TSTP Solution File: LCL514+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL514+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n014.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 13:47:18 EDT 2022
% Result : Theorem 64.88s 65.13s
% Output : Refutation 64.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LCL514+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 4 11:24:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.45/1.02 ============================== Prover9 ===============================
% 0.45/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.45/1.02 Process 20218 was started by sandbox on n014.cluster.edu,
% 0.45/1.02 Mon Jul 4 11:24:24 2022
% 0.45/1.02 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_20065_n014.cluster.edu".
% 0.45/1.02 ============================== end of head ===========================
% 0.45/1.02
% 0.45/1.02 ============================== INPUT =================================
% 0.45/1.02
% 0.45/1.02 % Reading from file /tmp/Prover9_20065_n014.cluster.edu
% 0.45/1.02
% 0.45/1.02 set(prolog_style_variables).
% 0.45/1.02 set(auto2).
% 0.45/1.02 % set(auto2) -> set(auto).
% 0.45/1.02 % set(auto) -> set(auto_inference).
% 0.45/1.02 % set(auto) -> set(auto_setup).
% 0.45/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.45/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/1.02 % set(auto) -> set(auto_limits).
% 0.45/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/1.02 % set(auto) -> set(auto_denials).
% 0.45/1.02 % set(auto) -> set(auto_process).
% 0.45/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.45/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.45/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.45/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.45/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.45/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.45/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.45/1.02 % set(auto2) -> assign(stats, some).
% 0.45/1.02 % set(auto2) -> clear(echo_input).
% 0.45/1.02 % set(auto2) -> set(quiet).
% 0.45/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.45/1.02 % set(auto2) -> clear(print_given).
% 0.45/1.02 assign(lrs_ticks,-1).
% 0.45/1.02 assign(sos_limit,10000).
% 0.45/1.02 assign(order,kbo).
% 0.45/1.02 set(lex_order_vars).
% 0.45/1.02 clear(print_given).
% 0.45/1.02
% 0.45/1.02 % formulas(sos). % not echoed (43 formulas)
% 0.45/1.02
% 0.45/1.02 ============================== end of input ==========================
% 0.45/1.02
% 0.45/1.02 % From the command line: assign(max_seconds, 300).
% 0.45/1.02
% 0.45/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/1.02
% 0.45/1.02 % Formulas that are not ordinary clauses:
% 0.45/1.02 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].
% 0.45/1.02 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].
% 0.45/1.02 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].
% 0.45/1.02 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 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].
% 0.45/1.02 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].
% 0.45/1.02 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 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].
% 0.45/1.02 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 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].
% 0.45/1.02 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].
% 0.45/1.02 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].
% 1.22/1.49 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].
% 1.22/1.49 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 1.22/1.49 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 1.22/1.49 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].
% 1.22/1.49 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].
% 1.22/1.49 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 1.22/1.49 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 1.22/1.49 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 1.22/1.49 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 1.22/1.49 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 1.22/1.49 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].
% 1.22/1.49 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].
% 1.22/1.49 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].
% 1.22/1.49 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].
% 1.22/1.49 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].
% 1.22/1.49 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].
% 1.22/1.49 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].
% 1.22/1.49
% 1.22/1.49 ============================== end of process non-clausal formulas ===
% 1.22/1.49
% 1.22/1.49 ============================== PROCESS INITIAL CLAUSES ===============
% 1.22/1.49
% 1.22/1.49 ============================== PREDICATE ELIMINATION =================
% 1.22/1.49
% 1.22/1.49 ============================== end predicate elimination =============
% 1.22/1.49
% 1.22/1.49 Auto_denials: (non-Horn, no changes).
% 1.22/1.49
% 1.22/1.49 Term ordering decisions:
% 1.22/1.49
% 1.22/1.49 % Assigning unary symbol not kb_weight 0 and highest precedence (93).
% 1.22/1.49 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.
% 1.22/1.49
% 1.22/1.49 ============================== end of process initial clauses ========
% 1.22/1.49
% 1.22/1.49 ============================== CLAUSES FOR SEARCH ====================
% 1.22/1.49
% 1.22/1.49 ============================== end of clauses for search =============
% 1.22/1.49
% 1.22/1.49 ============================== SEARCH ================================
% 1.22/1.49
% 1.22/1.49 % Starting search at 0.02 seconds.
% 1.22/1.49
% 1.22/1.49 Low Water (keep): wt=40.000, iters=3403
% 1.22/1.49
% 1.22/1.49 Low Water (keep): wt=38.000, iters=3343
% 1.22/1.49
% 1.22/1.49 Low Water (keep): wt=37.000, iters=3358
% 1.22/1.49
% 1.22/1.49 Low Water (keep): wt=36.000, iters=3380
% 1.22/1.49
% 1.22/1.49 Low Water (keep): wt=32.000, iters=3339
% 1.22/1.49
% 1.22/1.49 Low Water (keep): wt=31.000, iters=3375
% 1.22/1.49
% 1.22/1.49 Low Water (keep): wt=30.000, iters=3363
% 1.22/1.49
% 1.22/1.49 Low Water (keep): wt=29.000, iters=3549
% 1.22/1.49
% 1.22/1.49 Low Water (keep): wt=28.000, iters=3471
% 1.22/1.49
% 1.22/1.49 Low Water (keep): wt=27.000, iters=3376
% 1.22/1.49
% 64.85/65.13 Low Water (keep): wt=26.000, iters=3459
% 64.85/65.13
% 64.85/65.13 Low Water (keep): wt=25.000, iters=3414
% 64.85/65.13
% 64.85/65.13 Low Water (keep): wt=24.000, iters=3478
% 64.85/65.13
% 64.85/65.13 Low Water (keep): wt=23.000, iters=3334
% 64.85/65.13
% 64.85/65.13 Low Water (keep): wt=21.000, iters=3378
% 64.85/65.13
% 64.85/65.13 Low Water (keep): wt=20.000, iters=3393
% 64.85/65.13
% 64.85/65.13 Low Water (keep): wt=19.000, iters=3369
% 64.85/65.13
% 64.85/65.13 Low Water (keep): wt=18.000, iters=3335
% 64.85/65.13
% 64.85/65.13 Low Water (keep): wt=17.000, iters=3336
% 64.85/65.13
% 64.85/65.13 Low Water (displace): id=2416, wt=63.000
% 64.85/65.13
% 64.85/65.13 Low Water (displace): id=2415, wt=61.000
% 64.85/65.13
% 64.85/65.13 Low Water (displace): id=2009, wt=59.000
% 64.85/65.13
% 64.85/65.13 Low Water (displace): id=2008, wt=57.000
% 64.85/65.13
% 64.85/65.13 Low Water (displace): id=1652, wt=55.000
% 64.85/65.13
% 64.85/65.13 Low Water (displace): id=1651, wt=53.000
% 64.85/65.13
% 64.85/65.13 Low Water (displace): id=2449, wt=48.000
% 64.85/65.13
% 64.85/65.13 Low Water (displace): id=3345, wt=47.000
% 64.85/65.13
% 64.85/65.13 Low Water (displace): id=2038, wt=46.000
% 64.85/65.13
% 64.85/65.13 Low Water (displace): id=3344, wt=45.000
% 64.85/65.13
% 64.85/65.13 Low Water (displace): id=2454, wt=44.000
% 64.85/65.13
% 64.85/65.13 Low Water (displace): id=1243, wt=43.000
% 64.85/65.13
% 64.85/65.13 Low Water (displace): id=2447, wt=42.000
% 64.85/65.13
% 64.85/65.13 Low Water (displace): id=2439, wt=41.000
% 64.85/65.13
% 64.85/65.13 Low Water (displace): id=3385, wt=40.000
% 64.85/65.13
% 64.85/65.13 Low Water (displace): id=10628, wt=16.000
% 64.88/65.13
% 64.88/65.13 Low Water (displace): id=10629, wt=15.000
% 64.88/65.13
% 64.88/65.13 Low Water (displace): id=11096, wt=13.000
% 64.88/65.13
% 64.88/65.13 Low Water (displace): id=11724, wt=12.000
% 64.88/65.13
% 64.88/65.13 Low Water (displace): id=11759, wt=11.000
% 64.88/65.13
% 64.88/65.13 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 135 (0.00 of 1.07 sec).
