0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.12/0.33 % Computer : n013.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 180 0.12/0.33 % DateTime : Thu Aug 29 14:50:16 EDT 2019 0.12/0.33 % CPUTime : 0.42/1.03 ============================== Prover9 =============================== 0.42/1.03 Prover9 (32) version 2009-11A, November 2009. 0.42/1.03 Process 32558 was started by sandbox on n013.cluster.edu, 0.42/1.03 Thu Aug 29 14:50:17 2019 0.42/1.03 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 180 -f /tmp/Prover9_32405_n013.cluster.edu". 0.42/1.03 ============================== end of head =========================== 0.42/1.03 0.42/1.03 ============================== INPUT ================================= 0.42/1.03 0.42/1.03 % Reading from file /tmp/Prover9_32405_n013.cluster.edu 0.42/1.03 0.42/1.03 set(prolog_style_variables). 0.42/1.03 set(auto2). 0.42/1.03 % set(auto2) -> set(auto). 0.42/1.03 % set(auto) -> set(auto_inference). 0.42/1.03 % set(auto) -> set(auto_setup). 0.42/1.03 % set(auto_setup) -> set(predicate_elim). 0.42/1.03 % set(auto_setup) -> assign(eq_defs, unfold). 0.42/1.03 % set(auto) -> set(auto_limits). 0.42/1.03 % set(auto_limits) -> assign(max_weight, "100.000"). 0.42/1.03 % set(auto_limits) -> assign(sos_limit, 20000). 0.42/1.03 % set(auto) -> set(auto_denials). 0.42/1.03 % set(auto) -> set(auto_process). 0.42/1.03 % set(auto2) -> assign(new_constants, 1). 0.42/1.03 % set(auto2) -> assign(fold_denial_max, 3). 0.42/1.03 % set(auto2) -> assign(max_weight, "200.000"). 0.42/1.03 % set(auto2) -> assign(max_hours, 1). 0.42/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.42/1.03 % set(auto2) -> assign(max_seconds, 0). 0.42/1.03 % set(auto2) -> assign(max_minutes, 5). 0.42/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.42/1.03 % set(auto2) -> set(sort_initial_sos). 0.42/1.03 % set(auto2) -> assign(sos_limit, -1). 0.42/1.03 % set(auto2) -> assign(lrs_ticks, 3000). 0.42/1.03 % set(auto2) -> assign(max_megs, 400). 0.42/1.03 % set(auto2) -> assign(stats, some). 0.42/1.03 % set(auto2) -> clear(echo_input). 0.42/1.03 % set(auto2) -> set(quiet). 0.42/1.03 % set(auto2) -> clear(print_initial_clauses). 0.42/1.03 % set(auto2) -> clear(print_given). 0.42/1.03 assign(lrs_ticks,-1). 0.42/1.03 assign(sos_limit,10000). 0.42/1.03 assign(order,kbo). 0.42/1.03 set(lex_order_vars). 0.42/1.03 clear(print_given). 0.42/1.03 0.42/1.03 % formulas(sos). % not echoed (88 formulas) 0.42/1.03 0.42/1.03 ============================== end of input ========================== 0.42/1.03 0.42/1.03 % From the command line: assign(max_seconds, 180). 0.42/1.03 0.42/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.42/1.03 0.42/1.03 % Formulas that are not ordinary clauses: 0.42/1.03 1 (all X all Y is_a_theorem(implies(X,implies(Y,and(X,Y))))) <-> and_3 # label(and_3) # label(axiom) # label(non_clause). [assumption]. 0.42/1.03 2 r5 <-> (all P all Q all R is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))) # label(r5) # label(axiom) # label(non_clause). [assumption]. 0.42/1.03 3 substitution_of_equivalents <-> (all X all Y (is_a_theorem(equiv(X,Y)) -> X = Y)) # label(substitution_of_equivalents) # label(axiom) # label(non_clause). [assumption]. 0.42/1.03 4 (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))) <-> kn3 # label(kn3) # label(axiom) # label(non_clause). [assumption]. 0.42/1.03 5 implies_3 <-> (all X all Y all Z is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))) # label(implies_3) # label(axiom) # label(non_clause). [assumption]. 0.42/1.03 6 cn1 <-> (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))) # label(cn1) # label(axiom) # label(non_clause). [assumption]. 0.42/1.03 7 (all X all Y is_a_theorem(implies(equiv(X,Y),implies(X,Y)))) <-> equivalence_1 # label(equivalence_1) # label(axiom) # label(non_clause). [assumption]. 