TSTP Solution File: LCL526+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL526+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n028.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 13:47:22 EDT 2022
% Result : Theorem 3.90s 4.19s
% Output : Refutation 3.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL526+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.32 % Computer : n028.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Sun Jul 3 22:02:04 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.41/1.00 ============================== Prover9 ===============================
% 0.41/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.41/1.00 Process 3381 was started by sandbox on n028.cluster.edu,
% 0.41/1.00 Sun Jul 3 22:02:04 2022
% 0.41/1.00 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_3228_n028.cluster.edu".
% 0.41/1.00 ============================== end of head ===========================
% 0.41/1.00
% 0.41/1.00 ============================== INPUT =================================
% 0.41/1.00
% 0.41/1.00 % Reading from file /tmp/Prover9_3228_n028.cluster.edu
% 0.41/1.00
% 0.41/1.00 set(prolog_style_variables).
% 0.41/1.00 set(auto2).
% 0.41/1.00 % set(auto2) -> set(auto).
% 0.41/1.00 % set(auto) -> set(auto_inference).
% 0.41/1.00 % set(auto) -> set(auto_setup).
% 0.41/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.41/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.41/1.00 % set(auto) -> set(auto_limits).
% 0.41/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.41/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.41/1.00 % set(auto) -> set(auto_denials).
% 0.41/1.00 % set(auto) -> set(auto_process).
% 0.41/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.41/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.41/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.41/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.41/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.41/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.41/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.41/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.41/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.41/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.41/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.41/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.41/1.00 % set(auto2) -> assign(stats, some).
% 0.41/1.00 % set(auto2) -> clear(echo_input).
% 0.41/1.00 % set(auto2) -> set(quiet).
% 0.41/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.41/1.00 % set(auto2) -> clear(print_given).
% 0.41/1.00 assign(lrs_ticks,-1).
% 0.41/1.00 assign(sos_limit,10000).
% 0.41/1.00 assign(order,kbo).
% 0.41/1.00 set(lex_order_vars).
% 0.41/1.00 clear(print_given).
% 0.41/1.00
% 0.41/1.00 % formulas(sos). % not echoed (88 formulas)
% 0.41/1.00
% 0.41/1.00 ============================== end of input ==========================
% 0.41/1.00
% 0.41/1.00 % From the command line: assign(max_seconds, 300).
% 0.41/1.00
% 0.41/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.41/1.00
% 0.41/1.00 % Formulas that are not ordinary clauses:
% 0.41/1.00 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].
% 0.41/1.00 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].
% 0.41/1.00 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].
% 0.41/1.00 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 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].
% 0.41/1.00 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].
% 0.41/1.00 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 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].
% 0.41/1.00 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 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].
% 0.41/1.00 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].
% 0.41/1.00 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].
% 0.41/1.00 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].
% 0.41/1.00 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 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].
% 0.41/1.00 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].
% 0.41/1.00 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 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].
% 0.41/1.00 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].
% 0.41/1.00 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].
% 0.41/1.00 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].
% 0.41/1.00 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].
% 0.41/1.00 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].
% 0.41/1.00 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].
% 0.41/1.00 32 necessitation <-> (all X (is_a_theorem(X) -> is_a_theorem(necessarily(X)))) # label(necessitation) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 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].
% 0.41/1.00 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].
% 0.41/1.00 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].
% 0.41/1.00 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].
% 0.41/1.00 37 axiom_M <-> (all X is_a_theorem(implies(necessarily(X),X))) # label(axiom_M) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 38 axiom_4 <-> (all X is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))) # label(axiom_4) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 39 axiom_B <-> (all X is_a_theorem(implies(X,necessarily(possibly(X))))) # label(axiom_B) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 40 axiom_5 <-> (all X is_a_theorem(implies(possibly(X),necessarily(possibly(X))))) # label(axiom_5) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.00 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].
% 0.41/1.03 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].
% 0.41/1.03 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].
% 0.41/1.03 44 axiom_s4 <-> (all X is_a_theorem(strict_implies(necessarily(X),necessarily(necessarily(X))))) # label(axiom_s4) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 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].
% 0.41/1.03 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].
% 0.41/1.03 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].
% 0.41/1.03 48 axiom_m4 <-> (all X is_a_theorem(strict_implies(X,and(X,X)))) # label(axiom_m4) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 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].
% 0.41/1.03 50 axiom_m6 <-> (all X is_a_theorem(strict_implies(X,possibly(X)))) # label(axiom_m6) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 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].
% 0.41/1.03 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].
% 0.41/1.03 53 axiom_m9 <-> (all X is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X)))) # label(axiom_m9) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 54 axiom_m10 <-> (all X is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X))))) # label(axiom_m10) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 55 op_possibly -> (all X possibly(X) = not(necessarily(not(X)))) # label(op_possibly) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 56 op_necessarily -> (all X necessarily(X) = not(possibly(not(X)))) # label(op_necessarily) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 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].
% 0.41/1.03 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].
