrite([245354(6)]),unit_del(a,181096)]. 174.70/174.99 245404 equiv(A,A) = not(c_0). [resolve(245355,a,63,a)]. 174.70/174.99 246398 implies(A,equiv(not(c_0),implies(B,B))) = not(c_0). [para(245275(a,1),78(a,1,1,2)),rewrite([235868(2)]),flip(a)]. 174.70/174.99 246399 is_a_theorem(equiv(not(c_0),implies(A,A))). [para(245275(a,1),121(a,1,1)),rewrite([246398(6)]),unit_del(a,181096)]. 174.70/174.99 246444 implies(A,A) = not(c_0). [resolve(246399,a,63,a)]. 174.70/174.99 247051 and(not(c_0),not(c_0)) = not(c_0). [para(246444(a,1),88(a,1,1)),rewrite([246444(3),245404(6)])]. 174.70/174.99 247052 is_a_theorem(implies(implies(A,B),implies(not(c_0),implies(A,B)))). [para(246444(a,1),92(a,1,2,1))]. 174.70/174.99 247053 implies(A,and(B,not(B))) = implies(A,c_0). [para(246444(a,1),128(a,1,1,2)),rewrite([78(4)]),flip(a)]. 174.70/174.99 247172 implies(A,equiv(not(c_0),implies(c_0,B))) = not(c_0). [para(245276(a,1),78(a,1,1,2)),rewrite([235868(2)]),flip(a)]. 174.70/174.99 247173 is_a_theorem(equiv(not(c_0),implies(c_0,A))). [para(245276(a,1),121(a,1,1)),rewrite([247172(7)]),unit_del(a,181096)]. 174.70/174.99 247219 implies(c_0,A) = not(c_0). [resolve(247173,a,63,a)]. 174.70/174.99 247308 is_a_theorem(implies(not(c_0),implies(and(implies(not(c_0),A),not(A)),B))). [back_rewrite(239052),rewrite([247219(2)])]. 174.70/174.99 247310 is_a_theorem(implies(not(c_0),implies(and(A,not(implies(not(A),B))),C))). [back_rewrite(131788),rewrite([247219(2)])]. 174.70/174.99 247311 is_a_theorem(implies(not(c_0),implies(and(implies(not(A),A),not(A)),B))). [back_rewrite(131716),rewrite([247219(2)])]. 174.70/174.99 247315 and(implies(A,c_0),not(c_0)) = equiv(A,c_0). [para(247219(a,1),88(a,1,2))]. 174.70/174.99 247316 is_a_theorem(implies(implies(A,c_0),implies(not(c_0),implies(A,B)))). [para(247219(a,1),92(a,1,2,1))]. 174.70/174.99 247317 implies(A,and(c_0,not(B))) = implies(A,c_0). [para(247219(a,1),128(a,1,1,2)),rewrite([78(4)]),flip(a)]. 174.70/174.99 247318 implies(not(c_0),and(A,not(c_0))) = not(equiv(c_0,A)). [para(247219(a,1),256(a,1,1))]. 174.70/174.99 247346 is_a_theorem(implies(and(not(c_0),not(implies(A,B))),not(equiv(A,c_0)))). [para(247219(a,1),55935(a,1,1,1))]. 174.70/174.99 247348 is_a_theorem(implies(and(A,not(c_0)),implies(not(equiv(not(A),c_0)),B))). [para(247219(a,1),27107(a,1,1,2))]. 174.70/174.99 247373 is_a_theorem(implies(equiv(A,c_0),implies(implies(not(c_0),A),B))). [back_rewrite(245325),rewrite([247315(5)])]. 174.70/174.99 247480 implies(implies(A,c_0),and(and(B,not(B)),not(A))) = not(equiv(A,and(B,not(B)))). [para(247053(a,1),256(a,1,1))]. 174.70/174.99 247505 implies(and(A,not(A)),c_0) = not(c_0). [para(247053(a,1),246444(a,1))]. 174.70/174.99 247507 equiv(and(A,not(A)),c_0) = not(c_0). [para(247505(a,1),88(a,1,1)),rewrite([247053(6),246444(5),247051(5)]),flip(a)]. 174.70/174.99 247530 and(A,not(A)) = c_0. [para(247507(a,1),63(a,1)),flip(b),unit_del(a,181096)]. 174.70/174.99 247534 implies(implies(A,c_0),c_0) = not(equiv(A,c_0)). [back_rewrite(247480),rewrite([247530(4),247317(6),247530(6)])]. 174.70/174.99 247539 is_a_theorem(implies(A,not(equiv(implies(not(A),B),c_0)))). [back_rewrite(245331),rewrite([247534(6)])]. 