0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : tptp2X_and_run_prover9 %d %s 0.03/0.23 % Computer : n115.star.cs.uiowa.edu 0.03/0.23 % Model : x86_64 x86_64 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.23 % Memory : 32218.625MB 0.03/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.23 % CPULimit : 300 0.03/0.23 % DateTime : Sat Jul 14 06:00:55 CDT 2018 0.03/0.23 % CPUTime : 0.07/0.47 ============================== Prover9 =============================== 0.07/0.47 Prover9 (32) version 2009-11A, November 2009. 0.07/0.47 Process 41568 was started by sandbox2 on n115.star.cs.uiowa.edu, 0.07/0.47 Sat Jul 14 06:00:55 2018 0.07/0.47 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_41536_n115.star.cs.uiowa.edu". 0.07/0.47 ============================== end of head =========================== 0.07/0.47 0.07/0.47 ============================== INPUT ================================= 0.07/0.47 0.07/0.47 % Reading from file /tmp/Prover9_41536_n115.star.cs.uiowa.edu 0.07/0.47 0.07/0.47 set(prolog_style_variables). 0.07/0.47 set(auto2). 0.07/0.47 % set(auto2) -> set(auto). 0.07/0.47 % set(auto) -> set(auto_inference). 0.07/0.47 % set(auto) -> set(auto_setup). 0.07/0.47 % set(auto_setup) -> set(predicate_elim). 0.07/0.47 % set(auto_setup) -> assign(eq_defs, unfold). 0.07/0.47 % set(auto) -> set(auto_limits). 0.07/0.47 % set(auto_limits) -> assign(max_weight, "100.000"). 0.07/0.47 % set(auto_limits) -> assign(sos_limit, 20000). 0.07/0.47 % set(auto) -> set(auto_denials). 0.07/0.47 % set(auto) -> set(auto_process). 0.07/0.47 % set(auto2) -> assign(new_constants, 1). 0.07/0.47 % set(auto2) -> assign(fold_denial_max, 3). 0.07/0.47 % set(auto2) -> assign(max_weight, "200.000"). 0.07/0.47 % set(auto2) -> assign(max_hours, 1). 0.07/0.47 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.07/0.47 % set(auto2) -> assign(max_seconds, 0). 0.07/0.47 % set(auto2) -> assign(max_minutes, 5). 0.07/0.47 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.07/0.47 % set(auto2) -> set(sort_initial_sos). 0.07/0.47 % set(auto2) -> assign(sos_limit, -1). 0.07/0.47 % set(auto2) -> assign(lrs_ticks, 3000). 0.07/0.47 % set(auto2) -> assign(max_megs, 400). 0.07/0.47 % set(auto2) -> assign(stats, some). 0.07/0.47 % set(auto2) -> clear(echo_input). 0.07/0.47 % set(auto2) -> set(quiet). 0.07/0.47 % set(auto2) -> clear(print_initial_clauses). 0.07/0.47 % set(auto2) -> clear(print_given). 0.07/0.47 assign(lrs_ticks,-1). 0.07/0.47 assign(sos_limit,10000). 0.07/0.47 assign(order,kbo). 0.07/0.47 set(lex_order_vars). 0.07/0.47 clear(print_given). 0.07/0.47 0.07/0.47 % formulas(sos). % not echoed (77 formulas) 0.07/0.47 0.07/0.47 ============================== end of input ========================== 0.07/0.47 0.07/0.47 % From the command line: assign(max_seconds, 300). 0.07/0.47 0.07/0.47 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.07/0.47 0.07/0.47 % Formulas that are not ordinary clauses: 0.07/0.47 1 (all X all Y is_a_theorem(implies(and(X,Y),Y))) <-> and_2 # label(and_2) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 2 (all X all Y is_a_theorem(implies(equiv(X,Y),implies(Y,X)))) <-> equivalence_2 # label(equivalence_2) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 3 substitution_of_equivalents <-> (all X all Y (is_a_theorem(equiv(X,Y)) -> Y = X)) # label(substitution_of_equivalents) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 4 kn3 <-> (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))) # label(kn3) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 5 r5 <-> (all P all Q all R is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))) # label(r5) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 6 (all P is_a_theorem(implies(P,and(P,P)))) <-> kn1 # label(kn1) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 7 (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))) <-> cn1 # label(cn1) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 8 r4 <-> (all P all Q all R is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))) # label(r4) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 9 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 11 (all X all Y is_a_theorem(implies(Y,or(X,Y)))) <-> or_2 # label(or_2) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 12 modus_ponens <-> (all X all Y (is_a_theorem(X) & is_a_theorem(implies(X,Y)) -> is_a_theorem(Y))) # label(modus_ponens) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 13 implies_3 <-> (all X all Y all Z is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))) # label(implies_3) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 14 (all P is_a_theorem(implies(or(P,P),P))) <-> r1 # label(r1) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 15 (all X all Y is_a_theorem(implies(X,implies(Y,and(X,Y))))) <-> and_3 # label(and_3) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 16 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 17 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 18 (all P