0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : tptp2X_and_run_prover9 %d %s 0.03/0.26 % Computer : n130.star.cs.uiowa.edu 0.03/0.26 % Model : x86_64 x86_64 0.03/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.26 % Memory : 32218.625MB 0.03/0.26 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.26 % CPULimit : 300 0.03/0.26 % DateTime : Sat Jul 14 06:22:39 CDT 2018 0.03/0.27 % CPUTime : 0.24/0.53 ============================== Prover9 =============================== 0.24/0.53 Prover9 (32) version 2009-11A, November 2009. 0.24/0.53 Process 15772 was started by sandbox on n130.star.cs.uiowa.edu, 0.24/0.53 Sat Jul 14 06:22:40 2018 0.24/0.53 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_15740_n130.star.cs.uiowa.edu". 0.24/0.53 ============================== end of head =========================== 0.24/0.53 0.24/0.53 ============================== INPUT ================================= 0.24/0.53 0.24/0.53 % Reading from file /tmp/Prover9_15740_n130.star.cs.uiowa.edu 0.24/0.53 0.24/0.53 set(prolog_style_variables). 0.24/0.53 set(auto2). 0.24/0.53 % set(auto2) -> set(auto). 0.24/0.53 % set(auto) -> set(auto_inference). 0.24/0.53 % set(auto) -> set(auto_setup). 0.24/0.53 % set(auto_setup) -> set(predicate_elim). 0.24/0.53 % set(auto_setup) -> assign(eq_defs, unfold). 0.24/0.53 % set(auto) -> set(auto_limits). 0.24/0.53 % set(auto_limits) -> assign(max_weight, "100.000"). 0.24/0.53 % set(auto_limits) -> assign(sos_limit, 20000). 0.24/0.53 % set(auto) -> set(auto_denials). 0.24/0.53 % set(auto) -> set(auto_process). 0.24/0.53 % set(auto2) -> assign(new_constants, 1). 0.24/0.53 % set(auto2) -> assign(fold_denial_max, 3). 0.24/0.53 % set(auto2) -> assign(max_weight, "200.000"). 0.24/0.53 % set(auto2) -> assign(max_hours, 1). 0.24/0.53 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.24/0.53 % set(auto2) -> assign(max_seconds, 0). 0.24/0.53 % set(auto2) -> assign(max_minutes, 5). 0.24/0.53 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.24/0.53 % set(auto2) -> set(sort_initial_sos). 0.24/0.53 % set(auto2) -> assign(sos_limit, -1). 0.24/0.53 % set(auto2) -> assign(lrs_ticks, 3000). 0.24/0.53 % set(auto2) -> assign(max_megs, 400). 0.24/0.53 % set(auto2) -> assign(stats, some). 0.24/0.53 % set(auto2) -> clear(echo_input). 0.24/0.53 % set(auto2) -> set(quiet). 0.24/0.53 % set(auto2) -> clear(print_initial_clauses). 0.24/0.53 % set(auto2) -> clear(print_given). 0.24/0.53 assign(lrs_ticks,-1). 0.24/0.53 assign(sos_limit,10000). 0.24/0.53 assign(order,kbo). 0.24/0.53 set(lex_order_vars). 0.24/0.53 clear(print_given). 0.24/0.53 0.24/0.53 % formulas(sos). % not echoed (43 formulas) 0.24/0.53 0.24/0.53 ============================== end of input ========================== 0.24/0.53 0.24/0.53 % From the command line: assign(max_seconds, 300). 0.24/0.53 0.24/0.53 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.24/0.53 0.24/0.53 % Formulas that are not ordinary clauses: 0.24/0.53 1 (all X all Y is_a_theorem(implies(and(X,Y),Y))) <-> and_2 # label(and_2) # label(axiom) # label(non_clause). [assumption]. 0.24/0.53 2 (all X all Y is_a_theorem(implies(equiv(X,Y),implies(Y,X)))) <-> equivalence_2 # label(equivalence_2) # label(axiom) # label(non_clause). [assumption]. 0.24/0.53 3 substitution_of_equivalents <-> (all X all Y (is_a_theorem(equiv(X,Y)) -> Y = X)) # label(substitution_of_equivalents) # label(axiom) # label(non_clause). [assumption]. 0.24/0.53 4 kn3 <-> (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))) # label(kn3) # label(axiom) # label(non_clause). [assumption]. 0.24/0.53 5 r5 <-> (all P all Q all R is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))) # label(r5) # label(axiom) # label(non_clause). [assumption]. 0.24/0.53 6 (all P is_a_theorem(implies(P,and(P,P)))) <-> kn1 # label(kn1) # label(axiom) # label(non_clause). [assumption]. 0.24/0.53 7 (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))) <-> cn1 # label(cn1) # label(axiom) # label(non_clause). [assumption]. 0.24/0.53 8 r4 <-> (all P all Q all R is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))) # label(r4) # label(axiom) # label(non_clause). [assumption]. 0.24/0.53 9 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption]. 0.24/0.53 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption]. 0.24/0.53 11 (all X all Y is_a_theorem(implies(Y,or(X,Y)))) <-> or_2 # label(or_2) # label(axiom) # label(non_clause). [assumption]. 0.24/0.53 12 modus_ponens <-> (all X all Y (is_a_theorem(X) & is_a_theorem(implies(X,Y)) -> is_a_theorem(Y))) # label(modus_ponens) # label(axiom) # label(non_clause). [assumption]. 0.24/0.53 13 implies_3 <-> (all X all Y all Z is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))) # label(implies_3) # label(axiom) # label(non_clause). [assumption]. 0.24/0.53 14 (all P is_a_theorem(implies(or(P,P),P))) <-> r1 # label(r1) # label(axiom) # label(non_clause). [assumption]. 0.26/0.96 15 (all X all Y is_a_theorem(implies(X,implies(Y,and(X,Y))))) <-> and_3 # label(and_3) # label(axiom) # label(non_clause). [assumption]. 0.26/0.96 16 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption]. 0.26/0.96 17 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption]. 0.26/0.96 18 (all P is_a_theorem(implies(implies(not(P),P),P))) <-> cn3 # label(cn3) # label(axiom) # label(non_clause). [assumption]. 0.26/0.96 19 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption]. 0.26/0.96 20 (all X all Y is_a_theorem(implies(equiv(X,Y),implies(X,Y)))) <-> equivalence_1 # label(equivalence_1) # label(axiom) # label(non_clause). [assumption]. 0.26/0.96 21 or_3 <-> (all X all Y all Z is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))) # label(or_3) # label(axiom) # label(non_clause). [assumption]. 0.26/0.96 22 (all X all Y is_a_theorem(implies(X,implies(Y,X)))) <-> implies_1 # label(implies_1) # label(axiom) # label(non_clause). [assumption]. 0.26/0.96 23 modus_tollens <-> (all X all Y is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))) # label(modus_tollens) # label(axiom) # label(non_clause). [assumption]. 0.26/0.96 24 (all P all Q is_a_theorem(implies(and(P,Q),P))) <-> kn2 # label(kn2) # label(axiom) # label(non_clause). [assumption]. 0.26/0.96 25 (all X all Y is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))) <-> equivalence_3 # label(equivalence_3) # label(axiom) # label(non_clause). [assumption]. 0.26/0.96 26 implies_2 <-> (all X all Y is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))) # label(implies_2) # label(axiom) # label(non_clause). [assumption]. 