% 64.88/65.13
% 64.88/65.13 Low Water (keep): wt=16.000, iters=3335
% 64.88/65.13
% 64.88/65.13 Low Water (keep): wt=15.000, iters=3390
% 64.88/65.13
% 64.88/65.13 Low Water (keep): wt=14.000, iters=3335
% 64.88/65.13
% 64.88/65.13 Low Water (keep): wt=13.000, iters=3333
% 64.88/65.13
% 64.88/65.13 Low Water (keep): wt=12.000, iters=3389
% 64.88/65.13
% 64.88/65.13 ============================== PROOF =================================
% 64.88/65.13 % SZS status Theorem
% 64.88/65.13 % SZS output start Refutation
% 64.88/65.13
% 64.88/65.13 % Proof 1 at 59.23 (+ 4.90) seconds.
% 64.88/65.13 % Length of proof is 285.
% 64.88/65.13 % Level of proof is 88.
% 64.88/65.13 % Maximum clause weight is 18.000.
% 64.88/65.13 % Given clauses 7185.
% 64.88/65.13
% 64.88/65.13 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].
% 64.88/65.13 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].
% 64.88/65.13 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].
% 64.88/65.13 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 64.88/65.13 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 64.88/65.13 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].
% 64.88/65.13 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].
% 64.88/65.13 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].
% 64.88/65.13 33 op_implies_and # label(rosser_op_implies_and) # label(axiom). [assumption].
% 64.88/65.13 34 op_equiv # label(rosser_op_equiv) # label(axiom). [assumption].
% 64.88/65.13 35 modus_ponens # label(rosser_modus_ponens) # label(axiom). [assumption].
% 64.88/65.13 36 kn1 # label(rosser_kn1) # label(axiom). [assumption].
% 64.88/65.13 37 kn2 # label(rosser_kn2) # label(axiom). [assumption].
% 64.88/65.13 38 kn3 # label(rosser_kn3) # label(axiom). [assumption].
% 64.88/65.13 39 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption].
% 64.88/65.13 40 -equivalence_3 # label(hilbert_equivalence_3) # label(negated_conjecture). [assumption].
% 64.88/65.13 51 -kn1 | is_a_theorem(implies(A,and(A,A))) # label(kn1) # label(axiom). [clausify(16)].
% 64.88/65.13 52 is_a_theorem(implies(A,and(A,A))). [copy(51),unit_del(a,36)].
% 64.88/65.13 54 -kn2 | is_a_theorem(implies(and(A,B),A)) # label(kn2) # label(axiom). [clausify(17)].
% 64.88/65.13 55 is_a_theorem(implies(and(A,B),A)). [copy(54),unit_del(a,37)].
% 64.88/65.13 61 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(2)].
% 64.88/65.13 62 -is_a_theorem(equiv(A,B)) | B = A. [copy(61),unit_del(a,39)].
% 64.88/65.13 67 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 64.88/65.13 68 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(67),unit_del(a,35)].
% 64.88/65.13 78 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 64.88/65.13 79 not(and(A,not(B))) = implies(A,B). [copy(78),unit_del(a,33)].
% 64.88/65.13 88 -op_equiv | and(implies(A,B),implies(B,A)) = equiv(A,B) # label(op_equiv) # label(axiom). [clausify(31)].
% 64.88/65.13 89 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(88),unit_del(a,34)].
% 64.88/65.13 92 equivalence_3 | -is_a_theorem(implies(implies(c31,c32),implies(implies(c32,c31),equiv(c31,c32)))) # label(equivalence_3) # label(axiom). [clausify(15)].
% 64.88/65.13 93 -is_a_theorem(implies(implies(c31,c32),implies(implies(c32,c31),equiv(c31,c32)))). [copy(92),unit_del(a,40)].
% 64.88/65.13 108 -kn3 | is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))) # label(kn3) # label(axiom). [clausify(18)].
% 64.88/65.13 109 is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))). [copy(108),unit_del(a,38)].
% 64.88/65.13 124 -is_a_theorem(A) | is_a_theorem(and(A,A)). [resolve(68,b,52,a)].
% 64.88/65.13 125 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(79(a,1),79(a,1,1,2))].
% 64.88/65.13 132 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(and(B,C)),not(and(C,A)))). [resolve(109,a,68,b)].
% 64.88/65.13 137 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(C,and(B,not(A))),not(equiv(B,A))))). [para(89(a,1),109(a,1,2,2,1)),rewrite([125(5)])].
% 64.88/65.13 172 implies(implies(A,B),and(B,not(A))) = not(equiv(A,B)). [para(89(a,1),125(a,1,1)),flip(a)].
% 64.88/65.13 225 is_a_theorem(implies(not(and(A,B)),not(and(B,and(A,C))))). [resolve(132,a,55,a)].
% 64.88/65.13 226 is_a_theorem(implies(not(and(and(A,A),B)),not(and(B,A)))). [resolve(132,a,52,a)].