is_a_theorem(implies(implies(not(P),P),P))) <-> cn3 # label(cn3) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 19 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 20 (all X all Y is_a_theorem(implies(equiv(X,Y),implies(X,Y)))) <-> equivalence_1 # label(equivalence_1) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 21 or_3 <-> (all X all Y all Z is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))) # label(or_3) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 22 (all X all Y is_a_theorem(implies(X,implies(Y,X)))) <-> implies_1 # label(implies_1) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 23 modus_tollens <-> (all X all Y is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))) # label(modus_tollens) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 24 (all P all Q is_a_theorem(implies(and(P,Q),P))) <-> kn2 # label(kn2) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 25 (all X all Y is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))) <-> equivalence_3 # label(equivalence_3) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 26 implies_2 <-> (all X all Y is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))) # label(implies_2) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 27 op_or -> (all X all Y or(X,Y) = not(and(not(X),not(Y)))) # label(op_or) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 28 op_and -> (all X all Y and(X,Y) = not(or(not(X),not(Y)))) # label(op_and) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 29 op_implies_and -> (all X all Y not(and(X,not(Y))) = implies(X,Y)) # label(op_implies_and) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 30 op_implies_or -> (all X all Y or(not(X),Y) = implies(X,Y)) # label(op_implies_or) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 31 op_equiv -> (all X all Y equiv(X,Y) = and(implies(X,Y),implies(Y,X))) # label(op_equiv) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 32 axiom_m6 <-> (all X is_a_theorem(strict_implies(X,possibly(X)))) # label(axiom_m6) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 33 axiom_m5 <-> (all X all Y all Z is_a_theorem(strict_implies(and(strict_implies(X,Y),strict_implies(Y,Z)),strict_implies(X,Z)))) # label(axiom_m5) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 34 axiom_s1 <-> (all X all Y all Z is_a_theorem(implies(and(necessarily(implies(X,Y)),necessarily(implies(Y,Z))),necessarily(implies(X,Z))))) # label(axiom_s1) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 35 (all X is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X)))) <-> axiom_m9 # label(axiom_m9) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 36 (all P all Q is_a_theorem(strict_implies(possibly(and(P,Q)),P))) <-> axiom_m7 # label(axiom_m7) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 37 (all X all Y (is_a_theorem(strict_equiv(X,Y)) -> Y = X)) <-> substitution_strict_equiv # label(substitution_strict_equiv) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 38 (all X is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X))))) <-> axiom_m10 # label(axiom_m10) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 39 (all X all Y all Z is_a_theorem(strict_implies(and(and(X,Y),Z),and(X,and(Y,Z))))) <-> axiom_m3 # label(axiom_m3) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 40 (all X all Y is_a_theorem(implies(necessarily(implies(X,Y)),implies(necessarily(X),necessarily(Y))))) <-> axiom_K # label(axiom_K) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 41 (all X is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))) <-> axiom_4 # label(axiom_4) # label(axiom) # label(non_clause). [assumption]. 0.07/0.49 42 (all X all Y (is_a_theorem(strict_implies(X,Y)) & is_a_theorem(X) -> is_a_theorem(Y))) <-> modus_ponens_strict_implies # label(modus_ponens_strict_implies) # label(axiom) # label(non_clause). [assumption]. 0.07/0.49 43 axiom_s2 <-> (all P all Q is_a_theorem(strict_implies(possibly(and(P,Q)),and(possibly(P),possibly(Q))))) # label(axiom_s2) # label(axiom) # label(non_clause). [assumption]. 0.07/0.49 44 (all X is_a_theorem(implies(possibly(X),necessarily(possibly(X))))) <-> axiom_5 # label(axiom_5) # label(axiom) # label(non_clause). [assumption]. 0.07/0.49 45 (all X all Y is_a_theorem(strict_implies(and(X,Y),and(Y,X)))) <-> axiom_m1 # label(axiom_m1) # label(axiom) # label(non_clause). [assumption]. 0.07/0.49 46 axiom_m4 <-> (all X is_a_theorem(strict_implies(X,and(X,X)))) # label(axiom_m4) # label(axiom) # label(non_clause). [assumption]. 0.07/0.49 47 axiom_M <-> (all X is_a_theorem(implies(necessarily(X),X))) # label(axiom_M) # label(axiom) # label(non_clause). [assumption]. 0.07/0.49 48 (all X is_a_theorem(strict_implies(necessarily(X),necessarily(necessarily(X))))) <-> axiom_s4 # label(axiom_s4) # label(axiom) # label(non_clause). [assumption]. 0.07/0.49 49 necessitation <-> (all X (is_a_theorem(X) -> is_a_theorem(necessarily(X)))) # label(necessitation) # label(axiom) # label(non_clause). [assumption]. 