0.26/0.96 27 op_or -> (all X all Y or(X,Y) = not(and(not(X),not(Y)))) # label(op_or) # label(axiom) # label(non_clause). [assumption]. 0.26/0.96 28 op_and -> (all X all Y and(X,Y) = not(or(not(X),not(Y)))) # label(op_and) # label(axiom) # label(non_clause). [assumption]. 0.26/0.96 29 op_implies_and -> (all X all Y not(and(X,not(Y))) = implies(X,Y)) # label(op_implies_and) # label(axiom) # label(non_clause). [assumption]. 0.26/0.96 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]. 0.26/0.96 31 op_equiv -> (all X all Y equiv(X,Y) = and(implies(X,Y),implies(Y,X))) # label(op_equiv) # label(axiom) # label(non_clause). [assumption]. 0.26/0.96 0.26/0.96 ============================== end of process non-clausal formulas === 0.26/0.96 0.26/0.96 ============================== PROCESS INITIAL CLAUSES =============== 0.26/0.96 0.26/0.96 ============================== PREDICATE ELIMINATION ================= 0.26/0.96 0.26/0.96 ============================== end predicate elimination ============= 0.26/0.96 0.26/0.96 Auto_denials: (non-Horn, no changes). 0.26/0.96 0.26/0.96 Term ordering decisions: 0.26/0.96 0.26/0.96 % Assigning unary symbol not kb_weight 0 and highest precedence (94). 0.26/0.96 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. 0.26/0.96 0.26/0.96 ============================== end of process initial clauses ======== 0.26/0.96 0.26/0.96 ============================== CLAUSES FOR SEARCH ==================== 0.26/0.96 0.26/0.96 ============================== end of clauses for search ============= 0.26/0.96 0.26/0.96 ============================== SEARCH ================================ 0.26/0.96 0.26/0.96 % Starting search at 0.01 seconds. 0.26/0.96 0.26/0.96 Low Water (keep): wt=39.000, iters=3343 0.26/0.96 0.26/0.96 Low Water (keep): wt=36.000, iters=3380 0.26/0.96 0.26/0.96 Low Water (keep): wt=31.000, iters=3373 0.26/0.96 0.26/0.96 Low Water (keep): wt=30.000, iters=3371 0.26/0.96 0.26/0.96 Low Water (keep): wt=29.000, iters=3391 0.26/0.96 0.26/0.96 Low Water (keep): wt=28.000, iters=3355 0.26/0.96 0.26/0.96 Low Water (keep): wt=27.000, iters=3433 0.26/0.96 0.26/0.96 Low Water (keep): wt=25.000, iters=3389 0.26/0.96 0.26/0.96 Low Water (keep): wt=24.000, iters=3368 0.26/0.96 0.26/0.96 Low Water (keep): wt=23.000, iters=3381 176.99/177.32 176.99/177.32 Low Water (keep): wt=22.000, iters=3359 176.99/177.32 176.99/177.32 Low Water (keep): wt=21.000, iters=3334 176.99/177.32 176.99/177.32 Low Water (keep): wt=20.000, iters=3340 176.99/177.32 176.99/177.32 Low Water (keep): wt=19.000, iters=3335 176.99/177.32 176.99/177.32 Low Water (keep): wt=18.000, iters=3335 176.99/177.32 176.99/177.32 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 79 (0.00 of 1.53 sec). 176.99/177.32 176.99/177.32 Low Water (displace): id=2387, wt=111.000 176.99/177.32 176.99/177.32 Low Water (displace): id=2790, wt=103.000 176.99/177.32 176.99/177.32 Low Water (displace): id=3582, wt=83.000 176.99/177.32 176.99/177.32 Low Water (displace): id=1072, wt=75.000 176.99/177.32 176.99/177.32 Low Water (displace): id=1075, wt=55.000 176.99/177.32 176.99/177.32 Low Water (displace): id=2792, wt=51.000 176.99/177.32 176.99/177.32 Low Water (displace): id=1506, wt=47.000 176.99/177.32 176.99/177.32 Low Water (displace): id=1692, wt=43.000 176.99/177.32 176.99/177.32 Low Water (displace): id=3583, wt=41.000 176.99/177.32 176.99/177.32 Low Water (displace): id=2754, wt=40.000 176.99/177.32 176.99/177.32 Low Water (displace): id=3628, wt=39.000 176.99/177.32 176.99/177.32 Low Water (displace): id=2821, wt=38.000 176.99/177.32 176.99/177.32 Low Water (displace): id=3413, wt=37.000 176.99/177.32 176.99/177.32 Low Water (displace): id=10924, wt=35.000 176.99/177.32 176.99/177.32 Low Water (displace): id=10959, wt=34.000 176.99/177.32 176.99/177.32 Low Water (displace): id=11052, wt=33.000 176.99/177.32 176.99/177.32 Low Water (displace): id=11050, wt=32.000 176.99/177.32 176.99/177.32 Low Water (displace): id=11240, wt=17.000 176.99/177.32 176.99/177.32 Low Water (displace): id=11616, wt=16.000 176.99/177.32 176.99/177.32 Low Water (keep): wt=17.000, iters=3498 176.99/177.32 176.99/177.32 Low Water (displace): id=11926, wt=15.000 176.99/177.32 176.99/177.32 Low Water (displace): id=12022, wt=14.000 176.99/177.32 176.99/177.32 Low Water (displace): id=13457, wt=13.000 176.99/177.32 176.99/177.32 Low Water (keep): wt=16.000, iters=3340 176.99/177.32 176.99/177.32 Low Water (displace): id=17895, wt=12.000 176.99/177.32 176.99/177.32 Low Water (keep): wt=15.000, iters=4057 176.99/177.32 176.99/177.32 Low Water (keep): wt=14.000, iters=3351 176.99/177.32 176.99/177.32 Low Water (keep): wt=13.000, iters=3339 176.99/177.32 176.99/177.32 ============================== PROOF ================================= 176.99/177.32 % SZS status Theorem 176.99/177.32 % SZS output start Refutation 176.99/177.32 176.99/177.32 % Proof 1 at 169.52 (+ 7.23) seconds. 176.99/177.32 % Length of proof is 344. 176.99/177.32 % Level of proof is 99. 176.99/177.32 % Maximum clause weight is 19.000. 176.99/177.32 % Given clauses 8696. 176.99/177.32 176.99/177.32 3 substitution_of_equivalents <-> (all X all Y (is_a_theorem(equiv(X,Y)) -> Y = X)) # label(substitution_of_equivalents) # label(axiom) # label(non_clause). [assumption]. 176.99/177.32 7 (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))) <-> cn1 # label(cn1) # label(axiom) # label(non_clause). [assumption]. 176.99/177.32 9 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption]. 176.99/177.32 12 modus_ponens <-> (all X all Y (is_a_theorem(X) & is_a_theorem(implies(X,Y)) -> is_a_theorem(Y))) # label(modus_ponens) # label(axiom) # label(non_clause). [assumption]. 176.99/177.32 17 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption]. 176.99/177.32 18 (all P is_a_theorem(implies(implies(not(P),P),P))) <-> cn3 # label(cn3) # label(axiom) # label(non_clause). [assumption]. 176.99/177.32 29 op_implies_and -> (all X all Y not(and(X,not(Y))) = implies(X,Y)) # label(op_implies_and) # label(axiom) # label(non_clause). [assumption]. 176.99/177.32 31 op_equiv -> (all X all Y equiv(X,Y) = and(implies(X,Y),implies(Y,X))) # label(op_equiv) # label(axiom) # label(non_clause). [assumption]. 176.99/177.32 33 cn3 # label(luka_cn3) # label(axiom). [assumption]. 176.99/177.32 34 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption]. 176.99/177.32 35 cn1 # label(luka_cn1) # label(axiom). [assumption]. 176.99/177.32 36 modus_ponens # label(luka_modus_ponens) # label(axiom). [assumption]. 