TSTP Solution File: LCL481+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL481+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 13:47:07 EDT 2022
% Result : Theorem 113.98s 114.34s
% Output : Refutation 113.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : LCL481+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.11 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.32 % Computer : n025.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Sun Jul 3 07:14:25 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.40/0.98 ============================== Prover9 ===============================
% 0.40/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.40/0.98 Process 13870 was started by sandbox on n025.cluster.edu,
% 0.40/0.98 Sun Jul 3 07:14:26 2022
% 0.40/0.98 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_13717_n025.cluster.edu".
% 0.40/0.98 ============================== end of head ===========================
% 0.40/0.98
% 0.40/0.98 ============================== INPUT =================================
% 0.40/0.98
% 0.40/0.98 % Reading from file /tmp/Prover9_13717_n025.cluster.edu
% 0.40/0.98
% 0.40/0.98 set(prolog_style_variables).
% 0.40/0.98 set(auto2).
% 0.40/0.98 % set(auto2) -> set(auto).
% 0.40/0.98 % set(auto) -> set(auto_inference).
% 0.40/0.98 % set(auto) -> set(auto_setup).
% 0.40/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.40/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.40/0.98 % set(auto) -> set(auto_limits).
% 0.40/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.40/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.40/0.98 % set(auto) -> set(auto_denials).
% 0.40/0.98 % set(auto) -> set(auto_process).
% 0.40/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.40/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.40/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.40/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.40/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.40/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.40/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.40/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.40/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.40/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.40/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.40/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.40/0.98 % set(auto2) -> assign(stats, some).
% 0.40/0.98 % set(auto2) -> clear(echo_input).
% 0.40/0.98 % set(auto2) -> set(quiet).
% 0.40/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.40/0.98 % set(auto2) -> clear(print_given).
% 0.40/0.98 assign(lrs_ticks,-1).
% 0.40/0.98 assign(sos_limit,10000).
% 0.40/0.98 assign(order,kbo).
% 0.40/0.98 set(lex_order_vars).
% 0.40/0.98 clear(print_given).
% 0.40/0.98
% 0.40/0.98 % formulas(sos). % not echoed (43 formulas)
% 0.40/0.98
% 0.40/0.98 ============================== end of input ==========================
% 0.40/0.98
% 0.40/0.98 % From the command line: assign(max_seconds, 300).
% 0.40/0.98
% 0.40/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.40/0.98
% 0.40/0.98 % Formulas that are not ordinary clauses:
% 0.40/0.98 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].
% 0.40/0.98 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].
% 0.40/0.98 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].
% 0.40/0.98 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.98 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].
% 0.40/0.98 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].
% 0.40/0.98 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.98 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.98 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].
% 0.40/0.98 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.98 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.98 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].
% 0.40/0.98 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].
% 0.40/0.98 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].
% 1.10/1.45 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].
% 1.10/1.45 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 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].
% 1.10/1.45 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].
% 1.10/1.45 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 1.10/1.45 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].
% 1.10/1.45 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].
% 1.10/1.45 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].
% 1.10/1.45 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].
% 1.10/1.45 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].
% 1.10/1.45 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].
% 1.10/1.45 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].
% 1.10/1.45
% 1.10/1.45 ============================== end of process non-clausal formulas ===
% 1.10/1.45
% 1.10/1.45 ============================== PROCESS INITIAL CLAUSES ===============
% 1.10/1.45
% 1.10/1.45 ============================== PREDICATE ELIMINATION =================
% 1.10/1.45
% 1.10/1.45 ============================== end predicate elimination =============
% 1.10/1.45
% 1.10/1.45 Auto_denials: (non-Horn, no changes).
% 1.10/1.45
% 1.10/1.45 Term ordering decisions:
% 1.10/1.45
% 1.10/1.45 % Assigning unary symbol not kb_weight 0 and highest precedence (94).
% 1.10/1.45 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.
% 1.10/1.45
% 1.10/1.45 ============================== end of process initial clauses ========
% 1.10/1.45
% 1.10/1.45 ============================== CLAUSES FOR SEARCH ====================
% 1.10/1.45
% 1.10/1.45 ============================== end of clauses for search =============
% 1.10/1.45
% 1.10/1.45 ============================== SEARCH ================================
% 1.10/1.45
% 1.10/1.45 % Starting search at 0.02 seconds.