174.70/174.99 247552 is_a_theorem(implies(implies(not(c_0),A),not(equiv(A,c_0)))). [back_rewrite(245300),rewrite([247534(7)])]. 174.70/174.99 248368 is_a_theorem(implies(A,implies(not(equiv(not(A),c_0)),implies(B,c_0)))). [para(247534(a,1),62370(a,1,2,1))]. 174.70/174.99 248762 -is_a_theorem(implies(not(c_0),A)) | is_a_theorem(not(equiv(A,c_0))). [resolve(247552,a,71,b)]. 174.70/174.99 249261 is_a_theorem(not(equiv(implies(A,implies(B,implies(not(A),C))),c_0))). [resolve(248762,a,67506,a)]. 174.70/174.99 249330 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(c_0),implies(A,B))). [resolve(247052,a,71,b)]. 174.70/174.99 249514 is_a_theorem(implies(not(c_0),implies(equiv(A,c_0),implies(implies(not(c_0),A),B)))). [resolve(249330,a,247373,a)]. 174.70/174.99 253099 is_a_theorem(implies(A,implies(not(equiv(not(A),c_0)),c_0))). [para(245241(a,1),248368(a,1,2,2))]. 174.70/174.99 253152 -is_a_theorem(A) | is_a_theorem(implies(not(equiv(not(A),c_0)),c_0)). [resolve(253099,a,71,b)]. 174.70/174.99 255105 -is_a_theorem(implies(and(not(c_0),not(not(equiv(c50,c51)))),implies(c50,c51))). [ur(71,b,236277,a,c,75,a)]. 174.70/174.99 255729 is_a_theorem(implies(and(implies(not(c_0),A),not(A)),B)). [resolve(247308,a,222643,a)]. 174.70/174.99 255738 is_a_theorem(implies(not(equiv(c_0,not(implies(implies(not(c_0),A),A)))),B)). [resolve(255729,a,203092,a),rewrite([78(7)])]. 174.70/174.99 255799 is_a_theorem(implies(and(A,not(implies(not(A),B))),C)). [resolve(247310,a,222643,a)]. 174.70/174.99 255808 is_a_theorem(implies(not(equiv(c_0,not(implies(A,implies(not(A),B))))),C)). [resolve(255799,a,203092,a),rewrite([78(6)])]. 174.70/174.99 255842 is_a_theorem(implies(and(implies(not(A),A),not(A)),B)). [resolve(247311,a,222643,a)]. 174.70/174.99 255869 is_a_theorem(implies(implies(not(c_0),and(implies(not(A),A),not(A))),B)). [resolve(255842,a,226513,a)]. 174.70/174.99 255909 is_a_theorem(implies(and(not(c_0),not(not(equiv(A,B)))),not(equiv(implies(A,B),c_0)))). [para(256(a,1),247346(a,1,1,2,1))]. 174.70/174.99 256600 is_a_theorem(equiv(c_0,not(implies(implies(not(c_0),A),A)))). [resolve(255738,a,56220,a)]. 174.70/174.99 256605 not(implies(implies(not(c_0),A),A)) = c_0. [resolve(256600,a,63,a)]. 174.70/174.99 256607 implies(A,implies(implies(not(c_0),B),B)) = not(c_0). [para(256605(a,1),78(a,1,1,2)),rewrite([235868(2)]),flip(a)]. 174.70/174.99 256618 equiv(implies(implies(not(c_0),A),A),not(c_0)) = not(c_0). [para(256607(a,1),236065(a,1,2)),rewrite([247051(5)]),flip(a)]. 174.70/174.99 256627 implies(implies(not(c_0),A),A) = not(c_0). [para(256618(a,1),63(a,1)),flip(b),unit_del(a,181096)]. 174.70/174.99 256631 and(implies(A,implies(not(c_0),A)),not(c_0)) = equiv(A,implies(not(c_0),A)). [para(256627(a,1),88(a,1,2))]. 174.70/174.99 256714 is_a_theorem(equiv(c_0,not(implies(A,implies(not(A),B))))). [resolve(255808,a,56220,a)]. 174.70/174.99 256720 not(implies(A,implies(not(A),B))) = c_0. [resolve(256714,a,63,a)]. 174.70/174.99 256722 implies(A,implies(B,implies(not(B),C))) = not(c_0). [para(256720(a,1),78(a,1,1,2)),rewrite([235868(2)]),flip(a)]. 174.70/174.99 256737 equiv(implies(A,implies(not(A),B)),not(c_0)) = not(c_0). [para(256722(a,1),236065(a,1,2)),rewrite([247051(5)]),flip(a)]. 