TSTP Solution File: LCL521+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL521+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 13:47:21 EDT 2022
% Result : Theorem 56.20s 56.53s
% Output : Refutation 56.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL521+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 3 20:44:11 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.43/1.03 ============================== Prover9 ===============================
% 0.43/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.03 Process 31967 was started by sandbox on n025.cluster.edu,
% 0.43/1.03 Sun Jul 3 20:44:11 2022
% 0.43/1.03 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_31814_n025.cluster.edu".
% 0.43/1.03 ============================== end of head ===========================
% 0.43/1.03
% 0.43/1.03 ============================== INPUT =================================
% 0.43/1.03
% 0.43/1.03 % Reading from file /tmp/Prover9_31814_n025.cluster.edu
% 0.43/1.03
% 0.43/1.03 set(prolog_style_variables).
% 0.43/1.03 set(auto2).
% 0.43/1.03 % set(auto2) -> set(auto).
% 0.43/1.03 % set(auto) -> set(auto_inference).
% 0.43/1.03 % set(auto) -> set(auto_setup).
% 0.43/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.03 % set(auto) -> set(auto_limits).
% 0.43/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.03 % set(auto) -> set(auto_denials).
% 0.43/1.03 % set(auto) -> set(auto_process).
% 0.43/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.03 % set(auto2) -> assign(stats, some).
% 0.43/1.03 % set(auto2) -> clear(echo_input).
% 0.43/1.03 % set(auto2) -> set(quiet).
% 0.43/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.03 % set(auto2) -> clear(print_given).
% 0.43/1.03 assign(lrs_ticks,-1).
% 0.43/1.03 assign(sos_limit,10000).
% 0.43/1.03 assign(order,kbo).
% 0.43/1.03 set(lex_order_vars).
% 0.43/1.03 clear(print_given).
% 0.43/1.03
% 0.43/1.03 % formulas(sos). % not echoed (43 formulas)
% 0.43/1.03
% 0.43/1.03 ============================== end of input ==========================
% 0.43/1.03
% 0.43/1.03 % From the command line: assign(max_seconds, 300).
% 0.43/1.03
% 0.43/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.03
% 0.43/1.03 % Formulas that are not ordinary clauses:
% 0.43/1.03 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].
% 0.43/1.03 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].
% 0.43/1.03 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].
% 0.43/1.03 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 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].
% 0.43/1.03 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].
% 0.43/1.03 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 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].
% 0.43/1.03 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 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].
% 0.43/1.03 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].
% 0.43/1.03 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].
% 2.02/2.34 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].
% 2.02/2.34 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 2.02/2.34 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 2.02/2.34 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].
% 2.02/2.34 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].
% 2.02/2.34 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 2.02/2.34 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 2.02/2.34 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 2.02/2.34 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 2.02/2.34 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 2.02/2.34 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].
% 2.02/2.34 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].
% 2.02/2.34 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].
% 2.02/2.34 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].
% 2.02/2.34 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].
% 2.02/2.34 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].
% 2.02/2.34 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].
% 2.02/2.34
% 2.02/2.34 ============================== end of process non-clausal formulas ===
% 2.02/2.34
% 2.02/2.34 ============================== PROCESS INITIAL CLAUSES ===============
% 2.02/2.34
% 2.02/2.34 ============================== PREDICATE ELIMINATION =================
% 2.02/2.34
% 2.02/2.34 ============================== end predicate elimination =============
% 2.02/2.34
% 2.02/2.34 Auto_denials: (non-Horn, no changes).
% 2.02/2.34
% 2.02/2.34 Term ordering decisions:
% 2.02/2.34
% 2.02/2.34 % Assigning unary symbol not kb_weight 0 and highest precedence (93).
% 2.02/2.34 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.
% 2.02/2.34
% 2.02/2.34 ============================== end of process initial clauses ========
% 2.02/2.34
% 2.02/2.34 ============================== CLAUSES FOR SEARCH ====================
% 2.02/2.34
% 2.02/2.34 ============================== end of clauses for search =============
% 2.02/2.34
% 2.02/2.34 ============================== SEARCH ================================
% 2.02/2.34
% 2.02/2.34 % Starting search at 0.02 seconds.
% 2.02/2.34
% 2.02/2.34 Low Water (keep): wt=44.000, iters=3369
% 2.02/2.34
% 2.02/2.34 Low Water (keep): wt=42.000, iters=3355
% 2.02/2.34
% 2.02/2.34 Low Water (keep): wt=39.000, iters=3443
% 2.02/2.34
% 2.02/2.34 Low Water (keep): wt=37.000, iters=3345
% 2.02/2.34
% 2.02/2.34 Low Water (keep): wt=36.000, iters=3398
% 2.02/2.34
% 2.02/2.34 Low Water (keep): wt=34.000, iters=3386
% 2.02/2.34
% 2.02/2.34 Low Water (keep): wt=33.000, iters=3345
% 2.02/2.34
% 2.02/2.34 Low Water (keep): wt=32.000, iters=3381
% 2.02/2.34
% 2.02/2.34 Low Water (keep): wt=31.000, iters=3359
% 2.02/2.34
% 2.02/2.34 Low Water (keep): wt=30.000, iters=3475
% 2.02/2.34
% 56.20/56.53 Low Water (keep): wt=28.000, iters=3376
% 56.20/56.53
% 56.20/56.53 Low Water (keep): wt=26.000, iters=3342
% 56.20/56.53
% 56.20/56.53 Low Water (keep): wt=25.000, iters=3357
% 56.20/56.53
% 56.20/56.53 Low Water (keep): wt=24.000, iters=3486
% 56.20/56.53
% 56.20/56.53 Low Water (keep): wt=23.000, iters=3447
% 56.20/56.53
% 56.20/56.53 Low Water (keep): wt=22.000, iters=3367
% 56.20/56.53
% 56.20/56.53 Low Water (keep): wt=21.000, iters=3350
% 56.20/56.53
% 56.20/56.53 Low Water (keep): wt=20.000, iters=3360
% 56.20/56.53
% 56.20/56.53 Low Water (keep): wt=19.000, iters=3342
% 56.20/56.53
% 56.20/56.53 Low Water (keep): wt=18.000, iters=3348
% 56.20/56.53
% 56.20/56.53 Low Water (keep): wt=17.000, iters=3467
% 56.20/56.53
% 56.20/56.53 Low Water (keep): wt=16.000, iters=3359
% 56.20/56.53
% 56.20/56.53 Low Water (keep): wt=15.000, iters=3350
% 56.20/56.53
% 56.20/56.53 Low Water (keep): wt=14.000, iters=3333
% 56.20/56.53
% 56.20/56.53 Low Water (displace): id=10235, wt=48.000
% 56.20/56.53
% 56.20/56.53 Low Water (displace): id=10676, wt=46.000
% 56.20/56.53
% 56.20/56.53 Low Water (displace): id=10671, wt=44.000
% 56.20/56.53
% 56.20/56.53 Low Water (displace): id=18426, wt=13.000
% 56.20/56.53
% 56.20/56.53 Low Water (displace): id=18603, wt=12.000
% 56.20/56.53
% 56.20/56.53 Low Water (displace): id=18618, wt=10.000
% 56.20/56.53
% 56.20/56.53 Low Water (displace): id=18718, wt=9.000
% 56.20/56.53
% 56.20/56.53 Low Water (displace): id=18771, wt=8.000
% 56.20/56.53
% 56.20/56.53 Low Water (keep): wt=13.000, iters=3346
% 56.20/56.53
% 56.20/56.53 Low Water (keep): wt=12.000, iters=3335
% 56.20/56.53
% 56.20/56.53 Low Water (keep): wt=11.000, iters=3494
% 56.20/56.53
% 56.20/56.53 Low Water (keep): wt=10.000, iters=3335
% 56.20/56.53
% 56.20/56.53 ============================== PROOF =================================
% 56.20/56.53 % SZS status Theorem
% 56.20/56.53 % SZS output start Refutation
% 56.20/56.53
% 56.20/56.53 % Proof 1 at 53.20 (+ 2.29) seconds.
