TSTP Solution File: LCL551+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL551+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n015.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 13:47:31 EDT 2022
% Result : Theorem 246.32s 246.68s
% Output : Refutation 246.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL551+1 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n015.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 : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 3 15:48:00 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.41/1.04 ============================== Prover9 ===============================
% 0.41/1.04 Prover9 (32) version 2009-11A, November 2009.
% 0.41/1.04 Process 4666 was started by sandbox on n015.cluster.edu,
% 0.41/1.04 Sun Jul 3 15:48:01 2022
% 0.41/1.04 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_4513_n015.cluster.edu".
% 0.41/1.04 ============================== end of head ===========================
% 0.41/1.04
% 0.41/1.04 ============================== INPUT =================================
% 0.41/1.04
% 0.41/1.04 % Reading from file /tmp/Prover9_4513_n015.cluster.edu
% 0.41/1.04
% 0.41/1.04 set(prolog_style_variables).
% 0.41/1.04 set(auto2).
% 0.41/1.04 % set(auto2) -> set(auto).
% 0.41/1.04 % set(auto) -> set(auto_inference).
% 0.41/1.04 % set(auto) -> set(auto_setup).
% 0.41/1.04 % set(auto_setup) -> set(predicate_elim).
% 0.41/1.04 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.41/1.04 % set(auto) -> set(auto_limits).
% 0.41/1.04 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.41/1.04 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.41/1.04 % set(auto) -> set(auto_denials).
% 0.41/1.04 % set(auto) -> set(auto_process).
% 0.41/1.04 % set(auto2) -> assign(new_constants, 1).
% 0.41/1.04 % set(auto2) -> assign(fold_denial_max, 3).
% 0.41/1.04 % set(auto2) -> assign(max_weight, "200.000").
% 0.41/1.04 % set(auto2) -> assign(max_hours, 1).
% 0.41/1.04 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.41/1.04 % set(auto2) -> assign(max_seconds, 0).
% 0.41/1.04 % set(auto2) -> assign(max_minutes, 5).
% 0.41/1.04 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.41/1.04 % set(auto2) -> set(sort_initial_sos).
% 0.41/1.04 % set(auto2) -> assign(sos_limit, -1).
% 0.41/1.04 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.41/1.04 % set(auto2) -> assign(max_megs, 400).
% 0.41/1.04 % set(auto2) -> assign(stats, some).
% 0.41/1.04 % set(auto2) -> clear(echo_input).
% 0.41/1.04 % set(auto2) -> set(quiet).
% 0.41/1.04 % set(auto2) -> clear(print_initial_clauses).
% 0.41/1.04 % set(auto2) -> clear(print_given).
% 0.41/1.04 assign(lrs_ticks,-1).
% 0.41/1.04 assign(sos_limit,10000).
% 0.41/1.04 assign(order,kbo).
% 0.41/1.04 set(lex_order_vars).
% 0.41/1.04 clear(print_given).
% 0.41/1.04
% 0.41/1.04 % formulas(sos). % not echoed (77 formulas)
% 0.41/1.04
% 0.41/1.04 ============================== end of input ==========================
% 0.41/1.04
% 0.41/1.04 % From the command line: assign(max_seconds, 300).
% 0.41/1.04
% 0.41/1.04 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.41/1.04
% 0.41/1.04 % Formulas that are not ordinary clauses:
% 0.41/1.04 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].
% 0.41/1.04 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].
% 0.41/1.04 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].
% 0.41/1.04 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.04 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].
% 0.41/1.04 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].
% 0.41/1.04 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.04 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.04 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].
% 0.41/1.04 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.04 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.04 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].
% 0.41/1.04 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].
% 0.41/1.04 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].
% 0.41/1.04 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].
% 0.41/1.04 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.04 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.04 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].
% 0.41/1.04 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].
% 0.41/1.04 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.04 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.04 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.04 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.04 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.04 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].
% 0.41/1.04 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].
% 0.41/1.04 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].
% 0.41/1.04 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].
% 0.41/1.04 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].
% 0.41/1.04 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].
% 0.41/1.04 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].
% 0.41/1.04 32 necessitation <-> (all X (is_a_theorem(X) -> is_a_theorem(necessarily(X)))) # label(necessitation) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.04 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].
% 0.41/1.04 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].
% 0.41/1.04 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].
% 0.41/1.04 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].
% 0.41/1.04 37 axiom_M <-> (all X is_a_theorem(implies(necessarily(X),X))) # label(axiom_M) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.04 38 axiom_4 <-> (all X is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))) # label(axiom_4) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.04 39 axiom_B <-> (all X is_a_theorem(implies(X,necessarily(possibly(X))))) # label(axiom_B) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.04 40 axiom_5 <-> (all X is_a_theorem(implies(possibly(X),necessarily(possibly(X))))) # label(axiom_5) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.04 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 44 axiom_s4 <-> (all X is_a_theorem(strict_implies(necessarily(X),necessarily(necessarily(X))))) # label(axiom_s4) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 48 axiom_m4 <-> (all X is_a_theorem(strict_implies(X,and(X,X)))) # label(axiom_m4) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.07 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].