% 64.88/65.13 263 -is_a_theorem(not(and(A,B))) | is_a_theorem(not(and(B,and(A,C)))). [resolve(225,a,68,b)].
% 64.88/65.13 282 -is_a_theorem(not(and(and(A,A),B))) | is_a_theorem(not(and(B,A))). [resolve(226,a,68,b)].
% 64.88/65.13 301 -is_a_theorem(implies(A,B)) | is_a_theorem(not(and(not(B),and(A,C)))). [para(79(a,1),263(a,1))].
% 64.88/65.13 386 -is_a_theorem(implies(and(A,A),B)) | is_a_theorem(not(and(not(B),A))). [para(79(a,1),282(a,1))].
% 64.88/65.13 420 is_a_theorem(not(and(not(and(A,A)),and(A,B)))). [resolve(301,a,52,a)].
% 64.88/65.13 550 is_a_theorem(not(and(implies(not(A),A),and(not(A),B)))). [para(79(a,1),420(a,1,1,1))].
% 64.88/65.13 578 is_a_theorem(not(and(not(A),A))). [resolve(386,a,55,a)].
% 64.88/65.13 582 is_a_theorem(and(not(and(not(A),A)),not(and(not(A),A)))). [resolve(578,a,124,a)].
% 64.88/65.13 605 is_a_theorem(not(and(implies(A,B),and(A,not(B))))). [para(79(a,1),578(a,1,1,1))].
% 64.88/65.13 606 is_a_theorem(implies(not(not(A)),A)). [para(79(a,1),578(a,1))].
% 64.88/65.13 721 is_a_theorem(implies(not(and(A,B)),implies(B,not(A)))). [resolve(606,a,132,a),rewrite([79(6)])].
% 64.88/65.13 723 -is_a_theorem(not(not(A))) | is_a_theorem(A). [resolve(606,a,68,b)].
% 64.88/65.13 999 -is_a_theorem(not(and(A,B))) | is_a_theorem(implies(B,not(A))). [resolve(721,a,68,b)].
% 64.88/65.13 1030 is_a_theorem(implies(implies(A,B),implies(not(B),not(A)))). [para(79(a,1),721(a,1,1))].
% 64.88/65.13 1569 is_a_theorem(implies(and(A,not(B)),not(implies(A,B)))). [resolve(999,a,605,a)].
% 64.88/65.13 1570 is_a_theorem(implies(A,not(not(A)))). [resolve(999,a,578,a)].
% 64.88/65.13 1571 is_a_theorem(implies(and(not(A),B),not(implies(not(A),A)))). [resolve(999,a,550,a)].
% 64.88/65.13 1574 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(B),not(A))). [para(79(a,1),999(a,1))].
% 64.88/65.13 1577 is_a_theorem(not(and(not(not(not(and(A,A)))),A))). [resolve(1570,a,386,a)].
% 64.88/65.13 1581 -is_a_theorem(A) | is_a_theorem(not(not(A))). [resolve(1570,a,68,b)].
% 64.88/65.13 1622 is_a_theorem(not(not(implies(A,not(not(A)))))). [resolve(1581,a,1570,a)].
% 64.88/65.13 1650 is_a_theorem(not(not(implies(A,and(A,A))))). [resolve(1581,a,52,a)].
% 64.88/65.13 4002 -is_a_theorem(and(A,not(B))) | is_a_theorem(not(implies(A,B))). [resolve(1569,a,68,b)].
% 64.88/65.13 4570 is_a_theorem(implies(not(A),not(and(A,B)))). [resolve(1574,a,55,a)].
% 64.88/65.13 4571 is_a_theorem(implies(not(and(A,A)),not(A))). [resolve(1574,a,52,a)].
% 64.88/65.13 4579 -is_a_theorem(not(A)) | is_a_theorem(not(and(A,B))). [resolve(4570,a,68,b)].
% 64.88/65.13 4646 is_a_theorem(implies(not(A),implies(A,B))). [para(79(a,1),4570(a,1,2))].
% 64.88/65.13 4653 is_a_theorem(implies(not(and(implies(A,B),C)),implies(C,A))). [resolve(4646,a,132,a),rewrite([79(6)])].
% 64.88/65.13 4655 -is_a_theorem(not(A)) | is_a_theorem(implies(A,B)). [resolve(4646,a,68,b)].
% 64.88/65.13 4975 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(and(A,not(B)),C)). [para(79(a,1),4655(a,1))].
% 64.88/65.13 5057 -is_a_theorem(not(and(A,A))) | is_a_theorem(not(A)). [resolve(4571,a,68,b)].
% 64.88/65.13 5132 is_a_theorem(not(and(not(implies(A,and(A,A))),B))). [resolve(4579,a,1650,a)].
% 64.88/65.13 5137 is_a_theorem(not(and(not(implies(A,not(not(A)))),B))). [resolve(4579,a,1622,a)].
% 64.88/65.13 5142 is_a_theorem(not(and(and(not(A),A),B))). [resolve(4579,a,578,a)].
% 64.88/65.13 5393 -is_a_theorem(implies(not(A),A)) | is_a_theorem(not(not(A))). [para(79(a,1),5057(a,1))].
% 64.88/65.13 5401 is_a_theorem(implies(A,not(and(not(B),B)))). [resolve(5142,a,999,a)].
% 64.88/65.13 7245 is_a_theorem(implies(A,not(not(not(not(and(A,A))))))). [resolve(1577,a,999,a)].
% 64.88/65.13 9532 -is_a_theorem(A) | is_a_theorem(not(not(not(not(and(A,A)))))). [resolve(7245,a,68,b)].
% 64.88/65.13 10694 -is_a_theorem(and(not(A),B)) | is_a_theorem(not(implies(not(A),A))). [resolve(1571,a,68,b)].
% 64.88/65.13 11448 -is_a_theorem(not(and(implies(A,B),C))) | is_a_theorem(implies(C,A)). [resolve(4653,a,68,b)].
% 64.88/65.13 11461 is_a_theorem(implies(implies(implies(A,B),C),implies(not(C),A))). [para(79(a,1),4653(a,1,1))].
% 64.88/65.13 11462 is_a_theorem(implies(not(equiv(A,B)),implies(implies(B,A),A))). [para(89(a,1),4653(a,1,1,1))].
% 64.88/65.13 13552 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(not(C),A)). [para(79(a,1),11448(a,1))].
% 64.88/65.13 14449 is_a_theorem(implies(not(implies(not(A),B)),implies(B,C))). [resolve(13552,a,11461,a)].
% 64.88/65.13 14458 is_a_theorem(implies(not(implies(not(A),not(B))),B)). [resolve(13552,a,1030,a)].