% 56.20/56.53 % Length of proof is 307.
% 56.20/56.53 % Level of proof is 64.
% 56.20/56.53 % Maximum clause weight is 18.000.
% 56.20/56.53 % Given clauses 7990.
% 56.20/56.53
% 56.20/56.53 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].
% 56.20/56.53 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].
% 56.20/56.53 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 56.20/56.53 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 56.20/56.53 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].
% 56.20/56.53 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].
% 56.20/56.53 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].
% 56.20/56.53 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].
% 56.20/56.53 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].
% 56.20/56.53 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].
% 56.20/56.53 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].
% 56.20/56.53 32 op_or # label(rosser_op_or) # label(axiom). [assumption].
% 56.20/56.53 33 op_implies_and # label(rosser_op_implies_and) # label(axiom). [assumption].
% 56.20/56.53 34 op_equiv # label(rosser_op_equiv) # label(axiom). [assumption].
% 56.20/56.53 35 modus_ponens # label(rosser_modus_ponens) # label(axiom). [assumption].
% 56.20/56.53 36 kn1 # label(rosser_kn1) # label(axiom). [assumption].
% 56.20/56.53 37 kn2 # label(rosser_kn2) # label(axiom). [assumption].
% 56.20/56.53 38 kn3 # label(rosser_kn3) # label(axiom). [assumption].
% 56.20/56.53 39 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption].
% 56.20/56.53 40 op_implies_or # label(principia_op_implies_or) # label(axiom). [assumption].
% 56.20/56.53 41 op_and # label(principia_op_and) # label(axiom). [assumption].
% 56.20/56.53 42 -r4 # label(principia_r4) # label(negated_conjecture). [assumption].
% 56.20/56.53 53 -kn1 | is_a_theorem(implies(A,and(A,A))) # label(kn1) # label(axiom). [clausify(16)].
% 56.20/56.53 54 is_a_theorem(implies(A,and(A,A))). [copy(53),unit_del(a,36)].
% 56.20/56.53 56 -kn2 | is_a_theorem(implies(and(A,B),A)) # label(kn2) # label(axiom). [clausify(17)].
% 56.20/56.53 57 is_a_theorem(implies(and(A,B),A)). [copy(56),unit_del(a,37)].
% 56.20/56.53 63 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(2)].
% 56.20/56.53 64 -is_a_theorem(equiv(A,B)) | B = A. [copy(63),unit_del(a,39)].
% 56.20/56.53 69 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 56.20/56.53 70 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(69),unit_del(a,35)].
% 56.20/56.53 79 -op_implies_or | or(not(A),B) = implies(A,B) # label(op_implies_or) # label(axiom). [clausify(30)].
% 56.20/56.53 80 or(not(A),B) = implies(A,B). [copy(79),unit_del(a,40)].
% 56.20/56.53 81 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 56.20/56.53 82 not(and(A,not(B))) = implies(A,B). [copy(81),unit_del(a,33)].
% 56.20/56.53 87 -op_or | or(A,B) = not(and(not(A),not(B))) # label(op_or) # label(axiom). [clausify(27)].
% 56.20/56.53 88 or(A,B) = implies(not(A),B). [copy(87),rewrite([82(6)]),unit_del(a,32)].
% 56.20/56.53 89 -op_and | and(A,B) = not(or(not(A),not(B))) # label(op_and) # label(axiom). [clausify(28)].
% 56.20/56.53 90 not(implies(not(not(A)),not(B))) = and(A,B). [copy(89),rewrite([88(5)]),flip(b),unit_del(a,41)].
% 56.20/56.53 91 -op_equiv | and(implies(A,B),implies(B,A)) = equiv(A,B) # label(op_equiv) # label(axiom). [clausify(31)].
% 56.20/56.53 92 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(91),unit_del(a,34)].
% 56.20/56.53 100 r4 | -is_a_theorem(implies(or(c50,or(c51,c52)),or(c51,or(c50,c52)))) # label(r4) # label(axiom). [clausify(25)].
% 56.20/56.53 101 -is_a_theorem(implies(implies(not(c50),implies(not(c51),c52)),implies(not(c51),implies(not(c50),c52)))). [copy(100),rewrite([88(5),88(7),88(12),88(14)]),unit_del(a,42)].
% 56.20/56.53 110 -kn3 | is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))) # label(kn3) # label(axiom). [clausify(18)].
% 56.20/56.53 111 is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))). [copy(110),unit_del(a,38)].
% 56.20/56.53 114 implies(not(not(A)),B) = implies(A,B). [back_rewrite(80),rewrite([88(2)])].
% 56.20/56.53 125 not(implies(A,not(B))) = and(A,B). [back_rewrite(90),rewrite([114(4)])].
% 56.20/56.53 126 -is_a_theorem(and(A,B)) | is_a_theorem(A). [resolve(70,b,57,a)].
% 56.20/56.53 127 -is_a_theorem(A) | is_a_theorem(and(A,A)). [resolve(70,b,54,a)].
% 56.20/56.53 128 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(82(a,1),82(a,1,1,2))].
% 56.20/56.53 129 is_a_theorem(implies(implies(A,A),equiv(A,A))). [para(92(a,1),54(a,1,2))].
% 56.20/56.53 135 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(and(B,C)),not(and(C,A)))). [resolve(111,a,70,b)].
% 56.20/56.53 137 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))].
% 56.20/56.53 138 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))].
% 56.20/56.53 140 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)])].
% 56.20/56.53 141 is_a_theorem(implies(A,and(not(not(A)),not(not(A))))). [para(114(a,1),54(a,1))].
% 56.20/56.53 142 -is_a_theorem(not(not(A))) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [para(114(a,1),70(b,1))].
% 56.20/56.53 143 implies(not(implies(A,B)),C) = implies(and(A,not(B)),C). [para(82(a,1),114(a,1,1,1))].
% 56.20/56.53 145 and(implies(A,not(not(B))),implies(B,A)) = equiv(A,not(not(B))). [para(114(a,1),92(a,1,2))].
