TSTP Solution File: LCL559+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL559+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.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 13:47:34 EDT 2022
% Result : Timeout 296.71s 297.03s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL559+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.32 % Computer : n019.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 15:03:53 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.41/1.01 ============================== Prover9 ===============================
% 0.41/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.41/1.01 Process 19223 was started by sandbox on n019.cluster.edu,
% 0.41/1.01 Sun Jul 3 15:03:54 2022
% 0.41/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_19070_n019.cluster.edu".
% 0.41/1.01 ============================== end of head ===========================
% 0.41/1.01
% 0.41/1.01 ============================== INPUT =================================
% 0.41/1.01
% 0.41/1.01 % Reading from file /tmp/Prover9_19070_n019.cluster.edu
% 0.41/1.01
% 0.41/1.01 set(prolog_style_variables).
% 0.41/1.01 set(auto2).
% 0.41/1.01 % set(auto2) -> set(auto).
% 0.41/1.01 % set(auto) -> set(auto_inference).
% 0.41/1.01 % set(auto) -> set(auto_setup).
% 0.41/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.41/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.41/1.01 % set(auto) -> set(auto_limits).
% 0.41/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.41/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.41/1.01 % set(auto) -> set(auto_denials).
% 0.41/1.01 % set(auto) -> set(auto_process).
% 0.41/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.41/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.41/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.41/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.41/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.41/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.41/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.41/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.41/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.41/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.41/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.41/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.41/1.01 % set(auto2) -> assign(stats, some).
% 0.41/1.01 % set(auto2) -> clear(echo_input).
% 0.41/1.01 % set(auto2) -> set(quiet).
% 0.41/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.41/1.01 % set(auto2) -> clear(print_given).
% 0.41/1.01 assign(lrs_ticks,-1).
% 0.41/1.01 assign(sos_limit,10000).
% 0.41/1.01 assign(order,kbo).
% 0.41/1.01 set(lex_order_vars).
% 0.41/1.01 clear(print_given).
% 0.41/1.01
% 0.41/1.01 % formulas(sos). % not echoed (77 formulas)
% 0.41/1.01
% 0.41/1.01 ============================== end of input ==========================
% 0.41/1.01
% 0.41/1.01 % From the command line: assign(max_seconds, 300).
% 0.41/1.01
% 0.41/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.41/1.01
% 0.41/1.01 % Formulas that are not ordinary clauses:
% 0.41/1.01 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].
% 0.41/1.01 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].
% 0.41/1.01 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].
% 0.41/1.01 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 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].
% 0.41/1.01 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].
% 0.41/1.01 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 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].
% 0.41/1.01 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 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].
% 0.41/1.01 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].
% 0.41/1.01 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].
% 0.41/1.01 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].
% 0.41/1.01 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 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].
% 0.41/1.01 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].
% 0.41/1.01 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 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].
% 0.41/1.01 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].
% 0.41/1.01 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].
% 0.41/1.01 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].
% 0.41/1.01 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].
% 0.41/1.01 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].
% 0.41/1.01 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].
% 0.41/1.01 32 necessitation <-> (all X (is_a_theorem(X) -> is_a_theorem(necessarily(X)))) # label(necessitation) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 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].
% 0.41/1.01 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].
% 0.41/1.01 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].
% 0.41/1.01 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].
% 0.41/1.01 37 axiom_M <-> (all X is_a_theorem(implies(necessarily(X),X))) # label(axiom_M) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 38 axiom_4 <-> (all X is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))) # label(axiom_4) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 39 axiom_B <-> (all X is_a_theorem(implies(X,necessarily(possibly(X))))) # label(axiom_B) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 40 axiom_5 <-> (all X is_a_theorem(implies(possibly(X),necessarily(possibly(X))))) # label(axiom_5) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 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].
% 0.73/1.04 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].
% 0.73/1.04 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].
% 0.73/1.04 44 axiom_s4 <-> (all X is_a_theorem(strict_implies(necessarily(X),necessarily(necessarily(X))))) # label(axiom_s4) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 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].
% 0.73/1.04 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].
% 0.73/1.04 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].
% 0.73/1.04 48 axiom_m4 <-> (all X is_a_theorem(strict_implies(X,and(X,X)))) # label(axiom_m4) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 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].
% 0.73/1.04 50 axiom_m6 <-> (all X is_a_theorem(strict_implies(X,possibly(X)))) # label(axiom_m6) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 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].
% 0.73/1.04 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].
% 0.73/1.04 53 axiom_m9 <-> (all X is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X)))) # label(axiom_m9) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 54 axiom_m10 <-> (all X is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X))))) # label(axiom_m10) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 55 op_possibly -> (all X possibly(X) = not(necessarily(not(X)))) # label(op_possibly) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 56 op_necessarily -> (all X necessarily(X) = not(possibly(not(X)))) # label(op_necessarily) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 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].
% 0.73/1.04 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].
% 0.73/1.04
% 0.73/1.04 ============================== end of process non-clausal formulas ===
% 0.73/1.04
% 0.73/1.04 ============================== PROCESS INITIAL CLAUSES ===============
% 0.73/1.04
% 0.73/1.04 ============================== PREDICATE ELIMINATION =================
% 0.73/1.04
% 0.73/1.04 ============================== end predicate elimination =============
% 0.73/1.04
% 0.73/1.04 Auto_denials: (non-Horn, no changes).
% 0.73/1.04
% 0.73/1.04 Term ordering decisions:
% 0.73/1.04 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.
% 0.73/1.04
% 0.73/1.04 ============================== end of process initial clauses ========
% 0.73/1.04
% 0.73/1.04 ============================== CLAUSES FOR SEARCH ====================
% 296.71/297.03
% 296.71/297.03 ============================== end of clauses for search =============
% 296.71/297.03
% 296.71/297.03 ============================== SEARCH ================================
% 296.71/297.03
% 296.71/297.03 % Starting search at 0.04 seconds.
% 296.71/297.03
% 296.71/297.03 Low Water (keep): wt=23.000, iters=3355
% 296.71/297.03
% 296.71/297.03 Low Water (keep): wt=22.000, iters=3425
% 296.71/297.03
% 296.71/297.03 Low Water (keep): wt=21.000, iters=3381
% 296.71/297.03
% 296.71/297.03 Low Water (keep): wt=20.000, iters=3433
% 296.71/297.03
% 296.71/297.03 Low Water (keep): wt=19.000, iters=3351
% 296.71/297.03
% 296.71/297.03 Low Water (keep): wt=18.000, iters=3355
% 296.71/297.03
% 296.71/297.03 Low Water (keep): wt=17.000, iters=3370
% 296.71/297.03
% 296.71/297.03 Low Water (keep): wt=16.000, iters=3342
% 296.71/297.03
% 296.71/297.03 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 408 (0.00 of 2.04 sec).