% 1.10/1.45
% 1.10/1.45 Low Water (keep): wt=39.000, iters=3343
% 1.10/1.45
% 1.10/1.45 Low Water (keep): wt=36.000, iters=3380
% 1.10/1.45
% 1.10/1.45 Low Water (keep): wt=31.000, iters=3373
% 1.10/1.45
% 1.10/1.45 Low Water (keep): wt=30.000, iters=3371
% 1.10/1.45
% 1.10/1.45 Low Water (keep): wt=29.000, iters=3391
% 1.10/1.45
% 1.10/1.45 Low Water (keep): wt=28.000, iters=3355
% 1.10/1.45
% 1.10/1.45 Low Water (keep): wt=27.000, iters=3433
% 1.10/1.45
% 1.10/1.45 Low Water (keep): wt=25.000, iters=3389
% 1.10/1.45
% 1.10/1.45 Low Water (keep): wt=24.000, iters=3368
% 1.10/1.45
% 1.10/1.45 Low Water (keep): wt=23.000, iters=3381
% 1.10/1.45
% 113.98/114.34 Low Water (keep): wt=22.000, iters=3359
% 113.98/114.34
% 113.98/114.34 Low Water (keep): wt=21.000, iters=3334
% 113.98/114.34
% 113.98/114.34 Low Water (keep): wt=20.000, iters=3340
% 113.98/114.34
% 113.98/114.34 Low Water (keep): wt=19.000, iters=3335
% 113.98/114.34
% 113.98/114.34 Low Water (keep): wt=18.000, iters=3335
% 113.98/114.34
% 113.98/114.34 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 79 (0.00 of 1.19 sec).
% 113.98/114.34
% 113.98/114.34 Low Water (displace): id=2390, wt=111.000
% 113.98/114.34
% 113.98/114.34 Low Water (displace): id=2793, wt=103.000
% 113.98/114.34
% 113.98/114.34 Low Water (displace): id=3585, wt=83.000
% 113.98/114.34
% 113.98/114.34 Low Water (displace): id=1075, wt=75.000
% 113.98/114.34
% 113.98/114.34 Low Water (displace): id=1078, wt=55.000
% 113.98/114.34
% 113.98/114.34 Low Water (displace): id=2795, wt=51.000
% 113.98/114.34
% 113.98/114.34 Low Water (displace): id=1509, wt=47.000
% 113.98/114.34
% 113.98/114.34 Low Water (displace): id=1695, wt=43.000
% 113.98/114.34
% 113.98/114.34 Low Water (displace): id=3586, wt=41.000
% 113.98/114.34
% 113.98/114.34 Low Water (displace): id=2757, wt=40.000
% 113.98/114.34
% 113.98/114.34 Low Water (displace): id=3631, wt=39.000
% 113.98/114.34
% 113.98/114.34 Low Water (displace): id=2824, wt=38.000
% 113.98/114.34
% 113.98/114.34 Low Water (displace): id=3416, wt=37.000
% 113.98/114.34
% 113.98/114.34 Low Water (displace): id=10927, wt=35.000
% 113.98/114.34
% 113.98/114.34 Low Water (displace): id=10962, wt=34.000
% 113.98/114.34
% 113.98/114.34 Low Water (displace): id=11055, wt=33.000
% 113.98/114.34
% 113.98/114.34 Low Water (displace): id=11053, wt=32.000
% 113.98/114.34
% 113.98/114.34 Low Water (displace): id=11243, wt=17.000
% 113.98/114.34
% 113.98/114.34 Low Water (displace): id=11619, wt=16.000
% 113.98/114.34
% 113.98/114.34 Low Water (keep): wt=17.000, iters=3498
% 113.98/114.34
% 113.98/114.34 Low Water (displace): id=11929, wt=15.000
% 113.98/114.34
% 113.98/114.34 Low Water (displace): id=12025, wt=14.000
% 113.98/114.34
% 113.98/114.34 Low Water (displace): id=13460, wt=13.000
% 113.98/114.34
% 113.98/114.34 Low Water (keep): wt=16.000, iters=3340
% 113.98/114.34
% 113.98/114.34 Low Water (displace): id=17898, wt=12.000
% 113.98/114.34
% 113.98/114.34 Low Water (keep): wt=15.000, iters=4057
% 113.98/114.34
% 113.98/114.34 Low Water (keep): wt=14.000, iters=3351
% 113.98/114.34
% 113.98/114.34 Low Water (keep): wt=13.000, iters=3339
% 113.98/114.34
% 113.98/114.34 ============================== PROOF =================================
% 113.98/114.34 % SZS status Theorem
% 113.98/114.34 % SZS output start Refutation
% 113.98/114.34
% 113.98/114.34 % Proof 1 at 106.29 (+ 7.03) seconds.
