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 0.02/0.23 % Computer : n173.star.cs.uiowa.edu 0.02/0.23 % Model : x86_64 x86_64 0.02/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.02/0.23 % Memory : 32218.625MB 0.02/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.02/0.23 % CPULimit : 300 0.02/0.23 % DateTime : Sat Jul 14 05:51:55 CDT 2018 0.02/0.23 % CPUTime : 0.06/0.47 ============================== Prover9 =============================== 0.06/0.47 Prover9 (32) version 2009-11A, November 2009. 0.06/0.47 Process 5127 was started by sandbox2 on n173.star.cs.uiowa.edu, 0.06/0.47 Sat Jul 14 05:51:55 2018 0.06/0.47 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_5095_n173.star.cs.uiowa.edu". 0.06/0.47 ============================== end of head =========================== 0.06/0.47 0.06/0.47 ============================== INPUT ================================= 0.06/0.47 0.06/0.47 % Reading from file /tmp/Prover9_5095_n173.star.cs.uiowa.edu 0.06/0.47 0.06/0.47 set(prolog_style_variables). 0.06/0.47 set(auto2). 0.06/0.47 % set(auto2) -> set(auto). 0.06/0.47 % set(auto) -> set(auto_inference). 0.06/0.47 % set(auto) -> set(auto_setup). 0.06/0.47 % set(auto_setup) -> set(predicate_elim). 0.06/0.47 % set(auto_setup) -> assign(eq_defs, unfold). 0.06/0.47 % set(auto) -> set(auto_limits). 0.06/0.47 % set(auto_limits) -> assign(max_weight, "100.000"). 0.06/0.47 % set(auto_limits) -> assign(sos_limit, 20000). 0.06/0.47 % set(auto) -> set(auto_denials). 0.06/0.47 % set(auto) -> set(auto_process). 0.06/0.47 % set(auto2) -> assign(new_constants, 1). 0.06/0.47 % set(auto2) -> assign(fold_denial_max, 3). 0.06/0.47 % set(auto2) -> assign(max_weight, "200.000"). 0.06/0.47 % set(auto2) -> assign(max_hours, 1). 0.06/0.47 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.06/0.47 % set(auto2) -> assign(max_seconds, 0). 0.06/0.47 % set(auto2) -> assign(max_minutes, 5). 0.06/0.47 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.06/0.47 % set(auto2) -> set(sort_initial_sos). 0.06/0.47 % set(auto2) -> assign(sos_limit, -1). 0.06/0.47 % set(auto2) -> assign(lrs_ticks, 3000). 0.06/0.47 % set(auto2) -> assign(max_megs, 400). 0.06/0.47 % set(auto2) -> assign(stats, some). 0.06/0.47 % set(auto2) -> clear(echo_input). 0.06/0.47 % set(auto2) -> set(quiet). 0.06/0.47 % set(auto2) -> clear(print_initial_clauses). 0.06/0.47 % set(auto2) -> clear(print_given). 0.06/0.47 assign(lrs_ticks,-1). 0.06/0.47 assign(sos_limit,10000). 0.06/0.47 assign(order,kbo). 0.06/0.47 set(lex_order_vars). 0.06/0.47 clear(print_given). 0.06/0.47 0.06/0.47 % formulas(sos). % not echoed (89 formulas) 0.06/0.47 0.06/0.47 ============================== end of input ========================== 0.06/0.47 0.06/0.47 % From the command line: assign(max_seconds, 300). 0.06/0.47 0.06/0.47 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.06/0.47 0.06/0.47 % Formulas that are not ordinary clauses: 0.06/0.47 1 (all X all Y is_a_theorem(implies(and(X,Y),Y))) <-> and_2 # label(and_2) # label(axiom) # label(non_clause). [assumption]. 0.06/0.47 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]. 0.06/0.47 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]. 0.06/0.47 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]. 0.06/0.47 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]. 0.06/0.47 6 (all P is_a_theorem(implies(P,and(P,P)))) <-> kn1 # label(kn1) # label(axiom) # label(non_clause). [assumption]. 0.06/0.47 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]. 0.06/0.47 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]. 