176.99/177.32 37 cn2 # label(luka_cn2) # label(axiom). [assumption]. 176.99/177.32 39 op_equiv # label(luka_op_equiv) # label(axiom). [assumption]. 176.99/177.32 40 op_implies_and # label(hilbert_op_implies_and) # label(axiom). [assumption]. 176.99/177.32 41 -and_1 # label(hilbert_and_1) # label(negated_conjecture). [assumption]. 176.99/177.32 54 and_1 | -is_a_theorem(implies(and(c36,c37),c36)) # label(and_1) # label(axiom). [clausify(17)]. 176.99/177.32 55 -is_a_theorem(implies(and(c36,c37),c36)). [copy(54),unit_del(a,41)]. 176.99/177.32 60 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(3)]. 176.99/177.32 61 -is_a_theorem(equiv(A,B)) | B = A. [copy(60),unit_del(a,34)]. 176.99/177.32 62 -cn2 | is_a_theorem(implies(A,implies(not(A),B))) # label(cn2) # label(axiom). [clausify(9)]. 176.99/177.32 63 is_a_theorem(implies(A,implies(not(A),B))). [copy(62),unit_del(a,37)]. 176.99/177.32 65 is_a_theorem(implies(implies(not(A),A),A)) | -cn3 # label(cn3) # label(axiom). [clausify(18)]. 176.99/177.32 66 is_a_theorem(implies(implies(not(A),A),A)). [copy(65),unit_del(b,33)]. 176.99/177.32 69 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(12)]. 176.99/177.32 70 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(69),unit_del(a,36)]. 176.99/177.32 78 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)]. 176.99/177.32 79 not(and(A,not(B))) = implies(A,B). [copy(78),unit_del(a,40)]. 176.99/177.32 88 -op_equiv | equiv(A,B) = and(implies(A,B),implies(B,A)) # label(op_equiv) # label(axiom). [clausify(31)]. 176.99/177.32 89 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(88),flip(b),unit_del(a,39)]. 176.99/177.32 94 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))) | -cn1 # label(cn1) # label(axiom). [clausify(7)]. 176.99/177.32 95 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))). [copy(94),unit_del(b,35)]. 176.99/177.32 121 -is_a_theorem(implies(not(A),A)) | is_a_theorem(A). [resolve(70,b,66,a)]. 176.99/177.32 122 -is_a_theorem(A) | is_a_theorem(implies(not(A),B)). [resolve(70,b,63,a)]. 176.99/177.32 124 -is_a_theorem(implies(implies(implies(not(A),A),A),implies(and(c36,c37),c36))). [ur(70,a,66,a,c,55,a)]. 176.99/177.32 126 is_a_theorem(implies(and(A,not(B)),implies(implies(A,B),C))). [para(79(a,1),63(a,1,2,1))]. 176.99/177.32 127 is_a_theorem(implies(implies(implies(A,B),and(A,not(B))),and(A,not(B)))). [para(79(a,1),66(a,1,1,1))]. 176.99/177.32 128 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(79(a,1),79(a,1,1,2))]. 176.99/177.32 129 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(B,C),implies(A,C))). [resolve(95,a,70,b)]. 176.99/177.32 139 -is_a_theorem(implies(and(c36,c37),implies(not(c36),c36))). [ur(70,b,95,a,c,124,a)]. 176.99/177.32 149 -is_a_theorem(implies(implies(A,B),and(A,not(B)))) | is_a_theorem(and(A,not(B))). [para(79(a,1),121(a,1,1))]. 176.99/177.32 221 is_a_theorem(implies(implies(implies(implies(A,B),C),D),implies(and(A,not(B)),D))). [resolve(129,a,126,a)]. 176.99/177.32 222 is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))). [resolve(129,a,95,a)]. 176.99/177.32 223 is_a_theorem(implies(implies(A,B),implies(implies(not(A),A),B))). [resolve(129,a,66,a)]. 176.99/177.32 224 is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C))). [resolve(129,a,63,a)]. 176.99/177.32 225 is_a_theorem(implies(implies(implies(implies(not(A),A),B),C),implies(implies(A,B),C))). [resolve(223,a,129,a)]. 176.99/177.32 227 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(A),A),B)). [resolve(223,a,70,b)]. 176.99/177.32 289 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(not(A),D),B),C))). [resolve(224,a,129,a)]. 176.99/177.32 291 -is_a_theorem(implies(implies(not(A),B),C)) | is_a_theorem(implies(A,C)). [resolve(224,a,70,b)]. 176.99/177.32 292 -is_a_theorem(implies(implies(not(and(c36,c37)),A),implies(not(c36),c36))). [ur(70,b,224,a,c,139,a)]. 176.99/177.32 339 implies(implies(A,B),and(B,not(A))) = not(equiv(A,B)). [para(89(a,1),128(a,1,1)),flip(a)]. 176.99/177.32 408 is_a_theorem(implies(A,implies(implies(B,C),implies(not(A),C)))). [resolve(291,a,95,a)]. 176.99/177.32 409 is_a_theorem(implies(A,A)). [resolve(291,a,66,a)]. 176.99/177.32 411 -is_a_theorem(implies(implies(implies(A,B),C),D)) | is_a_theorem(implies(and(A,not(B)),D)). [para(79(a,1),291(a,1,1,1))]. 176.99/177.32 413 is_a_theorem(implies(not(implies(A,A)),B)). [resolve(409,a,122,a)]. 176.99/177.32 433 is_a_theorem(implies(implies(A,B),implies(not(implies(C,C)),B))). [resolve(413,a,129,a)]. 176.99/177.32 625 is_a_theorem(implies(implies(not(A),A),implies(implies(B,C),implies(not(A),C)))). [resolve(408,a,227,a)]. 176.99/177.32 626 is_a_theorem(implies(implies(implies(implies(A,B),implies(not(C),B)),D),implies(C,D))). [resolve(408,a,129,a)]. 176.99/177.32 743 is_a_theorem(implies(A,implies(not(implies(B,B)),C))). [resolve(433,a,291,a)]. 176.99/177.32 775 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),implies(D,C))). [resolve(743,a,129,a)]. 176.99/177.32 1282 is_a_theorem(implies(not(equiv(A,A)),and(A,not(A)))). [para(339(a,1),127(a,1,1))]. 176.99/177.32 1349 is_a_theorem(implies(implies(and(A,not(A)),B),implies(not(equiv(A,A)),B))). [resolve(1282,a,129,a)]. 176.99/177.32 1723 -is_a_theorem(implies(not(c36),not(and(c36,c37)))). [ur(129,b,292,a)]. 176.99/177.32 2267 -is_a_theorem(implies(implies(not(implies(A,A)),B),C)) | is_a_theorem(implies(D,C)). [resolve(775,a,70,b)]. 176.99/177.32 3000 is_a_theorem(implies(A,implies(B,B))). [resolve(2267,a,66,a)]. 176.99/177.32 3007 is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))). [resolve(3000,a,129,a)]. 176.99/177.32 3351 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(D,D),B),C))). [resolve(3007,a,129,a)]. 176.99/177.32 3353 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(implies(C,B)). [resolve(3007,a,70,b)]. 176.99/177.32 3428 is_a_theorem(implies(A,implies(B,implies(not(B),C)))). [resolve(3353,a,224,a)]. 176.99/177.32 3429 is_a_theorem(implies(A,implies(implies(not(B),B),B))). [resolve(3353,a,223,a)]. 176.99/177.32 3510 is_a_theorem(implies(implies(implies(A,implies(not(A),B)),C),implies(D,C))). [resolve(3428,a,129,a)]. 176.99/177.32 3800 is_a_theorem(implies(implies(implies(implies(not(A),A),A),B),implies(C,B))). [resolve(3429,a,129,a)]. 176.99/177.32 5423 -is_a_theorem(implies(implies(implies(not(A),A),A),B)) | is_a_theorem(implies(C,B)). [resolve(3800,a,70,b)]. 176.99/177.32 6315 -is_a_theorem(implies(not(A),A)) | is_a_theorem(implies(implies(B,C),implies(not(A),C))). [resolve(625,a,70,b)]. 