0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.34 % Computer : n026.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 960 0.13/0.34 % DateTime : Thu Jul 2 09:24:24 EDT 2020 0.13/0.34 % CPUTime : 0.44/1.03 ============================== Prover9 =============================== 0.44/1.03 Prover9 (32) version 2009-11A, November 2009. 0.44/1.03 Process 26398 was started by sandbox on n026.cluster.edu, 0.44/1.03 Thu Jul 2 09:24:25 2020 0.44/1.03 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 960 -f /tmp/Prover9_26243_n026.cluster.edu". 0.44/1.03 ============================== end of head =========================== 0.44/1.03 0.44/1.03 ============================== INPUT ================================= 0.44/1.03 0.44/1.03 % Reading from file /tmp/Prover9_26243_n026.cluster.edu 0.44/1.03 0.44/1.03 set(prolog_style_variables). 0.44/1.03 set(auto2). 0.44/1.03 % set(auto2) -> set(auto). 0.44/1.03 % set(auto) -> set(auto_inference). 0.44/1.03 % set(auto) -> set(auto_setup). 0.44/1.03 % set(auto_setup) -> set(predicate_elim). 0.44/1.03 % set(auto_setup) -> assign(eq_defs, unfold). 0.44/1.03 % set(auto) -> set(auto_limits). 0.44/1.03 % set(auto_limits) -> assign(max_weight, "100.000"). 0.44/1.03 % set(auto_limits) -> assign(sos_limit, 20000). 0.44/1.03 % set(auto) -> set(auto_denials). 0.44/1.03 % set(auto) -> set(auto_process). 0.44/1.03 % set(auto2) -> assign(new_constants, 1). 0.44/1.03 % set(auto2) -> assign(fold_denial_max, 3). 0.44/1.03 % set(auto2) -> assign(max_weight, "200.000"). 0.44/1.03 % set(auto2) -> assign(max_hours, 1). 0.44/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.44/1.03 % set(auto2) -> assign(max_seconds, 0). 0.44/1.03 % set(auto2) -> assign(max_minutes, 5). 0.44/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.44/1.03 % set(auto2) -> set(sort_initial_sos). 0.44/1.03 % set(auto2) -> assign(sos_limit, -1). 0.44/1.03 % set(auto2) -> assign(lrs_ticks, 3000). 0.44/1.03 % set(auto2) -> assign(max_megs, 400). 0.44/1.03 % set(auto2) -> assign(stats, some). 0.44/1.03 % set(auto2) -> clear(echo_input). 0.44/1.03 % set(auto2) -> set(quiet). 0.44/1.03 % set(auto2) -> clear(print_initial_clauses). 0.44/1.03 % set(auto2) -> clear(print_given). 0.44/1.03 assign(lrs_ticks,-1). 0.44/1.03 assign(sos_limit,10000). 0.44/1.03 assign(order,kbo). 0.44/1.03 set(lex_order_vars). 0.44/1.03 clear(print_given). 0.44/1.03 0.44/1.03 % formulas(sos). % not echoed (43 formulas) 0.44/1.03 0.44/1.03 ============================== end of input ========================== 0.44/1.03 0.44/1.03 % From the command line: assign(max_seconds, 960). 0.44/1.03 0.44/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.44/1.03 0.44/1.03 % Formulas that are not ordinary clauses: 0.44/1.03 1 (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]. 0.44/1.03 2 (all X all Y is_a_theorem(implies(Y,or(X,Y)))) <-> or_2 # label(or_2) # label(axiom) # label(non_clause). [assumption]. 0.44/1.03 3 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption]. 0.44/1.03 4 (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]. 0.44/1.03 5 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]. 0.44/1.03 6 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption]. 0.44/1.03 7 (all X all Y is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))) <-> modus_tollens # label(modus_tollens) # label(axiom) # label(non_clause). [assumption]. 0.44/1.03 8 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption]. 0.44/1.03 9 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption]. 0.44/1.03 10 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption]. 0.44/1.03 11 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption]. 0.44/1.03 12 (all X all Y (is_a_theorem(equiv(X,Y)) -> X = Y)) <-> substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom) # label(non_clause). [assumption]. 0.44/1.03 13 (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]. 0.44/1.03 14 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]. 1.19/1.47 15 (all P all Q is_a_theorem(implies(Q,or(P,Q)))) <-> r2 # label(r2) # label(axiom) # label(non_clause). [assumption]. 1.19/1.47 16 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]. 1.19/1.47 17 (all X all Y is_a_theorem(implies(X,or(X,Y)))) <-> or_1 # label(or_1) # label(axiom) # label(non_clause). [assumption]. 1.19/1.47 18 (all P is_a_theorem(implies(implies(not(P),P),P))) <-> cn3 # label(cn3) # label(axiom) # label(non_clause). [assumption]. 1.19/1.47 19 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption]. 1.19/1.47 20 (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]. 1.19/1.47 21 (all X all Y is_a_theorem(implies(and(X,Y),X))) <-> and_1 # label(and_1) # label(axiom) # label(non_clause). [assumption]. 1.19/1.47 22 (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]. 1.19/1.47 23 (all P all Q all R is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))) <-> r4 # label(r4) # label(axiom) # label(non_clause). [assumption]. 1.19/1.47 24 (all X all Y (is_a_theorem(X) & is_a_theorem(implies(X,Y)) -> is_a_theorem(Y))) <-> modus_ponens # label(modus_ponens) # label(axiom) # label(non_clause). [assumption]. 1.19/1.47 25 implies_2 <-> (all X all Y is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))) # label(implies_2) # label(axiom) # label(non_clause). [assumption]. 1.19/1.47 26 (all P all Q all R is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))) <-> r5 # label(r5) # label(axiom) # label(non_clause). [assumption]. 1.19/1.47 27 op_and -> (all X all Y and(X,Y) = not(or(not(X),not(Y)))) # label(op_and) # label(axiom) # label(non_clause). [assumption]. 1.19/1.47 28 op_equiv -> (all X all Y and(implies(X,Y),implies(Y,X)) = equiv(X,Y)) # label(op_equiv) # label(axiom) # label(non_clause). [assumption]. 1.19/1.47 29 op_or -> (all X all Y or(X,Y) = not(and(not(X),not(Y)))) # label(op_or) # label(axiom) # label(non_clause). [assumption]. 1.19/1.47 30 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]. 1.19/1.47 31 op_implies_or -> (all X all Y or(not(X),Y) = implies(X,Y)) # label(op_implies_or) # label(axiom) # label(non_clause). [assumption]. 1.19/1.47 1.19/1.47 ============================== end of process non-clausal formulas === 1.19/1.47 1.19/1.47 ============================== PROCESS INITIAL CLAUSES =============== 1.19/1.47 1.19/1.47 ============================== PREDICATE ELIMINATION ================= 1.19/1.47 1.19/1.47 ============================== end predicate elimination ============= 1.19/1.47 1.19/1.47 Auto_denials: (non-Horn, no changes). 