TSTP Solution File: LCL472+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL472+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n024.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 13:47:04 EDT 2022
% Result : Theorem 121.26s 121.59s
% Output : Refutation 121.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL472+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n024.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 : Sun Jul 3 22:46:14 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.43/1.00 ============================== Prover9 ===============================
% 0.43/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.00 Process 17527 was started by sandbox on n024.cluster.edu,
% 0.43/1.00 Sun Jul 3 22:46:15 2022
% 0.43/1.00 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_17374_n024.cluster.edu".
% 0.43/1.00 ============================== end of head ===========================
% 0.43/1.00
% 0.43/1.00 ============================== INPUT =================================
% 0.43/1.00
% 0.43/1.00 % Reading from file /tmp/Prover9_17374_n024.cluster.edu
% 0.43/1.00
% 0.43/1.00 set(prolog_style_variables).
% 0.43/1.00 set(auto2).
% 0.43/1.00 % set(auto2) -> set(auto).
% 0.43/1.00 % set(auto) -> set(auto_inference).
% 0.43/1.00 % set(auto) -> set(auto_setup).
% 0.43/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.00 % set(auto) -> set(auto_limits).
% 0.43/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.00 % set(auto) -> set(auto_denials).
% 0.43/1.00 % set(auto) -> set(auto_process).
% 0.43/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.00 % set(auto2) -> assign(stats, some).
% 0.43/1.00 % set(auto2) -> clear(echo_input).
% 0.43/1.00 % set(auto2) -> set(quiet).
% 0.43/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.00 % set(auto2) -> clear(print_given).
% 0.43/1.00 assign(lrs_ticks,-1).
% 0.43/1.00 assign(sos_limit,10000).
% 0.43/1.00 assign(order,kbo).
% 0.43/1.00 set(lex_order_vars).
% 0.43/1.00 clear(print_given).
% 0.43/1.00
% 0.43/1.00 % formulas(sos). % not echoed (43 formulas)
% 0.43/1.00
% 0.43/1.00 ============================== end of input ==========================
% 0.43/1.00
% 0.43/1.00 % From the command line: assign(max_seconds, 300).
% 0.43/1.00
% 0.43/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.00
% 0.43/1.00 % Formulas that are not ordinary clauses:
% 0.43/1.00 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].
% 0.43/1.00 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].
% 0.43/1.00 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].
% 0.43/1.00 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 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].
% 0.43/1.00 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].
% 0.43/1.00 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 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].
% 0.43/1.00 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 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].
% 0.43/1.00 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].
% 0.43/1.00 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].
% 1.28/1.55 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].
% 1.28/1.55 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.55 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.55 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].
% 1.28/1.55 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].
% 1.28/1.55 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.55 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.55 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.55 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.55 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.55 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].
% 1.28/1.55 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].
% 1.28/1.55 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].
% 1.28/1.55 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].
% 1.28/1.55 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].
% 1.28/1.55 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].
% 1.28/1.55 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].
% 1.28/1.55
% 1.28/1.55 ============================== end of process non-clausal formulas ===
% 1.28/1.55
% 1.28/1.55 ============================== PROCESS INITIAL CLAUSES ===============
% 1.28/1.55
% 1.28/1.55 ============================== PREDICATE ELIMINATION =================
% 1.28/1.55
% 1.28/1.55 ============================== end predicate elimination =============
% 1.28/1.55
% 1.28/1.55 Auto_denials: (non-Horn, no changes).
% 1.28/1.55
% 1.28/1.55 Term ordering decisions:
% 1.28/1.55
% 1.28/1.55 % Assigning unary symbol not kb_weight 0 and highest precedence (94).
% 1.28/1.55 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.
% 1.28/1.55
% 1.28/1.55 ============================== end of process initial clauses ========
% 1.28/1.55
% 1.28/1.55 ============================== CLAUSES FOR SEARCH ====================
% 1.28/1.55
% 1.28/1.55 ============================== end of clauses for search =============
% 1.28/1.55
% 1.28/1.55 ============================== SEARCH ================================
% 1.28/1.55
% 1.28/1.55 % Starting search at 0.02 seconds.
% 1.28/1.55
% 1.28/1.55 Low Water (keep): wt=43.000, iters=3363
% 1.28/1.55
% 1.28/1.55 Low Water (keep): wt=40.000, iters=3461
% 1.28/1.55
% 1.28/1.55 Low Water (keep): wt=36.000, iters=3339
% 1.28/1.55
% 1.28/1.55 Low Water (keep): wt=33.000, iters=3370
% 1.28/1.55
% 1.28/1.55 Low Water (keep): wt=32.000, iters=3369
% 1.28/1.55
% 1.28/1.55 Low Water (keep): wt=30.000, iters=3333
% 1.28/1.55
% 1.28/1.55 Low Water (keep): wt=27.000, iters=3407
% 1.28/1.55
% 1.28/1.55 Low Water (keep): wt=25.000, iters=3391
% 1.28/1.55
% 1.28/1.55 Low Water (keep): wt=24.000, iters=3454
% 1.28/1.55
% 1.28/1.55 Low Water (keep): wt=23.000, iters=3340
% 1.28/1.55
% 121.26/121.59 Low Water (keep): wt=22.000, iters=3363
% 121.26/121.59
% 121.26/121.59 Low Water (keep): wt=21.000, iters=3344
% 121.26/121.59
% 121.26/121.59 Low Water (keep): wt=20.000, iters=3337
% 121.26/121.59
% 121.26/121.59 Low Water (keep): wt=19.000, iters=3367
% 121.26/121.59
% 121.26/121.59 Low Water (keep): wt=18.000, iters=3362
% 121.26/121.59
% 121.26/121.59 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 90 (0.00 of 1.30 sec).
% 121.26/121.59
% 121.26/121.59 Low Water (displace): id=3600, wt=127.000
% 121.26/121.59
% 121.26/121.59 Low Water (displace): id=2049, wt=111.000
% 121.26/121.59
% 121.26/121.59 Low Water (displace): id=2462, wt=103.000
% 121.26/121.59
% 121.26/121.59 Low Water (displace): id=1682, wt=91.000
% 121.26/121.59
% 121.26/121.59 Low Water (displace): id=3159, wt=83.000
% 121.26/121.59
% 121.26/121.59 Low Water (displace): id=1537, wt=71.000
% 121.26/121.59
% 121.26/121.59 Low Water (displace): id=1536, wt=63.000
% 121.26/121.59
% 121.26/121.59 Low Water (displace): id=10017, wt=45.000
% 121.26/121.59
% 121.26/121.59 Low Water (displace): id=9673, wt=43.000
% 121.26/121.59
% 121.26/121.59 Low Water (displace): id=9672, wt=42.000
% 121.26/121.59
% 121.26/121.59 Low Water (displace): id=10021, wt=41.000
% 121.26/121.59
% 121.26/121.59 Low Water (displace): id=7669, wt=39.000
% 121.26/121.59
% 121.26/121.59 Low Water (displace): id=7667, wt=38.000
% 121.26/121.59
% 121.26/121.59 Low Water (displace): id=10025, wt=37.000
% 121.26/121.59
% 121.26/121.59 Low Water (displace): id=10739, wt=35.000
% 121.26/121.59
% 121.26/121.59 Low Water (displace): id=9667, wt=34.000
% 121.26/121.59
% 121.26/121.59 Low Water (displace): id=10812, wt=17.000
% 121.26/121.59
% 121.26/121.59 Low Water (displace): id=11528, wt=16.000
% 121.26/121.59
% 121.26/121.59 Low Water (displace): id=11535, wt=15.000
% 121.26/121.59
% 121.26/121.59 Low Water (keep): wt=17.000, iters=3335
% 121.26/121.59
% 121.26/121.59 Low Water (displace): id=12939, wt=14.000
% 121.26/121.59
% 121.26/121.59 Low Water (displace): id=12966, wt=13.000
% 121.26/121.59
% 121.26/121.59 Low Water (keep): wt=16.000, iters=3333
% 121.26/121.59
% 121.26/121.59 Low Water (keep): wt=15.000, iters=4003
% 121.26/121.59
% 121.26/121.59 Low Water (keep): wt=14.000, iters=3362
% 121.26/121.59
% 121.26/121.59 Low Water (keep): wt=13.000, iters=3333
% 121.26/121.59
% 121.26/121.59 Low Water (displace): id=130243, wt=12.000
% 121.26/121.59
% 121.26/121.59 Low Water (displace): id=132879, wt=11.000
% 121.26/121.59
% 121.26/121.59 ============================== PROOF =================================
% 121.26/121.59 % SZS status Theorem
% 121.26/121.59 % SZS output start Refutation
% 121.26/121.59
% 121.26/121.59 % Proof 1 at 113.30 (+ 7.26) seconds.