% 56.20/56.53 146 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)])].
% 56.20/56.53 147 not(and(A,and(B,C))) = implies(A,implies(B,not(C))). [para(125(a,1),82(a,1,1,2))].
% 56.20/56.53 149 implies(not(and(A,B)),C) = implies(implies(A,not(B)),C). [para(125(a,1),114(a,1,1,1))].
% 56.20/56.53 150 and(not(not(A)),B) = and(A,B). [para(114(a,1),125(a,1,1)),rewrite([125(3)]),flip(a)].
% 56.20/56.53 152 is_a_theorem(implies(implies(A,B),implies(implies(B,not(C)),implies(C,not(A))))). [back_rewrite(146),rewrite([149(6)])].
% 56.20/56.53 153 is_a_theorem(implies(implies(not(A),B),implies(implies(B,not(C)),implies(C,A)))). [back_rewrite(138),rewrite([149(6)])].
% 56.20/56.53 155 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(B,not(C)),not(and(C,A)))). [back_rewrite(135),rewrite([149(7)])].
% 56.20/56.53 157 is_a_theorem(implies(A,and(A,not(not(A))))). [back_rewrite(141),rewrite([150(5)])].
% 56.20/56.53 172 is_a_theorem(and(implies(and(A,B),A),implies(and(A,B),A))). [resolve(127,a,57,a)].
% 56.20/56.53 175 -is_a_theorem(implies(A,A)) | is_a_theorem(equiv(A,A)). [resolve(129,a,70,b)].
% 56.20/56.53 189 implies(implies(A,B),and(B,not(A))) = not(equiv(A,B)). [para(92(a,1),128(a,1,1)),flip(a)].
% 56.20/56.53 226 is_a_theorem(implies(A,and(A,not(not(not(not(A))))))). [para(114(a,1),157(a,1)),rewrite([150(7)])].
% 56.20/56.53 248 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))].
% 56.20/56.53 249 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)])].
% 56.20/56.53 284 is_a_theorem(implies(and(A,B),not(not(A)))). [para(150(a,1),57(a,1,1))].
% 56.20/56.53 287 -is_a_theorem(and(A,B)) | is_a_theorem(not(not(A))). [para(150(a,1),126(a,1))].
% 56.20/56.53 309 is_a_theorem(implies(and(A,B),not(not(not(not(A)))))). [para(150(a,1),284(a,1,1))].
% 56.20/56.53 551 is_a_theorem(implies(A,and(A,not(not(not(not(not(not(A))))))))). [para(114(a,1),226(a,1)),rewrite([150(9)])].
% 56.20/56.53 608 is_a_theorem(implies(and(A,B),not(not(not(not(not(not(A)))))))). [para(150(a,1),309(a,1,1))].
% 56.20/56.53 612 implies(and(A,not(not(B))),C) = implies(and(A,B),C). [para(125(a,1),143(a,1,1)),flip(a)].
% 56.20/56.53 850 equiv(A,not(not(B))) = equiv(A,B). [para(145(a,1),150(a,2)),rewrite([125(4),82(3),92(3)]),flip(a)].
% 56.20/56.53 924 -is_a_theorem(equiv(A,B)) | not(not(B)) = A. [para(850(a,1),64(a,1))].
% 56.20/56.53 1194 is_a_theorem(not(not(implies(and(A,B),A)))). [resolve(172,a,287,a)].
% 56.20/56.53 1234 is_a_theorem(not(and(and(not(A),B),A))). [para(125(a,1),1194(a,1,1))].
% 56.20/56.53 1628 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(B,not(C)),implies(C,not(A)))). [resolve(152,a,70,b)].
% 56.20/56.53 1794 -is_a_theorem(implies(not(A),B)) | is_a_theorem(implies(implies(B,not(C)),implies(C,A))). [resolve(153,a,70,b)].
% 56.20/56.53 1959 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)])].
% 56.20/56.53 1960 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)])].
% 56.20/56.53 2914 -is_a_theorem(implies(A,not(B))) | is_a_theorem(implies(B,implies(A,not(C)))). [resolve(1959,a,70,b)].
% 56.20/56.53 3018 -is_a_theorem(not(and(and(A,A),B))) | is_a_theorem(not(and(B,A))). [resolve(1960,a,142,b),rewrite([125(4)])].
% 56.20/56.53 8058 is_a_theorem(implies(A,A)). [resolve(3018,a,1234,a),rewrite([82(3)])].
% 56.20/56.53 8059 -is_a_theorem(implies(and(A,A),B)) | is_a_theorem(not(and(not(B),A))). [para(82(a,1),3018(a,1))].
% 56.20/56.53 8072 is_a_theorem(equiv(A,A)). [back_unit_del(175),unit_del(a,8058)].
% 56.20/56.53 8222 is_a_theorem(implies(A,implies(not(A),not(B)))). [resolve(8058,a,2914,a)].
% 56.20/56.53 8224 is_a_theorem(implies(implies(A,not(B)),not(and(B,A)))). [resolve(8058,a,155,a)].
% 56.20/56.53 8471 not(not(A)) = A. [resolve(8072,a,924,a)].
% 56.20/56.53 8573 not(and(A,B)) = implies(A,not(B)). [para(8471(a,1),82(a,1,1,2))].
% 56.20/56.53 8574 not(implies(A,B)) = and(A,not(B)). [para(82(a,1),8471(a,1,1))].
% 56.20/56.53 8577 is_a_theorem(implies(implies(A,not(B)),implies(B,implies(A,C)))). [para(8471(a,1),1959(a,1,2,2,2))].
% 56.20/56.53 8584 is_a_theorem(implies(implies(A,not(B)),implies(B,not(A)))). [back_rewrite(8224),rewrite([8573(4)])].
% 56.20/56.53 8589 -is_a_theorem(implies(and(A,A),B)) | is_a_theorem(implies(not(B),not(A))). [back_rewrite(8059),rewrite([8573(6)])].
% 56.20/56.53 8688 is_a_theorem(implies(A,implies(not(A),B))). [para(8471(a,1),8222(a,1,2,2))].
% 56.20/56.53 8765 -is_a_theorem(A) | is_a_theorem(implies(not(A),B)). [resolve(8688,a,70,b)].
% 56.20/56.53 8837 is_a_theorem(implies(not(A),implies(A,B))). [para(8471(a,1),8688(a,1,2,1))].
% 56.20/56.53 8839 is_a_theorem(implies(not(equiv(A,A)),B)). [resolve(8765,a,8072,a)].
% 56.20/56.53 8840 is_a_theorem(implies(and(A,not(A)),B)). [resolve(8765,a,8058,a),rewrite([8574(2)])].
% 56.20/56.53 11009 -is_a_theorem(implies(A,not(B))) | is_a_theorem(implies(B,not(A))). [resolve(8584,a,70,b)].
% 56.20/56.53 11100 is_a_theorem(implies(implies(A,B),implies(not(B),not(A)))). [para(8471(a,1),8584(a,1,1,2))].
% 56.20/56.53 12459 is_a_theorem(implies(A,implies(B,B))). [resolve(11009,a,8840,a),rewrite([8573(3),8471(2)])].
