0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.34 % Computer : n007.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 : 180 0.13/0.34 % DateTime : Thu Aug 29 15:06:21 EDT 2019 0.13/0.34 % CPUTime : 0.45/1.05 ============================== Prover9 =============================== 0.45/1.05 Prover9 (32) version 2009-11A, November 2009. 0.45/1.05 Process 32125 was started by sandbox2 on n007.cluster.edu, 0.45/1.05 Thu Aug 29 15:06:22 2019 0.45/1.05 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 180 -f /tmp/Prover9_31972_n007.cluster.edu". 0.45/1.05 ============================== end of head =========================== 0.45/1.05 0.45/1.05 ============================== INPUT ================================= 0.45/1.05 0.45/1.05 % Reading from file /tmp/Prover9_31972_n007.cluster.edu 0.45/1.05 0.45/1.05 set(prolog_style_variables). 0.45/1.05 set(auto2). 0.45/1.05 % set(auto2) -> set(auto). 0.45/1.05 % set(auto) -> set(auto_inference). 0.45/1.05 % set(auto) -> set(auto_setup). 0.45/1.05 % set(auto_setup) -> set(predicate_elim). 0.45/1.05 % set(auto_setup) -> assign(eq_defs, unfold). 0.45/1.05 % set(auto) -> set(auto_limits). 0.45/1.05 % set(auto_limits) -> assign(max_weight, "100.000"). 0.45/1.05 % set(auto_limits) -> assign(sos_limit, 20000). 0.45/1.05 % set(auto) -> set(auto_denials). 0.45/1.05 % set(auto) -> set(auto_process). 0.45/1.05 % set(auto2) -> assign(new_constants, 1). 0.45/1.05 % set(auto2) -> assign(fold_denial_max, 3). 0.45/1.05 % set(auto2) -> assign(max_weight, "200.000"). 0.45/1.05 % set(auto2) -> assign(max_hours, 1). 0.45/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.45/1.05 % set(auto2) -> assign(max_seconds, 0). 0.45/1.05 % set(auto2) -> assign(max_minutes, 5). 0.45/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.45/1.05 % set(auto2) -> set(sort_initial_sos). 0.45/1.05 % set(auto2) -> assign(sos_limit, -1). 0.45/1.05 % set(auto2) -> assign(lrs_ticks, 3000). 0.45/1.05 % set(auto2) -> assign(max_megs, 400). 0.45/1.05 % set(auto2) -> assign(stats, some). 0.45/1.05 % set(auto2) -> clear(echo_input). 0.45/1.05 % set(auto2) -> set(quiet). 0.45/1.05 % set(auto2) -> clear(print_initial_clauses). 0.45/1.05 % set(auto2) -> clear(print_given). 0.45/1.05 assign(lrs_ticks,-1). 0.45/1.05 assign(sos_limit,10000). 0.45/1.05 assign(order,kbo). 0.45/1.05 set(lex_order_vars). 0.45/1.05 clear(print_given). 0.45/1.05 0.45/1.05 % formulas(sos). % not echoed (43 formulas) 0.45/1.05 0.45/1.05 ============================== end of input ========================== 0.45/1.05 0.45/1.05 % From the command line: assign(max_seconds, 180). 0.45/1.05 0.45/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.45/1.05 0.45/1.05 % Formulas that are not ordinary clauses: 0.45/1.05 1 (all X all Y is_a_theorem(implies(X,implies(Y,and(X,Y))))) <-> and_3 # label(and_3) # label(axiom) # label(non_clause). [assumption]. 0.45/1.05 2 r5 <-> (all P all Q all R is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))) # label(r5) # label(axiom) # label(non_clause). [assumption]. 0.45/1.05 3 substitution_of_equivalents <-> (all X all Y (is_a_theorem(equiv(X,Y)) -> X = Y)) # label(substitution_of_equivalents) # label(axiom) # label(non_clause). [assumption]. 0.45/1.05 4 (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))) <-> kn3 # label(kn3) # label(axiom) # label(non_clause). [assumption]. 0.45/1.05 5 implies_3 <-> (all X all Y all Z is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))) # label(implies_3) # label(axiom) # label(non_clause). [assumption]. 0.45/1.05 6 cn1 <-> (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))) # label(cn1) # label(axiom) # label(non_clause). [assumption]. 0.45/1.05 7 (all X all Y is_a_theorem(implies(equiv(X,Y),implies(X,Y)))) <-> equivalence_1 # label(equivalence_1) # label(axiom) # label(non_clause). [assumption]. 0.45/1.05 8 (all X all Y is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))) <-> equivalence_3 # label(equivalence_3) # label(axiom) # label(non_clause). [assumption]. 0.45/1.05 9 modus_ponens <-> (all X all Y (is_a_theorem(X) & is_a_theorem(implies(X,Y)) -> is_a_theorem(Y))) # label(modus_ponens) # label(axiom) # label(non_clause). [assumption]. 0.45/1.05 10 (all P is_a_theorem(implies(P,and(P,P)))) <-> kn1 # label(kn1) # label(axiom) # label(non_clause). [assumption]. 0.45/1.05 11 (all X all Y is_a_theorem(implies(and(X,Y),X))) <-> and_1 # label(and_1) # label(axiom) # label(non_clause). [assumption]. 0.45/1.05 12 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption]. 0.45/1.05 13 (all P is_a_theorem(implies(implies(not(P),P),P))) <-> cn3 # label(cn3) # label(axiom) # label(non_clause). [assumption]. 1.29/1.60 14 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption]. 1.29/1.60 15 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption]. 1.29/1.60 16 (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) <-> cn2 # label(cn2) # label(axiom) # label(non_clause). [assumption]. 1.29/1.60 17 implies_2 <-> (all X all Y is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))) # label(implies_2) # label(axiom) # label(non_clause). [assumption]. 1.29/1.60 18 (all P all Q is_a_theorem(implies(Q,or(P,Q)))) <-> r2 # label(r2) # label(axiom) # label(non_clause). [assumption]. 1.29/1.60 19 (all X all Y all Z is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))) <-> or_3 # label(or_3) # label(axiom) # label(non_clause). [assumption]. 1.29/1.60 20 (all X all Y is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))) <-> modus_tollens # label(modus_tollens) # label(axiom) # label(non_clause). [assumption]. 1.29/1.60 21 equivalence_2 <-> (all X all Y is_a_theorem(implies(equiv(X,Y),implies(Y,X)))) # label(equivalence_2) # label(axiom) # label(non_clause). [assumption]. 1.29/1.60 22 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption]. 1.29/1.60 23 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption]. 1.29/1.60 24 (all P all Q all R is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))) <-> r4 # label(r4) # label(axiom) # label(non_clause). [assumption]. 1.29/1.60 25 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption]. 1.29/1.60 26 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption]. 1.29/1.60 27 op_and -> (all X all Y not(or(not(X),not(Y))) = and(X,Y)) # label(op_and) # label(axiom) # label(non_clause). [assumption]. 1.29/1.60 28 op_or -> (all X all Y or(X,Y) = not(and(not(X),not(Y)))) # label(op_or) # label(axiom) # label(non_clause). [assumption]. 1.29/1.60 29 op_equiv -> (all X all Y equiv(X,Y) = and(implies(X,Y),implies(Y,X))) # label(op_equiv) # label(axiom) # label(non_clause). [assumption]. 