0.42/1.03 8 (all X all Y is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))) <-> equivalence_3 # label(equivalence_3) # label(axiom) # label(non_clause). [assumption]. 0.42/1.03 9 modus_ponens <-> (all X all Y (is_a_theorem(X) & is_a_theorem(implies(X,Y)) -> is_a_theorem(Y))) # label(modus_ponens) # label(axiom) # label(non_clause). [assumption]. 0.42/1.03 10 (all P is_a_theorem(implies(P,and(P,P)))) <-> kn1 # label(kn1) # label(axiom) # label(non_clause). [assumption]. 0.42/1.03 11 (all X all Y is_a_theorem(implies(and(X,Y),X))) <-> and_1 # label(and_1) # label(axiom) # label(non_clause). [assumption]. 0.42/1.03 12 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption]. 0.42/1.03 13 (all P is_a_theorem(implies(implies(not(P),P),P))) <-> cn3 # label(cn3) # label(axiom) # label(non_clause). [assumption]. 0.42/1.04 14 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption]. 0.42/1.04 15 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption]. 0.42/1.04 16 (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) <-> cn2 # label(cn2) # label(axiom) # label(non_clause). [assumption]. 0.42/1.04 17 implies_2 <-> (all X all Y is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))) # label(implies_2) # label(axiom) # label(non_clause). [assumption]. 0.42/1.04 18 (all P all Q is_a_theorem(implies(Q,or(P,Q)))) <-> r2 # label(r2) # label(axiom) # label(non_clause). [assumption]. 0.42/1.04 19 (all X all Y all Z is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))) <-> or_3 # label(or_3) # label(axiom) # label(non_clause). [assumption]. 0.42/1.04 20 (all X all Y is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))) <-> modus_tollens # label(modus_tollens) # label(axiom) # label(non_clause). [assumption]. 0.42/1.04 21 equivalence_2 <-> (all X all Y is_a_theorem(implies(equiv(X,Y),implies(Y,X)))) # label(equivalence_2) # label(axiom) # label(non_clause). [assumption]. 0.42/1.04 22 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption]. 0.42/1.04 23 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption]. 0.42/1.04 24 (all P all Q all R is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))) <-> r4 # label(r4) # label(axiom) # label(non_clause). [assumption]. 0.42/1.04 25 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption]. 0.42/1.04 26 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption]. 0.42/1.04 27 op_and -> (all X all Y not(or(not(X),not(Y))) = and(X,Y)) # label(op_and) # label(axiom) # label(non_clause). [assumption]. 0.42/1.04 28 op_or -> (all X all Y or(X,Y) = not(and(not(X),not(Y)))) # label(op_or) # label(axiom) # label(non_clause). [assumption]. 0.42/1.04 29 op_equiv -> (all X all Y equiv(X,Y) = and(implies(X,Y),implies(Y,X))) # label(op_equiv) # label(axiom) # label(non_clause). [assumption]. 0.42/1.04 30 op_implies_or -> (all X all Y implies(X,Y) = or(not(X),Y)) # label(op_implies_or) # label(axiom) # label(non_clause). [assumption]. 0.42/1.04 31 op_implies_and -> (all X all Y implies(X,Y) = not(and(X,not(Y)))) # label(op_implies_and) # label(axiom) # label(non_clause). [assumption]. 0.42/1.04 32 (all X all Y all Z is_a_theorem(strict_implies(and(strict_implies(X,Y),strict_implies(Y,Z)),strict_implies(X,Z)))) <-> axiom_m5 # label(axiom_m5) # label(axiom) # label(non_clause). [assumption]. 0.42/1.04 33 (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]. 0.42/1.04 34 adjunction <-> (all X all Y (is_a_theorem(X) & is_a_theorem(Y) -> is_a_theorem(and(X,Y)))) # label(adjunction) # label(axiom) # label(non_clause). [assumption]. 0.42/1.04 35 axiom_B <-> (all X is_a_theorem(implies(X,necessarily(possibly(X))))) # label(axiom_B) # label(axiom) # label(non_clause). [assumption]. 0.42/1.04 36 (all X is_a_theorem(strict_implies(X,possibly(X)))) <-> axiom_m6 # label(axiom_m6) # label(axiom) # label(non_clause). [assumption]. 