0.00/0.09 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.09 % Command : tptp2X_and_run_prover9 %d %s 0.09/0.29 % Computer : n009.cluster.edu 0.09/0.29 % Model : x86_64 x86_64 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.09/0.29 % Memory : 8042.1875MB 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64 0.09/0.29 % CPULimit : 960 0.09/0.29 % DateTime : Thu Jul 2 06:43:06 EDT 2020 0.15/0.30 % CPUTime : 0.74/1.05 ============================== Prover9 =============================== 0.74/1.05 Prover9 (32) version 2009-11A, November 2009. 0.74/1.05 Process 26148 was started by sandbox2 on n009.cluster.edu, 0.74/1.05 Thu Jul 2 06:43:07 2020 0.74/1.05 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_25976_n009.cluster.edu". 0.74/1.05 ============================== end of head =========================== 0.74/1.05 0.74/1.05 ============================== INPUT ================================= 0.74/1.05 0.74/1.05 % Reading from file /tmp/Prover9_25976_n009.cluster.edu 0.74/1.05 0.74/1.05 set(prolog_style_variables). 0.74/1.05 set(auto2). 0.74/1.05 % set(auto2) -> set(auto). 0.74/1.05 % set(auto) -> set(auto_inference). 0.74/1.05 % set(auto) -> set(auto_setup). 0.74/1.05 % set(auto_setup) -> set(predicate_elim). 0.74/1.05 % set(auto_setup) -> assign(eq_defs, unfold). 0.74/1.05 % set(auto) -> set(auto_limits). 0.74/1.05 % set(auto_limits) -> assign(max_weight, "100.000"). 0.74/1.05 % set(auto_limits) -> assign(sos_limit, 20000). 0.74/1.05 % set(auto) -> set(auto_denials). 0.74/1.05 % set(auto) -> set(auto_process). 0.74/1.05 % set(auto2) -> assign(new_constants, 1). 0.74/1.05 % set(auto2) -> assign(fold_denial_max, 3). 0.74/1.05 % set(auto2) -> assign(max_weight, "200.000"). 0.74/1.05 % set(auto2) -> assign(max_hours, 1). 0.74/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.74/1.05 % set(auto2) -> assign(max_seconds, 0). 0.74/1.05 % set(auto2) -> assign(max_minutes, 5). 0.74/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.74/1.05 % set(auto2) -> set(sort_initial_sos). 0.74/1.05 % set(auto2) -> assign(sos_limit, -1). 0.74/1.05 % set(auto2) -> assign(lrs_ticks, 3000). 0.74/1.05 % set(auto2) -> assign(max_megs, 400). 0.74/1.05 % set(auto2) -> assign(stats, some). 0.74/1.05 % set(auto2) -> clear(echo_input). 0.74/1.05 % set(auto2) -> set(quiet). 0.74/1.05 % set(auto2) -> clear(print_initial_clauses). 0.74/1.05 % set(auto2) -> clear(print_given). 0.74/1.05 assign(lrs_ticks,-1). 0.74/1.05 assign(sos_limit,10000). 0.74/1.05 assign(order,kbo). 0.74/1.05 set(lex_order_vars). 0.74/1.05 clear(print_given). 0.74/1.05 0.74/1.05 % formulas(sos). % not echoed (88 formulas) 0.74/1.05 0.74/1.05 ============================== end of input ========================== 0.74/1.05 0.74/1.05 % From the command line: assign(max_seconds, 960). 0.74/1.05 0.74/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.74/1.05 0.74/1.05 % Formulas that are not ordinary clauses: 0.74/1.05 1 (all X all Y is_a_theorem(implies(equiv(X,Y),implies(X,Y)))) <-> equivalence_1 # label(equivalence_1) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 2 (all X all Y is_a_theorem(implies(Y,or(X,Y)))) <-> or_2 # label(or_2) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 3 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 4 (all X all Y is_a_theorem(implies(X,implies(Y,and(X,Y))))) <-> and_3 # label(and_3) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 5 or_3 <-> (all X all Y all Z is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))) # label(or_3) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 6 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 7 (all X all Y is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))) <-> modus_tollens # label(modus_tollens) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 8 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 9 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 10 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 11 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 12 (all X all Y (is_a_theorem(equiv(X,Y)) -> X = Y)) <-> substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 13 (all X all Y is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))) <-> equivalence_3 # label(equivalence_3) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 14 kn3 <-> (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))) # label(kn3) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 15 (all P all Q is_a_theorem(implies(Q,or(P,Q)))) <-> r2 # label(r2) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 16 implies_3 <-> (all X all Y all Z is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))) # label(implies_3) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 17 (all X all Y is_a_theorem(implies(X,or(X,Y)))) <-> or_1 # label(or_1) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 18 (all P is_a_theorem(implies(implies(not(P),P),P))) <-> cn3 # label(cn3) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 