TSTP Solution File: LCL522+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL522+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n003.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 13:47:21 EDT 2022
% Result : Theorem 17.42s 17.71s
% Output : Refutation 17.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL522+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n003.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 09:16:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.72/0.99 ============================== Prover9 ===============================
% 0.72/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.72/0.99 Process 16107 was started by sandbox on n003.cluster.edu,
% 0.72/0.99 Sun Jul 3 09:16:09 2022
% 0.72/0.99 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_15954_n003.cluster.edu".
% 0.72/0.99 ============================== end of head ===========================
% 0.72/0.99
% 0.72/0.99 ============================== INPUT =================================
% 0.72/0.99
% 0.72/0.99 % Reading from file /tmp/Prover9_15954_n003.cluster.edu
% 0.72/0.99
% 0.72/0.99 set(prolog_style_variables).
% 0.72/0.99 set(auto2).
% 0.72/0.99 % set(auto2) -> set(auto).
% 0.72/0.99 % set(auto) -> set(auto_inference).
% 0.72/0.99 % set(auto) -> set(auto_setup).
% 0.72/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.72/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.72/0.99 % set(auto) -> set(auto_limits).
% 0.72/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.72/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.72/0.99 % set(auto) -> set(auto_denials).
% 0.72/0.99 % set(auto) -> set(auto_process).
% 0.72/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.72/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.72/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.72/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.72/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.72/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.72/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.72/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.72/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.72/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.72/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.72/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.72/0.99 % set(auto2) -> assign(stats, some).
% 0.72/0.99 % set(auto2) -> clear(echo_input).
% 0.72/0.99 % set(auto2) -> set(quiet).
% 0.72/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.72/0.99 % set(auto2) -> clear(print_given).
% 0.72/0.99 assign(lrs_ticks,-1).
% 0.72/0.99 assign(sos_limit,10000).
% 0.72/0.99 assign(order,kbo).
% 0.72/0.99 set(lex_order_vars).
% 0.72/0.99 clear(print_given).
% 0.72/0.99
% 0.72/0.99 % formulas(sos). % not echoed (43 formulas)
% 0.72/0.99
% 0.72/0.99 ============================== end of input ==========================
% 0.72/0.99
% 0.72/0.99 % From the command line: assign(max_seconds, 300).
% 0.72/0.99
% 0.72/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.72/0.99
% 0.72/0.99 % Formulas that are not ordinary clauses:
% 0.72/0.99 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].
% 0.72/0.99 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].
% 0.72/0.99 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].
% 0.72/0.99 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.99 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].
% 0.72/0.99 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].
% 0.72/0.99 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.99 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.99 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].
% 0.72/0.99 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.99 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.99 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].
% 0.72/0.99 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].
% 0.72/0.99 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].
% 1.49/1.76 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].
% 1.49/1.76 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.76 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.76 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].
% 1.49/1.76 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].
% 1.49/1.76 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.76 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.76 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.76 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.76 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.76 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].
% 1.49/1.76 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].
% 1.49/1.76 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].
% 1.49/1.76 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].
% 1.49/1.76 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].
% 1.49/1.76 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].
% 1.49/1.76 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].
% 1.49/1.76
% 1.49/1.76 ============================== end of process non-clausal formulas ===
% 1.49/1.76
% 1.49/1.76 ============================== PROCESS INITIAL CLAUSES ===============
% 1.49/1.76
% 1.49/1.76 ============================== PREDICATE ELIMINATION =================
% 1.49/1.76
% 1.49/1.76 ============================== end predicate elimination =============
% 1.49/1.76
% 1.49/1.76 Auto_denials: (non-Horn, no changes).
% 1.49/1.76
% 1.49/1.76 Term ordering decisions:
% 1.49/1.76
% 1.49/1.76 % Assigning unary symbol not kb_weight 0 and highest precedence (93).
% 1.49/1.76 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. implies=1. or=1. and=1. equiv=1. not=0.
% 1.49/1.76
% 1.49/1.76 ============================== end of process initial clauses ========
% 1.49/1.76
% 1.49/1.76 ============================== CLAUSES FOR SEARCH ====================
% 1.49/1.76
% 1.49/1.76 ============================== end of clauses for search =============
% 1.49/1.76
% 1.49/1.76 ============================== SEARCH ================================
% 1.49/1.76
% 1.49/1.76 % Starting search at 0.02 seconds.
% 1.49/1.76
% 1.49/1.76 Low Water (keep): wt=43.000, iters=3335
% 1.49/1.76
% 1.49/1.76 Low Water (keep): wt=42.000, iters=3589
% 1.49/1.76
% 1.49/1.76 Low Water (keep): wt=38.000, iters=3497
% 1.49/1.76
% 1.49/1.76 Low Water (keep): wt=37.000, iters=3495
% 1.49/1.76
% 1.49/1.76 Low Water (keep): wt=36.000, iters=3578
% 1.49/1.76
% 1.49/1.76 Low Water (keep): wt=35.000, iters=3388
% 1.49/1.76
% 1.49/1.76 Low Water (keep): wt=34.000, iters=3433
% 1.49/1.76
% 1.49/1.76 Low Water (keep): wt=32.000, iters=3402
% 1.49/1.76
% 1.49/1.76 Low Water (keep): wt=31.000, iters=3472
% 1.49/1.76
% 1.49/1.76 Low Water (keep): wt=30.000, iters=3353
% 1.49/1.76
% 17.42/17.71 Low Water (keep): wt=29.000, iters=3460
% 17.42/17.71
% 17.42/17.71 Low Water (keep): wt=28.000, iters=3360
% 17.42/17.71
% 17.42/17.71 Low Water (keep): wt=27.000, iters=3350
% 17.42/17.71
% 17.42/17.71 Low Water (keep): wt=25.000, iters=3337
% 17.42/17.71
% 17.42/17.71 Low Water (keep): wt=24.000, iters=3379
% 17.42/17.71
% 17.42/17.71 Low Water (keep): wt=23.000, iters=3386
% 17.42/17.71
% 17.42/17.71 Low Water (keep): wt=22.000, iters=3408
% 17.42/17.71
% 17.42/17.71 Low Water (keep): wt=21.000, iters=3364
% 17.42/17.71
% 17.42/17.71 Low Water (keep): wt=20.000, iters=3370
% 17.42/17.71
% 17.42/17.71 Low Water (keep): wt=19.000, iters=3339
% 17.42/17.71
% 17.42/17.71 Low Water (keep): wt=18.000, iters=3364
% 17.42/17.71
% 17.42/17.71 Low Water (keep): wt=17.000, iters=3358
% 17.42/17.71
% 17.42/17.71 Low Water (keep): wt=16.000, iters=3342
% 17.42/17.71
% 17.42/17.71 Low Water (displace): id=10191, wt=46.000
% 17.42/17.71
% 17.42/17.71 Low Water (displace): id=10543, wt=44.000
% 17.42/17.71
% 17.42/17.71 Low Water (displace): id=10538, wt=42.000
% 17.42/17.71
% 17.42/17.71 Low Water (displace): id=18227, wt=15.000
% 17.42/17.71
% 17.42/17.71 Low Water (displace): id=18280, wt=14.000
% 17.42/17.71
% 17.42/17.71 Low Water (displace): id=18432, wt=13.000
% 17.42/17.71
% 17.42/17.71 Low Water (displace): id=18708, wt=12.000
% 17.42/17.71
% 17.42/17.71 Low Water (displace): id=18928, wt=10.000
% 17.42/17.71
% 17.42/17.71 Low Water (keep): wt=15.000, iters=3358
% 17.42/17.71
% 17.42/17.71 Low Water (displace): id=26933, wt=9.000
% 17.42/17.71
% 17.42/17.71 Low Water (keep): wt=14.000, iters=3342
% 17.42/17.71
% 17.42/17.71 Low Water (keep): wt=13.000, iters=3541
% 17.42/17.71
% 17.42/17.71 ============================== PROOF =================================
% 17.42/17.71 % SZS status Theorem
% 17.42/17.71 % SZS output start Refutation
% 17.42/17.71
% 17.42/17.71 % Proof 1 at 15.97 (+ 0.76) seconds.