% 121.26/121.59 % Length of proof is 340.
% 121.26/121.59 % Level of proof is 100.
% 121.26/121.59 % Maximum clause weight is 19.000.
% 121.26/121.59 % Given clauses 8920.
% 121.26/121.59
% 121.26/121.59 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].
% 121.26/121.59 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].
% 121.26/121.59 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].
% 121.26/121.59 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].
% 121.26/121.59 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 121.26/121.59 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 121.26/121.59 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].
% 121.26/121.59 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].
% 121.26/121.59 34 op_equiv # label(luka_op_equiv) # label(axiom). [assumption].
% 121.26/121.59 35 modus_ponens # label(luka_modus_ponens) # label(axiom). [assumption].
% 121.26/121.59 36 cn1 # label(luka_cn1) # label(axiom). [assumption].
% 121.26/121.59 37 cn2 # label(luka_cn2) # label(axiom). [assumption].
% 121.26/121.59 38 cn3 # label(luka_cn3) # label(axiom). [assumption].
% 121.26/121.59 39 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption].
% 121.26/121.59 40 op_implies_and # label(hilbert_op_implies_and) # label(axiom). [assumption].
% 121.26/121.59 41 -equivalence_1 # label(hilbert_equivalence_1) # label(negated_conjecture). [assumption].
% 121.26/121.59 60 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(2)].
% 121.26/121.59 61 -is_a_theorem(equiv(A,B)) | B = A. [copy(60),unit_del(a,39)].
% 121.26/121.59 62 -cn2 | is_a_theorem(implies(A,implies(not(A),B))) # label(cn2) # label(axiom). [clausify(20)].
% 121.26/121.59 63 is_a_theorem(implies(A,implies(not(A),B))). [copy(62),unit_del(a,37)].
% 121.26/121.59 65 -cn3 | is_a_theorem(implies(implies(not(A),A),A)) # label(cn3) # label(axiom). [clausify(21)].
% 121.26/121.59 66 is_a_theorem(implies(implies(not(A),A),A)). [copy(65),unit_del(a,38)].
% 121.26/121.59 68 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 121.26/121.59 69 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(68),unit_del(a,35)].
% 121.26/121.59 72 equivalence_1 | -is_a_theorem(implies(equiv(c27,c28),implies(c27,c28))) # label(equivalence_1) # label(axiom). [clausify(13)].
% 121.26/121.59 73 -is_a_theorem(implies(equiv(c27,c28),implies(c27,c28))). [copy(72),unit_del(a,41)].
% 121.26/121.59 79 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 121.26/121.59 80 not(and(A,not(B))) = implies(A,B). [copy(79),unit_del(a,40)].
% 121.26/121.59 89 -op_equiv | and(implies(A,B),implies(B,A)) = equiv(A,B) # label(op_equiv) # label(axiom). [clausify(31)].
% 121.26/121.59 90 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(89),unit_del(a,34)].
% 121.26/121.59 95 -cn1 | is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))) # label(cn1) # label(axiom). [clausify(19)].
% 121.26/121.59 96 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))). [copy(95),unit_del(a,36)].
% 121.26/121.59 122 -is_a_theorem(implies(not(A),A)) | is_a_theorem(A). [resolve(69,b,66,a)].
% 121.26/121.59 123 -is_a_theorem(A) | is_a_theorem(implies(not(A),B)). [resolve(69,b,63,a)].
% 121.26/121.59 127 is_a_theorem(implies(and(A,not(B)),implies(implies(A,B),C))). [para(80(a,1),63(a,1,2,1))].
% 121.26/121.59 128 is_a_theorem(implies(implies(implies(A,B),and(A,not(B))),and(A,not(B)))). [para(80(a,1),66(a,1,1,1))].
% 121.26/121.59 129 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(80(a,1),80(a,1,1,2))].
% 121.26/121.59 130 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(B,C),implies(A,C))). [resolve(96,a,69,b)].
% 121.26/121.59 132 -is_a_theorem(implies(implies(A,B),and(A,not(B)))) | is_a_theorem(and(A,not(B))). [para(80(a,1),122(a,1,1))].
% 121.26/121.59 226 is_a_theorem(implies(implies(implies(implies(A,B),C),D),implies(and(A,not(B)),D))). [resolve(130,a,127,a)].
% 121.26/121.59 227 is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))). [resolve(130,a,96,a)].
% 121.26/121.59 228 is_a_theorem(implies(implies(A,B),implies(implies(not(A),A),B))). [resolve(130,a,66,a)].
% 121.26/121.59 229 is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C))). [resolve(130,a,63,a)].
% 121.26/121.59 230 is_a_theorem(implies(implies(implies(implies(not(A),A),B),C),implies(implies(A,B),C))). [resolve(228,a,130,a)].
% 121.26/121.59 232 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(A),A),B)). [resolve(228,a,69,b)].
% 121.26/121.59 242 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(not(A),D),B),C))). [resolve(229,a,130,a)].
% 121.26/121.59 244 -is_a_theorem(implies(implies(not(A),B),C)) | is_a_theorem(implies(A,C)). [resolve(229,a,69,b)].
% 121.26/121.59 257 implies(implies(A,B),and(B,not(A))) = not(equiv(A,B)). [para(90(a,1),129(a,1,1)),flip(a)].
% 121.26/121.59 347 is_a_theorem(implies(A,implies(implies(B,C),implies(not(A),C)))). [resolve(244,a,96,a)].
% 121.26/121.59 348 is_a_theorem(implies(A,A)). [resolve(244,a,66,a)].
% 121.26/121.59 350 -is_a_theorem(implies(implies(implies(A,B),C),D)) | is_a_theorem(implies(and(A,not(B)),D)). [para(80(a,1),244(a,1,1,1))].
% 121.26/121.59 415 is_a_theorem(implies(not(implies(A,A)),B)). [resolve(348,a,123,a)].
% 121.26/121.59 435 is_a_theorem(implies(implies(A,B),implies(not(implies(C,C)),B))). [resolve(415,a,130,a)].
% 121.26/121.59 610 is_a_theorem(implies(implies(not(A),A),implies(implies(B,C),implies(not(A),C)))). [resolve(347,a,232,a)].
% 121.26/121.59 611 is_a_theorem(implies(implies(implies(implies(A,B),implies(not(C),B)),D),implies(C,D))). [resolve(347,a,130,a)].
% 121.26/121.59 639 is_a_theorem(implies(A,implies(not(implies(B,B)),C))). [resolve(435,a,244,a)].
% 121.26/121.59 756 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),implies(D,C))). [resolve(639,a,130,a)].
% 121.26/121.59 1025 is_a_theorem(implies(not(equiv(A,A)),and(A,not(A)))). [para(257(a,1),128(a,1,1))].
% 121.26/121.59 1204 is_a_theorem(implies(implies(and(A,not(A)),B),implies(not(equiv(A,A)),B))). [resolve(1025,a,130,a)].
% 121.26/121.59 2284 -is_a_theorem(implies(implies(not(implies(A,A)),B),C)) | is_a_theorem(implies(D,C)). [resolve(756,a,69,b)].