% 0.41/1.03
% 0.41/1.03 ============================== end of process non-clausal formulas ===
% 0.41/1.03
% 0.41/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.41/1.03
% 0.41/1.03 ============================== PREDICATE ELIMINATION =================
% 0.41/1.03
% 0.41/1.03 ============================== end predicate elimination =============
% 0.41/1.03
% 0.41/1.03 Auto_denials: (non-Horn, no changes).
% 0.41/1.03
% 0.41/1.03 Term ordering decisions:
% 0.41/1.03 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.
% 0.41/1.03
% 0.41/1.03 ============================== end of process initial clauses ========
% 0.41/1.03
% 0.41/1.03 ============================== CLAUSES FOR SEARCH ====================
% 0.41/1.03
% 3.90/4.19 ============================== end of clauses for search =============
% 3.90/4.19
% 3.90/4.19 ============================== SEARCH ================================
% 3.90/4.19
% 3.90/4.19 % Starting search at 0.05 seconds.
% 3.90/4.19
% 3.90/4.19 Low Water (keep): wt=22.000, iters=3392
% 3.90/4.19
% 3.90/4.19 Low Water (keep): wt=21.000, iters=3420
% 3.90/4.19
% 3.90/4.19 Low Water (keep): wt=20.000, iters=3350
% 3.90/4.19
% 3.90/4.19 Low Water (keep): wt=19.000, iters=3333
% 3.90/4.19
% 3.90/4.19 Low Water (keep): wt=18.000, iters=3335
% 3.90/4.19
% 3.90/4.19 Low Water (keep): wt=16.000, iters=3345
% 3.90/4.19
% 3.90/4.19 Low Water (keep): wt=15.000, iters=3335
% 3.90/4.19
% 3.90/4.19 Low Water (keep): wt=14.000, iters=3368
% 3.90/4.19
% 3.90/4.19 Low Water (keep): wt=13.000, iters=3341
% 3.90/4.19
% 3.90/4.19 Low Water (keep): wt=12.000, iters=3426
% 3.90/4.19
% 3.90/4.19 ============================== PROOF =================================
% 3.90/4.19 % SZS status Theorem
% 3.90/4.19 % SZS output start Refutation
% 3.90/4.19
% 3.90/4.19 % Proof 1 at 3.18 (+ 0.03) seconds.
% 3.90/4.19 % Length of proof is 54.
% 3.90/4.19 % Level of proof is 9.
% 3.90/4.19 % Maximum clause weight is 13.000.
% 3.90/4.19 % Given clauses 859.
% 3.90/4.19
% 3.90/4.19 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].
% 3.90/4.19 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].
% 3.90/4.19 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 3.90/4.19 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 3.90/4.19 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].
% 3.90/4.19 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].
% 3.90/4.19 37 axiom_M <-> (all X is_a_theorem(implies(necessarily(X),X))) # label(axiom_M) # label(axiom) # label(non_clause). [assumption].
% 3.90/4.19 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].
% 3.90/4.19 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].
% 3.90/4.19 59 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 3.90/4.19 63 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(2)].
% 3.90/4.19 74 -and_1 | is_a_theorem(implies(and(A,B),A)) # label(and_1) # label(axiom). [clausify(7)].
% 3.90/4.19 76 -and_2 | is_a_theorem(implies(and(A,B),B)) # label(and_2) # label(axiom). [clausify(8)].
% 3.90/4.19 90 -equivalence_3 | is_a_theorem(implies(implies(A,B),implies(implies(B,A),equiv(A,B)))) # label(equivalence_3) # label(axiom). [clausify(15)].
% 3.90/4.19 124 modus_ponens # label(hilbert_modus_ponens) # label(axiom). [assumption].
% 3.90/4.19 129 and_1 # label(hilbert_and_1) # label(axiom). [assumption].
% 3.90/4.19 130 and_2 # label(hilbert_and_2) # label(axiom). [assumption].
% 3.90/4.19 137 equivalence_3 # label(hilbert_equivalence_3) # label(axiom). [assumption].
% 3.90/4.19 138 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption].
% 3.90/4.19 151 substitution_strict_equiv | is_a_theorem(strict_equiv(c61,c62)) # label(substitution_strict_equiv) # label(axiom). [clausify(35)].
% 3.90/4.19 152 substitution_strict_equiv | c62 != c61 # label(substitution_strict_equiv) # label(axiom). [clausify(35)].
% 3.90/4.19 155 -axiom_M | is_a_theorem(implies(necessarily(A),A)) # label(axiom_M) # label(axiom). [clausify(37)].
% 3.90/4.19 195 -op_strict_implies | strict_implies(A,B) = necessarily(implies(A,B)) # label(op_strict_implies) # label(axiom). [clausify(57)].
% 3.90/4.19 196 -op_strict_implies | necessarily(implies(A,B)) = strict_implies(A,B). [copy(195),flip(b)].
% 3.90/4.19 197 -op_strict_equiv | strict_equiv(A,B) = and(strict_implies(A,B),strict_implies(B,A)) # label(op_strict_equiv) # label(axiom). [clausify(58)].