% 0.41/1.07 50 axiom_m6 <-> (all X is_a_theorem(strict_implies(X,possibly(X)))) # label(axiom_m6) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07 53 axiom_m9 <-> (all X is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X)))) # label(axiom_m9) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.07 54 axiom_m10 <-> (all X is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X))))) # label(axiom_m10) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.07 55 op_possibly -> (all X possibly(X) = not(necessarily(not(X)))) # label(op_possibly) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.07 56 op_necessarily -> (all X necessarily(X) = not(possibly(not(X)))) # label(op_necessarily) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.07 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].
% 0.41/1.07 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].
% 0.41/1.07
% 0.41/1.07 ============================== end of process non-clausal formulas ===
% 0.41/1.07
% 0.41/1.07 ============================== PROCESS INITIAL CLAUSES ===============
% 0.41/1.07
% 0.41/1.07 ============================== PREDICATE ELIMINATION =================
% 0.41/1.07
% 0.41/1.07 ============================== end predicate elimination =============
% 0.41/1.07
% 0.41/1.07 Auto_denials: (non-Horn, no changes).
% 0.41/1.07
% 0.41/1.07 Term ordering decisions:
% 0.41/1.07 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.
% 0.41/1.07
% 0.41/1.07 ============================== end of process initial clauses ========
% 0.41/1.07
% 0.41/1.07 ============================== CLAUSES FOR SEARCH ====================
% 0.41/1.07
% 246.32/246.68 ============================== end of clauses for search =============
% 246.32/246.68
% 246.32/246.68 ============================== SEARCH ================================
% 246.32/246.68
% 246.32/246.68 % Starting search at 0.04 seconds.
% 246.32/246.68
% 246.32/246.68 Low Water (keep): wt=23.000, iters=3355
% 246.32/246.68
% 246.32/246.68 Low Water (keep): wt=22.000, iters=3425
% 246.32/246.68
% 246.32/246.68 Low Water (keep): wt=21.000, iters=3381
% 246.32/246.68
% 246.32/246.68 Low Water (keep): wt=20.000, iters=3433
% 246.32/246.68
% 246.32/246.68 Low Water (keep): wt=19.000, iters=3351
% 246.32/246.68
% 246.32/246.68 Low Water (keep): wt=18.000, iters=3355
% 246.32/246.68
% 246.32/246.68 Low Water (keep): wt=17.000, iters=3370
% 246.32/246.68
% 246.32/246.68 Low Water (keep): wt=16.000, iters=3342
% 246.32/246.68
% 246.32/246.68 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 408 (0.00 of 2.07 sec).
% 246.32/246.68 % back CAC tautology: 10350 equiv(possibly(necessarily(not(A))),not(B)) = equiv(not(B),possibly(necessarily(not(A)))). [back_rewrite(4406),rewrite([10189(9),4405(9)]),flip(a)].
% 246.32/246.68
% 246.32/246.68 Low Water (displace): id=15329, wt=41.000
% 246.32/246.68
% 246.32/246.68 Low Water (displace): id=15321, wt=40.000
% 246.32/246.68
% 246.32/246.68 Low Water (displace): id=15328, wt=38.000
% 246.32/246.68
% 246.32/246.68 Low Water (displace): id=15326, wt=37.000
% 246.32/246.68
% 246.32/246.68 Low Water (displace): id=15362, wt=36.000
% 246.32/246.68
% 246.32/246.68 Low Water (displace): id=15325, wt=34.000
% 246.32/246.68
% 246.32/246.68 Low Water (displace): id=15385, wt=33.000
% 246.32/246.68
% 246.32/246.68 Low Water (displace): id=15170, wt=32.000
% 246.32/246.68
% 246.32/246.68 Low Water (displace): id=14509, wt=31.000
% 246.32/246.68
% 246.32/246.68 Low Water (displace): id=15031, wt=30.000
% 246.32/246.68
% 246.32/246.68 Low Water (displace): id=15388, wt=29.000
% 246.32/246.68
% 246.32/246.68 Low Water (displace): id=15434, wt=28.000
% 246.32/246.68
% 246.32/246.68 Low Water (displace): id=21023, wt=16.000
% 246.32/246.68
% 246.32/246.68 Low Water (displace): id=21086, wt=15.000
% 246.32/246.68 % back CAC tautology: 24458 or(or(A,B),not(C)) = or(not(C),or(A,B)). [para(24395(a,2),20505(a,1)),rewrite([20505(6)]),flip(a)].
% 246.32/246.68 % back CAC tautology: 24448 or(and(A,possibly(B)),not(C)) = or(not(C),and(A,possibly(B))). [para(24395(a,2),2200(a,2)),rewrite([2200(5)])].
% 246.32/246.68
% 246.32/246.68 Low Water (displace): id=25703, wt=14.000
% 246.32/246.68
% 246.32/246.68 Low Water (displace): id=26072, wt=13.000
% 246.32/246.68
% 246.32/246.68 Low Water (displace): id=26096, wt=12.000
% 246.32/246.68
% 246.32/246.68 Low Water (displace): id=26221, wt=11.000
% 246.32/246.68
% 246.32/246.68 Low Water (displace): id=26233, wt=10.000
% 246.32/246.68
% 246.32/246.68 Low Water (keep): wt=15.000, iters=3333
% 246.32/246.68
% 246.32/246.68 Low Water (displace): id=41941, wt=9.000
% 246.32/246.68
% 246.32/246.68 Low Water (keep): wt=14.000, iters=3338
% 246.32/246.68
% 246.32/246.68 Low Water (keep): wt=13.000, iters=3336
% 246.32/246.68
% 246.32/246.68 ============================== PROOF =================================
% 246.32/246.68 % SZS status Theorem
% 246.32/246.68 % SZS output start Refutation
% 246.32/246.68
% 246.32/246.68 % Proof 1 at 239.33 (+ 6.30) seconds.