% 56.20/56.53 12460 is_a_theorem(implies(A,equiv(B,B))). [resolve(11009,a,8839,a),rewrite([8471(3)])].
% 56.20/56.53 12461 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(B),not(A))). [para(8471(a,1),11009(a,1,2))].
% 56.20/56.53 13719 is_a_theorem(implies(implies(not(A),B),implies(not(B),A))). [para(8471(a,1),11100(a,1,2,2))].
% 56.20/56.53 14411 is_a_theorem(implies(and(A,B),and(B,A))). [resolve(12461,a,8584,a),rewrite([8574(3),8471(2),8574(4),8471(3)])].
% 56.20/56.53 14419 is_a_theorem(implies(implies(A,not(A)),not(A))). [resolve(12461,a,54,a),rewrite([8573(2)])].
% 56.20/56.53 14424 -is_a_theorem(and(A,B)) | is_a_theorem(and(B,A)). [resolve(14411,a,70,b)].
% 56.20/56.53 14518 is_a_theorem(implies(equiv(A,B),equiv(B,A))). [para(92(a,1),14411(a,1,1)),rewrite([92(4)])].
% 56.20/56.53 14599 is_a_theorem(implies(implies(not(A),A),A)). [para(8471(a,1),14419(a,1,1,2)),rewrite([8471(4)])].
% 56.20/56.53 16198 -is_a_theorem(implies(not(A),B)) | is_a_theorem(implies(not(B),A)). [resolve(13719,a,70,b)].
% 56.20/56.53 18070 -is_a_theorem(implies(A,not(B))) | is_a_theorem(implies(B,implies(A,C))). [resolve(8577,a,70,b)].
% 56.20/56.53 19724 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(B),implies(A,C))). [para(8471(a,1),18070(a,1,2))].
% 56.20/56.53 25997 is_a_theorem(implies(implies(implies(A,B),not(C)),implies(C,A))). [resolve(1628,a,8837,a),rewrite([8471(5)])].
% 56.20/56.53 26049 is_a_theorem(implies(and(A,not(B)),and(implies(B,C),A))). [resolve(25997,a,12461,a),rewrite([8574(2),8574(6),8471(5)])].
% 56.20/56.53 26054 -is_a_theorem(implies(implies(A,B),not(C))) | is_a_theorem(implies(C,A)). [resolve(25997,a,70,b)].
% 56.20/56.53 26733 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(not(C),A)). [para(8471(a,1),26054(a,1,2))].
% 56.20/56.53 27292 is_a_theorem(implies(and(A,B),B)). [resolve(26733,a,8584,a),rewrite([8574(3),8471(2)])].
% 56.20/56.53 27324 is_a_theorem(implies(A,implies(and(B,not(A)),C))). [resolve(27292,a,18070,a)].
% 56.20/56.53 27327 is_a_theorem(implies(A,implies(B,A))). [resolve(27292,a,11009,a),rewrite([8573(3),8471(2)])].
% 56.20/56.53 27764 is_a_theorem(implies(implies(implies(A,B),not(C)),implies(C,not(B)))). [resolve(27327,a,1628,a)].
% 56.20/56.53 27849 is_a_theorem(implies(implies(implies(A,not(B)),not(C)),implies(C,B))). [resolve(1794,a,27327,a)].
% 56.20/56.53 27911 is_a_theorem(implies(implies(equiv(A,A),not(B)),implies(B,C))). [resolve(1794,a,12460,a)].
% 56.20/56.53 27912 is_a_theorem(implies(implies(implies(A,A),not(B)),implies(B,C))). [resolve(1794,a,12459,a)].
% 56.20/56.53 32944 is_a_theorem(implies(and(A,not(B)),and(equiv(C,C),A))). [resolve(27911,a,12461,a),rewrite([8574(2),8574(6),8471(5)])].
% 56.20/56.53 32971 is_a_theorem(implies(and(A,not(B)),and(implies(C,C),A))). [resolve(27912,a,12461,a),rewrite([8574(2),8574(6),8471(5)])].
% 56.20/56.53 34771 is_a_theorem(implies(implies(equiv(A,A),B),B)). [resolve(32944,a,8589,a),rewrite([8573(4),8471(3),8471(4)])].
% 56.20/56.53 34803 is_a_theorem(implies(A,and(equiv(B,B),A))). [resolve(34771,a,11009,a),rewrite([8574(4),8471(3)])].
% 56.20/56.53 34887 -is_a_theorem(A) | is_a_theorem(and(equiv(B,B),A)). [resolve(34803,a,70,b)].
% 56.20/56.53 35290 is_a_theorem(and(equiv(A,A),implies(B,implies(C,C)))). [resolve(34887,a,12459,a)].
% 56.20/56.53 35681 is_a_theorem(and(implies(A,implies(B,B)),equiv(C,C))). [resolve(35290,a,14424,a)].
% 56.20/56.53 36433 is_a_theorem(implies(implies(implies(A,A),B),B)). [resolve(32971,a,8589,a),rewrite([8573(4),8471(3),8471(4)])].
% 56.20/56.53 36458 is_a_theorem(implies(A,and(implies(B,B),A))). [resolve(36433,a,11009,a),rewrite([8574(4),8471(3)])].
% 56.20/56.53 36506 -is_a_theorem(A) | is_a_theorem(and(implies(B,B),A)). [resolve(36458,a,70,b)].
% 56.20/56.53 36546 is_a_theorem(and(implies(A,A),implies(implies(implies(B,B),C),C))). [resolve(36506,a,36433,a)].
% 56.20/56.53 36683 is_a_theorem(and(implies(A,A),implies(B,implies(C,B)))). [resolve(36506,a,27327,a)].
% 56.20/56.53 36876 is_a_theorem(and(implies(A,A),implies(implies(not(B),B),B))). [resolve(36506,a,14599,a)].
% 56.20/56.53 36906 is_a_theorem(and(implies(A,A),implies(B,implies(C,C)))). [resolve(36506,a,12459,a)].
% 56.20/56.53 36945 is_a_theorem(and(implies(A,A),implies(B,implies(not(B),C)))). [resolve(36506,a,8688,a)].
% 56.20/56.53 37101 is_a_theorem(and(implies(A,implies(B,A)),implies(C,C))). [resolve(36683,a,14424,a)].
% 56.20/56.53 37254 is_a_theorem(and(implies(A,implies(B,B)),implies(C,C))). [resolve(36906,a,14424,a)].
% 56.20/56.53 44458 is_a_theorem(and(implies(A,implies(not(A),B)),implies(C,C))). [resolve(36945,a,14424,a)].
% 56.20/56.53 57897 is_a_theorem(implies(and(A,B),and(implies(C,B),A))). [resolve(27764,a,12461,a),rewrite([8574(3),8471(2),8574(5),8471(4)])].
% 56.20/56.53 57995 is_a_theorem(implies(implies(implies(A,B),not(B)),not(B))). [resolve(57897,a,8589,a),rewrite([8573(3)])].
