TSTP Solution File: LCL538+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL538+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 13:47:26 EDT 2022
% Result : Theorem 2.44s 2.78s
% Output : Refutation 2.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL538+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 4 20:57:27 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.46/1.07 ============================== Prover9 ===============================
% 0.46/1.07 Prover9 (32) version 2009-11A, November 2009.
% 0.46/1.07 Process 16923 was started by sandbox on n025.cluster.edu,
% 0.46/1.07 Mon Jul 4 20:57:27 2022
% 0.46/1.07 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_16770_n025.cluster.edu".
% 0.46/1.07 ============================== end of head ===========================
% 0.46/1.07
% 0.46/1.07 ============================== INPUT =================================
% 0.46/1.07
% 0.46/1.07 % Reading from file /tmp/Prover9_16770_n025.cluster.edu
% 0.46/1.07
% 0.46/1.07 set(prolog_style_variables).
% 0.46/1.07 set(auto2).
% 0.46/1.07 % set(auto2) -> set(auto).
% 0.46/1.07 % set(auto) -> set(auto_inference).
% 0.46/1.07 % set(auto) -> set(auto_setup).
% 0.46/1.07 % set(auto_setup) -> set(predicate_elim).
% 0.46/1.07 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.46/1.07 % set(auto) -> set(auto_limits).
% 0.46/1.07 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.46/1.07 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.46/1.07 % set(auto) -> set(auto_denials).
% 0.46/1.07 % set(auto) -> set(auto_process).
% 0.46/1.07 % set(auto2) -> assign(new_constants, 1).
% 0.46/1.07 % set(auto2) -> assign(fold_denial_max, 3).
% 0.46/1.07 % set(auto2) -> assign(max_weight, "200.000").
% 0.46/1.07 % set(auto2) -> assign(max_hours, 1).
% 0.46/1.07 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.46/1.07 % set(auto2) -> assign(max_seconds, 0).
% 0.46/1.07 % set(auto2) -> assign(max_minutes, 5).
% 0.46/1.07 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.46/1.07 % set(auto2) -> set(sort_initial_sos).
% 0.46/1.07 % set(auto2) -> assign(sos_limit, -1).
% 0.46/1.07 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.46/1.07 % set(auto2) -> assign(max_megs, 400).
% 0.46/1.07 % set(auto2) -> assign(stats, some).
% 0.46/1.07 % set(auto2) -> clear(echo_input).
% 0.46/1.07 % set(auto2) -> set(quiet).
% 0.46/1.07 % set(auto2) -> clear(print_initial_clauses).
% 0.46/1.07 % set(auto2) -> clear(print_given).
% 0.46/1.07 assign(lrs_ticks,-1).
% 0.46/1.07 assign(sos_limit,10000).
% 0.46/1.07 assign(order,kbo).
% 0.46/1.07 set(lex_order_vars).
% 0.46/1.07 clear(print_given).
% 0.46/1.07
% 0.46/1.07 % formulas(sos). % not echoed (89 formulas)
% 0.46/1.07
% 0.46/1.07 ============================== end of input ==========================
% 0.46/1.07
% 0.46/1.07 % From the command line: assign(max_seconds, 300).
% 0.46/1.07
% 0.46/1.07 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.46/1.07
% 0.46/1.07 % Formulas that are not ordinary clauses:
% 0.46/1.07 1 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].
% 0.46/1.07 2 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].
% 0.46/1.07 3 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].
% 0.46/1.07 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 5 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].
% 0.46/1.07 6 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].
% 0.46/1.07 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 9 and_3 <-> (all X all Y is_a_theorem(implies(X,implies(Y,and(X,Y))))) # label(and_3) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 12 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].
% 0.46/1.07 13 equivalence_1 <-> (all X all Y is_a_theorem(implies(equiv(X,Y),implies(X,Y)))) # label(equivalence_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 14 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].
% 0.46/1.07 15 equivalence_3 <-> (all X all Y is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))) # label(equivalence_3) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 18 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].
% 0.46/1.07 19 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].
% 0.46/1.07 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 25 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].
% 0.46/1.07 26 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].
% 0.46/1.07 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].
% 0.46/1.07 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].
% 0.46/1.07 29 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].
% 0.46/1.07 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].
% 0.46/1.07 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].
% 0.46/1.07 32 necessitation <-> (all X (is_a_theorem(X) -> is_a_theorem(necessarily(X)))) # label(necessitation) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 33 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].
% 0.46/1.07 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].
% 0.46/1.07 35 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].
% 0.46/1.07 36 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].
% 0.46/1.07 37 axiom_M <-> (all X is_a_theorem(implies(necessarily(X),X))) # label(axiom_M) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 38 axiom_4 <-> (all X is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))) # label(axiom_4) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 39 axiom_B <-> (all X is_a_theorem(implies(X,necessarily(possibly(X))))) # label(axiom_B) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 40 axiom_5 <-> (all X is_a_theorem(implies(possibly(X),necessarily(possibly(X))))) # label(axiom_5) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.07 41 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].