0.42/1.04 37 (all X is_a_theorem(strict_implies(necessarily(X),necessarily(necessarily(X))))) <-> axiom_s4 # label(axiom_s4) # label(axiom) # label(non_clause). [assumption]. 0.42/1.04 38 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]. 0.42/1.04 39 (all X all Y (is_a_theorem(strict_equiv(X,Y)) -> X = Y)) <-> substitution_strict_equiv # label(substitution_strict_equiv) # label(axiom) # label(non_clause). [assumption]. 0.42/1.04 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]. 0.42/1.04 41 necessitation <-> (all X (is_a_theorem(X) -> is_a_theorem(necessarily(X)))) # label(necessitation) # label(axiom) # label(non_clause). [assumption]. 0.77/1.07 42 (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]. 0.77/1.07 43 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 44 (all X is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))) <-> axiom_4 # label(axiom_4) # label(axiom) # label(non_clause). [assumption]. 0.77/1.07 45 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]. 0.77/1.07 46 (all X is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X))))) <-> axiom_m10 # label(axiom_m10) # label(axiom) # label(non_clause). [assumption]. 0.77/1.07 47 modus_ponens_strict_implies <-> (all X all Y (is_a_theorem(X) & is_a_theorem(strict_implies(X,Y)) -> is_a_theorem(Y))) # label(modus_ponens_strict_implies) # label(axiom) # label(non_clause). [assumption]. 0.77/1.07 48 (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 49 (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 50 (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 51 axiom_M <-> (all X is_a_theorem(implies(necessarily(X),X))) # label(axiom_M) # label(axiom) # label(non_clause). [assumption]. 0.77/1.07 52 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 53 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 54 axiom_m3 <-> (all X all Y all Z is_a_theorem(strict_implies(and(and(X,Y),Z),and(X,and(Y,Z))))) # label(axiom_m3) # 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_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 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]. 0.77/1.07 58 op_possibly -> (all X not(necessarily(not(X))) = possibly(X)) # label(op_possibly) # 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 ============= 0.77/1.07 0.77/1.07 Auto_denials: (non-Horn, no changes). 0.77/1.07 0.77/1.07 Term ordering decisions: 0.77/1.07 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. 0.77/1.07 0.77/1.07 ============================== end of process initial clauses ======== 0.77/1.07 0.77/1.07 ============================== CLAUSES FOR SEARCH ==================== 67.45/67.76 67.45/67.76 ============================== end of clauses for search ============= 67.45/67.76 67.45/67.76 ============================== SEARCH ================================ 67.45/67.76 67.45/67.76 % Starting search at 0.04 seconds. 67.45/67.76 67.45/67.76 Low Water (keep): wt=22.000, iters=3335 67.45/67.76 67.45/67.76 Low Water (keep): wt=21.000, iters=3363 67.45/67.76 67.45/67.76 Low Water (keep): wt=20.000, iters=3355 67.45/67.76 67.45/67.76 Low Water (keep): wt=19.000, iters=3360 67.45/67.76 67.45/67.76 Low Water (keep): wt=18.000, iters=3350 67.45/67.76 67.45/67.76 Low Water (keep): wt=17.000, iters=3367 67.45/67.76 67.45/67.76 Low Water (keep): wt=16.000, iters=3341 67.45/67.76 67.45/67.76 Low Water (keep): wt=15.000, iters=3487 67.45/67.76 67.45/67.76 Low Water (keep): wt=14.000, iters=3462 67.45/67.76 67.45/67.76 Low Water (keep): wt=13.000, iters=3444 67.45/67.76 67.45/67.76 Low Water (keep): wt=12.000, iters=3333 67.45/67.76 67.45/67.76 Low Water (keep): wt=11.000, iters=3356 67.45/67.76 67.45/67.76 Low Water (displace): id=15575, wt=32.000 67.45/67.76 67.45/67.76 Low Water (displace): id=26032, wt=10.000 67.45/67.76 67.45/67.76 Low Water (displace): id=27754, wt=9.000 67.45/67.76 67.45/67.76 Low Water (displace): id=28945, wt=8.000 67.45/67.76 67.45/67.76 Low Water (keep): wt=10.000, iters=3333 67.45/67.76 67.45/67.76 ============================== PROOF ================================= 67.45/67.76 % SZS status Theorem 67.45/67.76 % SZS output start Refutation 67.45/67.76 67.45/67.76 % Proof 1 at 63.56 (+ 3.17) seconds. 