0.07/0.49 50 (all P all Q is_a_theorem(strict_implies(strict_implies(P,Q),strict_implies(possibly(P),possibly(Q))))) <-> axiom_m8 # label(axiom_m8) # label(axiom) # label(non_clause). [assumption]. 0.07/0.49 51 axiom_B <-> (all X is_a_theorem(implies(X,necessarily(possibly(X))))) # label(axiom_B) # label(axiom) # label(non_clause). [assumption]. 0.07/0.49 52 axiom_s3 <-> (all X all Y is_a_theorem(strict_implies(strict_implies(X,Y),strict_implies(not(possibly(Y)),not(possibly(X)))))) # label(axiom_s3) # label(axiom) # label(non_clause). [assumption]. 0.07/0.49 53 adjunction <-> (all X all Y (is_a_theorem(Y) & is_a_theorem(X) -> is_a_theorem(and(X,Y)))) # label(adjunction) # label(axiom) # label(non_clause). [assumption]. 0.07/0.49 54 (all X all Y is_a_theorem(strict_implies(and(X,Y),X))) <-> axiom_m2 # label(axiom_m2) # label(axiom) # label(non_clause). [assumption]. 0.07/0.49 55 op_strict_equiv -> (all X all Y and(strict_implies(X,Y),strict_implies(Y,X)) = strict_equiv(X,Y)) # label(op_strict_equiv) # label(axiom) # label(non_clause). [assumption]. 0.07/0.49 56 op_necessarily -> (all X not(possibly(not(X))) = necessarily(X)) # label(op_necessarily) # label(axiom) # label(non_clause). [assumption]. 0.07/0.49 57 op_strict_implies -> (all X all Y necessarily(implies(X,Y)) = strict_implies(X,Y)) # label(op_strict_implies) # label(axiom) # label(non_clause). [assumption]. 0.07/0.49 58 op_possibly -> (all X not(necessarily(not(X))) = possibly(X)) # label(op_possibly) # label(axiom) # label(non_clause). [assumption]. 0.07/0.49 0.07/0.49 ============================== end of process non-clausal formulas === 0.07/0.49 0.07/0.49 ============================== PROCESS INITIAL CLAUSES =============== 0.07/0.49 0.07/0.49 ============================== PREDICATE ELIMINATION ================= 0.07/0.49 0.07/0.49 ============================== end predicate elimination ============= 0.07/0.49 0.07/0.49 Auto_denials: (non-Horn, no changes). 0.07/0.49 0.07/0.49 Term ordering decisions: 0.07/0.49 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. c56=1. c57=1. c58=1. c59=1. c60=1. c61=1. c62=1. c63=1. c64=1. c65=1. c66=1. c67=1. c68=1. c69=1. c70=1. c71=1. c72=1. c73=1. c74=1. c75=1. c76=1. c77=1. c78=1. c79=1. c80=1. c81=1. c82=1. c83=1. c84=1. c85=1. c86=1. c87=1. c88=1. c89=1. c90=1. c91=1. c92=1. c93=1. c94=1. implies=1. and=1. strict_implies=1. or=1. equiv=1. strict_equiv=1. necessarily=1. possibly=1. not=1. 0.07/0.49 0.07/0.49 ============================== end of process initial clauses ======== 0.07/0.49 0.07/0.49 ============================== CLAUSES FOR SEARCH ==================== 268.90/269.15 268.90/269.15 ============================== end of clauses for search ============= 268.90/269.15 268.90/269.15 ============================== SEARCH ================================ 268.90/269.15 268.90/269.15 % Starting search at 0.03 seconds. 268.90/269.15 268.90/269.15 Low Water (keep): wt=35.000, iters=3340 268.90/269.15 268.90/269.15 Low Water (keep): wt=26.000, iters=3378 268.90/269.15 268.90/269.15 Low Water (keep): wt=25.000, iters=3366 268.90/269.15 268.90/269.15 Low Water (keep): wt=23.000, iters=3349 268.90/269.15 268.90/269.15 Low Water (keep): wt=22.000, iters=3385 268.90/269.15 268.90/269.15 Low Water (keep): wt=21.000, iters=3410 268.90/269.15 268.90/269.15 Low Water (keep): wt=20.000, iters=3373 268.90/269.15 268.90/269.15 Low Water (keep): wt=19.000, iters=3371 268.90/269.15 268.90/269.15 Low Water (keep): wt=18.000, iters=3400 268.90/269.15 268.90/269.15 Low Water (keep): wt=17.000, iters=3335 268.90/269.15 268.90/269.15 Low Water (keep): wt=16.000, iters=3340 268.90/269.15 268.90/269.15 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 382 (0.00 of 3.06 sec). 268.90/269.15 % back CAC tautology: 9627 equiv(not(A),B) = equiv(B,not(A)). [back_rewrite(281),rewrite([8934(4),280(4)])]. 268.90/269.15 % back CAC tautology: 9418 equiv(possibly(necessarily(not(A))),B) = equiv(B,possibly(necessarily(not(A)))). [back_rewrite(2525),rewrite([8934(8),2411(8)])]. 268.90/269.15 % back CAC tautology: 9416 equiv(implies(A,necessarily(not(B))),C) = equiv(C,implies(A,necessarily(not(B)))). [back_rewrite(2527),rewrite([8934(8),2414(8)])]. 268.90/269.15 % back CAC tautology: 9415 equiv(implies(A,and(B,not(C))),D) = equiv(D,implies(A,and(B,not(C)))). [back_rewrite(2528),rewrite([8934(8),2416(8)])]. 268.90/269.15 268.90/269.15 Low Water (displace): id=17218, wt=36.000 268.90/269.15 268.90/269.15 Low Water (displace): id=17212, wt=33.000 268.90/269.15 268.90/269.15 Low Water (displace): id=17599, wt=32.000 268.90/269.15 268.90/269.15 Low Water (displace): id=22695, wt=17.000 268.90/269.15 268.90/269.15 Low Water (displace): id=22996, wt=16.000 268.90/269.15 268.90/269.15 Low Water (displace): id=23023, wt=15.000 268.90/269.15 268.90/269.15 Low Water (displace): id=23035, wt=14.000 268.90/269.15 % back CAC tautology: 26237 or(or(A,B),not(C)) = or(not(C),or(A,B)). [para(26173(a,2),23289(a,1)),rewrite([23289(6)]),flip(a)]. 