1.29/1.60 30 op_implies_or -> (all X all Y implies(X,Y) = or(not(X),Y)) # label(op_implies_or) # label(axiom) # label(non_clause). [assumption]. 1.29/1.60 31 op_implies_and -> (all X all Y implies(X,Y) = not(and(X,not(Y)))) # label(op_implies_and) # label(axiom) # label(non_clause). [assumption]. 1.29/1.60 1.29/1.60 ============================== end of process non-clausal formulas === 1.29/1.60 1.29/1.60 ============================== PROCESS INITIAL CLAUSES =============== 1.29/1.60 1.29/1.60 ============================== PREDICATE ELIMINATION ================= 1.29/1.60 1.29/1.60 ============================== end predicate elimination ============= 1.29/1.60 1.29/1.60 Auto_denials: (non-Horn, no changes). 1.29/1.60 1.29/1.60 Term ordering decisions: 1.29/1.60 1.29/1.60 % Assigning unary symbol not kb_weight 0 and highest precedence (94). 1.29/1.60 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. c10=1. c11=1. c12=1. c13=1. c14=1. c15=1. c16=1. c17=1. c18=1. c19=1. c20=1. c21=1. c22=1. c23=1. c24=1. c25=1. c26=1. c27=1. c28=1. c29=1. c30=1. c31=1. c32=1. c33=1. c34=1. c35=1. c36=1. c37=1. c38=1. c39=1. c40=1. c41=1. c42=1. c43=1. c44=1. c45=1. c46=1. c47=1. c48=1. c49=1. c50=1. c51=1. c52=1. c53=1. c54=1. c55=1. implies=1. or=1. and=1. equiv=1. not=0. 1.29/1.60 1.29/1.60 ============================== end of process initial clauses ======== 1.29/1.60 1.29/1.60 ============================== CLAUSES FOR SEARCH ==================== 1.29/1.60 1.29/1.60 ============================== end of clauses for search ============= 1.29/1.60 1.29/1.60 ============================== SEARCH ================================ 1.29/1.60 1.29/1.60 % Starting search at 0.02 seconds. 1.29/1.60 1.29/1.60 Low Water (keep): wt=91.000, iters=3421 1.29/1.60 1.29/1.60 Low Water (keep): wt=45.000, iters=3381 1.29/1.60 1.29/1.60 Low Water (keep): wt=43.000, iters=3388 1.29/1.60 1.29/1.60 Low Water (keep): wt=38.000, iters=3480 1.29/1.60 1.29/1.60 Low Water (keep): wt=33.000, iters=3369 1.29/1.60 1.29/1.60 Low Water (keep): wt=32.000, iters=3381 1.29/1.60 1.29/1.60 Low Water (keep): wt=31.000, iters=3380 1.29/1.60 1.29/1.60 Low Water (keep): wt=30.000, iters=3400 1.29/1.60 1.29/1.60 Low Water (keep): wt=25.000, iters=3368 1.29/1.60 1.29/1.60 Low Water (keep): wt=24.000, iters=3439 126.13/126.42 126.13/126.42 Low Water (keep): wt=23.000, iters=3353 126.13/126.42 126.13/126.42 Low Water (keep): wt=22.000, iters=3337 126.13/126.42 126.13/126.42 Low Water (keep): wt=21.000, iters=3355 126.13/126.42 126.13/126.42 Low Water (keep): wt=20.000, iters=3350 126.13/126.42 126.13/126.42 Low Water (keep): wt=19.000, iters=3370 126.13/126.42 126.13/126.42 Low Water (keep): wt=18.000, iters=3359 126.13/126.42 126.13/126.42 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 87 (0.00 of 1.42 sec). 126.13/126.42 126.13/126.42 Low Water (displace): id=2105, wt=127.000 126.13/126.42 126.13/126.42 Low Water (displace): id=2527, wt=111.000 126.13/126.42 126.13/126.42 Low Water (displace): id=3241, wt=91.000 126.13/126.42 126.13/126.42 Low Water (displace): id=1998, wt=83.000 126.13/126.42 126.13/126.42 Low Water (displace): id=1993, wt=79.000 126.13/126.42 126.13/126.42 Low Water (displace): id=2000, wt=71.000 126.13/126.42 126.13/126.42 Low Water (displace): id=1999, wt=63.000 126.13/126.42 126.13/126.42 Low Water (displace): id=10055, wt=45.000 126.13/126.42 126.13/126.42 Low Water (displace): id=9565, wt=43.000 126.13/126.42 126.13/126.42 Low Water (displace): id=10738, wt=17.000 126.13/126.42 126.13/126.42 Low Water (displace): id=11815, wt=15.000 126.13/126.42 126.13/126.42 Low Water (displace): id=12136, wt=14.000 126.13/126.42 126.13/126.42 Low Water (keep): wt=17.000, iters=3343 126.13/126.42 126.13/126.42 Low Water (displace): id=13373, wt=12.000 126.13/126.42 126.13/126.42 Low Water (keep): wt=16.000, iters=3333 126.13/126.42 126.13/126.42 Low Water (keep): wt=15.000, iters=4530 126.13/126.42 126.13/126.42 Low Water (keep): wt=14.000, iters=3731 126.13/126.42 126.13/126.42 Low Water (keep): wt=13.000, iters=3333 126.13/126.42 126.13/126.42 Low Water (displace): id=165727, wt=11.000 126.13/126.42 126.13/126.42 ============================== PROOF ================================= 126.13/126.42 % SZS status Theorem 126.13/126.42 % SZS output start Refutation 126.13/126.42 126.13/126.42 % Proof 1 at 118.08 (+ 7.28) seconds. 126.13/126.42 % Length of proof is 348. 126.13/126.42 % Level of proof is 96. 126.13/126.42 % Maximum clause weight is 19.000. 126.13/126.42 % Given clauses 8552. 126.13/126.42 126.13/126.42 3 substitution_of_equivalents <-> (all X all Y (is_a_theorem(equiv(X,Y)) -> X = Y)) # label(substitution_of_equivalents) # label(axiom) # label(non_clause). [assumption]. 126.13/126.42 6 cn1 <-> (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))) # label(cn1) # label(axiom) # label(non_clause). [assumption]. 126.13/126.42 7 (all X all Y is_a_theorem(implies(equiv(X,Y),implies(X,Y)))) <-> equivalence_1 # label(equivalence_1) # label(axiom) # label(non_clause). [assumption]. 126.13/126.42 9 modus_ponens <-> (all X all Y (is_a_theorem(X) & is_a_theorem(implies(X,Y)) -> is_a_theorem(Y))) # label(modus_ponens) # label(axiom) # label(non_clause). [assumption]. 126.13/126.42 13 (all P is_a_theorem(implies(implies(not(P),P),P))) <-> cn3 # label(cn3) # label(axiom) # label(non_clause). [assumption]. 126.13/126.42 16 (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) <-> cn2 # label(cn2) # label(axiom) # label(non_clause). [assumption]. 126.13/126.42 29 op_equiv -> (all X all Y equiv(X,Y) = and(implies(X,Y),implies(Y,X))) # label(op_equiv) # label(axiom) # label(non_clause). [assumption]. 126.13/126.42 31 op_implies_and -> (all X all Y implies(X,Y) = not(and(X,not(Y)))) # label(op_implies_and) # label(axiom) # label(non_clause). [assumption]. 126.13/126.42 32 modus_ponens # label(luka_modus_ponens) # label(axiom). [assumption]. 126.13/126.42 34 cn3 # label(luka_cn3) # label(axiom). [assumption]. 126.13/126.42 35 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption]. 126.13/126.42 36 op_equiv # label(luka_op_equiv) # label(axiom). [assumption]. 126.13/126.42 37 cn1 # label(luka_cn1) # label(axiom). [assumption]. 126.13/126.42 38 cn2 # label(luka_cn2) # label(axiom). [assumption]. 126.13/126.42 40 op_implies_and # label(hilbert_op_implies_and) # label(axiom). [assumption]. 126.13/126.42 41 -equivalence_1 # label(hilbert_equivalence_1) # label(negated_conjecture). [assumption]. 