% 56.20/56.53 58004 is_a_theorem(implies(and(implies(A,B),A),equiv(B,A))). [para(92(a,1),57897(a,1,2))].
% 56.20/56.53 58129 is_a_theorem(implies(A,and(implies(B,A),A))). [resolve(57995,a,12461,a),rewrite([8471(2),8574(4),8471(3)])].
% 56.20/56.53 59121 -is_a_theorem(and(implies(A,B),A)) | is_a_theorem(equiv(B,A)). [resolve(58004,a,70,b)].
% 56.20/56.53 59220 is_a_theorem(equiv(implies(and(A,not(A)),B),implies(A,A))). [resolve(59121,a,44458,a),rewrite([8574(2)])].
% 56.20/56.53 59223 is_a_theorem(equiv(implies(A,A),implies(B,B))). [resolve(59121,a,37254,a)].
% 56.20/56.53 59225 is_a_theorem(equiv(implies(A,implies(B,B)),implies(B,B))). [resolve(59121,a,37101,a)].
% 56.20/56.53 59227 is_a_theorem(equiv(implies(A,A),equiv(B,B))). [resolve(59121,a,35681,a)].
% 56.20/56.53 59277 implies(A,A) = implies(B,B). [resolve(59223,a,64,a)].
% 56.20/56.53 59281 implies(A,A) = c_0. [new_symbol(59277)].
% 56.20/56.53 59283 is_a_theorem(equiv(c_0,equiv(A,A))). [back_rewrite(59227),rewrite([59281(1)])].
% 56.20/56.53 59284 is_a_theorem(equiv(implies(A,c_0),c_0)). [back_rewrite(59225),rewrite([59281(1),59281(3)])].
% 56.20/56.53 59286 is_a_theorem(equiv(implies(and(A,not(A)),B),c_0)). [back_rewrite(59220),rewrite([59281(4)])].
% 56.20/56.53 59541 is_a_theorem(and(c_0,implies(implies(not(A),A),A))). [back_rewrite(36876),rewrite([59281(1)])].
% 56.20/56.53 59555 is_a_theorem(and(c_0,implies(A,implies(B,A)))). [back_rewrite(36683),rewrite([59281(1)])].
% 56.20/56.53 59568 is_a_theorem(and(c_0,implies(implies(c_0,A),A))). [back_rewrite(36546),rewrite([59281(1),59281(2)])].
% 56.20/56.53 60730 is_a_theorem(c_0). [back_rewrite(8058),rewrite([59281(1)])].
% 56.20/56.53 61244 and(c_0,c_0) = equiv(A,A). [para(59281(a,1),92(a,1,1)),rewrite([59281(2)])].
% 56.20/56.53 61250 and(A,not(A)) = not(c_0). [para(59281(a,1),8574(a,1,1)),flip(a)].
% 56.20/56.53 61330 is_a_theorem(equiv(implies(not(c_0),A),c_0)). [back_rewrite(59286),rewrite([61250(2)])].
% 56.20/56.53 61624 equiv(A,A) = c_0. [resolve(59283,a,64,a)].
% 56.20/56.53 61702 and(c_0,c_0) = c_0. [back_rewrite(61244),rewrite([61624(4)])].
% 56.20/56.53 61836 implies(A,c_0) = c_0. [resolve(59284,a,64,a),flip(a)].
% 56.20/56.53 61843 and(c_0,implies(c_0,A)) = equiv(A,c_0). [para(61836(a,1),92(a,1,1))].
% 56.20/56.53 61849 implies(c_0,and(c_0,not(A))) = not(equiv(A,c_0)). [para(61836(a,1),189(a,1,1))].
% 56.20/56.53 61865 -is_a_theorem(and(c_0,A)) | is_a_theorem(equiv(c_0,A)). [para(61836(a,1),59121(a,1,1))].
% 56.20/56.53 63204 and(implies(A,B),and(A,not(B))) = not(c_0). [para(8574(a,1),61250(a,1,2))].
% 56.20/56.53 63302 implies(not(c_0),A) = c_0. [resolve(61330,a,64,a),flip(a)].
% 56.20/56.53 63334 and(implies(A,not(c_0)),c_0) = equiv(A,not(c_0)). [para(63302(a,1),92(a,1,2))].
% 56.20/56.53 63335 is_a_theorem(implies(implies(c_0,A),implies(implies(A,and(B,c_0)),not(equiv(B,not(c_0)))))). [para(63302(a,1),140(a,1,1,1)),rewrite([8471(5)])].
% 56.20/56.53 65380 is_a_theorem(equiv(c_0,implies(implies(c_0,A),A))). [resolve(61865,a,59568,a)].
% 56.20/56.53 65381 is_a_theorem(equiv(c_0,implies(A,implies(B,A)))). [resolve(61865,a,59555,a)].
% 56.20/56.53 66077 implies(implies(c_0,A),A) = c_0. [resolve(65380,a,64,a)].
% 56.20/56.53 66131 and(implies(A,implies(c_0,A)),c_0) = equiv(A,implies(c_0,A)). [para(66077(a,1),92(a,1,2))].
% 56.20/56.53 66233 implies(A,implies(B,A)) = c_0. [resolve(65381,a,64,a)].
% 56.20/56.53 66241 equiv(A,implies(c_0,A)) = c_0. [back_rewrite(66131),rewrite([66233(3),61702(3)]),flip(a)].
% 56.20/56.53 66255 and(c_0,implies(implies(A,B),B)) = equiv(B,implies(A,B)). [para(66233(a,1),92(a,1,1))].
% 56.20/56.53 66263 and(A,and(B,not(A))) = not(c_0). [para(66233(a,1),8574(a,1,1)),rewrite([8574(4)]),flip(a)].
% 56.20/56.53 66265 is_a_theorem(implies(implies(not(A),B),implies(c_0,implies(and(C,not(B)),A)))). [para(66233(a,1),248(a,1,2,1)),rewrite([8574(5)])].
% 56.20/56.53 66267 is_a_theorem(implies(implies(A,B),implies(c_0,implies(and(C,not(B)),not(A))))). [para(66233(a,1),249(a,1,2,1)),rewrite([8574(4)])].
% 56.20/56.53 66307 is_a_theorem(equiv(A,implies(not(A),A))). [back_rewrite(59541),rewrite([66255(5)])].
% 56.20/56.53 66312 implies(c_0,A) = A. [para(66241(a,1),64(a,1)),unit_del(a,60730)].
% 56.20/56.53 66342 is_a_theorem(implies(implies(A,B),implies(and(C,not(B)),not(A)))). [back_rewrite(66267),rewrite([66312(7)])].
% 56.20/56.53 66343 is_a_theorem(implies(implies(not(A),B),implies(and(C,not(B)),A))). [back_rewrite(66265),rewrite([66312(7)])].
% 56.20/56.53 66735 is_a_theorem(implies(A,implies(implies(A,and(B,c_0)),not(equiv(B,not(c_0)))))). [back_rewrite(63335),rewrite([66312(2)])].