19 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 20 (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))) <-> cn1 # label(cn1) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 21 (all X all Y is_a_theorem(implies(and(X,Y),X))) <-> and_1 # label(and_1) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 22 (all X all Y is_a_theorem(implies(equiv(X,Y),implies(Y,X)))) <-> equivalence_2 # label(equivalence_2) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 23 (all P all Q all R is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))) <-> r4 # label(r4) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 24 (all X all Y (is_a_theorem(X) & is_a_theorem(implies(X,Y)) -> is_a_theorem(Y))) <-> modus_ponens # label(modus_ponens) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 25 implies_2 <-> (all X all Y is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))) # label(implies_2) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 26 (all P all Q all R is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))) <-> r5 # label(r5) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 27 op_and -> (all X all Y and(X,Y) = not(or(not(X),not(Y)))) # label(op_and) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 28 op_equiv -> (all X all Y and(implies(X,Y),implies(Y,X)) = equiv(X,Y)) # label(op_equiv) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 29 op_or -> (all X all Y or(X,Y) = not(and(not(X),not(Y)))) # label(op_or) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 30 op_implies_and -> (all X all Y not(and(X,not(Y))) = implies(X,Y)) # label(op_implies_and) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 31 op_implies_or -> (all X all Y or(not(X),Y) = implies(X,Y)) # label(op_implies_or) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 32 axiom_K <-> (all X all Y is_a_theorem(implies(necessarily(implies(X,Y)),implies(necessarily(X),necessarily(Y))))) # label(axiom_K) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 33 (all X is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))) <-> axiom_4 # label(axiom_4) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 34 (all P all Q is_a_theorem(strict_implies(possibly(and(P,Q)),and(possibly(P),possibly(Q))))) <-> axiom_s2 # label(axiom_s2) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 35 (all X is_a_theorem(implies(necessarily(X),X))) <-> axiom_M # label(axiom_M) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 36 substitution_strict_equiv <-> (all X all Y (is_a_theorem(strict_equiv(X,Y)) -> X = Y)) # label(substitution_strict_equiv) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 37 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]. 0.74/1.05 38 (all X is_a_theorem(strict_implies(necessarily(X),necessarily(necessarily(X))))) <-> axiom_s4 # label(axiom_s4) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 39 axiom_m1 <-> (all X all Y is_a_theorem(strict_implies(and(X,Y),and(Y,X)))) # label(axiom_m1) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 40 axiom_m8 <-> (all P all Q is_a_theorem(strict_implies(strict_implies(P,Q),strict_implies(possibly(P),possibly(Q))))) # label(axiom_m8) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 41 (all X is_a_theorem(strict_implies(X,and(X,X)))) <-> axiom_m4 # label(axiom_m4) # label(axiom) # label(non_clause). [assumption]. 0.77/1.07 42 axiom_m2 <-> (all X all Y is_a_theorem(strict_implies(and(X,Y),X))) # label(axiom_m2) # label(axiom) # label(non_clause). [assumption]. 0.77/1.07 43 necessitation <-> (all X (is_a_theorem(X) -> is_a_theorem(necessarily(X)))) # label(necessitation) # label(axiom) # label(non_clause). [assumption]. 0.77/1.07 44 axiom_m7 <-> (all P all Q is_a_theorem(strict_implies(possibly(and(P,Q)),P))) # label(axiom_m7) # label(axiom) # label(non_clause). [assumption]. 0.77/1.07 45 (all X is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X)))) <-> axiom_m9 # label(axiom_m9) # label(axiom) # label(non_clause). [assumption]. 0.77/1.07 46 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]. 0.77/1.07 47 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]. 0.77/1.07 48 (all X is_a_theorem(implies(X,necessarily(possibly(X))))) <-> axiom_B # label(axiom_B) # label(axiom) # label(non_clause). [assumption]. 0.77/1.07 49 axiom_m6 <-> (all X is_a_theorem(strict_implies(X,possibly(X)))) # label(axiom_m6) # label(axiom) # label(non_clause). [assumption]. 0.77/1.07 50 axiom_m10 <-> (all X is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X))))) # label(axiom_m10) # label(axiom) # label(non_clause). [assumption]. 0.77/1.07 51 (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]. 0.77/1.07 52 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]. 0.77/1.07 53 (all X is_a_theorem(implies(possibly(X),necessarily(possibly(X))))) <-> axiom_5 # label(axiom_5) # label(axiom) # label(non_clause). [assumption]. 