268.90/269.15 % back CAC tautology: 24102 or(necessarily(possibly(A)),strict_implies(B,C)) = or(strict_implies(B,C),necessarily(possibly(A))). [para(212(a,1),12504(a,1,2,1)),rewrite([200(4),274(7),218(9)])]. 268.90/269.15 268.90/269.15 Low Water (displace): id=27373, wt=12.000 268.90/269.15 268.90/269.15 Low Water (displace): id=27374, wt=10.000 268.90/269.15 268.90/269.15 Low Water (displace): id=27432, wt=8.000 268.90/269.15 268.90/269.15 Low Water (keep): wt=15.000, iters=3394 268.90/269.15 268.90/269.15 Low Water (keep): wt=14.000, iters=3342 268.90/269.15 268.90/269.15 Low Water (keep): wt=13.000, iters=3333 268.90/269.15 268.90/269.15 Low Water (keep): wt=12.000, iters=3760 268.90/269.15 268.90/269.15 ============================== PROOF ================================= 268.90/269.15 % SZS status Theorem 268.90/269.15 % SZS output start Refutation 268.90/269.15 268.90/269.15 % Proof 1 at 263.52 (+ 5.16) seconds. 268.90/269.15 % Length of proof is 194. 268.90/269.15 % Level of proof is 42. 268.90/269.15 % Maximum clause weight is 20.000. 268.90/269.15 % Given clauses 24403. 268.90/269.15 268.90/269.15 26 implies_2 <-> (all X all Y is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))) # label(implies_2) # label(axiom) # label(non_clause). [assumption]. 268.90/269.15 27 op_or -> (all X all Y or(X,Y) = not(and(not(X),not(Y)))) # label(op_or) # label(axiom) # label(non_clause). [assumption]. 268.90/269.15 29 op_implies_and -> (all X all Y not(and(X,not(Y))) = implies(X,Y)) # label(op_implies_and) # label(axiom) # label(non_clause). [assumption]. 268.90/269.15 33 axiom_m5 <-> (all X all Y all Z is_a_theorem(strict_implies(and(strict_implies(X,Y),strict_implies(Y,Z)),strict_implies(X,Z)))) # label(axiom_m5) # label(axiom) # label(non_clause). [assumption]. 268.90/269.15 37 (all X all Y (is_a_theorem(strict_equiv(X,Y)) -> Y = X)) <-> substitution_strict_equiv # label(substitution_strict_equiv) # label(axiom) # label(non_clause). [assumption]. 268.90/269.15 39 (all X all Y all Z is_a_theorem(strict_implies(and(and(X,Y),Z),and(X,and(Y,Z))))) <-> axiom_m3 # label(axiom_m3) # label(axiom) # label(non_clause). [assumption]. 268.90/269.15 42 (all X all Y (is_a_theorem(strict_implies(X,Y)) & is_a_theorem(X) -> is_a_theorem(Y))) <-> modus_ponens_strict_implies # label(modus_ponens_strict_implies) # label(axiom) # label(non_clause). [assumption]. 268.90/269.15 45 (all X all Y is_a_theorem(strict_implies(and(X,Y),and(Y,X)))) <-> axiom_m1 # label(axiom_m1) # label(axiom) # label(non_clause). [assumption]. 268.90/269.15 46 axiom_m4 <-> (all X is_a_theorem(strict_implies(X,and(X,X)))) # label(axiom_m4) # label(axiom) # label(non_clause). [assumption]. 268.90/269.15 53 adjunction <-> (all X all Y (is_a_theorem(Y) & is_a_theorem(X) -> is_a_theorem(and(X,Y)))) # label(adjunction) # label(axiom) # label(non_clause). [assumption]. 268.90/269.15 54 (all X all Y is_a_theorem(strict_implies(and(X,Y),X))) <-> axiom_m2 # label(axiom_m2) # label(axiom) # label(non_clause). [assumption]. 268.90/269.15 55 op_strict_equiv -> (all X all Y and(strict_implies(X,Y),strict_implies(Y,X)) = strict_equiv(X,Y)) # label(op_strict_equiv) # label(axiom) # label(non_clause). [assumption]. 268.90/269.15 57 op_strict_implies -> (all X all Y necessarily(implies(X,Y)) = strict_implies(X,Y)) # label(op_strict_implies) # label(axiom) # label(non_clause). [assumption]. 268.90/269.15 113 implies_2 | -is_a_theorem(implies(implies(c54,implies(c54,c55)),implies(c54,c55))) # label(implies_2) # label(axiom). [clausify(26)]. 268.90/269.15 114 -op_or | or(A,B) = not(and(not(A),not(B))) # label(op_or) # label(axiom). [clausify(27)]. 268.90/269.15 115 -op_or | not(and(not(A),not(B))) = or(A,B). [copy(114),flip(b)]. 268.90/269.15 117 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)]. 268.90/269.15 123 -axiom_m5 | is_a_theorem(strict_implies(and(strict_implies(A,B),strict_implies(B,C)),strict_implies(A,C))) # label(axiom_m5) # label(axiom). [clausify(33)]. 268.90/269.15 133 -is_a_theorem(strict_equiv(A,B)) | B = A | -substitution_strict_equiv # label(substitution_strict_equiv) # label(axiom). [clausify(37)]. 268.90/269.15 137 is_a_theorem(strict_implies(and(and(A,B),C),and(A,and(B,C)))) | -axiom_m3 # label(axiom_m3) # label(axiom). [clausify(39)]. 268.90/269.15 145 -is_a_theorem(strict_implies(A,B)) | -is_a_theorem(A) | is_a_theorem(B) | -modus_ponens_strict_implies # label(modus_ponens_strict_implies) # label(axiom). [clausify(42)]. 268.90/269.15 151 is_a_theorem(strict_implies(and(A,B),and(B,A))) | -axiom_m1 # label(axiom_m1) # label(axiom). [clausify(45)]. 268.90/269.15 152 -axiom_m4 | is_a_theorem(strict_implies(A,and(A,A))) # label(axiom_m4) # label(axiom). [clausify(46)]. 268.90/269.15 167 -adjunction | -is_a_theorem(A) | -is_a_theorem(B) | is_a_theorem(and(B,A)) # label(adjunction) # label(axiom). [clausify(53)]. 268.90/269.15 172 is_a_theorem(strict_implies(and(A,B),A)) | -axiom_m2 # label(axiom_m2) # label(axiom). [clausify(54)]. 