% 113.98/114.34 % Length of proof is 344.
% 113.98/114.34 % Level of proof is 99.
% 113.98/114.34 % Maximum clause weight is 19.000.
% 113.98/114.34 % Given clauses 8696.
% 113.98/114.34
% 113.98/114.34 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].
% 113.98/114.34 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].
% 113.98/114.34 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 113.98/114.34 19 cn1 <-> (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))) # label(cn1) # label(axiom) # label(non_clause). [assumption].
% 113.98/114.34 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 113.98/114.34 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 113.98/114.34 29 op_implies_and -> (all X all Y implies(X,Y) = not(and(X,not(Y)))) # label(op_implies_and) # label(axiom) # label(non_clause). [assumption].
% 113.98/114.34 31 op_equiv -> (all X all Y equiv(X,Y) = and(implies(X,Y),implies(Y,X))) # label(op_equiv) # label(axiom) # label(non_clause). [assumption].
% 113.98/114.34 34 op_equiv # label(luka_op_equiv) # label(axiom). [assumption].
% 113.98/114.34 35 modus_ponens # label(luka_modus_ponens) # label(axiom). [assumption].
% 113.98/114.34 36 cn1 # label(luka_cn1) # label(axiom). [assumption].
% 113.98/114.34 37 cn2 # label(luka_cn2) # label(axiom). [assumption].
% 113.98/114.34 38 cn3 # label(luka_cn3) # label(axiom). [assumption].
% 113.98/114.34 39 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption].
% 113.98/114.34 40 op_implies_and # label(rosser_op_implies_and) # label(axiom). [assumption].
% 113.98/114.34 41 -kn2 # label(rosser_kn2) # label(negated_conjecture). [assumption].
% 113.98/114.34 54 kn2 | -is_a_theorem(implies(and(c34,c35),c34)) # label(kn2) # label(axiom). [clausify(17)].
% 113.98/114.34 55 -is_a_theorem(implies(and(c34,c35),c34)). [copy(54),unit_del(a,41)].
% 113.98/114.34 60 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(2)].
% 113.98/114.34 61 -is_a_theorem(equiv(A,B)) | B = A. [copy(60),unit_del(a,39)].
% 113.98/114.34 62 -cn2 | is_a_theorem(implies(A,implies(not(A),B))) # label(cn2) # label(axiom). [clausify(20)].
% 113.98/114.34 63 is_a_theorem(implies(A,implies(not(A),B))). [copy(62),unit_del(a,37)].
% 113.98/114.34 65 -cn3 | is_a_theorem(implies(implies(not(A),A),A)) # label(cn3) # label(axiom). [clausify(21)].
% 113.98/114.34 66 is_a_theorem(implies(implies(not(A),A),A)). [copy(65),unit_del(a,38)].
% 113.98/114.34 68 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 113.98/114.34 69 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(68),unit_del(a,35)].
% 113.98/114.34 79 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 113.98/114.34 80 not(and(A,not(B))) = implies(A,B). [copy(79),unit_del(a,40)].
% 113.98/114.34 89 -op_equiv | and(implies(A,B),implies(B,A)) = equiv(A,B) # label(op_equiv) # label(axiom). [clausify(31)].
% 113.98/114.34 90 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(89),unit_del(a,34)].