% 64.88/65.13 15007 is_a_theorem(not(not(implies(not(A),not(A))))). [resolve(14449,a,5393,a)].
% 64.88/65.13 15037 is_a_theorem(implies(not(A),not(A))). [resolve(15007,a,723,a)].
% 64.88/65.13 15072 is_a_theorem(implies(not(and(not(A),B)),implies(B,A))). [resolve(15037,a,132,a),rewrite([79(6)])].
% 64.88/65.13 16763 -is_a_theorem(not(and(not(A),B))) | is_a_theorem(implies(B,A)). [resolve(15072,a,68,b)].
% 64.88/65.13 16785 is_a_theorem(implies(not(equiv(A,B)),not(equiv(B,A)))). [para(172(a,1),15072(a,1,2)),rewrite([79(3),89(3)])].
% 64.88/65.13 18113 is_a_theorem(implies(A,implies(B,not(not(B))))). [resolve(16763,a,5137,a)].
% 64.88/65.13 18116 is_a_theorem(implies(A,implies(B,and(B,B)))). [resolve(16763,a,5132,a)].
% 64.88/65.13 18122 is_a_theorem(implies(A,not(not(and(A,A))))). [resolve(16763,a,1577,a)].
% 64.88/65.13 18125 is_a_theorem(implies(A,A)). [resolve(16763,a,578,a)].
% 64.88/65.13 18141 -is_a_theorem(implies(not(A),B)) | is_a_theorem(implies(not(B),A)). [para(79(a,1),16763(a,1))].
% 64.88/65.13 18226 is_a_theorem(not(not(not(not(equiv(A,A)))))). [resolve(18125,a,9532,a),rewrite([89(3)])].
% 64.88/65.13 18227 is_a_theorem(implies(and(A,not(A)),B)). [resolve(18125,a,4975,a)].
% 64.88/65.13 18233 is_a_theorem(implies(not(and(A,B)),not(and(B,A)))). [resolve(18125,a,132,a)].
% 64.88/65.13 19372 is_a_theorem(implies(not(A),implies(B,B))). [resolve(18227,a,1574,a),rewrite([79(4)])].
% 64.88/65.13 19795 is_a_theorem(implies(not(and(implies(A,A),B)),implies(B,C))). [resolve(19372,a,132,a),rewrite([79(6)])].
% 64.88/65.13 20229 -is_a_theorem(A) | is_a_theorem(not(not(and(A,A)))). [resolve(18122,a,68,b)].
% 64.88/65.13 20241 is_a_theorem(implies(not(A),not(implies(not(A),A)))). [para(79(a,1),18122(a,1,2,1))].
% 64.88/65.13 20643 is_a_theorem(not(and(not(not(not(equiv(A,A)))),B))). [resolve(18226,a,4579,a)].
% 64.88/65.13 23018 -is_a_theorem(not(A)) | is_a_theorem(not(implies(not(A),A))). [resolve(20241,a,68,b)].
% 64.88/65.13 24142 -is_a_theorem(not(equiv(A,B))) | is_a_theorem(not(equiv(B,A))). [resolve(16785,a,68,b)].
% 64.88/65.13 24339 is_a_theorem(implies(not(not(equiv(A,B))),equiv(B,A))). [resolve(18141,a,16785,a)].
% 64.88/65.13 24340 is_a_theorem(implies(not(implies(A,B)),and(not(B),A))). [resolve(18141,a,15072,a)].
% 64.88/65.13 24346 is_a_theorem(implies(not(implies(implies(A,B),B)),equiv(B,A))). [resolve(18141,a,11462,a)].
% 64.88/65.13 24351 is_a_theorem(implies(not(implies(A,B)),and(implies(B,C),A))). [resolve(18141,a,4653,a)].
% 64.88/65.13 24353 is_a_theorem(implies(not(not(A)),and(A,A))). [resolve(18141,a,4571,a)].
% 64.88/65.13 24383 is_a_theorem(implies(not(and(A,A)),not(not(not(A))))). [resolve(24353,a,1574,a)].
% 64.88/65.13 25233 is_a_theorem(implies(not(not(and(A,B))),and(B,A))). [resolve(18233,a,18141,a)].
% 64.88/65.13 25246 -is_a_theorem(not(and(A,B))) | is_a_theorem(not(and(B,A))). [resolve(18233,a,68,b)].
% 64.88/65.13 25248 is_a_theorem(implies(implies(A,B),not(and(not(B),A)))). [para(79(a,1),18233(a,1,1))].
% 64.88/65.13 28555 -is_a_theorem(not(implies(A,B))) | is_a_theorem(and(not(B),A)). [resolve(24340,a,68,b)].
% 64.88/65.13 29510 is_a_theorem(implies(not(not(not(not(A)))),and(A,A))). [resolve(24383,a,18141,a)].
% 64.88/65.13 29523 -is_a_theorem(not(and(A,A))) | is_a_theorem(not(not(not(A)))). [resolve(24383,a,68,b)].
% 64.88/65.13 30008 -is_a_theorem(not(not(and(A,B)))) | is_a_theorem(and(B,A)). [resolve(25233,a,68,b)].
% 64.88/65.13 30476 -is_a_theorem(implies(A,B)) | is_a_theorem(not(and(not(B),A))). [para(79(a,1),25246(a,1))].
% 64.88/65.13 30482 is_a_theorem(implies(not(not(and(not(A),B))),B)). [resolve(25248,a,13552,a)].
% 64.88/65.13 30504 is_a_theorem(implies(not(A),not(and(not(B),A)))). [resolve(30482,a,18141,a)].
% 64.88/65.13 30775 is_a_theorem(not(not(implies(not(A),not(and(not(B),A)))))). [resolve(30504,a,1581,a)].
% 64.88/65.13 30780 -is_a_theorem(not(A)) | is_a_theorem(not(and(not(B),A))). [resolve(30504,a,68,b)].
% 64.88/65.13 33119 is_a_theorem(implies(not(and(A,A)),not(not(not(not(not(A))))))). [resolve(29510,a,1574,a)].
% 64.88/65.13 33214 -is_a_theorem(implies(not(A),A)) | is_a_theorem(not(not(not(not(A))))). [para(79(a,1),29523(a,1))].
% 64.88/65.13 40073 is_a_theorem(implies(not(implies(A,B)),and(implies(C,C),A))). [resolve(19795,a,30476,a),rewrite([79(7)])].
% 64.88/65.13 41928 is_a_theorem(not(implies(not(and(not(A),A)),and(not(A),A)))). [resolve(582,a,10694,a)].
% 64.88/65.13 44438 -is_a_theorem(not(implies(implies(A,B),B))) | is_a_theorem(equiv(B,A)). [resolve(24346,a,68,b)].