% 0.83/1.10 42 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].
% 0.83/1.10 43 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].
% 0.83/1.10 44 axiom_s4 <-> (all X is_a_theorem(strict_implies(necessarily(X),necessarily(necessarily(X))))) # label(axiom_s4) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 45 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].
% 0.83/1.10 46 axiom_m2 <-> (all X all Y is_a_theorem(strict_implies(and(X,Y),X))) # label(axiom_m2) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 47 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].
% 0.83/1.10 48 axiom_m4 <-> (all X is_a_theorem(strict_implies(X,and(X,X)))) # label(axiom_m4) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 49 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].
% 0.83/1.10 50 axiom_m6 <-> (all X is_a_theorem(strict_implies(X,possibly(X)))) # label(axiom_m6) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 51 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].
% 0.83/1.10 52 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].
% 0.83/1.10 53 axiom_m9 <-> (all X is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X)))) # label(axiom_m9) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 54 axiom_m10 <-> (all X is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X))))) # label(axiom_m10) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 55 op_possibly -> (all X possibly(X) = not(necessarily(not(X)))) # label(op_possibly) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 56 op_necessarily -> (all X necessarily(X) = not(possibly(not(X)))) # label(op_necessarily) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 57 op_strict_implies -> (all X all Y strict_implies(X,Y) = necessarily(implies(X,Y))) # label(op_strict_implies) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10 58 op_strict_equiv -> (all X all Y strict_equiv(X,Y) = and(strict_implies(X,Y),strict_implies(Y,X))) # label(op_strict_equiv) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.10
% 0.83/1.10 ============================== end of process non-clausal formulas ===
% 0.83/1.10
% 0.83/1.10 ============================== PROCESS INITIAL CLAUSES ===============
% 0.83/1.10
% 0.83/1.10 ============================== PREDICATE ELIMINATION =================
% 0.83/1.10
% 0.83/1.10 ============================== end predicate elimination =============
% 0.83/1.10
% 0.83/1.10 Auto_denials: (non-Horn, no changes).
% 0.83/1.10
% 0.83/1.10 Term ordering decisions:
% 0.83/1.10 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.
% 0.83/1.10
% 0.83/1.10 ============================== end of process initial clauses ========
% 0.83/1.10
% 0.83/1.10 ============================== CLAUSES FOR SEARCH ====================
% 2.44/2.78
% 2.44/2.78 ============================== end of clauses for search =============
% 2.44/2.78
% 2.44/2.78 ============================== SEARCH ================================
% 2.44/2.78
% 2.44/2.78 % Starting search at 0.05 seconds.
% 2.44/2.78
% 2.44/2.78 Low Water (keep): wt=21.000, iters=3373
% 2.44/2.78
% 2.44/2.78 Low Water (keep): wt=19.000, iters=3344
% 2.44/2.78
% 2.44/2.78 Low Water (keep): wt=17.000, iters=3333
% 2.44/2.78
% 2.44/2.78 Low Water (keep): wt=16.000, iters=3357
% 2.44/2.78
% 2.44/2.78 Low Water (keep): wt=15.000, iters=3373
% 2.44/2.78
% 2.44/2.78 Low Water (keep): wt=14.000, iters=3356
% 2.44/2.78
% 2.44/2.78 Low Water (keep): wt=13.000, iters=3406
% 2.44/2.78
% 2.44/2.78 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 68 (0.00 of 1.70 sec).
% 2.44/2.78
% 2.44/2.78 ============================== PROOF =================================
% 2.44/2.78 % SZS status Theorem
% 2.44/2.78 % SZS output start Refutation
% 2.44/2.78
% 2.44/2.78 % Proof 1 at 1.71 (+ 0.02) seconds.
% 2.44/2.78 % Length of proof is 36.
% 2.44/2.78 % Level of proof is 8.
% 2.44/2.78 % Maximum clause weight is 12.000.
% 2.44/2.78 % Given clauses 514.
% 2.44/2.78
% 2.44/2.78 1 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].
% 2.44/2.78 32 necessitation <-> (all X (is_a_theorem(X) -> is_a_theorem(necessarily(X)))) # label(necessitation) # label(axiom) # label(non_clause). [assumption].
% 2.44/2.78 33 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].
% 2.44/2.78 36 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].
% 2.44/2.78 37 axiom_M <-> (all X is_a_theorem(implies(necessarily(X),X))) # label(axiom_M) # label(axiom) # label(non_clause). [assumption].
% 2.44/2.78 57 op_strict_implies -> (all X all Y strict_implies(X,Y) = necessarily(implies(X,Y))) # label(op_strict_implies) # label(axiom) # label(non_clause). [assumption].
% 2.44/2.78 59 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 2.44/2.78 124 modus_ponens # label(hilbert_modus_ponens) # label(axiom). [assumption].
% 2.44/2.78 139 -necessitation | -is_a_theorem(A) | is_a_theorem(necessarily(A)) # label(necessitation) # label(axiom). [clausify(32)].