174.70/174.99 256749 implies(A,implies(not(A),B)) = not(c_0). [para(256737(a,1),63(a,1)),flip(b),unit_del(a,181096)]. 174.70/174.99 256752 and(not(c_0),implies(implies(not(A),B),A)) = equiv(A,implies(not(A),B)). [para(256749(a,1),88(a,1,1))]. 174.70/174.99 256753 and(implies(implies(not(A),B),A),not(c_0)) = equiv(implies(not(A),B),A). [para(256749(a,1),88(a,1,2))]. 174.70/174.99 256904 is_a_theorem(equiv(A,implies(not(A),A))). [resolve(255869,a,131,a),rewrite([78(7),256752(6)])]. 174.70/174.99 256940 implies(not(A),A) = A. [resolve(256904,a,63,a)]. 174.70/174.99 257366 is_a_theorem(implies(A,not(equiv(A,c_0)))). [para(256940(a,1),247539(a,1,2,1,1))]. 174.70/174.99 257368 is_a_theorem(implies(implies(not(A),c_0),implies(not(c_0),A))). [para(256940(a,1),247316(a,1,2,2))]. 174.70/174.99 257377 is_a_theorem(not(equiv(implies(A,implies(B,A)),c_0))). [para(256940(a,1),249261(a,1,1,1,2,2))]. 174.70/174.99 257412 is_a_theorem(implies(and(A,not(c_0)),equiv(not(A),c_0))). [para(256940(a,1),247348(a,1,2))]. 174.70/174.99 258298 -is_a_theorem(A) | is_a_theorem(not(equiv(A,c_0))). [resolve(257366,a,71,b)]. 174.70/174.99 258493 is_a_theorem(not(equiv(implies(A,not(equiv(A,c_0))),c_0))). [resolve(258298,a,257366,a)]. 174.70/174.99 261331 is_a_theorem(not(equiv(implies(implies(not(A),c_0),implies(not(c_0),A)),c_0))). [resolve(257368,a,258298,a)]. 174.70/174.99 261442 is_a_theorem(implies(not(equiv(A,c_0)),not(equiv(c_0,A)))). [para(247318(a,1),257368(a,1,2)),rewrite([78(4),247534(4)])]. 174.70/174.99 261506 -is_a_theorem(and(A,not(c_0))) | is_a_theorem(equiv(not(A),c_0)). [resolve(257412,a,71,b)]. 174.70/174.99 262327 -is_a_theorem(not(equiv(A,c_0))) | is_a_theorem(not(equiv(c_0,A))). [resolve(261442,a,71,b)]. 174.70/174.99 262566 is_a_theorem(not(equiv(c_0,implies(A,not(equiv(A,c_0)))))). [resolve(262327,a,258493,a)]. 174.70/174.99 262567 is_a_theorem(not(equiv(c_0,implies(A,implies(B,A))))). [resolve(262327,a,257377,a)]. 174.70/174.99 262644 is_a_theorem(and(implies(A,implies(B,A)),not(c_0))). [resolve(262567,a,119058,a)]. 174.70/174.99 262660 is_a_theorem(equiv(not(implies(A,implies(B,A))),c_0)). [resolve(262644,a,261506,a)]. 174.70/174.99 262714 not(implies(A,implies(B,A))) = c_0. [resolve(262660,a,63,a),flip(a)]. 174.70/174.99 262716 implies(A,implies(B,implies(C,B))) = not(c_0). [para(262714(a,1),78(a,1,1,2)),rewrite([235868(2)]),flip(a)]. 174.70/174.99 262718 implies(A,implies(B,A)) = not(c_0). [para(262714(a,1),256940(a,1,1)),rewrite([262716(4)]),flip(a)]. 174.70/174.99 262723 equiv(A,implies(not(c_0),A)) = not(c_0). [back_rewrite(256631),rewrite([262718(4),247051(5)]),flip(a)]. 174.70/174.99 262809 implies(not(c_0),A) = A. [para(262723(a,1),63(a,1)),unit_del(a,181096)]. 174.70/174.99 262836 is_a_theorem(not(equiv(implies(implies(not(A),c_0),A),c_0))). [back_rewrite(261331),rewrite([262809(6)])]. 174.70/174.99 262904 is_a_theorem(implies(equiv(A,c_0),implies(A,B))). [back_rewrite(249514),rewrite([262809(7),262809(7)])]. 174.70/174.99 262958 not(equiv(c_0,A)) = and(A,not(c_0)). [back_rewrite(247318),rewrite([262809(6)]),flip(a)]. 174.70/174.99 262965 equiv(not(c_0),A) = and(A,not(c_0)). [back_rewrite(236066),rewrite([262809(3)]),flip(a)]. 