% 296.71/297.03 % back CAC tautology: 10351 equiv(possibly(necessarily(not(A))),not(B)) = equiv(not(B),possibly(necessarily(not(A)))). [back_rewrite(4407),rewrite([10190(9),4406(9)]),flip(a)].
% 296.71/297.03
% 296.71/297.03 Low Water (displace): id=15330, wt=41.000
% 296.71/297.03
% 296.71/297.03 Low Water (displace): id=15322, wt=40.000
% 296.71/297.03
% 296.71/297.03 Low Water (displace): id=15329, wt=38.000
% 296.71/297.03
% 296.71/297.03 Low Water (displace): id=15327, wt=37.000
% 296.71/297.03
% 296.71/297.03 Low Water (displace): id=15363, wt=36.000
% 296.71/297.03
% 296.71/297.03 Low Water (displace): id=15326, wt=34.000
% 296.71/297.03
% 296.71/297.03 Low Water (displace): id=15386, wt=33.000
% 296.71/297.03
% 296.71/297.03 Low Water (displace): id=15171, wt=32.000
% 296.71/297.03
% 296.71/297.03 Low Water (displace): id=14510, wt=31.000
% 296.71/297.03
% 296.71/297.03 Low Water (displace): id=15032, wt=30.000
% 296.71/297.03
% 296.71/297.03 Low Water (displace): id=15389, wt=29.000
% 296.71/297.03
% 296.71/297.03 Low Water (displace): id=15435, wt=28.000
% 296.71/297.03
% 296.71/297.03 Low Water (displace): id=21023, wt=16.000
% 296.71/297.03
% 296.71/297.03 Low Water (displace): id=21084, wt=15.000
% 296.71/297.03 % back CAC tautology: 24473 or(or(A,B),not(C)) = or(not(C),or(A,B)). [para(24410(a,2),20506(a,1)),rewrite([20506(6)]),flip(a)].
% 296.71/297.03 % back CAC tautology: 24463 or(and(A,possibly(B)),not(C)) = or(not(C),and(A,possibly(B))). [para(24410(a,2),2201(a,2)),rewrite([2201(5)])].
% 296.71/297.03
% 296.71/297.03 Low Water (displace): id=25718, wt=14.000
% 296.71/297.03
% 296.71/297.03 Low Water (displace): id=26088, wt=13.000
% 296.71/297.03
% 296.71/297.03 Low Water (displace): id=26111, wt=12.000
% 296.71/297.03
% 296.71/297.03 Low Water (displace): id=26194, wt=10.000
% 296.71/297.03
% 296.71/297.03 Low Water (keep): wt=15.000, iters=3334
% 296.71/297.03
% 296.71/297.03 Low Water (displace): id=41872, wt=9.000
% 296.71/297.03
% 296.71/297.03 Low Water (keep): wt=14.000, iters=3333
% 296.71/297.03
% 296.71/297.03 Low Water (keep): wt=13.000, iters=3333
% 296.71/297.03
% 296.71/297.03 Low Water (keep): wt=12.000, iters=3601
% 296.71/297.03
% 296.71/297.03 ============================== PROOF =================================
% 296.71/297.03 % SZS status Theorem
% 296.71/297.03 % SZS output start Refutation
% 296.71/297.03
% 296.71/297.03 % Proof 1 at 287.17 (+ 8.84) seconds.
% 296.71/297.03 % Length of proof is 260.
% 296.71/297.03 % Level of proof is 58.
% 296.71/297.03 % Maximum clause weight is 20.000.
% 296.71/297.03 % Given clauses 34237.
% 296.71/297.03
% 296.71/297.03 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].
% 296.71/297.03 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 296.71/297.03 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].
% 296.71/297.03 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].
% 296.71/297.03 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].
% 296.71/297.03 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].
% 296.71/297.03 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].
% 296.71/297.03 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].
% 296.71/297.03 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].
% 296.71/297.03 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].
% 296.71/297.03 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].
% 296.71/297.03 48 axiom_m4 <-> (all X is_a_theorem(strict_implies(X,and(X,X)))) # label(axiom_m4) # label(axiom) # label(non_clause). [assumption].
% 296.71/297.03 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].
% 296.71/297.03 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].
% 296.71/297.03 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].
% 296.71/297.03 63 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(2)].
% 296.71/297.03 83 or_2 | -is_a_theorem(implies(c23,or(c22,c23))) # label(or_2) # label(axiom). [clausify(11)].
% 296.71/297.03 114 -op_or | or(A,B) = not(and(not(A),not(B))) # label(op_or) # label(axiom). [clausify(27)].
% 296.71/297.03 115 -op_or | not(and(not(A),not(B))) = or(A,B). [copy(114),flip(b)].
% 296.71/297.03 118 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 296.71/297.03 120 -op_equiv | and(implies(A,B),implies(B,A)) = equiv(A,B) # label(op_equiv) # label(axiom). [clausify(31)].
% 296.71/297.03 124 -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)].
% 296.71/297.03 128 -adjunction | -is_a_theorem(A) | -is_a_theorem(B) | is_a_theorem(and(A,B)) # label(adjunction) # label(axiom). [clausify(34)].
% 296.71/297.03 132 -substitution_strict_equiv | -is_a_theorem(strict_equiv(A,B)) | B = A # label(substitution_strict_equiv) # label(axiom). [clausify(35)].
% 296.71/297.03 153 -axiom_m1 | is_a_theorem(strict_implies(and(A,B),and(B,A))) # label(axiom_m1) # label(axiom). [clausify(45)].
% 296.71/297.03 155 -axiom_m2 | is_a_theorem(strict_implies(and(A,B),A)) # label(axiom_m2) # label(axiom). [clausify(46)].
% 296.71/297.03 157 -axiom_m3 | is_a_theorem(strict_implies(and(and(A,B),C),and(A,and(B,C)))) # label(axiom_m3) # label(axiom). [clausify(47)].
% 296.71/297.03 159 -axiom_m4 | is_a_theorem(strict_implies(A,and(A,A))) # label(axiom_m4) # label(axiom). [clausify(48)].
% 296.71/297.03 161 -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)].