% 56.20/56.53 66748 not(equiv(A,c_0)) = and(c_0,not(A)). [back_rewrite(61849),rewrite([66312(5)]),flip(a)].
% 56.20/56.53 66751 equiv(A,c_0) = and(c_0,A). [back_rewrite(61843),rewrite([66312(3)]),flip(a)].
% 56.20/56.53 67245 and(c_0,not(A)) = not(A). [back_rewrite(66748),rewrite([66751(2),8573(3),66312(3)]),flip(a)].
% 56.20/56.53 67405 implies(not(A),A) = A. [resolve(66307,a,64,a)].
% 56.20/56.53 67425 is_a_theorem(implies(implies(A,B),implies(implies(B,not(A)),not(A)))). [para(67405(a,1),152(a,1,2,2)),rewrite([8471(3)])].
% 56.20/56.53 67429 implies(A,not(A)) = not(A). [para(8471(a,1),67405(a,1,1))].
% 56.20/56.53 69120 -is_a_theorem(and(c_0,A)) | c_0 = A. [para(66751(a,1),64(a,1))].
% 56.20/56.53 69121 and(c_0,A) = A. [para(8471(a,1),67245(a,1,2)),rewrite([8471(4)])].
% 56.20/56.53 69145 -is_a_theorem(A) | c_0 = A. [back_rewrite(69120),rewrite([69121(2)])].
% 56.20/56.53 69180 equiv(A,implies(B,A)) = implies(implies(B,A),A). [back_rewrite(66255),rewrite([69121(4)]),flip(a)].
% 56.20/56.53 69187 is_a_theorem(implies(A,and(A,c_0))). [para(69121(a,1),14411(a,1,1))].
% 56.20/56.53 69218 implies(A,and(implies(B,A),A)) = c_0. [resolve(69145,a,58129,a),flip(a)].
% 56.20/56.53 69316 implies(A,implies(and(B,not(A)),C)) = c_0. [resolve(69145,a,27324,a),flip(a)].
% 56.20/56.53 69324 implies(and(A,B),B) = c_0. [resolve(69145,a,27292,a),flip(a)].
% 56.20/56.53 69354 implies(and(A,not(B)),and(implies(B,C),A)) = c_0. [resolve(69145,a,26049,a),flip(a)].
% 56.20/56.53 69458 implies(equiv(A,B),equiv(B,A)) = c_0. [resolve(69145,a,14518,a),flip(a)].
% 56.20/56.53 69460 implies(and(A,B),and(B,A)) = c_0. [resolve(69145,a,14411,a),flip(a)].
% 56.20/56.53 69466 implies(implies(not(A),B),implies(not(B),A)) = c_0. [resolve(69145,a,13719,a),flip(a)].
% 56.20/56.53 69490 implies(A,implies(not(A),B)) = c_0. [resolve(69145,a,8688,a),flip(a)].
% 56.20/56.53 69520 implies(and(A,B),A) = c_0. [resolve(69145,a,57,a),flip(a)].
% 56.20/56.53 69598 implies(A,and(A,c_0)) = c_0. [resolve(69187,a,69145,a),flip(a)].
% 56.20/56.53 69605 and(A,A) = A. [para(67429(a,1),8574(a,1,1)),rewrite([8471(2),8471(2)]),flip(a)].
% 56.20/56.53 69797 and(and(A,B),not(B)) = not(c_0). [para(69324(a,1),8574(a,1,1)),flip(a)].
% 56.20/56.53 69803 and(implies(A,and(A,B)),c_0) = equiv(A,and(A,B)). [para(69520(a,1),92(a,1,2))].
% 56.20/56.53 69809 equiv(A,and(A,c_0)) = c_0. [para(69598(a,1),92(a,1,1)),rewrite([69520(4),69605(3)]),flip(a)].
% 56.20/56.53 69811 and(A,c_0) = A. [para(69809(a,1),64(a,1)),unit_del(a,60730)].
% 56.20/56.53 69812 equiv(A,and(A,B)) = implies(A,and(A,B)). [back_rewrite(69803),rewrite([69811(4)]),flip(a)].
% 56.20/56.53 69819 is_a_theorem(implies(A,implies(implies(A,B),not(equiv(B,not(c_0)))))). [back_rewrite(66735),rewrite([69811(2)])].
% 56.20/56.53 69822 equiv(A,not(c_0)) = implies(A,not(c_0)). [back_rewrite(63334),rewrite([69811(5)]),flip(a)].
% 56.20/56.53 69832 is_a_theorem(implies(A,implies(implies(A,B),B))). [back_rewrite(69819),rewrite([69822(4),8574(5),8471(4),69811(3)])].
% 56.20/56.53 69957 implies(A,not(c_0)) = not(A). [para(69811(a,1),8573(a,1,1)),flip(a)].
% 56.20/56.53 69958 equiv(A,not(c_0)) = not(A). [back_rewrite(69822),rewrite([69957(6)])].
% 56.20/56.53 69987 -is_a_theorem(not(A)) | not(c_0) = A. [para(69958(a,1),64(a,1))].
% 56.20/56.53 70072 -is_a_theorem(A) | not(c_0) = not(A). [para(8471(a,1),69987(a,1))].
% 56.20/56.53 70148 equiv(A,implies(not(A),B)) = implies(implies(not(A),B),A). [para(69490(a,1),92(a,1,1)),rewrite([69121(5)]),flip(a)].
% 56.20/56.53 70154 implies(A,implies(implies(A,B),B)) = c_0. [resolve(69832,a,69145,a),flip(a)].
% 56.20/56.53 70157 is_a_theorem(implies(and(implies(A,B),not(B)),implies(A,C))). [resolve(69832,a,19724,a),rewrite([8574(3)])].
% 56.20/56.53 70418 equiv(equiv(A,B),equiv(B,A)) = c_0. [para(69458(a,1),92(a,1,1)),rewrite([69458(4),69605(3)]),flip(a)].
% 56.20/56.53 70421 equiv(and(A,B),and(B,A)) = c_0. [para(69460(a,1),92(a,1,1)),rewrite([69460(4),69605(3)]),flip(a)].
% 56.20/56.53 70575 equiv(A,B) = equiv(B,A). [para(70418(a,1),64(a,1)),unit_del(a,60730)].
% 56.20/56.53 71162 and(A,B) = and(B,A). [para(70421(a,1),64(a,1)),unit_del(a,60730)].
% 56.20/56.53 71425 is_a_theorem(implies(and(not(A),implies(B,A)),implies(B,C))). [back_rewrite(70157),rewrite([71162(3)])].
% 56.20/56.53 71481 and(not(A),and(B,A)) = not(c_0). [back_rewrite(69797),rewrite([71162(3)])].
% 56.20/56.53 71503 implies(and(A,not(B)),and(A,implies(B,C))) = c_0. [back_rewrite(69354),rewrite([71162(4)])].
% 56.20/56.53 71517 implies(A,and(A,implies(B,A))) = c_0. [back_rewrite(69218),rewrite([71162(2)])].
% 56.20/56.53 71739 implies(A,not(B)) = implies(B,not(A)). [para(71162(a,1),8573(a,1,1)),rewrite([8573(2)])].