% 121.26/121.59 3020 is_a_theorem(implies(A,implies(B,B))). [resolve(2284,a,66,a)].
% 121.26/121.59 3027 is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))). [resolve(3020,a,130,a)].
% 121.26/121.59 3373 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(D,D),B),C))). [resolve(3027,a,130,a)].
% 121.26/121.59 3375 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(implies(C,B)). [resolve(3027,a,69,b)].
% 121.26/121.59 3448 is_a_theorem(implies(A,implies(B,implies(not(B),C)))). [resolve(3375,a,229,a)].
% 121.26/121.59 3449 is_a_theorem(implies(A,implies(implies(not(B),B),B))). [resolve(3375,a,228,a)].
% 121.26/121.59 3529 is_a_theorem(implies(implies(implies(A,implies(not(A),B)),C),implies(D,C))). [resolve(3448,a,130,a)].
% 121.26/121.59 3829 is_a_theorem(implies(implies(implies(implies(not(A),A),A),B),implies(C,B))). [resolve(3449,a,130,a)].
% 121.26/121.59 5537 -is_a_theorem(implies(implies(implies(not(A),A),A),B)) | is_a_theorem(implies(C,B)). [resolve(3829,a,69,b)].
% 121.26/121.59 6819 -is_a_theorem(implies(not(A),A)) | is_a_theorem(implies(implies(B,C),implies(not(A),C))). [resolve(610,a,69,b)].
% 121.26/121.59 7375 -is_a_theorem(implies(and(A,not(A)),B)) | is_a_theorem(implies(not(equiv(A,A)),B)). [resolve(1204,a,69,b)].
% 121.26/121.59 7782 is_a_theorem(implies(A,implies(implies(implies(B,B),C),C))). [resolve(3373,a,5537,a)].
% 121.26/121.59 7792 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(implies(D,D),B),C)). [resolve(3373,a,69,b)].
% 121.26/121.59 7864 is_a_theorem(implies(implies(implies(implies(implies(A,A),B),B),C),implies(D,C))). [resolve(7782,a,130,a)].
% 121.26/121.59 7866 is_a_theorem(implies(implies(implies(A,A),B),B)). [resolve(7782,a,122,a)].
% 121.26/121.59 7910 is_a_theorem(implies(implies(A,B),implies(implies(implies(C,C),A),B))). [resolve(7866,a,130,a)].
% 121.26/121.59 7911 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(B). [resolve(7866,a,69,b)].
% 121.26/121.59 8086 is_a_theorem(implies(A,implies(implies(implies(B,B),not(A)),C))). [resolve(7910,a,244,a)].
% 121.26/121.59 8090 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(C,C),A),B)). [resolve(7910,a,69,b)].
% 121.26/121.59 8114 is_a_theorem(implies(implies(implies(implies(implies(A,A),not(B)),C),D),implies(B,D))). [resolve(8086,a,130,a)].
% 121.26/121.59 8579 is_a_theorem(implies(implies(implies(A,A),implies(implies(B,B),C)),implies(D,C))). [resolve(8090,a,3027,a)].
% 121.26/121.59 10085 is_a_theorem(implies(implies(implies(A,A),B),implies(implies(B,C),implies(D,C)))). [resolve(7792,a,96,a)].
% 121.26/121.59 10156 -is_a_theorem(implies(implies(implies(implies(A,A),B),B),C)) | is_a_theorem(implies(D,C)). [resolve(7864,a,69,b)].
% 121.26/121.59 10707 -is_a_theorem(implies(implies(A,A),implies(implies(B,B),C))) | is_a_theorem(implies(D,C)). [resolve(8579,a,69,b)].
% 121.26/121.59 10955 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(implies(implies(B,C),implies(D,C))). [resolve(10085,a,69,b)].
% 121.26/121.59 11611 is_a_theorem(implies(A,implies(and(B,not(B)),C))). [resolve(226,a,10156,a)].
% 121.26/121.59 11646 is_a_theorem(implies(and(A,not(A)),B)). [resolve(11611,a,7911,a)].
% 121.26/121.59 11706 is_a_theorem(implies(not(equiv(A,A)),B)). [back_unit_del(7375),unit_del(a,11646)].
% 121.26/121.59 11837 is_a_theorem(implies(implies(A,B),implies(not(equiv(C,C)),B))). [resolve(11706,a,6819,a)].
% 121.26/121.59 12766 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),C),implies(D,C))). [resolve(11837,a,10955,a)].
% 121.26/121.59 13179 is_a_theorem(implies(A,implies(B,equiv(C,C)))). [resolve(12766,a,5537,a)].
% 121.26/121.59 13232 is_a_theorem(implies(implies(implies(A,equiv(B,B)),C),implies(D,C))). [resolve(13179,a,10955,a)].
% 121.26/121.59 13235 is_a_theorem(implies(A,equiv(B,B))). [resolve(13179,a,10707,a)].
% 121.26/121.59 13314 is_a_theorem(implies(implies(equiv(A,A),B),implies(C,B))). [resolve(13235,a,10955,a)].
% 121.26/121.59 13636 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(equiv(D,D),B),C))). [resolve(13314,a,130,a)].
% 121.26/121.59 14157 -is_a_theorem(implies(implies(implies(not(A),A),B),C)) | is_a_theorem(implies(implies(A,B),C)). [resolve(230,a,69,b)].
% 121.26/121.59 14899 is_a_theorem(implies(A,implies(implies(equiv(B,B),C),C))). [resolve(13636,a,10156,a)].
% 121.26/121.59 14915 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(equiv(D,D),B),C)). [resolve(13636,a,69,b)].
% 121.26/121.59 14926 is_a_theorem(implies(implies(implies(implies(equiv(A,A),B),B),C),implies(D,C))). [resolve(14899,a,10955,a)].
% 121.26/121.59 14938 is_a_theorem(implies(implies(equiv(A,A),B),B)). [resolve(14899,a,7911,a)].
% 121.26/121.59 14969 is_a_theorem(implies(A,implies(implies(implies(not(implies(B,B)),C),D),D))). [resolve(242,a,10156,a)].
% 121.26/121.59 14976 is_a_theorem(implies(A,implies(implies(implies(not(not(B)),C),B),B))). [resolve(242,a,5537,a)].
% 121.26/121.59 14986 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(implies(not(A),D),B),C)). [resolve(242,a,69,b)].
% 121.26/121.59 15016 is_a_theorem(implies(implies(A,B),implies(implies(equiv(C,C),A),B))). [resolve(14938,a,130,a)].
% 121.26/121.59 15017 -is_a_theorem(implies(equiv(A,A),B)) | is_a_theorem(B). [resolve(14938,a,69,b)].
% 121.26/121.59 15185 is_a_theorem(implies(implies(implies(not(not(A)),B),A),A)). [resolve(14976,a,15017,a)].
% 121.26/121.59 15223 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(not(A)),C),A),B))). [resolve(15185,a,130,a)].
% 121.26/121.59 15224 -is_a_theorem(implies(implies(not(not(A)),B),A)) | is_a_theorem(A). [resolve(15185,a,69,b)].
% 121.26/121.59 15368 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(equiv(C,C),A),B)). [resolve(15016,a,69,b)].
% 121.26/121.59 16917 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),C)). [resolve(14969,a,15224,a)].
% 121.26/121.59 16958 -is_a_theorem(implies(implies(not(implies(A,A)),B),C)) | is_a_theorem(C). [resolve(16917,a,69,b)].
% 121.26/121.59 18244 is_a_theorem(implies(implies(equiv(A,A),B),implies(implies(B,C),implies(D,C)))). [resolve(14915,a,10085,a)].
% 121.26/121.59 18319 -is_a_theorem(implies(implies(implies(equiv(A,A),B),B),C)) | is_a_theorem(implies(D,C)). [resolve(14926,a,69,b)].