174.70/174.99 262977 is_a_theorem(and(implies(A,not(equiv(A,c_0))),not(c_0))). [back_rewrite(262566),rewrite([262958(7)])]. 174.70/174.99 262982 -is_a_theorem(not(equiv(A,c_0))) | is_a_theorem(and(A,not(c_0))). [back_rewrite(262327),rewrite([262958(7)])]. 174.70/174.99 264574 is_a_theorem(implies(equiv(not(A),c_0),A)). [para(256940(a,1),262904(a,1,2))]. 174.70/174.99 264585 is_a_theorem(implies(not(equiv(not(implies(equiv(not(A),c_0),A)),c_0)),c_0)). [resolve(264574,a,253152,a)]. 174.70/174.99 265802 -is_a_theorem(and(A,not(c_0))) | not(c_0) = A. [para(262965(a,1),63(a,1)),flip(b)]. 174.70/174.99 268365 implies(A,not(equiv(A,c_0))) = not(c_0). [resolve(262977,a,265802,a),flip(a)]. 174.70/174.99 268397 and(implies(not(equiv(A,c_0)),A),not(c_0)) = equiv(not(equiv(A,c_0)),A). [para(268365(a,1),88(a,1,2))]. 174.70/174.99 268718 is_a_theorem(equiv(implies(not(A),c_0),A)). [resolve(262982,a,262836,a),rewrite([256753(7)])]. 174.70/174.99 268785 implies(not(A),c_0) = A. [resolve(268718,a,63,a),flip(a)]. 174.70/174.99 268832 is_a_theorem(equiv(not(implies(equiv(not(A),c_0),A)),c_0)). [back_rewrite(264585),rewrite([268785(10)])]. 174.70/174.99 268942 implies(implies(A,B),c_0) = and(A,not(B)). [para(78(a,1),268785(a,1,1))]. 174.70/174.99 268943 equiv(not(A),c_0) = and(A,not(c_0)). [para(268785(a,1),88(a,1,1)),rewrite([247219(3)]),flip(a)]. 174.70/174.99 269073 not(equiv(A,c_0)) = and(A,not(c_0)). [back_rewrite(247534),rewrite([268942(4)]),flip(a)]. 174.70/174.99 269162 is_a_theorem(and(implies(and(A,not(c_0)),A),not(c_0))). [back_rewrite(268832),rewrite([268943(3),268943(7)])]. 174.70/174.99 270402 and(implies(and(A,not(c_0)),A),not(c_0)) = equiv(and(A,not(c_0)),A). [back_rewrite(268397),rewrite([269073(3),269073(10)])]. 174.70/174.99 270701 is_a_theorem(implies(and(not(c_0),not(not(equiv(A,B)))),and(implies(A,B),not(c_0)))). [back_rewrite(255909),rewrite([269073(10)])]. 174.70/175.00 270807 is_a_theorem(equiv(and(A,not(c_0)),A)). [back_rewrite(269162),rewrite([270402(7)])]. 174.70/175.00 271959 and(A,not(c_0)) = A. [resolve(270807,a,63,a),flip(a)]. 174.70/175.00 271999 is_a_theorem(implies(and(not(c_0),not(not(equiv(A,B)))),implies(A,B))). [back_rewrite(270701),rewrite([271959(10)])]. 174.70/175.00 272000 $F. [resolve(271999,a,255105,a)]. 174.70/175.00 174.70/175.00 % SZS output end Refutation 174.70/175.00 ============================== end of proof ========================== 174.70/175.00 174.70/175.00 ============================== STATISTICS ============================ 174.70/175.00 174.70/175.00 Given=8920. Generated=14529434. Kept=271951. proofs=1. 174.70/175.00 Usable=962. Sos=6521. Demods=99. Limbo=40, Disabled=264499. Hints=0. 174.70/175.00 Megabytes=190.32. 174.70/175.00 User_CPU=164.54, System_CPU=9.36, Wall_clock=174. 174.70/175.00 174.70/175.00 ============================== end of statistics ===================== 174.70/175.00 174.70/175.00 ============================== end of search ========================= 174.70/175.00 174.70/175.00 THEOREM PROVED 174.70/175.00 % SZS status Theorem 174.70/175.00 174.70/175.00 Exiting with 1 proof. 174.70/175.00 174.70/175.00 Process 12912 exit (max_proofs) Mon Jul 3 11:30:22 2023 174.70/175.00 Prover9 interrupted 174.70/175.00 EOF