67.45/67.76 % Length of proof is 172. 67.45/67.76 % Level of proof is 34. 67.45/67.76 % Maximum clause weight is 20.000. 67.45/67.76 % Given clauses 19256. 67.45/67.76 67.45/67.76 1 (all X all Y is_a_theorem(implies(X,implies(Y,and(X,Y))))) <-> and_3 # label(and_3) # label(axiom) # label(non_clause). [assumption]. 67.45/67.76 3 substitution_of_equivalents <-> (all X all Y (is_a_theorem(equiv(X,Y)) -> X = Y)) # label(substitution_of_equivalents) # label(axiom) # label(non_clause). [assumption]. 67.45/67.76 5 implies_3 <-> (all X all Y all Z is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))) # label(implies_3) # label(axiom) # label(non_clause). [assumption]. 67.45/67.76 8 (all X all Y is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))) <-> equivalence_3 # label(equivalence_3) # label(axiom) # label(non_clause). [assumption]. 67.45/67.76 9 modus_ponens <-> (all X all Y (is_a_theorem(X) & is_a_theorem(implies(X,Y)) -> is_a_theorem(Y))) # label(modus_ponens) # label(axiom) # label(non_clause). [assumption]. 67.45/67.76 11 (all X all Y is_a_theorem(implies(and(X,Y),X))) <-> and_1 # label(and_1) # label(axiom) # label(non_clause). [assumption]. 67.45/67.76 17 implies_2 <-> (all X all Y is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))) # label(implies_2) # label(axiom) # label(non_clause). [assumption]. 67.45/67.76 19 (all X all Y all Z is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))) <-> or_3 # label(or_3) # label(axiom) # label(non_clause). [assumption]. 67.45/67.76 20 (all X all Y is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))) <-> modus_tollens # label(modus_tollens) # label(axiom) # label(non_clause). [assumption]. 67.45/67.76 22 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption]. 67.45/67.76 23 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption]. 67.45/67.76 28 op_or -> (all X all Y or(X,Y) = not(and(not(X),not(Y)))) # label(op_or) # label(axiom) # label(non_clause). [assumption]. 67.45/67.76 29 op_equiv -> (all X all Y equiv(X,Y) = and(implies(X,Y),implies(Y,X))) # label(op_equiv) # label(axiom) # label(non_clause). [assumption]. 67.45/67.76 31 op_implies_and -> (all X all Y implies(X,Y) = not(and(X,not(Y)))) # label(op_implies_and) # label(axiom) # label(non_clause). [assumption]. 67.45/67.76 38 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]. 67.45/67.76 41 necessitation <-> (all X (is_a_theorem(X) -> is_a_theorem(necessarily(X)))) # label(necessitation) # label(axiom) # label(non_clause). [assumption]. 67.45/67.76 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]. 67.45/67.76 60 is_a_theorem(implies(A,implies(B,and(A,B)))) | -and_3 # label(and_3) # label(axiom). [clausify(1)]. 67.45/67.76 63 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(3)]. 67.45/67.76 68 -implies_3 | is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))) # label(implies_3) # label(axiom). [clausify(5)]. 67.45/67.76 75 is_a_theorem(implies(implies(A,B),implies(implies(B,A),equiv(A,B)))) | -equivalence_3 # label(equivalence_3) # label(axiom). [clausify(8)]. 67.45/67.76 76 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(9)]. 67.45/67.76 83 is_a_theorem(implies(and(A,B),A)) | -and_1 # label(and_1) # label(axiom). [clausify(11)]. 67.45/67.76 94 -implies_2 | is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))) # label(implies_2) # label(axiom). [clausify(17)]. 67.45/67.76 99 is_a_theorem(implies(implies(A,B),implies(implies(C,B),implies(or(A,C),B)))) | -or_3 # label(or_3) # label(axiom). [clausify(19)]. 