% 246.32/246.68 % Length of proof is 191.
% 246.32/246.68 % Level of proof is 40.
% 246.32/246.68 % Maximum clause weight is 17.000.
% 246.32/246.68 % Given clauses 25424.
% 246.32/246.68
% 246.32/246.68 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].
% 246.32/246.68 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].
% 246.32/246.68 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].
% 246.32/246.68 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].
% 246.32/246.68 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].
% 246.32/246.68 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].
% 246.32/246.68 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].
% 246.32/246.68 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].
% 246.32/246.68 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].
% 246.32/246.68 48 axiom_m4 <-> (all X is_a_theorem(strict_implies(X,and(X,X)))) # label(axiom_m4) # label(axiom) # label(non_clause). [assumption].
% 246.32/246.68 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].
% 246.32/246.68 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].
% 246.32/246.68 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].
% 246.32/246.68 67 modus_tollens | -is_a_theorem(implies(implies(not(c6),not(c5)),implies(c5,c6))) # label(modus_tollens) # label(axiom). [clausify(3)].
% 246.32/246.68 114 -op_or | or(A,B) = not(and(not(A),not(B))) # label(op_or) # label(axiom). [clausify(27)].
% 246.32/246.68 115 -op_or | not(and(not(A),not(B))) = or(A,B). [copy(114),flip(b)].
% 246.32/246.68 118 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 246.32/246.68 124 -modus_ponens_strict_implies | -is_a_theorem(A) | -is_a_theorem(strict_implies(A,B)) | is_a_theorem(B) # label(modus_ponens_strict_implies) # label(axiom). [clausify(33)].
% 246.32/246.68 128 -adjunction | -is_a_theorem(A) | -is_a_theorem(B) | is_a_theorem(and(A,B)) # label(adjunction) # label(axiom). [clausify(34)].
% 246.32/246.68 132 -substitution_strict_equiv | -is_a_theorem(strict_equiv(A,B)) | B = A # label(substitution_strict_equiv) # label(axiom). [clausify(35)].
% 246.32/246.68 153 -axiom_m1 | is_a_theorem(strict_implies(and(A,B),and(B,A))) # label(axiom_m1) # label(axiom). [clausify(45)].
% 246.32/246.68 155 -axiom_m2 | is_a_theorem(strict_implies(and(A,B),A)) # label(axiom_m2) # label(axiom). [clausify(46)].
% 246.32/246.68 157 -axiom_m3 | is_a_theorem(strict_implies(and(and(A,B),C),and(A,and(B,C)))) # label(axiom_m3) # label(axiom). [clausify(47)].
% 246.32/246.68 159 -axiom_m4 | is_a_theorem(strict_implies(A,and(A,A))) # label(axiom_m4) # label(axiom). [clausify(48)].
% 246.32/246.68 161 -axiom_m5 | is_a_theorem(strict_implies(and(strict_implies(A,B),strict_implies(B,C)),strict_implies(A,C))) # label(axiom_m5) # label(axiom). [clausify(49)].
% 246.32/246.68 177 -op_strict_implies | strict_implies(A,B) = necessarily(implies(A,B)) # label(op_strict_implies) # label(axiom). [clausify(57)].
% 246.32/246.68 178 -op_strict_implies | necessarily(implies(A,B)) = strict_implies(A,B). [copy(177),flip(b)].
% 246.32/246.68 179 -op_strict_equiv | strict_equiv(A,B) = and(strict_implies(A,B),strict_implies(B,A)) # label(op_strict_equiv) # label(axiom). [clausify(58)].
% 246.32/246.68 180 -op_strict_equiv | and(strict_implies(A,B),strict_implies(B,A)) = strict_equiv(A,B). [copy(179),flip(b)].
% 246.32/246.68 182 op_or # label(s1_0_op_or) # label(axiom). [assumption].
% 246.32/246.68 184 op_strict_implies # label(s1_0_op_strict_implies) # label(axiom). [assumption].
% 246.32/246.68 186 op_strict_equiv # label(s1_0_op_strict_equiv) # label(axiom). [assumption].
% 246.32/246.68 187 modus_ponens_strict_implies # label(s1_0_modus_ponens_strict_implies) # label(axiom). [assumption].
% 246.32/246.68 188 substitution_strict_equiv # label(s1_0_substitution_strict_equiv) # label(axiom). [assumption].
% 246.32/246.68 189 adjunction # label(s1_0_adjunction) # label(axiom). [assumption].
% 246.32/246.68 190 axiom_m1 # label(s1_0_axiom_m1) # label(axiom). [assumption].
% 246.32/246.68 191 axiom_m2 # label(s1_0_axiom_m2) # label(axiom). [assumption].
% 246.32/246.68 192 axiom_m3 # label(s1_0_axiom_m3) # label(axiom). [assumption].
% 246.32/246.68 193 axiom_m4 # label(s1_0_axiom_m4) # label(axiom). [assumption].
% 246.32/246.68 194 axiom_m5 # label(s1_0_axiom_m5) # label(axiom). [assumption].