% 296.71/297.03 177 -op_strict_implies | strict_implies(A,B) = necessarily(implies(A,B)) # label(op_strict_implies) # label(axiom). [clausify(57)].
% 296.71/297.03 178 -op_strict_implies | necessarily(implies(A,B)) = strict_implies(A,B). [copy(177),flip(b)].
% 296.71/297.03 179 -op_strict_equiv | strict_equiv(A,B) = and(strict_implies(A,B),strict_implies(B,A)) # label(op_strict_equiv) # label(axiom). [clausify(58)].
% 296.71/297.03 180 -op_strict_equiv | and(strict_implies(A,B),strict_implies(B,A)) = strict_equiv(A,B). [copy(179),flip(b)].
% 296.71/297.03 182 op_or # label(s1_0_op_or) # label(axiom). [assumption].
% 296.71/297.03 184 op_strict_implies # label(s1_0_op_strict_implies) # label(axiom). [assumption].
% 296.71/297.03 185 op_equiv # label(s1_0_op_equiv) # label(axiom). [assumption].
% 296.71/297.03 186 op_strict_equiv # label(s1_0_op_strict_equiv) # label(axiom). [assumption].
% 296.71/297.03 187 modus_ponens_strict_implies # label(s1_0_modus_ponens_strict_implies) # label(axiom). [assumption].
% 296.71/297.03 188 substitution_strict_equiv # label(s1_0_substitution_strict_equiv) # label(axiom). [assumption].
% 296.71/297.03 189 adjunction # label(s1_0_adjunction) # label(axiom). [assumption].
% 296.71/297.03 190 axiom_m1 # label(s1_0_axiom_m1) # label(axiom). [assumption].
% 296.71/297.03 191 axiom_m2 # label(s1_0_axiom_m2) # label(axiom). [assumption].
% 296.71/297.03 192 axiom_m3 # label(s1_0_axiom_m3) # label(axiom). [assumption].
% 296.71/297.03 193 axiom_m4 # label(s1_0_axiom_m4) # label(axiom). [assumption].
% 296.71/297.03 194 axiom_m5 # label(s1_0_axiom_m5) # label(axiom). [assumption].
% 296.71/297.03 195 op_implies_and # label(hilbert_op_implies_and) # label(axiom). [assumption].
% 296.71/297.03 196 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption].
% 296.71/297.03 197 -or_2 # label(hilbert_or_2) # label(negated_conjecture). [assumption].
% 296.71/297.03 200 not(and(not(A),not(B))) = or(A,B). [back_unit_del(115),unit_del(a,182)].
% 296.71/297.03 201 necessarily(implies(A,B)) = strict_implies(A,B). [back_unit_del(178),unit_del(a,184)].
% 296.71/297.03 202 and(implies(A,B),implies(B,A)) = equiv(A,B). [back_unit_del(120),unit_del(a,185)].
% 296.71/297.03 203 and(strict_implies(A,B),strict_implies(B,A)) = strict_equiv(A,B). [back_unit_del(180),unit_del(a,186)].
% 296.71/297.03 204 -is_a_theorem(A) | -is_a_theorem(strict_implies(A,B)) | is_a_theorem(B). [back_unit_del(124),unit_del(a,187)].
% 296.71/297.03 205 -is_a_theorem(strict_equiv(A,B)) | B = A. [back_unit_del(132),unit_del(a,188)].
% 296.71/297.03 206 -is_a_theorem(A) | -is_a_theorem(B) | is_a_theorem(and(A,B)). [back_unit_del(128),unit_del(a,189)].
% 296.71/297.03 207 is_a_theorem(strict_implies(and(A,B),and(B,A))). [back_unit_del(153),unit_del(a,190)].
% 296.71/297.03 208 is_a_theorem(strict_implies(and(A,B),A)). [back_unit_del(155),unit_del(a,191)].
% 296.71/297.03 209 is_a_theorem(strict_implies(and(and(A,B),C),and(A,and(B,C)))). [back_unit_del(157),unit_del(a,192)].
% 296.71/297.03 210 is_a_theorem(strict_implies(A,and(A,A))). [back_unit_del(159),unit_del(a,193)].
% 296.71/297.03 211 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)].
% 296.71/297.03 212 not(and(A,not(B))) = implies(A,B). [back_unit_del(118),unit_del(a,195)].
% 296.71/297.03 213 -is_a_theorem(equiv(A,B)) | B = A. [back_unit_del(63),unit_del(a,196)].
% 296.71/297.03 214 -is_a_theorem(implies(c23,or(c22,c23))). [back_unit_del(83),unit_del(a,197)].
% 296.71/297.03 219 implies(not(A),B) = or(A,B). [back_rewrite(200),rewrite([212(4)])].
% 296.71/297.03 240 -is_a_theorem(A) | is_a_theorem(and(A,strict_implies(and(B,C),and(C,B)))). [resolve(207,a,206,b)].
% 296.71/297.03 247 -is_a_theorem(A) | is_a_theorem(and(A,strict_implies(and(B,C),B))). [resolve(208,a,206,b)].
% 296.71/297.03 248 -is_a_theorem(A) | is_a_theorem(and(strict_implies(and(B,C),B),A)). [resolve(208,a,206,a)].
% 296.71/297.03 263 -is_a_theorem(A) | is_a_theorem(and(A,strict_implies(B,and(B,B)))). [resolve(210,a,206,b)].
% 296.71/297.03 271 -is_a_theorem(and(strict_implies(A,B),strict_implies(B,C))) | is_a_theorem(strict_implies(A,C)). [resolve(211,a,204,b)].
% 296.71/297.03 277 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(212(a,1),212(a,1,1,2))].
% 296.71/297.03 280 necessarily(or(A,B)) = strict_implies(not(A),B). [para(219(a,1),201(a,1,1))].
% 296.71/297.03 281 and(or(A,B),implies(B,not(A))) = equiv(not(A),B). [para(219(a,1),202(a,1,1))].
% 296.71/297.03 282 and(implies(A,not(B)),or(B,A)) = equiv(A,not(B)). [para(219(a,1),202(a,1,2))].
% 296.71/297.03 283 or(and(A,not(B)),C) = implies(implies(A,B),C). [para(212(a,1),219(a,1,1)),flip(a)].
% 296.71/297.03 465 is_a_theorem(and(strict_implies(and(and(A,B),C),and(A,and(B,C))),strict_implies(and(D,E),and(E,D)))). [resolve(240,a,209,a)].