126.13/126.42 60 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(3)]. 126.13/126.42 61 -is_a_theorem(equiv(A,B)) | B = A. [copy(60),unit_del(a,35)]. 126.13/126.42 62 is_a_theorem(implies(implies(not(A),A),A)) | -cn3 # label(cn3) # label(axiom). [clausify(13)]. 126.13/126.42 63 is_a_theorem(implies(implies(not(A),A),A)). [copy(62),unit_del(b,34)]. 126.13/126.42 64 is_a_theorem(implies(A,implies(not(A),B))) | -cn2 # label(cn2) # label(axiom). [clausify(16)]. 126.13/126.42 65 is_a_theorem(implies(A,implies(not(A),B))). [copy(64),unit_del(b,38)]. 126.13/126.42 68 -is_a_theorem(implies(equiv(c17,c18),implies(c17,c18))) | equivalence_1 # label(equivalence_1) # label(axiom). [clausify(7)]. 126.13/126.42 69 -is_a_theorem(implies(equiv(c17,c18),implies(c17,c18))). [copy(68),unit_del(b,41)]. 126.13/126.42 70 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(9)]. 126.13/126.42 71 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(70),unit_del(a,32)]. 126.13/126.42 77 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(31)]. 126.13/126.42 78 not(and(A,not(B))) = implies(A,B). [copy(77),unit_del(a,40)]. 126.13/126.42 86 -op_equiv | equiv(A,B) = and(implies(A,B),implies(B,A)) # label(op_equiv) # label(axiom). [clausify(29)]. 126.13/126.42 87 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(86),flip(b),unit_del(a,36)]. 126.13/126.42 94 -cn1 | is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))) # label(cn1) # label(axiom). [clausify(6)]. 126.13/126.42 95 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))). [copy(94),unit_del(a,37)]. 126.13/126.42 120 -is_a_theorem(A) | is_a_theorem(implies(not(A),B)). [resolve(71,b,65,a)]. 126.13/126.42 121 -is_a_theorem(implies(not(A),A)) | is_a_theorem(A). [resolve(71,b,63,a)]. 126.13/126.42 125 is_a_theorem(implies(implies(implies(A,B),and(A,not(B))),and(A,not(B)))). [para(78(a,1),63(a,1,1,1))]. 126.13/126.42 126 is_a_theorem(implies(and(A,not(B)),implies(implies(A,B),C))). [para(78(a,1),65(a,1,2,1))]. 126.13/126.42 127 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(78(a,1),78(a,1,1,2))]. 126.13/126.42 128 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(B,C),implies(A,C))). [resolve(95,a,71,b)]. 126.13/126.42 152 -is_a_theorem(implies(implies(A,B),and(A,not(B)))) | is_a_theorem(and(A,not(B))). [para(78(a,1),121(a,1,1))]. 126.13/126.42 223 is_a_theorem(implies(implies(implies(implies(A,B),C),D),implies(and(A,not(B)),D))). [resolve(128,a,126,a)]. 126.13/126.42 225 is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))). [resolve(128,a,95,a)]. 126.13/126.42 226 is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C))). [resolve(128,a,65,a)]. 126.13/126.42 227 is_a_theorem(implies(implies(A,B),implies(implies(not(A),A),B))). [resolve(128,a,63,a)]. 126.13/126.42 228 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(not(A),D),B),C))). [resolve(226,a,128,a)]. 126.13/126.42 230 -is_a_theorem(implies(implies(not(A),B),C)) | is_a_theorem(implies(A,C)). [resolve(226,a,71,b)]. 126.13/126.42 243 is_a_theorem(implies(implies(implies(implies(not(A),A),B),C),implies(implies(A,B),C))). [resolve(227,a,128,a)]. 126.13/126.42 245 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(A),A),B)). [resolve(227,a,71,b)]. 126.13/126.42 255 implies(implies(A,B),and(B,not(A))) = not(equiv(A,B)). [para(87(a,1),127(a,1,1)),flip(a)]. 126.13/126.42 316 is_a_theorem(implies(A,implies(implies(B,C),implies(not(A),C)))). [resolve(230,a,95,a)]. 126.13/126.42 318 is_a_theorem(implies(A,A)). [resolve(230,a,63,a)]. 126.13/126.42 319 -is_a_theorem(implies(implies(implies(A,B),C),D)) | is_a_theorem(implies(and(A,not(B)),D)). [para(78(a,1),230(a,1,1,1))]. 126.13/126.42 321 is_a_theorem(implies(not(implies(A,A)),B)). [resolve(318,a,120,a)]. 126.13/126.42 335 is_a_theorem(implies(implies(A,B),implies(not(implies(C,C)),B))). [resolve(321,a,128,a)]. 126.13/126.42 628 is_a_theorem(implies(implies(not(A),A),implies(implies(B,C),implies(not(A),C)))). [resolve(316,a,245,a)]. 126.13/126.42 630 is_a_theorem(implies(implies(implies(implies(A,B),implies(not(C),B)),D),implies(C,D))). [resolve(316,a,128,a)]. 126.13/126.42 659 is_a_theorem(implies(A,implies(not(implies(B,B)),C))). [resolve(335,a,230,a)]. 126.13/126.42 781 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),implies(D,C))). [resolve(659,a,128,a)]. 126.13/126.42 1056 is_a_theorem(implies(not(equiv(A,A)),and(A,not(A)))). [para(255(a,1),125(a,1,1))]. 126.13/126.42 1246 is_a_theorem(implies(implies(and(A,not(A)),B),implies(not(equiv(A,A)),B))). [resolve(1056,a,128,a)]. 126.13/126.42 2288 -is_a_theorem(implies(implies(not(implies(A,A)),B),C)) | is_a_theorem(implies(D,C)). [resolve(781,a,71,b)]. 126.13/126.42 3028 is_a_theorem(implies(A,implies(B,B))). [resolve(2288,a,63,a)]. 126.13/126.42 3035 is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))). [resolve(3028,a,128,a)]. 126.13/126.42 3173 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(D,D),B),C))). [resolve(3035,a,128,a)]. 126.13/126.42 3175 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(implies(C,B)). [resolve(3035,a,71,b)]. 126.13/126.42 3454 is_a_theorem(implies(A,implies(B,implies(C,C)))). [resolve(3175,a,3035,a)]. 126.13/126.42 3456 is_a_theorem(implies(A,implies(implies(not(B),B),B))). [resolve(3175,a,227,a)]. 126.13/126.42 3457 is_a_theorem(implies(A,implies(B,implies(not(B),C)))). [resolve(3175,a,226,a)]. 126.13/126.42 3463 is_a_theorem(implies(implies(implies(A,implies(B,B)),C),implies(D,C))). [resolve(3454,a,128,a)]. 126.13/126.42 3537 is_a_theorem(implies(implies(implies(implies(not(A),A),A),B),implies(C,B))). [resolve(3456,a,128,a)]. 126.13/126.42 3613 is_a_theorem(implies(implies(implies(A,implies(not(A),B)),C),implies(D,C))). [resolve(3457,a,128,a)]. 126.13/126.42 5202 -is_a_theorem(implies(implies(implies(not(A),A),A),B)) | is_a_theorem(implies(C,B)). [resolve(3537,a,71,b)]. 126.13/126.42 6824 -is_a_theorem(implies(not(A),A)) | is_a_theorem(implies(implies(B,C),implies(not(A),C))). [resolve(628,a,71,b)]. 126.13/126.42 7404 -is_a_theorem(implies(and(A,not(A)),B)) | is_a_theorem(implies(not(equiv(A,A)),B)). [resolve(1246,a,71,b)]. 126.13/126.42 7858 is_a_theorem(implies(A,implies(implies(implies(B,B),C),C))). [resolve(3173,a,5202,a)]. 126.13/126.42 7867 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(implies(D,D),B),C)). [resolve(3173,a,71,b)]. 126.13/126.42 7883 is_a_theorem(implies(implies(implies(implies(implies(A,A),B),B),C),implies(D,C))). [resolve(7858,a,128,a)]. 126.13/126.42 7884 is_a_theorem(implies(implies(implies(A,A),B),B)). [resolve(7858,a,121,a)]. 