0.06/0.47 9 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption]. 0.06/0.47 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption]. 0.06/0.47 11 (all X all Y is_a_theorem(implies(Y,or(X,Y)))) <-> or_2 # label(or_2) # label(axiom) # label(non_clause). [assumption]. 0.06/0.47 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]. 0.06/0.47 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]. 0.06/0.47 14 (all P is_a_theorem(implies(or(P,P),P))) <-> r1 # label(r1) # label(axiom) # label(non_clause). [assumption]. 0.06/0.47 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]. 0.06/0.47 16 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption]. 0.06/0.47 17 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption]. 0.06/0.47 18 (all P is_a_theorem(implies(implies(not(P),P),P))) <-> cn3 # label(cn3) # label(axiom) # label(non_clause). [assumption]. 0.06/0.47 19 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption]. 0.06/0.47 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]. 0.06/0.47 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]. 0.06/0.47 22 (all X all Y is_a_theorem(implies(X,implies(Y,X)))) <-> implies_1 # label(implies_1) # label(axiom) # label(non_clause). [assumption]. 0.06/0.47 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]. 0.06/0.47 24 (all P all Q is_a_theorem(implies(and(P,Q),P))) <-> kn2 # label(kn2) # label(axiom) # label(non_clause). [assumption]. 0.06/0.47 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]. 0.06/0.47 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]. 0.06/0.47 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]. 0.06/0.47 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]. 0.06/0.47 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]. 0.06/0.47 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]. 0.06/0.47 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]. 0.06/0.47 32 axiom_m6 <-> (all X is_a_theorem(strict_implies(X,possibly(X)))) # label(axiom_m6) # label(axiom) # label(non_clause). [assumption]. 0.06/0.47 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]. 0.06/0.47 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]. 0.06/0.47 35 (all X is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X)))) <-> axiom_m9 # label(axiom_m9) # label(axiom) # label(non_clause). [assumption]. 0.06/0.47 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]. 0.06/0.47 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]. 0.06/0.47 38 (all X is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X))))) <-> axiom_m10 # label(axiom_m10) # label(axiom) # label(non_clause). [assumption]. 0.06/0.47 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]. 0.06/0.47 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]. 0.06/0.47 41 (all X is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))) <-> axiom_4 # label(axiom_4) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 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]. 0.06/0.49 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]. 0.06/0.49 44 (all X is_a_theorem(implies(possibly(X),necessarily(possibly(X))))) <-> axiom_5 # label(axiom_5) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 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]. 