% 3.90/4.19 198 -op_strict_equiv | and(strict_implies(A,B),strict_implies(B,A)) = strict_equiv(A,B). [copy(197),flip(b)].
% 3.90/4.19 202 axiom_M # label(km5_axiom_M) # label(axiom). [assumption].
% 3.90/4.19 205 op_strict_implies # label(s1_0_op_strict_implies) # label(axiom). [assumption].
% 3.90/4.19 206 op_strict_equiv # label(s1_0_op_strict_equiv) # label(axiom). [assumption].
% 3.90/4.19 207 -substitution_strict_equiv # label(s1_0_substitution_strict_equiv) # label(negated_conjecture). [assumption].
% 3.90/4.19 211 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [back_unit_del(59),unit_del(a,124)].
% 3.90/4.19 216 is_a_theorem(implies(and(A,B),A)). [back_unit_del(74),unit_del(a,129)].
% 3.90/4.19 217 is_a_theorem(implies(and(A,B),B)). [back_unit_del(76),unit_del(a,130)].
% 3.90/4.19 224 is_a_theorem(implies(implies(A,B),implies(implies(B,A),equiv(A,B)))). [back_unit_del(90),unit_del(a,137)].
% 3.90/4.19 225 -is_a_theorem(equiv(A,B)) | B = A. [back_unit_del(63),unit_del(a,138)].
% 3.90/4.19 230 is_a_theorem(implies(necessarily(A),A)). [back_unit_del(155),unit_del(a,202)].
% 3.90/4.19 232 necessarily(implies(A,B)) = strict_implies(A,B). [back_unit_del(196),unit_del(a,205)].
% 3.90/4.19 233 and(strict_implies(A,B),strict_implies(B,A)) = strict_equiv(A,B). [back_unit_del(198),unit_del(a,206)].
% 3.90/4.19 234 c62 != c61. [back_unit_del(152),unit_del(a,207)].
% 3.90/4.19 235 is_a_theorem(strict_equiv(c61,c62)). [back_unit_del(151),unit_del(a,207)].
% 3.90/4.19 263 -is_a_theorem(and(A,B)) | is_a_theorem(A). [resolve(216,a,211,b)].
% 3.90/4.19 266 -is_a_theorem(and(A,B)) | is_a_theorem(B). [resolve(217,a,211,b)].
% 3.90/4.19 287 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(B,A),equiv(A,B))). [resolve(224,a,211,b)].
% 3.90/4.19 326 -is_a_theorem(necessarily(A)) | is_a_theorem(A). [resolve(230,a,211,b)].
% 3.90/4.19 428 -is_a_theorem(strict_implies(A,B)) | is_a_theorem(implies(A,B)). [para(232(a,1),326(a,1))].
% 3.90/4.19 582 -is_a_theorem(strict_equiv(A,B)) | is_a_theorem(strict_implies(A,B)). [para(233(a,1),263(a,1))].
% 3.90/4.19 583 -is_a_theorem(strict_equiv(A,B)) | is_a_theorem(strict_implies(B,A)). [para(233(a,1),266(a,1))].
% 3.90/4.19 14575 is_a_theorem(strict_implies(c61,c62)). [resolve(582,a,235,a)].
% 3.90/4.19 14577 is_a_theorem(implies(c61,c62)). [resolve(14575,a,428,a)].
% 3.90/4.19 14585 is_a_theorem(implies(implies(c62,c61),equiv(c61,c62))). [resolve(14577,a,287,a)].
% 3.90/4.19 14826 is_a_theorem(strict_implies(c62,c61)). [resolve(583,a,235,a)].
% 3.90/4.19 14828 is_a_theorem(implies(c62,c61)). [resolve(14826,a,428,a)].
% 3.90/4.19 19996 is_a_theorem(equiv(c61,c62)). [resolve(14585,a,211,b),unit_del(a,14828)].
% 3.90/4.19 20015 $F. [resolve(19996,a,225,a),unit_del(a,234)].
% 3.90/4.19
% 3.90/4.19 % SZS output end Refutation
% 3.90/4.19 ============================== end of proof ==========================
% 3.90/4.19
% 3.90/4.19 ============================== STATISTICS ============================
% 3.90/4.19
% 3.90/4.19 Given=859. Generated=30212. Kept=19950. proofs=1.
% 3.90/4.19 Usable=604. Sos=9390. Demods=76. Limbo=18, Disabled=10084. Hints=0.
% 3.90/4.19 Megabytes=17.73.
% 3.90/4.19 User_CPU=3.18, System_CPU=0.03, Wall_clock=3.
% 3.90/4.19
% 3.90/4.19 ============================== end of statistics =====================
% 3.90/4.19
% 3.90/4.19 ============================== end of search =========================
% 3.90/4.19
% 3.90/4.19 THEOREM PROVED
% 3.90/4.19 % SZS status Theorem
% 3.90/4.19
% 3.90/4.19 Exiting with 1 proof.
% 3.90/4.19
% 3.90/4.19 Process 3381 exit (max_proofs) Sun Jul 3 22:02:07 2022
% 3.90/4.19 Prover9 interrupted
%------------------------------------------------------------------------------