126.13/126.42 7929 is_a_theorem(implies(implies(A,B),implies(implies(implies(C,C),A),B))). [resolve(7884,a,128,a)]. 126.13/126.42 7930 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(B). [resolve(7884,a,71,b)]. 126.13/126.42 8101 is_a_theorem(implies(A,implies(implies(implies(B,B),not(A)),C))). [resolve(7929,a,230,a)]. 126.13/126.42 8104 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(C,C),A),B)). [resolve(7929,a,71,b)]. 126.13/126.42 8128 is_a_theorem(implies(implies(implies(implies(implies(A,A),not(B)),C),D),implies(B,D))). [resolve(8101,a,128,a)]. 126.13/126.42 8603 is_a_theorem(implies(implies(implies(A,A),implies(implies(B,B),C)),implies(D,C))). [resolve(8104,a,3035,a)]. 126.13/126.42 10111 is_a_theorem(implies(implies(implies(A,A),B),implies(implies(B,C),implies(D,C)))). [resolve(7867,a,95,a)]. 126.13/126.42 10184 -is_a_theorem(implies(implies(implies(implies(A,A),B),B),C)) | is_a_theorem(implies(D,C)). [resolve(7883,a,71,b)]. 126.13/126.42 10729 -is_a_theorem(implies(implies(A,A),implies(implies(B,B),C))) | is_a_theorem(implies(D,C)). [resolve(8603,a,71,b)]. 126.13/126.42 10976 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(implies(implies(B,C),implies(D,C))). [resolve(10111,a,71,b)]. 126.13/126.42 11629 is_a_theorem(implies(A,implies(and(B,not(B)),C))). [resolve(223,a,10184,a)]. 126.13/126.42 11659 is_a_theorem(implies(and(A,not(A)),B)). [resolve(11629,a,7930,a)]. 126.13/126.42 11719 is_a_theorem(implies(not(equiv(A,A)),B)). [back_unit_del(7404),unit_del(a,11659)]. 126.13/126.42 11851 is_a_theorem(implies(implies(A,B),implies(not(equiv(C,C)),B))). [resolve(11719,a,6824,a)]. 126.13/126.42 12777 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),C),implies(D,C))). [resolve(11851,a,10976,a)]. 126.13/126.42 13234 is_a_theorem(implies(A,implies(B,equiv(C,C)))). [resolve(12777,a,5202,a)]. 126.13/126.42 13258 is_a_theorem(implies(A,equiv(B,B))). [resolve(13234,a,10729,a)]. 126.13/126.42 13337 is_a_theorem(implies(implies(equiv(A,A),B),implies(C,B))). [resolve(13258,a,10976,a)]. 126.13/126.42 13658 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(equiv(D,D),B),C))). [resolve(13337,a,128,a)]. 126.13/126.42 14064 is_a_theorem(implies(A,implies(implies(implies(not(implies(B,B)),C),D),D))). [resolve(228,a,10184,a)]. 126.13/126.42 14072 is_a_theorem(implies(A,implies(implies(implies(not(not(B)),C),B),B))). [resolve(228,a,5202,a)]. 126.13/126.42 14237 is_a_theorem(implies(implies(implies(not(not(A)),B),A),A)). [resolve(14072,a,7930,a)]. 126.13/126.42 14262 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(not(A)),C),A),B))). [resolve(14237,a,128,a)]. 126.13/126.42 14263 -is_a_theorem(implies(implies(not(not(A)),B),A)) | is_a_theorem(A). [resolve(14237,a,71,b)]. 126.13/126.42 14545 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),C)). [resolve(14064,a,14263,a)]. 126.13/126.42 14589 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(implies(C,C)),D),A),B))). [resolve(14545,a,128,a)]. 126.13/126.42 14590 -is_a_theorem(implies(implies(not(implies(A,A)),B),C)) | is_a_theorem(C). [resolve(14545,a,71,b)]. 126.13/126.42 14635 -is_a_theorem(not(equiv(not(implies(A,A)),B))) | is_a_theorem(and(B,not(not(implies(A,A))))). [para(255(a,1),14590(a,1))]. 126.13/126.42 15038 -is_a_theorem(implies(implies(implies(not(A),A),B),C)) | is_a_theorem(implies(implies(A,B),C)). [resolve(243,a,71,b)]. 126.13/126.42 15159 is_a_theorem(implies(A,implies(implies(equiv(B,B),C),C))). [resolve(13658,a,10184,a)]. 126.13/126.42 15175 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(equiv(D,D),B),C)). [resolve(13658,a,71,b)]. 126.13/126.42 15208 is_a_theorem(implies(implies(equiv(A,A),B),B)). [resolve(15159,a,14590,a)]. 126.13/126.42 15210 is_a_theorem(implies(implies(implies(implies(equiv(A,A),B),B),C),implies(D,C))). [resolve(15159,a,10976,a)]. 126.13/126.42 15260 -is_a_theorem(implies(equiv(A,A),B)) | is_a_theorem(B). [resolve(15208,a,71,b)]. 126.13/126.42 18238 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(not(A)),C),A),B)). [resolve(14262,a,71,b)]. 126.13/126.42 18348 is_a_theorem(implies(implies(equiv(A,A),B),implies(implies(B,C),implies(D,C)))). [resolve(15175,a,10111,a)]. 126.13/126.42 18427 -is_a_theorem(implies(implies(implies(equiv(A,A),B),B),C)) | is_a_theorem(implies(D,C)). [resolve(15210,a,71,b)]. 126.13/126.42 20347 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),and(A,not(A))),C)). [resolve(18238,a,11659,a),rewrite([78(3)])]. 126.13/126.42 20533 -is_a_theorem(implies(equiv(A,A),B)) | is_a_theorem(implies(implies(B,C),implies(D,C))). [resolve(18348,a,71,b)]. 126.13/126.42 20720 is_a_theorem(implies(A,implies(implies(implies(not(equiv(B,B)),C),D),D))). [resolve(18427,a,228,a)]. 126.13/126.42 20748 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),C),C)). [resolve(20720,a,15260,a)]. 126.13/126.42 20788 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(equiv(C,C)),D),A),B))). [resolve(20748,a,128,a)]. 126.13/126.42 22717 is_a_theorem(implies(and(not(equiv(A,A)),not(B)),C)). [resolve(319,a,20748,a)]. 126.13/126.42 22719 is_a_theorem(implies(and(not(implies(A,A)),not(B)),C)). [resolve(319,a,20347,a)]. 126.13/126.42 22727 is_a_theorem(implies(and(not(not(A)),not(B)),A)). [resolve(319,a,14237,a)]. 126.13/126.42 22737 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),implies(C,D))). [resolve(319,a,7883,a)]. 126.13/126.42 22739 is_a_theorem(implies(and(A,not(implies(not(A),B))),implies(C,D))). [resolve(319,a,3613,a)]. 126.13/126.42 22740 is_a_theorem(implies(and(implies(not(A),A),not(A)),implies(B,C))). [resolve(319,a,3537,a)]. 126.13/126.42 22741 is_a_theorem(implies(and(A,not(implies(B,B))),implies(C,D))). [resolve(319,a,3463,a)]. 126.13/126.42 22750 is_a_theorem(implies(and(A,not(B)),implies(implies(implies(not(A),C),B),D))). [resolve(319,a,228,a)]. 126.13/126.42 22752 is_a_theorem(implies(and(implies(A,B),not(implies(C,B))),implies(implies(C,A),D))). [resolve(319,a,225,a)]. 126.13/126.42 22777 is_a_theorem(implies(implies(implies(not(not(A)),B),and(not(not(A)),not(B))),A)). [resolve(22727,a,245,a),rewrite([78(5)])]. 126.13/126.42 22778 is_a_theorem(implies(implies(A,B),implies(and(not(not(A)),not(C)),B))). [resolve(22727,a,128,a)]. 126.13/126.42 23141 is_a_theorem(implies(implies(implies(A,A),and(not(equiv(B,B)),not(C))),D)). [resolve(22717,a,8104,a)]. 126.13/126.42 23182 is_a_theorem(implies(implies(implies(A,A),and(not(implies(B,B)),not(C))),D)). [resolve(22719,a,8104,a)]. 126.13/126.42 23636 is_a_theorem(implies(implies(implies(A,B),C),implies(and(D,not(implies(E,E))),C))). [resolve(22741,a,128,a)]. 