1.19/1.47 1.19/1.47 Term ordering decisions: 1.19/1.47 1.19/1.47 % Assigning unary symbol not kb_weight 0 and highest precedence (94). 1.19/1.47 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. c10=1. c11=1. c12=1. c13=1. c14=1. c15=1. c16=1. c17=1. c18=1. c19=1. c20=1. c21=1. c22=1. c23=1. c24=1. c25=1. c26=1. c27=1. c28=1. c29=1. c30=1. c31=1. c32=1. c33=1. c34=1. c35=1. c36=1. c37=1. c38=1. c39=1. c40=1. c41=1. c42=1. c43=1. c44=1. c45=1. c46=1. c47=1. c48=1. c49=1. c50=1. c51=1. c52=1. c53=1. c54=1. c55=1. implies=1. or=1. and=1. equiv=1. not=0. 1.19/1.47 1.19/1.47 ============================== end of process initial clauses ======== 1.19/1.47 1.19/1.47 ============================== CLAUSES FOR SEARCH ==================== 1.19/1.47 1.19/1.47 ============================== end of clauses for search ============= 1.19/1.47 1.19/1.47 ============================== SEARCH ================================ 1.19/1.47 1.19/1.47 % Starting search at 0.01 seconds. 1.19/1.47 1.19/1.47 Low Water (keep): wt=43.000, iters=3397 1.19/1.47 1.19/1.47 Low Water (keep): wt=34.000, iters=3348 1.19/1.47 1.19/1.47 Low Water (keep): wt=31.000, iters=3345 1.19/1.47 1.19/1.47 Low Water (keep): wt=30.000, iters=3345 1.19/1.47 1.19/1.47 Low Water (keep): wt=29.000, iters=3348 1.19/1.47 1.19/1.47 Low Water (keep): wt=27.000, iters=3389 1.19/1.47 1.19/1.47 Low Water (keep): wt=25.000, iters=3346 1.19/1.47 1.19/1.47 Low Water (keep): wt=24.000, iters=3382 1.19/1.47 1.19/1.47 Low Water (keep): wt=23.000, iters=3359 1.19/1.47 1.19/1.47 Low Water (keep): wt=22.000, iters=3335 1.19/1.47 113.67/113.96 Low Water (keep): wt=21.000, iters=3349 113.67/113.96 113.67/113.96 Low Water (keep): wt=20.000, iters=3345 113.67/113.96 113.67/113.96 Low Water (keep): wt=19.000, iters=3367 113.67/113.96 113.67/113.96 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 80 (0.00 of 1.13 sec). 113.67/113.96 113.67/113.96 Low Water (displace): id=1671, wt=111.000 113.67/113.96 113.67/113.96 Low Water (displace): id=2038, wt=103.000 113.67/113.96 113.67/113.96 Low Water (displace): id=3153, wt=83.000 113.67/113.96 113.67/113.96 Low Water (displace): id=3592, wt=79.000 113.67/113.96 113.67/113.96 Low Water (displace): id=1524, wt=75.000 113.67/113.96 113.67/113.96 Low Water (displace): id=1526, wt=55.000 113.67/113.96 113.67/113.96 Low Water (displace): id=9468, wt=45.000 113.67/113.96 113.67/113.96 Low Water (displace): id=9161, wt=43.000 113.67/113.96 113.67/113.96 Low Water (displace): id=9160, wt=42.000 113.67/113.96 113.67/113.96 Low Water (displace): id=9472, wt=41.000 113.67/113.96 113.67/113.96 Low Water (displace): id=7184, wt=39.000 113.67/113.96 113.67/113.96 Low Water (displace): id=7182, wt=38.000 113.67/113.96 113.67/113.96 Low Water (displace): id=9476, wt=37.000 113.67/113.96 113.67/113.96 Low Water (displace): id=10492, wt=35.000 113.67/113.96 113.67/113.96 Low Water (displace): id=9155, wt=34.000 113.67/113.96 113.67/113.96 Low Water (displace): id=10688, wt=33.000 113.67/113.96 113.67/113.96 Low Water (displace): id=10911, wt=18.000 113.67/113.96 113.67/113.96 Low Water (keep): wt=18.000, iters=3407 113.67/113.96 113.67/113.96 Low Water (displace): id=11510, wt=16.000 113.67/113.96 113.67/113.96 Low Water (displace): id=11998, wt=15.000 113.67/113.96 113.67/113.96 Low Water (keep): wt=17.000, iters=3339 113.67/113.96 113.67/113.96 Low Water (displace): id=13390, wt=14.000 113.67/113.96 113.67/113.96 Low Water (displace): id=13396, wt=13.000 113.67/113.96 113.67/113.96 Low Water (keep): wt=16.000, iters=3337 113.67/113.96 113.67/113.96 Low Water (keep): wt=15.000, iters=3943 113.67/113.96 113.67/113.96 Low Water (keep): wt=14.000, iters=3345 113.67/113.96 113.67/113.96 Low Water (displace): id=117698, wt=12.000 113.67/113.96 113.67/113.96 Low Water (displace): id=117954, wt=11.000 113.67/113.96 113.67/113.96 Low Water (displace): id=118409, wt=10.000 113.67/113.96 113.67/113.96 Low Water (keep): wt=13.000, iters=3334 113.67/113.96 113.67/113.96 ============================== PROOF ================================= 113.67/113.96 % SZS status Theorem 113.67/113.96 % SZS output start Refutation 113.67/113.96 113.67/113.96 % Proof 1 at 105.92 (+ 6.99) seconds. 113.67/113.96 % Length of proof is 347. 113.67/113.96 % Level of proof is 98. 113.67/113.96 % Maximum clause weight is 19.000. 113.67/113.96 % Given clauses 8697. 113.67/113.96 113.67/113.96 9 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption]. 113.67/113.96 12 (all X all Y (is_a_theorem(equiv(X,Y)) -> X = Y)) <-> substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom) # label(non_clause). [assumption]. 113.67/113.96 18 (all P is_a_theorem(implies(implies(not(P),P),P))) <-> cn3 # label(cn3) # label(axiom) # label(non_clause). [assumption]. 113.67/113.96 19 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption]. 113.67/113.96 20 (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]. 113.67/113.96 24 (all X all Y (is_a_theorem(X) & is_a_theorem(implies(X,Y)) -> is_a_theorem(Y))) <-> modus_ponens # label(modus_ponens) # label(axiom) # label(non_clause). [assumption]. 113.67/113.96 28 op_equiv -> (all X all Y and(implies(X,Y),implies(Y,X)) = equiv(X,Y)) # label(op_equiv) # label(axiom) # label(non_clause). [assumption]. 113.67/113.96 30 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]. 113.67/113.96 32 op_equiv # label(luka_op_equiv) # label(axiom). [assumption]. 113.67/113.96 33 cn1 # label(luka_cn1) # label(axiom). [assumption]. 113.67/113.96 35 cn2 # label(luka_cn2) # label(axiom). [assumption]. 113.67/113.96 36 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption]. 113.67/113.96 38 modus_ponens # label(luka_modus_ponens) # label(axiom). [assumption]. 113.67/113.96 39 cn3 # label(luka_cn3) # label(axiom). [assumption]. 113.67/113.96 40 op_implies_and # label(hilbert_op_implies_and) # label(axiom). [assumption]. 113.67/113.96 41 -and_2 # label(hilbert_and_2) # label(negated_conjecture). [assumption]. 113.67/113.96 56 and_2 | -is_a_theorem(implies(and(c37,c38),c38)) # label(and_2) # label(axiom). [clausify(19)]. 113.67/113.96 57 -is_a_theorem(implies(and(c37,c38),c38)). [copy(56),unit_del(a,41)]. 113.67/113.96 60 -cn2 | is_a_theorem(implies(A,implies(not(A),B))) # label(cn2) # label(axiom). [clausify(9)]. 113.67/113.96 61 is_a_theorem(implies(A,implies(not(A),B))). [copy(60),unit_del(a,35)]. 