0.77/1.07 54 modus_ponens_strict_implies <-> (all X all Y (is_a_theorem(strict_implies(X,Y)) & is_a_theorem(X) -> is_a_theorem(Y))) # label(modus_ponens_strict_implies) # label(axiom) # label(non_clause). [assumption]. 0.77/1.07 55 op_necessarily -> (all X necessarily(X) = not(possibly(not(X)))) # label(op_necessarily) # label(axiom) # label(non_clause). [assumption]. 0.77/1.07 56 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]. 0.77/1.07 57 op_possibly -> (all X possibly(X) = not(necessarily(not(X)))) # label(op_possibly) # label(axiom) # label(non_clause). [assumption]. 0.77/1.07 58 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]. 0.77/1.07 0.77/1.07 ============================== end of process non-clausal formulas === 0.77/1.07 0.77/1.07 ============================== PROCESS INITIAL CLAUSES =============== 0.77/1.07 0.77/1.07 ============================== PREDICATE ELIMINATION ================= 0.77/1.07 0.77/1.07 ============================== end predicate elimination ============= 0.77/1.08 0.77/1.08 Auto_denials: (non-Horn, no changes). 0.77/1.08 0.77/1.08 Term ordering decisions: 0.77/1.08 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. 0.77/1.08 0.77/1.08 ============================== end of process initial clauses ======== 0.77/1.08 0.77/1.08 ============================== CLAUSES FOR SEARCH ==================== 0.77/1.09 0.77/1.09 ============================== end of clauses for search ============= 0.77/1.09 0.77/1.09 ============================== SEARCH ================================ 0.77/1.09 0.77/1.09 % Starting search at 0.04 seconds. 0.77/1.09 0.77/1.09 ============================== PROOF ================================= 0.77/1.09 % SZS status Theorem 0.77/1.09 % SZS output start Refutation 0.77/1.09 0.77/1.09 % Proof 1 at 0.05 (+ 0.01) seconds. 0.77/1.09 % Length of proof is 19. 0.77/1.09 % Level of proof is 5. 0.77/1.09 % Maximum clause weight is 9.000. 0.77/1.09 % Given clauses 101. 0.77/1.09 0.77/1.09 43 necessitation <-> (all X (is_a_theorem(X) -> is_a_theorem(necessarily(X)))) # label(necessitation) # label(axiom) # label(non_clause). [assumption]. 0.77/1.09 50 axiom_m10 <-> (all X is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X))))) # label(axiom_m10) # label(axiom) # label(non_clause). [assumption]. 0.77/1.09 53 (all X is_a_theorem(implies(possibly(X),necessarily(possibly(X))))) <-> axiom_5 # label(axiom_5) # label(axiom) # label(non_clause). [assumption]. 0.77/1.09 56 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]. 0.77/1.09 162 -necessitation | -is_a_theorem(A) | is_a_theorem(necessarily(A)) # label(necessitation) # label(axiom). [clausify(43)]. 0.77/1.09 178 axiom_m10 | -is_a_theorem(strict_implies(possibly(c85),necessarily(possibly(c85)))) # label(axiom_m10) # label(axiom). [clausify(50)]. 0.77/1.09 184 is_a_theorem(implies(possibly(A),necessarily(possibly(A)))) | -axiom_5 # label(axiom_5) # label(axiom). [clausify(53)]. 0.77/1.09 191 -op_strict_implies | strict_implies(A,B) = necessarily(implies(A,B)) # label(op_strict_implies) # label(axiom). [clausify(56)]. 0.77/1.09 192 -op_strict_implies | necessarily(implies(A,B)) = strict_implies(A,B). [copy(191),flip(b)]. 0.77/1.09 198 necessitation # label(km5_necessitation) # label(axiom). [assumption]. 0.77/1.09 201 axiom_5 # label(km5_axiom_5) # label(axiom). [assumption]. 0.77/1.09 202 op_strict_implies # label(s1_0_op_strict_implies) # label(axiom). [assumption]. 0.77/1.09 205 -axiom_m10 # label(s1_0_m10_axiom_m10) # label(negated_conjecture). [assumption]. 0.77/1.09 226 -is_a_theorem(A) | is_a_theorem(necessarily(A)). [back_unit_del(162),unit_del(a,198)]. 0.77/1.09 229 is_a_theorem(implies(possibly(A),necessarily(possibly(A)))). [back_unit_del(184),unit_del(b,201)]. 0.77/1.09 230 necessarily(implies(A,B)) = strict_implies(A,B). [back_unit_del(192),unit_del(a,202)]. 0.77/1.09 232 -is_a_theorem(strict_implies(possibly(c85),necessarily(possibly(c85)))). [back_unit_del(178),unit_del(a,205)]. 0.77/1.09 348 is_a_theorem(strict_implies(possibly(A),necessarily(possibly(A)))). [resolve(229,a,226,a),rewrite([230(5)])]. 0.77/1.09 349 $F. [resolve(348,a,232,a)]. 0.77/1.09 0.77/1.09 % SZS output end Refutation 0.77/1.09 ============================== end of proof ========================== 0.77/1.09 0.77/1.09 ============================== STATISTICS ============================ 0.77/1.09 0.77/1.09 Given=101. Generated=312. Kept=286. proofs=1. 0.77/1.09 Usable=99. Sos=118. Demods=14. Limbo=0, Disabled=214. Hints=0. 0.77/1.09 Megabytes=1.01. 0.77/1.09 User_CPU=0.05, System_CPU=0.01, Wall_clock=0. 0.77/1.09 0.77/1.09 ============================== end of statistics ===================== 0.77/1.09 0.77/1.09 ============================== end of search ========================= 0.77/1.09 0.77/1.09 THEOREM PROVED 0.77/1.09 % SZS status Theorem 0.77/1.09 0.77/1.09 Exiting with 1 proof. 0.77/1.09 0.77/1.09 Process 26148 exit (max_proofs) Thu Jul 2 06:43:07 2020 0.77/1.09 Prover9 interrupted 0.77/1.09 EOF