% 246.32/246.68 195 op_implies_and # label(hilbert_op_implies_and) # label(axiom). [assumption].
% 246.32/246.68 197 -modus_tollens # label(hilbert_modus_tollens) # label(negated_conjecture). [assumption].
% 246.32/246.68 200 not(and(not(A),not(B))) = or(A,B). [back_unit_del(115),unit_del(a,182)].
% 246.32/246.68 201 necessarily(implies(A,B)) = strict_implies(A,B). [back_unit_del(178),unit_del(a,184)].
% 246.32/246.68 203 and(strict_implies(A,B),strict_implies(B,A)) = strict_equiv(A,B). [back_unit_del(180),unit_del(a,186)].
% 246.32/246.68 204 -is_a_theorem(A) | -is_a_theorem(strict_implies(A,B)) | is_a_theorem(B). [back_unit_del(124),unit_del(a,187)].
% 246.32/246.68 205 -is_a_theorem(strict_equiv(A,B)) | B = A. [back_unit_del(132),unit_del(a,188)].
% 246.32/246.68 206 -is_a_theorem(A) | -is_a_theorem(B) | is_a_theorem(and(A,B)). [back_unit_del(128),unit_del(a,189)].
% 246.32/246.68 207 is_a_theorem(strict_implies(and(A,B),and(B,A))). [back_unit_del(153),unit_del(a,190)].
% 246.32/246.68 208 is_a_theorem(strict_implies(and(A,B),A)). [back_unit_del(155),unit_del(a,191)].
% 246.32/246.68 209 is_a_theorem(strict_implies(and(and(A,B),C),and(A,and(B,C)))). [back_unit_del(157),unit_del(a,192)].
% 246.32/246.68 210 is_a_theorem(strict_implies(A,and(A,A))). [back_unit_del(159),unit_del(a,193)].
% 246.32/246.68 211 is_a_theorem(strict_implies(and(strict_implies(A,B),strict_implies(B,C)),strict_implies(A,C))). [back_unit_del(161),unit_del(a,194)].
% 246.32/246.68 212 not(and(A,not(B))) = implies(A,B). [back_unit_del(118),unit_del(a,195)].
% 246.32/246.68 214 -is_a_theorem(implies(implies(not(c6),not(c5)),implies(c5,c6))). [back_unit_del(67),unit_del(a,197)].
% 246.32/246.68 219 implies(not(A),B) = or(A,B). [back_rewrite(200),rewrite([212(4)])].
% 246.32/246.68 220 -is_a_theorem(implies(or(c6,not(c5)),implies(c5,c6))). [back_rewrite(214),rewrite([219(5)])].
% 246.32/246.68 239 -is_a_theorem(A) | is_a_theorem(and(A,strict_implies(and(B,C),and(C,B)))). [resolve(207,a,206,b)].
% 246.32/246.68 246 -is_a_theorem(A) | is_a_theorem(and(A,strict_implies(and(B,C),B))). [resolve(208,a,206,b)].
% 246.32/246.68 247 -is_a_theorem(A) | is_a_theorem(and(strict_implies(and(B,C),B),A)). [resolve(208,a,206,a)].
% 246.32/246.68 262 -is_a_theorem(A) | is_a_theorem(and(A,strict_implies(B,and(B,B)))). [resolve(210,a,206,b)].
% 246.32/246.68 270 -is_a_theorem(and(strict_implies(A,B),strict_implies(B,C))) | is_a_theorem(strict_implies(A,C)). [resolve(211,a,204,b)].
% 246.32/246.68 276 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(212(a,1),212(a,1,1,2))].
% 246.32/246.68 279 necessarily(or(A,B)) = strict_implies(not(A),B). [para(219(a,1),201(a,1,1))].
% 246.32/246.68 282 or(and(A,not(B)),C) = implies(implies(A,B),C). [para(212(a,1),219(a,1,1)),flip(a)].
% 246.32/246.68 466 is_a_theorem(and(strict_implies(and(A,B),and(B,A)),strict_implies(and(C,D),and(D,C)))). [resolve(239,a,207,a)].
% 246.32/246.68 604 is_a_theorem(and(strict_implies(A,and(A,A)),strict_implies(and(B,C),B))). [resolve(246,a,210,a)].
% 246.32/246.68 606 is_a_theorem(and(strict_implies(and(A,B),A),strict_implies(and(C,D),C))). [resolve(246,a,208,a)].
% 246.32/246.68 2315 implies(A,and(not(B),not(C))) = not(and(A,or(B,C))). [para(219(a,1),276(a,1,1,2)),flip(a)].
% 246.32/246.68 9035 is_a_theorem(strict_implies(A,A)). [resolve(604,a,270,a)].
% 246.32/246.68 9041 is_a_theorem(strict_equiv(A,and(A,A))). [para(203(a,1),604(a,1))].
% 246.32/246.68 9086 is_a_theorem(and(strict_implies(A,A),strict_implies(B,and(B,B)))). [resolve(9035,a,262,a)].
% 246.32/246.68 9087 is_a_theorem(and(strict_implies(and(A,B),A),strict_implies(C,C))). [resolve(9035,a,247,a)].
% 246.32/246.68 9097 -is_a_theorem(A) | is_a_theorem(and(A,strict_implies(B,B))). [resolve(9035,a,206,b)].
% 246.32/246.68 9217 and(A,A) = A. [resolve(9041,a,205,a)].