113.67/113.96 63 -is_a_theorem(equiv(A,B)) | B = A | -substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [clausify(12)]. 113.67/113.96 64 -is_a_theorem(equiv(A,B)) | B = A. [copy(63),unit_del(c,36)]. 113.67/113.96 65 is_a_theorem(implies(implies(not(A),A),A)) | -cn3 # label(cn3) # label(axiom). [clausify(18)]. 113.67/113.96 66 is_a_theorem(implies(implies(not(A),A),A)). [copy(65),unit_del(b,39)]. 113.67/113.96 75 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) | -modus_ponens # label(modus_ponens) # label(axiom). [clausify(24)]. 113.67/113.96 76 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(75),unit_del(d,38)]. 113.67/113.96 78 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(30)]. 113.67/113.96 79 not(and(A,not(B))) = implies(A,B). [copy(78),unit_del(a,40)]. 113.67/113.96 87 -op_equiv | and(implies(A,B),implies(B,A)) = equiv(A,B) # label(op_equiv) # label(axiom). [clausify(28)]. 113.67/113.96 88 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(87),unit_del(a,32)]. 113.67/113.96 93 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))) | -cn1 # label(cn1) # label(axiom). [clausify(20)]. 113.67/113.96 94 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))). [copy(93),unit_del(b,33)]. 113.67/113.96 120 -is_a_theorem(implies(not(A),A)) | is_a_theorem(A). [resolve(76,b,66,a)]. 113.67/113.96 121 -is_a_theorem(A) | is_a_theorem(implies(not(A),B)). [resolve(76,b,61,a)]. 113.67/113.96 125 is_a_theorem(implies(and(A,not(B)),implies(implies(A,B),C))). [para(79(a,1),61(a,1,2,1))]. 113.67/113.96 126 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))]. 113.67/113.96 127 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(79(a,1),79(a,1,1,2))]. 113.67/113.96 128 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(B,C),implies(A,C))). [resolve(94,a,76,b)]. 113.67/113.96 224 is_a_theorem(implies(implies(implies(implies(A,B),C),D),implies(and(A,not(B)),D))). [resolve(128,a,125,a)]. 113.67/113.96 225 is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))). [resolve(128,a,94,a)]. 113.67/113.96 226 is_a_theorem(implies(implies(A,B),implies(implies(not(A),A),B))). [resolve(128,a,66,a)]. 113.67/113.96 227 is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C))). [resolve(128,a,61,a)]. 113.67/113.96 228 is_a_theorem(implies(implies(implies(implies(not(A),A),B),C),implies(implies(A,B),C))). [resolve(226,a,128,a)]. 113.67/113.96 230 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(A),A),B)). [resolve(226,a,76,b)]. 113.67/113.96 240 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(not(A),D),B),C))). [resolve(227,a,128,a)]. 113.67/113.96 242 -is_a_theorem(implies(implies(not(A),B),C)) | is_a_theorem(implies(A,C)). [resolve(227,a,76,b)]. 113.67/113.96 255 implies(implies(A,B),and(B,not(A))) = not(equiv(A,B)). [para(88(a,1),127(a,1,1)),flip(a)]. 113.67/113.96 256 -is_a_theorem(implies(implies(A,and(B,not(C))),and(A,implies(B,C)))) | is_a_theorem(and(A,implies(B,C))). [para(127(a,1),120(a,1,1))]. 113.67/113.96 344 is_a_theorem(implies(A,implies(implies(B,C),implies(not(A),C)))). [resolve(242,a,94,a)]. 113.67/113.96 345 is_a_theorem(implies(A,A)). [resolve(242,a,66,a)]. 113.67/113.96 347 -is_a_theorem(implies(implies(implies(A,B),C),D)) | is_a_theorem(implies(and(A,not(B)),D)). [para(79(a,1),242(a,1,1,1))]. 113.67/113.96 411 is_a_theorem(implies(not(implies(A,A)),B)). [resolve(345,a,121,a)]. 113.67/113.96 431 is_a_theorem(implies(implies(A,B),implies(not(implies(C,C)),B))). [resolve(411,a,128,a)]. 113.67/113.96 608 is_a_theorem(implies(implies(not(A),A),implies(implies(B,C),implies(not(A),C)))). [resolve(344,a,230,a)]. 113.67/113.96 609 is_a_theorem(implies(implies(implies(implies(A,B),implies(not(C),B)),D),implies(C,D))). [resolve(344,a,128,a)]. 113.67/113.96 637 is_a_theorem(implies(A,implies(not(implies(B,B)),C))). [resolve(431,a,242,a)]. 113.67/113.96 752 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),implies(D,C))). [resolve(637,a,128,a)]. 113.67/113.96 1022 is_a_theorem(implies(not(equiv(A,A)),and(A,not(A)))). [para(255(a,1),126(a,1,1))]. 113.67/113.96 1202 is_a_theorem(implies(implies(and(A,not(A)),B),implies(not(equiv(A,A)),B))). [resolve(1022,a,128,a)]. 113.67/113.96 2275 -is_a_theorem(implies(implies(not(implies(A,A)),B),C)) | is_a_theorem(implies(D,C)). [resolve(752,a,76,b)]. 113.67/113.96 3014 is_a_theorem(implies(A,implies(B,B))). [resolve(2275,a,66,a)]. 113.67/113.96 3021 is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))). [resolve(3014,a,128,a)]. 113.67/113.96 3365 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(D,D),B),C))). [resolve(3021,a,128,a)]. 113.67/113.96 3367 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(implies(C,B)). [resolve(3021,a,76,b)]. 113.67/113.96 3438 is_a_theorem(implies(A,implies(B,implies(C,C)))). [resolve(3367,a,3021,a)]. 113.67/113.96 3440 is_a_theorem(implies(A,implies(B,implies(not(B),C)))). [resolve(3367,a,227,a)]. 113.67/113.96 3441 is_a_theorem(implies(A,implies(implies(not(B),B),B))). [resolve(3367,a,226,a)]. 113.67/113.96 3447 is_a_theorem(implies(implies(implies(A,implies(B,B)),C),implies(D,C))). [resolve(3438,a,128,a)]. 113.67/113.96 3521 is_a_theorem(implies(implies(implies(A,implies(not(A),B)),C),implies(D,C))). [resolve(3440,a,128,a)]. 113.67/113.96 3817 is_a_theorem(implies(implies(implies(implies(not(A),A),A),B),implies(C,B))). [resolve(3441,a,128,a)]. 113.67/113.96 5380 -is_a_theorem(implies(implies(implies(not(A),A),A),B)) | is_a_theorem(implies(C,B)). [resolve(3817,a,76,b)]. 113.67/113.96 6230 -is_a_theorem(implies(not(A),A)) | is_a_theorem(implies(implies(B,C),implies(not(A),C))). [resolve(608,a,76,b)]. 113.67/113.96 6962 -is_a_theorem(implies(and(A,not(A)),B)) | is_a_theorem(implies(not(equiv(A,A)),B)). [resolve(1202,a,76,b)]. 113.67/113.96 7350 is_a_theorem(implies(A,implies(implies(implies(B,B),C),C))). [resolve(3365,a,5380,a)]. 113.67/113.96 7360 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(implies(D,D),B),C)). [resolve(3365,a,76,b)]. 113.67/113.96 7414 is_a_theorem(implies(implies(implies(implies(implies(A,A),B),B),C),implies(D,C))). [resolve(7350,a,128,a)]. 113.67/113.96 7416 is_a_theorem(implies(implies(implies(A,A),B),B)). [resolve(7350,a,120,a)]. 113.67/113.96 7471 is_a_theorem(implies(implies(A,B),implies(implies(implies(C,C),A),B))). [resolve(7416,a,128,a)]. 113.67/113.96 7472 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(B). [resolve(7416,a,76,b)]. 