% 17.42/17.71 % Length of proof is 289.
% 17.42/17.71 % Level of proof is 66.
% 17.42/17.71 % Maximum clause weight is 27.000.
% 17.42/17.71 % Given clauses 4058.
% 17.42/17.71
% 17.42/17.71 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].
% 17.42/17.71 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].
% 17.42/17.71 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 17.42/17.71 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 17.42/17.71 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].
% 17.42/17.71 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].
% 17.42/17.71 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].
% 17.42/17.71 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].
% 17.42/17.71 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].
% 17.42/17.71 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].
% 17.42/17.71 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].
% 17.42/17.71 32 op_or # label(rosser_op_or) # label(axiom). [assumption].
% 17.42/17.71 33 op_implies_and # label(rosser_op_implies_and) # label(axiom). [assumption].
% 17.42/17.71 34 op_equiv # label(rosser_op_equiv) # label(axiom). [assumption].
% 17.42/17.71 35 modus_ponens # label(rosser_modus_ponens) # label(axiom). [assumption].
% 17.42/17.71 36 kn1 # label(rosser_kn1) # label(axiom). [assumption].
% 17.42/17.71 37 kn2 # label(rosser_kn2) # label(axiom). [assumption].
% 17.42/17.71 38 kn3 # label(rosser_kn3) # label(axiom). [assumption].
% 17.42/17.71 39 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption].
% 17.42/17.71 40 op_implies_or # label(principia_op_implies_or) # label(axiom). [assumption].
% 17.42/17.71 41 op_and # label(principia_op_and) # label(axiom). [assumption].
% 17.42/17.71 42 -r5 # label(principia_r5) # label(negated_conjecture). [assumption].
% 17.42/17.71 53 -kn1 | is_a_theorem(implies(A,and(A,A))) # label(kn1) # label(axiom). [clausify(16)].
% 17.42/17.71 54 is_a_theorem(implies(A,and(A,A))). [copy(53),unit_del(a,36)].
% 17.42/17.71 56 -kn2 | is_a_theorem(implies(and(A,B),A)) # label(kn2) # label(axiom). [clausify(17)].
% 17.42/17.71 57 is_a_theorem(implies(and(A,B),A)). [copy(56),unit_del(a,37)].
% 17.42/17.71 63 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(2)].
% 17.42/17.71 64 -is_a_theorem(equiv(A,B)) | B = A. [copy(63),unit_del(a,39)].
% 17.42/17.71 69 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 17.42/17.71 70 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(69),unit_del(a,35)].
% 17.42/17.71 79 -op_implies_or | or(not(A),B) = implies(A,B) # label(op_implies_or) # label(axiom). [clausify(30)].
% 17.42/17.71 80 or(not(A),B) = implies(A,B). [copy(79),unit_del(a,40)].
% 17.42/17.71 81 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 17.42/17.71 82 not(and(A,not(B))) = implies(A,B). [copy(81),unit_del(a,33)].
% 17.42/17.71 87 -op_or | or(A,B) = not(and(not(A),not(B))) # label(op_or) # label(axiom). [clausify(27)].
% 17.42/17.71 88 or(A,B) = implies(not(A),B). [copy(87),rewrite([82(6)]),unit_del(a,32)].
% 17.42/17.71 89 -op_and | and(A,B) = not(or(not(A),not(B))) # label(op_and) # label(axiom). [clausify(28)].
% 17.42/17.71 90 not(implies(not(not(A)),not(B))) = and(A,B). [copy(89),rewrite([88(5)]),flip(b),unit_del(a,41)].
% 17.42/17.71 91 -op_equiv | and(implies(A,B),implies(B,A)) = equiv(A,B) # label(op_equiv) # label(axiom). [clausify(31)].
% 17.42/17.71 92 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(91),unit_del(a,34)].
% 17.42/17.71 104 r5 | -is_a_theorem(implies(implies(c54,c55),implies(or(c53,c54),or(c53,c55)))) # label(r5) # label(axiom). [clausify(26)].
% 17.42/17.71 105 -is_a_theorem(implies(implies(c54,c55),implies(implies(not(c53),c54),implies(not(c53),c55)))). [copy(104),rewrite([88(7),88(11)]),unit_del(a,42)].
% 17.42/17.71 110 -kn3 | is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))) # label(kn3) # label(axiom). [clausify(18)].
% 17.42/17.71 111 is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))). [copy(110),unit_del(a,38)].
% 17.42/17.71 114 implies(not(not(A)),B) = implies(A,B). [back_rewrite(80),rewrite([88(2)])].
% 17.42/17.71 125 not(implies(A,not(B))) = and(A,B). [back_rewrite(90),rewrite([114(4)])].
% 17.42/17.71 126 -is_a_theorem(and(A,B)) | is_a_theorem(A). [resolve(70,b,57,a)].
% 17.42/17.71 127 -is_a_theorem(A) | is_a_theorem(and(A,A)). [resolve(70,b,54,a)].
% 17.42/17.71 128 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(82(a,1),82(a,1,1,2))].
% 17.42/17.71 129 is_a_theorem(implies(implies(A,A),equiv(A,A))). [para(92(a,1),54(a,1,2))].
% 17.42/17.71 135 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(and(B,C)),not(and(C,A)))). [resolve(111,a,70,b)].
% 17.42/17.71 137 is_a_theorem(implies(implies(A,B),implies(implies(B,C),not(and(not(C),A))))). [para(82(a,1),111(a,1,2,1))].