176.99/177.32 6981 -is_a_theorem(implies(and(A,not(A)),B)) | is_a_theorem(implies(not(equiv(A,A)),B)). [resolve(1349,a,70,b)]. 176.99/177.32 7292 is_a_theorem(implies(A,implies(implies(implies(B,B),C),C))). [resolve(3351,a,5423,a)]. 176.99/177.32 7302 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(implies(D,D),B),C)). [resolve(3351,a,70,b)]. 176.99/177.32 7317 is_a_theorem(implies(implies(implies(implies(implies(A,A),B),B),C),implies(D,C))). [resolve(7292,a,129,a)]. 176.99/177.32 7319 is_a_theorem(implies(implies(implies(A,A),B),B)). [resolve(7292,a,121,a)]. 176.99/177.32 7361 is_a_theorem(implies(implies(A,B),implies(implies(implies(C,C),A),B))). [resolve(7319,a,129,a)]. 176.99/177.32 7362 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(B). [resolve(7319,a,70,b)]. 176.99/177.32 7528 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(C,C),A),B)). [resolve(7361,a,70,b)]. 176.99/177.32 8012 is_a_theorem(implies(implies(implies(A,A),implies(implies(B,B),C)),implies(D,C))). [resolve(7528,a,3007,a)]. 176.99/177.32 9509 is_a_theorem(implies(implies(implies(A,A),B),implies(implies(B,C),implies(D,C)))). [resolve(7302,a,95,a)]. 176.99/177.32 9568 -is_a_theorem(implies(implies(implies(implies(A,A),B),B),C)) | is_a_theorem(implies(D,C)). [resolve(7317,a,70,b)]. 176.99/177.32 10110 -is_a_theorem(implies(implies(A,A),implies(implies(B,B),C))) | is_a_theorem(implies(D,C)). [resolve(8012,a,70,b)]. 176.99/177.32 10380 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(implies(implies(B,C),implies(D,C))). [resolve(9509,a,70,b)]. 176.99/177.32 11080 is_a_theorem(implies(A,implies(and(B,not(B)),C))). [resolve(221,a,9568,a)]. 176.99/177.32 11110 is_a_theorem(implies(and(A,not(A)),B)). [resolve(11080,a,7362,a)]. 176.99/177.32 11170 is_a_theorem(implies(not(equiv(A,A)),B)). [back_unit_del(6981),unit_del(a,11110)]. 176.99/177.32 11394 is_a_theorem(implies(implies(A,B),implies(not(equiv(C,C)),B))). [resolve(11170,a,6315,a)]. 176.99/177.32 12285 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),C),implies(D,C))). [resolve(11394,a,10380,a)]. 176.99/177.32 12715 is_a_theorem(implies(A,implies(B,equiv(C,C)))). [resolve(12285,a,5423,a)]. 176.99/177.32 12737 is_a_theorem(implies(implies(implies(A,equiv(B,B)),C),implies(D,C))). [resolve(12715,a,10380,a)]. 176.99/177.32 12740 is_a_theorem(implies(A,equiv(B,B))). [resolve(12715,a,10110,a)]. 176.99/177.32 12818 is_a_theorem(implies(implies(equiv(A,A),B),implies(C,B))). [resolve(12740,a,10380,a)]. 176.99/177.32 13190 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(equiv(D,D),B),C))). [resolve(12818,a,129,a)]. 176.99/177.32 13239 -is_a_theorem(implies(implies(implies(not(A),A),B),C)) | is_a_theorem(implies(implies(A,B),C)). [resolve(225,a,70,b)]. 176.99/177.32 14392 is_a_theorem(implies(A,implies(implies(equiv(B,B),C),C))). [resolve(13190,a,9568,a)]. 176.99/177.32 14408 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(equiv(D,D),B),C)). [resolve(13190,a,70,b)]. 176.99/177.32 14421 is_a_theorem(implies(implies(implies(implies(equiv(A,A),B),B),C),implies(D,C))). [resolve(14392,a,10380,a)]. 176.99/177.32 14433 is_a_theorem(implies(implies(equiv(A,A),B),B)). [resolve(14392,a,7362,a)]. 176.99/177.32 14473 is_a_theorem(implies(implies(A,B),implies(implies(equiv(C,C),A),B))). [resolve(14433,a,129,a)]. 176.99/177.32 14474 -is_a_theorem(implies(equiv(A,A),B)) | is_a_theorem(B). [resolve(14433,a,70,b)]. 176.99/177.32 14653 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(equiv(C,C),A),B)). [resolve(14473,a,70,b)]. 176.99/177.32 16731 is_a_theorem(implies(implies(equiv(A,A),B),implies(implies(B,C),implies(D,C)))). [resolve(14408,a,9509,a)]. 176.99/177.32 16803 -is_a_theorem(implies(implies(implies(equiv(A,A),B),B),C)) | is_a_theorem(implies(D,C)). [resolve(14421,a,70,b)]. 176.99/177.32 18183 -is_a_theorem(implies(equiv(A,A),B)) | is_a_theorem(implies(implies(B,C),implies(D,C))). [resolve(16731,a,70,b)]. 176.99/177.32 19395 is_a_theorem(implies(A,implies(implies(implies(not(equiv(B,B)),C),D),D))). [resolve(289,a,16803,a)]. 176.99/177.32 19402 is_a_theorem(implies(A,implies(implies(implies(not(implies(B,B)),C),D),D))). [resolve(289,a,9568,a)]. 176.99/177.32 19409 is_a_theorem(implies(A,implies(implies(implies(not(not(B)),C),B),B))). [resolve(289,a,5423,a)]. 176.99/177.32 19419 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(implies(not(A),D),B),C)). [resolve(289,a,70,b)]. 176.99/177.32 19442 is_a_theorem(implies(implies(implies(not(not(A)),B),A),A)). [resolve(19409,a,14474,a)]. 176.99/177.32 19478 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(not(A)),C),A),B))). [resolve(19442,a,129,a)]. 176.99/177.32 19479 -is_a_theorem(implies(implies(not(not(A)),B),A)) | is_a_theorem(A). [resolve(19442,a,70,b)]. 176.99/177.32 19508 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),C),C)). [resolve(19395,a,19479,a)]. 176.99/177.32 19555 -is_a_theorem(implies(implies(not(equiv(A,A)),B),C)) | is_a_theorem(C). [resolve(19508,a,70,b)]. 176.99/177.32 19573 -is_a_theorem(not(equiv(not(equiv(A,A)),B))) | is_a_theorem(and(B,not(not(equiv(A,A))))). [para(339(a,1),19555(a,1))]. 176.99/177.32 19586 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),C)). [resolve(19402,a,19555,a)]. 176.99/177.32 19632 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(implies(C,C)),D),A),B))). [resolve(19586,a,129,a)]. 176.99/177.32 19765 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(not(A)),C),A),B)). [resolve(19478,a,70,b)]. 176.99/177.32 20426 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),and(A,not(A))),C)). [resolve(19765,a,11110,a),rewrite([79(3)])]. 176.99/177.32 21111 is_a_theorem(implies(and(not(implies(A,A)),not(B)),C)). [resolve(411,a,20426,a)]. 176.99/177.32 21114 is_a_theorem(implies(and(not(equiv(A,A)),not(B)),C)). [resolve(411,a,19508,a)]. 176.99/177.32 21116 is_a_theorem(implies(and(not(not(A)),not(B)),A)). [resolve(411,a,19442,a)]. 176.99/177.32 21123 is_a_theorem(implies(and(A,not(equiv(B,B))),implies(C,D))). [resolve(411,a,12737,a)]. 176.99/177.32 21129 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),implies(C,D))). [resolve(411,a,7317,a)]. 176.99/177.32 21131 is_a_theorem(implies(and(implies(not(A),A),not(A)),implies(B,C))). [resolve(411,a,3800,a)]. 176.99/177.32 21132 is_a_theorem(implies(and(A,not(implies(not(A),B))),implies(C,D))). [resolve(411,a,3510,a)]. 176.99/177.32 21141 is_a_theorem(implies(and(A,not(B)),implies(implies(implies(not(A),C),B),D))). [resolve(411,a,289,a)]. 176.99/177.32 21143 is_a_theorem(implies(and(not(A),not(B)),implies(A,C))). [resolve(411,a,224,a)]. 