% 64.88/65.13 44625 -is_a_theorem(not(implies(A,B))) | is_a_theorem(and(implies(B,C),A)). [resolve(24351,a,68,b)].
% 64.88/65.13 48413 is_a_theorem(not(not(implies(not(not(A)),implies(not(B),A))))). [para(79(a,1),30775(a,1,1,1,2))].
% 64.88/65.13 53270 -is_a_theorem(not(implies(A,B))) | is_a_theorem(and(implies(C,C),A)). [resolve(40073,a,68,b)].
% 64.88/65.13 55641 is_a_theorem(implies(not(A),implies(not(not(B)),implies(not(C),B)))). [resolve(48413,a,30780,a),rewrite([79(9)])].
% 64.88/65.13 76472 is_a_theorem(implies(not(not(not(not(not(not(A)))))),and(A,A))). [resolve(33119,a,30476,a),rewrite([79(10)])].
% 64.88/65.13 76491 -is_a_theorem(not(and(A,A))) | is_a_theorem(not(not(not(not(not(A)))))). [resolve(33119,a,68,b)].
% 64.88/65.13 80482 is_a_theorem(and(implies(A,A),not(and(not(B),B)))). [resolve(41928,a,53270,a)].
% 64.88/65.13 80569 is_a_theorem(not(implies(implies(A,A),and(not(B),B)))). [resolve(80482,a,4002,a)].
% 64.88/65.13 80655 is_a_theorem(and(implies(and(not(A),A),B),implies(C,C))). [resolve(80569,a,44625,a)].
% 64.88/65.13 80668 is_a_theorem(and(not(and(not(A),A)),implies(B,B))). [resolve(80569,a,28555,a)].
% 64.88/65.13 80830 is_a_theorem(and(implies(not(not(A)),A),implies(B,B))). [para(79(a,1),80668(a,1,1))].
% 64.88/65.13 80925 is_a_theorem(not(implies(implies(not(not(A)),A),and(B,not(B))))). [resolve(80830,a,1581,a),rewrite([125(6)])].
% 64.88/65.13 81135 is_a_theorem(not(implies(implies(and(not(A),A),B),and(C,not(C))))). [resolve(80655,a,1581,a),rewrite([125(6)])].
% 64.88/65.13 85210 is_a_theorem(not(not(not(not(implies(not(not(A)),implies(not(B),A))))))). [resolve(55641,a,33214,a)].
% 64.88/65.13 88403 -is_a_theorem(not(not(not(not(not(not(A))))))) | is_a_theorem(and(A,A)). [resolve(76472,a,68,b)].
% 64.88/65.13 88453 is_a_theorem(not(not(not(not(not(not(not(not(equiv(A,A)))))))))). [resolve(76491,a,20643,a)].
% 64.88/65.13 92714 is_a_theorem(equiv(and(A,not(A)),not(implies(A,A)))). [resolve(80925,a,44438,a),rewrite([79(5)])].
% 64.88/65.13 92788 not(implies(A,A)) = and(A,not(A)). [resolve(92714,a,62,a)].
% 64.88/65.13 92810 not(and(A,and(B,not(B)))) = implies(A,implies(B,B)). [para(92788(a,1),79(a,1,1,2))].
% 64.88/65.13 98062 is_a_theorem(and(not(not(equiv(A,A))),not(not(equiv(A,A))))). [resolve(88453,a,88403,a)].
% 64.88/65.13 103090 is_a_theorem(not(implies(not(not(equiv(A,A))),not(equiv(A,A))))). [resolve(98062,a,10694,a)].
% 64.88/65.13 105338 is_a_theorem(and(implies(A,A),not(not(equiv(B,B))))). [resolve(103090,a,53270,a)].
% 64.88/65.13 105410 is_a_theorem(not(implies(implies(A,A),not(equiv(B,B))))). [resolve(105338,a,4002,a)].
% 64.88/65.13 105552 is_a_theorem(and(implies(not(equiv(A,A)),B),implies(C,C))). [resolve(105410,a,44625,a)].
% 64.88/65.13 106421 is_a_theorem(not(implies(implies(not(equiv(A,A)),B),and(C,not(C))))). [resolve(105552,a,1581,a),rewrite([125(6)])].
% 64.88/65.13 119810 is_a_theorem(equiv(and(A,not(A)),and(not(B),B))). [resolve(81135,a,44438,a)].
% 64.88/65.13 119886 and(not(A),A) = and(B,not(B)). [resolve(119810,a,62,a)].
% 64.88/65.13 119893 and(not(A),A) = c_0. [new_symbol(119886)].
% 64.88/65.13 119896 and(A,not(A)) = c_0. [back_rewrite(119886),rewrite([119893(2)]),flip(a)].
% 64.88/65.13 121099 is_a_theorem(implies(A,not(c_0))). [back_rewrite(5401),rewrite([119893(2)])].
% 64.88/65.13 121115 is_a_theorem(not(and(c_0,A))). [back_rewrite(5142),rewrite([119893(2)])].
% 64.88/65.13 121326 is_a_theorem(and(not(c_0),not(c_0))). [back_rewrite(582),rewrite([119893(2),119893(4)])].
% 64.88/65.13 121327 is_a_theorem(not(c_0)). [back_rewrite(578),rewrite([119893(2)])].
% 64.88/65.13 121412 is_a_theorem(not(implies(implies(not(equiv(A,A)),B),c_0))). [back_rewrite(106421),rewrite([119896(5)])].
% 64.88/65.13 121476 implies(A,implies(B,B)) = not(and(A,c_0)). [back_rewrite(92810),rewrite([119896(2)]),flip(a)].
% 64.88/65.13 121479 not(implies(A,A)) = c_0. [back_rewrite(92788),rewrite([119896(4)])].
% 64.88/65.13 122566 is_a_theorem(not(implies(implies(A,not(c_0)),and(A,not(not(c_0)))))). [resolve(121099,a,20229,a),rewrite([125(8)])].
% 64.88/65.13 122575 is_a_theorem(implies(not(and(not(c_0),A)),not(and(A,B)))). [resolve(121099,a,132,a)].
% 64.88/65.13 122709 is_a_theorem(not(implies(not(and(c_0,A)),and(c_0,A)))). [resolve(121115,a,23018,a)].
% 64.88/65.13 122787 implies(not(not(A)),A) = not(c_0). [para(119893(a,1),79(a,1,1)),flip(a)].
% 64.88/65.13 122817 implies(A,A) = not(c_0). [para(119896(a,1),79(a,1,1)),flip(a)].
% 64.88/65.13 122825 not(equiv(A,A)) = implies(not(c_0),c_0). [para(119896(a,1),172(a,1,2)),rewrite([122817(1)]),flip(a)].