113.67/113.96 7715 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(C,C),A),B)). [resolve(7471,a,76,b)]. 113.67/113.96 8194 is_a_theorem(implies(implies(implies(A,A),implies(implies(B,B),C)),implies(D,C))). [resolve(7715,a,3021,a)]. 113.67/113.96 9536 is_a_theorem(implies(implies(implies(A,A),B),implies(implies(B,C),implies(D,C)))). [resolve(7360,a,94,a)]. 113.67/113.96 9607 -is_a_theorem(implies(implies(implies(implies(A,A),B),B),C)) | is_a_theorem(implies(D,C)). [resolve(7414,a,76,b)]. 113.67/113.96 10169 -is_a_theorem(implies(implies(A,A),implies(implies(B,B),C))) | is_a_theorem(implies(D,C)). [resolve(8194,a,76,b)]. 113.67/113.96 10434 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(implies(implies(B,C),implies(D,C))). [resolve(9536,a,76,b)]. 113.67/113.96 11062 is_a_theorem(implies(A,implies(and(B,not(B)),C))). [resolve(224,a,9607,a)]. 113.67/113.96 11092 is_a_theorem(implies(and(A,not(A)),B)). [resolve(11062,a,7472,a)]. 113.67/113.96 11163 is_a_theorem(implies(not(equiv(A,A)),B)). [back_unit_del(6962),unit_del(a,11092)]. 113.67/113.96 11324 is_a_theorem(implies(implies(A,B),implies(not(equiv(C,C)),B))). [resolve(11163,a,6230,a)]. 113.67/113.96 12329 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),C),implies(D,C))). [resolve(11324,a,10434,a)]. 113.67/113.96 12823 is_a_theorem(implies(A,implies(B,equiv(C,C)))). [resolve(12329,a,5380,a)]. 113.67/113.96 12860 is_a_theorem(implies(A,equiv(B,B))). [resolve(12823,a,10169,a)]. 113.67/113.96 12957 is_a_theorem(implies(implies(equiv(A,A),B),implies(C,B))). [resolve(12860,a,10434,a)]. 113.67/113.96 13350 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(equiv(D,D),B),C))). [resolve(12957,a,128,a)]. 113.67/113.96 13743 -is_a_theorem(implies(implies(implies(not(A),A),B),C)) | is_a_theorem(implies(implies(A,B),C)). [resolve(228,a,76,b)]. 113.67/113.96 14389 is_a_theorem(implies(A,implies(implies(implies(not(implies(B,B)),C),D),D))). [resolve(240,a,9607,a)]. 113.67/113.96 14396 is_a_theorem(implies(A,implies(implies(implies(not(not(B)),C),B),B))). [resolve(240,a,5380,a)]. 113.67/113.96 14406 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(implies(not(A),D),B),C)). [resolve(240,a,76,b)]. 113.67/113.96 14455 is_a_theorem(implies(implies(implies(not(not(A)),B),A),A)). [resolve(14396,a,7472,a)]. 113.67/113.96 14479 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(not(A)),C),A),B))). [resolve(14455,a,128,a)]. 113.67/113.96 14480 -is_a_theorem(implies(implies(not(not(A)),B),A)) | is_a_theorem(A). [resolve(14455,a,76,b)]. 113.67/113.96 14498 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),C)). [resolve(14389,a,14480,a)]. 113.67/113.96 14570 -is_a_theorem(implies(implies(not(implies(A,A)),B),C)) | is_a_theorem(C). [resolve(14498,a,76,b)]. 113.67/113.96 14592 -is_a_theorem(not(equiv(not(implies(A,A)),B))) | is_a_theorem(and(B,not(not(implies(A,A))))). [para(255(a,1),14570(a,1))]. 113.67/113.96 14677 is_a_theorem(implies(A,implies(implies(equiv(B,B),C),C))). [resolve(13350,a,9607,a)]. 113.67/113.96 14693 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(equiv(D,D),B),C)). [resolve(13350,a,76,b)]. 113.67/113.96 14703 is_a_theorem(implies(implies(equiv(A,A),B),B)). [resolve(14677,a,14570,a)]. 113.67/113.96 14705 is_a_theorem(implies(implies(implies(implies(equiv(A,A),B),B),C),implies(D,C))). [resolve(14677,a,10434,a)]. 113.67/113.96 14761 -is_a_theorem(implies(equiv(A,A),B)) | is_a_theorem(B). [resolve(14703,a,76,b)]. 113.67/113.96 17416 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(not(A)),C),A),B)). [resolve(14479,a,76,b)]. 113.67/113.96 17494 is_a_theorem(implies(implies(equiv(A,A),B),implies(implies(B,C),implies(D,C)))). [resolve(14693,a,9536,a)]. 113.67/113.96 17574 -is_a_theorem(implies(implies(implies(equiv(A,A),B),B),C)) | is_a_theorem(implies(D,C)). [resolve(14705,a,76,b)]. 113.67/113.96 19744 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),and(A,not(A))),C)). [resolve(17416,a,11092,a),rewrite([79(3)])]. 113.67/113.96 19930 -is_a_theorem(implies(equiv(A,A),B)) | is_a_theorem(implies(implies(B,C),implies(D,C))). [resolve(17494,a,76,b)]. 113.67/113.96 19977 is_a_theorem(implies(A,implies(implies(implies(not(equiv(B,B)),C),D),D))). [resolve(17574,a,240,a)]. 113.67/113.96 20011 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),C),C)). [resolve(19977,a,14761,a)]. 113.67/113.96 20062 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(equiv(C,C)),D),A),B))). [resolve(20011,a,128,a)]. 113.67/113.96 21886 is_a_theorem(implies(and(not(equiv(A,A)),not(B)),C)). [resolve(347,a,20011,a)]. 113.67/113.96 21888 is_a_theorem(implies(and(not(implies(A,A)),not(B)),C)). [resolve(347,a,19744,a)]. 113.67/113.96 21895 is_a_theorem(implies(and(not(not(A)),not(B)),A)). [resolve(347,a,14455,a)]. 113.67/113.96 21904 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),implies(C,D))). [resolve(347,a,7414,a)]. 113.67/113.96 21906 is_a_theorem(implies(and(implies(not(A),A),not(A)),implies(B,C))). [resolve(347,a,3817,a)]. 113.67/113.96 21907 is_a_theorem(implies(and(A,not(implies(not(A),B))),implies(C,D))). [resolve(347,a,3521,a)]. 113.67/113.96 21908 is_a_theorem(implies(and(A,not(implies(B,B))),implies(C,D))). [resolve(347,a,3447,a)]. 113.67/113.96 21917 is_a_theorem(implies(and(A,not(B)),implies(implies(implies(not(A),C),B),D))). [resolve(347,a,240,a)]. 113.67/113.96 21920 is_a_theorem(implies(and(implies(A,B),not(implies(C,B))),implies(implies(C,A),D))). [resolve(347,a,225,a)]. 113.67/113.96 21966 is_a_theorem(implies(implies(implies(A,A),and(not(not(B)),not(C))),B)). [resolve(21895,a,7715,a)]. 113.67/113.96 21973 is_a_theorem(implies(implies(implies(not(not(A)),B),and(not(not(A)),not(B))),A)). [resolve(21895,a,230,a),rewrite([79(5)])]. 113.67/113.96 21974 is_a_theorem(implies(implies(A,B),implies(and(not(not(A)),not(C)),B))). [resolve(21895,a,128,a)]. 113.67/113.96 22407 is_a_theorem(implies(implies(implies(A,A),and(not(equiv(B,B)),not(C))),D)). [resolve(21886,a,7715,a)]. 113.67/113.96 22450 is_a_theorem(implies(implies(implies(A,A),and(not(implies(B,B)),not(C))),D)). [resolve(21888,a,7715,a)]. 113.67/113.96 22840 is_a_theorem(implies(implies(implies(A,B),C),implies(and(D,not(implies(E,E))),C))). [resolve(21908,a,128,a)]. 113.67/113.96 23109 is_a_theorem(implies(and(implies(not(A),A),not(A)),not(equiv(B,C)))). [para(255(a,1),21906(a,1,2))]. 113.67/113.96 23138 is_a_theorem(implies(and(A,not(implies(not(A),B))),not(equiv(C,D)))). [para(255(a,1),21907(a,1,2))]. 