0.06/0.49 46 axiom_m4 <-> (all X is_a_theorem(strict_implies(X,and(X,X)))) # label(axiom_m4) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 47 axiom_M <-> (all X is_a_theorem(implies(necessarily(X),X))) # label(axiom_M) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 48 (all X is_a_theorem(strict_implies(necessarily(X),necessarily(necessarily(X))))) <-> axiom_s4 # label(axiom_s4) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 49 necessitation <-> (all X (is_a_theorem(X) -> is_a_theorem(necessarily(X)))) # label(necessitation) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 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]. 0.06/0.49 51 axiom_B <-> (all X is_a_theorem(implies(X,necessarily(possibly(X))))) # label(axiom_B) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 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]. 0.06/0.49 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]. 0.06/0.49 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]. 0.06/0.49 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]. 0.06/0.49 56 op_necessarily -> (all X not(possibly(not(X))) = necessarily(X)) # label(op_necessarily) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 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]. 0.06/0.49 58 op_possibly -> (all X not(necessarily(not(X))) = possibly(X)) # label(op_possibly) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 0.06/0.49 ============================== end of process non-clausal formulas === 0.06/0.49 0.06/0.49 ============================== PROCESS INITIAL CLAUSES =============== 0.06/0.49 0.06/0.49 ============================== PREDICATE ELIMINATION ================= 0.06/0.49 0.06/0.49 ============================== end predicate elimination ============= 0.06/0.49 0.06/0.49 Auto_denials: (non-Horn, no changes). 0.06/0.49 0.06/0.49 Term ordering decisions: 0.06/0.49 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. 0.06/0.49 0.06/0.49 ============================== end of process initial clauses ======== 0.06/0.49 0.06/0.49 ============================== CLAUSES FOR SEARCH ==================== 98.65/98.90 98.65/98.90 ============================== end of clauses for search ============= 98.65/98.90 98.65/98.90 ============================== SEARCH ================================ 98.65/98.90 98.65/98.90 % Starting search at 0.02 seconds. 98.65/98.90 98.65/98.90 Low Water (keep): wt=25.000, iters=3341 98.65/98.90 98.65/98.90 Low Water (keep): wt=22.000, iters=3341 98.65/98.90 98.65/98.90 Low Water (keep): wt=21.000, iters=3336 98.65/98.90 98.65/98.90 Low Water (keep): wt=20.000, iters=3345 98.65/98.90 98.65/98.90 Low Water (keep): wt=19.000, iters=3479 98.65/98.90 98.65/98.90 Low Water (keep): wt=18.000, iters=3375 98.65/98.90 98.65/98.90 Low Water (keep): wt=17.000, iters=3345 98.65/98.90 98.65/98.90 Low Water (keep): wt=16.000, iters=3369 98.65/98.90 98.65/98.90 Low Water (keep): wt=15.000, iters=3348 98.65/98.90 98.65/98.90 Low Water (keep): wt=14.000, iters=3341 98.65/98.90 98.65/98.90 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 60 (0.00 of 2.06 sec). 98.65/98.90 98.65/98.90 Low Water (keep): wt=13.000, iters=3339 98.65/98.90 98.65/98.90 Low Water (keep): wt=12.000, iters=4046 98.65/98.90 98.65/98.90 Low Water (keep): wt=11.000, iters=3333 98.65/98.90 98.65/98.90 Low Water (displace): id=14190, wt=28.000 98.65/98.90 98.65/98.90 Low Water (displace): id=18472, wt=10.000 98.65/98.90 98.65/98.90 Low Water (displace): id=18481, wt=9.000 98.65/98.90 98.65/98.90 Low Water (keep): wt=10.000, iters=3361 98.65/98.90 98.65/98.90 ============================== PROOF ================================= 98.65/98.90 % SZS status Theorem 98.65/98.90 % SZS output start Refutation 98.65/98.90 98.65/98.90 % Proof 1 at 94.44 (+ 3.98) seconds. 98.65/98.90 % Length of proof is 174. 98.65/98.90 % Level of proof is 29. 98.65/98.90 % Maximum clause weight is 24.000. 