% 64.88/65.13 122889 not(not(c_0)) = c_0. [back_rewrite(121479),rewrite([122817(1)])].
% 64.88/65.13 122890 not(and(A,c_0)) = implies(A,not(c_0)). [back_rewrite(121476),rewrite([122817(1)]),flip(a)].
% 64.88/65.13 123121 -is_a_theorem(not(implies(A,B))) | is_a_theorem(and(not(c_0),A)). [back_rewrite(53270),rewrite([122817(4)])].
% 64.88/65.13 123317 is_a_theorem(not(implies(implies(A,not(c_0)),and(A,c_0)))). [back_rewrite(122566),rewrite([122889(6)])].
% 64.88/65.13 124029 and(not(c_0),not(c_0)) = equiv(A,A). [para(122817(a,1),89(a,1,1)),rewrite([122817(3)])].
% 64.88/65.13 129486 not(equiv(A,A)) = not(equiv(B,B)). [para(122825(a,2),122825(a,2))].
% 64.88/65.13 130966 equiv(A,A) = equiv(B,B). [para(124029(a,1),124029(a,1))].
% 64.88/65.13 132417 and(equiv(A,A),not(equiv(B,B))) = c_0. [para(129486(a,1),119896(a,1,2))].
% 64.88/65.13 135930 is_a_theorem(equiv(c_0,not(equiv(A,A)))). [resolve(121412,a,44438,a)].
% 64.88/65.13 136003 not(equiv(A,A)) = c_0. [resolve(135930,a,62,a)].
% 64.88/65.13 136006 and(equiv(A,A),c_0) = c_0. [back_rewrite(132417),rewrite([136003(3)])].
% 64.88/65.13 136026 implies(A,equiv(B,B)) = implies(A,not(c_0)). [para(136003(a,1),79(a,1,1,2)),rewrite([122890(3)]),flip(a)].
% 64.88/65.13 136028 is_a_theorem(implies(implies(not(c_0),A),implies(implies(A,c_0),c_0))). [para(136003(a,1),137(a,1,2,2)),rewrite([122817(1),119896(5)])].
% 64.88/65.13 136100 implies(equiv(A,A),not(c_0)) = not(c_0). [para(136006(a,1),122890(a,1,1)),flip(a)].
% 64.88/65.13 136152 equiv(equiv(A,A),not(c_0)) = and(not(c_0),not(c_0)). [para(136100(a,1),89(a,1,1)),rewrite([136026(6),122817(7)]),flip(a)].
% 64.88/65.13 137859 is_a_theorem(and(not(c_0),not(and(c_0,A)))). [resolve(123121,a,122709,a)].
% 64.88/65.13 137892 is_a_theorem(not(implies(not(c_0),and(c_0,A)))). [resolve(137859,a,4002,a)].
% 64.88/65.13 138020 is_a_theorem(and(implies(and(c_0,A),B),not(c_0))). [resolve(137892,a,44625,a)].
% 64.88/65.13 138439 is_a_theorem(not(implies(implies(and(c_0,A),B),c_0))). [resolve(138020,a,4002,a)].
% 64.88/65.13 138759 is_a_theorem(equiv(c_0,and(c_0,A))). [resolve(138439,a,44438,a)].
% 64.88/65.13 138811 and(c_0,A) = c_0. [resolve(138759,a,62,a)].
% 64.88/65.13 138831 implies(c_0,A) = not(c_0). [para(138811(a,1),79(a,1,1)),flip(a)].
% 64.88/65.13 138837 implies(implies(A,c_0),c_0) = not(equiv(A,c_0)). [para(138811(a,1),172(a,1,2))].
% 64.88/65.13 138879 is_a_theorem(implies(implies(not(c_0),A),not(equiv(A,c_0)))). [back_rewrite(136028),rewrite([138837(7)])].
% 64.88/65.13 138887 implies(not(c_0),and(A,not(c_0))) = not(equiv(c_0,A)). [para(138831(a,1),172(a,1,1))].
% 64.88/65.13 138890 -is_a_theorem(not(implies(not(c_0),A))) | is_a_theorem(equiv(A,c_0)). [para(138831(a,1),44438(a,1,1,1))].
% 64.88/65.13 138988 is_a_theorem(and(not(c_0),implies(A,not(c_0)))). [resolve(123317,a,123121,a)].
% 64.88/65.13 139078 is_a_theorem(not(implies(not(c_0),and(A,c_0)))). [resolve(138988,a,1581,a),rewrite([125(7),122889(5)])].
% 64.88/65.13 139112 is_a_theorem(and(implies(and(A,c_0),B),not(c_0))). [resolve(139078,a,44625,a)].
% 64.88/65.13 139616 is_a_theorem(not(implies(implies(and(A,c_0),B),c_0))). [resolve(139112,a,4002,a)].
% 64.88/65.13 139887 is_a_theorem(equiv(c_0,and(A,c_0))). [resolve(139616,a,44438,a)].
% 64.88/65.13 139939 and(A,c_0) = c_0. [resolve(139887,a,62,a)].
% 64.88/65.13 139957 implies(A,not(c_0)) = not(c_0). [back_rewrite(122890),rewrite([139939(2)]),flip(a)].
% 64.88/65.13 139961 and(not(c_0),implies(not(c_0),A)) = equiv(A,not(c_0)). [para(139957(a,1),89(a,1,1))].
% 64.88/65.13 139962 and(implies(not(c_0),A),not(c_0)) = equiv(not(c_0),A). [para(139957(a,1),89(a,1,2))].
% 64.88/65.13 139970 implies(not(c_0),and(not(c_0),not(A))) = not(equiv(A,not(c_0))). [para(139957(a,1),172(a,1,1))].
% 64.88/65.13 140532 -is_a_theorem(implies(not(c_0),A)) | is_a_theorem(not(equiv(A,c_0))). [resolve(138879,a,68,b)].
% 64.88/65.13 141040 is_a_theorem(not(equiv(implies(A,and(A,A)),c_0))). [resolve(140532,a,18116,a)].
% 64.88/65.13 141043 is_a_theorem(not(equiv(implies(A,not(not(A))),c_0))). [resolve(140532,a,18113,a)].
% 64.88/65.13 141104 is_a_theorem(not(equiv(c_0,implies(A,and(A,A))))). [resolve(141040,a,24142,a)].
% 64.88/65.13 141267 is_a_theorem(not(equiv(c_0,implies(A,not(not(A)))))). [resolve(141043,a,24142,a)].
% 64.88/65.13 144034 is_a_theorem(implies(not(not(and(A,B))),and(not(c_0),A))). [resolve(122575,a,30476,a),rewrite([79(9)])].