113.67/113.96 23411 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),not(equiv(C,D)))). [para(255(a,1),21904(a,1,2))]. 113.67/113.96 23749 is_a_theorem(implies(and(not(not(not(implies(A,A)))),not(B)),C)). [resolve(21974,a,14570,a)]. 113.67/113.96 23753 is_a_theorem(implies(implies(implies(and(not(not(A)),not(B)),A),C),implies(D,C))). [resolve(21974,a,10434,a)]. 113.67/113.96 23896 is_a_theorem(implies(implies(implies(A,A),and(not(not(not(implies(B,B)))),not(C))),D)). [resolve(23749,a,7715,a)]. 113.67/113.96 26078 is_a_theorem(implies(and(A,implies(B,not(A))),implies(not(equiv(not(A),B)),C))). [para(255(a,1),21917(a,1,2,1)),rewrite([79(4)])]. 113.67/113.96 26452 is_a_theorem(and(implies(A,A),implies(not(equiv(B,B)),C))). [resolve(22407,a,256,a)]. 113.67/113.96 26687 is_a_theorem(and(implies(A,A),implies(not(implies(B,B)),C))). [resolve(22450,a,256,a)]. 113.67/113.96 29178 -is_a_theorem(implies(implies(implies(A,B),implies(not(C),B)),D)) | is_a_theorem(implies(C,D)). [resolve(609,a,76,b)]. 113.67/113.96 41341 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),and(not(not(C)),not(D))),C)). [resolve(14406,a,21966,a)]. 113.67/113.96 50691 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(equiv(C,C)),D),A),B)). [resolve(20062,a,76,b)]. 113.67/113.96 53099 is_a_theorem(implies(implies(not(A),and(not(not(A)),not(not(A)))),A)). [resolve(21973,a,13743,a)]. 113.67/113.96 53262 -is_a_theorem(implies(not(A),and(not(not(A)),not(not(A))))) | is_a_theorem(A). [resolve(53099,a,76,b)]. 113.67/113.96 54324 is_a_theorem(implies(A,implies(and(B,not(implies(C,C))),D))). [resolve(22840,a,17574,a)]. 113.67/113.96 54363 is_a_theorem(implies(implies(implies(and(A,not(implies(B,B))),C),D),implies(E,D))). [resolve(54324,a,19930,a)]. 113.67/113.96 58261 -is_a_theorem(and(A,implies(B,not(A)))) | is_a_theorem(implies(not(equiv(not(A),B)),C)). [resolve(26078,a,76,b)]. 113.67/113.96 59068 is_a_theorem(implies(A,implies(B,implies(not(A),C)))). [resolve(29178,a,23753,a)]. 113.67/113.96 59077 is_a_theorem(implies(A,implies(implies(implies(not(A),B),C),implies(D,C)))). [resolve(29178,a,9536,a)]. 113.67/113.96 59156 is_a_theorem(implies(implies(implies(A,implies(not(B),C)),D),implies(B,D))). [resolve(59068,a,128,a)]. 113.67/113.96 63876 is_a_theorem(implies(A,implies(B,implies(C,implies(not(B),D))))). [resolve(59156,a,3367,a)]. 113.67/113.96 108302 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),and(not(implies(C,C)),not(D))),E)). [resolve(50691,a,21888,a)]. 113.67/113.96 109922 is_a_theorem(implies(and(and(A,not(implies(B,B))),not(C)),implies(D,E))). [resolve(54363,a,347,a)]. 113.67/113.96 110068 is_a_theorem(implies(and(and(A,not(implies(B,B))),not(C)),not(equiv(D,E)))). [para(255(a,1),109922(a,1,2))]. 113.67/113.96 112524 is_a_theorem(implies(not(equiv(not(implies(A,A)),not(implies(B,B)))),C)). [resolve(58261,a,26687,a)]. 113.67/113.96 112526 is_a_theorem(implies(not(equiv(not(implies(A,A)),not(equiv(B,B)))),C)). [resolve(58261,a,26452,a)]. 113.67/113.96 112562 is_a_theorem(equiv(not(implies(A,A)),not(implies(B,B)))). [resolve(112524,a,53262,a)]. 113.67/113.96 112652 not(implies(A,A)) = not(implies(B,B)). [resolve(112562,a,64,a)]. 113.67/113.96 112660 not(implies(A,A)) = c_0. [new_symbol(112652)]. 113.67/113.96 112661 is_a_theorem(implies(not(equiv(c_0,not(equiv(A,A)))),B)). [back_rewrite(112526),rewrite([112660(2)])]. 113.67/113.96 112670 is_a_theorem(implies(and(and(A,c_0),not(B)),not(equiv(C,D)))). [back_rewrite(110068),rewrite([112660(2)])]. 113.67/113.96 112681 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),and(c_0,not(C))),D)). [back_rewrite(108302),rewrite([112660(5)])]. 113.67/113.96 113040 is_a_theorem(implies(implies(implies(c_0,A),and(not(not(B)),not(C))),B)). [back_rewrite(41341),rewrite([112660(2)])]. 113.67/113.96 113200 is_a_theorem(implies(implies(implies(A,A),and(not(not(c_0)),not(B))),C)). [back_rewrite(23896),rewrite([112660(3)])]. 113.67/113.96 113454 -is_a_theorem(not(equiv(c_0,A))) | is_a_theorem(and(A,not(c_0))). [back_rewrite(14592),rewrite([112660(2),112660(6)])]. 113.67/113.96 113458 -is_a_theorem(implies(implies(c_0,A),B)) | is_a_theorem(B). [back_rewrite(14570),rewrite([112660(2)])]. 113.67/113.96 115040 is_a_theorem(implies(c_0,A)). [back_rewrite(411),rewrite([112660(2)])]. 113.67/113.96 115164 implies(A,implies(B,B)) = not(and(A,c_0)). [para(112660(a,1),79(a,1,1,2)),flip(a)]. 113.67/113.96 120949 is_a_theorem(equiv(c_0,not(equiv(A,A)))). [resolve(112661,a,53262,a)]. 113.67/113.96 121060 not(equiv(A,A)) = c_0. [resolve(120949,a,64,a)]. 113.67/113.96 121136 is_a_theorem(implies(implies(implies(c_0,A),and(c_0,not(B))),C)). [back_rewrite(112681),rewrite([121060(2)])]. 113.67/113.96 121151 implies(A,equiv(B,B)) = not(and(A,c_0)). [para(121060(a,1),79(a,1,1,2)),flip(a)]. 113.67/113.96 121186 is_a_theorem(implies(and(implies(not(A),A),not(A)),c_0)). [para(121060(a,1),23109(a,1,2))]. 113.67/113.96 121187 is_a_theorem(implies(and(A,not(implies(not(A),B))),c_0)). [para(121060(a,1),23138(a,1,2))]. 113.67/113.96 121194 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),c_0)). [para(121060(a,1),23411(a,1,2))]. 113.67/113.96 124359 -is_a_theorem(implies(not(and(implies(A,A),c_0)),B)) | is_a_theorem(B). [para(115164(a,1),7472(a,1,1))]. 113.67/113.96 126417 is_a_theorem(implies(implies(c_0,A),implies(and(implies(not(B),B),not(B)),A))). [resolve(121186,a,128,a)]. 113.67/113.96 126488 is_a_theorem(implies(implies(c_0,A),implies(and(B,not(implies(not(B),C))),A))). [resolve(121187,a,128,a)]. 113.67/113.96 134610 is_a_theorem(and(implies(c_0,A),implies(c_0,B))). [resolve(121136,a,256,a)]. 113.67/113.96 134647 is_a_theorem(implies(not(equiv(not(implies(c_0,A)),c_0)),B)). [resolve(134610,a,58261,a)]. 113.67/113.96 134846 is_a_theorem(equiv(not(implies(c_0,A)),c_0)). [resolve(134647,a,53262,a)]. 113.67/113.96 134924 not(implies(c_0,A)) = c_0. [resolve(134846,a,64,a),flip(a)]. 113.67/113.96 134927 implies(A,implies(c_0,B)) = not(and(A,c_0)). [para(134924(a,1),79(a,1,1,2)),flip(a)]. 113.67/113.96 135792 is_a_theorem(implies(and(implies(not(and(implies(A,A),c_0)),B),not(B)),c_0)). [para(115164(a,1),121194(a,1,1,1,1))]. 113.67/113.96 136426 is_a_theorem(implies(and(and(A,c_0),not(B)),c_0)). [para(121060(a,1),112670(a,1,2))]. 113.67/113.96 136441 is_a_theorem(implies(implies(c_0,A),implies(and(and(B,c_0),not(C)),A))). [resolve(136426,a,128,a)]. 113.67/113.96 140795 is_a_theorem(implies(not(equiv(c_0,not(not(A)))),A)). [para(255(a,1),113040(a,1,1))]. 