% 113.98/114.34 95 -cn1 | is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))) # label(cn1) # label(axiom). [clausify(19)].
% 113.98/114.34 96 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))). [copy(95),unit_del(a,36)].
% 113.98/114.34 124 -is_a_theorem(implies(not(A),A)) | is_a_theorem(A). [resolve(69,b,66,a)].
% 113.98/114.34 125 -is_a_theorem(A) | is_a_theorem(implies(not(A),B)). [resolve(69,b,63,a)].
% 113.98/114.34 127 -is_a_theorem(implies(implies(implies(not(A),A),A),implies(and(c34,c35),c34))). [ur(69,a,66,a,c,55,a)].
% 113.98/114.34 129 is_a_theorem(implies(and(A,not(B)),implies(implies(A,B),C))). [para(80(a,1),63(a,1,2,1))].
% 113.98/114.34 130 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))].
% 113.98/114.34 131 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(80(a,1),80(a,1,1,2))].
% 113.98/114.34 132 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(B,C),implies(A,C))). [resolve(96,a,69,b)].
% 113.98/114.34 142 -is_a_theorem(implies(and(c34,c35),implies(not(c34),c34))). [ur(69,b,96,a,c,127,a)].
% 113.98/114.34 152 -is_a_theorem(implies(implies(A,B),and(A,not(B)))) | is_a_theorem(and(A,not(B))). [para(80(a,1),124(a,1,1))].
% 113.98/114.34 224 is_a_theorem(implies(implies(implies(implies(A,B),C),D),implies(and(A,not(B)),D))). [resolve(132,a,129,a)].
% 113.98/114.34 225 is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))). [resolve(132,a,96,a)].
% 113.98/114.34 226 is_a_theorem(implies(implies(A,B),implies(implies(not(A),A),B))). [resolve(132,a,66,a)].
% 113.98/114.34 227 is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C))). [resolve(132,a,63,a)].
% 113.98/114.34 228 is_a_theorem(implies(implies(implies(implies(not(A),A),B),C),implies(implies(A,B),C))). [resolve(226,a,132,a)].
% 113.98/114.34 230 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(A),A),B)). [resolve(226,a,69,b)].
% 113.98/114.34 292 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(not(A),D),B),C))). [resolve(227,a,132,a)].
% 113.98/114.34 294 -is_a_theorem(implies(implies(not(A),B),C)) | is_a_theorem(implies(A,C)). [resolve(227,a,69,b)].
% 113.98/114.34 295 -is_a_theorem(implies(implies(not(and(c34,c35)),A),implies(not(c34),c34))). [ur(69,b,227,a,c,142,a)].
% 113.98/114.34 342 implies(implies(A,B),and(B,not(A))) = not(equiv(A,B)). [para(90(a,1),131(a,1,1)),flip(a)].
% 113.98/114.34 411 is_a_theorem(implies(A,implies(implies(B,C),implies(not(A),C)))). [resolve(294,a,96,a)].
% 113.98/114.34 412 is_a_theorem(implies(A,A)). [resolve(294,a,66,a)].
% 113.98/114.34 414 -is_a_theorem(implies(implies(implies(A,B),C),D)) | is_a_theorem(implies(and(A,not(B)),D)). [para(80(a,1),294(a,1,1,1))].
% 113.98/114.34 416 is_a_theorem(implies(not(implies(A,A)),B)). [resolve(412,a,125,a)].
% 113.98/114.34 436 is_a_theorem(implies(implies(A,B),implies(not(implies(C,C)),B))). [resolve(416,a,132,a)].
% 113.98/114.34 628 is_a_theorem(implies(implies(not(A),A),implies(implies(B,C),implies(not(A),C)))). [resolve(411,a,230,a)].
% 113.98/114.34 629 is_a_theorem(implies(implies(implies(implies(A,B),implies(not(C),B)),D),implies(C,D))). [resolve(411,a,132,a)].
% 113.98/114.34 746 is_a_theorem(implies(A,implies(not(implies(B,B)),C))). [resolve(436,a,294,a)].
% 113.98/114.34 778 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),implies(D,C))). [resolve(746,a,132,a)].