67.45/67.76 101 is_a_theorem(implies(implies(not(A),not(B)),implies(B,A))) | -modus_tollens # label(modus_tollens) # label(axiom). [clausify(20)]. 67.45/67.76 104 -implies_1 | is_a_theorem(implies(A,implies(B,A))) # label(implies_1) # label(axiom). [clausify(22)]. 67.45/67.76 106 -or_1 | is_a_theorem(implies(A,or(A,B))) # label(or_1) # label(axiom). [clausify(23)]. 67.45/67.76 115 -op_or | not(and(not(A),not(B))) = or(A,B) # label(op_or) # label(axiom). [clausify(28)]. 67.45/67.76 116 -op_equiv | equiv(A,B) = and(implies(A,B),implies(B,A)) # label(op_equiv) # label(axiom). [clausify(29)]. 67.45/67.76 117 -op_equiv | and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(116),flip(b)]. 67.45/67.76 119 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(31)]. 67.45/67.76 120 modus_tollens # label(hilbert_modus_tollens) # label(axiom). [assumption]. 67.45/67.76 122 and_1 # label(hilbert_and_1) # label(axiom). [assumption]. 67.45/67.76 123 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption]. 67.45/67.76 124 and_3 # label(hilbert_and_3) # label(axiom). [assumption]. 67.45/67.76 125 implies_1 # label(hilbert_implies_1) # label(axiom). [assumption]. 67.45/67.76 126 or_1 # label(hilbert_or_1) # label(axiom). [assumption]. 67.45/67.76 128 modus_ponens # label(hilbert_modus_ponens) # label(axiom). [assumption]. 67.45/67.76 130 equivalence_3 # label(hilbert_equivalence_3) # label(axiom). [assumption]. 67.45/67.76 131 or_3 # label(hilbert_or_3) # label(axiom). [assumption]. 67.45/67.76 132 implies_2 # label(hilbert_implies_2) # label(axiom). [assumption]. 67.45/67.76 133 op_equiv # label(hilbert_op_equiv) # label(axiom). [assumption]. 67.45/67.76 135 op_implies_and # label(hilbert_op_implies_and) # label(axiom). [assumption]. 67.45/67.76 136 implies_3 # label(hilbert_implies_3) # label(axiom). [assumption]. 67.45/67.76 137 op_or # label(hilbert_op_or) # label(axiom). [assumption]. 67.45/67.76 153 axiom_m1 | -is_a_theorem(strict_implies(and(c66,c67),and(c67,c66))) # label(axiom_m1) # label(axiom). [clausify(38)]. 67.45/67.76 159 -necessitation | -is_a_theorem(A) | is_a_theorem(necessarily(A)) # label(necessitation) # label(axiom). [clausify(41)]. 67.45/67.76 194 -op_strict_implies | necessarily(implies(A,B)) = strict_implies(A,B) # label(op_strict_implies) # label(axiom). [clausify(57)]. 67.45/67.76 200 necessitation # label(km5_necessitation) # label(axiom). [assumption]. 67.45/67.76 202 op_strict_implies # label(s1_0_op_strict_implies) # label(axiom). [assumption]. 67.45/67.76 205 -axiom_m1 # label(s1_0_axiom_m1) # label(negated_conjecture). [assumption]. 67.45/67.76 206 is_a_theorem(implies(implies(not(A),not(B)),implies(B,A))). [back_unit_del(101),unit_del(b,120)]. 67.45/67.76 208 is_a_theorem(implies(and(A,B),A)). [back_unit_del(83),unit_del(b,122)]. 67.45/67.76 209 -is_a_theorem(equiv(A,B)) | B = A. [back_unit_del(63),unit_del(a,123)]. 67.45/67.76 210 is_a_theorem(implies(A,implies(B,and(A,B)))). [back_unit_del(60),unit_del(b,124)]. 67.45/67.76 211 is_a_theorem(implies(A,implies(B,A))). [back_unit_del(104),unit_del(a,125)]. 67.45/67.76 212 is_a_theorem(implies(A,or(A,B))). [back_unit_del(106),unit_del(a,126)]. 67.45/67.76 214 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [back_unit_del(76),unit_del(a,128)]. 67.45/67.76 216 is_a_theorem(implies(implies(A,B),implies(implies(B,A),equiv(A,B)))). [back_unit_del(75),unit_del(b,130)]. 67.45/67.76 217 is_a_theorem(implies(implies(A,B),implies(implies(C,B),implies(or(A,C),B)))). [back_unit_del(99),unit_del(b,131)]. 67.45/67.76 218 is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))). [back_unit_del(94),unit_del(a,132)]. 67.45/67.76 219 and(implies(A,B),implies(B,A)) = equiv(A,B). [back_unit_del(117),unit_del(a,133)]. 