126.13/126.42 23910 is_a_theorem(implies(and(A,not(implies(not(A),B))),not(equiv(C,D)))). [para(255(a,1),22739(a,1,2))]. 126.13/126.42 23943 is_a_theorem(implies(and(implies(not(A),A),not(A)),not(equiv(B,C)))). [para(255(a,1),22740(a,1,2))]. 126.13/126.42 24194 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),not(equiv(C,D)))). [para(255(a,1),22737(a,1,2))]. 126.13/126.42 24559 is_a_theorem(implies(and(not(not(not(implies(A,A)))),not(B)),C)). [resolve(22778,a,14590,a)]. 126.13/126.42 24563 is_a_theorem(implies(implies(implies(and(not(not(A)),not(B)),A),C),implies(D,C))). [resolve(22778,a,10976,a)]. 126.13/126.42 24681 is_a_theorem(implies(implies(implies(A,A),and(not(not(not(implies(B,B)))),not(C))),D)). [resolve(24559,a,8104,a)]. 126.13/126.42 27130 is_a_theorem(implies(and(A,implies(B,not(A))),implies(not(equiv(not(A),B)),C))). [para(255(a,1),22750(a,1,2,1)),rewrite([78(4)])]. 126.13/126.42 27463 is_a_theorem(and(implies(A,A),implies(not(equiv(B,B)),C))). [resolve(23141,a,152,a),rewrite([78(6)])]. 126.13/126.42 27741 is_a_theorem(and(implies(A,A),implies(not(implies(B,B)),C))). [resolve(23182,a,152,a),rewrite([78(6)])]. 126.13/126.42 30560 -is_a_theorem(implies(implies(implies(A,B),implies(not(C),B)),D)) | is_a_theorem(implies(C,D)). [resolve(630,a,71,b)]. 126.13/126.42 33367 -is_a_theorem(implies(implies(implies(implies(A,A),not(B)),C),D)) | is_a_theorem(implies(B,D)). [resolve(8128,a,71,b)]. 126.13/126.42 40053 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(implies(C,C)),D),A),B)). [resolve(14589,a,71,b)]. 126.13/126.42 54120 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(equiv(C,C)),D),A),B)). [resolve(20788,a,71,b)]. 126.13/126.42 56203 is_a_theorem(implies(and(implies(A,B),not(implies(C,B))),not(equiv(C,A)))). [para(255(a,1),22752(a,1,2))]. 126.13/126.42 56412 is_a_theorem(implies(implies(not(A),and(not(not(A)),not(not(A)))),A)). [resolve(22777,a,15038,a)]. 126.13/126.42 56481 -is_a_theorem(implies(not(A),and(not(not(A)),not(not(A))))) | is_a_theorem(A). [resolve(56412,a,71,b)]. 126.13/126.42 57659 is_a_theorem(implies(A,implies(and(B,not(implies(C,C))),D))). [resolve(23636,a,18427,a)]. 126.13/126.42 57703 is_a_theorem(implies(implies(implies(and(A,not(implies(B,B))),C),D),implies(E,D))). [resolve(57659,a,20533,a)]. 126.13/126.42 61493 -is_a_theorem(and(A,implies(B,not(A)))) | is_a_theorem(implies(not(equiv(not(A),B)),C)). [resolve(27130,a,71,b)]. 126.13/126.42 62324 is_a_theorem(implies(A,implies(B,implies(not(A),C)))). [resolve(30560,a,24563,a)]. 126.13/126.42 62333 is_a_theorem(implies(A,implies(implies(implies(not(A),B),C),implies(D,C)))). [resolve(30560,a,10111,a)]. 126.13/126.42 62420 is_a_theorem(implies(implies(implies(A,implies(not(B),C)),D),implies(B,D))). [resolve(62324,a,128,a)]. 126.13/126.42 67462 is_a_theorem(implies(A,implies(B,implies(C,implies(not(B),D))))). [resolve(62420,a,3175,a)]. 126.13/126.42 74563 is_a_theorem(implies(A,and(implies(B,B),not(not(A))))). [resolve(33367,a,125,a)]. 126.13/126.42 74689 is_a_theorem(implies(implies(and(implies(A,A),not(not(B))),C),implies(B,C))). [resolve(74563,a,128,a)]. 126.13/126.42 91587 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),and(not(not(C)),not(D))),C)). [resolve(40053,a,22727,a)]. 126.13/126.42 115907 is_a_theorem(implies(and(and(A,not(implies(B,B))),not(C)),implies(D,E))). [resolve(57703,a,319,a)]. 126.13/126.42 116078 is_a_theorem(implies(and(and(A,not(implies(B,B))),not(C)),not(equiv(D,E)))). [para(255(a,1),115907(a,1,2))]. 126.13/126.42 118502 is_a_theorem(implies(not(equiv(not(implies(A,A)),not(implies(B,B)))),C)). [resolve(61493,a,27741,a)]. 126.13/126.42 118504 is_a_theorem(implies(not(equiv(not(implies(A,A)),not(equiv(B,B)))),C)). [resolve(61493,a,27463,a)]. 126.13/126.42 118540 is_a_theorem(equiv(not(implies(A,A)),not(implies(B,B)))). [resolve(118502,a,56481,a)]. 126.13/126.42 118637 not(implies(A,A)) = not(implies(B,B)). [resolve(118540,a,61,a)]. 126.13/126.42 118647 not(implies(A,A)) = c_0. [new_symbol(118637)]. 126.13/126.42 118649 is_a_theorem(implies(not(equiv(c_0,not(equiv(A,A)))),B)). [back_rewrite(118504),rewrite([118647(2)])]. 126.13/126.42 118698 is_a_theorem(implies(and(and(A,c_0),not(B)),not(equiv(C,D)))). [back_rewrite(116078),rewrite([118647(2)])]. 126.13/126.42 118792 is_a_theorem(implies(implies(implies(c_0,A),and(not(not(B)),not(C))),B)). [back_rewrite(91587),rewrite([118647(2)])]. 126.13/126.42 119184 is_a_theorem(implies(implies(implies(A,A),and(not(not(c_0)),not(B))),C)). [back_rewrite(24681),rewrite([118647(3)])]. 126.13/126.42 119234 is_a_theorem(implies(and(c_0,not(A)),B)). [back_rewrite(22719),rewrite([118647(2)])]. 126.13/126.42 119330 -is_a_theorem(not(equiv(c_0,A))) | is_a_theorem(and(A,not(c_0))). [back_rewrite(14635),rewrite([118647(2),118647(6)])]. 126.13/126.42 119334 -is_a_theorem(implies(implies(c_0,A),B)) | is_a_theorem(B). [back_rewrite(14590),rewrite([118647(2)])]. 126.13/126.42 120746 is_a_theorem(implies(c_0,A)). [back_rewrite(321),rewrite([118647(2)])]. 126.13/126.42 121247 implies(A,implies(B,B)) = not(and(A,c_0)). [para(118647(a,1),78(a,1,1,2)),flip(a)]. 126.13/126.42 123552 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),and(c_0,not(C))),D)). [resolve(119234,a,54120,a)]. 126.13/126.42 127247 is_a_theorem(equiv(c_0,not(equiv(A,A)))). [resolve(118649,a,56481,a)]. 126.13/126.42 127345 not(equiv(A,A)) = c_0. [resolve(127247,a,61,a)]. 126.13/126.42 127407 is_a_theorem(implies(implies(implies(c_0,A),and(c_0,not(B))),C)). [back_rewrite(123552),rewrite([127345(2)])]. 126.13/126.42 127450 implies(A,equiv(B,B)) = not(and(A,c_0)). [para(127345(a,1),78(a,1,1,2)),flip(a)]. 126.13/126.42 127496 is_a_theorem(implies(and(A,not(implies(not(A),B))),c_0)). [para(127345(a,1),23910(a,1,2))]. 126.13/126.42 127497 is_a_theorem(implies(and(implies(not(A),A),not(A)),c_0)). [para(127345(a,1),23943(a,1,2))]. 126.13/126.42 127509 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),c_0)). [para(127345(a,1),24194(a,1,2))]. 126.13/126.42 131311 -is_a_theorem(implies(not(and(implies(A,A),c_0)),B)) | is_a_theorem(B). [para(121247(a,1),7930(a,1,1))]. 126.13/126.42 133850 is_a_theorem(implies(implies(c_0,A),implies(and(B,not(implies(not(B),C))),A))). [resolve(127496,a,128,a)]. 126.13/126.42 133927 is_a_theorem(implies(implies(c_0,A),implies(and(implies(not(B),B),not(B)),A))). [resolve(127497,a,128,a)]. 126.13/126.42 141578 is_a_theorem(and(implies(c_0,A),implies(c_0,B))). [resolve(127407,a,152,a),rewrite([78(6)])]. 126.13/126.42 141612 is_a_theorem(implies(not(equiv(not(implies(c_0,A)),c_0)),B)). [resolve(141578,a,61493,a)]. 