% 296.71/297.03 467 is_a_theorem(and(strict_implies(and(A,B),and(B,A)),strict_implies(and(C,D),and(D,C)))). [resolve(240,a,207,a)].
% 296.71/297.03 605 is_a_theorem(and(strict_implies(A,and(A,A)),strict_implies(and(B,C),B))). [resolve(247,a,210,a)].
% 296.71/297.03 607 is_a_theorem(and(strict_implies(and(A,B),A),strict_implies(and(C,D),C))). [resolve(247,a,208,a)].
% 296.71/297.03 2316 implies(A,and(not(B),not(C))) = not(and(A,or(B,C))). [para(219(a,1),277(a,1,1,2)),flip(a)].
% 296.71/297.03 2429 and(or(A,not(B)),or(B,not(A))) = equiv(not(A),not(B)). [para(219(a,1),281(a,1,2))].
% 296.71/297.03 9036 is_a_theorem(strict_implies(A,A)). [resolve(605,a,271,a)].
% 296.71/297.03 9042 is_a_theorem(strict_equiv(A,and(A,A))). [para(203(a,1),605(a,1))].
% 296.71/297.03 9087 is_a_theorem(and(strict_implies(A,A),strict_implies(B,and(B,B)))). [resolve(9036,a,263,a)].
% 296.71/297.03 9088 is_a_theorem(and(strict_implies(and(A,B),A),strict_implies(C,C))). [resolve(9036,a,248,a)].
% 296.71/297.03 9089 is_a_theorem(and(strict_implies(A,A),strict_implies(and(B,C),B))). [resolve(9036,a,247,a)].
% 296.71/297.03 9098 -is_a_theorem(A) | is_a_theorem(and(A,strict_implies(B,B))). [resolve(9036,a,206,b)].
% 296.71/297.03 9101 is_a_theorem(strict_implies(and(and(A,B),C),and(and(B,C),A))). [resolve(465,a,271,a)].
% 296.71/297.03 9218 and(A,A) = A. [resolve(9042,a,205,a)].
% 296.71/297.03 9223 is_a_theorem(and(strict_implies(A,A),strict_implies(B,B))). [back_rewrite(9087),rewrite([9218(2)])].
% 296.71/297.03 9658 strict_equiv(A,A) = strict_implies(A,A). [para(9218(a,1),203(a,1)),flip(a)].
% 296.71/297.03 9659 is_a_theorem(strict_implies(and(A,B),and(A,and(A,B)))). [para(9218(a,1),209(a,1,1,1))].
% 296.71/297.03 9662 or(A,A) = not(not(A)). [para(9218(a,1),212(a,1,1)),rewrite([219(4)]),flip(a)].
% 296.71/297.03 9675 implies(or(A,A),B) = or(not(A),B). [para(9218(a,1),283(a,1,1)),rewrite([219(4)]),flip(a)].
% 296.71/297.03 9780 is_a_theorem(strict_equiv(and(A,B),and(B,A))). [para(203(a,1),467(a,1))].
% 296.71/297.03 9921 strict_implies(or(A,A),B) = strict_implies(not(not(A)),B). [para(9662(a,2),280(a,2,1)),rewrite([280(3)]),flip(a)].
% 296.71/297.03 9938 not(or(A,A)) = not(not(not(A))). [para(9662(a,2),9662(a,2,1)),rewrite([9662(3)]),flip(a)].
% 296.71/297.03 10190 and(A,B) = and(B,A). [resolve(9780,a,205,a)].
% 296.71/297.03 10306 is_a_theorem(strict_implies(and(A,and(B,C)),and(B,and(C,A)))). [back_rewrite(9101),rewrite([10190(2),10190(4)])].
% 296.71/297.03 10455 equiv(not(A),B) = equiv(B,not(A)). [back_rewrite(282),rewrite([10190(4),281(4)])].
% 296.71/297.03 10496 and(or(A,B),implies(B,not(A))) = equiv(B,not(A)). [back_rewrite(281),rewrite([10455(6)])].
% 296.71/297.03 10497 equiv(A,B) = equiv(B,A). [para(10190(a,1),202(a,1)),rewrite([202(3)])].
% 296.71/297.03 10498 strict_equiv(A,B) = strict_equiv(B,A). [para(10190(a,1),203(a,1)),rewrite([203(3)])].
% 296.71/297.03 10499 is_a_theorem(strict_implies(and(A,B),B)). [para(10190(a,1),208(a,1,1))].
% 296.71/297.03 10504 -is_a_theorem(and(strict_implies(A,B),strict_implies(C,A))) | is_a_theorem(strict_implies(C,B)). [para(10190(a,1),271(a,1))].
% 296.71/297.03 10575 -is_a_theorem(A) | is_a_theorem(and(A,strict_implies(and(B,C),C))). [resolve(10499,a,206,b)].
% 296.71/297.03 10595 -is_a_theorem(equiv(A,B)) | A = B. [para(10497(a,1),213(a,1))].
% 296.71/297.03 10599 -is_a_theorem(strict_equiv(A,B)) | A = B. [para(10498(a,1),205(a,1))].
% 296.71/297.03 10768 implies(A,or(B,B)) = implies(A,not(not(B))). [para(9938(a,1),212(a,1,1,2)),rewrite([212(5)]),flip(a)].
% 296.71/297.03 10769 or(or(A,A),B) = or(not(not(A)),B). [para(9938(a,1),219(a,1,1)),rewrite([219(4)]),flip(a)].
% 296.71/297.03 10785 not(not(not(or(A,A)))) = not(not(not(not(not(A))))). [para(9938(a,1),9938(a,2,1,1)),rewrite([9662(3)])].
% 296.71/297.03 10962 is_a_theorem(and(strict_implies(A,A),strict_implies(and(B,C),C))). [para(10190(a,1),9089(a,1,2,1))].
% 296.71/297.03 11008 is_a_theorem(strict_implies(and(A,and(B,C)),B)). [resolve(607,a,271,a),rewrite([10190(2)])].
% 296.71/297.03 11034 is_a_theorem(strict_implies(and(A,and(B,C)),C)). [para(10190(a,1),11008(a,1,1,2))].
% 296.71/297.03 11050 -is_a_theorem(A) | is_a_theorem(and(A,strict_implies(and(B,and(C,D)),D))). [resolve(11034,a,206,b)].
% 296.71/297.03 11155 is_a_theorem(and(strict_implies(and(A,B),and(A,and(A,B))),strict_implies(and(C,D),D))). [resolve(10575,a,9659,a)].