67.45/67.76 221 not(and(A,not(B))) = implies(A,B). [back_unit_del(119),unit_del(a,135)]. 67.45/67.76 222 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))). [back_unit_del(68),unit_del(a,136)]. 67.45/67.76 223 implies(not(A),B) = or(A,B). [back_unit_del(115),rewrite([221(5)]),unit_del(a,137)]. 67.45/67.76 228 -is_a_theorem(A) | is_a_theorem(necessarily(A)). [back_unit_del(159),unit_del(a,200)]. 67.45/67.76 230 necessarily(implies(A,B)) = strict_implies(A,B). [back_unit_del(194),unit_del(a,202)]. 67.45/67.76 232 -is_a_theorem(strict_implies(and(c66,c67),and(c67,c66))). [back_unit_del(153),unit_del(a,205)]. 67.45/67.76 236 is_a_theorem(implies(or(A,not(B)),implies(B,A))). [back_rewrite(206),rewrite([223(3)])]. 67.45/67.76 265 -is_a_theorem(A) | is_a_theorem(implies(B,A)). [resolve(214,b,211,a)]. 67.45/67.76 272 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(B,A),equiv(A,B))). [resolve(216,a,214,b)]. 67.45/67.76 275 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(C,B),implies(or(A,C),B))). [resolve(217,a,214,b)]. 67.45/67.76 278 -is_a_theorem(implies(A,implies(A,B))) | is_a_theorem(implies(A,B)). [resolve(218,a,214,b)]. 67.45/67.76 284 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(221(a,1),221(a,1,1,2))]. 67.45/67.76 285 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(B,C),implies(A,C))). [resolve(222,a,214,b)]. 67.45/67.76 290 is_a_theorem(or(A,implies(B,not(A)))). [para(223(a,1),211(a,1))]. 67.45/67.76 291 is_a_theorem(or(A,or(not(A),B))). [para(223(a,1),212(a,1))]. 67.45/67.76 300 and(or(A,B),implies(B,not(A))) = equiv(not(A),B). [para(223(a,1),219(a,1,1))]. 67.45/67.76 301 and(implies(A,not(B)),or(B,A)) = equiv(A,not(B)). [para(223(a,1),219(a,1,2))]. 67.45/67.76 303 or(and(A,not(B)),C) = implies(implies(A,B),C). [para(221(a,1),223(a,1,1)),flip(a)]. 67.45/67.76 360 -is_a_theorem(or(A,not(B))) | is_a_theorem(implies(B,A)). [resolve(236,a,214,b)]. 67.45/67.76 364 is_a_theorem(implies(or(A,not(not(B))),or(B,A))). [para(223(a,1),236(a,1,2))]. 67.45/67.76 2061 is_a_theorem(implies(implies(implies(A,B),implies(A,implies(A,B))),equiv(implies(A,implies(A,B)),implies(A,B)))). [resolve(272,a,218,a)]. 67.45/67.76 2723 is_a_theorem(implies(A,A)). [resolve(278,a,211,a)]. 67.45/67.76 2724 is_a_theorem(implies(A,and(A,A))). [resolve(278,a,210,a)]. 67.45/67.76 2729 is_a_theorem(implies(implies(A,B),implies(or(B,A),B))). [resolve(2723,a,275,a)]. 67.45/67.76 2735 is_a_theorem(implies(A,implies(B,B))). [resolve(2723,a,265,a)]. 67.45/67.76 2756 is_a_theorem(strict_implies(A,A)). [resolve(2723,a,228,a),rewrite([230(2)])]. 67.45/67.76 2768 is_a_theorem(implies(A,strict_implies(B,B))). [resolve(2756,a,265,a)]. 67.45/67.76 2924 is_a_theorem(implies(implies(and(A,A),A),equiv(A,and(A,A)))). [resolve(2724,a,272,a)]. 67.45/67.76 3026 is_a_theorem(implies(implies(implies(A,A),B),equiv(B,implies(A,A)))). [resolve(2735,a,272,a)]. 67.45/67.76 3126 is_a_theorem(implies(implies(strict_implies(A,A),B),equiv(B,strict_implies(A,A)))). [resolve(2768,a,272,a)]. 67.45/67.76 3718 implies(implies(A,and(B,not(C))),D) = or(and(A,implies(B,C)),D). [para(284(a,1),223(a,1,1))]. 67.45/67.76 3874 is_a_theorem(implies(implies(strict_implies(A,A),B),implies(C,B))). [resolve(285,a,2768,a)]. 67.45/67.76 3875 is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))). [resolve(285,a,2735,a)]. 67.45/67.76 3912 is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))). [resolve(285,a,211,a)]. 67.45/67.76 5558 and(or(A,not(B)),or(B,not(A))) = equiv(not(A),not(B)). [para(223(a,1),300(a,1,2))]. 67.45/67.76 14302 -is_a_theorem(or(A,implies(B,C))) | is_a_theorem(implies(and(B,not(C)),A)). [para(221(a,1),360(a,1,2))]. 67.45/67.76 20164 is_a_theorem(equiv(implies(A,implies(A,B)),implies(A,B))). [resolve(2061,a,214,b),unit_del(a,211)]. 67.45/67.76 21105 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(or(B,A),B)). [resolve(2729,a,214,b)]. 