268.90/269.15 173 -op_strict_equiv | strict_equiv(A,B) = and(strict_implies(A,B),strict_implies(B,A)) # label(op_strict_equiv) # label(axiom). [clausify(55)]. 268.90/269.16 174 -op_strict_equiv | and(strict_implies(A,B),strict_implies(B,A)) = strict_equiv(A,B). [copy(173),flip(b)]. 268.90/269.16 177 -op_strict_implies | necessarily(implies(A,B)) = strict_implies(A,B) # label(op_strict_implies) # label(axiom). [clausify(57)]. 268.90/269.16 180 axiom_m1 # label(s1_0_axiom_m1) # label(axiom). [assumption]. 268.90/269.16 181 substitution_strict_equiv # label(s1_0_substitution_strict_equiv) # label(axiom). [assumption]. 268.90/269.16 182 op_strict_implies # label(s1_0_op_strict_implies) # label(axiom). [assumption]. 268.90/269.16 183 adjunction # label(s1_0_adjunction) # label(axiom). [assumption]. 268.90/269.16 184 axiom_m3 # label(s1_0_axiom_m3) # label(axiom). [assumption]. 268.90/269.16 185 axiom_m5 # label(s1_0_axiom_m5) # label(axiom). [assumption]. 268.90/269.16 186 axiom_m4 # label(s1_0_axiom_m4) # label(axiom). [assumption]. 268.90/269.16 187 op_strict_equiv # label(s1_0_op_strict_equiv) # label(axiom). [assumption]. 268.90/269.16 188 modus_ponens_strict_implies # label(s1_0_modus_ponens_strict_implies) # label(axiom). [assumption]. 268.90/269.16 189 axiom_m2 # label(s1_0_axiom_m2) # label(axiom). [assumption]. 268.90/269.16 190 op_or # label(s1_0_op_or) # label(axiom). [assumption]. 268.90/269.16 195 op_implies_and # label(hilbert_op_implies_and) # label(axiom). [assumption]. 268.90/269.16 196 -implies_2 # label(hilbert_implies_2) # label(negated_conjecture). [assumption]. 268.90/269.16 198 is_a_theorem(strict_implies(and(A,B),and(B,A))). [back_unit_del(151),unit_del(b,180)]. 268.90/269.16 199 -is_a_theorem(strict_equiv(A,B)) | B = A. [back_unit_del(133),unit_del(c,181)]. 268.90/269.16 200 necessarily(implies(A,B)) = strict_implies(A,B). [back_unit_del(177),unit_del(a,182)]. 268.90/269.16 201 -is_a_theorem(A) | -is_a_theorem(B) | is_a_theorem(and(B,A)). [back_unit_del(167),unit_del(a,183)]. 268.90/269.16 202 is_a_theorem(strict_implies(and(and(A,B),C),and(A,and(B,C)))). [back_unit_del(137),unit_del(b,184)]. 268.90/269.16 203 is_a_theorem(strict_implies(and(strict_implies(A,B),strict_implies(B,C)),strict_implies(A,C))). [back_unit_del(123),unit_del(a,185)]. 268.90/269.16 204 is_a_theorem(strict_implies(A,and(A,A))). [back_unit_del(152),unit_del(a,186)]. 268.90/269.16 205 and(strict_implies(A,B),strict_implies(B,A)) = strict_equiv(A,B). [back_unit_del(174),unit_del(a,187)]. 268.90/269.16 206 -is_a_theorem(strict_implies(A,B)) | -is_a_theorem(A) | is_a_theorem(B). [back_unit_del(145),unit_del(d,188)]. 268.90/269.16 207 is_a_theorem(strict_implies(and(A,B),A)). [back_unit_del(172),unit_del(b,189)]. 268.90/269.16 208 not(and(not(A),not(B))) = or(A,B). [back_unit_del(115),unit_del(a,190)]. 268.90/269.16 212 not(and(A,not(B))) = implies(A,B). [back_unit_del(117),unit_del(a,195)]. 268.90/269.16 213 -is_a_theorem(implies(implies(c54,implies(c54,c55)),implies(c54,c55))). [back_unit_del(113),unit_del(a,196)]. 268.90/269.16 218 implies(not(A),B) = or(A,B). [back_rewrite(208),rewrite([212(4)])]. 268.90/269.16 234 -is_a_theorem(A) | is_a_theorem(and(A,strict_implies(and(B,C),and(C,B)))). [resolve(201,a,198,a)]. 268.90/269.16 250 -is_a_theorem(A) | is_a_theorem(and(strict_implies(B,and(B,B)),A)). [resolve(204,a,201,b)]. 268.90/269.16 251 -is_a_theorem(A) | is_a_theorem(and(A,strict_implies(B,and(B,B)))). [resolve(204,a,201,a)]. 268.90/269.16 259 -is_a_theorem(and(strict_implies(A,B),strict_implies(B,C))) | is_a_theorem(strict_implies(A,C)). [resolve(206,a,203,a)]. 268.90/269.16 263 -is_a_theorem(A) | is_a_theorem(and(strict_implies(and(B,C),B),A)). [resolve(207,a,201,b)]. 268.90/269.16 276 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(212(a,1),212(a,1,1,2))]. 268.90/269.16 278 necessarily(or(A,B)) = strict_implies(not(A),B). [para(218(a,1),200(a,1,1))]. 268.90/269.16 282 or(and(A,not(B)),C) = implies(implies(A,B),C). [para(212(a,1),218(a,1,1)),flip(a)]. 268.90/269.16 411 is_a_theorem(and(strict_implies(and(and(A,B),C),and(A,and(B,C))),strict_implies(and(D,E),and(E,D)))). [resolve(234,a,202,a)]. 268.90/269.16 412 is_a_theorem(and(strict_implies(and(A,B),and(B,A)),strict_implies(and(C,D),and(D,C)))). [resolve(234,a,198,a)]. 268.90/269.16 1028 is_a_theorem(and(strict_implies(A,and(A,A)),strict_implies(and(B,C),B))). [resolve(250,a,207,a)]. 268.90/269.16 1649 is_a_theorem(and(strict_implies(and(A,B),A),strict_implies(and(C,D),C))). [resolve(263,a,207,a)]. 268.90/269.16 2297 implies(A,and(not(B),not(C))) = not(and(A,or(B,C))). [para(218(a,1),276(a,1,1,2)),flip(a)]. 268.90/269.16 8833 is_a_theorem(strict_implies(and(and(A,B),C),and(and(B,C),A))). [resolve(411,a,259,a)]. 268.90/269.16 8865 is_a_theorem(strict_equiv(and(A,B),and(B,A))). [para(205(a,1),412(a,1))]. 268.90/269.16 8934 and(A,B) = and(B,A). [resolve(8865,a,199,a)]. 268.90/269.16 8960 is_a_theorem(strict_implies(and(A,and(B,C)),and(B,and(C,A)))). [back_rewrite(8833),rewrite([8934(2),8934(4)])]. 