98.65/98.90 % Given clauses 21208. 98.65/98.90 98.65/98.90 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]. 98.65/98.90 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption]. 98.65/98.90 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]. 98.65/98.90 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]. 98.65/98.90 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]. 98.65/98.90 17 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption]. 98.65/98.90 22 (all X all Y is_a_theorem(implies(X,implies(Y,X)))) <-> implies_1 # label(implies_1) # label(axiom) # label(non_clause). [assumption]. 98.65/98.90 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]. 98.65/98.90 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]. 98.65/98.90 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]. 98.65/98.90 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]. 98.65/98.90 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]. 98.65/98.90 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]. 98.65/98.90 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]. 98.65/98.90 47 axiom_M <-> (all X is_a_theorem(implies(necessarily(X),X))) # label(axiom_M) # label(axiom) # label(non_clause). [assumption]. 98.65/98.90 49 necessitation <-> (all X (is_a_theorem(X) -> is_a_theorem(necessarily(X)))) # label(necessitation) # label(axiom) # label(non_clause). [assumption]. 98.65/98.90 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]. 98.65/98.90 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]. 98.65/98.90 63 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(3)]. 98.65/98.90 78 -or_1 | is_a_theorem(implies(A,or(A,B))) # label(or_1) # label(axiom). [clausify(10)]. 98.65/98.90 82 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(12)]. 98.65/98.90 86 -implies_3 | is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))) # label(implies_3) # label(axiom). [clausify(13)]. 98.65/98.90 91 is_a_theorem(implies(A,implies(B,and(A,B)))) | -and_3 # label(and_3) # label(axiom). [clausify(15)]. 98.65/98.90 94 -and_1 | is_a_theorem(implies(and(A,B),A)) # label(and_1) # label(axiom). [clausify(17)]. 98.65/98.90 105 is_a_theorem(implies(A,implies(B,A))) | -implies_1 # label(implies_1) # label(axiom). [clausify(22)]. 98.65/98.90 106 -modus_tollens | is_a_theorem(implies(implies(not(A),not(B)),implies(B,A))) # label(modus_tollens) # label(axiom). [clausify(23)]. 98.65/98.90 111 is_a_theorem(implies(implies(A,B),implies(implies(B,A),equiv(A,B)))) | -equivalence_3 # label(equivalence_3) # label(axiom). [clausify(25)]. 98.65/98.90 112 -implies_2 | is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))) # label(implies_2) # label(axiom). [clausify(26)]. 98.65/98.90 114 -op_or | or(A,B) = not(and(not(A),not(B))) # label(op_or) # label(axiom). [clausify(27)]. 98.65/98.90 115 -op_or | not(and(not(A),not(B))) = or(A,B). [copy(114),flip(b)]. 98.65/98.90 117 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)]. 98.65/98.90 119 -op_equiv | equiv(A,B) = and(implies(A,B),implies(B,A)) # label(op_equiv) # label(axiom). [clausify(31)]. 98.65/98.90 120 -op_equiv | and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(119),flip(b)]. 98.65/98.90 121 implies_3 # label(hilbert_implies_3) # label(axiom). [assumption]. 98.65/98.90 122 and_3 # label(hilbert_and_3) # label(axiom). [assumption]. 98.65/98.90 123 op_or # label(hilbert_op_or) # label(axiom). [assumption]. 98.65/98.90 125 and_1 # label(hilbert_and_1) # label(axiom). [assumption]. 98.65/98.90 126 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption]. 