% 246.32/246.68 9222 is_a_theorem(and(strict_implies(A,A),strict_implies(B,B))). [back_rewrite(9086),rewrite([9217(2)])].
% 246.32/246.68 9657 strict_equiv(A,A) = strict_implies(A,A). [para(9217(a,1),203(a,1)),flip(a)].
% 246.32/246.68 9658 is_a_theorem(strict_implies(and(A,B),and(A,and(A,B)))). [para(9217(a,1),209(a,1,1,1))].
% 246.32/246.68 9661 or(A,A) = not(not(A)). [para(9217(a,1),212(a,1,1)),rewrite([219(4)]),flip(a)].
% 246.32/246.68 9674 implies(or(A,A),B) = or(not(A),B). [para(9217(a,1),282(a,1,1)),rewrite([219(4)]),flip(a)].
% 246.32/246.68 9779 is_a_theorem(strict_equiv(and(A,B),and(B,A))). [para(203(a,1),466(a,1))].
% 246.32/246.68 9920 strict_implies(or(A,A),B) = strict_implies(not(not(A)),B). [para(9661(a,2),279(a,2,1)),rewrite([279(3)]),flip(a)].
% 246.32/246.68 9937 not(or(A,A)) = not(not(not(A))). [para(9661(a,2),9661(a,2,1)),rewrite([9661(3)]),flip(a)].
% 246.32/246.68 10189 and(A,B) = and(B,A). [resolve(9779,a,205,a)].
% 246.32/246.68 10497 strict_equiv(A,B) = strict_equiv(B,A). [para(10189(a,1),203(a,1)),rewrite([203(3)])].
% 246.32/246.68 10498 is_a_theorem(strict_implies(and(A,B),B)). [para(10189(a,1),208(a,1,1))].
% 246.32/246.68 10503 -is_a_theorem(and(strict_implies(A,B),strict_implies(C,A))) | is_a_theorem(strict_implies(C,B)). [para(10189(a,1),270(a,1))].
% 246.32/246.68 10574 -is_a_theorem(A) | is_a_theorem(and(A,strict_implies(and(B,C),C))). [resolve(10498,a,206,b)].
% 246.32/246.68 10598 -is_a_theorem(strict_equiv(A,B)) | A = B. [para(10497(a,1),205(a,1))].
% 246.32/246.68 10767 implies(A,or(B,B)) = implies(A,not(not(B))). [para(9937(a,1),212(a,1,1,2)),rewrite([212(5)]),flip(a)].
% 246.32/246.68 10768 or(or(A,A),B) = or(not(not(A)),B). [para(9937(a,1),219(a,1,1)),rewrite([219(4)]),flip(a)].
% 246.32/246.68 11007 is_a_theorem(strict_implies(and(A,and(B,C)),B)). [resolve(606,a,270,a),rewrite([10189(2)])].
% 246.32/246.68 11033 is_a_theorem(strict_implies(and(A,and(B,C)),C)). [para(10189(a,1),11007(a,1,1,2))].
% 246.32/246.68 11049 -is_a_theorem(A) | is_a_theorem(and(A,strict_implies(and(B,and(C,D)),D))). [resolve(11033,a,206,b)].
% 246.32/246.68 11154 is_a_theorem(and(strict_implies(and(A,B),and(A,and(A,B))),strict_implies(and(C,D),D))). [resolve(10574,a,9658,a)].
% 246.32/246.68 12105 and(strict_implies(A,not(not(B))),strict_implies(or(B,B),A)) = strict_equiv(A,not(not(B))). [para(9920(a,2),203(a,1,2))].
% 246.32/246.68 12106 -is_a_theorem(or(A,A)) | -is_a_theorem(strict_implies(not(not(A)),B)) | is_a_theorem(B). [para(9920(a,1),204(b,1))].
% 246.32/246.68 12851 strict_implies(A,or(B,B)) = strict_implies(A,not(not(B))). [para(10767(a,1),201(a,1,1)),rewrite([201(4)]),flip(a)].
% 246.32/246.68 12852 or(A,or(B,B)) = or(A,not(not(B))). [para(10767(a,1),219(a,1)),rewrite([219(4)]),flip(a)].
% 246.32/246.68 13451 strict_equiv(A,or(B,B)) = strict_equiv(A,not(not(B))). [para(12851(a,1),203(a,1,1)),rewrite([12105(6)]),flip(a)].
% 246.32/246.68 13453 -is_a_theorem(A) | -is_a_theorem(strict_implies(A,or(B,B))) | is_a_theorem(not(not(B))). [para(12851(a,2),204(b,1))].
% 246.32/246.68 13666 or(or(A,A),not(not(B))) = or(not(not(A)),or(B,B)). [para(12852(a,1),10768(a,1))].
% 246.32/246.68 13667 or(or(A,A),or(B,B)) = or(not(not(A)),not(not(B))). [para(12852(a,1),10768(a,2))].
% 246.32/246.68 13757 -is_a_theorem(strict_equiv(A,not(not(B)))) | or(B,B) = A. [para(13451(a,1),205(a,1))].
% 246.32/246.68 13758 -is_a_theorem(strict_equiv(A,or(B,B))) | not(not(B)) = A. [para(13451(a,2),205(a,1))].