% 17.42/17.71 138 is_a_theorem(implies(implies(not(A),B),implies(not(and(B,C)),implies(C,A)))). [para(82(a,1),111(a,1,2,2))].
% 17.42/17.71 140 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(C,and(B,not(A))),not(equiv(B,A))))). [para(92(a,1),111(a,1,2,2,1)),rewrite([128(5)])].
% 17.42/17.71 141 is_a_theorem(implies(A,and(not(not(A)),not(not(A))))). [para(114(a,1),54(a,1))].
% 17.42/17.71 142 -is_a_theorem(not(not(A))) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [para(114(a,1),70(b,1))].
% 17.42/17.71 143 implies(not(implies(A,B)),C) = implies(and(A,not(B)),C). [para(82(a,1),114(a,1,1,1))].
% 17.42/17.71 145 and(implies(A,not(not(B))),implies(B,A)) = equiv(A,not(not(B))). [para(114(a,1),92(a,1,2))].
% 17.42/17.71 146 is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),implies(C,not(A))))). [para(114(a,1),111(a,1,1)),rewrite([82(7)])].
% 17.42/17.71 147 not(and(A,and(B,C))) = implies(A,implies(B,not(C))). [para(125(a,1),82(a,1,1,2))].
% 17.42/17.71 149 implies(not(and(A,B)),C) = implies(implies(A,not(B)),C). [para(125(a,1),114(a,1,1,1))].
% 17.42/17.71 150 and(not(not(A)),B) = and(A,B). [para(114(a,1),125(a,1,1)),rewrite([125(3)]),flip(a)].
% 17.42/17.71 152 is_a_theorem(implies(implies(A,B),implies(implies(B,not(C)),implies(C,not(A))))). [back_rewrite(146),rewrite([149(6)])].
% 17.42/17.71 153 is_a_theorem(implies(implies(not(A),B),implies(implies(B,not(C)),implies(C,A)))). [back_rewrite(138),rewrite([149(6)])].
% 17.42/17.71 155 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(B,not(C)),not(and(C,A)))). [back_rewrite(135),rewrite([149(7)])].
% 17.42/17.71 157 is_a_theorem(implies(A,and(A,not(not(A))))). [back_rewrite(141),rewrite([150(5)])].
% 17.42/17.71 172 is_a_theorem(and(implies(and(A,B),A),implies(and(A,B),A))). [resolve(127,a,57,a)].
% 17.42/17.71 175 -is_a_theorem(implies(A,A)) | is_a_theorem(equiv(A,A)). [resolve(129,a,70,b)].
% 17.42/17.71 189 implies(implies(A,B),and(B,not(A))) = not(equiv(A,B)). [para(92(a,1),128(a,1,1)),flip(a)].
% 17.42/17.71 226 is_a_theorem(implies(A,and(A,not(not(not(not(A))))))). [para(114(a,1),157(a,1)),rewrite([150(7)])].
% 17.42/17.71 248 is_a_theorem(implies(implies(not(A),B),implies(implies(B,C),implies(not(C),A)))). [para(82(a,1),137(a,1,2,2))].
% 17.42/17.71 249 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(not(C),not(A))))). [para(114(a,1),137(a,1,1)),rewrite([82(7)])].
% 17.42/17.71 284 is_a_theorem(implies(and(A,B),not(not(A)))). [para(150(a,1),57(a,1,1))].
% 17.42/17.71 287 -is_a_theorem(and(A,B)) | is_a_theorem(not(not(A))). [para(150(a,1),126(a,1))].
% 17.42/17.71 309 is_a_theorem(implies(and(A,B),not(not(not(not(A)))))). [para(150(a,1),284(a,1,1))].
% 17.42/17.71 424 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(C,and(B,not(A))),not(equiv(B,A)))). [resolve(140,a,70,b)].
% 17.42/17.71 551 is_a_theorem(implies(A,and(A,not(not(not(not(not(not(A))))))))). [para(114(a,1),226(a,1)),rewrite([150(9)])].
% 17.42/17.71 608 is_a_theorem(implies(and(A,B),not(not(not(not(not(not(A)))))))). [para(150(a,1),309(a,1,1))].
% 17.42/17.71 612 implies(and(A,not(not(B))),C) = implies(and(A,B),C). [para(125(a,1),143(a,1,1)),flip(a)].
% 17.42/17.71 850 equiv(A,not(not(B))) = equiv(A,B). [para(145(a,1),150(a,2)),rewrite([125(4),82(3),92(3)]),flip(a)].
% 17.42/17.71 924 -is_a_theorem(equiv(A,B)) | not(not(B)) = A. [para(850(a,1),64(a,1))].
% 17.42/17.71 1194 is_a_theorem(not(not(implies(and(A,B),A)))). [resolve(172,a,287,a)].
% 17.42/17.71 1232 is_a_theorem(not(and(and(not(A),B),A))). [para(125(a,1),1194(a,1,1))].
% 17.42/17.71 1596 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(B,not(C)),implies(C,not(A)))). [resolve(152,a,70,b)].
% 17.42/17.71 1750 -is_a_theorem(implies(not(A),B)) | is_a_theorem(implies(implies(B,not(C)),implies(C,A))). [resolve(153,a,70,b)].
% 17.42/17.71 1913 is_a_theorem(implies(implies(A,not(B)),implies(B,implies(A,not(C))))). [resolve(155,a,608,a),rewrite([114(8),114(6),114(4),147(5)])].
% 17.42/17.71 1914 is_a_theorem(implies(implies(and(A,A),not(B)),not(and(B,A)))). [resolve(155,a,551,a),rewrite([612(9),612(7),612(5)])].
% 17.42/17.71 2987 -is_a_theorem(implies(A,not(B))) | is_a_theorem(implies(B,implies(A,not(C)))). [resolve(1913,a,70,b)].
% 17.42/17.71 3088 -is_a_theorem(not(and(and(A,A),B))) | is_a_theorem(not(and(B,A))). [resolve(1914,a,142,b),rewrite([125(4)])].
% 17.42/17.71 8123 is_a_theorem(implies(A,A)). [resolve(3088,a,1232,a),rewrite([82(3)])].
% 17.42/17.71 8124 -is_a_theorem(implies(and(A,A),B)) | is_a_theorem(not(and(not(B),A))). [para(82(a,1),3088(a,1))].
% 17.42/17.71 8137 is_a_theorem(equiv(A,A)). [back_unit_del(175),unit_del(a,8123)].
% 17.42/17.71 8142 is_a_theorem(implies(A,implies(not(A),not(B)))). [resolve(8123,a,2987,a)].
% 17.42/17.71 8144 is_a_theorem(implies(implies(A,not(B)),not(and(B,A)))). [resolve(8123,a,155,a)].
% 17.42/17.71 8367 not(not(A)) = A. [resolve(8137,a,924,a)].