% 121.26/121.59 18511 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(not(A)),C),A),B)). [resolve(15223,a,69,b)].
% 121.26/121.59 19832 -is_a_theorem(implies(equiv(A,A),B)) | is_a_theorem(implies(implies(B,C),implies(D,C))). [resolve(18244,a,69,b)].
% 121.26/121.59 19938 is_a_theorem(implies(A,implies(implies(implies(not(equiv(B,B)),C),D),D))). [resolve(18319,a,242,a)].
% 121.26/121.59 19962 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),C),C)). [resolve(19938,a,16958,a)].
% 121.26/121.59 20006 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(equiv(C,C)),D),A),B))). [resolve(19962,a,130,a)].
% 121.26/121.59 20007 -is_a_theorem(implies(implies(not(equiv(A,A)),B),C)) | is_a_theorem(C). [resolve(19962,a,69,b)].
% 121.26/121.59 20026 -is_a_theorem(not(equiv(not(equiv(A,A)),B))) | is_a_theorem(and(B,not(not(equiv(A,A))))). [para(257(a,1),20007(a,1))].
% 121.26/121.59 20628 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),and(A,not(A))),C)). [resolve(18511,a,11646,a),rewrite([80(3)])].
% 121.26/121.59 22703 is_a_theorem(implies(and(not(implies(A,A)),not(B)),C)). [resolve(350,a,20628,a)].
% 121.26/121.59 22705 is_a_theorem(implies(and(not(equiv(A,A)),not(B)),C)). [resolve(350,a,19962,a)].
% 121.26/121.59 22711 is_a_theorem(implies(and(not(not(A)),not(B)),A)). [resolve(350,a,15185,a)].
% 121.26/121.59 22715 is_a_theorem(implies(and(A,not(equiv(B,B))),implies(C,D))). [resolve(350,a,13232,a)].
% 121.26/121.59 22722 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),implies(C,D))). [resolve(350,a,7864,a)].
% 121.26/121.59 22724 is_a_theorem(implies(and(implies(not(A),A),not(A)),implies(B,C))). [resolve(350,a,3829,a)].
% 121.26/121.59 22725 is_a_theorem(implies(and(A,not(implies(not(A),B))),implies(C,D))). [resolve(350,a,3529,a)].
% 121.26/121.59 22734 is_a_theorem(implies(and(A,not(B)),implies(implies(implies(not(A),C),B),D))). [resolve(350,a,242,a)].
% 121.26/121.59 22737 is_a_theorem(implies(and(implies(A,B),not(implies(C,B))),implies(implies(C,A),D))). [resolve(350,a,227,a)].
% 121.26/121.59 22768 is_a_theorem(implies(implies(implies(not(not(A)),B),and(not(not(A)),not(B))),A)). [resolve(22711,a,232,a),rewrite([80(5)])].
% 121.26/121.59 22769 is_a_theorem(implies(implies(A,B),implies(and(not(not(A)),not(C)),B))). [resolve(22711,a,130,a)].
% 121.26/121.59 23085 is_a_theorem(implies(implies(equiv(A,A),and(not(implies(B,B)),not(C))),D)). [resolve(22703,a,15368,a)].
% 121.26/121.59 23133 is_a_theorem(implies(implies(implies(A,A),and(not(equiv(B,B)),not(C))),D)). [resolve(22705,a,8090,a)].
% 121.26/121.59 23574 is_a_theorem(implies(implies(implies(A,B),C),implies(and(D,not(equiv(E,E))),C))). [resolve(22715,a,130,a)].
% 121.26/121.59 23878 is_a_theorem(implies(and(implies(not(A),A),not(A)),not(equiv(B,C)))). [para(257(a,1),22724(a,1,2))].
% 121.26/121.59 23907 is_a_theorem(implies(and(A,not(implies(not(A),B))),not(equiv(C,D)))). [para(257(a,1),22725(a,1,2))].
% 121.26/121.59 24168 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),not(equiv(C,D)))). [para(257(a,1),22722(a,1,2))].
% 121.26/121.59 24558 is_a_theorem(implies(and(not(not(not(equiv(A,A)))),not(B)),C)). [resolve(22769,a,20007,a)].
% 121.26/121.59 24570 is_a_theorem(implies(implies(implies(and(not(not(A)),not(B)),A),C),implies(D,C))). [resolve(22769,a,10955,a)].
% 121.26/121.59 27108 is_a_theorem(implies(and(A,implies(B,not(A))),implies(not(equiv(not(A),B)),C))). [para(257(a,1),22734(a,1,2,1)),rewrite([80(4)])].
% 121.26/121.60 27461 is_a_theorem(and(equiv(A,A),implies(not(implies(B,B)),C))). [resolve(23085,a,132,a),rewrite([80(6)])].
% 121.26/121.60 27755 is_a_theorem(and(implies(A,A),implies(not(equiv(B,B)),C))). [resolve(23133,a,132,a),rewrite([80(6)])].
% 121.26/121.60 30595 -is_a_theorem(implies(implies(implies(A,B),implies(not(C),B)),D)) | is_a_theorem(implies(C,D)). [resolve(611,a,69,b)].
% 121.26/121.60 33437 -is_a_theorem(implies(implies(implies(implies(A,A),not(B)),C),D)) | is_a_theorem(implies(B,D)). [resolve(8114,a,69,b)].
% 121.26/121.60 53809 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(equiv(C,C)),D),A),B)). [resolve(20006,a,69,b)].
% 121.26/121.60 55936 is_a_theorem(implies(and(implies(A,B),not(implies(C,B))),not(equiv(C,A)))). [para(257(a,1),22737(a,1,2))].
% 121.26/121.60 56155 is_a_theorem(implies(implies(not(A),and(not(not(A)),not(not(A)))),A)). [resolve(22768,a,14157,a)].
% 121.26/121.60 56221 -is_a_theorem(implies(not(A),and(not(not(A)),not(not(A))))) | is_a_theorem(A). [resolve(56155,a,69,b)].
% 121.26/121.60 56454 is_a_theorem(implies(A,implies(and(B,not(equiv(C,C))),D))). [resolve(23574,a,18319,a)].
% 121.26/121.60 56498 is_a_theorem(implies(implies(implies(and(A,not(equiv(B,B))),C),D),implies(E,D))). [resolve(56454,a,19832,a)].
% 121.26/121.60 61387 -is_a_theorem(and(A,implies(B,not(A)))) | is_a_theorem(implies(not(equiv(not(A),B)),C)). [resolve(27108,a,69,b)].
% 121.26/121.60 62362 is_a_theorem(implies(A,implies(B,implies(not(A),C)))). [resolve(30595,a,24570,a)].
% 121.26/121.60 62371 is_a_theorem(implies(A,implies(implies(implies(not(A),B),C),implies(D,C)))). [resolve(30595,a,10085,a)].
% 121.26/121.60 62462 is_a_theorem(implies(implies(implies(A,implies(not(B),C)),D),implies(B,D))). [resolve(62362,a,130,a)].
% 121.26/121.60 67507 is_a_theorem(implies(A,implies(B,implies(C,implies(not(B),D))))). [resolve(62462,a,3375,a)].
% 121.26/121.60 74596 is_a_theorem(implies(A,and(implies(B,B),not(not(A))))). [resolve(33437,a,128,a)].
% 121.26/121.60 74722 is_a_theorem(implies(implies(and(implies(A,A),not(not(B))),C),implies(B,C))). [resolve(74596,a,130,a)].
% 121.26/121.60 113951 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),and(not(not(C)),not(D))),C)). [resolve(53809,a,22711,a)].
% 121.26/121.60 114844 is_a_theorem(implies(and(and(A,not(equiv(B,B))),not(C)),implies(D,E))). [resolve(56498,a,350,a)].
% 121.26/121.60 115025 is_a_theorem(implies(and(and(A,not(equiv(B,B))),not(C)),not(equiv(D,E)))). [para(257(a,1),114844(a,1,2))].