% 246.32/246.68 13763 strict_equiv(A,not(or(B,B))) = strict_equiv(A,not(not(not(B)))). [para(9661(a,2),13451(a,2,2,1)),rewrite([9661(3)]),flip(a)].
% 246.32/246.68 15884 -is_a_theorem(and(strict_implies(or(A,A),B),strict_implies(C,not(not(A))))) | is_a_theorem(strict_implies(C,B)). [para(9920(a,2),10503(a,1,1))].
% 246.32/246.68 17907 not(and(not(A),or(B,C))) = or(A,and(not(B),not(C))). [para(2315(a,1),219(a,1))].
% 246.32/246.68 17913 not(and(A,or(B,C))) = not(and(A,or(C,B))). [para(10189(a,1),2315(a,1,2)),rewrite([2315(4)])].
% 246.32/246.68 19789 -is_a_theorem(strict_equiv(A,not(not(not(B))))) | not(or(B,B)) = A. [para(13763(a,1),205(a,1))].
% 246.32/246.68 19866 not(and(or(A,B),or(B,A))) = not(or(A,B)). [para(9217(a,1),17913(a,1,1)),flip(a)].
% 246.32/246.68 20498 not(or(A,B)) = not(or(B,A)). [para(10189(a,1),19866(a,1,1)),rewrite([19866(4)])].
% 246.32/246.68 20504 implies(A,or(B,C)) = implies(A,or(C,B)). [para(20498(a,1),212(a,1,1,2)),rewrite([212(4)])].
% 246.32/246.68 20527 strict_implies(A,or(B,C)) = strict_implies(A,or(C,B)). [para(20504(a,1),201(a,1,1)),rewrite([201(3)])].
% 246.32/246.68 20779 and(strict_implies(A,or(B,C)),strict_implies(or(C,B),A)) = strict_equiv(A,or(C,B)). [para(20527(a,1),203(a,1,1))].
% 246.32/246.68 24384 or(A,and(not(B),not(C))) = implies(or(B,C),A). [para(10189(a,1),17907(a,1,1)),rewrite([212(4)]),flip(a)].
% 246.32/246.68 24395 or(not(A),B) = or(B,not(A)). [para(9217(a,1),24384(a,1,2)),rewrite([9674(4)]),flip(a)].
% 246.32/246.68 24398 implies(or(A,B),C) = implies(or(B,A),C). [para(10189(a,1),24384(a,1,2)),rewrite([24384(4)])].
% 246.32/246.68 24439 implies(or(A,A),B) = or(B,not(A)). [back_rewrite(9674),rewrite([24395(4)])].
% 246.32/246.68 24445 strict_implies(not(not(A)),B) = strict_implies(not(B),not(A)). [para(24395(a,1),279(a,1,1)),rewrite([279(3)]),flip(a)].
% 246.32/246.68 24539 -is_a_theorem(or(A,A)) | -is_a_theorem(strict_implies(not(B),not(A))) | is_a_theorem(B). [back_rewrite(12106),rewrite([24445(5)])].
% 246.32/246.68 24541 strict_implies(or(A,A),B) = strict_implies(not(B),not(A)). [back_rewrite(9920),rewrite([24445(5)])].
% 246.32/246.68 24596 strict_implies(or(A,B),C) = strict_implies(or(B,A),C). [para(24398(a,1),201(a,1,1)),rewrite([201(3)])].
% 246.32/246.68 24598 strict_equiv(A,or(B,C)) = strict_equiv(A,or(C,B)). [back_rewrite(20779),rewrite([24596(4),203(5)])].
% 246.32/246.68 24700 is_a_theorem(strict_implies(or(A,A),A)). [para(24541(a,2),9035(a,1))].
% 246.32/246.68 24705 is_a_theorem(and(strict_implies(or(A,A),A),strict_implies(B,B))). [para(24541(a,2),9222(a,1,1))].
% 246.32/246.68 24713 is_a_theorem(and(strict_implies(and(A,B),A),strict_implies(or(C,C),C))). [para(24541(a,2),9087(a,1,2))].
% 246.32/246.68 25090 -is_a_theorem(A) | is_a_theorem(and(A,strict_implies(or(B,B),B))). [resolve(24700,a,206,b)].
% 246.32/246.68 25148 is_a_theorem(and(strict_implies(or(A,A),A),strict_implies(or(B,B),B))). [para(24541(a,2),24705(a,1,2))].
% 246.32/246.68 25264 -is_a_theorem(strict_equiv(A,or(B,C))) | or(C,B) = A. [para(24598(a,1),205(a,1))].
% 246.32/246.68 25290 or(A,B) = or(B,A). [para(9657(a,1),25264(a,1)),unit_del(a,9035)].
% 246.32/246.68 25311 strict_implies(not(A),B) = strict_implies(not(B),A). [para(25290(a,1),279(a,1,1)),rewrite([279(2)])].
% 246.32/246.68 25315 or(or(A,A),or(B,B)) = or(not(not(B)),not(not(A))). [para(13667(a,2),25290(a,2)),flip(a)].
% 246.32/246.68 25335 and(strict_implies(A,not(B)),strict_implies(not(A),B)) = strict_equiv(A,not(B)). [para(25311(a,1),203(a,1,1)),rewrite([10189(5),10497(7)])].
% 246.32/246.68 25407 -is_a_theorem(or(A,A)) | -is_a_theorem(strict_implies(or(B,B),not(A))) | is_a_theorem(not(B)). [para(9661(a,2),24539(b,1,1))].