% 296.71/297.03 12106 and(strict_implies(A,not(not(B))),strict_implies(or(B,B),A)) = strict_equiv(A,not(not(B))). [para(9921(a,2),203(a,1,2))].
% 296.71/297.03 12107 -is_a_theorem(or(A,A)) | -is_a_theorem(strict_implies(not(not(A)),B)) | is_a_theorem(B). [para(9921(a,1),204(b,1))].
% 296.71/297.03 12852 strict_implies(A,or(B,B)) = strict_implies(A,not(not(B))). [para(10768(a,1),201(a,1,1)),rewrite([201(4)]),flip(a)].
% 296.71/297.03 12853 or(A,or(B,B)) = or(A,not(not(B))). [para(10768(a,1),219(a,1)),rewrite([219(4)]),flip(a)].
% 296.71/297.03 13452 strict_equiv(A,or(B,B)) = strict_equiv(A,not(not(B))). [para(12852(a,1),203(a,1,1)),rewrite([12106(6)]),flip(a)].
% 296.71/297.03 13454 -is_a_theorem(A) | -is_a_theorem(strict_implies(A,or(B,B))) | is_a_theorem(not(not(B))). [para(12852(a,2),204(b,1))].
% 296.71/297.03 13661 or(A,not(or(B,B))) = or(A,not(not(not(B)))). [para(9662(a,2),12853(a,2,2,1)),rewrite([9662(3)]),flip(a)].
% 296.71/297.03 13667 or(or(A,A),not(not(B))) = or(not(not(A)),or(B,B)). [para(12853(a,1),10769(a,1))].
% 296.71/297.03 13668 or(or(A,A),or(B,B)) = or(not(not(A)),not(not(B))). [para(12853(a,1),10769(a,2))].
% 296.71/297.03 13758 -is_a_theorem(strict_equiv(A,not(not(B)))) | or(B,B) = A. [para(13452(a,1),205(a,1))].
% 296.71/297.03 13759 -is_a_theorem(strict_equiv(A,or(B,B))) | not(not(B)) = A. [para(13452(a,2),205(a,1))].
% 296.71/297.03 13764 strict_equiv(A,not(or(B,B))) = strict_equiv(A,not(not(not(B)))). [para(9662(a,2),13452(a,2,2,1)),rewrite([9662(3)]),flip(a)].
% 296.71/297.03 15885 -is_a_theorem(and(strict_implies(or(A,A),B),strict_implies(C,not(not(A))))) | is_a_theorem(strict_implies(C,B)). [para(9921(a,2),10504(a,1,1))].
% 296.71/297.03 17908 not(and(not(A),or(B,C))) = or(A,and(not(B),not(C))). [para(2316(a,1),219(a,1))].
% 296.71/297.03 17914 not(and(A,or(B,C))) = not(and(A,or(C,B))). [para(10190(a,1),2316(a,1,2)),rewrite([2316(4)])].
% 296.71/297.03 19747 or(or(A,A),not(or(B,B))) = or(not(not(A)),not(not(not(B)))). [para(13661(a,1),10769(a,2))].
% 296.71/297.03 19790 -is_a_theorem(strict_equiv(A,not(not(not(B))))) | not(or(B,B)) = A. [para(13764(a,1),205(a,1))].
% 296.71/297.03 19867 not(and(or(A,B),or(B,A))) = not(or(A,B)). [para(9218(a,1),17914(a,1,1)),flip(a)].
% 296.71/297.03 20499 not(or(A,B)) = not(or(B,A)). [para(10190(a,1),19867(a,1,1)),rewrite([19867(4)])].
% 296.71/297.03 20505 implies(A,or(B,C)) = implies(A,or(C,B)). [para(20499(a,1),212(a,1,1,2)),rewrite([212(4)])].
% 296.71/297.03 20527 strict_implies(A,or(B,C)) = strict_implies(A,or(C,B)). [para(20505(a,1),201(a,1,1)),rewrite([201(3)])].
% 296.71/297.03 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))].
% 296.71/297.03 24399 or(A,and(not(B),not(C))) = implies(or(B,C),A). [para(10190(a,1),17908(a,1,1)),rewrite([212(4)]),flip(a)].
% 296.71/297.03 24410 or(not(A),B) = or(B,not(A)). [para(9218(a,1),24399(a,1,2)),rewrite([9675(4)]),flip(a)].
% 296.71/297.03 24413 implies(or(A,B),C) = implies(or(B,A),C). [para(10190(a,1),24399(a,1,2)),rewrite([24399(4)])].
% 296.71/297.03 24454 implies(or(A,A),B) = or(B,not(A)). [back_rewrite(9675),rewrite([24410(4)])].
% 296.71/297.03 24460 strict_implies(not(not(A)),B) = strict_implies(not(B),not(A)). [para(24410(a,1),280(a,1,1)),rewrite([280(3)]),flip(a)].
% 296.71/297.03 24554 -is_a_theorem(or(A,A)) | -is_a_theorem(strict_implies(not(B),not(A))) | is_a_theorem(B). [back_rewrite(12107),rewrite([24460(5)])].
% 296.71/297.03 24556 strict_implies(or(A,A),B) = strict_implies(not(B),not(A)). [back_rewrite(9921),rewrite([24460(5)])].
% 296.71/297.03 24611 strict_implies(or(A,B),C) = strict_implies(or(B,A),C). [para(24413(a,1),201(a,1,1)),rewrite([201(3)])].
% 296.71/297.03 24613 strict_equiv(A,or(B,C)) = strict_equiv(A,or(C,B)). [back_rewrite(20779),rewrite([24611(4),203(5)])].
% 296.71/297.03 24715 is_a_theorem(strict_implies(or(A,A),A)). [para(24556(a,2),9036(a,1))].
% 296.71/297.03 24719 strict_implies(or(A,A),not(B)) = strict_implies(or(B,B),not(A)). [para(9662(a,2),24556(a,2,1))].
% 296.71/297.03 24720 is_a_theorem(and(strict_implies(or(A,A),A),strict_implies(B,B))). [para(24556(a,2),9223(a,1,1))].
% 296.71/297.03 24728 is_a_theorem(and(strict_implies(and(A,B),A),strict_implies(or(C,C),C))). [para(24556(a,2),9088(a,1,2))].
% 296.71/297.03 25105 -is_a_theorem(A) | is_a_theorem(and(A,strict_implies(or(B,B),B))). [resolve(24715,a,206,b)].
% 296.71/297.03 25163 is_a_theorem(and(strict_implies(or(A,A),A),strict_implies(or(B,B),B))). [para(24556(a,2),24720(a,1,2))].