% 17.42/17.71 8470 not(and(A,B)) = implies(A,not(B)). [para(8367(a,1),82(a,1,1,2))].
% 17.42/17.71 8471 not(implies(A,B)) = and(A,not(B)). [para(82(a,1),8367(a,1,1))].
% 17.42/17.71 8474 is_a_theorem(implies(implies(A,not(B)),implies(B,implies(A,C)))). [para(8367(a,1),1913(a,1,2,2,2))].
% 17.42/17.71 8481 is_a_theorem(implies(implies(A,not(B)),implies(B,not(A)))). [back_rewrite(8144),rewrite([8470(4)])].
% 17.42/17.71 8486 -is_a_theorem(implies(and(A,A),B)) | is_a_theorem(implies(not(B),not(A))). [back_rewrite(8124),rewrite([8470(6)])].
% 17.42/17.71 8671 is_a_theorem(implies(A,implies(not(A),B))). [para(8367(a,1),8142(a,1,2,2))].
% 17.42/17.71 8675 -is_a_theorem(A) | is_a_theorem(implies(not(A),B)). [resolve(8671,a,70,b)].
% 17.42/17.71 8751 is_a_theorem(implies(not(A),implies(A,B))). [para(8367(a,1),8671(a,1,2,1))].
% 17.42/17.71 8829 is_a_theorem(implies(and(A,and(not(A),not(B))),C)). [resolve(8675,a,8671,a),rewrite([8471(4),8471(3)])].
% 17.42/17.71 8830 is_a_theorem(implies(not(equiv(A,A)),B)). [resolve(8675,a,8137,a)].
% 17.42/17.71 10987 -is_a_theorem(implies(A,not(B))) | is_a_theorem(implies(B,not(A))). [resolve(8481,a,70,b)].
% 17.42/17.71 11078 is_a_theorem(implies(implies(A,B),implies(not(B),not(A)))). [para(8367(a,1),8481(a,1,1,2))].
% 17.42/17.71 11317 is_a_theorem(implies(and(A,and(not(A),B)),C)). [para(8367(a,1),8829(a,1,1,2,2))].
% 17.42/17.71 11412 is_a_theorem(implies(and(not(A),and(A,B)),C)). [para(8367(a,1),11317(a,1,1,2,1))].
% 17.42/17.71 12675 is_a_theorem(implies(A,equiv(B,B))). [resolve(10987,a,8830,a),rewrite([8367(3)])].
% 17.42/17.71 12676 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(B),not(A))). [para(8367(a,1),10987(a,1,2))].
% 17.42/17.71 13794 is_a_theorem(implies(implies(not(A),B),implies(not(B),A))). [para(8367(a,1),11078(a,1,2,2))].
% 17.42/17.71 14475 is_a_theorem(implies(and(A,B),and(B,A))). [resolve(12676,a,8481,a),rewrite([8471(3),8367(2),8471(4),8367(3)])].
% 17.42/17.71 14484 is_a_theorem(implies(implies(A,not(A)),not(A))). [resolve(12676,a,54,a),rewrite([8470(2)])].
% 17.42/17.71 14485 -is_a_theorem(not(equiv(A,B))) | is_a_theorem(not(equiv(B,A))). [para(189(a,1),12676(a,1)),rewrite([8470(6),8367(5),8471(6),189(7)])].
% 17.42/17.71 14489 -is_a_theorem(and(A,B)) | is_a_theorem(and(B,A)). [resolve(14475,a,70,b)].
% 17.42/17.71 14586 is_a_theorem(implies(equiv(A,B),equiv(B,A))). [para(92(a,1),14475(a,1,1)),rewrite([92(4)])].
% 17.42/17.71 14848 is_a_theorem(implies(implies(not(A),A),A)). [para(8367(a,1),14484(a,1,1,2)),rewrite([8367(4)])].
% 17.42/17.71 15972 -is_a_theorem(implies(not(A),B)) | is_a_theorem(implies(not(B),A)). [resolve(13794,a,70,b)].
% 17.42/17.71 17564 is_a_theorem(implies(implies(A,and(A,A)),not(equiv(A,not(A))))). [resolve(424,a,14848,a),rewrite([8367(2)])].
% 17.42/17.71 17769 is_a_theorem(implies(and(A,and(B,not(C))),and(B,A))). [resolve(8474,a,12676,a),rewrite([8471(3),8471(2),8471(6),8367(5)])].
% 17.42/17.71 17774 -is_a_theorem(implies(A,not(B))) | is_a_theorem(implies(B,implies(A,C))). [resolve(8474,a,70,b)].
% 17.42/17.71 20671 is_a_theorem(implies(and(A,and(B,C)),and(B,A))). [para(8367(a,1),17769(a,1,1,2,2))].
% 17.42/17.71 20678 -is_a_theorem(and(A,and(B,C))) | is_a_theorem(and(B,A)). [resolve(20671,a,70,b)].
% 17.42/17.71 20876 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(B),implies(A,C))). [para(8367(a,1),17774(a,1,2))].
% 17.42/17.71 21603 is_a_theorem(implies(and(not(A),B),implies(implies(B,A),C))). [resolve(20876,a,11078,a),rewrite([8471(4),8367(3)])].
% 17.42/17.71 22641 is_a_theorem(implies(and(not(A),B),not(equiv(B,A)))). [para(189(a,1),21603(a,1,2))].
% 17.42/17.71 22655 -is_a_theorem(and(not(A),B)) | is_a_theorem(not(equiv(B,A))). [resolve(22641,a,70,b)].
% 17.42/17.71 22704 -is_a_theorem(and(A,B)) | is_a_theorem(not(equiv(B,not(A)))). [para(8367(a,1),22655(a,1,1))].
% 17.42/17.71 26133 is_a_theorem(implies(implies(implies(A,B),not(C)),implies(C,A))). [resolve(1596,a,8751,a),rewrite([8367(5)])].
% 17.42/17.71 26217 is_a_theorem(implies(and(A,not(B)),and(implies(B,C),A))). [resolve(26133,a,12676,a),rewrite([8471(2),8471(6),8367(5)])].
% 17.42/17.71 26302 is_a_theorem(implies(implies(implies(A,B),A),A)). [resolve(26217,a,8486,a),rewrite([8470(4),8367(3),8367(4)])].
% 17.42/17.71 26315 is_a_theorem(implies(and(implies(A,B),not(B)),equiv(B,A))). [para(92(a,1),26217(a,1,2))].
% 17.42/17.71 26317 is_a_theorem(implies(and(A,B),and(implies(not(B),C),A))). [para(8367(a,1),26217(a,1,1,2))].
% 17.42/17.71 26336 is_a_theorem(implies(A,and(implies(not(A),B),A))). [resolve(26302,a,10987,a),rewrite([8471(5),8367(4)])].