% 121.26/121.60 118428 is_a_theorem(implies(not(equiv(not(implies(A,A)),not(equiv(B,B)))),C)). [resolve(61387,a,27755,a)].
% 121.26/121.60 118431 is_a_theorem(implies(not(equiv(not(equiv(A,A)),not(implies(B,B)))),C)). [resolve(61387,a,27461,a)].
% 121.26/121.60 118466 is_a_theorem(equiv(not(implies(A,A)),not(equiv(B,B)))). [resolve(118428,a,56221,a)].
% 121.26/121.60 118575 not(equiv(A,A)) = not(implies(B,B)). [resolve(118466,a,61,a)].
% 121.26/121.60 118585 not(equiv(A,A)) = c_0. [new_symbol(118575)].
% 121.26/121.60 118589 not(implies(A,A)) = c_0. [back_rewrite(118575),rewrite([118585(2)]),flip(a)].
% 121.26/121.60 118600 is_a_theorem(implies(c_0,A)). [back_rewrite(118431),rewrite([118585(2),118589(3),118585(4)])].
% 121.26/121.60 118610 is_a_theorem(implies(and(and(A,c_0),not(B)),not(equiv(C,D)))). [back_rewrite(115025),rewrite([118585(2)])].
% 121.26/121.60 118627 is_a_theorem(implies(implies(implies(c_0,A),and(not(not(B)),not(C))),B)). [back_rewrite(113951),rewrite([118585(2)])].
% 121.26/121.60 119005 is_a_theorem(implies(and(not(not(c_0)),not(A)),B)). [back_rewrite(24558),rewrite([118585(2)])].
% 121.26/121.60 119040 is_a_theorem(implies(implies(implies(A,A),and(c_0,not(B))),C)). [back_rewrite(23133),rewrite([118585(3)])].
% 121.26/121.60 119059 -is_a_theorem(not(equiv(c_0,A))) | is_a_theorem(and(A,not(c_0))). [back_rewrite(20026),rewrite([118585(2),118585(6)])].
% 121.26/121.60 119064 -is_a_theorem(implies(implies(c_0,A),B)) | is_a_theorem(B). [back_rewrite(20007),rewrite([118585(2)])].
% 121.26/121.60 121030 implies(A,equiv(B,B)) = not(and(A,c_0)). [para(118585(a,1),80(a,1,1,2)),flip(a)].
% 121.26/121.60 121178 is_a_theorem(implies(and(implies(not(A),A),not(A)),c_0)). [para(118585(a,1),23878(a,1,2))].
% 121.26/121.60 121181 is_a_theorem(implies(and(A,not(implies(not(A),B))),c_0)). [para(118585(a,1),23907(a,1,2))].
% 121.26/121.60 121203 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),c_0)). [para(118585(a,1),24168(a,1,2))].
% 121.26/121.60 122279 implies(A,implies(B,B)) = not(and(A,c_0)). [para(118589(a,1),80(a,1,1,2)),flip(a)].
% 121.26/121.60 126300 is_a_theorem(implies(implies(equiv(A,A),and(not(not(c_0)),not(B))),C)). [resolve(119005,a,15368,a)].
% 121.26/121.60 130632 -is_a_theorem(implies(not(and(equiv(A,A),c_0)),B)) | is_a_theorem(B). [para(121030(a,1),7911(a,1,1))].
% 121.26/121.60 131717 is_a_theorem(implies(implies(c_0,A),implies(and(implies(not(B),B),not(B)),A))). [resolve(121178,a,130,a)].
% 121.26/121.60 131789 is_a_theorem(implies(implies(c_0,A),implies(and(B,not(implies(not(B),C))),A))). [resolve(121181,a,130,a)].
% 121.26/121.60 137186 is_a_theorem(implies(implies(implies(c_0,A),and(c_0,not(B))),C)). [resolve(119040,a,14986,a),rewrite([118589(2)])].
% 121.26/121.60 138412 is_a_theorem(implies(and(implies(not(and(equiv(A,A),c_0)),B),not(B)),c_0)). [para(121030(a,1),121203(a,1,1,1,1))].
% 121.26/121.60 143313 is_a_theorem(and(implies(c_0,A),implies(c_0,B))). [resolve(137186,a,132,a),rewrite([80(6)])].
% 121.26/121.60 143348 is_a_theorem(implies(not(equiv(not(implies(c_0,A)),c_0)),B)). [resolve(143313,a,61387,a)].
% 121.26/121.60 143534 is_a_theorem(equiv(not(implies(c_0,A)),c_0)). [resolve(143348,a,56221,a)].
% 121.26/121.60 143628 not(implies(c_0,A)) = c_0. [resolve(143534,a,61,a),flip(a)].
% 121.26/121.60 143632 implies(A,implies(c_0,B)) = not(and(A,c_0)). [para(143628(a,1),80(a,1,1,2)),flip(a)].
% 121.26/121.60 147090 is_a_theorem(implies(and(and(A,c_0),not(B)),c_0)). [para(118585(a,1),118610(a,1,2))].
% 121.26/121.60 147158 is_a_theorem(implies(implies(c_0,A),implies(and(and(B,c_0),not(C)),A))). [resolve(147090,a,130,a)].
% 121.26/121.60 166178 is_a_theorem(implies(not(equiv(c_0,not(not(A)))),A)). [para(257(a,1),118627(a,1,1))].
% 121.26/121.60 166249 is_a_theorem(implies(implies(A,B),implies(not(equiv(c_0,not(not(A)))),B))). [resolve(166178,a,130,a)].
% 121.26/121.60 180869 is_a_theorem(and(equiv(A,A),implies(not(not(c_0)),B))). [resolve(126300,a,132,a),rewrite([80(7)])].
% 121.26/121.60 180903 is_a_theorem(implies(not(equiv(c_0,not(not(c_0)))),A)). [resolve(180869,a,61387,a),rewrite([118585(2)])].
% 121.26/121.60 180968 is_a_theorem(equiv(c_0,not(not(c_0)))). [resolve(180903,a,56221,a)].
% 121.26/121.60 181063 not(not(c_0)) = c_0. [resolve(180968,a,61,a)].
% 121.26/121.60 181096 not(and(A,c_0)) = implies(A,not(c_0)). [para(181063(a,1),80(a,1,1,2))].
% 121.26/121.60 181097 is_a_theorem(not(c_0)). [para(181063(a,1),122(a,1,1)),unit_del(a,118600)].
% 121.26/121.60 181105 implies(implies(not(c_0),A),and(A,c_0)) = not(equiv(not(c_0),A)). [para(181063(a,1),257(a,1,2,2))].
% 121.26/121.60 181107 is_a_theorem(implies(A,not(c_0))). [para(181063(a,1),3448(a,1,2,2,1)),rewrite([143632(5),181096(5),122279(6),181096(3)])].
% 121.26/121.60 181864 implies(A,implies(c_0,B)) = implies(A,not(c_0)). [back_rewrite(143632),rewrite([181096(6)])].
% 121.26/121.60 181917 is_a_theorem(implies(and(implies(implies(equiv(A,A),not(c_0)),B),not(B)),c_0)). [back_rewrite(138412),rewrite([181096(4)])].
% 121.26/121.60 182138 -is_a_theorem(implies(implies(equiv(A,A),not(c_0)),B)) | is_a_theorem(B). [back_rewrite(130632),rewrite([181096(4)])].
% 121.26/121.60 182292 implies(A,implies(B,B)) = implies(A,not(c_0)). [back_rewrite(122279),rewrite([181096(5)])].
% 121.26/121.60 182636 implies(A,equiv(B,B)) = implies(A,not(c_0)). [back_rewrite(121030),rewrite([181096(5)])].
% 121.26/121.60 183256 is_a_theorem(implies(implies(not(c_0),A),implies(B,A))). [resolve(181107,a,19832,a)].