113.67/113.96 140811 is_a_theorem(implies(implies(A,B),implies(not(equiv(c_0,not(not(A)))),B))). [resolve(140795,a,128,a)]. 113.67/113.96 140878 is_a_theorem(and(implies(A,A),implies(not(not(c_0)),B))). [resolve(113200,a,256,a)]. 113.67/113.96 140882 is_a_theorem(implies(not(equiv(c_0,not(not(c_0)))),A)). [resolve(140878,a,58261,a),rewrite([112660(2)])]. 113.67/113.96 140898 is_a_theorem(equiv(c_0,not(not(c_0)))). [resolve(140882,a,53262,a)]. 113.67/113.96 140927 not(not(c_0)) = c_0. [resolve(140898,a,64,a)]. 113.67/113.96 140933 not(and(A,c_0)) = implies(A,not(c_0)). [para(140927(a,1),79(a,1,1,2))]. 113.67/113.96 140934 is_a_theorem(not(c_0)). [para(140927(a,1),120(a,1,1)),unit_del(a,115040)]. 113.67/113.96 140943 implies(implies(not(c_0),A),and(A,c_0)) = not(equiv(not(c_0),A)). [para(140927(a,1),255(a,1,2,2))]. 113.67/113.96 140945 is_a_theorem(implies(A,not(c_0))). [para(140927(a,1),3440(a,1,2,2,1)),rewrite([134927(5),140933(5),115164(6),140933(3)])]. 113.67/113.96 141595 is_a_theorem(implies(and(implies(implies(implies(A,A),not(c_0)),B),not(B)),c_0)). [back_rewrite(135792),rewrite([140933(4)])]. 113.67/113.96 141759 implies(A,implies(c_0,B)) = implies(A,not(c_0)). [back_rewrite(134927),rewrite([140933(6)])]. 113.67/113.96 142102 -is_a_theorem(implies(implies(implies(A,A),not(c_0)),B)) | is_a_theorem(B). [back_rewrite(124359),rewrite([140933(4)])]. 113.67/113.96 142164 implies(A,equiv(B,B)) = implies(A,not(c_0)). [back_rewrite(121151),rewrite([140933(5)])]. 113.67/113.96 142629 implies(A,implies(B,B)) = implies(A,not(c_0)). [back_rewrite(115164),rewrite([140933(5)])]. 113.67/113.96 143128 is_a_theorem(implies(implies(not(c_0),A),implies(B,A))). [resolve(140945,a,19930,a)]. 113.67/113.96 144115 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(not(c_0),B),C))). [resolve(143128,a,128,a)]. 113.67/113.96 162239 is_a_theorem(implies(and(and(A,c_0),not(B)),C)). [resolve(136441,a,113458,a)]. 113.67/113.96 173031 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(equiv(c_0,not(not(A)))),B)). [resolve(140811,a,76,b)]. 113.67/113.96 177142 is_a_theorem(implies(A,implies(implies(not(c_0),B),B))). [resolve(144115,a,17574,a)]. 113.67/113.96 177143 is_a_theorem(implies(implies(A,B),implies(implies(not(c_0),A),B))). [resolve(144115,a,13743,a)]. 113.67/113.96 177145 is_a_theorem(implies(and(A,not(B)),implies(implies(not(c_0),B),C))). [resolve(144115,a,347,a)]. 113.67/113.96 177150 is_a_theorem(implies(implies(not(c_0),A),A)). [resolve(177142,a,142102,a)]. 113.67/113.96 177188 -is_a_theorem(implies(not(c_0),A)) | is_a_theorem(A). [resolve(177150,a,76,b)]. 113.67/113.96 177664 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(c_0),A),B)). [resolve(177143,a,76,b)]. 113.67/113.96 177849 is_a_theorem(implies(implies(not(c_0),and(and(A,c_0),not(B))),C)). [resolve(177664,a,162239,a)]. 113.67/113.96 178351 is_a_theorem(and(not(c_0),implies(and(A,c_0),B))). [resolve(177849,a,256,a)]. 113.67/113.96 178354 is_a_theorem(implies(not(equiv(c_0,and(A,c_0))),B)). [resolve(178351,a,58261,a),rewrite([140927(3)])]. 113.67/113.96 178366 is_a_theorem(equiv(c_0,and(A,c_0))). [resolve(178354,a,53262,a)]. 113.67/113.96 178382 and(A,c_0) = c_0. [resolve(178366,a,64,a)]. 113.67/113.96 178441 implies(implies(not(c_0),A),c_0) = not(equiv(not(c_0),A)). [back_rewrite(140943),rewrite([178382(5)])]. 113.67/113.96 178442 implies(A,not(c_0)) = not(c_0). [back_rewrite(140933),rewrite([178382(2)]),flip(a)]. 113.67/113.96 178460 implies(A,implies(B,B)) = not(c_0). [back_rewrite(142629),rewrite([178442(5)])]. 113.67/113.96 178471 implies(A,equiv(B,B)) = not(c_0). [back_rewrite(142164),rewrite([178442(5)])]. 113.67/113.96 178499 implies(A,implies(c_0,B)) = not(c_0). [back_rewrite(141759),rewrite([178442(6)])]. 113.67/113.96 178500 is_a_theorem(implies(and(implies(not(c_0),A),not(A)),c_0)). [back_rewrite(141595),rewrite([178442(4)])]. 113.67/113.96 178567 and(not(c_0),implies(not(c_0),A)) = equiv(A,not(c_0)). [para(178442(a,1),88(a,1,1))]. 113.67/113.96 178568 and(implies(not(c_0),A),not(c_0)) = equiv(not(c_0),A). [para(178442(a,1),88(a,1,2))]. 113.67/113.96 180913 is_a_theorem(implies(implies(c_0,A),implies(and(implies(not(c_0),B),not(B)),A))). [resolve(178500,a,128,a)]. 113.67/113.96 181430 implies(not(c_0),c_0) = c_0. [para(121060(a,1),178441(a,2)),rewrite([178442(5)])]. 113.67/113.96 181454 not(equiv(not(c_0),implies(A,A))) = c_0. [para(178460(a,1),178441(a,1,1)),rewrite([181430(4)]),flip(a)]. 113.67/113.96 181455 not(equiv(not(c_0),equiv(A,A))) = c_0. [para(178471(a,1),178441(a,1,1)),rewrite([181430(4)]),flip(a)]. 113.67/113.96 181456 not(equiv(not(c_0),implies(c_0,A))) = c_0. [para(178499(a,1),178441(a,1,1)),rewrite([181430(4)]),flip(a)]. 113.67/113.96 181459 is_a_theorem(implies(implies(not(c_0),A),implies(implies(A,c_0),c_0))). [para(181430(a,1),94(a,1,2,2))]. 113.67/113.96 181484 is_a_theorem(implies(and(implies(A,c_0),not(c_0)),implies(implies(not(c_0),A),B))). [para(181430(a,1),21920(a,1,1,2,1))]. 113.67/113.96 181489 is_a_theorem(implies(A,implies(implies(implies(not(A),B),c_0),c_0))). [para(181430(a,1),59077(a,1,2,2))]. 113.67/113.96 181524 implies(A,equiv(not(c_0),implies(B,B))) = not(c_0). [para(181454(a,1),79(a,1,1,2)),rewrite([178382(2)]),flip(a)]. 113.67/113.96 181525 is_a_theorem(equiv(not(c_0),implies(A,A))). [para(181454(a,1),120(a,1,1)),rewrite([181524(6)]),unit_del(a,140934)]. 113.67/113.96 181575 implies(A,A) = not(c_0). [resolve(181525,a,64,a)]. 113.67/113.96 182879 and(not(c_0),not(c_0)) = equiv(A,A). [para(181575(a,1),88(a,1,1)),rewrite([181575(3)])]. 113.67/113.96 182880 is_a_theorem(implies(implies(A,B),implies(not(c_0),implies(A,B)))). [para(181575(a,1),94(a,1,2,1))]. 113.67/113.96 182881 implies(A,and(B,not(B))) = implies(A,c_0). [para(181575(a,1),127(a,1,1,2)),rewrite([79(4)]),flip(a)]. 113.67/113.96 182926 implies(A,equiv(not(c_0),equiv(B,B))) = not(c_0). [para(181455(a,1),79(a,1,1,2)),rewrite([178382(2)]),flip(a)]. 113.67/113.96 182927 is_a_theorem(equiv(not(c_0),equiv(A,A))). [para(181455(a,1),120(a,1,1)),rewrite([182926(6)]),unit_del(a,140934)]. 113.67/113.96 183009 equiv(A,A) = not(c_0). [resolve(182927,a,64,a)]. 113.67/113.96 183269 and(not(c_0),not(c_0)) = not(c_0). [back_rewrite(182879),rewrite([183009(6)])]. 113.67/113.96 183318 implies(A,equiv(not(c_0),implies(c_0,B))) = not(c_0). [para(181456(a,1),79(a,1,1,2)),rewrite([178382(2)]),flip(a)]. 