% 113.98/114.34 1285 is_a_theorem(implies(not(equiv(A,A)),and(A,not(A)))). [para(342(a,1),130(a,1,1))].
% 113.98/114.34 1352 is_a_theorem(implies(implies(and(A,not(A)),B),implies(not(equiv(A,A)),B))). [resolve(1285,a,132,a)].
% 113.98/114.34 1726 -is_a_theorem(implies(not(c34),not(and(c34,c35)))). [ur(132,b,295,a)].
% 113.98/114.34 2270 -is_a_theorem(implies(implies(not(implies(A,A)),B),C)) | is_a_theorem(implies(D,C)). [resolve(778,a,69,b)].
% 113.98/114.34 3003 is_a_theorem(implies(A,implies(B,B))). [resolve(2270,a,66,a)].
% 113.98/114.34 3010 is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))). [resolve(3003,a,132,a)].
% 113.98/114.34 3354 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(D,D),B),C))). [resolve(3010,a,132,a)].
% 113.98/114.34 3356 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(implies(C,B)). [resolve(3010,a,69,b)].
% 113.98/114.34 3431 is_a_theorem(implies(A,implies(B,implies(not(B),C)))). [resolve(3356,a,227,a)].
% 113.98/114.34 3432 is_a_theorem(implies(A,implies(implies(not(B),B),B))). [resolve(3356,a,226,a)].
% 113.98/114.34 3513 is_a_theorem(implies(implies(implies(A,implies(not(A),B)),C),implies(D,C))). [resolve(3431,a,132,a)].
% 113.98/114.34 3803 is_a_theorem(implies(implies(implies(implies(not(A),A),A),B),implies(C,B))). [resolve(3432,a,132,a)].
% 113.98/114.34 5426 -is_a_theorem(implies(implies(implies(not(A),A),A),B)) | is_a_theorem(implies(C,B)). [resolve(3803,a,69,b)].
% 113.98/114.34 6318 -is_a_theorem(implies(not(A),A)) | is_a_theorem(implies(implies(B,C),implies(not(A),C))). [resolve(628,a,69,b)].
% 113.98/114.34 6984 -is_a_theorem(implies(and(A,not(A)),B)) | is_a_theorem(implies(not(equiv(A,A)),B)). [resolve(1352,a,69,b)].
% 113.98/114.34 7295 is_a_theorem(implies(A,implies(implies(implies(B,B),C),C))). [resolve(3354,a,5426,a)].
% 113.98/114.34 7305 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(implies(D,D),B),C)). [resolve(3354,a,69,b)].
% 113.98/114.34 7320 is_a_theorem(implies(implies(implies(implies(implies(A,A),B),B),C),implies(D,C))). [resolve(7295,a,132,a)].
% 113.98/114.34 7322 is_a_theorem(implies(implies(implies(A,A),B),B)). [resolve(7295,a,124,a)].
% 113.98/114.34 7364 is_a_theorem(implies(implies(A,B),implies(implies(implies(C,C),A),B))). [resolve(7322,a,132,a)].
% 113.98/114.34 7365 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(B). [resolve(7322,a,69,b)].
% 113.98/114.34 7531 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(C,C),A),B)). [resolve(7364,a,69,b)].
% 113.98/114.34 8015 is_a_theorem(implies(implies(implies(A,A),implies(implies(B,B),C)),implies(D,C))). [resolve(7531,a,3010,a)].
% 113.98/114.34 9512 is_a_theorem(implies(implies(implies(A,A),B),implies(implies(B,C),implies(D,C)))). [resolve(7305,a,96,a)].
% 113.98/114.34 9571 -is_a_theorem(implies(implies(implies(implies(A,A),B),B),C)) | is_a_theorem(implies(D,C)). [resolve(7320,a,69,b)].
% 113.98/114.34 10113 -is_a_theorem(implies(implies(A,A),implies(implies(B,B),C))) | is_a_theorem(implies(D,C)). [resolve(8015,a,69,b)].
% 113.98/114.34 10383 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(implies(implies(B,C),implies(D,C))). [resolve(9512,a,69,b)].