126.13/126.42 141796 is_a_theorem(equiv(not(implies(c_0,A)),c_0)). [resolve(141612,a,56481,a)]. 126.13/126.42 141888 not(implies(c_0,A)) = c_0. [resolve(141796,a,61,a),flip(a)]. 126.13/126.42 141906 implies(A,implies(c_0,B)) = not(and(A,c_0)). [para(141888(a,1),78(a,1,1,2)),flip(a)]. 126.13/126.42 143445 is_a_theorem(implies(and(implies(not(and(implies(A,A),c_0)),B),not(B)),c_0)). [para(121247(a,1),127509(a,1,1,1,1))]. 126.13/126.42 147876 is_a_theorem(implies(and(and(A,c_0),not(B)),c_0)). [para(127345(a,1),118698(a,1,2))]. 126.13/126.42 147944 is_a_theorem(implies(implies(c_0,A),implies(and(and(B,c_0),not(C)),A))). [resolve(147876,a,128,a)]. 126.13/126.42 167274 is_a_theorem(implies(not(equiv(c_0,not(not(A)))),A)). [para(255(a,1),118792(a,1,1))]. 126.13/126.42 167345 is_a_theorem(implies(implies(A,B),implies(not(equiv(c_0,not(not(A)))),B))). [resolve(167274,a,128,a)]. 126.13/126.42 168574 is_a_theorem(and(implies(A,A),implies(not(not(c_0)),B))). [resolve(119184,a,152,a),rewrite([78(7)])]. 126.13/126.42 168612 is_a_theorem(implies(not(equiv(c_0,not(not(c_0)))),A)). [resolve(168574,a,61493,a),rewrite([118647(2)])]. 126.13/126.42 168682 is_a_theorem(equiv(c_0,not(not(c_0)))). [resolve(168612,a,56481,a)]. 126.13/126.42 168777 not(not(c_0)) = c_0. [resolve(168682,a,61,a)]. 126.13/126.42 168781 not(and(A,c_0)) = implies(A,not(c_0)). [para(168777(a,1),78(a,1,1,2))]. 126.13/126.42 168782 is_a_theorem(not(c_0)). [para(168777(a,1),121(a,1,1)),unit_del(a,120746)]. 126.13/126.42 168789 implies(implies(not(c_0),A),and(A,c_0)) = not(equiv(not(c_0),A)). [para(168777(a,1),255(a,1,2,2))]. 126.13/126.42 168792 is_a_theorem(implies(A,not(c_0))). [para(168777(a,1),3457(a,1,2,2,1)),rewrite([141906(5),168781(5),121247(6),168781(3)])]. 126.13/126.42 169436 is_a_theorem(implies(and(implies(implies(implies(A,A),not(c_0)),B),not(B)),c_0)). [back_rewrite(143445),rewrite([168781(4)])]. 126.13/126.42 169599 implies(A,implies(c_0,B)) = implies(A,not(c_0)). [back_rewrite(141906),rewrite([168781(6)])]. 126.13/126.42 169940 -is_a_theorem(implies(implies(implies(A,A),not(c_0)),B)) | is_a_theorem(B). [back_rewrite(131311),rewrite([168781(4)])]. 126.13/126.42 169980 implies(A,equiv(B,B)) = implies(A,not(c_0)). [back_rewrite(127450),rewrite([168781(5)])]. 126.13/126.42 170422 implies(A,implies(B,B)) = implies(A,not(c_0)). [back_rewrite(121247),rewrite([168781(5)])]. 126.13/126.42 171091 is_a_theorem(implies(implies(not(c_0),A),implies(B,A))). [resolve(168792,a,20533,a)]. 126.13/126.42 172192 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(not(c_0),B),C))). [resolve(171091,a,128,a)]. 126.13/126.42 194698 is_a_theorem(implies(and(and(A,c_0),not(B)),C)). [resolve(147944,a,119334,a)]. 126.13/126.42 200288 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(equiv(c_0,not(not(A)))),B)). [resolve(167345,a,71,b)]. 126.13/126.42 213319 is_a_theorem(implies(A,implies(implies(not(c_0),B),B))). [resolve(172192,a,18427,a)]. 126.13/126.42 213325 is_a_theorem(implies(implies(A,B),implies(implies(not(c_0),A),B))). [resolve(172192,a,15038,a)]. 126.13/126.42 213350 is_a_theorem(implies(implies(not(c_0),A),A)). [resolve(213319,a,169940,a)]. 126.13/126.42 213485 -is_a_theorem(implies(not(c_0),A)) | is_a_theorem(A). [resolve(213350,a,71,b)]. 126.13/126.42 217259 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(c_0),A),B)). [resolve(213325,a,71,b)]. 126.13/126.42 218711 is_a_theorem(implies(implies(not(c_0),and(and(A,c_0),not(B))),C)). [resolve(217259,a,194698,a)]. 126.13/126.42 225908 is_a_theorem(and(not(c_0),implies(and(A,c_0),B))). [resolve(218711,a,152,a),rewrite([78(7)])]. 126.13/126.42 225942 is_a_theorem(implies(not(equiv(c_0,and(A,c_0))),B)). [resolve(225908,a,61493,a),rewrite([168777(3)])]. 126.13/126.42 226010 is_a_theorem(equiv(c_0,and(A,c_0))). [resolve(225942,a,56481,a)]. 126.13/126.42 226104 and(A,c_0) = c_0. [resolve(226010,a,61,a)]. 126.13/126.42 226148 implies(implies(not(c_0),A),c_0) = not(equiv(not(c_0),A)). [back_rewrite(168789),rewrite([226104(5)])]. 126.13/126.42 226149 implies(A,not(c_0)) = not(c_0). [back_rewrite(168781),rewrite([226104(2)]),flip(a)]. 126.13/126.42 226170 implies(A,implies(B,B)) = not(c_0). [back_rewrite(170422),rewrite([226149(5)])]. 126.13/126.42 226178 implies(A,equiv(B,B)) = not(c_0). [back_rewrite(169980),rewrite([226149(5)])]. 126.13/126.42 226197 implies(A,implies(c_0,B)) = not(c_0). [back_rewrite(169599),rewrite([226149(6)])]. 126.13/126.42 226203 is_a_theorem(implies(and(implies(not(c_0),A),not(A)),c_0)). [back_rewrite(169436),rewrite([226149(4)])]. 126.13/126.42 226210 and(not(c_0),implies(not(c_0),A)) = equiv(A,not(c_0)). [para(226149(a,1),87(a,1,1))]. 126.13/126.42 226211 and(implies(not(c_0),A),not(c_0)) = equiv(not(c_0),A). [para(226149(a,1),87(a,1,2))]. 126.13/126.42 226422 is_a_theorem(implies(implies(and(not(c_0),not(not(A))),B),implies(A,B))). [para(226149(a,1),74689(a,1,1,1,1))]. 126.13/126.42 228695 is_a_theorem(implies(implies(c_0,A),implies(and(implies(not(c_0),B),not(B)),A))). [resolve(226203,a,128,a)]. 126.13/126.42 229195 implies(not(c_0),c_0) = c_0. [para(127345(a,1),226148(a,2)),rewrite([226149(5)])]. 126.13/126.42 229218 not(equiv(not(c_0),implies(A,A))) = c_0. [para(226170(a,1),226148(a,1,1)),rewrite([229195(4)]),flip(a)]. 126.13/126.42 229219 not(equiv(not(c_0),equiv(A,A))) = c_0. [para(226178(a,1),226148(a,1,1)),rewrite([229195(4)]),flip(a)]. 126.13/126.42 229220 not(equiv(not(c_0),implies(c_0,A))) = c_0. [para(226197(a,1),226148(a,1,1)),rewrite([229195(4)]),flip(a)]. 126.13/126.42 229223 is_a_theorem(implies(implies(not(c_0),A),implies(implies(A,c_0),c_0))). [para(229195(a,1),95(a,1,2,2))]. 126.13/126.42 229248 is_a_theorem(implies(and(implies(A,c_0),not(c_0)),implies(implies(not(c_0),A),B))). [para(229195(a,1),22752(a,1,1,2,1))]. 126.13/126.42 229254 is_a_theorem(implies(A,implies(implies(implies(not(A),B),c_0),c_0))). [para(229195(a,1),62333(a,1,2,2))]. 126.13/126.42 229315 implies(A,equiv(not(c_0),implies(B,B))) = not(c_0). [para(229218(a,1),78(a,1,1,2)),rewrite([226104(2)]),flip(a)]. 126.13/126.42 229316 is_a_theorem(equiv(not(c_0),implies(A,A))). [para(229218(a,1),121(a,1,1)),rewrite([229315(6)]),unit_del(a,168782)]. 126.13/126.42 229364 implies(A,A) = not(c_0). [resolve(229316,a,61,a)]. 126.13/126.42 230364 equiv(A,A) = and(not(c_0),not(c_0)). [para(229364(a,1),87(a,1,1)),rewrite([229364(3)]),flip(a)]. 126.13/126.42 230365 is_a_theorem(implies(implies(A,B),implies(not(c_0),implies(A,B)))). [para(229364(a,1),95(a,1,2,1))]. 126.13/126.42 230366 implies(A,and(B,not(B))) = implies(A,c_0). [para(229364(a,1),127(a,1,1,2)),rewrite([78(4)]),flip(a)]. 