% 64.88/65.13 149722 is_a_theorem(not(not(implies(not(not(and(A,B))),and(not(c_0),A))))). [resolve(144034,a,1581,a)].
% 64.88/65.13 149727 -is_a_theorem(not(not(and(A,B)))) | is_a_theorem(and(not(c_0),A)). [resolve(144034,a,68,b)].
% 64.88/65.13 157580 equiv(A,A) = not(c_0). [para(136152(a,1),62(a,1)),flip(b),unit_del(a,121326)].
% 64.88/65.13 157582 and(not(c_0),not(c_0)) = not(c_0). [para(130966(a,1),136152(a,1,1)),rewrite([157580(1),157580(5)]),flip(a)].
% 64.88/65.13 158407 -is_a_theorem(not(equiv(c_0,A))) | is_a_theorem(and(A,not(c_0))). [para(138887(a,1),68(b,1)),unit_del(a,121327)].
% 64.88/65.13 158468 is_a_theorem(and(implies(A,not(not(A))),not(c_0))). [resolve(158407,a,141267,a)].
% 64.88/65.13 158470 is_a_theorem(and(implies(A,and(A,A)),not(c_0))). [resolve(158407,a,141104,a)].
% 64.88/65.13 158670 is_a_theorem(not(implies(implies(A,not(not(A))),c_0))). [resolve(158468,a,4002,a)].
% 64.88/65.13 158736 is_a_theorem(not(implies(implies(A,and(A,A)),c_0))). [resolve(158470,a,4002,a)].
% 64.88/65.13 158742 is_a_theorem(and(not(c_0),implies(A,not(not(A))))). [resolve(158670,a,123121,a)].
% 64.88/65.13 158831 is_a_theorem(and(not(c_0),implies(A,and(A,A)))). [resolve(158736,a,123121,a)].
% 64.88/65.13 158904 is_a_theorem(not(implies(not(c_0),and(A,not(not(not(A))))))). [resolve(158742,a,1581,a),rewrite([125(7)])].
% 64.88/65.13 160108 is_a_theorem(equiv(and(A,not(not(not(A)))),c_0)). [resolve(158904,a,138890,a)].
% 64.88/65.13 160137 and(A,not(not(not(A)))) = c_0. [resolve(160108,a,62,a),flip(a)].
% 64.88/65.13 160144 implies(A,not(not(A))) = not(c_0). [para(160137(a,1),79(a,1,1)),flip(a)].
% 64.88/65.13 160159 equiv(A,not(not(A))) = not(c_0). [para(160144(a,1),89(a,1,1)),rewrite([122787(5),157582(5)]),flip(a)].
% 64.88/65.13 160169 not(not(A)) = A. [para(160159(a,1),62(a,1)),unit_del(a,121327)].
% 64.88/65.13 160229 -is_a_theorem(and(A,B)) | is_a_theorem(and(not(c_0),A)). [back_rewrite(149727),rewrite([160169(3)])].
% 64.88/65.13 160230 is_a_theorem(implies(and(A,B),and(not(c_0),A))). [back_rewrite(149722),rewrite([160169(3),160169(7)])].
% 64.88/65.13 160364 is_a_theorem(implies(A,implies(not(B),A))). [back_rewrite(85210),rewrite([160169(2),160169(5),160169(5)])].
% 64.88/65.13 160405 -is_a_theorem(and(A,B)) | is_a_theorem(and(B,A)). [back_rewrite(30008),rewrite([160169(3)])].
% 64.88/65.13 160412 is_a_theorem(implies(and(A,B),and(B,A))). [back_rewrite(25233),rewrite([160169(3)])].
% 64.88/65.13 160413 is_a_theorem(implies(equiv(A,B),equiv(B,A))). [back_rewrite(24339),rewrite([160169(3)])].
% 64.88/65.13 160764 not(and(A,B)) = implies(A,not(B)). [para(160169(a,1),79(a,1,1,2))].
% 64.88/65.13 160765 not(implies(A,B)) = and(A,not(B)). [para(79(a,1),160169(a,1,1))].
% 64.88/65.13 160801 is_a_theorem(implies(and(A,B),B)). [para(160169(a,1),14458(a,1,1,1,1)),rewrite([160765(3),160169(2)])].
% 64.88/65.13 161877 -is_a_theorem(and(not(c_0),not(A))) | is_a_theorem(equiv(A,c_0)). [back_rewrite(138890),rewrite([160765(4)])].
% 64.88/65.13 164686 is_a_theorem(implies(A,implies(B,A))). [para(160169(a,1),160364(a,1,2,1))].
% 64.88/65.13 164785 -is_a_theorem(A) | is_a_theorem(implies(B,A)). [resolve(164686,a,68,b)].
% 64.88/65.13 165134 is_a_theorem(implies(A,implies(and(B,C),C))). [resolve(164785,a,160801,a)].
% 64.88/65.13 166045 is_a_theorem(not(equiv(implies(and(A,B),B),c_0))). [resolve(165134,a,140532,a)].
% 64.88/65.13 168360 is_a_theorem(not(equiv(c_0,implies(and(A,B),B)))). [resolve(166045,a,24142,a)].
% 64.88/65.13 168721 is_a_theorem(and(implies(and(A,B),B),not(c_0))). [resolve(168360,a,158407,a)].
% 64.88/65.13 169083 is_a_theorem(and(not(c_0),implies(and(A,B),B))). [resolve(168721,a,160405,a)].
% 64.88/65.13 169551 -is_a_theorem(and(not(c_0),A)) | is_a_theorem(equiv(not(A),c_0)). [para(160169(a,1),161877(a,1,2))].
% 64.88/65.13 170007 is_a_theorem(equiv(and(and(A,B),not(B)),c_0)). [resolve(169551,a,169083,a),rewrite([160765(3)])].
% 64.88/65.13 170036 and(and(A,B),not(B)) = c_0. [resolve(170007,a,62,a),flip(a)].
% 64.88/65.13 170169 implies(and(A,B),B) = not(c_0). [para(170036(a,1),160764(a,1,1)),rewrite([160169(5)]),flip(a)].
% 64.88/65.13 170195 and(not(c_0),implies(A,and(B,A))) = equiv(and(B,A),A). [para(170169(a,1),89(a,1,1))].
% 64.88/65.13 170208 is_a_theorem(equiv(and(A,A),A)). [back_rewrite(158831),rewrite([170195(5)])].
% 64.88/65.13 170254 and(A,A) = A. [resolve(170208,a,62,a),flip(a)].