% 17.42/17.71 27141 -is_a_theorem(and(implies(A,B),not(B))) | is_a_theorem(equiv(B,A)). [resolve(26315,a,70,b)].
% 17.42/17.71 27165 -is_a_theorem(and(A,B)) | is_a_theorem(and(implies(not(B),C),A)). [resolve(26317,a,70,b)].
% 17.42/17.71 27477 is_a_theorem(implies(implies(equiv(A,A),not(B)),implies(B,C))). [resolve(1750,a,12675,a)].
% 17.42/17.71 27741 -is_a_theorem(and(implies(A,not(B)),B)) | is_a_theorem(equiv(not(B),A)). [para(8367(a,1),27141(a,1,2))].
% 17.42/17.71 28450 is_a_theorem(implies(and(A,not(B)),and(equiv(C,C),A))). [resolve(27477,a,12676,a),rewrite([8471(2),8471(6),8367(5)])].
% 17.42/17.71 28898 is_a_theorem(implies(implies(equiv(A,A),B),B)). [resolve(28450,a,8486,a),rewrite([8470(4),8367(3),8367(4)])].
% 17.42/17.71 28922 is_a_theorem(implies(A,and(equiv(B,B),A))). [resolve(28898,a,10987,a),rewrite([8471(4),8367(3)])].
% 17.42/17.71 29093 -is_a_theorem(A) | is_a_theorem(and(equiv(B,B),A)). [resolve(28922,a,70,b)].
% 17.42/17.71 29268 is_a_theorem(and(equiv(A,A),implies(implies(equiv(B,B),C),C))). [resolve(29093,a,28898,a)].
% 17.42/17.71 29506 is_a_theorem(and(equiv(A,A),implies(B,equiv(C,C)))). [resolve(29093,a,12675,a)].
% 17.42/17.71 29555 is_a_theorem(and(equiv(A,A),implies(B,B))). [resolve(29093,a,8123,a)].
% 17.42/17.71 29578 is_a_theorem(and(equiv(A,A),implies(and(B,C),B))). [resolve(29093,a,57,a)].
% 17.42/17.71 29579 is_a_theorem(and(equiv(A,A),implies(B,and(B,B)))). [resolve(29093,a,54,a)].
% 17.42/17.71 29614 is_a_theorem(and(implies(and(A,not(A)),B),equiv(C,C))). [resolve(29555,a,27165,a),rewrite([8471(2)])].
% 17.42/17.71 29725 is_a_theorem(and(implies(and(A,not(equiv(B,B))),C),equiv(D,D))). [resolve(29506,a,27165,a),rewrite([8471(3)])].
% 17.42/17.71 29793 is_a_theorem(and(implies(and(A,B),A),equiv(C,C))). [resolve(29578,a,14489,a)].
% 17.42/17.71 39390 is_a_theorem(not(equiv(A,not(A)))). [resolve(17564,a,70,b),unit_del(a,54)].
% 17.42/17.71 39431 is_a_theorem(not(equiv(not(A),A))). [resolve(39390,a,14485,a)].
% 17.42/17.71 39512 is_a_theorem(and(equiv(A,A),not(equiv(not(B),B)))). [resolve(39431,a,29093,a)].
% 17.42/17.71 40508 is_a_theorem(and(implies(equiv(not(A),A),B),equiv(C,C))). [resolve(39512,a,27165,a),rewrite([8367(4)])].
% 17.42/17.71 40517 is_a_theorem(not(equiv(not(equiv(not(A),A)),not(equiv(B,B))))). [resolve(39512,a,22704,a)].
% 17.42/17.71 48064 is_a_theorem(equiv(not(equiv(A,A)),equiv(not(B),B))). [resolve(27741,a,40508,a)].
% 17.42/17.71 48074 is_a_theorem(equiv(not(equiv(A,A)),and(not(equiv(A,A)),B))). [resolve(27741,a,29793,a)].
% 17.42/17.71 48076 is_a_theorem(equiv(not(equiv(A,A)),and(B,not(B)))). [resolve(27741,a,29614,a)].
% 17.42/17.71 48108 not(equiv(A,A)) = equiv(not(B),B). [resolve(48064,a,64,a),flip(a)].
% 17.42/17.71 48112 not(equiv(A,A)) = c_0. [new_symbol(48108)].
% 17.42/17.71 48114 equiv(not(A),A) = c_0. [back_rewrite(48108),rewrite([48112(2)]),flip(a)].
% 17.42/17.71 48115 is_a_theorem(equiv(c_0,and(A,not(A)))). [back_rewrite(48076),rewrite([48112(2)])].
% 17.42/17.71 48117 is_a_theorem(equiv(c_0,and(c_0,A))). [back_rewrite(48074),rewrite([48112(2),48112(3)])].
% 17.42/17.71 48135 is_a_theorem(not(c_0)). [back_rewrite(40517),rewrite([48114(2),48112(4),48114(4)])].
% 17.42/17.71 48252 is_a_theorem(and(implies(and(A,c_0),B),equiv(C,C))). [back_rewrite(29725),rewrite([48112(2)])].
% 17.42/17.71 49863 equiv(A,A) = not(c_0). [para(48112(a,1),8367(a,1,1)),flip(a)].
% 17.42/17.71 50099 is_a_theorem(and(implies(and(A,c_0),B),not(c_0))). [back_rewrite(48252),rewrite([49863(4)])].
% 17.42/17.71 50534 is_a_theorem(and(not(c_0),implies(A,and(A,A)))). [back_rewrite(29579),rewrite([49863(1)])].
% 17.42/17.71 50535 is_a_theorem(and(not(c_0),implies(and(A,B),A))). [back_rewrite(29578),rewrite([49863(1)])].
% 17.42/17.71 50578 is_a_theorem(and(not(c_0),implies(implies(not(c_0),A),A))). [back_rewrite(29268),rewrite([49863(1),49863(3)])].
% 17.42/17.71 50581 -is_a_theorem(A) | is_a_theorem(and(not(c_0),A)). [back_rewrite(29093),rewrite([49863(2)])].
% 17.42/17.71 50588 is_a_theorem(implies(A,and(not(c_0),A))). [back_rewrite(28922),rewrite([49863(1)])].
% 17.42/17.71 50595 is_a_theorem(implies(implies(not(c_0),A),A)). [back_rewrite(28898),rewrite([49863(1)])].
% 17.42/17.71 50867 and(c_0,A) = c_0. [resolve(48117,a,64,a)].
% 17.42/17.71 50878 implies(c_0,not(A)) = not(c_0). [para(50867(a,1),8470(a,1,1)),flip(a)].
% 17.42/17.71 51057 and(A,not(A)) = c_0. [resolve(48115,a,64,a)].
% 17.42/17.71 51154 implies(A,A) = not(c_0). [para(51057(a,1),8470(a,1,1)),rewrite([8367(4)]),flip(a)].