126.13/126.42 230436 implies(A,equiv(not(c_0),equiv(B,B))) = not(c_0). [para(229219(a,1),78(a,1,1,2)),rewrite([226104(2)]),flip(a)]. 126.13/126.42 230437 is_a_theorem(equiv(not(c_0),equiv(A,A))). [para(229219(a,1),121(a,1,1)),rewrite([230436(6)]),unit_del(a,168782)]. 126.13/126.42 230483 equiv(A,A) = not(c_0). [resolve(230437,a,61,a)]. 126.13/126.42 230706 and(not(c_0),not(c_0)) = not(c_0). [back_rewrite(230364),rewrite([230483(1)]),flip(a)]. 126.13/126.42 230769 implies(A,equiv(not(c_0),implies(c_0,B))) = not(c_0). [para(229220(a,1),78(a,1,1,2)),rewrite([226104(2)]),flip(a)]. 126.13/126.42 230770 is_a_theorem(equiv(not(c_0),implies(c_0,A))). [para(229220(a,1),121(a,1,1)),rewrite([230769(7)]),unit_del(a,168782)]. 126.13/126.42 230820 implies(c_0,A) = not(c_0). [resolve(230770,a,61,a)]. 126.13/126.42 231035 is_a_theorem(implies(not(c_0),implies(and(implies(not(c_0),A),not(A)),B))). [back_rewrite(228695),rewrite([230820(2)])]. 126.13/126.42 231038 is_a_theorem(implies(not(c_0),implies(and(implies(not(A),A),not(A)),B))). [back_rewrite(133927),rewrite([230820(2)])]. 126.13/126.42 231039 is_a_theorem(implies(not(c_0),implies(and(A,not(implies(not(A),B))),C))). [back_rewrite(133850),rewrite([230820(2)])]. 126.13/126.42 231042 and(implies(A,c_0),not(c_0)) = equiv(A,c_0). [para(230820(a,1),87(a,1,2))]. 126.13/126.42 231043 is_a_theorem(implies(implies(A,c_0),implies(not(c_0),implies(A,B)))). [para(230820(a,1),95(a,1,2,1))]. 126.13/126.42 231044 implies(A,and(c_0,not(B))) = implies(A,c_0). [para(230820(a,1),127(a,1,1,2)),rewrite([78(4)]),flip(a)]. 126.13/126.42 231047 implies(not(c_0),and(A,not(c_0))) = not(equiv(c_0,A)). [para(230820(a,1),255(a,1,1))]. 126.13/126.42 231082 is_a_theorem(implies(and(not(c_0),not(implies(A,B))),not(equiv(A,c_0)))). [para(230820(a,1),56203(a,1,1,1))]. 126.13/126.42 231091 is_a_theorem(implies(and(A,not(c_0)),implies(not(equiv(not(A),c_0)),B))). [para(230820(a,1),27130(a,1,1,2))]. 126.13/126.42 231132 is_a_theorem(implies(equiv(A,c_0),implies(implies(not(c_0),A),B))). [back_rewrite(229248),rewrite([231042(5)])]. 126.13/126.42 231280 implies(implies(A,c_0),and(and(B,not(B)),not(A))) = not(equiv(A,and(B,not(B)))). [para(230366(a,1),255(a,1,1))]. 126.13/126.42 231305 implies(and(A,not(A)),c_0) = not(c_0). [para(230366(a,1),229364(a,1))]. 126.13/126.42 231307 equiv(and(A,not(A)),c_0) = not(c_0). [para(231305(a,1),87(a,1,1)),rewrite([230366(6),229364(5),230706(5)]),flip(a)]. 126.13/126.42 231330 and(A,not(A)) = c_0. [para(231307(a,1),61(a,1)),flip(b),unit_del(a,168782)]. 126.13/126.42 231334 implies(implies(A,c_0),c_0) = not(equiv(A,c_0)). [back_rewrite(231280),rewrite([231330(4),231044(6),231330(6)])]. 126.13/126.42 231339 is_a_theorem(implies(A,not(equiv(implies(not(A),B),c_0)))). [back_rewrite(229254),rewrite([231334(6)])]. 126.13/126.42 231352 is_a_theorem(implies(implies(not(c_0),A),not(equiv(A,c_0)))). [back_rewrite(229223),rewrite([231334(7)])]. 126.13/126.42 232170 is_a_theorem(implies(A,implies(not(equiv(not(A),c_0)),implies(B,c_0)))). [para(231334(a,1),62333(a,1,2,1))]. 126.13/126.42 232598 -is_a_theorem(implies(not(c_0),A)) | is_a_theorem(not(equiv(A,c_0))). [resolve(231352,a,71,b)]. 126.13/126.42 233117 is_a_theorem(not(equiv(implies(A,implies(B,implies(not(A),C))),c_0))). [resolve(232598,a,67462,a)]. 126.13/126.42 233186 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(c_0),implies(A,B))). [resolve(230365,a,71,b)]. 126.13/126.42 233387 is_a_theorem(implies(not(c_0),implies(equiv(A,c_0),implies(implies(not(c_0),A),B)))). [resolve(233186,a,231132,a)]. 126.13/126.42 236920 is_a_theorem(implies(A,implies(not(equiv(not(A),c_0)),c_0))). [para(229195(a,1),232170(a,1,2,2))]. 126.13/126.42 236973 -is_a_theorem(A) | is_a_theorem(implies(not(equiv(not(A),c_0)),c_0)). [resolve(236920,a,71,b)]. 126.13/126.42 238848 -is_a_theorem(implies(and(not(c_0),not(not(equiv(c17,c18)))),implies(c17,c18))). [ur(71,b,226422,a,c,69,a)]. 126.13/126.42 239387 is_a_theorem(implies(and(implies(not(c_0),A),not(A)),B)). [resolve(231035,a,213485,a)]. 126.13/126.42 239396 is_a_theorem(implies(not(equiv(c_0,not(implies(implies(not(c_0),A),A)))),B)). [resolve(239387,a,200288,a),rewrite([78(7)])]. 126.13/126.42 239497 is_a_theorem(implies(and(implies(not(A),A),not(A)),B)). [resolve(231038,a,213485,a)]. 126.13/126.42 239505 is_a_theorem(implies(not(equiv(c_0,not(implies(implies(not(A),A),A)))),B)). [resolve(239497,a,200288,a),rewrite([78(6)])]. 126.13/126.42 239597 is_a_theorem(implies(and(A,not(implies(not(A),B))),C)). [resolve(231039,a,213485,a)]. 126.13/126.42 239606 is_a_theorem(implies(not(equiv(c_0,not(implies(A,implies(not(A),B))))),C)). [resolve(239597,a,200288,a),rewrite([78(6)])]. 126.13/126.42 239645 is_a_theorem(implies(and(not(c_0),not(not(equiv(A,B)))),not(equiv(implies(A,B),c_0)))). [para(255(a,1),231082(a,1,1,2,1))]. 126.13/126.42 240352 is_a_theorem(equiv(c_0,not(implies(implies(not(c_0),A),A)))). [resolve(239396,a,56481,a)]. 126.13/126.42 240357 not(implies(implies(not(c_0),A),A)) = c_0. [resolve(240352,a,61,a)]. 126.13/126.42 240359 implies(A,implies(implies(not(c_0),B),B)) = not(c_0). [para(240357(a,1),78(a,1,1,2)),rewrite([226104(2)]),flip(a)]. 126.13/126.42 240370 equiv(implies(implies(not(c_0),A),A),not(c_0)) = not(c_0). [para(240359(a,1),226210(a,1,2)),rewrite([230706(5)]),flip(a)]. 126.13/126.42 240382 implies(implies(not(c_0),A),A) = not(c_0). [para(240370(a,1),61(a,1)),flip(b),unit_del(a,168782)]. 126.13/126.42 240385 and(implies(A,implies(not(c_0),A)),not(c_0)) = equiv(A,implies(not(c_0),A)). [para(240382(a,1),87(a,1,2))]. 126.13/126.42 240464 is_a_theorem(equiv(c_0,not(implies(implies(not(A),A),A)))). [resolve(239505,a,56481,a)]. 126.13/126.42 240469 not(implies(implies(not(A),A),A)) = c_0. [resolve(240464,a,61,a)]. 126.13/126.42 240471 implies(A,implies(implies(not(B),B),B)) = not(c_0). [para(240469(a,1),78(a,1,1,2)),rewrite([226104(2)]),flip(a)]. 126.13/126.42 240482 equiv(implies(implies(not(A),A),A),not(c_0)) = not(c_0). [para(240471(a,1),226210(a,1,2)),rewrite([230706(5)]),flip(a)]. 126.13/126.42 240488 implies(implies(not(A),A),A) = not(c_0). [para(240482(a,1),61(a,1)),flip(b),unit_del(a,168782)]. 126.13/126.42 240493 and(implies(A,implies(not(A),A)),not(c_0)) = equiv(A,implies(not(A),A)). [para(240488(a,1),87(a,1,2))]. 126.13/126.42 241343 is_a_theorem(equiv(c_0,not(implies(A,implies(not(A),B))))). [resolve(239606,a,56481,a)]. 126.13/126.42 241349 not(implies(A,implies(not(A),B))) = c_0. [resolve(241343,a,61,a)]. 