268.90/269.16 9637 -is_a_theorem(A) | -is_a_theorem(B) | is_a_theorem(and(A,B)). [back_rewrite(201),rewrite([8934(3)])]. 268.90/269.16 9677 strict_equiv(A,B) = strict_equiv(B,A). [para(8934(a,1),205(a,1)),rewrite([205(3)])]. 268.90/269.16 9678 is_a_theorem(strict_implies(and(A,B),B)). [para(8934(a,1),207(a,1,1))]. 268.90/269.16 9683 -is_a_theorem(and(strict_implies(A,B),strict_implies(C,A))) | is_a_theorem(strict_implies(C,B)). [para(8934(a,1),259(a,1))]. 268.90/269.16 9914 -is_a_theorem(strict_equiv(A,B)) | A = B. [para(9677(a,1),199(a,1))]. 268.90/269.16 10032 -is_a_theorem(A) | is_a_theorem(and(A,strict_implies(and(B,C),C))). [resolve(9637,a,9678,a),rewrite([8934(4)])]. 268.90/269.16 12829 is_a_theorem(strict_implies(A,A)). [resolve(1028,a,259,a)]. 268.90/269.16 12837 is_a_theorem(strict_equiv(A,and(A,A))). [para(205(a,1),1028(a,1))]. 268.90/269.16 12839 is_a_theorem(and(strict_implies(A,A),strict_implies(and(B,C),C))). [resolve(12829,a,10032,a)]. 268.90/269.16 12840 -is_a_theorem(A) | is_a_theorem(and(A,strict_implies(B,B))). [resolve(12829,a,9637,b)]. 268.90/269.16 12862 is_a_theorem(and(strict_implies(A,A),strict_implies(B,and(B,B)))). [resolve(12829,a,251,a)]. 268.90/269.16 12928 and(A,A) = A. [resolve(12837,a,9914,a),flip(a)]. 268.90/269.16 12935 is_a_theorem(and(strict_implies(A,A),strict_implies(B,B))). [back_rewrite(12862),rewrite([12928(2)])]. 268.90/269.16 13305 strict_equiv(A,A) = strict_implies(A,A). [para(12928(a,1),205(a,1)),flip(a)]. 268.90/269.16 13307 or(A,A) = not(not(A)). [para(12928(a,1),212(a,1,1)),rewrite([218(4)]),flip(a)]. 268.90/269.16 13312 implies(or(A,A),B) = or(not(A),B). [para(12928(a,1),282(a,1,1)),rewrite([218(4)]),flip(a)]. 268.90/269.16 13395 strict_implies(or(A,A),B) = strict_implies(not(not(A)),B). [para(13307(a,2),278(a,2,1)),rewrite([278(3)]),flip(a)]. 268.90/269.16 13406 not(or(A,A)) = not(not(not(A))). [para(13307(a,2),13307(a,2,1)),rewrite([13307(3)]),flip(a)]. 268.90/269.16 13584 implies(A,or(B,B)) = implies(A,not(not(B))). [para(13406(a,1),212(a,1,1,2)),rewrite([212(5)]),flip(a)]. 268.90/269.16 14347 and(strict_implies(A,not(not(B))),strict_implies(or(B,B),A)) = strict_equiv(A,not(not(B))). [para(13395(a,2),205(a,1,2))]. 268.90/269.16 14348 -is_a_theorem(strict_implies(not(not(A)),B)) | -is_a_theorem(or(A,A)) | is_a_theorem(B). [para(13395(a,1),206(a,1))]. 268.90/269.16 14349 -is_a_theorem(strict_implies(or(A,A),B)) | -is_a_theorem(not(not(A))) | is_a_theorem(B). [para(13395(a,2),206(a,1))]. 268.90/269.16 14966 strict_implies(A,or(B,B)) = strict_implies(A,not(not(B))). [para(13584(a,1),200(a,1,1)),rewrite([200(4)]),flip(a)]. 268.90/269.16 15292 strict_equiv(A,or(B,B)) = strict_equiv(A,not(not(B))). [para(14966(a,1),205(a,1,1)),rewrite([14347(6)]),flip(a)]. 268.90/269.16 15294 -is_a_theorem(strict_implies(A,or(B,B))) | -is_a_theorem(A) | is_a_theorem(not(not(B))). [para(14966(a,2),206(a,1))]. 268.90/269.16 15627 -is_a_theorem(strict_equiv(A,or(B,B))) | not(not(B)) = A. [para(15292(a,2),199(a,1))]. 268.90/269.16 15646 strict_equiv(A,not(or(B,B))) = strict_equiv(A,not(not(not(B)))). [para(13307(a,2),15292(a,2,2,1)),rewrite([13307(3)]),flip(a)]. 268.90/269.16 15701 is_a_theorem(strict_implies(and(A,and(B,C)),B)). [resolve(1649,a,259,a),rewrite([8934(2)])]. 268.90/269.16 15733 is_a_theorem(strict_implies(and(A,and(B,C)),C)). [para(8934(a,1),15701(a,1,1,2))]. 268.90/269.16 15769 -is_a_theorem(A) | is_a_theorem(and(A,strict_implies(and(B,and(C,D)),D))). [resolve(15733,a,9637,b)]. 268.90/269.16 17007 is_a_theorem(strict_implies(and(A,B),and(B,and(A,B)))). [para(12928(a,1),8960(a,1,1,2)),rewrite([8934(2)])]. 268.90/269.16 17034 is_a_theorem(and(strict_implies(and(A,B),and(B,and(A,B))),strict_implies(and(C,D),D))). [resolve(17007,a,10032,a)]. 268.90/269.16 17362 -is_a_theorem(and(strict_implies(or(A,A),B),strict_implies(C,not(not(A))))) | is_a_theorem(strict_implies(C,B)). [para(13395(a,2),9683(a,1,1))]. 268.90/269.16 19722 not(and(not(A),or(B,C))) = or(A,and(not(B),not(C))). [para(2297(a,1),218(a,1))]. 268.90/269.16 19727 not(and(A,or(B,C))) = not(and(A,or(C,B))). [para(8934(a,1),2297(a,1,2)),rewrite([2297(4)])]. 268.90/269.16 22214 -is_a_theorem(strict_equiv(A,not(not(not(B))))) | not(or(B,B)) = A. [para(15646(a,1),199(a,1))]. 268.90/269.16 22450 not(and(or(A,B),or(B,A))) = not(or(A,B)). [para(12928(a,1),19727(a,1,1)),flip(a)]. 268.90/269.16 23282 not(or(A,B)) = not(or(B,A)). [para(8934(a,1),22450(a,1,1)),rewrite([22450(4)])]. 268.90/269.16 23288 implies(A,or(B,C)) = implies(A,or(C,B)). [para(23282(a,1),212(a,1,1,2)),rewrite([212(4)])]. 268.90/269.16 23315 strict_implies(A,or(B,C)) = strict_implies(A,or(C,B)). [para(23288(a,1),200(a,1,1)),rewrite([200(3)])]. 268.90/269.16 23579 and(strict_implies(A,or(B,C)),strict_implies(or(C,B),A)) = strict_equiv(A,or(C,B)). [para(23315(a,1),205(a,1,1))]. 268.90/269.16 26157 or(A,and(not(B),not(C))) = implies(or(B,C),A). [para(8934(a,1),19722(a,1,1)),rewrite([212(4)]),flip(a)]. 268.90/269.16 26172 implies(or(A,B),C) = implies(or(B,A),C). [para(8934(a,1),26157(a,1,2)),rewrite([26157(4)])]. 