% 17.42/17.71 52786 is_a_theorem(implies(implies(A,and(A,c_0)),not(equiv(A,not(c_0))))). [resolve(50595,a,424,a),rewrite([8367(3)])].
% 17.42/17.71 52828 is_a_theorem(implies(implies(not(A),c_0),implies(not(c_0),implies(B,A)))). [para(50878(a,1),153(a,1,2,1))].
% 17.42/17.71 52830 implies(c_0,A) = not(c_0). [para(8367(a,1),50878(a,1,2))].
% 17.42/17.71 52850 -is_a_theorem(and(not(c_0),A)) | is_a_theorem(equiv(not(A),c_0)). [para(50878(a,1),27141(a,1,1)),rewrite([8367(4)])].
% 17.42/17.71 52887 and(not(c_0),implies(A,c_0)) = equiv(c_0,A). [para(52830(a,1),92(a,1,1))].
% 17.42/17.71 52891 implies(not(c_0),and(A,not(c_0))) = not(equiv(c_0,A)). [para(52830(a,1),189(a,1,1))].
% 17.42/17.71 53455 is_a_theorem(equiv(c_0,and(A,c_0))). [resolve(50099,a,27741,a),rewrite([8367(3)])].
% 17.42/17.71 53492 and(A,c_0) = c_0. [resolve(53455,a,64,a)].
% 17.42/17.71 53515 is_a_theorem(implies(implies(A,c_0),not(equiv(A,not(c_0))))). [back_rewrite(52786),rewrite([53492(2)])].
% 17.42/17.71 53569 implies(A,not(c_0)) = not(c_0). [para(53492(a,1),8470(a,1,1)),flip(a)].
% 17.42/17.71 53575 and(not(c_0),implies(not(c_0),A)) = equiv(A,not(c_0)). [para(53569(a,1),92(a,1,1))].
% 17.42/17.71 53576 and(implies(not(c_0),A),not(c_0)) = equiv(not(c_0),A). [para(53569(a,1),92(a,1,2))].
% 17.42/17.71 53581 implies(not(c_0),and(not(c_0),not(A))) = not(equiv(A,not(c_0))). [para(53569(a,1),189(a,1,1))].
% 17.42/17.71 56697 is_a_theorem(equiv(and(implies(not(c_0),A),not(A)),c_0)). [resolve(52850,a,50578,a),rewrite([8471(5)])].
% 17.42/17.71 56701 is_a_theorem(equiv(and(and(A,B),not(A)),c_0)). [resolve(52850,a,50535,a),rewrite([8471(3)])].
% 17.42/17.71 56759 and(and(A,B),not(A)) = c_0. [resolve(56701,a,64,a),flip(a)].
% 17.42/17.71 56777 implies(and(A,B),A) = not(c_0). [para(56759(a,1),8470(a,1,1)),rewrite([8367(5)]),flip(a)].
% 17.42/17.71 56836 and(not(c_0),implies(A,and(A,B))) = equiv(and(A,B),A). [para(56777(a,1),92(a,1,1))].
% 17.42/17.71 56837 and(implies(A,and(A,B)),not(c_0)) = equiv(A,and(A,B)). [para(56777(a,1),92(a,1,2))].
% 17.42/17.71 56838 implies(equiv(A,B),implies(A,B)) = not(c_0). [para(92(a,1),56777(a,1,1))].
% 17.42/17.71 56890 is_a_theorem(equiv(and(A,A),A)). [back_rewrite(50534),rewrite([56836(5)])].
% 17.42/17.71 56956 and(A,A) = A. [resolve(56890,a,64,a),flip(a)].
% 17.42/17.71 56976 implies(A,not(A)) = not(A). [para(56956(a,1),8470(a,1,1)),flip(a)].
% 17.42/17.71 57004 implies(not(A),A) = A. [para(56976(a,1),88(a,2)),rewrite([8367(2),88(1),8367(4)])].
% 17.42/17.71 57008 is_a_theorem(implies(A,implies(implies(A,not(B)),implies(B,A)))). [para(56976(a,1),153(a,1,1)),rewrite([8367(2),8367(2)])].
% 17.42/17.71 57012 is_a_theorem(implies(implies(not(A),B),implies(implies(B,A),A))). [para(56976(a,1),248(a,1,2,2)),rewrite([8367(2),8367(5)])].
% 17.42/17.71 57553 is_a_theorem(implies(implies(A,c_0),equiv(c_0,A))). [para(52887(a,1),50588(a,1,2))].
% 17.42/17.71 57572 -is_a_theorem(implies(A,c_0)) | is_a_theorem(equiv(c_0,A)). [resolve(57553,a,70,b)].
% 17.42/17.71 57891 is_a_theorem(equiv(c_0,and(not(A),and(A,B)))). [resolve(57572,a,11412,a)].
% 17.42/17.71 57905 and(not(A),and(A,B)) = c_0. [resolve(57891,a,64,a)].
% 17.42/17.71 57992 implies(not(A),implies(A,not(B))) = not(c_0). [para(57905(a,1),8470(a,1,1)),rewrite([8470(5)]),flip(a)].
% 17.42/17.71 58217 is_a_theorem(and(not(c_0),implies(implies(A,c_0),not(equiv(A,not(c_0)))))). [resolve(53515,a,50581,a)].
% 17.42/17.71 59388 and(implies(not(c_0),A),not(A)) = c_0. [resolve(56697,a,64,a),flip(a)].
% 17.42/17.71 59405 implies(implies(not(c_0),A),A) = not(c_0). [para(59388(a,1),8470(a,1,1)),rewrite([8367(7)]),flip(a)].
% 17.42/17.71 59445 and(not(c_0),implies(A,implies(not(c_0),A))) = equiv(implies(not(c_0),A),A). [para(59405(a,1),92(a,1,1))].
% 17.42/17.71 59597 is_a_theorem(implies(implies(A,equiv(B,C)),implies(not(c_0),implies(and(B,not(C)),not(A))))). [para(56838(a,1),249(a,1,2,1)),rewrite([8471(6)])].
% 17.42/17.71 59827 implies(not(A),implies(A,B)) = not(c_0). [para(8367(a,1),57992(a,1,2,2))].
% 17.42/17.71 59831 is_a_theorem(implies(implies(not(A),not(B)),implies(not(c_0),implies(and(B,C),A)))). [para(57992(a,1),248(a,1,2,1)),rewrite([8471(8),8367(7)])].
% 17.42/17.71 59849 and(not(c_0),implies(implies(A,B),not(A))) = equiv(not(A),implies(A,B)). [para(59827(a,1),92(a,1,1))].
% 17.42/17.71 63034 is_a_theorem(implies(A,implies(not(c_0),A))). [para(57004(a,1),57008(a,1,2,2)),rewrite([8367(2),51154(1)])].