113.67/113.96 183319 is_a_theorem(equiv(not(c_0),implies(c_0,A))). [para(181456(a,1),120(a,1,1)),rewrite([183318(7)]),unit_del(a,140934)]. 113.67/113.96 183451 implies(c_0,A) = not(c_0). [resolve(183319,a,64,a)]. 113.67/113.96 183602 is_a_theorem(implies(not(c_0),implies(and(implies(not(c_0),A),not(A)),B))). [back_rewrite(180913),rewrite([183451(2)])]. 113.67/113.96 183609 is_a_theorem(implies(not(c_0),implies(and(A,not(implies(not(A),B))),C))). [back_rewrite(126488),rewrite([183451(2)])]. 113.67/113.96 183610 is_a_theorem(implies(not(c_0),implies(and(implies(not(A),A),not(A)),B))). [back_rewrite(126417),rewrite([183451(2)])]. 113.67/113.96 183613 and(implies(A,c_0),not(c_0)) = equiv(A,c_0). [para(183451(a,1),88(a,1,2))]. 113.67/113.96 183614 is_a_theorem(implies(implies(A,c_0),implies(not(c_0),implies(A,B)))). [para(183451(a,1),94(a,1,2,1))]. 113.67/113.96 183615 implies(A,and(c_0,not(B))) = implies(A,c_0). [para(183451(a,1),127(a,1,1,2)),rewrite([79(4)]),flip(a)]. 113.67/113.96 183617 implies(not(c_0),and(A,not(c_0))) = not(equiv(c_0,A)). [para(183451(a,1),255(a,1,1))]. 113.67/113.96 183687 is_a_theorem(implies(and(A,not(c_0)),implies(not(equiv(not(A),c_0)),B))). [para(183451(a,1),26078(a,1,1,2))]. 113.67/113.96 183739 is_a_theorem(implies(equiv(A,c_0),implies(implies(not(c_0),A),B))). [back_rewrite(181484),rewrite([183613(5)])]. 113.67/113.96 183748 implies(implies(A,c_0),and(and(B,not(B)),not(A))) = not(equiv(A,and(B,not(B)))). [para(182881(a,1),255(a,1,1))]. 113.67/113.96 183776 implies(and(A,not(A)),c_0) = not(c_0). [para(182881(a,1),181575(a,1))]. 113.67/113.96 184176 equiv(and(A,not(A)),c_0) = not(c_0). [para(183776(a,1),88(a,1,1)),rewrite([182881(6),181575(5),183269(5)]),flip(a)]. 113.67/113.96 184201 and(A,not(A)) = c_0. [para(184176(a,1),64(a,1)),flip(b),unit_del(a,140934)]. 113.67/113.96 184204 implies(implies(A,c_0),c_0) = not(equiv(A,c_0)). [back_rewrite(183748),rewrite([184201(4),183615(6),184201(6)])]. 113.67/113.96 184214 is_a_theorem(implies(A,not(equiv(implies(not(A),B),c_0)))). [back_rewrite(181489),rewrite([184204(6)])]. 113.67/113.96 184226 is_a_theorem(implies(implies(not(c_0),A),not(equiv(A,c_0)))). [back_rewrite(181459),rewrite([184204(7)])]. 113.67/113.96 184884 equiv(c_0,implies(A,c_0)) = and(not(c_0),not(equiv(A,c_0))). [para(184204(a,1),88(a,1,2)),rewrite([183451(4)]),flip(a)]. 113.67/113.96 185029 is_a_theorem(implies(A,implies(not(equiv(not(A),c_0)),implies(B,c_0)))). [para(184204(a,1),59077(a,1,2,1))]. 113.67/113.96 185450 -is_a_theorem(implies(not(c_0),A)) | is_a_theorem(not(equiv(A,c_0))). [resolve(184226,a,76,b)]. 113.67/113.96 185949 is_a_theorem(not(equiv(implies(A,implies(B,implies(not(A),C))),c_0))). [resolve(185450,a,63876,a)]. 113.67/113.96 186090 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(c_0),implies(A,B))). [resolve(182880,a,76,b)]. 113.67/113.96 186318 is_a_theorem(implies(not(c_0),implies(equiv(A,c_0),implies(implies(not(c_0),A),B)))). [resolve(186090,a,183739,a)]. 113.67/113.96 189594 is_a_theorem(implies(and(A,implies(B,c_0)),implies(not(equiv(c_0,B)),C))). [para(183617(a,1),177145(a,1,2,1)),rewrite([79(4)])]. 113.67/113.96 189778 is_a_theorem(implies(A,implies(not(equiv(not(A),c_0)),c_0))). [para(181430(a,1),185029(a,1,2,2))]. 113.67/113.96 189874 -is_a_theorem(A) | is_a_theorem(implies(not(equiv(not(A),c_0)),c_0)). [resolve(189778,a,76,b)]. 113.67/113.96 192100 is_a_theorem(implies(and(implies(not(c_0),A),not(A)),B)). [resolve(183602,a,177188,a)]. 113.67/113.96 192109 is_a_theorem(implies(not(equiv(c_0,not(implies(implies(not(c_0),A),A)))),B)). [resolve(192100,a,173031,a),rewrite([79(7)])]. 113.67/113.96 192184 is_a_theorem(implies(and(A,not(implies(not(A),B))),C)). [resolve(183609,a,177188,a)]. 113.67/113.96 192193 is_a_theorem(implies(not(equiv(c_0,not(implies(A,implies(not(A),B))))),C)). [resolve(192184,a,173031,a),rewrite([79(6)])]. 113.67/113.96 192241 is_a_theorem(implies(and(implies(not(A),A),not(A)),B)). [resolve(183610,a,177188,a)]. 113.67/113.96 192248 is_a_theorem(implies(implies(not(c_0),and(implies(not(A),A),not(A))),B)). [resolve(192241,a,177664,a)]. 113.67/113.96 193032 is_a_theorem(equiv(c_0,not(implies(implies(not(c_0),A),A)))). [resolve(192109,a,53262,a)]. 113.67/113.96 193038 not(implies(implies(not(c_0),A),A)) = c_0. [resolve(193032,a,64,a)]. 113.67/113.96 193040 implies(A,implies(implies(not(c_0),B),B)) = not(c_0). [para(193038(a,1),79(a,1,1,2)),rewrite([178382(2)]),flip(a)]. 113.67/113.96 193065 equiv(implies(implies(not(c_0),A),A),not(c_0)) = not(c_0). [para(193040(a,1),178567(a,1,2)),rewrite([183269(5)]),flip(a)]. 113.67/113.96 193076 implies(implies(not(c_0),A),A) = not(c_0). [para(193065(a,1),64(a,1)),flip(b),unit_del(a,140934)]. 113.67/113.96 193079 and(implies(A,implies(not(c_0),A)),not(c_0)) = equiv(A,implies(not(c_0),A)). [para(193076(a,1),88(a,1,2))]. 113.67/113.96 193179 is_a_theorem(equiv(c_0,not(implies(A,implies(not(A),B))))). [resolve(192193,a,53262,a)]. 113.67/113.96 193195 not(implies(A,implies(not(A),B))) = c_0. [resolve(193179,a,64,a)]. 113.67/113.96 193197 implies(A,implies(B,implies(not(B),C))) = not(c_0). [para(193195(a,1),79(a,1,1,2)),rewrite([178382(2)]),flip(a)]. 113.67/113.96 193213 equiv(implies(A,implies(not(A),B)),not(c_0)) = not(c_0). [para(193197(a,1),178567(a,1,2)),rewrite([183269(5)]),flip(a)]. 113.67/113.96 193222 implies(A,implies(not(A),B)) = not(c_0). [para(193213(a,1),64(a,1)),flip(b),unit_del(a,140934)]. 113.67/113.96 193235 and(not(c_0),implies(implies(not(A),B),A)) = equiv(A,implies(not(A),B)). [para(193222(a,1),88(a,1,1))]. 113.67/113.96 193236 and(implies(implies(not(A),B),A),not(c_0)) = equiv(implies(not(A),B),A). [para(193222(a,1),88(a,1,2))]. 113.67/113.96 193326 is_a_theorem(equiv(A,implies(not(A),A))). [resolve(192248,a,256,a),rewrite([193235(6)])]. 113.67/113.96 193362 implies(not(A),A) = A. [resolve(193326,a,64,a)]. 113.67/113.96 193705 is_a_theorem(implies(A,not(equiv(A,c_0)))). [para(193362(a,1),184214(a,1,2,1,1))]. 113.67/113.96 193709 is_a_theorem(implies(implies(not(A),c_0),implies(not(c_0),A))). [para(193362(a,1),183614(a,1,2,2))]. 113.67/113.96 193724 is_a_theorem(not(equiv(implies(A,implies(B,A)),c_0))). [para(193362(a,1),185949(a,1,1,1,2,2))]. 113.67/113.96 193767 is_a_theorem(implies(and(A,not(c_0)),equiv(not(A),c_0))). [para(193362(a,1),183687(a,1,2))]. 113.67/113.96 193780 is_a_theorem(implies(and(A,implies(B,c_0)),equiv(c_0,B))). [para(193362(a,1),189594(a,1,2))]. 113.67/113.96 195057 -is_a_theorem(A) | is_a_theorem(not(equiv(A,c_0))). [resolve(193705,a,76,b)]. 