176.99/177.32 21144 is_a_theorem(implies(and(implies(A,B),not(implies(C,B))),implies(implies(C,A),D))). [resolve(411,a,222,a)]. 176.99/177.32 21155 is_a_theorem(implies(implies(equiv(A,A),and(not(not(B)),not(C))),B)). [resolve(21116,a,14653,a)]. 176.99/177.32 21169 is_a_theorem(implies(implies(implies(not(not(A)),B),and(not(not(A)),not(B))),A)). [resolve(21116,a,227,a),rewrite([79(5)])]. 176.99/177.32 21170 is_a_theorem(implies(implies(A,B),implies(and(not(not(A)),not(C)),B))). [resolve(21116,a,129,a)]. 176.99/177.32 21459 is_a_theorem(implies(implies(equiv(A,A),and(not(implies(B,B)),not(C))),D)). [resolve(21111,a,14653,a)]. 176.99/177.32 21507 is_a_theorem(implies(implies(implies(A,A),and(not(equiv(B,B)),not(C))),D)). [resolve(21114,a,7528,a)]. 176.99/177.32 21555 is_a_theorem(implies(implies(implies(not(A),B),and(not(A),not(B))),implies(A,C))). [resolve(21143,a,227,a),rewrite([79(4)])]. 176.99/177.32 21856 is_a_theorem(implies(implies(implies(A,B),C),implies(and(D,not(equiv(E,E))),C))). [resolve(21123,a,129,a)]. 176.99/177.32 22164 is_a_theorem(implies(and(implies(not(A),A),not(A)),not(equiv(B,C)))). [para(339(a,1),21131(a,1,2))]. 176.99/177.32 22202 is_a_theorem(implies(and(A,not(implies(not(A),B))),not(equiv(C,D)))). [para(339(a,1),21132(a,1,2))]. 176.99/177.32 22471 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),not(equiv(C,D)))). [para(339(a,1),21129(a,1,2))]. 176.99/177.32 22819 is_a_theorem(implies(and(not(not(not(equiv(A,A)))),not(B)),C)). [resolve(21170,a,19555,a)]. 176.99/177.32 22830 is_a_theorem(implies(implies(implies(and(not(not(A)),not(B)),A),C),implies(D,C))). [resolve(21170,a,10380,a)]. 176.99/177.32 22984 is_a_theorem(implies(implies(implies(A,A),and(not(not(not(equiv(B,B)))),not(C))),D)). [resolve(22819,a,7528,a)]. 176.99/177.32 25244 is_a_theorem(implies(and(A,implies(B,not(A))),implies(not(equiv(not(A),B)),C))). [para(339(a,1),21141(a,1,2,1)),rewrite([79(4)])]. 176.99/177.32 25557 is_a_theorem(and(equiv(A,A),implies(not(implies(B,B)),C))). [resolve(21459,a,149,a),rewrite([79(6)])]. 176.99/177.32 25810 is_a_theorem(and(implies(A,A),implies(not(equiv(B,B)),C))). [resolve(21507,a,149,a),rewrite([79(6)])]. 176.99/177.32 28620 -is_a_theorem(implies(implies(implies(A,B),implies(not(C),B)),D)) | is_a_theorem(implies(C,D)). [resolve(626,a,70,b)]. 176.99/177.32 47642 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),and(not(not(C)),not(D))),C)). [resolve(19419,a,21155,a)]. 176.99/177.32 50856 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(implies(C,C)),D),A),B)). [resolve(19632,a,70,b)]. 176.99/177.32 53140 is_a_theorem(implies(implies(not(A),and(not(not(A)),not(not(A)))),A)). [resolve(21169,a,13239,a)]. 176.99/177.32 53205 -is_a_theorem(implies(not(A),and(not(not(A)),not(not(A))))) | is_a_theorem(A). [resolve(53140,a,70,b)]. 176.99/177.32 53242 is_a_theorem(implies(implies(A,and(not(A),not(A))),implies(A,B))). [resolve(21555,a,13239,a)]. 176.99/177.32 53285 is_a_theorem(implies(implies(implies(not(A),B),and(not(A),not(A))),implies(A,C))). [resolve(53242,a,19419,a)]. 176.99/177.32 53431 is_a_theorem(implies(A,implies(and(B,not(equiv(C,C))),D))). [resolve(21856,a,16803,a)]. 176.99/177.32 53474 is_a_theorem(implies(implies(implies(and(A,not(equiv(B,B))),C),D),implies(E,D))). [resolve(53431,a,18183,a)]. 176.99/177.32 57917 -is_a_theorem(and(A,implies(B,not(A)))) | is_a_theorem(implies(not(equiv(not(A),B)),C)). [resolve(25244,a,70,b)]. 176.99/177.32 59056 is_a_theorem(implies(A,implies(B,implies(not(A),C)))). [resolve(28620,a,22830,a)]. 176.99/177.32 59065 is_a_theorem(implies(A,implies(implies(implies(not(A),B),C),implies(D,C)))). [resolve(28620,a,9509,a)]. 176.99/177.32 59145 is_a_theorem(implies(implies(implies(A,implies(not(B),C)),D),implies(B,D))). [resolve(59056,a,129,a)]. 176.99/177.32 63989 is_a_theorem(implies(A,implies(B,implies(C,implies(not(B),D))))). [resolve(59145,a,3353,a)]. 176.99/177.32 64045 -is_a_theorem(implies(implies(A,implies(not(not(c36)),B)),not(and(c36,c37)))). [ur(70,b,59145,a,c,1723,a)]. 176.99/177.32 109200 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),and(not(equiv(C,C)),not(D))),E)). [resolve(50856,a,21114,a)]. 176.99/177.32 109989 is_a_theorem(implies(and(and(A,not(equiv(B,B))),not(C)),implies(D,E))). [resolve(53474,a,411,a)]. 176.99/177.32 110141 is_a_theorem(implies(and(and(A,not(equiv(B,B))),not(C)),not(equiv(D,E)))). [para(339(a,1),109989(a,1,2))]. 176.99/177.32 113446 is_a_theorem(implies(not(equiv(not(implies(A,A)),not(equiv(B,B)))),C)). [resolve(57917,a,25810,a)]. 176.99/177.32 113449 is_a_theorem(implies(not(equiv(not(equiv(A,A)),not(implies(B,B)))),C)). [resolve(57917,a,25557,a)]. 176.99/177.32 113489 is_a_theorem(equiv(not(implies(A,A)),not(equiv(B,B)))). [resolve(113446,a,53205,a)]. 176.99/177.32 113586 not(equiv(A,A)) = not(implies(B,B)). [resolve(113489,a,61,a)]. 176.99/177.32 113594 not(equiv(A,A)) = c_0. [new_symbol(113586)]. 176.99/177.32 113598 not(implies(A,A)) = c_0. [back_rewrite(113586),rewrite([113594(2)]),flip(a)]. 176.99/177.32 113609 is_a_theorem(implies(c_0,A)). [back_rewrite(113449),rewrite([113594(2),113598(3),113594(4)])]. 176.99/177.32 113617 is_a_theorem(implies(and(and(A,c_0),not(B)),not(equiv(C,D)))). [back_rewrite(110141),rewrite([113594(2)])]. 176.99/177.32 113631 is_a_theorem(implies(implies(implies(c_0,A),and(c_0,not(B))),C)). [back_rewrite(109200),rewrite([113598(2),113594(4)])]. 176.99/177.32 113978 is_a_theorem(implies(implies(implies(c_0,A),and(not(not(B)),not(C))),B)). [back_rewrite(47642),rewrite([113594(2)])]. 176.99/177.32 114185 is_a_theorem(implies(implies(implies(A,A),and(not(not(c_0)),not(B))),C)). [back_rewrite(22984),rewrite([113594(3)])]. 176.99/177.32 114256 -is_a_theorem(not(equiv(c_0,A))) | is_a_theorem(and(A,not(c_0))). [back_rewrite(19573),rewrite([113594(2),113594(6)])]. 176.99/177.32 114260 -is_a_theorem(implies(implies(c_0,A),B)) | is_a_theorem(B). [back_rewrite(19555),rewrite([113594(2)])]. 176.99/177.32 116058 implies(A,equiv(B,B)) = not(and(A,c_0)). [para(113594(a,1),79(a,1,1,2)),flip(a)]. 176.99/177.32 116187 is_a_theorem(implies(and(implies(not(A),A),not(A)),c_0)). [para(113594(a,1),22164(a,1,2))]. 176.99/177.32 116188 is_a_theorem(implies(and(A,not(implies(not(A),B))),c_0)). [para(113594(a,1),22202(a,1,2))]. 176.99/177.32 116210 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),c_0)). [para(113594(a,1),22471(a,1,2))]. 176.99/177.32 117243 implies(A,implies(B,B)) = not(and(A,c_0)). [para(113598(a,1),79(a,1,1,2)),flip(a)]. 