98.65/98.90 127 implies_2 # label(hilbert_implies_2) # label(axiom). [assumption]. 98.65/98.90 130 op_implies_and # label(hilbert_op_implies_and) # label(axiom). [assumption]. 98.65/98.90 131 or_1 # label(hilbert_or_1) # label(axiom). [assumption]. 98.65/98.90 134 implies_1 # label(hilbert_implies_1) # label(axiom). [assumption]. 98.65/98.90 135 modus_tollens # label(hilbert_modus_tollens) # label(axiom). [assumption]. 98.65/98.90 136 op_equiv # label(hilbert_op_equiv) # label(axiom). [assumption]. 98.65/98.90 137 modus_ponens # label(hilbert_modus_ponens) # label(axiom). [assumption]. 98.65/98.90 138 equivalence_3 # label(hilbert_equivalence_3) # label(axiom). [assumption]. 98.65/98.90 168 -is_a_theorem(strict_implies(and(c80,c81),and(c81,c80))) | axiom_m1 # label(axiom_m1) # label(axiom). [clausify(45)]. 98.65/98.90 172 -axiom_M | is_a_theorem(implies(necessarily(A),A)) # label(axiom_M) # label(axiom). [clausify(47)]. 98.65/98.90 176 -necessitation | -is_a_theorem(A) | is_a_theorem(necessarily(A)) # label(necessitation) # label(axiom). [clausify(49)]. 98.65/98.90 185 -adjunction | -is_a_theorem(A) | -is_a_theorem(B) | is_a_theorem(and(B,A)) # label(adjunction) # label(axiom). [clausify(53)]. 98.65/98.90 186 adjunction | is_a_theorem(c92) # label(adjunction) # label(axiom). [clausify(53)]. 98.65/98.90 187 adjunction | is_a_theorem(c91) # label(adjunction) # label(axiom). [clausify(53)]. 98.65/98.90 188 adjunction | -is_a_theorem(and(c91,c92)) # label(adjunction) # label(axiom). [clausify(53)]. 98.65/98.90 195 -op_strict_implies | necessarily(implies(A,B)) = strict_implies(A,B) # label(op_strict_implies) # label(axiom). [clausify(57)]. 98.65/98.90 198 axiom_M # label(km4b_axiom_M) # label(axiom). [assumption]. 98.65/98.90 201 necessitation # label(km4b_necessitation) # label(axiom). [assumption]. 98.65/98.90 205 op_strict_implies # label(s1_0_op_strict_implies) # label(axiom). [assumption]. 98.65/98.90 207 -axiom_m1 # label(s1_0_axiom_m1) # label(negated_conjecture). [assumption]. 98.65/98.90 208 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))). [back_unit_del(86),unit_del(a,121)]. 98.65/98.90 209 is_a_theorem(implies(A,implies(B,and(A,B)))). [back_unit_del(91),unit_del(b,122)]. 98.65/98.90 210 not(and(not(A),not(B))) = or(A,B). [back_unit_del(115),unit_del(a,123)]. 98.65/98.90 212 is_a_theorem(implies(and(A,B),A)). [back_unit_del(94),unit_del(a,125)]. 98.65/98.90 213 -is_a_theorem(equiv(A,B)) | B = A. [back_unit_del(63),unit_del(a,126)]. 98.65/98.90 214 is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))). [back_unit_del(112),unit_del(a,127)]. 98.65/98.90 217 not(and(A,not(B))) = implies(A,B). [back_unit_del(117),unit_del(a,130)]. 98.65/98.90 218 is_a_theorem(implies(A,or(A,B))). [back_unit_del(78),unit_del(a,131)]. 98.65/98.90 221 is_a_theorem(implies(A,implies(B,A))). [back_unit_del(105),unit_del(b,134)]. 98.65/98.90 222 is_a_theorem(implies(implies(not(A),not(B)),implies(B,A))). [back_unit_del(106),unit_del(a,135)]. 98.65/98.90 223 and(implies(A,B),implies(B,A)) = equiv(A,B). [back_unit_del(120),unit_del(a,136)]. 98.65/98.90 224 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [back_unit_del(82),unit_del(a,137)]. 98.65/98.90 225 is_a_theorem(implies(implies(A,B),implies(implies(B,A),equiv(A,B)))). [back_unit_del(111),unit_del(b,138)]. 98.65/98.90 227 is_a_theorem(implies(necessarily(A),A)). [back_unit_del(172),unit_del(a,198)]. 98.65/98.90 230 -is_a_theorem(A) | is_a_theorem(necessarily(A)). [back_unit_del(176),unit_del(a,201)]. 98.65/98.90 233 necessarily(implies(A,B)) = strict_implies(A,B). [back_unit_del(195),unit_del(a,205)]. 