% 113.98/114.34 11083 is_a_theorem(implies(A,implies(and(B,not(B)),C))). [resolve(224,a,9571,a)].
% 113.98/114.34 11113 is_a_theorem(implies(and(A,not(A)),B)). [resolve(11083,a,7365,a)].
% 113.98/114.34 11173 is_a_theorem(implies(not(equiv(A,A)),B)). [back_unit_del(6984),unit_del(a,11113)].
% 113.98/114.34 11397 is_a_theorem(implies(implies(A,B),implies(not(equiv(C,C)),B))). [resolve(11173,a,6318,a)].
% 113.98/114.34 12288 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),C),implies(D,C))). [resolve(11397,a,10383,a)].
% 113.98/114.34 12718 is_a_theorem(implies(A,implies(B,equiv(C,C)))). [resolve(12288,a,5426,a)].
% 113.98/114.34 12740 is_a_theorem(implies(implies(implies(A,equiv(B,B)),C),implies(D,C))). [resolve(12718,a,10383,a)].
% 113.98/114.34 12743 is_a_theorem(implies(A,equiv(B,B))). [resolve(12718,a,10113,a)].
% 113.98/114.34 12821 is_a_theorem(implies(implies(equiv(A,A),B),implies(C,B))). [resolve(12743,a,10383,a)].
% 113.98/114.34 13193 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(equiv(D,D),B),C))). [resolve(12821,a,132,a)].
% 113.98/114.34 13242 -is_a_theorem(implies(implies(implies(not(A),A),B),C)) | is_a_theorem(implies(implies(A,B),C)). [resolve(228,a,69,b)].
% 113.98/114.34 14395 is_a_theorem(implies(A,implies(implies(equiv(B,B),C),C))). [resolve(13193,a,9571,a)].
% 113.98/114.34 14411 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(equiv(D,D),B),C)). [resolve(13193,a,69,b)].
% 113.98/114.34 14424 is_a_theorem(implies(implies(implies(implies(equiv(A,A),B),B),C),implies(D,C))). [resolve(14395,a,10383,a)].
% 113.98/114.34 14436 is_a_theorem(implies(implies(equiv(A,A),B),B)). [resolve(14395,a,7365,a)].
% 113.98/114.34 14476 is_a_theorem(implies(implies(A,B),implies(implies(equiv(C,C),A),B))). [resolve(14436,a,132,a)].
% 113.98/114.34 14477 -is_a_theorem(implies(equiv(A,A),B)) | is_a_theorem(B). [resolve(14436,a,69,b)].
% 113.98/114.34 14656 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(equiv(C,C),A),B)). [resolve(14476,a,69,b)].
% 113.98/114.34 16734 is_a_theorem(implies(implies(equiv(A,A),B),implies(implies(B,C),implies(D,C)))). [resolve(14411,a,9512,a)].
% 113.98/114.34 16806 -is_a_theorem(implies(implies(implies(equiv(A,A),B),B),C)) | is_a_theorem(implies(D,C)). [resolve(14424,a,69,b)].
% 113.98/114.34 18186 -is_a_theorem(implies(equiv(A,A),B)) | is_a_theorem(implies(implies(B,C),implies(D,C))). [resolve(16734,a,69,b)].
% 113.98/114.34 19398 is_a_theorem(implies(A,implies(implies(implies(not(equiv(B,B)),C),D),D))). [resolve(292,a,16806,a)].
% 113.98/114.34 19405 is_a_theorem(implies(A,implies(implies(implies(not(implies(B,B)),C),D),D))). [resolve(292,a,9571,a)].
% 113.98/114.34 19412 is_a_theorem(implies(A,implies(implies(implies(not(not(B)),C),B),B))). [resolve(292,a,5426,a)].
% 113.98/114.34 19422 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(implies(not(A),D),B),C)). [resolve(292,a,69,b)].
% 113.98/114.34 19445 is_a_theorem(implies(implies(implies(not(not(A)),B),A),A)). [resolve(19412,a,14477,a)].
% 113.98/114.34 19481 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(not(A)),C),A),B))). [resolve(19445,a,132,a)].