% 246.32/246.68 25430 is_a_theorem(strict_implies(not(A),not(and(A,B)))). [resolve(24713,a,10503,a),rewrite([9661(3),25311(4)])].
% 246.32/246.68 25468 is_a_theorem(strict_implies(not(A),implies(A,B))). [para(212(a,1),25430(a,1,2))].
% 246.32/246.68 25510 is_a_theorem(and(strict_implies(not(A),implies(A,B)),strict_implies(or(C,C),C))). [resolve(25468,a,25090,a)].
% 246.32/246.68 25514 is_a_theorem(and(strict_implies(not(A),implies(A,B)),strict_implies(and(C,and(D,E)),E))). [resolve(25468,a,11049,a)].
% 246.32/246.68 25555 is_a_theorem(strict_implies(or(A,A),or(A,B))). [para(9661(a,2),25468(a,1,1)),rewrite([219(3)])].
% 246.32/246.68 25843 is_a_theorem(and(strict_implies(or(A,A),or(A,B)),strict_implies(C,C))). [resolve(25555,a,9097,a)].
% 246.32/246.68 27172 is_a_theorem(strict_implies(not(A),not(or(A,A)))). [resolve(25148,a,10503,a),rewrite([9661(3),25311(4)])].
% 246.32/246.68 27212 is_a_theorem(strict_implies(not(A),not(not(not(A))))). [para(9661(a,1),27172(a,1,2,1))].
% 246.32/246.68 27359 is_a_theorem(and(strict_implies(not(A),not(not(not(A)))),strict_implies(B,B))). [resolve(27212,a,9097,a)].
% 246.32/246.68 30676 is_a_theorem(strict_implies(not(not(not(A))),implies(A,B))). [resolve(25510,a,10503,a),rewrite([9661(3)])].
% 246.32/246.68 30687 -is_a_theorem(not(not(not(A)))) | is_a_theorem(implies(A,B)). [resolve(30676,a,204,b)].
% 246.32/246.68 30718 -is_a_theorem(not(not(not(or(A,A))))) | is_a_theorem(or(B,not(A))). [para(9937(a,2),30687(a,1,1,1)),rewrite([219(8),25290(7)])].
% 246.32/246.68 30964 is_a_theorem(strict_equiv(and(A,B),and(A,and(A,B)))). [para(203(a,1),11154(a,1))].
% 246.32/246.68 30965 and(A,and(A,B)) = and(A,B). [resolve(30964,a,10598,a),flip(a)].
% 246.32/246.68 33994 is_a_theorem(strict_equiv(not(A),not(not(not(A))))). [para(25335(a,1),27359(a,1))].
% 246.32/246.68 34267 not(or(A,A)) = not(A). [resolve(33994,a,19789,a)].
% 246.32/246.68 34268 not(not(not(A))) = not(A). [resolve(33994,a,13757,a),rewrite([9661(3)])].
% 246.32/246.68 34367 -is_a_theorem(not(A)) | is_a_theorem(or(B,not(A))). [back_rewrite(30718),rewrite([34267(2),34268(3)])].
% 246.32/246.68 34898 implies(A,or(B,B)) = implies(A,B). [para(34267(a,1),212(a,1,1,2)),rewrite([212(3)]),flip(a)].
% 246.32/246.68 34900 or(A,or(B,B)) = or(B,A). [para(34267(a,1),219(a,1,1)),rewrite([219(2),25290(3)]),flip(a)].
% 246.32/246.68 34942 or(not(not(A)),not(not(B))) = or(B,not(not(A))). [para(34267(a,1),13666(a,2,1,1)),rewrite([9661(3),34267(2),34900(9)])].
% 246.32/246.68 35143 or(A,not(not(B))) = or(B,A). [back_rewrite(25315),rewrite([34900(3),34900(2),25290(6),34942(6)]),flip(a)].
% 246.32/246.68 35591 strict_implies(A,or(B,B)) = strict_implies(A,B). [para(34898(a,1),201(a,1,1)),rewrite([201(2)]),flip(a)].
% 246.32/246.68 35652 -is_a_theorem(A) | -is_a_theorem(strict_implies(A,B)) | is_a_theorem(not(not(B))). [back_rewrite(13453),rewrite([35591(3)])].
% 246.32/246.68 35653 strict_implies(A,not(not(B))) = strict_implies(A,B). [back_rewrite(12851),rewrite([35591(2)]),flip(a)].
% 246.32/246.68 35744 -is_a_theorem(and(strict_implies(or(A,A),B),strict_implies(C,A))) | is_a_theorem(strict_implies(C,B)). [back_rewrite(15884),rewrite([35653(5)])].
% 246.32/246.68 36596 -is_a_theorem(A) | is_a_theorem(not(not(A))). [resolve(35652,b,9035,a)].
% 246.32/246.68 37247 is_a_theorem(not(not(strict_implies(A,A)))). [resolve(36596,a,9035,a)].
% 246.32/246.68 37848 is_a_theorem(or(A,strict_implies(B,B))). [resolve(37247,a,34367,a),rewrite([35143(4),25290(2)])].
% 246.32/246.68 58228 -is_a_theorem(strict_implies(or(A,A),not(strict_implies(B,B)))) | is_a_theorem(not(A)). [resolve(25407,a,37848,a)].