% 296.71/297.03 25279 -is_a_theorem(strict_equiv(A,or(B,C))) | or(C,B) = A. [para(24613(a,1),205(a,1))].
% 296.71/297.03 25305 or(A,B) = or(B,A). [para(9658(a,1),25279(a,1)),unit_del(a,9036)].
% 296.71/297.03 25326 strict_implies(not(A),B) = strict_implies(not(B),A). [para(25305(a,1),280(a,1,1)),rewrite([280(2)])].
% 296.71/297.03 25327 and(or(A,B),implies(A,not(B))) = equiv(A,not(B)). [para(25305(a,1),10496(a,1,1))].
% 296.71/297.03 25330 or(or(A,A),or(B,B)) = or(not(not(B)),not(not(A))). [para(13668(a,2),25305(a,2)),flip(a)].
% 296.71/297.03 25350 and(strict_implies(A,not(B)),strict_implies(not(A),B)) = strict_equiv(A,not(B)). [para(25326(a,1),203(a,1,1)),rewrite([10190(5),10498(7)])].
% 296.71/297.03 25445 is_a_theorem(strict_implies(not(A),not(and(A,B)))). [resolve(24728,a,10504,a),rewrite([9662(3),25326(4)])].
% 296.71/297.03 25477 -is_a_theorem(not(A)) | is_a_theorem(not(and(A,B))). [resolve(25445,a,204,b)].
% 296.71/297.03 25483 is_a_theorem(strict_implies(not(A),implies(A,B))). [para(212(a,1),25445(a,1,2))].
% 296.71/297.03 25487 is_a_theorem(strict_implies(or(A,A),implies(B,A))). [para(9662(a,2),25445(a,1,1)),rewrite([10190(3),212(4)])].
% 296.71/297.03 25529 is_a_theorem(and(strict_implies(not(A),implies(A,B)),strict_implies(and(C,and(D,E)),E))). [resolve(25483,a,11050,a)].
% 296.71/297.03 25570 is_a_theorem(strict_implies(or(A,A),or(A,B))). [para(9662(a,2),25483(a,1,1)),rewrite([219(3)])].
% 296.71/297.03 25572 is_a_theorem(strict_implies(not(not(not(A))),or(B,not(A)))). [para(9938(a,1),25483(a,1,1)),rewrite([24454(5)])].
% 296.71/297.03 25738 -is_a_theorem(not(not(not(or(A,A))))) | is_a_theorem(implies(B,not(not(not(A))))). [para(10785(a,2),25477(a,1)),rewrite([10190(10),212(11)])].
% 296.71/297.03 25773 is_a_theorem(and(strict_implies(or(A,A),implies(B,A)),strict_implies(C,C))). [resolve(25487,a,9098,a)].
% 296.71/297.03 25858 is_a_theorem(and(strict_implies(or(A,A),or(A,B)),strict_implies(C,C))). [resolve(25570,a,9098,a)].
% 296.71/297.03 26323 is_a_theorem(strict_implies(not(not(implies(A,B))),or(C,implies(A,B)))). [para(212(a,1),25572(a,1,1,1,1)),rewrite([212(6)])].
% 296.71/297.03 27159 is_a_theorem(strict_implies(not(A),not(or(A,A)))). [resolve(25163,a,10504,a),rewrite([9662(3),25326(4)])].
% 296.71/297.03 27199 is_a_theorem(strict_implies(not(A),not(not(not(A))))). [para(9662(a,1),27159(a,1,2,1))].
% 296.71/297.03 27346 is_a_theorem(and(strict_implies(not(A),not(not(not(A)))),strict_implies(B,B))). [resolve(27199,a,9098,a)].
% 296.71/297.03 29532 -is_a_theorem(not(not(implies(A,B)))) | is_a_theorem(or(C,implies(A,B))). [resolve(26323,a,204,b)].
% 296.71/297.03 30965 is_a_theorem(strict_equiv(and(A,B),and(A,and(A,B)))). [para(203(a,1),11155(a,1))].
% 296.71/297.03 30966 and(A,and(A,B)) = and(A,B). [resolve(30965,a,10599,a),flip(a)].
% 296.71/297.03 34001 is_a_theorem(strict_equiv(not(A),not(not(not(A))))). [para(25350(a,1),27346(a,1))].
% 296.71/297.03 34276 not(or(A,A)) = not(A). [resolve(34001,a,19790,a)].
% 296.71/297.03 34277 not(not(not(A))) = not(A). [resolve(34001,a,13758,a),rewrite([9662(3)])].
% 296.71/297.03 34470 -is_a_theorem(not(A)) | is_a_theorem(implies(B,not(A))). [back_rewrite(25738),rewrite([34276(2),34277(3),34277(5)])].
% 296.71/297.03 34570 or(or(A,A),not(B)) = or(not(B),not(not(A))). [back_rewrite(19747),rewrite([34276(3),34277(8),25305(7)])].
% 296.71/297.03 34912 implies(A,or(B,B)) = implies(A,B). [para(34276(a,1),212(a,1,1,2)),rewrite([212(3)]),flip(a)].
% 296.71/297.03 34913 not(not(implies(A,B))) = implies(A,B). [para(212(a,1),34276(a,2)),rewrite([9662(5),212(3)])].
% 296.71/297.03 34914 or(A,or(B,B)) = or(B,A). [para(34276(a,1),219(a,1,1)),rewrite([219(2),25305(3)]),flip(a)].
% 296.71/297.03 34956 or(not(not(A)),not(not(B))) = or(B,not(not(A))). [para(34276(a,1),13667(a,2,1,1)),rewrite([9662(3),34276(2),34914(9)])].
% 296.71/297.03 35090 implies(A,not(not(B))) = implies(A,B). [back_rewrite(10768),rewrite([34912(2)]),flip(a)].
% 296.71/297.03 35121 -is_a_theorem(implies(A,B)) | is_a_theorem(or(C,implies(A,B))). [back_rewrite(29532),rewrite([34913(3)])].
% 296.71/297.03 35159 or(A,not(not(B))) = or(B,A). [back_rewrite(25330),rewrite([34914(3),34914(2),25305(6),34956(6)]),flip(a)].
% 296.71/297.03 35287 or(or(A,A),not(B)) = or(A,not(B)). [back_rewrite(34570),rewrite([35159(7)])].
% 296.71/297.03 35529 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(C,implies(A,B))). [para(212(a,1),34470(a,1)),rewrite([212(5)])].