% 56.20/56.53 71775 is_a_theorem(implies(implies(A,B),implies(A,and(A,B)))). [back_rewrite(67425),rewrite([71739(3),71739(5),8574(4),8471(3)])].
% 56.20/56.53 71776 is_a_theorem(implies(implies(A,B),implies(A,implies(C,B)))). [back_rewrite(66342),rewrite([71739(5),8573(4),8471(3)])].
% 56.20/56.53 71790 is_a_theorem(implies(implies(A,and(B,C)),implies(A,C))). [back_rewrite(27849),rewrite([71739(4),8574(3),8471(2)])].
% 56.20/56.53 71876 and(not(c_0),implies(A,B)) = not(c_0). [para(66263(a,1),71481(a,1,2)),rewrite([8573(3),8471(2),71162(4)])].
% 56.20/56.53 71907 and(implies(A,not(B)),implies(not(A),B)) = equiv(B,not(A)). [para(71739(a,1),92(a,1,1))].
% 56.20/56.53 71952 implies(A,implies(B,and(A,B))) = c_0. [para(71739(a,1),70154(a,1,2,1)),rewrite([71739(2),71739(4),8574(3),8471(2)])].
% 56.20/56.53 71954 and(not(c_0),not(equiv(A,B))) = not(c_0). [para(189(a,1),71876(a,1,2))].
% 56.20/56.53 72165 is_a_theorem(implies(and(A,implies(A,B)),B)). [para(71952(a,1),16198(a,1)),rewrite([71162(4),8574(6),8573(5),8471(4)]),unit_del(a,60730)].
% 56.20/56.53 72192 and(not(A),and(B,implies(B,A))) = not(c_0). [resolve(72165,a,70072,a),rewrite([8574(6),71162(6)]),flip(a)].
% 56.20/56.53 72515 is_a_theorem(implies(and(and(A,B),not(C)),B)). [para(69316(a,1),16198(a,1)),rewrite([8471(4),8574(5)]),unit_del(a,60730)].
% 56.20/56.53 72569 implies(and(and(A,B),not(C)),B) = c_0. [resolve(72515,a,69145,a),flip(a)].
% 56.20/56.53 74032 implies(implies(A,B),implies(A,and(A,B))) = c_0. [resolve(71775,a,69145,a),flip(a)].
% 56.20/56.53 74066 implies(implies(A,B),implies(A,implies(C,B))) = c_0. [resolve(71776,a,69145,a),flip(a)].
% 56.20/56.53 74226 implies(implies(A,and(B,C)),implies(A,C)) = c_0. [resolve(71790,a,69145,a),flip(a)].
% 56.20/56.53 74266 -is_a_theorem(implies(implies(not(c50),implies(not(c51),c52)),and(A,implies(not(c51),implies(not(c50),c52))))). [ur(70,b,71790,a,c,101,a)].
% 56.20/56.53 74275 not(equiv(not(c_0),equiv(A,B))) = equiv(A,B). [para(71954(a,1),189(a,1,2)),rewrite([71739(4),66312(4),71739(5),8471(4),66312(3),70575(5)]),flip(a)].
% 56.20/56.53 80153 equiv(c_0,implies(A,B)) = implies(A,B). [para(66233(a,1),69180(a,1,2)),rewrite([70575(3),66233(5),66312(6)])].
% 56.20/56.53 80414 -is_a_theorem(implies(A,B)) | implies(A,B) = c_0. [para(80153(a,1),64(a,1))].
% 56.20/56.53 80415 and(c_0,implies(A,B)) = implies(A,B). [para(80153(a,1),92(a,2)),rewrite([66312(3),61836(4),71162(3)])].
% 56.20/56.53 80617 equiv(implies(not(A),B),implies(not(B),A)) = c_0. [para(69466(a,1),92(a,1,1)),rewrite([69466(6),69605(3),70575(6)]),flip(a)].
% 56.20/56.53 80680 -is_a_theorem(implies(A,and(A,B))) | and(A,B) = A. [para(69812(a,1),64(a,1))].
% 56.20/56.53 80693 equiv(not(c_0),implies(A,B)) = and(A,not(B)). [para(63204(a,1),69812(a,1,2)),rewrite([70575(4),63204(9),71739(8),8574(7),66312(8)])].
% 56.20/56.53 81068 is_a_theorem(implies(and(implies(A,not(B)),implies(C,and(A,B))),implies(C,D))). [para(8573(a,1),71425(a,1,1,1))].
% 56.20/56.53 82429 equiv(implies(A,B),implies(A,and(A,B))) = c_0. [para(74032(a,1),92(a,1,1)),rewrite([74226(5),69605(3)]),flip(a)].
% 56.20/56.53 82635 implies(implies(A,B),B) = implies(not(B),and(A,not(B))). [para(69180(a,1),74275(a,1,1,2)),rewrite([80693(5),71162(3),8573(4),8574(3),69180(6)]),flip(a)].
% 56.20/56.53 82697 equiv(A,implies(B,A)) = implies(not(A),and(B,not(A))). [back_rewrite(69180),rewrite([82635(4)])].
% 56.20/56.53 82710 is_a_theorem(implies(implies(A,B),implies(and(A,C),B))). [para(8471(a,1),66343(a,1,2,1,2)),rewrite([71739(3),8471(2),71162(2)])].
% 56.20/56.53 82719 implies(implies(A,B),implies(and(A,C),B)) = c_0. [resolve(82710,a,80414,a)].
% 56.20/56.53 83449 implies(not(A),B) = implies(not(B),A). [para(80617(a,1),64(a,1)),unit_del(a,60730)].
% 56.20/56.53 83559 equiv(A,not(B)) = equiv(B,not(A)). [para(83449(a,1),92(a,1,1)),rewrite([71162(5),71907(5),70575(4)])].
% 56.20/56.53 83753 -is_a_theorem(equiv(A,not(B))) | not(A) = B. [para(83559(a,1),64(a,1))].
% 56.20/56.53 83758 -is_a_theorem(equiv(A,B)) | not(A) = not(B). [para(8471(a,1),83753(a,1,2))].
% 56.20/56.53 83762 -is_a_theorem(implies(A,and(A,B))) | implies(A,not(B)) = not(A). [para(69812(a,1),83758(a,1)),rewrite([8573(6)]),flip(b)].
% 56.20/56.53 83810 and(A,implies(B,A)) = A. [para(71517(a,1),80680(a,1)),unit_del(a,60730)].
% 56.20/56.53 83830 implies(A,and(B,not(A))) = not(A). [para(83810(a,1),8573(a,1,1)),rewrite([8574(3)]),flip(a)].
% 56.20/56.53 83993 implies(implies(A,not(B)),A) = A. [para(83830(a,1),83449(a,1)),rewrite([8471(2),8471(2),71162(1),8573(2)]),flip(a)].
% 56.20/56.53 84061 implies(implies(A,B),A) = A. [para(8471(a,1),83993(a,1,1,2))].