% 121.26/121.60 184328 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(not(c_0),B),C))). [resolve(183256,a,130,a)].
% 121.26/121.60 197119 is_a_theorem(implies(and(and(A,c_0),not(B)),C)). [resolve(147158,a,119064,a)].
% 121.26/121.60 203093 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(equiv(c_0,not(not(A)))),B)). [resolve(166249,a,69,b)].
% 121.26/121.60 222478 is_a_theorem(implies(A,implies(implies(not(c_0),B),B))). [resolve(184328,a,18319,a)].
% 121.26/121.60 222484 is_a_theorem(implies(implies(A,B),implies(implies(not(c_0),A),B))). [resolve(184328,a,14157,a)].
% 121.26/121.60 222510 is_a_theorem(implies(implies(not(c_0),A),A)). [resolve(222478,a,182138,a)].
% 121.26/121.60 222644 -is_a_theorem(implies(not(c_0),A)) | is_a_theorem(A). [resolve(222510,a,69,b)].
% 121.26/121.60 226514 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(c_0),A),B)). [resolve(222484,a,69,b)].
% 121.26/121.60 227984 is_a_theorem(implies(implies(not(c_0),and(and(A,c_0),not(B))),C)). [resolve(226514,a,197119,a)].
% 121.26/121.60 235672 is_a_theorem(and(not(c_0),implies(and(A,c_0),B))). [resolve(227984,a,132,a),rewrite([80(7)])].
% 121.26/121.60 235707 is_a_theorem(implies(not(equiv(c_0,and(A,c_0))),B)). [resolve(235672,a,61387,a),rewrite([181063(3)])].
% 121.26/121.60 235777 is_a_theorem(equiv(c_0,and(A,c_0))). [resolve(235707,a,56221,a)].
% 121.26/121.60 235869 and(A,c_0) = c_0. [resolve(235777,a,61,a)].
% 121.26/121.60 235910 implies(implies(not(c_0),A),c_0) = not(equiv(not(c_0),A)). [back_rewrite(181105),rewrite([235869(5)])].
% 121.26/121.60 235911 implies(A,not(c_0)) = not(c_0). [back_rewrite(181096),rewrite([235869(2)]),flip(a)].
% 121.26/121.60 235939 implies(A,equiv(B,B)) = not(c_0). [back_rewrite(182636),rewrite([235911(5)])].
% 121.26/121.60 235946 implies(A,implies(B,B)) = not(c_0). [back_rewrite(182292),rewrite([235911(5)])].
% 121.26/121.60 235958 is_a_theorem(implies(and(implies(not(c_0),A),not(A)),c_0)). [back_rewrite(181917),rewrite([235911(4)])].
% 121.26/121.60 235960 implies(A,implies(c_0,B)) = not(c_0). [back_rewrite(181864),rewrite([235911(6)])].
% 121.26/121.60 236066 and(not(c_0),implies(not(c_0),A)) = equiv(A,not(c_0)). [para(235911(a,1),90(a,1,1))].
% 121.26/121.60 236067 and(implies(not(c_0),A),not(c_0)) = equiv(not(c_0),A). [para(235911(a,1),90(a,1,2))].
% 121.26/121.60 236278 is_a_theorem(implies(implies(and(not(c_0),not(not(A))),B),implies(A,B))). [para(235911(a,1),74722(a,1,1,1,1))].
% 121.26/121.60 239053 is_a_theorem(implies(implies(c_0,A),implies(and(implies(not(c_0),B),not(B)),A))). [resolve(235958,a,130,a)].
% 121.26/121.60 245242 implies(not(c_0),c_0) = c_0. [para(118585(a,1),235910(a,2)),rewrite([235911(5)])].
% 121.26/121.60 245275 not(equiv(not(c_0),equiv(A,A))) = c_0. [para(235939(a,1),235910(a,1,1)),rewrite([245242(4)]),flip(a)].
% 121.26/121.60 245276 not(equiv(not(c_0),implies(A,A))) = c_0. [para(235946(a,1),235910(a,1,1)),rewrite([245242(4)]),flip(a)].
% 121.26/121.60 245277 not(equiv(not(c_0),implies(c_0,A))) = c_0. [para(235960(a,1),235910(a,1,1)),rewrite([245242(4)]),flip(a)].
% 121.26/121.60 245301 is_a_theorem(implies(implies(not(c_0),A),implies(implies(A,c_0),c_0))). [para(245242(a,1),96(a,1,2,2))].
% 121.26/121.60 245326 is_a_theorem(implies(and(implies(A,c_0),not(c_0)),implies(implies(not(c_0),A),B))). [para(245242(a,1),22737(a,1,1,2,1))].
% 121.26/121.60 245332 is_a_theorem(implies(A,implies(implies(implies(not(A),B),c_0),c_0))). [para(245242(a,1),62371(a,1,2,2))].
% 121.26/121.60 245355 implies(A,equiv(not(c_0),equiv(B,B))) = not(c_0). [para(245275(a,1),80(a,1,1,2)),rewrite([235869(2)]),flip(a)].
% 121.26/121.60 245356 is_a_theorem(equiv(not(c_0),equiv(A,A))). [para(245275(a,1),122(a,1,1)),rewrite([245355(6)]),unit_del(a,181097)].
% 121.26/121.60 245405 equiv(A,A) = not(c_0). [resolve(245356,a,61,a)].
% 121.26/121.60 246399 implies(A,equiv(not(c_0),implies(B,B))) = not(c_0). [para(245276(a,1),80(a,1,1,2)),rewrite([235869(2)]),flip(a)].
% 121.26/121.60 246400 is_a_theorem(equiv(not(c_0),implies(A,A))). [para(245276(a,1),122(a,1,1)),rewrite([246399(6)]),unit_del(a,181097)].
% 121.26/121.60 246445 implies(A,A) = not(c_0). [resolve(246400,a,61,a)].
% 121.26/121.60 247052 and(not(c_0),not(c_0)) = not(c_0). [para(246445(a,1),90(a,1,1)),rewrite([246445(3),245405(6)])].
% 121.26/121.60 247053 is_a_theorem(implies(implies(A,B),implies(not(c_0),implies(A,B)))). [para(246445(a,1),96(a,1,2,1))].
% 121.26/121.60 247054 implies(A,and(B,not(B))) = implies(A,c_0). [para(246445(a,1),129(a,1,1,2)),rewrite([80(4)]),flip(a)].
% 121.26/121.60 247173 implies(A,equiv(not(c_0),implies(c_0,B))) = not(c_0). [para(245277(a,1),80(a,1,1,2)),rewrite([235869(2)]),flip(a)].
% 121.26/121.60 247174 is_a_theorem(equiv(not(c_0),implies(c_0,A))). [para(245277(a,1),122(a,1,1)),rewrite([247173(7)]),unit_del(a,181097)].
% 121.26/121.60 247220 implies(c_0,A) = not(c_0). [resolve(247174,a,61,a)].
% 121.26/121.60 247309 is_a_theorem(implies(not(c_0),implies(and(implies(not(c_0),A),not(A)),B))). [back_rewrite(239053),rewrite([247220(2)])].
% 121.26/121.60 247311 is_a_theorem(implies(not(c_0),implies(and(A,not(implies(not(A),B))),C))). [back_rewrite(131789),rewrite([247220(2)])].
% 121.26/121.60 247312 is_a_theorem(implies(not(c_0),implies(and(implies(not(A),A),not(A)),B))). [back_rewrite(131717),rewrite([247220(2)])].
% 121.26/121.60 247316 and(implies(A,c_0),not(c_0)) = equiv(A,c_0). [para(247220(a,1),90(a,1,2))].
% 121.26/121.60 247317 is_a_theorem(implies(implies(A,c_0),implies(not(c_0),implies(A,B)))). [para(247220(a,1),96(a,1,2,1))].
% 121.26/121.60 247318 implies(A,and(c_0,not(B))) = implies(A,c_0). [para(247220(a,1),129(a,1,1,2)),rewrite([80(4)]),flip(a)].