126.13/126.42 241351 implies(A,implies(B,implies(not(B),C))) = not(c_0). [para(241349(a,1),78(a,1,1,2)),rewrite([226104(2)]),flip(a)]. 126.13/126.42 241390 equiv(implies(A,implies(not(A),B)),not(c_0)) = not(c_0). [para(241351(a,1),226210(a,1,2)),rewrite([230706(5)]),flip(a)]. 126.13/126.42 241396 implies(A,implies(not(A),B)) = not(c_0). [para(241390(a,1),61(a,1)),flip(b),unit_del(a,168782)]. 126.13/126.42 241399 equiv(A,implies(not(A),A)) = not(c_0). [back_rewrite(240493),rewrite([241396(3),230706(5)]),flip(a)]. 126.13/126.42 241403 and(implies(implies(not(A),B),A),not(c_0)) = equiv(implies(not(A),B),A). [para(241396(a,1),87(a,1,2))]. 126.13/126.42 241440 implies(not(A),A) = A. [para(241399(a,1),61(a,1)),unit_del(a,168782)]. 126.13/126.42 241738 is_a_theorem(implies(A,not(equiv(A,c_0)))). [para(241440(a,1),231339(a,1,2,1,1))]. 126.13/126.42 241740 is_a_theorem(implies(implies(not(A),c_0),implies(not(c_0),A))). [para(241440(a,1),231043(a,1,2,2))]. 126.13/126.42 241745 is_a_theorem(not(equiv(implies(A,implies(B,A)),c_0))). [para(241440(a,1),233117(a,1,1,1,2,2))]. 126.13/126.42 241782 is_a_theorem(implies(and(A,not(c_0)),equiv(not(A),c_0))). [para(241440(a,1),231091(a,1,2))]. 126.13/126.42 242465 -is_a_theorem(A) | is_a_theorem(not(equiv(A,c_0))). [resolve(241738,a,71,b)]. 126.13/126.42 242638 is_a_theorem(not(equiv(implies(A,not(equiv(A,c_0))),c_0))). [resolve(242465,a,241738,a)]. 126.13/126.42 245143 is_a_theorem(not(equiv(implies(implies(not(A),c_0),implies(not(c_0),A)),c_0))). [resolve(241740,a,242465,a)]. 126.13/126.42 245256 is_a_theorem(implies(not(equiv(A,c_0)),not(equiv(c_0,A)))). [para(231047(a,1),241740(a,1,2)),rewrite([78(4),231334(4)])]. 126.13/126.42 245371 -is_a_theorem(and(A,not(c_0))) | is_a_theorem(equiv(not(A),c_0)). [resolve(241782,a,71,b)]. 126.13/126.42 246187 -is_a_theorem(not(equiv(A,c_0))) | is_a_theorem(not(equiv(c_0,A))). [resolve(245256,a,71,b)]. 126.13/126.42 246469 is_a_theorem(not(equiv(c_0,implies(A,not(equiv(A,c_0)))))). [resolve(246187,a,242638,a)]. 126.13/126.42 246470 is_a_theorem(not(equiv(c_0,implies(A,implies(B,A))))). [resolve(246187,a,241745,a)]. 126.13/126.42 246515 is_a_theorem(and(implies(A,implies(B,A)),not(c_0))). [resolve(246470,a,119330,a)]. 126.13/126.42 246527 is_a_theorem(equiv(not(implies(A,implies(B,A))),c_0)). [resolve(246515,a,245371,a)]. 126.13/126.42 246577 not(implies(A,implies(B,A))) = c_0. [resolve(246527,a,61,a),flip(a)]. 126.13/126.42 246630 implies(A,implies(B,implies(C,B))) = not(c_0). [para(246577(a,1),78(a,1,1,2)),rewrite([226104(2)]),flip(a)]. 126.13/126.42 246632 implies(A,implies(B,A)) = not(c_0). [para(246577(a,1),241440(a,1,1)),rewrite([246630(4)]),flip(a)]. 126.13/126.42 246638 equiv(A,implies(not(c_0),A)) = not(c_0). [back_rewrite(240385),rewrite([246632(4),230706(5)]),flip(a)]. 126.13/126.42 246667 implies(not(c_0),A) = A. [para(246638(a,1),61(a,1)),unit_del(a,168782)]. 126.13/126.42 246696 is_a_theorem(not(equiv(implies(implies(not(A),c_0),A),c_0))). [back_rewrite(245143),rewrite([246667(6)])]. 126.13/126.42 246765 is_a_theorem(implies(equiv(A,c_0),implies(A,B))). [back_rewrite(233387),rewrite([246667(7),246667(7)])]. 126.13/126.42 246820 not(equiv(c_0,A)) = and(A,not(c_0)). [back_rewrite(231047),rewrite([246667(6)]),flip(a)]. 126.13/126.42 246827 equiv(not(c_0),A) = and(A,not(c_0)). [back_rewrite(226211),rewrite([246667(3)]),flip(a)]. 126.13/126.42 246840 is_a_theorem(and(implies(A,not(equiv(A,c_0))),not(c_0))). [back_rewrite(246469),rewrite([246820(7)])]. 126.13/126.42 246847 -is_a_theorem(not(equiv(A,c_0))) | is_a_theorem(and(A,not(c_0))). [back_rewrite(246187),rewrite([246820(7)])]. 126.13/126.42 248672 is_a_theorem(implies(equiv(not(A),c_0),A)). [para(241440(a,1),246765(a,1,2))]. 126.13/126.42 248683 is_a_theorem(implies(not(equiv(not(implies(equiv(not(A),c_0),A)),c_0)),c_0)). [resolve(248672,a,236973,a)]. 126.13/126.42 249841 -is_a_theorem(and(A,not(c_0))) | not(c_0) = A. [para(246827(a,1),61(a,1)),flip(b)]. 126.13/126.42 252519 implies(A,not(equiv(A,c_0))) = not(c_0). [resolve(246840,a,249841,a),flip(a)]. 126.13/126.42 252523 and(implies(not(equiv(A,c_0)),A),not(c_0)) = equiv(not(equiv(A,c_0)),A). [para(252519(a,1),87(a,1,2))]. 126.13/126.42 252878 is_a_theorem(equiv(implies(not(A),c_0),A)). [resolve(246847,a,246696,a),rewrite([241403(7)])]. 126.13/126.42 252918 implies(not(A),c_0) = A. [resolve(252878,a,61,a),flip(a)]. 126.13/126.42 252966 is_a_theorem(equiv(not(implies(equiv(not(A),c_0),A)),c_0)). [back_rewrite(248683),rewrite([252918(10)])]. 126.13/126.42 253077 implies(implies(A,B),c_0) = and(A,not(B)). [para(78(a,1),252918(a,1,1))]. 126.13/126.42 253078 equiv(not(A),c_0) = and(A,not(c_0)). [para(252918(a,1),87(a,1,1)),rewrite([230820(3)]),flip(a)]. 126.13/126.42 253250 not(equiv(A,c_0)) = and(A,not(c_0)). [back_rewrite(231334),rewrite([253077(4)]),flip(a)]. 126.13/126.42 253338 is_a_theorem(and(implies(and(A,not(c_0)),A),not(c_0))). [back_rewrite(252966),rewrite([253078(3),253078(7)])]. 126.13/126.42 254601 and(implies(and(A,not(c_0)),A),not(c_0)) = equiv(and(A,not(c_0)),A). [back_rewrite(252523),rewrite([253250(3),253250(10)])]. 126.13/126.42 254906 is_a_theorem(implies(and(not(c_0),not(not(equiv(A,B)))),and(implies(A,B),not(c_0)))). [back_rewrite(239645),rewrite([253250(10)])]. 126.13/126.42 255020 is_a_theorem(equiv(and(A,not(c_0)),A)). [back_rewrite(253338),rewrite([254601(7)])]. 126.13/126.42 256335 and(A,not(c_0)) = A. [resolve(255020,a,61,a),flip(a)]. 126.13/126.42 256375 is_a_theorem(implies(and(not(c_0),not(not(equiv(A,B)))),implies(A,B))). [back_rewrite(254906),rewrite([256335(10)])]. 126.13/126.42 256376 $F. [resolve(256375,a,238848,a)]. 126.13/126.42 126.13/126.42 % SZS output end Refutation 126.13/126.42 ============================== end of proof ========================== 126.13/126.42 126.13/126.42 ============================== STATISTICS ============================ 126.13/126.42 126.13/126.42 Given=8552. Generated=13391377. Kept=256328. proofs=1. 126.13/126.42 Usable=989. Sos=6952. Demods=97. Limbo=40, Disabled=248418. Hints=0. 126.13/126.42 Megabytes=178.02. 126.13/126.42 User_CPU=118.08, System_CPU=7.28, Wall_clock=125. 126.13/126.42 126.13/126.42 ============================== end of statistics ===================== 126.13/126.42 126.13/126.42 ============================== end of search ========================= 126.13/126.42 126.13/126.42 THEOREM PROVED 126.13/126.42 % SZS status Theorem 126.13/126.42 126.13/126.42 Exiting with 1 proof. 126.13/126.42 126.13/126.42 Process 32125 exit (max_proofs) Thu Aug 29 15:08:27 2019 126.13/126.42 Prover9 interrupted 126.13/126.42 EOF