67.45/67.76 21140 is_a_theorem(equiv(A,and(A,A))). [resolve(2924,a,214,b),unit_del(a,208)]. 67.45/67.76 21171 and(A,A) = A. [resolve(21140,a,209,a)]. 67.45/67.76 21174 equiv(A,A) = implies(A,A). [para(21171(a,1),219(a,1)),flip(a)]. 67.45/67.76 21175 not(not(A)) = or(A,A). [para(21171(a,1),221(a,1,1)),rewrite([223(4)])]. 67.45/67.76 21178 implies(or(A,A),B) = or(not(A),B). [para(21171(a,1),303(a,1,1)),rewrite([223(4)]),flip(a)]. 67.45/67.76 21213 is_a_theorem(implies(A,not(not(A)))). [para(21175(a,2),212(a,1,2))]. 67.45/67.76 21219 is_a_theorem(or(A,not(not(not(A))))). [para(21175(a,2),291(a,1,2))]. 67.45/67.76 21255 implies(implies(A,B),and(A,not(B))) = not(implies(A,B)). [para(21175(a,2),303(a,1)),rewrite([221(3)]),flip(a)]. 67.45/67.76 21547 -is_a_theorem(A) | is_a_theorem(not(not(A))). [resolve(21213,a,214,b)]. 67.45/67.76 22105 is_a_theorem(not(not(implies(or(A,not(not(B))),or(B,A))))). [resolve(21547,a,364,a)]. 67.45/67.76 22145 is_a_theorem(or(not(A),A)). [resolve(21219,a,360,a),rewrite([223(3)])]. 67.45/67.76 23261 is_a_theorem(implies(implies(strict_implies(A,A),B),B)). [resolve(3874,a,278,a)]. 67.45/67.76 23285 is_a_theorem(implies(implies(implies(A,A),B),B)). [resolve(3875,a,278,a)]. 67.45/67.76 23610 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(B,C)). [resolve(3912,a,214,b)]. 67.45/67.76 23972 -is_a_theorem(implies(strict_implies(A,A),B)) | is_a_theorem(B). [resolve(23261,a,214,b)]. 67.45/67.76 23978 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(B). [resolve(23285,a,214,b)]. 67.45/67.76 36361 is_a_theorem(implies(and(A,not(not(B))),B)). [resolve(14302,a,290,a)]. 67.45/67.76 36441 is_a_theorem(implies(and(A,or(B,B)),B)). [para(21175(a,1),36361(a,1,1,2))]. 67.45/67.76 36526 is_a_theorem(implies(equiv(A,not(A)),A)). [para(301(a,1),36441(a,1,1))]. 67.45/67.76 39215 implies(A,implies(A,B)) = implies(A,B). [resolve(20164,a,209,a),flip(a)]. 67.45/67.76 39344 is_a_theorem(implies(or(A,equiv(A,not(A))),A)). [resolve(21105,a,36526,a)]. 67.45/67.76 40758 is_a_theorem(implies(A,equiv(A,strict_implies(B,B)))). [resolve(23610,a,3126,a)]. 67.45/67.76 40759 is_a_theorem(implies(A,equiv(A,implies(B,B)))). [resolve(23610,a,3026,a)]. 67.45/67.76 40780 is_a_theorem(equiv(implies(A,A),strict_implies(B,B))). [resolve(40758,a,23978,a)]. 67.45/67.76 40787 -is_a_theorem(A) | is_a_theorem(equiv(A,strict_implies(B,B))). [resolve(40758,a,214,b)]. 67.45/67.76 40800 is_a_theorem(equiv(strict_implies(A,A),implies(B,B))). [resolve(40759,a,23972,a)]. 67.45/67.76 40864 strict_implies(A,A) = implies(B,B). [resolve(40780,a,209,a)]. 67.45/67.76 40865 strict_implies(A,A) = c_0. [new_symbol(40864)]. 67.45/67.76 40866 implies(A,A) = c_0. [back_rewrite(40864),rewrite([40865(1)]),flip(a)]. 67.45/67.76 40869 is_a_theorem(c_0). [back_rewrite(40800),rewrite([40865(1),40866(2),21174(3),40866(3)])]. 67.45/67.76 40871 -is_a_theorem(A) | is_a_theorem(equiv(A,c_0)). [back_rewrite(40787),rewrite([40865(2)])]. 67.45/67.76 41459 is_a_theorem(implies(implies(c_0,A),A)). [back_rewrite(23261),rewrite([40865(1)])]. 67.45/67.76 42983 implies(A,c_0) = c_0. [para(40866(a,1),39215(a,1,2)),rewrite([40866(3)])]. 67.45/67.76 43303 and(implies(c_0,A),c_0) = equiv(c_0,A). [para(42983(a,1),219(a,1,2))]. 67.45/67.76 43622 is_a_theorem(equiv(or(not(A),A),c_0)). [resolve(40871,a,22145,a)]. 67.45/67.76 43640 is_a_theorem(equiv(implies(A,not(not(A))),c_0)). [resolve(40871,a,21213,a)]. 67.45/67.76 43698 is_a_theorem(equiv(implies(A,implies(B,A)),c_0)). [resolve(40871,a,211,a)]. 67.45/67.76 43699 is_a_theorem(equiv(implies(and(A,B),A),c_0)). [resolve(40871,a,208,a)]. 67.45/67.76 43812 is_a_theorem(equiv(implies(implies(c_0,A),A),c_0)). [resolve(41459,a,40871,a)]. 67.45/67.76 45497 or(not(A),A) = c_0. [resolve(43622,a,209,a),flip(a)]. 67.45/67.76 46195 implies(A,not(not(A))) = c_0. [resolve(43640,a,209,a),flip(a)]. 