176.99/177.32 126200 -is_a_theorem(implies(not(and(equiv(A,A),c_0)),B)) | is_a_theorem(B). [para(116058(a,1),7362(a,1,1))]. 176.99/177.32 127289 is_a_theorem(implies(implies(c_0,A),implies(and(implies(not(B),B),not(B)),A))). [resolve(116187,a,129,a)]. 176.99/177.32 127403 is_a_theorem(implies(implies(c_0,A),implies(and(B,not(implies(not(B),C))),A))). [resolve(116188,a,129,a)]. 176.99/177.32 129116 is_a_theorem(and(implies(c_0,A),implies(c_0,B))). [resolve(113631,a,149,a),rewrite([79(6)])]. 176.99/177.32 129150 is_a_theorem(implies(not(equiv(not(implies(c_0,A)),c_0)),B)). [resolve(129116,a,57917,a)]. 176.99/177.32 129330 is_a_theorem(equiv(not(implies(c_0,A)),c_0)). [resolve(129150,a,53205,a)]. 176.99/177.32 129423 not(implies(c_0,A)) = c_0. [resolve(129330,a,61,a),flip(a)]. 176.99/177.32 129425 implies(A,implies(c_0,B)) = not(and(A,c_0)). [para(129423(a,1),79(a,1,1,2)),flip(a)]. 176.99/177.32 134395 is_a_theorem(implies(and(implies(not(and(equiv(A,A),c_0)),B),not(B)),c_0)). [para(116058(a,1),116210(a,1,1,1,1))]. 176.99/177.32 141158 is_a_theorem(implies(and(and(A,c_0),not(B)),c_0)). [para(113594(a,1),113617(a,1,2))]. 176.99/177.32 141237 is_a_theorem(implies(implies(c_0,A),implies(and(and(B,c_0),not(C)),A))). [resolve(141158,a,129,a)]. 176.99/177.32 164282 is_a_theorem(implies(not(equiv(c_0,not(not(A)))),A)). [para(339(a,1),113978(a,1,1))]. 176.99/177.32 164353 is_a_theorem(implies(implies(A,B),implies(not(equiv(c_0,not(not(A)))),B))). [resolve(164282,a,129,a)]. 176.99/177.32 166255 is_a_theorem(and(implies(A,A),implies(not(not(c_0)),B))). [resolve(114185,a,149,a),rewrite([79(7)])]. 176.99/177.32 166293 is_a_theorem(implies(not(equiv(c_0,not(not(c_0)))),A)). [resolve(166255,a,57917,a),rewrite([113598(2)])]. 176.99/177.32 166363 is_a_theorem(equiv(c_0,not(not(c_0)))). [resolve(166293,a,53205,a)]. 176.99/177.32 166456 not(not(c_0)) = c_0. [resolve(166363,a,61,a)]. 176.99/177.32 166475 not(and(A,c_0)) = implies(A,not(c_0)). [para(166456(a,1),79(a,1,1,2))]. 176.99/177.32 166476 is_a_theorem(not(c_0)). [para(166456(a,1),121(a,1,1)),unit_del(a,113609)]. 176.99/177.32 166483 implies(implies(not(c_0),A),and(A,c_0)) = not(equiv(not(c_0),A)). [para(166456(a,1),339(a,1,2,2))]. 176.99/177.32 166486 is_a_theorem(implies(A,not(c_0))). [para(166456(a,1),3428(a,1,2,2,1)),rewrite([129425(5),166475(5),117243(6),166475(3)])]. 176.99/177.32 167115 is_a_theorem(implies(and(implies(implies(equiv(A,A),not(c_0)),B),not(B)),c_0)). [back_rewrite(134395),rewrite([166475(4)])]. 176.99/177.32 167317 implies(A,implies(c_0,B)) = implies(A,not(c_0)). [back_rewrite(129425),rewrite([166475(6)])]. 176.99/177.32 167551 -is_a_theorem(implies(implies(equiv(A,A),not(c_0)),B)) | is_a_theorem(B). [back_rewrite(126200),rewrite([166475(4)])]. 176.99/177.32 167718 implies(A,implies(B,B)) = implies(A,not(c_0)). [back_rewrite(117243),rewrite([166475(5)])]. 176.99/177.32 168077 implies(A,equiv(B,B)) = implies(A,not(c_0)). [back_rewrite(116058),rewrite([166475(5)])]. 176.99/177.32 168621 is_a_theorem(implies(implies(not(c_0),A),implies(B,A))). [resolve(166486,a,18183,a)]. 176.99/177.32 169685 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(not(c_0),B),C))). [resolve(168621,a,129,a)]. 176.99/177.32 188392 is_a_theorem(implies(and(and(A,c_0),not(B)),C)). [resolve(141237,a,114260,a)]. 176.99/177.32 199452 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(equiv(c_0,not(not(A)))),B)). [resolve(164353,a,70,b)]. 176.99/177.32 212805 is_a_theorem(implies(A,implies(implies(not(c_0),B),B))). [resolve(169685,a,16803,a)]. 176.99/177.32 212810 is_a_theorem(implies(implies(A,B),implies(implies(not(c_0),A),B))). [resolve(169685,a,13239,a)]. 176.99/177.32 212836 is_a_theorem(implies(implies(not(c_0),A),A)). [resolve(212805,a,167551,a)]. 176.99/177.32 212972 -is_a_theorem(implies(not(c_0),A)) | is_a_theorem(A). [resolve(212836,a,70,b)]. 176.99/177.32 216849 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(c_0),A),B)). [resolve(212810,a,70,b)]. 176.99/177.32 218340 is_a_theorem(implies(implies(not(c_0),and(and(A,c_0),not(B))),C)). [resolve(216849,a,188392,a)]. 176.99/177.32 226076 is_a_theorem(and(not(c_0),implies(and(A,c_0),B))). [resolve(218340,a,149,a),rewrite([79(7)])]. 176.99/177.32 226110 is_a_theorem(implies(not(equiv(c_0,and(A,c_0))),B)). [resolve(226076,a,57917,a),rewrite([166456(3)])]. 176.99/177.32 226179 is_a_theorem(equiv(c_0,and(A,c_0))). [resolve(226110,a,53205,a)]. 176.99/177.32 226273 and(A,c_0) = c_0. [resolve(226179,a,61,a)]. 176.99/177.32 226322 implies(implies(not(c_0),A),c_0) = not(equiv(not(c_0),A)). [back_rewrite(166483),rewrite([226273(5)])]. 176.99/177.32 226323 implies(A,not(c_0)) = not(c_0). [back_rewrite(166475),rewrite([226273(2)]),flip(a)]. 176.99/177.32 226344 implies(A,equiv(B,B)) = not(c_0). [back_rewrite(168077),rewrite([226323(5)])]. 176.99/177.32 226351 implies(A,implies(B,B)) = not(c_0). [back_rewrite(167718),rewrite([226323(5)])]. 176.99/177.32 226368 implies(A,implies(c_0,B)) = not(c_0). [back_rewrite(167317),rewrite([226323(6)])]. 176.99/177.32 226371 is_a_theorem(implies(and(implies(not(c_0),A),not(A)),c_0)). [back_rewrite(167115),rewrite([226323(4)])]. 176.99/177.32 226419 and(not(c_0),implies(not(c_0),A)) = equiv(A,not(c_0)). [para(226323(a,1),89(a,1,1))]. 176.99/177.32 226420 and(implies(not(c_0),A),not(c_0)) = equiv(not(c_0),A). [para(226323(a,1),89(a,1,2))]. 176.99/177.32 228890 is_a_theorem(implies(implies(c_0,A),implies(and(implies(not(c_0),B),not(B)),A))). [resolve(226371,a,129,a)]. 176.99/177.32 229604 implies(not(c_0),c_0) = c_0. [para(113594(a,1),226322(a,2)),rewrite([226323(5)])]. 176.99/177.32 229632 not(equiv(not(c_0),equiv(A,A))) = c_0. [para(226344(a,1),226322(a,1,1)),rewrite([229604(4)]),flip(a)]. 176.99/177.32 229633 not(equiv(not(c_0),implies(A,A))) = c_0. [para(226351(a,1),226322(a,1,1)),rewrite([229604(4)]),flip(a)]. 176.99/177.32 229634 not(equiv(not(c_0),implies(c_0,A))) = c_0. [para(226368(a,1),226322(a,1,1)),rewrite([229604(4)]),flip(a)]. 176.99/177.32 229637 is_a_theorem(implies(implies(not(c_0),A),implies(implies(A,c_0),c_0))). [para(229604(a,1),95(a,1,2,2))]. 176.99/177.32 229662 is_a_theorem(implies(and(implies(A,c_0),not(c_0)),implies(implies(not(c_0),A),B))). [para(229604(a,1),21144(a,1,1,2,1))]. 176.99/177.32 229666 is_a_theorem(implies(A,implies(implies(implies(not(A),B),c_0),c_0))). [para(229604(a,1),59065(a,1,2,2))]. 176.99/177.32 229692 implies(A,equiv(not(c_0),equiv(B,B))) = not(c_0). [para(229632(a,1),79(a,1,1,2)),rewrite([226273(2)]),flip(a)]. 