98.65/98.90 235 -is_a_theorem(strict_implies(and(c80,c81),and(c81,c80))). [back_unit_del(168),unit_del(b,207)]. 98.65/98.90 238 implies(not(A),B) = or(A,B). [back_rewrite(210),rewrite([217(4)])]. 98.65/98.90 243 is_a_theorem(implies(or(A,not(B)),implies(B,A))). [back_rewrite(222),rewrite([238(3)])]. 98.65/98.90 269 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(217(a,1),217(a,1,1,2))]. 98.65/98.90 278 -is_a_theorem(A) | is_a_theorem(implies(B,A)). [resolve(224,b,221,a)]. 98.65/98.90 284 -is_a_theorem(implies(A,implies(A,B))) | is_a_theorem(implies(A,B)). [resolve(224,b,214,a)]. 98.65/98.90 287 -is_a_theorem(A) | is_a_theorem(implies(B,and(A,B))). [resolve(224,b,209,a)]. 98.65/98.90 288 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(B,C),implies(A,C))). [resolve(224,b,208,a)]. 98.65/98.90 289 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(B,A),equiv(A,B))). [resolve(225,a,224,b)]. 98.65/98.90 355 or(and(A,not(B)),C) = implies(implies(A,B),C). [para(217(a,1),238(a,1,1)),flip(a)]. 98.65/98.90 356 is_a_theorem(or(A,or(not(A),B))). [para(238(a,1),218(a,1))]. 98.65/98.90 378 -is_a_theorem(or(A,not(B))) | is_a_theorem(implies(B,A)). [resolve(243,a,224,b)]. 98.65/98.90 383 is_a_theorem(implies(or(A,not(not(B))),or(B,A))). [para(238(a,1),243(a,1,2))]. 98.65/98.90 1720 implies(implies(A,B),and(B,not(A))) = not(equiv(A,B)). [para(223(a,1),269(a,1,1)),flip(a)]. 98.65/98.90 3043 is_a_theorem(implies(A,A)). [resolve(284,a,221,a)]. 98.65/98.90 3045 is_a_theorem(implies(A,and(A,A))). [resolve(284,a,209,a)]. 98.65/98.90 3081 is_a_theorem(strict_implies(A,A)). [resolve(3043,a,230,a),rewrite([233(2)])]. 98.65/98.90 3089 is_a_theorem(implies(A,strict_implies(B,B))). [resolve(3081,a,278,a)]. 98.65/98.90 3121 -adjunction | -is_a_theorem(A) | is_a_theorem(and(A,strict_implies(B,B))). [resolve(3081,a,185,b)]. 98.65/98.90 3257 is_a_theorem(implies(A,and(c91,A))) | adjunction. [resolve(287,a,187,b)]. 98.65/98.90 3408 is_a_theorem(implies(implies(A,B),implies(necessarily(A),B))). [resolve(288,a,227,a)]. 98.65/98.90 3410 is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))). [resolve(288,a,221,a)]. 98.65/98.90 3531 is_a_theorem(implies(implies(and(A,A),A),equiv(A,and(A,A)))). [resolve(289,a,3045,a)]. 98.65/98.90 3557 is_a_theorem(implies(implies(implies(A,B),or(B,not(A))),equiv(or(B,not(A)),implies(A,B)))). [resolve(289,a,243,a)]. 98.65/98.90 3562 is_a_theorem(implies(implies(implies(implies(A,B),equiv(B,A)),implies(B,A)),equiv(implies(B,A),implies(implies(A,B),equiv(B,A))))). [resolve(289,a,225,a)]. 98.65/98.90 3868 is_a_theorem(implies(implies(strict_implies(A,A),B),equiv(B,strict_implies(A,A)))). [resolve(3089,a,289,a)]. 98.65/98.90 3869 is_a_theorem(implies(implies(strict_implies(A,A),B),implies(C,B))). [resolve(3089,a,288,a)]. 98.65/98.90 9096 adjunction | -is_a_theorem(A) | is_a_theorem(and(c91,A)). [resolve(3257,a,224,b)]. 98.65/98.90 10553 adjunction | is_a_theorem(and(c91,c92)). [resolve(9096,b,186,b),merge(c)]. 98.65/98.90 10565 adjunction. [resolve(10553,b,188,b),merge(b)]. 98.65/98.90 13384 -is_a_theorem(A) | is_a_theorem(and(A,strict_implies(B,B))). [back_unit_del(3121),unit_del(a,10565)]. 98.65/98.90 17877 is_a_theorem(and(strict_implies(A,A),strict_implies(B,B))). [resolve(13384,a,3081,a)]. 98.65/98.90 19119 is_a_theorem(necessarily(and(strict_implies(A,A),strict_implies(B,B)))). [resolve(17877,a,230,a)]. 98.65/98.90 19154 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(necessarily(A),B)). [resolve(3408,a,224,b)]. 