% 56.20/56.53 84856 implies(A,and(A,B)) = implies(A,B). [para(82429(a,1),64(a,1)),unit_del(a,60730)].
% 56.20/56.53 84862 -is_a_theorem(implies(A,B)) | implies(A,not(B)) = not(A). [back_rewrite(83762),rewrite([84856(2)])].
% 56.20/56.53 84879 -is_a_theorem(implies(A,B)) | and(A,B) = A. [back_rewrite(80680),rewrite([84856(2)])].
% 56.20/56.53 84894 implies(not(A),and(B,not(A))) = implies(not(A),B). [para(84856(a,1),88(a,2)),rewrite([71162(2),88(3)])].
% 56.20/56.53 84914 implies(not(A),and(B,implies(B,A))) = A. [para(72192(a,1),84856(a,1,2)),rewrite([69957(4),8471(2)]),flip(a)].
% 56.20/56.53 84955 equiv(A,implies(B,A)) = implies(not(A),B). [back_rewrite(82697),rewrite([84894(6)])].
% 56.20/56.53 84963 implies(implies(A,B),B) = implies(not(A),B). [back_rewrite(82635),rewrite([84894(6),83449(4)])].
% 56.20/56.53 85088 and(implies(A,B),implies(A,implies(C,B))) = implies(A,B). [para(74066(a,1),84879(a,1)),unit_del(a,60730)].
% 56.20/56.53 85599 and(A,implies(A,B)) = and(A,B). [para(84914(a,1),84914(a,1,2,2)),rewrite([8573(3),8574(2),84856(3),71162(4),61250(4),71739(5),8574(4),8471(3),66312(3)]),flip(a)].
% 56.20/56.53 86143 implies(implies(not(A),B),A) = implies(B,A). [para(71739(a,1),84955(a,2)),rewrite([83449(2),70148(3),8471(5)])].
% 56.20/56.53 86201 equiv(A,implies(not(A),B)) = implies(B,A). [back_rewrite(70148),rewrite([86143(6)])].
% 56.20/56.53 86441 implies(A,and(B,A)) = implies(A,B). [para(84963(a,1),71739(a,1)),rewrite([71739(3),8471(2),8574(4),8471(3)]),flip(a)].
% 56.20/56.53 86462 implies(and(A,not(B)),implies(A,implies(C,B))) = implies(A,implies(C,B)). [para(74066(a,1),84963(a,1,1)),rewrite([66312(4),8574(4)]),flip(a)].
% 56.20/56.53 86493 and(implies(A,B),implies(not(A),B)) = B. [para(84963(a,1),85599(a,1,2)),rewrite([71162(6),83810(6)])].
% 56.20/56.53 87311 and(implies(A,not(B)),implies(B,A)) = not(B). [para(71739(a,1),86493(a,1,2)),rewrite([8471(4)])].
% 56.20/56.53 87529 and(implies(A,B),implies(and(A,C),B)) = implies(A,B). [para(82719(a,1),84879(a,1)),unit_del(a,60730)].
% 56.20/56.53 87543 implies(and(A,not(B)),implies(and(A,C),B)) = implies(and(A,C),B). [para(82719(a,1),84963(a,1,1)),rewrite([66312(4),8574(4)]),flip(a)].
% 56.20/56.53 88319 implies(A,implies(and(B,A),C)) = implies(and(B,A),C). [para(72569(a,1),84862(a,1)),rewrite([71739(7),8573(6),8471(5),8573(9),8471(8)]),unit_del(a,60730)].
% 56.20/56.53 91107 implies(and(A,implies(B,C)),implies(A,B)) = implies(A,B). [para(71503(a,1),87311(a,1,2)),rewrite([8573(5),8471(4),71162(6),80415(6),8573(7),8471(6)])].
% 56.20/56.53 102150 implies(and(A,implies(B,C)),B) = implies(A,B). [para(91107(a,1),85088(a,1,2)),rewrite([71162(5),87529(5)]),flip(a)].
% 56.20/56.53 102159 implies(and(A,implies(B,not(C))),C) = implies(A,C). [para(71739(a,1),102150(a,1,1,2))].
% 56.20/56.53 102161 implies(and(A,B),implies(B,C)) = implies(A,implies(B,C)). [para(84061(a,1),102150(a,1,1,2))].
% 56.20/56.53 102171 implies(implies(A,and(B,C)),B) = implies(not(A),B). [para(102159(a,1),84963(a,1,1)),rewrite([84963(2),71739(4),8573(6),8574(5),8471(4)]),flip(a)].
% 56.20/56.53 102216 implies(not(A),implies(B,and(A,C))) = implies(B,A). [para(102171(a,1),84955(a,1,2)),rewrite([83449(2),86201(3)]),flip(a)].
% 56.20/56.53 102314 implies(and(A,not(B)),implies(C,B)) = implies(C,implies(A,B)). [para(86493(a,1),102216(a,1,2,2)),rewrite([8574(2)])].
% 56.20/56.53 102355 implies(and(A,B),implies(A,C)) = implies(and(A,B),C). [back_rewrite(87543),rewrite([102314(5)])].
% 56.20/56.53 102357 implies(A,implies(B,C)) = implies(B,implies(A,C)). [back_rewrite(86462),rewrite([102355(5),102314(4)])].
% 56.20/56.53 102361 implies(and(A,B),C) = implies(A,implies(B,C)). [back_rewrite(102161),rewrite([102357(3),88319(3)])].
% 56.20/56.53 102531 is_a_theorem(implies(A,implies(implies(B,not(C)),implies(implies(A,and(B,C)),D)))). [back_rewrite(81068),rewrite([102357(7),102361(6)])].
% 56.20/56.53 102536 -is_a_theorem(implies(implies(not(c50),implies(not(c51),c52)),A)). [back_rewrite(74266),rewrite([102357(14),86441(16)])].
% 56.20/56.53 102537 $F. [resolve(102536,a,102531,a)].
% 56.20/56.53
% 56.20/56.53 % SZS output end Refutation
% 56.20/56.53 ============================== end of proof ==========================
% 56.20/56.53
% 56.20/56.53 ============================== STATISTICS ============================
% 56.20/56.53
% 56.20/56.53 Given=7990. Generated=4528443. Kept=102486. proofs=1.
% 56.20/56.53 Usable=3669. Sos=7747. Demods=1998. Limbo=179, Disabled=90962. Hints=0.
% 56.20/56.53 Megabytes=63.13.
% 56.20/56.53 User_CPU=53.21, System_CPU=2.29, Wall_clock=56.
% 56.20/56.53
% 56.20/56.53 ============================== end of statistics =====================
% 56.20/56.53
% 56.20/56.53 ============================== end of search =========================
% 56.20/56.53
% 56.20/56.53 THEOREM PROVED
% 56.20/56.53 % SZS status Theorem
% 56.20/56.53
% 56.20/56.53 Exiting with 1 proof.
% 56.20/56.53
% 56.20/56.53 Process 31967 exit (max_proofs) Sun Jul 3 20:45:07 2022
% 56.20/56.53 Prover9 interrupted
%------------------------------------------------------------------------------