176.99/177.32 229693 is_a_theorem(equiv(not(c_0),equiv(A,A))). [para(229632(a,1),121(a,1,1)),rewrite([229692(6)]),unit_del(a,166476)]. 176.99/177.32 229740 equiv(A,A) = not(c_0). [resolve(229693,a,61,a)]. 176.99/177.32 230331 implies(A,equiv(not(c_0),implies(B,B))) = not(c_0). [para(229633(a,1),79(a,1,1,2)),rewrite([226273(2)]),flip(a)]. 176.99/177.32 230332 is_a_theorem(equiv(not(c_0),implies(A,A))). [para(229633(a,1),121(a,1,1)),rewrite([230331(6)]),unit_del(a,166476)]. 176.99/177.32 230393 implies(A,A) = not(c_0). [resolve(230332,a,61,a)]. 176.99/177.32 231435 and(not(c_0),not(c_0)) = not(c_0). [para(230393(a,1),89(a,1,1)),rewrite([230393(3),229740(6)])]. 176.99/177.32 231436 is_a_theorem(implies(implies(A,B),implies(not(c_0),implies(A,B)))). [para(230393(a,1),95(a,1,2,1))]. 176.99/177.32 231437 implies(A,and(B,not(B))) = implies(A,c_0). [para(230393(a,1),128(a,1,1,2)),rewrite([79(4)]),flip(a)]. 176.99/177.32 231482 implies(A,equiv(not(c_0),implies(c_0,B))) = not(c_0). [para(229634(a,1),79(a,1,1,2)),rewrite([226273(2)]),flip(a)]. 176.99/177.32 231483 is_a_theorem(equiv(not(c_0),implies(c_0,A))). [para(229634(a,1),121(a,1,1)),rewrite([231482(7)]),unit_del(a,166476)]. 176.99/177.32 231580 implies(c_0,A) = not(c_0). [resolve(231483,a,61,a)]. 176.99/177.32 231787 is_a_theorem(implies(not(c_0),implies(and(implies(not(c_0),A),not(A)),B))). [back_rewrite(228890),rewrite([231580(2)])]. 176.99/177.32 231789 is_a_theorem(implies(not(c_0),implies(and(A,not(implies(not(A),B))),C))). [back_rewrite(127403),rewrite([231580(2)])]. 176.99/177.32 231790 is_a_theorem(implies(not(c_0),implies(and(implies(not(A),A),not(A)),B))). [back_rewrite(127289),rewrite([231580(2)])]. 176.99/177.32 231793 and(implies(A,c_0),not(c_0)) = equiv(A,c_0). [para(231580(a,1),89(a,1,2))]. 176.99/177.32 231794 is_a_theorem(implies(implies(A,c_0),implies(not(c_0),implies(A,B)))). [para(231580(a,1),95(a,1,2,1))]. 176.99/177.32 231795 implies(A,and(c_0,not(B))) = implies(A,c_0). [para(231580(a,1),128(a,1,1,2)),rewrite([79(4)]),flip(a)]. 176.99/177.32 231798 implies(not(c_0),and(A,not(c_0))) = not(equiv(c_0,A)). [para(231580(a,1),339(a,1,1))]. 176.99/177.32 231827 is_a_theorem(implies(and(A,not(c_0)),implies(not(equiv(not(A),c_0)),B))). [para(231580(a,1),25244(a,1,1,2))]. 176.99/177.32 231850 is_a_theorem(implies(equiv(A,c_0),implies(implies(not(c_0),A),B))). [back_rewrite(229662),rewrite([231793(5)])]. 176.99/177.32 231858 implies(implies(A,c_0),and(and(B,not(B)),not(A))) = not(equiv(A,and(B,not(B)))). [para(231437(a,1),339(a,1,1))]. 176.99/177.32 231884 implies(and(A,not(A)),c_0) = not(c_0). [para(231437(a,1),230393(a,1))]. 176.99/177.32 232196 equiv(and(A,not(A)),c_0) = not(c_0). [para(231884(a,1),89(a,1,1)),rewrite([231437(6),230393(5),231435(5)]),flip(a)]. 176.99/177.32 232216 and(A,not(A)) = c_0. [para(232196(a,1),61(a,1)),flip(b),unit_del(a,166476)]. 176.99/177.32 232220 implies(implies(A,c_0),c_0) = not(equiv(A,c_0)). [back_rewrite(231858),rewrite([232216(4),231795(6),232216(6)])]. 176.99/177.32 232233 is_a_theorem(implies(A,not(equiv(implies(not(A),B),c_0)))). [back_rewrite(229666),rewrite([232220(6)])]. 176.99/177.32 232245 is_a_theorem(implies(implies(not(c_0),A),not(equiv(A,c_0)))). [back_rewrite(229637),rewrite([232220(7)])]. 176.99/177.32 232788 is_a_theorem(implies(A,implies(not(equiv(not(A),c_0)),implies(B,c_0)))). [para(232220(a,1),59065(a,1,2,1))]. 176.99/177.32 233132 -is_a_theorem(implies(not(c_0),A)) | is_a_theorem(not(equiv(A,c_0))). [resolve(232245,a,70,b)]. 176.99/177.32 233620 is_a_theorem(not(equiv(implies(A,implies(B,implies(not(A),C))),c_0))). [resolve(233132,a,63989,a)]. 176.99/177.32 233706 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(c_0),implies(A,B))). [resolve(231436,a,70,b)]. 176.99/177.32 233904 is_a_theorem(implies(not(c_0),implies(equiv(A,c_0),implies(implies(not(c_0),A),B)))). [resolve(233706,a,231850,a)]. 176.99/177.32 237487 is_a_theorem(implies(A,implies(not(equiv(not(A),c_0)),c_0))). [para(229604(a,1),232788(a,1,2,2))]. 176.99/177.32 237540 -is_a_theorem(A) | is_a_theorem(implies(not(equiv(not(A),c_0)),c_0)). [resolve(237487,a,70,b)]. 176.99/177.32 239865 is_a_theorem(implies(and(implies(not(c_0),A),not(A)),B)). [resolve(231787,a,212972,a)]. 176.99/177.32 239889 is_a_theorem(implies(not(equiv(c_0,not(implies(implies(not(c_0),A),A)))),B)). [resolve(239865,a,199452,a),rewrite([79(7)])]. 176.99/177.32 239950 is_a_theorem(implies(and(A,not(implies(not(A),B))),C)). [resolve(231789,a,212972,a)]. 176.99/177.32 239959 is_a_theorem(implies(not(equiv(c_0,not(implies(A,implies(not(A),B))))),C)). [resolve(239950,a,199452,a),rewrite([79(6)])]. 176.99/177.32 239997 is_a_theorem(implies(and(implies(not(A),A),not(A)),B)). [resolve(231790,a,212972,a)]. 176.99/177.32 240004 is_a_theorem(implies(implies(not(c_0),and(implies(not(A),A),not(A))),B)). [resolve(239997,a,216849,a)]. 176.99/177.32 240685 is_a_theorem(equiv(c_0,not(implies(implies(not(c_0),A),A)))). [resolve(239889,a,53205,a)]. 176.99/177.32 240690 not(implies(implies(not(c_0),A),A)) = c_0. [resolve(240685,a,61,a)]. 176.99/177.32 240692 implies(A,implies(implies(not(c_0),B),B)) = not(c_0). [para(240690(a,1),79(a,1,1,2)),rewrite([226273(2)]),flip(a)]. 176.99/177.32 240705 equiv(implies(implies(not(c_0),A),A),not(c_0)) = not(c_0). [para(240692(a,1),226419(a,1,2)),rewrite([231435(5)]),flip(a)]. 176.99/177.32 240726 implies(implies(not(c_0),A),A) = not(c_0). [para(240705(a,1),61(a,1)),flip(b),unit_del(a,166476)]. 176.99/177.32 240729 and(implies(A,implies(not(c_0),A)),not(c_0)) = equiv(A,implies(not(c_0),A)). [para(240726(a,1),89(a,1,2))]. 176.99/177.32 240960 is_a_theorem(equiv(c_0,not(implies(A,implies(not(A),B))))). [resolve(239959,a,53205,a)]. 176.99/177.32 240969 not(implies(A,implies(not(A),B))) = c_0. [resolve(240960,a,61,a)]. 176.99/177.32 241114 implies(A,implies(B,implies(not(B),C))) = not(c_0). [para(240969(a,1),79(a,1,1,2)),rewrite([226273(2)]),flip(a)]. 176.99/177.32 241129 equiv(implies(A,implies(not(A),B)),not(c_0)) = not(c_0). [para(241114(a,1),226419(a,1,2)),rewrite([231435(5)]),flip(a)]. 176.99/177.32 241135 implies(A,implies(not(A),B)) = not(c_0). [para(241129(a,1),61(a,1)),flip(b),unit_del(a,166476)]. 176.99/177.32 241138 and(not(c_0),implies(implies(not(A),B),A)) = equiv(A,implies(not(A),B)). [para(241135(a,1),89(a,1,1))]. 176.99/177.32 241139 and(implies(implies(not(A),B),A),not(c_0)) = equiv(implies(not(A),B),A). [para(241135(a,1),89(a,1,2))]. 176.99/177.32 241259 is_a_theorem(equiv(A,implies(not(A),A))). [resolve(240004,a,149,a),rewrite([79(7),241138(6)])]. 