98.65/98.90 19337 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(B,C)). [resolve(3410,a,224,b)]. 98.65/98.90 19361 is_a_theorem(equiv(A,and(A,A))). [resolve(3531,a,224,b),unit_del(a,212)]. 98.65/98.90 19378 and(A,A) = A. [resolve(19361,a,213,a)]. 98.65/98.90 19381 or(A,A) = not(not(A)). [para(19378(a,1),217(a,1,1)),rewrite([238(4)]),flip(a)]. 98.65/98.90 19382 equiv(A,A) = implies(A,A). [para(19378(a,1),223(a,1)),flip(a)]. 98.65/98.90 19386 implies(or(A,A),B) = or(not(A),B). [para(19378(a,1),355(a,1,1)),rewrite([238(4)]),flip(a)]. 98.65/98.90 19402 not(and(A,or(B,B))) = implies(A,not(B)). [para(19381(a,2),217(a,1,1,2))]. 98.65/98.90 19403 is_a_theorem(implies(A,not(not(A)))). [para(19381(a,1),218(a,1,2))]. 98.65/98.90 19406 is_a_theorem(or(A,not(not(not(A))))). [para(19381(a,1),356(a,1,2))]. 98.65/98.90 20210 is_a_theorem(or(not(A),A)). [resolve(19406,a,378,a),rewrite([238(3)])]. 98.65/98.90 21554 is_a_theorem(implies(implies(strict_implies(A,A),B),B)). [resolve(3869,a,284,a)]. 98.65/98.90 21678 -is_a_theorem(implies(strict_implies(A,A),B)) | is_a_theorem(B). [resolve(21554,a,224,b)]. 98.65/98.90 24283 is_a_theorem(implies(necessarily(A),implies(B,A))). [resolve(19154,a,221,a)]. 98.65/98.90 24403 -is_a_theorem(necessarily(A)) | is_a_theorem(implies(B,A)). [resolve(24283,a,224,b)]. 98.65/98.90 24452 is_a_theorem(implies(A,and(strict_implies(B,B),strict_implies(C,C)))). [resolve(24403,a,19119,a)]. 98.65/98.90 33495 is_a_theorem(implies(A,equiv(A,strict_implies(B,B)))). [resolve(19337,a,3868,a)]. 98.65/98.90 33528 is_a_theorem(equiv(strict_implies(A,A),strict_implies(B,B))). [resolve(33495,a,21678,a)]. 98.65/98.90 33533 -is_a_theorem(A) | is_a_theorem(equiv(A,strict_implies(B,B))). [resolve(33495,a,224,b)]. 98.65/98.90 33640 is_a_theorem(necessarily(equiv(strict_implies(A,A),strict_implies(B,B)))). [resolve(33528,a,230,a)]. 98.65/98.90 33641 strict_implies(A,A) = strict_implies(B,B). [resolve(33528,a,213,a)]. 98.65/98.90 33642 strict_implies(A,A) = c_0. [new_symbol(33641)]. 98.65/98.90 33643 is_a_theorem(c_0). [back_rewrite(33640),rewrite([33642(1),33642(2),19382(3),233(4),33642(3)])]. 98.65/98.90 33647 -is_a_theorem(A) | is_a_theorem(equiv(A,c_0)). [back_rewrite(33533),rewrite([33642(2)])]. 98.65/98.90 33932 is_a_theorem(implies(A,c_0)). [back_rewrite(24452),rewrite([33642(1),33642(2),19378(3)])]. 98.65/98.90 34315 is_a_theorem(implies(implies(c_0,A),A)). [back_rewrite(21554),rewrite([33642(1)])]. 98.65/98.90 36348 is_a_theorem(equiv(implies(A,c_0),c_0)). [resolve(33647,a,33932,a)]. 98.65/98.90 36610 is_a_theorem(equiv(or(not(A),A),c_0)). [resolve(33647,a,20210,a)]. 98.65/98.90 36623 is_a_theorem(equiv(implies(A,not(not(A))),c_0)). [resolve(33647,a,19403,a)]. 98.65/98.90 36708 is_a_theorem(equiv(implies(A,implies(B,A)),c_0)). [resolve(33647,a,221,a)]. 98.65/98.90 36710 is_a_theorem(equiv(implies(A,or(A,B)),c_0)). [resolve(33647,a,218,a)]. 98.65/98.90 36711 is_a_theorem(equiv(implies(and(A,B),A),c_0)). [resolve(33647,a,212,a)]. 98.65/98.90 36864 is_a_theorem(equiv(implies(implies(c_0,A),A),c_0)). [resolve(34315,a,33647,a)]. 98.65/98.90 38270 implies(A,c_0) = c_0. [resolve(36348,a,213,a),flip(a)]. 98.65/98.90 38272 and(implies(c_0,A),c_0) = equiv(c_0,A). [para(38270(a,1),223(a,1,2))]. 98.65/98.90 39130 or(not(A),A) = c_0. [resolve(36610,a,213,a),flip(a)]. 98.65/98.90 40022 implies(A,not(not(A))) = c_0. [resolve(36623,a,213,a),flip(a)]. 98.65/98.90 40023 equiv(A,not(not(A))) = c_0. [para(40022(a,1),223(a,1,1)),rewrite([238(4),39130(3),19378(3)]),flip(a)]. 98.65/98.90 40029 not(not(A)) = A. [para(40023(a,1),213(a,1)),unit_del(a,33643)]. 