% 17.42/17.71 63043 is_a_theorem(equiv(implies(not(c_0),A),A)). [resolve(63034,a,50581,a),rewrite([59445(7)])].
% 17.42/17.71 63087 implies(not(c_0),A) = A. [resolve(63043,a,64,a),flip(a)].
% 17.42/17.71 63289 is_a_theorem(implies(implies(not(A),not(B)),implies(and(B,C),A))). [back_rewrite(59831),rewrite([63087(8)])].
% 17.42/17.71 63304 is_a_theorem(implies(implies(A,equiv(B,C)),implies(and(B,not(C)),not(A)))). [back_rewrite(59597),rewrite([63087(9)])].
% 17.42/17.71 63514 not(equiv(A,not(c_0))) = and(not(c_0),not(A)). [back_rewrite(53581),rewrite([63087(7)]),flip(a)].
% 17.42/17.71 63516 equiv(not(c_0),A) = and(A,not(c_0)). [back_rewrite(53576),rewrite([63087(3)]),flip(a)].
% 17.42/17.71 63517 equiv(A,not(c_0)) = and(not(c_0),A). [back_rewrite(53575),rewrite([63087(5)]),flip(a)].
% 17.42/17.71 63526 not(equiv(c_0,A)) = and(A,not(c_0)). [back_rewrite(52891),rewrite([63087(6)]),flip(a)].
% 17.42/17.71 63533 is_a_theorem(implies(implies(not(A),c_0),implies(B,A))). [back_rewrite(52828),rewrite([63087(7)])].
% 17.42/17.71 63575 is_a_theorem(equiv(not(A),implies(A,c_0))). [back_rewrite(58217),rewrite([63517(7),8470(8),63087(8),59849(7)])].
% 17.42/17.71 63867 and(not(c_0),not(A)) = not(A). [back_rewrite(63514),rewrite([63517(3),8470(4),63087(4)]),flip(a)].
% 17.42/17.71 64413 is_a_theorem(implies(A,implies(implies(A,B),implies(not(B),c_0)))). [para(63087(a,1),248(a,1,1))].
% 17.42/17.71 67337 implies(A,c_0) = not(A). [resolve(63575,a,64,a)].
% 17.42/17.71 67372 is_a_theorem(implies(A,implies(implies(A,B),B))). [back_rewrite(64413),rewrite([67337(4),8367(3)])].
% 17.42/17.71 67387 is_a_theorem(implies(A,implies(B,A))). [back_rewrite(63533),rewrite([67337(3),8367(2)])].
% 17.42/17.71 67492 equiv(c_0,A) = not(A). [back_rewrite(52887),rewrite([67337(4),63867(4)]),flip(a)].
% 17.42/17.71 67678 and(A,not(c_0)) = A. [back_rewrite(63526),rewrite([67492(2),8367(2)]),flip(a)].
% 17.42/17.71 67731 equiv(not(c_0),A) = A. [back_rewrite(63516),rewrite([67678(6)])].
% 17.42/17.71 67735 equiv(A,and(A,B)) = implies(A,and(A,B)). [back_rewrite(56837),rewrite([67678(5)]),flip(a)].
% 17.42/17.71 68853 is_a_theorem(implies(and(A,B),B)). [resolve(67387,a,15972,a),rewrite([8471(3),8367(2)])].
% 17.42/17.71 68855 is_a_theorem(implies(implies(implies(A,not(B)),not(C)),implies(C,B))). [resolve(67387,a,1750,a)].
% 17.42/17.71 70036 -is_a_theorem(A) | not(c_0) = A. [para(67731(a,1),64(a,1)),flip(b)].
% 17.42/17.71 71172 implies(and(A,B),B) = not(c_0). [resolve(70036,a,68853,a),flip(a)].
% 17.42/17.71 71215 implies(A,and(implies(not(A),B),A)) = not(c_0). [resolve(70036,a,26336,a),flip(a)].
% 17.42/17.71 71282 implies(equiv(A,B),equiv(B,A)) = not(c_0). [resolve(70036,a,14586,a),flip(a)].
% 17.42/17.71 71284 implies(and(A,B),and(B,A)) = not(c_0). [resolve(70036,a,14475,a),flip(a)].
% 17.42/17.71 71308 implies(implies(not(A),B),implies(implies(B,not(C)),implies(C,A))) = not(c_0). [resolve(70036,a,153,a),flip(a)].
% 17.42/17.71 71429 implies(A,implies(implies(A,B),B)) = not(c_0). [resolve(67372,a,70036,a),flip(a)].
% 17.42/17.71 71432 is_a_theorem(implies(and(implies(not(A),B),not(B)),A)). [resolve(67372,a,15972,a),rewrite([8471(4)])].
% 17.42/17.71 71449 and(and(A,B),not(B)) = c_0. [para(71172(a,1),8471(a,1,1)),rewrite([8367(3)]),flip(a)].
% 17.42/17.71 72222 equiv(equiv(A,B),equiv(B,A)) = not(c_0). [para(71282(a,1),92(a,1,1)),rewrite([71282(5),56956(5)]),flip(a)].
% 17.42/17.71 72225 equiv(and(A,B),and(B,A)) = not(c_0). [para(71284(a,1),92(a,1,1)),rewrite([71284(5),56956(5)]),flip(a)].
% 17.42/17.71 72537 is_a_theorem(implies(and(implies(not(A),not(B)),B),A)). [para(8367(a,1),71432(a,1,1,2))].
% 17.42/17.71 72773 equiv(A,B) = equiv(B,A). [para(72222(a,1),64(a,1)),unit_del(a,48135)].
% 17.42/17.71 73219 and(A,B) = and(B,A). [para(72225(a,1),64(a,1)),unit_del(a,48135)].
% 17.42/17.71 73462 is_a_theorem(implies(and(A,implies(not(B),not(A))),B)). [back_rewrite(72537),rewrite([73219(4)])].
% 17.42/17.71 73758 and(not(A),and(B,A)) = c_0. [back_rewrite(71449),rewrite([73219(3)])].
% 17.42/17.71 73793 implies(A,and(A,implies(not(A),B))) = not(c_0). [back_rewrite(71215),rewrite([73219(3)])].
% 17.42/17.71 73951 -is_a_theorem(and(A,and(B,C))) | is_a_theorem(and(A,B)). [back_rewrite(20678),rewrite([73219(4)])].
% 17.42/17.71 73965 implies(A,not(B)) = implies(B,not(A)). [para(73219(a,1),8470(a,1,1)),rewrite([8470(2)])].
% 17.42/17.71 74036 is_a_theorem(implies(and(A,implies(A,B)),B)). [back_rewrite(73462),rewrite([73965(3),8367(2)])].