% 121.26/121.60 247319 implies(not(c_0),and(A,not(c_0))) = not(equiv(c_0,A)). [para(247220(a,1),257(a,1,1))].
% 121.26/121.60 247347 is_a_theorem(implies(and(not(c_0),not(implies(A,B))),not(equiv(A,c_0)))). [para(247220(a,1),55936(a,1,1,1))].
% 121.26/121.60 247349 is_a_theorem(implies(and(A,not(c_0)),implies(not(equiv(not(A),c_0)),B))). [para(247220(a,1),27108(a,1,1,2))].
% 121.26/121.60 247374 is_a_theorem(implies(equiv(A,c_0),implies(implies(not(c_0),A),B))). [back_rewrite(245326),rewrite([247316(5)])].
% 121.26/121.60 247481 implies(implies(A,c_0),and(and(B,not(B)),not(A))) = not(equiv(A,and(B,not(B)))). [para(247054(a,1),257(a,1,1))].
% 121.26/121.60 247506 implies(and(A,not(A)),c_0) = not(c_0). [para(247054(a,1),246445(a,1))].
% 121.26/121.60 247508 equiv(and(A,not(A)),c_0) = not(c_0). [para(247506(a,1),90(a,1,1)),rewrite([247054(6),246445(5),247052(5)]),flip(a)].
% 121.26/121.60 247531 and(A,not(A)) = c_0. [para(247508(a,1),61(a,1)),flip(b),unit_del(a,181097)].
% 121.26/121.60 247535 implies(implies(A,c_0),c_0) = not(equiv(A,c_0)). [back_rewrite(247481),rewrite([247531(4),247318(6),247531(6)])].
% 121.26/121.60 247540 is_a_theorem(implies(A,not(equiv(implies(not(A),B),c_0)))). [back_rewrite(245332),rewrite([247535(6)])].
% 121.26/121.60 247553 is_a_theorem(implies(implies(not(c_0),A),not(equiv(A,c_0)))). [back_rewrite(245301),rewrite([247535(7)])].
% 121.26/121.60 248369 is_a_theorem(implies(A,implies(not(equiv(not(A),c_0)),implies(B,c_0)))). [para(247535(a,1),62371(a,1,2,1))].
% 121.26/121.60 248763 -is_a_theorem(implies(not(c_0),A)) | is_a_theorem(not(equiv(A,c_0))). [resolve(247553,a,69,b)].
% 121.26/121.60 249262 is_a_theorem(not(equiv(implies(A,implies(B,implies(not(A),C))),c_0))). [resolve(248763,a,67507,a)].
% 121.26/121.60 249331 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(c_0),implies(A,B))). [resolve(247053,a,69,b)].
% 121.26/121.60 249515 is_a_theorem(implies(not(c_0),implies(equiv(A,c_0),implies(implies(not(c_0),A),B)))). [resolve(249331,a,247374,a)].
% 121.26/121.60 253100 is_a_theorem(implies(A,implies(not(equiv(not(A),c_0)),c_0))). [para(245242(a,1),248369(a,1,2,2))].
% 121.26/121.60 253153 -is_a_theorem(A) | is_a_theorem(implies(not(equiv(not(A),c_0)),c_0)). [resolve(253100,a,69,b)].
% 121.26/121.60 255106 -is_a_theorem(implies(and(not(c_0),not(not(equiv(c27,c28)))),implies(c27,c28))). [ur(69,b,236278,a,c,73,a)].
% 121.26/121.60 255730 is_a_theorem(implies(and(implies(not(c_0),A),not(A)),B)). [resolve(247309,a,222644,a)].
% 121.26/121.60 255739 is_a_theorem(implies(not(equiv(c_0,not(implies(implies(not(c_0),A),A)))),B)). [resolve(255730,a,203093,a),rewrite([80(7)])].
% 121.26/121.60 255800 is_a_theorem(implies(and(A,not(implies(not(A),B))),C)). [resolve(247311,a,222644,a)].
% 121.26/121.60 255809 is_a_theorem(implies(not(equiv(c_0,not(implies(A,implies(not(A),B))))),C)). [resolve(255800,a,203093,a),rewrite([80(6)])].
% 121.26/121.60 255843 is_a_theorem(implies(and(implies(not(A),A),not(A)),B)). [resolve(247312,a,222644,a)].
% 121.26/121.60 255870 is_a_theorem(implies(implies(not(c_0),and(implies(not(A),A),not(A))),B)). [resolve(255843,a,226514,a)].
% 121.26/121.60 255910 is_a_theorem(implies(and(not(c_0),not(not(equiv(A,B)))),not(equiv(implies(A,B),c_0)))). [para(257(a,1),247347(a,1,1,2,1))].
% 121.26/121.60 256601 is_a_theorem(equiv(c_0,not(implies(implies(not(c_0),A),A)))). [resolve(255739,a,56221,a)].
% 121.26/121.60 256606 not(implies(implies(not(c_0),A),A)) = c_0. [resolve(256601,a,61,a)].
% 121.26/121.60 256608 implies(A,implies(implies(not(c_0),B),B)) = not(c_0). [para(256606(a,1),80(a,1,1,2)),rewrite([235869(2)]),flip(a)].
% 121.26/121.60 256619 equiv(implies(implies(not(c_0),A),A),not(c_0)) = not(c_0). [para(256608(a,1),236066(a,1,2)),rewrite([247052(5)]),flip(a)].
% 121.26/121.60 256628 implies(implies(not(c_0),A),A) = not(c_0). [para(256619(a,1),61(a,1)),flip(b),unit_del(a,181097)].
% 121.26/121.60 256632 and(implies(A,implies(not(c_0),A)),not(c_0)) = equiv(A,implies(not(c_0),A)). [para(256628(a,1),90(a,1,2))].
% 121.26/121.60 256715 is_a_theorem(equiv(c_0,not(implies(A,implies(not(A),B))))). [resolve(255809,a,56221,a)].
% 121.26/121.60 256721 not(implies(A,implies(not(A),B))) = c_0. [resolve(256715,a,61,a)].
% 121.26/121.60 256723 implies(A,implies(B,implies(not(B),C))) = not(c_0). [para(256721(a,1),80(a,1,1,2)),rewrite([235869(2)]),flip(a)].
% 121.26/121.60 256738 equiv(implies(A,implies(not(A),B)),not(c_0)) = not(c_0). [para(256723(a,1),236066(a,1,2)),rewrite([247052(5)]),flip(a)].
% 121.26/121.60 256750 implies(A,implies(not(A),B)) = not(c_0). [para(256738(a,1),61(a,1)),flip(b),unit_del(a,181097)].
% 121.26/121.60 256753 and(not(c_0),implies(implies(not(A),B),A)) = equiv(A,implies(not(A),B)). [para(256750(a,1),90(a,1,1))].
% 121.26/121.60 256754 and(implies(implies(not(A),B),A),not(c_0)) = equiv(implies(not(A),B),A). [para(256750(a,1),90(a,1,2))].
% 121.26/121.60 256905 is_a_theorem(equiv(A,implies(not(A),A))). [resolve(255870,a,132,a),rewrite([80(7),256753(6)])].
% 121.26/121.60 256941 implies(not(A),A) = A. [resolve(256905,a,61,a)].
% 121.26/121.60 257367 is_a_theorem(implies(A,not(equiv(A,c_0)))). [para(256941(a,1),247540(a,1,2,1,1))].
% 121.26/121.60 257369 is_a_theorem(implies(implies(not(A),c_0),implies(not(c_0),A))). [para(256941(a,1),247317(a,1,2,2))].
% 121.26/121.60 257378 is_a_theorem(not(equiv(implies(A,implies(B,A)),c_0))). [para(256941(a,1),249262(a,1,1,1,2,2))].