% 296.71/297.03 35596 strict_implies(A,or(B,B)) = strict_implies(A,B). [para(34912(a,1),201(a,1,1)),rewrite([201(2)]),flip(a)].
% 296.71/297.03 35656 -is_a_theorem(A) | -is_a_theorem(strict_implies(A,B)) | is_a_theorem(not(not(B))). [back_rewrite(13454),rewrite([35596(3)])].
% 296.71/297.03 35657 strict_implies(A,not(not(B))) = strict_implies(A,B). [back_rewrite(12852),rewrite([35596(2)]),flip(a)].
% 296.71/297.03 35745 -is_a_theorem(and(strict_implies(or(A,A),B),strict_implies(C,A))) | is_a_theorem(strict_implies(C,B)). [back_rewrite(15885),rewrite([35657(5)])].
% 296.71/297.03 35831 not(not(or(A,B))) = or(A,B). [para(219(a,1),34913(a,1,1,1)),rewrite([219(5)])].
% 296.71/297.03 36142 strict_implies(not(A),not(or(B,C))) = strict_implies(or(B,C),A). [para(35831(a,1),25326(a,1,1)),flip(a)].
% 296.71/297.03 36593 -is_a_theorem(A) | is_a_theorem(not(not(A))). [resolve(35656,b,9036,a)].
% 296.71/297.03 37150 is_a_theorem(not(not(and(strict_implies(A,A),strict_implies(and(B,C),C))))). [resolve(36593,a,10962,a)].
% 296.71/297.03 37244 is_a_theorem(not(not(strict_implies(A,A)))). [resolve(36593,a,9036,a)].
% 296.71/297.03 37810 is_a_theorem(implies(A,strict_implies(B,B))). [resolve(37244,a,34470,a),rewrite([35090(4)])].
% 296.71/297.03 37960 is_a_theorem(or(A,implies(B,strict_implies(C,C)))). [resolve(37810,a,35121,a)].
% 296.71/297.03 37998 -is_a_theorem(A) | is_a_theorem(and(A,implies(B,strict_implies(C,C)))). [resolve(37810,a,206,b)].
% 296.71/297.03 39091 is_a_theorem(or(A,or(B,strict_implies(C,C)))). [para(219(a,1),37960(a,1,2))].
% 296.71/297.03 39594 -is_a_theorem(strict_implies(or(A,strict_implies(B,B)),C)) | is_a_theorem(C). [resolve(39091,a,24554,a),rewrite([36142(5)])].
% 296.71/297.03 49881 equiv(or(A,A),not(not(B))) = equiv(not(A),not(B)). [para(35287(a,1),25327(a,1,1)),rewrite([35090(6),24454(4),2429(5)]),flip(a)].
% 296.71/297.03 57962 is_a_theorem(implies(A,and(strict_implies(B,B),strict_implies(and(C,D),D)))). [resolve(37150,a,34470,a),rewrite([35090(7)])].
% 296.71/297.03 58427 is_a_theorem(strict_implies(and(A,and(B,not(C))),implies(C,D))). [resolve(25529,a,10504,a)].
% 296.71/297.03 61018 is_a_theorem(implies(A,and(strict_implies(B,B),strict_implies(C,C)))). [para(9218(a,1),57962(a,1,2,2,1))].
% 296.71/297.03 61020 is_a_theorem(implies(A,implies(B,and(strict_implies(C,C),strict_implies(D,D))))). [resolve(61018,a,35529,a)].
% 296.71/297.03 68037 is_a_theorem(strict_implies(A,or(A,B))). [resolve(35745,a,25858,a)].
% 296.71/297.03 68040 is_a_theorem(strict_implies(A,implies(B,A))). [resolve(35745,a,25773,a)].
% 296.71/297.03 68059 is_a_theorem(and(strict_implies(A,or(A,B)),strict_implies(or(C,C),C))). [resolve(68037,a,25105,a)].
% 296.71/297.03 68099 -is_a_theorem(A) | is_a_theorem(and(A,strict_implies(B,implies(C,B)))). [resolve(68040,a,206,b)].
% 296.71/297.03 69155 is_a_theorem(strict_equiv(A,or(A,A))). [para(203(a,1),68059(a,1))].
% 296.71/297.03 69178 not(not(A)) = A. [resolve(69155,a,13759,a)].
% 296.71/297.03 69179 or(A,A) = A. [resolve(69155,a,10599,a),flip(a)].
% 296.71/297.03 69272 equiv(not(A),not(B)) = equiv(A,B). [back_rewrite(49881),rewrite([69179(1),69178(2)]),flip(a)].
% 296.71/297.03 69668 strict_implies(A,not(B)) = strict_implies(B,not(A)). [back_rewrite(24719),rewrite([69179(1),69179(3)])].
% 296.71/297.03 69676 or(A,not(B)) = implies(B,A). [back_rewrite(24454),rewrite([69179(1)]),flip(a)].
% 296.71/297.03 70199 not(and(A,B)) = implies(A,not(B)). [para(69178(a,1),212(a,1,1,2))].
% 296.71/297.03 70200 not(implies(A,B)) = and(A,not(B)). [para(212(a,1),69178(a,1,1))].
% 296.71/297.03 70799 -is_a_theorem(strict_implies(strict_implies(A,A),B)) | is_a_theorem(B). [para(69179(a,1),39594(a,1,1))].
% 296.71/297.03 74614 -is_a_theorem(equiv(A,B)) | not(A) = not(B). [para(69272(a,1),10595(a,1))].
% 296.71/297.03 74706 implies(A,not(B)) = implies(B,not(A)). [para(10190(a,1),70199(a,1,1)),rewrite([70199(2)])].
% 296.71/297.03 74708 implies(A,implies(A,not(B))) = implies(A,not(B)). [para(30966(a,1),70199(a,1,1)),rewrite([70199(2),70199(4)]),flip(a)].
% 296.71/297.03 74712 or(A,implies(B,not(C))) = implies(and(B,C),A). [para(70199(a,1),69676(a,1,2))].
% 296.71/297.03 74721 implies(and(A,not(B)),C) = or(C,implies(A,B)). [para(70200(a,1),219(a,1,1)),rewrite([25305(5)])].
% 296.71/297.03 74722 and(not(A),not(B)) = not(or(A,B)). [para(219(a,1),70200(a,1,1)),flip(a)].
% 296.71/297.03 76534 is_a_theorem(strict_implies(and(A,not(or(B,C))),implies(C,D))). [para(74722(a,1),58427(a,1,1,2))].