% 64.88/65.13 170304 -is_a_theorem(A) | is_a_theorem(and(not(c_0),A)). [para(170254(a,1),160229(a,1))].
% 64.88/65.13 170305 is_a_theorem(implies(A,and(not(c_0),A))). [para(170254(a,1),160230(a,1,1))].
% 64.88/65.13 170540 is_a_theorem(equiv(and(not(c_0),A),A)). [resolve(170305,a,170304,a),rewrite([170195(7)])].
% 64.88/65.13 170669 and(not(c_0),A) = A. [resolve(170540,a,62,a),flip(a)].
% 64.88/65.13 170825 not(equiv(A,not(c_0))) = implies(not(c_0),not(A)). [back_rewrite(139970),rewrite([170669(6)]),flip(a)].
% 64.88/65.13 170826 equiv(A,not(c_0)) = implies(not(c_0),A). [back_rewrite(139961),rewrite([170669(6)]),flip(a)].
% 64.88/65.13 170830 implies(not(c_0),not(A)) = not(A). [back_rewrite(170825),rewrite([170826(3),160765(4),170669(4)]),flip(a)].
% 64.88/65.13 171046 is_a_theorem(implies(implies(not(c_0),A),implies(implies(A,not(B)),not(equiv(not(c_0),B))))). [para(170669(a,1),137(a,1,2,1,2)),rewrite([139957(3)])].
% 64.88/65.13 171088 is_a_theorem(implies(A,and(A,not(c_0)))). [para(170669(a,1),160412(a,1,1))].
% 64.88/65.13 172572 is_a_theorem(implies(implies(A,c_0),not(A))). [resolve(171088,a,1574,a),rewrite([160764(4),160169(3)])].
% 64.88/65.13 173501 implies(not(c_0),A) = A. [para(160169(a,1),170830(a,1,2)),rewrite([160169(5)])].
% 64.88/65.13 173504 is_a_theorem(implies(A,implies(implies(A,not(B)),not(equiv(not(c_0),B))))). [back_rewrite(171046),rewrite([173501(3)])].
% 64.88/65.13 173505 equiv(A,not(c_0)) = A. [back_rewrite(170826),rewrite([173501(6)])].
% 64.88/65.13 173530 equiv(not(c_0),A) = and(A,not(c_0)). [back_rewrite(139962),rewrite([173501(3)]),flip(a)].
% 64.88/65.13 173532 is_a_theorem(implies(A,implies(implies(A,not(B)),implies(B,c_0)))). [back_rewrite(173504),rewrite([173530(5),160764(6),160169(5)])].
% 64.88/65.13 173577 -is_a_theorem(A) | not(c_0) = A. [para(173505(a,1),62(a,1))].
% 64.88/65.13 173578 implies(implies(A,c_0),not(A)) = not(c_0). [resolve(173577,a,172572,a),flip(a)].
% 64.88/65.13 173615 implies(equiv(A,B),equiv(B,A)) = not(c_0). [resolve(173577,a,160413,a),flip(a)].
% 64.88/65.13 173616 implies(and(A,B),and(B,A)) = not(c_0). [resolve(173577,a,160412,a),flip(a)].
% 64.88/65.13 173656 implies(not(A),implies(A,B)) = not(c_0). [resolve(173577,a,4646,a),flip(a)].
% 64.88/65.13 175493 equiv(implies(A,c_0),not(A)) = not(c_0). [para(173578(a,1),89(a,1,1)),rewrite([173656(6),170254(5)]),flip(a)].
% 64.88/65.13 175741 implies(A,c_0) = not(A). [para(175493(a,1),62(a,1)),flip(b),unit_del(a,121327)].
% 64.88/65.13 175761 is_a_theorem(implies(A,implies(implies(A,not(B)),not(B)))). [back_rewrite(173532),rewrite([175741(4)])].
% 64.88/65.13 176191 equiv(equiv(A,B),equiv(B,A)) = not(c_0). [para(173615(a,1),89(a,1,1)),rewrite([173615(5),170254(5)]),flip(a)].
% 64.88/65.13 176234 equiv(and(A,B),and(B,A)) = not(c_0). [para(173616(a,1),89(a,1,1)),rewrite([173616(5),170254(5)]),flip(a)].
% 64.88/65.13 176284 is_a_theorem(implies(and(implies(A,not(B)),B),not(A))). [resolve(175761,a,1574,a),rewrite([160765(5),160169(4)])].
% 64.88/65.13 176419 equiv(A,B) = equiv(B,A). [para(176191(a,1),62(a,1)),unit_del(a,121327)].
% 64.88/65.13 176501 and(A,B) = and(B,A). [para(176234(a,1),62(a,1)),unit_del(a,121327)].
% 64.88/65.13 176567 is_a_theorem(implies(and(A,implies(B,not(A))),not(B))). [back_rewrite(176284),rewrite([176501(3)])].
% 64.88/65.13 176845 implies(A,not(B)) = implies(B,not(A)). [para(176501(a,1),160764(a,1,1)),rewrite([160764(2)])].
% 64.88/65.13 176862 is_a_theorem(implies(A,implies(B,and(B,A)))). [back_rewrite(176567),rewrite([176845(2),176845(5),160764(4),160765(3),160169(2)])].
% 64.88/65.14 177041 is_a_theorem(implies(implies(A,B),implies(implies(B,A),equiv(A,B)))). [para(89(a,1),176862(a,1,2,2)),rewrite([176419(3)])].
% 64.88/65.14 177042 $F. [resolve(177041,a,93,a)].
% 64.88/65.14
% 64.88/65.14 % SZS output end Refutation
% 64.88/65.14 ============================== end of proof ==========================
% 64.88/65.14
% 64.88/65.14 ============================== STATISTICS ============================
% 64.88/65.14
% 64.88/65.14 Given=7185. Generated=9687077. Kept=176991. proofs=1.
% 64.88/65.14 Usable=203. Sos=791. Demods=151. Limbo=2, Disabled=176066. Hints=0.
% 64.88/65.14 Megabytes=120.16.
% 64.88/65.14 User_CPU=59.23, System_CPU=4.90, Wall_clock=64.
% 64.88/65.14
% 64.88/65.14 ============================== end of statistics =====================
% 64.88/65.14
% 64.88/65.14 ============================== end of search =========================
% 64.88/65.14
% 64.88/65.14 THEOREM PROVED
% 64.88/65.14 % SZS status Theorem
% 64.88/65.14
% 64.88/65.14 Exiting with 1 proof.
% 64.88/65.14
% 64.88/65.14 Process 20218 exit (max_proofs) Mon Jul 4 11:25:28 2022
% 64.88/65.14 Prover9 interrupted
%------------------------------------------------------------------------------