% 121.26/121.60 257413 is_a_theorem(implies(and(A,not(c_0)),equiv(not(A),c_0))). [para(256941(a,1),247349(a,1,2))].
% 121.26/121.60 258299 -is_a_theorem(A) | is_a_theorem(not(equiv(A,c_0))). [resolve(257367,a,69,b)].
% 121.26/121.60 258494 is_a_theorem(not(equiv(implies(A,not(equiv(A,c_0))),c_0))). [resolve(258299,a,257367,a)].
% 121.26/121.60 261332 is_a_theorem(not(equiv(implies(implies(not(A),c_0),implies(not(c_0),A)),c_0))). [resolve(257369,a,258299,a)].
% 121.26/121.60 261443 is_a_theorem(implies(not(equiv(A,c_0)),not(equiv(c_0,A)))). [para(247319(a,1),257369(a,1,2)),rewrite([80(4),247535(4)])].
% 121.26/121.60 261507 -is_a_theorem(and(A,not(c_0))) | is_a_theorem(equiv(not(A),c_0)). [resolve(257413,a,69,b)].
% 121.26/121.60 262328 -is_a_theorem(not(equiv(A,c_0))) | is_a_theorem(not(equiv(c_0,A))). [resolve(261443,a,69,b)].
% 121.26/121.60 262567 is_a_theorem(not(equiv(c_0,implies(A,not(equiv(A,c_0)))))). [resolve(262328,a,258494,a)].
% 121.26/121.60 262568 is_a_theorem(not(equiv(c_0,implies(A,implies(B,A))))). [resolve(262328,a,257378,a)].
% 121.26/121.60 262645 is_a_theorem(and(implies(A,implies(B,A)),not(c_0))). [resolve(262568,a,119059,a)].
% 121.26/121.60 262661 is_a_theorem(equiv(not(implies(A,implies(B,A))),c_0)). [resolve(262645,a,261507,a)].
% 121.26/121.60 262715 not(implies(A,implies(B,A))) = c_0. [resolve(262661,a,61,a),flip(a)].
% 121.26/121.60 262717 implies(A,implies(B,implies(C,B))) = not(c_0). [para(262715(a,1),80(a,1,1,2)),rewrite([235869(2)]),flip(a)].
% 121.26/121.60 262719 implies(A,implies(B,A)) = not(c_0). [para(262715(a,1),256941(a,1,1)),rewrite([262717(4)]),flip(a)].
% 121.26/121.60 262724 equiv(A,implies(not(c_0),A)) = not(c_0). [back_rewrite(256632),rewrite([262719(4),247052(5)]),flip(a)].
% 121.26/121.60 262810 implies(not(c_0),A) = A. [para(262724(a,1),61(a,1)),unit_del(a,181097)].
% 121.26/121.60 262837 is_a_theorem(not(equiv(implies(implies(not(A),c_0),A),c_0))). [back_rewrite(261332),rewrite([262810(6)])].
% 121.26/121.60 262905 is_a_theorem(implies(equiv(A,c_0),implies(A,B))). [back_rewrite(249515),rewrite([262810(7),262810(7)])].
% 121.26/121.60 262959 not(equiv(c_0,A)) = and(A,not(c_0)). [back_rewrite(247319),rewrite([262810(6)]),flip(a)].
% 121.26/121.60 262966 equiv(not(c_0),A) = and(A,not(c_0)). [back_rewrite(236067),rewrite([262810(3)]),flip(a)].
% 121.26/121.60 262978 is_a_theorem(and(implies(A,not(equiv(A,c_0))),not(c_0))). [back_rewrite(262567),rewrite([262959(7)])].
% 121.26/121.60 262983 -is_a_theorem(not(equiv(A,c_0))) | is_a_theorem(and(A,not(c_0))). [back_rewrite(262328),rewrite([262959(7)])].
% 121.26/121.60 264575 is_a_theorem(implies(equiv(not(A),c_0),A)). [para(256941(a,1),262905(a,1,2))].
% 121.26/121.60 264586 is_a_theorem(implies(not(equiv(not(implies(equiv(not(A),c_0),A)),c_0)),c_0)). [resolve(264575,a,253153,a)].
% 121.26/121.60 265803 -is_a_theorem(and(A,not(c_0))) | not(c_0) = A. [para(262966(a,1),61(a,1)),flip(b)].
% 121.26/121.60 268366 implies(A,not(equiv(A,c_0))) = not(c_0). [resolve(262978,a,265803,a),flip(a)].
% 121.26/121.60 268398 and(implies(not(equiv(A,c_0)),A),not(c_0)) = equiv(not(equiv(A,c_0)),A). [para(268366(a,1),90(a,1,2))].
% 121.26/121.60 268719 is_a_theorem(equiv(implies(not(A),c_0),A)). [resolve(262983,a,262837,a),rewrite([256754(7)])].
% 121.26/121.60 268786 implies(not(A),c_0) = A. [resolve(268719,a,61,a),flip(a)].
% 121.26/121.60 268833 is_a_theorem(equiv(not(implies(equiv(not(A),c_0),A)),c_0)). [back_rewrite(264586),rewrite([268786(10)])].
% 121.26/121.60 268943 implies(implies(A,B),c_0) = and(A,not(B)). [para(80(a,1),268786(a,1,1))].
% 121.26/121.60 268944 equiv(not(A),c_0) = and(A,not(c_0)). [para(268786(a,1),90(a,1,1)),rewrite([247220(3)]),flip(a)].
% 121.26/121.60 269074 not(equiv(A,c_0)) = and(A,not(c_0)). [back_rewrite(247535),rewrite([268943(4)]),flip(a)].
% 121.26/121.60 269163 is_a_theorem(and(implies(and(A,not(c_0)),A),not(c_0))). [back_rewrite(268833),rewrite([268944(3),268944(7)])].
% 121.26/121.60 270403 and(implies(and(A,not(c_0)),A),not(c_0)) = equiv(and(A,not(c_0)),A). [back_rewrite(268398),rewrite([269074(3),269074(10)])].
% 121.26/121.60 270702 is_a_theorem(implies(and(not(c_0),not(not(equiv(A,B)))),and(implies(A,B),not(c_0)))). [back_rewrite(255910),rewrite([269074(10)])].
% 121.26/121.60 270808 is_a_theorem(equiv(and(A,not(c_0)),A)). [back_rewrite(269163),rewrite([270403(7)])].
% 121.26/121.60 271960 and(A,not(c_0)) = A. [resolve(270808,a,61,a),flip(a)].
% 121.26/121.60 272000 is_a_theorem(implies(and(not(c_0),not(not(equiv(A,B)))),implies(A,B))). [back_rewrite(270702),rewrite([271960(10)])].
% 121.26/121.60 272001 $F. [resolve(272000,a,255106,a)].
% 121.26/121.60
% 121.26/121.60 % SZS output end Refutation
% 121.26/121.60 ============================== end of proof ==========================
% 121.26/121.60
% 121.26/121.60 ============================== STATISTICS ============================
% 121.26/121.60
% 121.26/121.60 Given=8920. Generated=14529433. Kept=271950. proofs=1.
% 121.26/121.60 Usable=962. Sos=6521. Demods=99. Limbo=40, Disabled=264498. Hints=0.
% 121.26/121.60 Megabytes=190.34.
% 121.26/121.60 User_CPU=113.30, System_CPU=7.26, Wall_clock=121.
% 121.26/121.60
% 121.26/121.60 ============================== end of statistics =====================
% 121.26/121.60
% 121.26/121.60 ============================== end of search =========================
% 121.26/121.60
% 121.26/121.60 THEOREM PROVED
% 121.26/121.60 % SZS status Theorem
% 121.26/121.60
% 121.26/121.60 Exiting with 1 proof.
% 121.26/121.60
% 121.26/121.60 Process 17527 exit (max_proofs) Sun Jul 3 22:48:16 2022
% 121.26/121.60 Prover9 interrupted
%------------------------------------------------------------------------------