% 296.71/297.03 77356 implies(A,implies(A,B)) = implies(A,B). [para(69178(a,1),74708(a,1,2,2)),rewrite([69178(4)])].
% 296.71/297.03 77363 strict_implies(A,implies(A,B)) = strict_implies(A,B). [para(77356(a,1),201(a,1,1)),rewrite([201(2)]),flip(a)].
% 296.71/297.03 78064 is_a_theorem(strict_implies(not(or(A,or(B,C))),implies(C,D))). [para(74722(a,1),76534(a,1,1))].
% 296.71/297.03 78325 is_a_theorem(strict_implies(and(A,not(B)),or(C,or(A,D)))). [para(25326(a,1),78064(a,1)),rewrite([70200(2),25305(3)])].
% 296.71/297.03 78386 is_a_theorem(strict_implies(and(A,B),or(C,or(A,D)))). [para(69178(a,1),78325(a,1,1,2))].
% 296.71/297.03 78397 is_a_theorem(strict_implies(and(A,B),or(C,implies(D,A)))). [para(69676(a,1),78386(a,1,2,2))].
% 296.71/297.03 78418 is_a_theorem(strict_implies(and(A,not(B)),implies(and(B,C),D))). [para(74706(a,1),78397(a,1,2,2)),rewrite([10190(2),74712(5)])].
% 296.71/297.03 78448 is_a_theorem(strict_implies(and(A,not(A)),B)). [para(77363(a,1),78418(a,1))].
% 296.71/297.03 78480 is_a_theorem(strict_implies(A,implies(B,B))). [para(69668(a,1),78448(a,1)),rewrite([70199(3),69178(2)])].
% 296.71/297.03 78691 is_a_theorem(and(strict_implies(A,implies(B,B)),strict_implies(C,implies(D,C)))). [resolve(78480,a,68099,a)].
% 296.71/297.03 83159 is_a_theorem(strict_equiv(implies(A,A),implies(B,implies(A,A)))). [para(203(a,1),78691(a,1)),rewrite([10498(4)])].
% 296.71/297.03 83250 implies(A,implies(B,B)) = implies(B,B). [resolve(83159,a,10599,a),flip(a)].
% 296.71/297.03 83257 strict_implies(A,implies(B,B)) = strict_implies(B,B). [para(83250(a,1),201(a,1,1)),rewrite([201(2)]),flip(a)].
% 296.71/297.03 83258 or(A,implies(B,B)) = implies(B,B). [para(83250(a,1),219(a,1)),flip(a)].
% 296.71/297.03 83311 strict_implies(and(A,not(A)),B) = strict_implies(A,A). [para(83257(a,1),25326(a,1)),rewrite([70200(3)]),flip(a)].
% 296.71/297.03 83467 strict_implies(A,A) = strict_implies(B,B). [para(83311(a,1),83257(a,1))].
% 296.71/297.03 83468 strict_implies(A,A) = c_0. [new_symbol(83467)].
% 296.71/297.03 84458 -is_a_theorem(strict_implies(c_0,A)) | is_a_theorem(A). [back_rewrite(70799),rewrite([83468(1)])].
% 296.71/297.03 84777 is_a_theorem(implies(A,implies(B,c_0))). [back_rewrite(61020),rewrite([83468(1),83468(2),9218(3)])].
% 296.71/297.03 85318 -is_a_theorem(A) | is_a_theorem(and(A,implies(B,c_0))). [back_rewrite(37998),rewrite([83468(2)])].
% 296.71/297.03 88880 is_a_theorem(and(implies(A,implies(B,c_0)),implies(C,c_0))). [resolve(85318,a,84777,a)].
% 296.71/297.03 92186 is_a_theorem(equiv(c_0,implies(A,c_0))). [para(202(a,1),88880(a,1))].
% 296.71/297.03 92203 and(A,not(c_0)) = not(c_0). [resolve(92186,a,74614,a),rewrite([70200(5)]),flip(a)].
% 296.71/297.03 92215 implies(A,c_0) = c_0. [resolve(92186,a,10595,a),flip(a)].
% 296.71/297.03 92348 or(c_0,implies(A,B)) = c_0. [para(92215(a,1),74721(a,1)),flip(a)].
% 296.71/297.03 92609 implies(A,A) = c_0. [para(83250(a,1),92348(a,1,2)),rewrite([83258(3)])].
% 296.71/297.03 92644 and(A,not(A)) = not(c_0). [para(92609(a,1),70200(a,1,1)),flip(a)].
% 296.71/297.03 92931 is_a_theorem(strict_implies(c_0,implies(and(A,B),A))). [para(92644(a,1),10306(a,1,2,2)),rewrite([10190(2),92203(6),69668(6),70199(5),70199(4),219(5),74712(4)])].
% 296.71/297.03 93270 is_a_theorem(implies(and(A,B),A)). [resolve(92931,a,84458,a)].
% 296.71/297.03 93358 is_a_theorem(implies(and(A,B),B)). [para(10190(a,1),93270(a,1,1))].
% 296.71/297.03 93434 is_a_theorem(implies(A,or(B,A))). [para(74722(a,1),93358(a,1,1)),rewrite([74706(4),69178(3)])].
% 296.71/297.03 93435 $F. [resolve(93434,a,214,a)].
% 296.71/297.03
% 296.71/297.03 % SZS output end Refutation
% 296.71/297.03 ============================== end of proof ==========================
% 296.71/297.03
% 296.71/297.03 ============================== STATISTICS ============================
% 296.71/297.03
% 296.71/297.03 Given=34237. Generated=16897984. Kept=93370. proofs=1.
% 296.71/297.03 Usable=15521. Sos=6323. Demods=197. Limbo=59, Disabled=71601. Hints=0.
% 296.71/297.03 Megabytes=114.11.
% 296.71/297.03 User_CPU=287.17, System_CPU=8.84, Wall_clock=296.
% 296.71/297.03
% 296.71/297.03 ============================== end of statistics =====================
% 296.71/297.03
% 296.71/297.03 ============================== end of search =========================
% 296.71/297.03
% 296.71/297.03 THEOREM PROVED
% 296.71/297.03 % SZS status Theorem
% 296.71/297.03
% 296.71/297.03 Exiting with 1 proof.
% 296.71/297.03
% 296.71/297.03 Process 19223 exit (max_proofs) Sun Jul 3 15:08:50 2022
% 296.71/297.03 Prover9 interrupted
%------------------------------------------------------------------------------