% 17.42/17.71 74071 is_a_theorem(implies(implies(A,and(B,C)),implies(A,C))). [back_rewrite(68855),rewrite([73965(4),8471(3),8367(2)])].
% 17.42/17.71 74082 is_a_theorem(implies(implies(A,equiv(B,C)),implies(A,implies(B,C)))). [back_rewrite(63304),rewrite([73965(6),8470(5),8367(4)])].
% 17.42/17.71 74083 is_a_theorem(implies(implies(A,B),implies(and(A,C),B))). [back_rewrite(63289),rewrite([73965(3),8367(2)])].
% 17.42/17.71 74166 implies(and(A,implies(A,B)),B) = not(c_0). [resolve(74036,a,70036,a),flip(a)].
% 17.42/17.71 74262 implies(A,implies(B,and(A,B))) = not(c_0). [para(73965(a,1),71429(a,1,2,1)),rewrite([73965(2),73965(4),8471(3),8367(2)])].
% 17.42/17.71 74872 -is_a_theorem(and(A,and(B,C))) | is_a_theorem(and(A,C)). [para(73219(a,1),73951(a,1,2))].
% 17.42/17.71 75018 is_a_theorem(implies(A,and(A,implies(B,A)))). [para(56976(a,1),74071(a,1,2)),rewrite([73965(5),8471(4),8470(3),8367(2)])].
% 17.42/17.71 75025 implies(A,and(A,implies(B,A))) = not(c_0). [resolve(75018,a,70036,a),flip(a)].
% 17.42/17.71 75221 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(and(A,C),B)). [resolve(74083,a,70,b)].
% 17.42/17.71 75709 is_a_theorem(implies(and(A,and(B,implies(B,C))),C)). [para(74166(a,1),75221(a,1)),rewrite([73219(6)]),unit_del(a,48135)].
% 17.42/17.71 76322 -is_a_theorem(and(A,and(B,implies(B,implies(implies(c54,c55),implies(implies(not(c53),c54),implies(not(c53),c55))))))). [ur(70,b,75709,a,c,105,a)].
% 17.42/17.71 76839 is_a_theorem(implies(implies(implies(A,and(A,not(B))),B),B)). [para(74262(a,1),57012(a,1,1)),rewrite([73219(4),63087(8)])].
% 17.42/17.71 77766 -is_a_theorem(implies(A,and(A,B))) | and(A,B) = A. [para(67735(a,1),64(a,1))].
% 17.42/17.71 80468 is_a_theorem(implies(A,and(A,implies(B,and(B,A))))). [para(8367(a,1),76839(a,1,1,1,2,2)),rewrite([73965(4),8471(3),8470(2),73965(6),8471(5),8470(4),8471(3),8367(2)])].
% 17.42/17.71 80827 and(A,implies(B,and(A,B))) = A. [resolve(77766,a,80468,a),rewrite([73219(1)])].
% 17.42/17.71 80829 and(A,implies(B,A)) = A. [para(75025(a,1),77766(a,1)),unit_del(a,48135)].
% 17.42/17.71 80834 and(A,implies(not(A),B)) = A. [para(73793(a,1),77766(a,1)),unit_del(a,48135)].
% 17.42/17.71 80857 -is_a_theorem(and(A,B)) | is_a_theorem(and(A,implies(C,B))). [para(80829(a,1),74872(a,1,2))].
% 17.42/17.72 80909 and(A,implies(B,and(B,A))) = A. [para(80827(a,1),73219(a,2)),rewrite([73219(1),73219(3)])].
% 17.42/17.72 81061 and(A,and(B,A)) = and(B,A). [para(73758(a,1),80909(a,1,2,2)),rewrite([67337(4),8367(3),73219(2)])].
% 17.42/17.72 81422 implies(A,implies(B,not(A))) = implies(B,not(A)). [para(81061(a,1),8470(a,1,1)),rewrite([8470(2),8470(4)]),flip(a)].
% 17.42/17.72 81438 -is_a_theorem(and(A,B)) | is_a_theorem(and(B,implies(C,A))). [para(73219(a,1),80857(a,1))].
% 17.42/17.72 81610 -is_a_theorem(A) | is_a_theorem(and(implies(not(A),B),implies(C,A))). [para(80834(a,1),81438(a,1))].
% 17.42/17.72 84369 implies(not(A),implies(B,A)) = implies(B,A). [para(81422(a,1),88(a,2)),rewrite([8367(2),88(2),8367(5)])].
% 17.42/17.72 86653 is_a_theorem(implies(implies(not(A),equiv(A,B)),implies(B,A))). [para(84369(a,1),74082(a,1,2)),rewrite([72773(2)])].
% 17.42/17.72 86946 is_a_theorem(and(implies(and(and(A,not(B)),implies(not(B),equiv(B,A))),C),implies(D,implies(implies(not(B),equiv(B,A)),implies(A,B))))). [resolve(86653,a,81610,a),rewrite([8471(6),8471(5),73219(6)])].
% 17.42/17.72 87013 is_a_theorem(and(implies(and(and(A,not(B)),implies(not(B),equiv(A,B))),C),implies(D,implies(implies(not(B),equiv(A,B)),implies(A,B))))). [back_rewrite(86946),rewrite([72773(4),72773(9)])].
% 17.42/17.72 88361 implies(implies(A,B),implies(implies(C,A),implies(C,B))) = not(c_0). [para(73965(a,1),71308(a,1,1)),rewrite([8367(2),73965(4),8367(3)])].
% 17.42/17.72 88416 -is_a_theorem(and(A,B)). [back_rewrite(76322),rewrite([88361(13),53569(3),67678(3)])].
% 17.42/17.72 88417 $F. [resolve(88416,a,87013,a)].
% 17.42/17.72
% 17.42/17.72 % SZS output end Refutation
% 17.42/17.72 ============================== end of proof ==========================
% 17.42/17.72
% 17.42/17.72 ============================== STATISTICS ============================
% 17.42/17.72
% 17.42/17.72 Given=4058. Generated=1450969. Kept=88366. proofs=1.
% 17.42/17.72 Usable=779. Sos=7491. Demods=1869. Limbo=55, Disabled=80112. Hints=0.
% 17.42/17.72 Megabytes=54.46.
% 17.42/17.72 User_CPU=15.97, System_CPU=0.76, Wall_clock=17.
% 17.42/17.72
% 17.42/17.72 ============================== end of statistics =====================
% 17.42/17.72
% 17.42/17.72 ============================== end of search =========================
% 17.42/17.72
% 17.42/17.72 THEOREM PROVED
% 17.42/17.72 % SZS status Theorem
% 17.42/17.72
% 17.42/17.72 Exiting with 1 proof.
% 17.42/17.72
% 17.42/17.72 Process 16107 exit (max_proofs) Sun Jul 3 09:16:26 2022
% 17.42/17.72 Prover9 interrupted
%------------------------------------------------------------------------------