176.99/177.32 241295 implies(not(A),A) = A. [resolve(241259,a,61,a)]. 176.99/177.32 241327 implies(A,and(not(B),not(B))) = not(and(A,B)). [para(241295(a,1),128(a,1,1,2)),flip(a)]. 176.99/177.32 241574 -is_a_theorem(implies(implies(A,not(c36)),not(and(c36,c37)))). [para(241295(a,1),64045(a,1,1,2))]. 176.99/177.32 241643 is_a_theorem(implies(A,not(equiv(A,c_0)))). [para(241295(a,1),232233(a,1,2,1,1))]. 176.99/177.32 241645 is_a_theorem(implies(implies(not(A),c_0),implies(not(c_0),A))). [para(241295(a,1),231794(a,1,2,2))]. 176.99/177.32 241658 is_a_theorem(not(equiv(implies(A,implies(B,A)),c_0))). [para(241295(a,1),233620(a,1,1,1,2,2))]. 176.99/177.32 241709 is_a_theorem(implies(and(A,not(c_0)),equiv(not(A),c_0))). [para(241295(a,1),231827(a,1,2))]. 176.99/177.32 241831 is_a_theorem(implies(not(and(implies(not(A),B),A)),implies(A,C))). [back_rewrite(53285),rewrite([241327(6)])]. 176.99/177.32 242823 -is_a_theorem(A) | is_a_theorem(not(equiv(A,c_0))). [resolve(241643,a,70,b)]. 176.99/177.32 242885 is_a_theorem(not(equiv(implies(A,not(equiv(A,c_0))),c_0))). [resolve(242823,a,241643,a)]. 176.99/177.32 245795 is_a_theorem(not(equiv(implies(implies(not(A),c_0),implies(not(c_0),A)),c_0))). [resolve(241645,a,242823,a)]. 176.99/177.32 245873 is_a_theorem(implies(not(equiv(A,c_0)),not(equiv(c_0,A)))). [para(231798(a,1),241645(a,1,2)),rewrite([79(4),232220(4)])]. 176.99/177.32 245983 -is_a_theorem(and(A,not(c_0))) | is_a_theorem(equiv(not(A),c_0)). [resolve(241709,a,70,b)]. 176.99/177.32 246855 -is_a_theorem(not(equiv(A,c_0))) | is_a_theorem(not(equiv(c_0,A))). [resolve(245873,a,70,b)]. 176.99/177.32 247311 is_a_theorem(not(equiv(c_0,implies(A,not(equiv(A,c_0)))))). [resolve(246855,a,242885,a)]. 176.99/177.32 247312 is_a_theorem(not(equiv(c_0,implies(A,implies(B,A))))). [resolve(246855,a,241658,a)]. 176.99/177.32 247355 is_a_theorem(and(implies(A,implies(B,A)),not(c_0))). [resolve(247312,a,114256,a)]. 176.99/177.32 247370 is_a_theorem(equiv(not(implies(A,implies(B,A))),c_0)). [resolve(247355,a,245983,a)]. 176.99/177.32 247423 not(implies(A,implies(B,A))) = c_0. [resolve(247370,a,61,a),flip(a)]. 176.99/177.32 247488 implies(A,implies(B,implies(C,B))) = not(c_0). [para(247423(a,1),79(a,1,1,2)),rewrite([226273(2)]),flip(a)]. 176.99/177.32 247490 implies(A,implies(B,A)) = not(c_0). [para(247423(a,1),241295(a,1,1)),rewrite([247488(4)]),flip(a)]. 176.99/177.32 247495 equiv(A,implies(not(c_0),A)) = not(c_0). [back_rewrite(240729),rewrite([247490(4),231435(5)]),flip(a)]. 176.99/177.32 247518 implies(not(c_0),A) = A. [para(247495(a,1),61(a,1)),unit_del(a,166476)]. 176.99/177.32 247544 is_a_theorem(not(equiv(implies(implies(not(A),c_0),A),c_0))). [back_rewrite(245795),rewrite([247518(6)])]. 176.99/177.32 247611 is_a_theorem(implies(equiv(A,c_0),implies(A,B))). [back_rewrite(233904),rewrite([247518(7),247518(7)])]. 176.99/177.32 247658 not(equiv(c_0,A)) = and(A,not(c_0)). [back_rewrite(231798),rewrite([247518(6)]),flip(a)]. 176.99/177.32 247666 equiv(not(c_0),A) = and(A,not(c_0)). [back_rewrite(226420),rewrite([247518(3)]),flip(a)]. 176.99/177.32 247679 is_a_theorem(and(implies(A,not(equiv(A,c_0))),not(c_0))). [back_rewrite(247311),rewrite([247658(7)])]. 176.99/177.32 247690 -is_a_theorem(not(equiv(A,c_0))) | is_a_theorem(and(A,not(c_0))). [back_rewrite(246855),rewrite([247658(7)])]. 176.99/177.32 249489 is_a_theorem(implies(equiv(not(A),c_0),A)). [para(241295(a,1),247611(a,1,2))]. 176.99/177.32 249500 is_a_theorem(implies(not(equiv(not(implies(equiv(not(A),c_0),A)),c_0)),c_0)). [resolve(249489,a,237540,a)]. 176.99/177.32 250699 -is_a_theorem(and(A,not(c_0))) | not(c_0) = A. [para(247666(a,1),61(a,1)),flip(b)]. 176.99/177.32 253411 implies(A,not(equiv(A,c_0))) = not(c_0). [resolve(247679,a,250699,a),flip(a)]. 176.99/177.32 253415 and(implies(not(equiv(A,c_0)),A),not(c_0)) = equiv(not(equiv(A,c_0)),A). [para(253411(a,1),89(a,1,2))]. 176.99/177.32 253764 is_a_theorem(equiv(implies(not(A),c_0),A)). [resolve(247690,a,247544,a),rewrite([241139(7)])]. 176.99/177.32 253803 implies(not(A),c_0) = A. [resolve(253764,a,61,a),flip(a)]. 176.99/177.32 253859 is_a_theorem(equiv(not(implies(equiv(not(A),c_0),A)),c_0)). [back_rewrite(249500),rewrite([253803(10)])]. 176.99/177.32 253967 implies(implies(A,B),c_0) = and(A,not(B)). [para(79(a,1),253803(a,1,1))]. 176.99/177.32 253968 equiv(not(A),c_0) = and(A,not(c_0)). [para(253803(a,1),89(a,1,1)),rewrite([231580(3)]),flip(a)]. 176.99/177.32 253972 implies(A,and(not(B),not(c_0))) = not(and(A,B)). [para(253803(a,1),128(a,1,1,2)),flip(a)]. 176.99/177.32 254084 not(equiv(A,c_0)) = and(A,not(c_0)). [back_rewrite(232220),rewrite([253967(4)]),flip(a)]. 176.99/177.32 254204 is_a_theorem(and(implies(and(A,not(c_0)),A),not(c_0))). [back_rewrite(253859),rewrite([253968(3),253968(7)])]. 176.99/177.32 255449 and(implies(and(A,not(c_0)),A),not(c_0)) = equiv(and(A,not(c_0)),A). [back_rewrite(253415),rewrite([254084(3),254084(10)])]. 176.99/177.34 255823 is_a_theorem(equiv(and(A,not(c_0)),A)). [back_rewrite(254204),rewrite([255449(7)])]. 176.99/177.34 257095 and(A,not(c_0)) = A. [resolve(255823,a,61,a),flip(a)]. 176.99/177.34 257246 not(and(A,B)) = implies(A,not(B)). [back_rewrite(253972),rewrite([257095(4)]),flip(a)]. 176.99/177.34 257985 is_a_theorem(implies(implies(implies(not(A),B),not(A)),implies(A,C))). [back_rewrite(241831),rewrite([257246(4)])]. 176.99/177.34 258012 -is_a_theorem(implies(implies(A,not(c36)),implies(c36,not(c37)))). [back_rewrite(241574),rewrite([257246(7)])]. 176.99/177.34 258013 $F. [resolve(258012,a,257985,a)]. 176.99/177.34 176.99/177.34 % SZS output end Refutation 176.99/177.34 ============================== end of proof ========================== 176.99/177.34 176.99/177.34 ============================== STATISTICS ============================ 176.99/177.34 176.99/177.34 Given=8696. Generated=13825011. Kept=257963. proofs=1. 176.99/177.34 Usable=865. Sos=4495. Demods=86. Limbo=766, Disabled=251908. Hints=0. 176.99/177.34 Megabytes=179.65. 176.99/177.34 User_CPU=169.52, System_CPU=7.23, Wall_clock=177. 176.99/177.34 176.99/177.34 ============================== end of statistics ===================== 176.99/177.34 176.99/177.34 ============================== end of search ========================= 176.99/177.34 176.99/177.34 THEOREM PROVED 176.99/177.34 % SZS status Theorem 176.99/177.34 176.99/177.34 Exiting with 1 proof. 176.99/177.34 176.99/177.34 Process 15772 exit (max_proofs) Sat Jul 14 06:25:37 2018 176.99/177.34 Prover9 interrupted 176.99/177.35 EOF