268.90/269.16 26173 or(not(A),B) = or(B,not(A)). [para(12928(a,1),26157(a,1,2)),rewrite([13312(4)]),flip(a)]. 268.90/269.16 26221 implies(or(A,A),B) = or(B,not(A)). [back_rewrite(13312),rewrite([26173(4)])]. 268.90/269.16 26225 strict_implies(not(not(A)),B) = strict_implies(not(B),not(A)). [para(26173(a,1),278(a,1,1)),rewrite([278(3)]),flip(a)]. 268.90/269.16 26314 -is_a_theorem(strict_implies(not(A),not(B))) | -is_a_theorem(or(B,B)) | is_a_theorem(A). [back_rewrite(14348),rewrite([26225(3)])]. 268.90/269.16 26319 strict_implies(or(A,A),B) = strict_implies(not(B),not(A)). [back_rewrite(13395),rewrite([26225(5)])]. 268.90/269.16 26370 strict_implies(or(A,B),C) = strict_implies(or(B,A),C). [para(26172(a,1),200(a,1,1)),rewrite([200(3)])]. 268.90/269.16 26372 strict_equiv(A,or(B,C)) = strict_equiv(A,or(C,B)). [back_rewrite(23579),rewrite([26370(4),205(5)])]. 268.90/269.16 26477 is_a_theorem(strict_implies(or(A,A),A)). [para(26319(a,2),12829(a,1))]. 268.90/269.16 26481 strict_implies(or(A,A),not(B)) = strict_implies(or(B,B),not(A)). [para(13307(a,2),26319(a,2,1))]. 268.90/269.16 26482 is_a_theorem(and(strict_implies(or(A,A),A),strict_implies(B,B))). [para(26319(a,2),12935(a,1,1))]. 268.90/269.16 26487 is_a_theorem(and(strict_implies(or(A,A),A),strict_implies(and(B,C),C))). [para(26319(a,2),12839(a,1,1))]. 268.90/269.16 26845 -is_a_theorem(A) | is_a_theorem(and(A,strict_implies(or(B,B),B))). [resolve(26477,a,9637,b)]. 268.90/269.16 26896 is_a_theorem(and(strict_implies(or(A,A),A),strict_implies(or(B,B),B))). [para(26319(a,2),26482(a,1,2))]. 268.90/269.16 27005 -is_a_theorem(strict_equiv(A,or(B,C))) | or(C,B) = A. [para(26372(a,1),199(a,1))]. 268.90/269.16 27030 or(A,B) = or(B,A). [para(13305(a,1),27005(a,1)),unit_del(a,12829)]. 268.90/269.16 27051 strict_implies(not(A),B) = strict_implies(not(B),A). [para(27030(a,1),278(a,1,1)),rewrite([278(2)])]. 268.90/269.16 27077 and(strict_implies(A,not(B)),strict_implies(not(A),B)) = strict_equiv(A,not(B)). [para(27051(a,1),205(a,1,1)),rewrite([8934(5),9677(7)])]. 268.90/269.16 27173 is_a_theorem(strict_implies(not(A),not(and(B,A)))). [resolve(26487,a,259,a),rewrite([13307(3),27051(4)])]. 268.90/269.16 27263 is_a_theorem(strict_implies(not(A),not(and(A,B)))). [para(8934(a,1),27173(a,1,2,1))]. 268.90/269.16 27264 is_a_theorem(strict_implies(or(A,A),implies(B,A))). [para(13307(a,2),27173(a,1,1)),rewrite([212(4)])]. 268.90/269.16 27462 is_a_theorem(strict_implies(not(A),implies(A,B))). [para(212(a,1),27263(a,1,2))]. 268.90/269.16 27471 is_a_theorem(and(strict_implies(not(A),implies(A,B)),strict_implies(and(C,and(D,E)),E))). [resolve(27462,a,15769,a)]. 268.90/269.16 27514 is_a_theorem(strict_implies(or(A,A),or(A,B))). [para(13307(a,2),27462(a,1,1)),rewrite([218(3)])]. 268.90/269.16 27611 -is_a_theorem(not(not(A))) | is_a_theorem(implies(B,A)). [resolve(27264,a,14349,a)]. 268.90/269.16 27749 is_a_theorem(and(strict_implies(or(A,A),or(A,B)),strict_implies(C,C))). [resolve(27514,a,12840,a)]. 268.90/269.16 27776 -is_a_theorem(not(or(A,A))) | is_a_theorem(implies(B,not(A))). [para(13307(a,2),27611(a,1,1))]. 268.90/269.16 28923 is_a_theorem(strict_implies(not(A),not(or(A,A)))). [resolve(26896,a,9683,a),rewrite([13307(3),27051(4)])]. 268.90/269.16 28962 is_a_theorem(strict_implies(not(A),not(not(not(A))))). [para(13307(a,1),28923(a,1,2,1))]. 268.90/269.16 29062 is_a_theorem(and(strict_implies(not(A),not(not(not(A)))),strict_implies(B,B))). [resolve(28962,a,12840,a)]. 268.90/269.16 35397 is_a_theorem(strict_equiv(not(A),not(not(not(A))))). [para(27077(a,1),29062(a,1))]. 268.90/269.16 35747 not(or(A,A)) = not(A). [resolve(35397,a,22214,a)]. 268.90/269.16 35945 -is_a_theorem(not(A)) | is_a_theorem(implies(B,not(A))). [back_rewrite(27776),rewrite([35747(2)])]. 268.90/269.16 36353 implies(A,or(B,B)) = implies(A,B). [para(35747(a,1),212(a,1,1,2)),rewrite([212(3)]),flip(a)]. 268.90/269.16 36354 not(not(implies(A,B))) = implies(A,B). [para(212(a,1),35747(a,2)),rewrite([13307(5),212(3)])]. 268.90/269.16 36523 implies(A,not(not(B))) = implies(A,B). [back_rewrite(13584),rewrite([36353(2)]),flip(a)]. 268.90/269.16 36850 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(C,implies(A,B))). [para(212(a,1),35945(a,1)),rewrite([212(5)])]. 268.90/269.16 36931 strict_implies(A,or(B,B)) = strict_implies(A,B). [para(36353(a,1),200(a,1,1)),rewrite([200(2)]),flip(a)]. 268.90/269.16 36996 -is_a_theorem(strict_implies(A,B)) | -is_a_theorem(A) | is_a_theorem(not(not(B))). [back_rewrite(15294),rewrite([36931(2)])]. 268.90/269.16 36999 strict_implies(A,not(not(B))) = strict_implies(A,B). [back_rewrite(14966),rewrite([36931(2)]),flip(a)]. 268.90/269.16 37105 -is_a_theorem(and(strict_implies(or(A,A),B),strict_implies(C,A))) | is_a_theorem(strict_implies(C,B)). [back_rewrite(17362),rewrite([36999(5)])]. 268.90/269.16 37174 not(not(or(A,B))) = or(A,B). [para(218(a,1),36354(a,1,1,1)),rewrite([218(5)])]. 268.90/269.16 37389 strict_implies(not(A),not(or(B,C))) = strict_implies(or(B,C),A). [para(37174(a,1),27051(a,1,1)),flip(a)]. 