113.67/113.96 195208 is_a_theorem(not(equiv(implies(A,not(equiv(A,c_0))),c_0))). [resolve(195057,a,193705,a)]. 113.67/113.96 197916 is_a_theorem(not(equiv(implies(implies(not(A),c_0),implies(not(c_0),A)),c_0))). [resolve(193709,a,195057,a)]. 113.67/113.96 197985 is_a_theorem(implies(not(equiv(A,c_0)),not(equiv(c_0,A)))). [para(183617(a,1),193709(a,1,2)),rewrite([79(4),184204(4)])]. 113.67/113.96 198111 -is_a_theorem(and(A,not(c_0))) | is_a_theorem(equiv(not(A),c_0)). [resolve(193767,a,76,b)]. 113.67/113.96 198192 is_a_theorem(implies(and(A,not(equiv(B,c_0))),and(not(c_0),not(equiv(B,c_0))))). [para(184204(a,1),193780(a,1,1,2)),rewrite([184884(8)])]. 113.67/113.96 198836 -is_a_theorem(not(equiv(A,c_0))) | is_a_theorem(not(equiv(c_0,A))). [resolve(197985,a,76,b)]. 113.67/113.96 199452 is_a_theorem(not(equiv(c_0,implies(A,not(equiv(A,c_0)))))). [resolve(198836,a,195208,a)]. 113.67/113.96 199453 is_a_theorem(not(equiv(c_0,implies(A,implies(B,A))))). [resolve(198836,a,193724,a)]. 113.67/113.96 199496 is_a_theorem(and(implies(A,implies(B,A)),not(c_0))). [resolve(199453,a,113454,a)]. 113.67/113.96 199509 is_a_theorem(equiv(not(implies(A,implies(B,A))),c_0)). [resolve(199496,a,198111,a)]. 113.67/113.96 199595 not(implies(A,implies(B,A))) = c_0. [resolve(199509,a,64,a),flip(a)]. 113.67/113.96 199597 implies(A,implies(B,implies(C,B))) = not(c_0). [para(199595(a,1),79(a,1,1,2)),rewrite([178382(2)]),flip(a)]. 113.67/113.96 199600 implies(A,implies(B,A)) = not(c_0). [para(199595(a,1),193362(a,1,1)),rewrite([199597(4)]),flip(a)]. 113.67/113.96 199605 equiv(A,implies(not(c_0),A)) = not(c_0). [back_rewrite(193079),rewrite([199600(4),183269(5)]),flip(a)]. 113.67/113.96 199632 implies(not(c_0),A) = A. [para(199605(a,1),64(a,1)),unit_del(a,140934)]. 113.67/113.96 199661 is_a_theorem(not(equiv(implies(implies(not(A),c_0),A),c_0))). [back_rewrite(197916),rewrite([199632(6)])]. 113.67/113.96 199737 is_a_theorem(implies(equiv(A,c_0),implies(A,B))). [back_rewrite(186318),rewrite([199632(7),199632(7)])]. 113.67/113.96 199785 not(equiv(c_0,A)) = and(A,not(c_0)). [back_rewrite(183617),rewrite([199632(6)]),flip(a)]. 113.67/113.96 199795 equiv(not(c_0),A) = and(A,not(c_0)). [back_rewrite(178568),rewrite([199632(3)]),flip(a)]. 113.67/113.96 199808 is_a_theorem(and(implies(A,not(equiv(A,c_0))),not(c_0))). [back_rewrite(199452),rewrite([199785(7)])]. 113.67/113.96 199814 -is_a_theorem(not(equiv(A,c_0))) | is_a_theorem(and(A,not(c_0))). [back_rewrite(198836),rewrite([199785(7)])]. 113.67/113.96 200985 implies(A,and(not(c_0),not(B))) = not(and(A,B)). [para(199632(a,1),127(a,1,1,2)),flip(a)]. 113.67/113.96 201031 is_a_theorem(not(and(and(A,not(equiv(B,c_0))),equiv(B,c_0)))). [back_rewrite(198192),rewrite([200985(11)])]. 113.67/113.96 201520 is_a_theorem(implies(equiv(not(A),c_0),A)). [para(193362(a,1),199737(a,1,2))]. 113.67/113.96 201705 is_a_theorem(implies(not(equiv(not(implies(equiv(not(A),c_0),A)),c_0)),c_0)). [resolve(201520,a,189874,a)]. 113.67/113.96 202832 -is_a_theorem(and(A,not(c_0))) | not(c_0) = A. [para(199795(a,1),64(a,1)),flip(b)]. 113.67/113.96 205426 implies(A,not(equiv(A,c_0))) = not(c_0). [resolve(199808,a,202832,a),flip(a)]. 113.67/113.96 205430 and(implies(not(equiv(A,c_0)),A),not(c_0)) = equiv(not(equiv(A,c_0)),A). [para(205426(a,1),88(a,1,2))]. 113.67/113.96 205789 is_a_theorem(equiv(implies(not(A),c_0),A)). [resolve(199814,a,199661,a),rewrite([193236(7)])]. 113.67/113.96 205828 implies(not(A),c_0) = A. [resolve(205789,a,64,a),flip(a)]. 113.67/113.96 205891 is_a_theorem(equiv(not(implies(equiv(not(A),c_0),A)),c_0)). [back_rewrite(201705),rewrite([205828(10)])]. 113.67/113.96 206018 implies(implies(A,B),c_0) = and(A,not(B)). [para(79(a,1),205828(a,1,1))]. 113.67/113.96 206019 equiv(not(A),c_0) = and(A,not(c_0)). [para(205828(a,1),88(a,1,1)),rewrite([183451(3)]),flip(a)]. 113.67/113.96 206023 implies(A,and(not(B),not(c_0))) = not(and(A,B)). [para(205828(a,1),127(a,1,1,2)),flip(a)]. 113.67/113.96 206069 implies(and(A,not(c_0)),c_0) = equiv(c_0,A). [para(199785(a,1),205828(a,1,1))]. 113.67/113.96 206166 not(equiv(A,c_0)) = and(A,not(c_0)). [back_rewrite(184204),rewrite([206018(4)]),flip(a)]. 113.67/113.96 206326 is_a_theorem(and(implies(and(A,not(c_0)),A),not(c_0))). [back_rewrite(205891),rewrite([206019(3),206019(7)])]. 113.67/113.96 207614 and(implies(and(A,not(c_0)),A),not(c_0)) = equiv(and(A,not(c_0)),A). [back_rewrite(205430),rewrite([206166(3),206166(10)])]. 113.67/113.96 207674 is_a_theorem(not(and(and(A,and(B,not(c_0))),equiv(B,c_0)))). [back_rewrite(201031),rewrite([206166(3)])]. 113.67/113.96 208046 is_a_theorem(equiv(and(A,not(c_0)),A)). [back_rewrite(206326),rewrite([207614(7)])]. 113.67/113.96 209147 and(A,not(c_0)) = A. [resolve(208046,a,64,a),flip(a)]. 113.67/113.96 209202 is_a_theorem(not(and(and(A,B),equiv(B,c_0)))). [back_rewrite(207674),rewrite([209147(3)])]. 113.67/113.96 209320 equiv(c_0,A) = implies(A,c_0). [back_rewrite(206069),rewrite([209147(3)]),flip(a)]. 113.67/113.96 209330 not(and(A,B)) = implies(A,not(B)). [back_rewrite(206023),rewrite([209147(4)]),flip(a)]. 113.67/113.96 209624 not(implies(A,c_0)) = A. [back_rewrite(199785),rewrite([209320(2),209147(6)])]. 113.67/113.96 209632 equiv(A,c_0) = implies(A,c_0). [back_rewrite(183613),rewrite([209147(5)]),flip(a)]. 113.67/113.96 209771 is_a_theorem(implies(and(A,B),B)). [back_rewrite(209202),rewrite([209632(3),209330(5),209624(4)])]. 113.67/113.96 209772 $F. [resolve(209771,a,57,a)]. 113.67/113.96 113.67/113.96 % SZS output end Refutation 113.67/113.96 ============================== end of proof ========================== 113.67/113.96 113.67/113.96 ============================== STATISTICS ============================ 113.67/113.96 113.67/113.96 Given=8697. Generated=13591551. Kept=209724. proofs=1. 113.67/113.96 Usable=801. Sos=5129. Demods=88. Limbo=441, Disabled=203424. Hints=0. 113.67/113.96 Megabytes=142.99. 113.67/113.96 User_CPU=105.92, System_CPU=6.99, Wall_clock=113. 113.67/113.96 113.67/113.96 ============================== end of statistics ===================== 113.67/113.96 113.67/113.96 ============================== end of search ========================= 113.67/113.96 113.67/113.96 THEOREM PROVED 113.67/113.96 % SZS status Theorem 113.67/113.96 113.67/113.96 Exiting with 1 proof. 113.67/113.96 113.67/113.96 Process 26398 exit (max_proofs) Thu Jul 2 09:26:18 2020 113.67/113.96 Prover9 interrupted 113.67/113.96 EOF