% 2.44/2.78 143 modus_ponens_strict_implies | is_a_theorem(c57) # label(modus_ponens_strict_implies) # label(axiom). [clausify(33)].
% 2.44/2.78 144 modus_ponens_strict_implies | is_a_theorem(strict_implies(c57,c58)) # label(modus_ponens_strict_implies) # label(axiom). [clausify(33)].
% 2.44/2.78 145 modus_ponens_strict_implies | -is_a_theorem(c58) # label(modus_ponens_strict_implies) # label(axiom). [clausify(33)].
% 2.44/2.78 153 -axiom_K | is_a_theorem(implies(necessarily(implies(A,B)),implies(necessarily(A),necessarily(B)))) # label(axiom_K) # label(axiom). [clausify(36)].
% 2.44/2.78 155 -axiom_M | is_a_theorem(implies(necessarily(A),A)) # label(axiom_M) # label(axiom). [clausify(37)].
% 2.44/2.78 195 -op_strict_implies | strict_implies(A,B) = necessarily(implies(A,B)) # label(op_strict_implies) # label(axiom). [clausify(57)].
% 2.44/2.78 196 -op_strict_implies | necessarily(implies(A,B)) = strict_implies(A,B). [copy(195),flip(b)].
% 2.44/2.78 200 necessitation # label(km4b_necessitation) # label(axiom). [assumption].
% 2.44/2.78 201 axiom_K # label(km4b_axiom_K) # label(axiom). [assumption].
% 2.44/2.78 202 axiom_M # label(km4b_axiom_M) # label(axiom). [assumption].
% 2.44/2.78 206 op_strict_implies # label(s1_0_op_strict_implies) # label(axiom). [assumption].
% 2.44/2.78 208 -modus_ponens_strict_implies # label(s1_0_modus_ponens_strict_implies) # label(negated_conjecture). [assumption].
% 2.44/2.78 212 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [back_unit_del(59),unit_del(a,124)].
% 2.44/2.78 229 -is_a_theorem(A) | is_a_theorem(necessarily(A)). [back_unit_del(139),unit_del(a,200)].
% 2.44/2.78 230 is_a_theorem(implies(necessarily(implies(A,B)),implies(necessarily(A),necessarily(B)))). [back_unit_del(153),unit_del(a,201)].
% 2.44/2.78 231 is_a_theorem(implies(necessarily(A),A)). [back_unit_del(155),unit_del(a,202)].
% 2.44/2.78 234 necessarily(implies(A,B)) = strict_implies(A,B). [back_unit_del(196),unit_del(a,206)].
% 2.44/2.78 236 -is_a_theorem(c58). [back_unit_del(145),unit_del(a,208)].
% 2.44/2.78 237 is_a_theorem(strict_implies(c57,c58)). [back_unit_del(144),unit_del(a,208)].
% 2.44/2.78 238 is_a_theorem(c57). [back_unit_del(143),unit_del(a,208)].
% 2.44/2.78 243 is_a_theorem(implies(strict_implies(A,B),implies(necessarily(A),necessarily(B)))). [back_rewrite(230),rewrite([234(2)])].
% 2.44/2.78 325 -is_a_theorem(necessarily(A)) | is_a_theorem(A). [resolve(231,a,212,b)].
% 2.44/2.78 347 is_a_theorem(necessarily(c57)). [resolve(238,a,229,a)].
% 2.44/2.78 374 -is_a_theorem(strict_implies(A,B)) | is_a_theorem(implies(necessarily(A),necessarily(B))). [resolve(243,a,212,b)].
% 2.44/2.78 9734 is_a_theorem(implies(necessarily(c57),necessarily(c58))). [resolve(374,a,237,a)].
% 2.44/2.78 9752 is_a_theorem(necessarily(c58)). [resolve(9734,a,212,b),unit_del(a,347)].
% 2.44/2.78 9767 $F. [resolve(9752,a,325,a),unit_del(a,236)].
% 2.44/2.78
% 2.44/2.78 % SZS output end Refutation
% 2.44/2.78 ============================== end of proof ==========================
% 2.44/2.78
% 2.44/2.78 ============================== STATISTICS ============================
% 2.44/2.78
% 2.44/2.78 Given=514. Generated=16879. Kept=9702. proofs=1.
% 2.44/2.78 Usable=501. Sos=9003. Demods=25. Limbo=12, Disabled=333. Hints=0.
% 2.44/2.78 Megabytes=12.76.
% 2.44/2.78 User_CPU=1.71, System_CPU=0.02, Wall_clock=2.
% 2.44/2.78
% 2.44/2.78 ============================== end of statistics =====================
% 2.44/2.78
% 2.44/2.78 ============================== end of search =========================
% 2.44/2.78
% 2.44/2.78 THEOREM PROVED
% 2.44/2.78 % SZS status Theorem
% 2.44/2.78
% 2.44/2.78 Exiting with 1 proof.
% 2.44/2.78
% 2.44/2.78 Process 16923 exit (max_proofs) Mon Jul 4 20:57:29 2022
% 2.44/2.78 Prover9 interrupted
%------------------------------------------------------------------------------