% 246.32/246.68 58367 is_a_theorem(strict_implies(and(A,and(B,not(C))),implies(C,D))). [resolve(25514,a,10503,a)].
% 246.32/246.68 67782 is_a_theorem(strict_implies(A,or(A,B))). [resolve(35744,a,25843,a)].
% 246.32/246.68 67804 is_a_theorem(and(strict_implies(A,or(A,B)),strict_implies(or(C,C),C))). [resolve(67782,a,25090,a)].
% 246.32/246.68 68832 is_a_theorem(strict_equiv(A,or(A,A))). [para(203(a,1),67804(a,1))].
% 246.32/246.68 68855 not(not(A)) = A. [resolve(68832,a,13758,a)].
% 246.32/246.68 68856 or(A,A) = A. [resolve(68832,a,10598,a),flip(a)].
% 246.32/246.68 69199 -is_a_theorem(strict_implies(A,not(strict_implies(B,B)))) | is_a_theorem(not(A)). [back_rewrite(58228),rewrite([68856(1)])].
% 246.32/246.68 69343 or(A,not(B)) = implies(B,A). [back_rewrite(24439),rewrite([68856(1)]),flip(a)].
% 246.32/246.68 69815 -is_a_theorem(implies(implies(c5,c6),implies(c5,c6))). [back_rewrite(220),rewrite([69343(4)])].
% 246.32/246.68 69846 not(and(A,B)) = implies(A,not(B)). [para(68855(a,1),212(a,1,1,2))].
% 246.32/246.68 69847 not(implies(A,B)) = and(A,not(B)). [para(212(a,1),68855(a,1,1))].
% 246.32/246.68 75277 implies(A,not(B)) = implies(B,not(A)). [para(10189(a,1),69846(a,1,1)),rewrite([69846(2)])].
% 246.32/246.68 75279 implies(A,implies(A,not(B))) = implies(A,not(B)). [para(30965(a,1),69846(a,1,1)),rewrite([69846(2),69846(4)]),flip(a)].
% 246.32/246.68 75283 or(A,implies(B,not(C))) = implies(and(B,C),A). [para(69846(a,1),69343(a,1,2))].
% 246.32/246.68 75311 and(not(A),not(B)) = not(or(A,B)). [para(219(a,1),69847(a,1,1)),flip(a)].
% 246.32/246.68 77083 is_a_theorem(strict_implies(and(A,not(or(B,C))),implies(C,D))). [para(75311(a,1),58367(a,1,1,2))].
% 246.32/246.68 77838 implies(A,implies(A,B)) = implies(A,B). [para(68855(a,1),75279(a,1,2,2)),rewrite([68855(4)])].
% 246.32/246.68 77845 strict_implies(A,implies(A,B)) = strict_implies(A,B). [para(77838(a,1),201(a,1,1)),rewrite([201(2)]),flip(a)].
% 246.32/246.68 78676 is_a_theorem(strict_implies(not(or(A,or(B,C))),implies(C,D))). [para(75311(a,1),77083(a,1,1))].
% 246.32/246.68 78965 is_a_theorem(strict_implies(and(A,not(B)),or(C,or(A,D)))). [para(25311(a,1),78676(a,1)),rewrite([69847(2),25290(3)])].
% 246.32/246.68 79018 is_a_theorem(strict_implies(and(A,B),or(C,or(A,D)))). [para(68855(a,1),78965(a,1,1,2))].
% 246.32/246.68 79029 is_a_theorem(strict_implies(and(A,B),or(C,implies(D,A)))). [para(69343(a,1),79018(a,1,2,2))].
% 246.32/246.68 79050 is_a_theorem(strict_implies(and(A,not(B)),implies(and(B,C),D))). [para(75277(a,1),79029(a,1,2,2)),rewrite([10189(2),75283(5)])].
% 246.32/246.68 79080 is_a_theorem(strict_implies(and(A,not(A)),B)). [para(77845(a,1),79050(a,1))].
% 246.32/246.68 79089 is_a_theorem(implies(A,A)). [resolve(79080,a,69199,a),rewrite([69846(3),68855(2)])].
% 246.32/246.68 79090 $F. [resolve(79089,a,69815,a)].
% 246.32/246.68
% 246.32/246.68 % SZS output end Refutation
% 246.32/246.68 ============================== end of proof ==========================
% 246.32/246.68
% 246.32/246.68 ============================== STATISTICS ============================
% 246.32/246.68
% 246.32/246.68 Given=25424. Generated=11288279. Kept=79025. proofs=1.
% 246.32/246.68 Usable=12463. Sos=9582. Demods=165. Limbo=8, Disabled=57106. Hints=0.
% 246.32/246.68 Megabytes=108.48.
% 246.32/246.68 User_CPU=239.34, System_CPU=6.30, Wall_clock=246.
% 246.32/246.68
% 246.32/246.68 ============================== end of statistics =====================
% 246.32/246.68
% 246.32/246.68 ============================== end of search =========================
% 246.32/246.68
% 246.32/246.68 THEOREM PROVED
% 246.32/246.68 % SZS status Theorem
% 246.32/246.68
% 246.32/246.68 Exiting with 1 proof.
% 246.32/246.68
% 246.32/246.68 Process 4666 exit (max_proofs) Sun Jul 3 15:52:07 2022
% 246.32/246.68 Prover9 interrupted
%------------------------------------------------------------------------------