98.65/98.90 40066 or(A,A) = A. [back_rewrite(19381),rewrite([40029(3)])]. 98.65/98.90 40073 is_a_theorem(implies(or(A,B),or(B,A))). [back_rewrite(383),rewrite([40029(2)])]. 98.65/98.90 40121 not(and(A,B)) = implies(A,not(B)). [back_rewrite(19402),rewrite([40066(1)])]. 98.65/98.90 40122 or(not(A),B) = implies(A,B). [back_rewrite(19386),rewrite([40066(1)]),flip(a)]. 98.65/98.90 43503 implies(A,implies(B,A)) = c_0. [resolve(36708,a,213,a),flip(a)]. 98.65/98.90 43534 implies(A,or(A,B)) = c_0. [resolve(36710,a,213,a),flip(a)]. 98.65/98.90 43560 implies(and(A,B),A) = c_0. [resolve(36711,a,213,a),flip(a)]. 98.65/98.90 43758 implies(implies(c_0,A),A) = c_0. [resolve(36864,a,213,a),flip(a)]. 98.65/98.90 43759 equiv(implies(c_0,A),A) = c_0. [para(43758(a,1),223(a,1,1)),rewrite([43503(4),19378(3)]),flip(a)]. 98.65/98.90 43778 implies(c_0,A) = A. [para(43759(a,1),213(a,1)),flip(b),unit_del(a,33643)]. 98.65/98.90 43815 equiv(c_0,A) = and(A,c_0). [back_rewrite(38272),rewrite([43778(2)]),flip(a)]. 98.65/98.90 43938 implies(A,and(A,not(c_0))) = implies(A,not(c_0)). [para(43778(a,1),1720(a,1,1)),rewrite([43815(6),40121(7)])]. 98.65/98.90 43959 is_a_theorem(equiv(or(A,not(c_0)),A)). [para(43778(a,1),3557(a,1,1,1)),rewrite([43534(4),43778(6),43778(6)])]. 98.65/98.90 43960 is_a_theorem(equiv(A,and(A,c_0))). [para(43778(a,1),3562(a,1,1,2)),rewrite([38270(2),43815(3),43778(4),43560(3),43778(3),38270(3),43815(4),43778(5),43778(5)])]. 98.65/98.90 44615 and(A,c_0) = A. [resolve(43960,a,213,a)]. 98.65/98.90 44618 equiv(c_0,A) = A. [back_rewrite(43815),rewrite([44615(4)])]. 98.65/98.90 44619 -is_a_theorem(A) | c_0 = A. [para(44618(a,1),213(a,1)),flip(b)]. 98.65/98.90 44620 implies(A,not(c_0)) = not(A). [para(44618(a,1),1720(a,2,1)),rewrite([43778(2),43938(4)])]. 98.65/98.90 47530 or(A,not(c_0)) = A. [resolve(43959,a,213,a),flip(a)]. 98.65/98.90 47532 not(implies(A,B)) = and(A,not(B)). [para(47530(a,1),355(a,1)),rewrite([44620(6)]),flip(a)]. 98.65/98.90 51554 implies(or(A,B),or(B,A)) = c_0. [resolve(40073,a,44619,a),flip(a)]. 98.65/98.90 51556 is_a_theorem(equiv(or(A,B),or(B,A))). [resolve(40073,a,289,a),rewrite([51554(3),43778(5)])]. 98.65/98.90 53733 or(A,B) = or(B,A). [resolve(51556,a,213,a)]. 98.65/98.90 53951 or(A,not(B)) = implies(B,A). [back_rewrite(40122),rewrite([53733(2)])]. 98.65/98.90 56305 and(not(A),not(B)) = not(or(A,B)). [para(238(a,1),47532(a,1,1)),flip(a)]. 98.65/98.90 64270 and(not(A),B) = and(B,not(A)). [para(40029(a,1),56305(a,1,2)),rewrite([53951(4),47532(4)])]. 98.65/98.90 64311 and(A,B) = and(B,A). [para(40029(a,1),64270(a,1,1)),rewrite([40029(3)])]. 98.65/98.90 64513 $F. [back_rewrite(235),rewrite([64311(6),33642(7)]),unit_del(a,33643)]. 98.65/98.90 98.65/98.90 % SZS output end Refutation 98.65/98.90 ============================== end of proof ========================== 98.65/98.90 98.65/98.90 ============================== STATISTICS ============================ 98.65/98.90 98.65/98.90 Given=21208. Generated=8206603. Kept=64449. proofs=1. 98.65/98.90 Usable=5131. Sos=6877. Demods=1051. Limbo=202, Disabled=52386. Hints=0. 98.65/98.90 Megabytes=49.26. 98.65/98.90 User_CPU=94.45, System_CPU=3.98, Wall_clock=98. 98.65/98.90 98.65/98.90 ============================== end of statistics ===================== 98.65/98.90 98.65/98.90 ============================== end of search ========================= 98.65/98.90 98.65/98.90 THEOREM PROVED 98.65/98.90 % SZS status Theorem 98.65/98.90 98.65/98.90 Exiting with 1 proof. 98.65/98.90 98.65/98.90 Process 5127 exit (max_proofs) Sat Jul 14 05:53:33 2018 98.65/98.90 Prover9 interrupted 98.65/98.91 EOF