67.45/67.76 46197 equiv(A,not(not(A))) = c_0. [para(46195(a,1),219(a,1,1)),rewrite([223(4),45497(3),21171(3)]),flip(a)]. 67.45/67.76 46202 not(not(A)) = A. [para(46197(a,1),209(a,1)),unit_del(a,40869)]. 67.45/67.76 46222 is_a_theorem(implies(or(A,B),or(B,A))). [back_rewrite(22105),rewrite([46202(2),46202(5)])]. 67.45/67.76 46228 or(A,A) = A. [back_rewrite(21175),rewrite([46202(2)]),flip(a)]. 67.45/67.76 46263 or(not(A),B) = implies(A,B). [back_rewrite(21178),rewrite([46228(1)]),flip(a)]. 67.45/67.76 46636 is_a_theorem(implies(implies(A,equiv(not(A),A)),not(A))). [para(46202(a,1),39344(a,1,1,2,2)),rewrite([46263(4)])]. 67.45/67.76 50950 not(implies(A,B)) = and(A,not(B)). [para(46228(a,1),303(a,1)),rewrite([21255(6)]),flip(a)]. 67.45/67.76 50959 equiv(not(A),A) = and(A,not(A)). [para(46228(a,1),5558(a,1,2)),rewrite([46202(2),46228(1),46202(5)]),flip(a)]. 67.45/67.76 51074 is_a_theorem(or(and(A,c_0),not(A))). [back_rewrite(46636),rewrite([50959(2),3718(5),40866(1)])]. 67.45/67.76 54852 is_a_theorem(implies(A,and(A,c_0))). [resolve(51074,a,360,a)]. 67.45/67.76 55021 is_a_theorem(implies(implies(and(A,c_0),A),equiv(A,and(A,c_0)))). [resolve(54852,a,272,a)]. 67.45/67.76 58681 implies(A,implies(B,A)) = c_0. [resolve(43698,a,209,a),flip(a)]. 67.45/67.76 58698 implies(and(A,B),A) = c_0. [resolve(43699,a,209,a),flip(a)]. 67.45/67.76 58701 is_a_theorem(implies(c_0,equiv(A,and(A,c_0)))). [back_rewrite(55021),rewrite([58698(3)])]. 67.45/67.76 58925 implies(implies(c_0,A),A) = c_0. [resolve(43812,a,209,a),flip(a)]. 67.45/67.76 58928 equiv(implies(c_0,A),A) = c_0. [para(58925(a,1),219(a,1,1)),rewrite([58681(4),21171(3)]),flip(a)]. 67.45/67.76 58944 implies(c_0,A) = A. [para(58928(a,1),209(a,1)),flip(b),unit_del(a,40869)]. 67.45/67.76 58961 is_a_theorem(equiv(A,and(A,c_0))). [back_rewrite(58701),rewrite([58944(5)])]. 67.45/67.76 58985 equiv(c_0,A) = and(A,c_0). [back_rewrite(43303),rewrite([58944(2)]),flip(a)]. 67.45/67.76 59406 and(A,c_0) = A. [resolve(58961,a,209,a)]. 67.45/67.76 59416 equiv(c_0,A) = A. [back_rewrite(58985),rewrite([59406(4)])]. 67.45/67.76 59500 -is_a_theorem(A) | c_0 = A. [para(59416(a,1),209(a,1)),flip(b)]. 67.45/67.76 65038 implies(or(A,B),or(B,A)) = c_0. [resolve(46222,a,59500,a),flip(a)]. 67.45/67.76 65040 is_a_theorem(equiv(or(A,B),or(B,A))). [resolve(46222,a,272,a),rewrite([65038(3),58944(5)])]. 67.45/67.76 66340 or(A,B) = or(B,A). [resolve(65040,a,209,a)]. 67.45/67.76 66578 or(A,not(B)) = implies(B,A). [back_rewrite(46263),rewrite([66340(2)])]. 67.45/67.76 69104 and(not(A),not(B)) = not(or(A,B)). [para(223(a,1),50950(a,1,1)),flip(a)]. 67.45/67.76 78910 and(not(A),B) = and(B,not(A)). [para(46202(a,1),69104(a,1,2)),rewrite([66578(4),50950(4)])]. 67.45/67.76 78945 and(A,B) = and(B,A). [para(46202(a,1),78910(a,1,1)),rewrite([46202(3)])]. 67.45/67.76 79155 $F. [back_rewrite(232),rewrite([78945(6),40865(7)]),unit_del(a,40869)]. 67.45/67.76 67.45/67.76 % SZS output end Refutation 67.45/67.76 ============================== end of proof ========================== 67.45/67.76 67.45/67.76 ============================== STATISTICS ============================ 67.45/67.76 67.45/67.76 Given=19256. Generated=6128472. Kept=79092. proofs=1. 67.45/67.76 Usable=4827. Sos=7350. Demods=1070. Limbo=210, Disabled=66851. Hints=0. 67.45/67.76 Megabytes=53.05. 67.45/67.76 User_CPU=63.56, System_CPU=3.17, Wall_clock=66. 67.45/67.76 67.45/67.76 ============================== end of statistics ===================== 67.45/67.76 67.45/67.76 ============================== end of search ========================= 67.45/67.76 67.45/67.76 THEOREM PROVED 67.45/67.76 % SZS status Theorem 67.45/67.76 67.45/67.76 Exiting with 1 proof. 67.45/67.76 67.45/67.76 Process 32558 exit (max_proofs) Thu Aug 29 14:51:23 2019 67.45/67.76 Prover9 interrupted 67.45/67.76 EOF