268.90/269.16 37844 -is_a_theorem(A) | is_a_theorem(not(not(A))). [resolve(36996,a,12829,a)]. 268.90/269.16 38540 is_a_theorem(not(not(strict_implies(A,A)))). [resolve(37844,a,12829,a)]. 268.90/269.16 39263 is_a_theorem(implies(A,strict_implies(B,B))). [resolve(38540,a,35945,a),rewrite([36523(4)])]. 268.90/269.16 39414 is_a_theorem(implies(A,implies(B,strict_implies(C,C)))). [resolve(39263,a,36850,a)]. 268.90/269.16 40633 is_a_theorem(or(implies(A,strict_implies(B,B)),not(C))). [para(26221(a,1),39414(a,1))]. 268.90/269.16 44364 is_a_theorem(or(or(A,strict_implies(B,B)),not(C))). [para(218(a,1),40633(a,1,1))]. 268.90/269.16 45623 is_a_theorem(or(or(A,strict_implies(B,B)),or(C,D))). [para(37174(a,1),44364(a,1,2))]. 268.90/269.16 50887 -is_a_theorem(strict_implies(or(A,strict_implies(B,B)),C)) | is_a_theorem(C). [resolve(45623,a,26314,b),rewrite([37389(5)])]. 268.90/269.16 51449 -is_a_theorem(strict_implies(or(A,A),not(strict_implies(B,B)))) | is_a_theorem(not(A)). [para(26481(a,1),50887(a,1))]. 268.90/269.16 54379 is_a_theorem(strict_equiv(and(A,B),and(B,and(A,B)))). [para(205(a,1),17034(a,1))]. 268.90/269.16 54410 and(A,and(B,A)) = and(B,A). [resolve(54379,a,9914,a),flip(a)]. 268.90/269.16 59696 is_a_theorem(strict_implies(and(A,and(B,not(C))),implies(C,D))). [resolve(27471,a,9683,a)]. 268.90/269.16 65482 is_a_theorem(strict_implies(A,or(A,B))). [resolve(37105,a,27749,a)]. 268.90/269.16 65502 is_a_theorem(and(strict_implies(A,or(A,B)),strict_implies(or(C,C),C))). [resolve(65482,a,26845,a)]. 268.90/269.16 67683 is_a_theorem(strict_equiv(A,or(A,A))). [para(205(a,1),65502(a,1))]. 268.90/269.16 67706 not(not(A)) = A. [resolve(67683,a,15627,a)]. 268.90/269.16 67709 or(A,A) = A. [resolve(67683,a,9914,a),flip(a)]. 268.90/269.16 68107 -is_a_theorem(strict_implies(A,not(strict_implies(B,B)))) | is_a_theorem(not(A)). [back_rewrite(51449),rewrite([67709(1)])]. 268.90/269.16 68207 or(A,not(B)) = implies(B,A). [back_rewrite(26221),rewrite([67709(1)]),flip(a)]. 268.90/269.16 68652 not(and(A,B)) = implies(A,not(B)). [para(67706(a,1),212(a,1,1,2))]. 268.90/269.16 68653 not(implies(A,B)) = and(A,not(B)). [para(212(a,1),67706(a,1,1))]. 268.90/269.16 75750 implies(A,not(B)) = implies(B,not(A)). [para(8934(a,1),68652(a,1,1)),rewrite([68652(2)])]. 268.90/269.16 75752 implies(A,implies(B,not(A))) = implies(B,not(A)). [para(54410(a,1),68652(a,1,1)),rewrite([68652(2),68652(4)]),flip(a)]. 268.90/269.16 75756 or(A,implies(B,not(C))) = implies(and(B,C),A). [para(68652(a,1),68207(a,1,2))]. 268.90/269.16 75770 and(not(A),not(B)) = not(or(A,B)). [para(218(a,1),68653(a,1,1)),flip(a)]. 268.90/269.16 77331 is_a_theorem(strict_implies(and(A,not(or(B,C))),implies(C,D))). [para(75770(a,1),59696(a,1,1,2))]. 268.90/269.16 78172 implies(A,implies(A,B)) = implies(A,B). [para(218(a,1),75752(a,1,2)),rewrite([68207(2),75750(5),67706(4)])]. 268.90/269.16 78175 -is_a_theorem(implies(implies(c54,c55),implies(c54,c55))). [back_rewrite(213),rewrite([78172(5)])]. 268.90/269.16 78180 strict_implies(A,implies(A,B)) = strict_implies(A,B). [para(78172(a,1),200(a,1,1)),rewrite([200(2)]),flip(a)]. 268.90/269.16 79215 is_a_theorem(strict_implies(not(or(A,or(B,C))),implies(C,D))). [para(75770(a,1),77331(a,1,1))]. 268.90/269.16 79578 is_a_theorem(strict_implies(and(A,not(B)),or(C,or(A,D)))). [para(27051(a,1),79215(a,1)),rewrite([68653(2),27030(3)])]. 268.90/269.16 79638 is_a_theorem(strict_implies(and(A,B),or(C,or(A,D)))). [para(67706(a,1),79578(a,1,1,2))]. 268.90/269.16 79649 is_a_theorem(strict_implies(and(A,B),or(C,implies(D,A)))). [para(68207(a,1),79638(a,1,2,2))]. 268.90/269.16 79670 is_a_theorem(strict_implies(and(A,not(B)),implies(and(B,C),D))). [para(75750(a,1),79649(a,1,2,2)),rewrite([8934(2),75756(5)])]. 268.90/269.16 79700 is_a_theorem(strict_implies(and(A,not(A)),B)). [para(78180(a,1),79670(a,1))]. 268.90/269.16 79710 is_a_theorem(implies(A,A)). [resolve(79700,a,68107,a),rewrite([68652(3),67706(2)])]. 268.90/269.16 79711 $F. [resolve(79710,a,78175,a)]. 268.90/269.16 268.90/269.16 % SZS output end Refutation 268.90/269.16 ============================== end of proof ========================== 268.90/269.16 268.90/269.16 ============================== STATISTICS ============================ 268.90/269.16 268.90/269.16 Given=24403. Generated=9577238. Kept=79647. proofs=1. 268.90/269.16 Usable=11525. Sos=9580. Demods=157. Limbo=9, Disabled=58667. Hints=0. 268.90/269.16 Megabytes=102.22. 268.90/269.16 User_CPU=263.52, System_CPU=5.16, Wall_clock=269. 268.90/269.16 268.90/269.16 ============================== end of statistics ===================== 268.90/269.16 268.90/269.16 ============================== end of search ========================= 268.90/269.16 268.90/269.16 THEOREM PROVED 268.90/269.16 % SZS status Theorem 268.90/269.16 268.90/269.16 Exiting with 1 proof. 268.90/269.16 268.90/269.16 Process 41568 exit (max_proofs) Sat Jul 14 06:05:24 2018 268.90/269.16 Prover9 interrupted 268.90/269.17 EOF