% 113.98/114.34 19482 -is_a_theorem(implies(implies(not(not(A)),B),A)) | is_a_theorem(A). [resolve(19445,a,69,b)].
% 113.98/114.34 19511 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),C),C)). [resolve(19398,a,19482,a)].
% 113.98/114.34 19558 -is_a_theorem(implies(implies(not(equiv(A,A)),B),C)) | is_a_theorem(C). [resolve(19511,a,69,b)].
% 113.98/114.34 19576 -is_a_theorem(not(equiv(not(equiv(A,A)),B))) | is_a_theorem(and(B,not(not(equiv(A,A))))). [para(342(a,1),19558(a,1))].
% 113.98/114.34 19589 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),C)). [resolve(19405,a,19558,a)].
% 113.98/114.34 19635 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(implies(C,C)),D),A),B))). [resolve(19589,a,132,a)].
% 113.98/114.34 19768 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(not(A)),C),A),B)). [resolve(19481,a,69,b)].
% 113.98/114.34 20429 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),and(A,not(A))),C)). [resolve(19768,a,11113,a),rewrite([80(3)])].
% 113.98/114.34 21114 is_a_theorem(implies(and(not(implies(A,A)),not(B)),C)). [resolve(414,a,20429,a)].
% 113.98/114.34 21117 is_a_theorem(implies(and(not(equiv(A,A)),not(B)),C)). [resolve(414,a,19511,a)].
% 113.98/114.34 21119 is_a_theorem(implies(and(not(not(A)),not(B)),A)). [resolve(414,a,19445,a)].
% 113.98/114.34 21126 is_a_theorem(implies(and(A,not(equiv(B,B))),implies(C,D))). [resolve(414,a,12740,a)].
% 113.98/114.34 21132 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),implies(C,D))). [resolve(414,a,7320,a)].
% 113.98/114.34 21134 is_a_theorem(implies(and(implies(not(A),A),not(A)),implies(B,C))). [resolve(414,a,3803,a)].
% 113.98/114.34 21135 is_a_theorem(implies(and(A,not(implies(not(A),B))),implies(C,D))). [resolve(414,a,3513,a)].
% 113.98/114.34 21144 is_a_theorem(implies(and(A,not(B)),implies(implies(implies(not(A),C),B),D))). [resolve(414,a,292,a)].
% 113.98/114.34 21146 is_a_theorem(implies(and(not(A),not(B)),implies(A,C))). [resolve(414,a,227,a)].
% 113.98/114.34 21147 is_a_theorem(implies(and(implies(A,B),not(implies(C,B))),implies(implies(C,A),D))). [resolve(414,a,225,a)].
% 113.98/114.34 21158 is_a_theorem(implies(implies(equiv(A,A),and(not(not(B)),not(C))),B)). [resolve(21119,a,14656,a)].
% 113.98/114.34 21172 is_a_theorem(implies(implies(implies(not(not(A)),B),and(not(not(A)),not(B))),A)). [resolve(21119,a,230,a),rewrite([80(5)])].
% 113.98/114.34 21173 is_a_theorem(implies(implies(A,B),implies(and(not(not(A)),not(C)),B))). [resolve(21119,a,132,a)].
% 113.98/114.34 21462 is_a_theorem(implies(implies(equiv(A,A),and(not(implies(B,B)),not(C))),D)). [resolve(21114,a,14656,a)].
% 113.98/114.34 21510 is_a_theorem(implies(implies(implies(A,A),and(not(equiv(B,B)),not(C))),D)). [resolve(21117,a,7531,a)].
% 113.98/114.34 21558 is_a_theorem(implies(implies(implies(not(A),B),and(not(A),not(B))),implies(A,C))). [resolve(21146,a,230,a),rewrite([80(4)])].
% 113.98/114.34 21859 is_a_theorem(implies(implies(implies(A,B),C),implies(and(D,not(equiv(E,E))),C))). [resolve(21126,a,132,a)].
% 113.98/114.34 22167 is_a_theorem(implies(and(implies(not(A),A),not(A)),not(equiv(B,C)))). [para(342(a,1),21134(a,1,2))].
% 113.98/114.34 22205 is_a_theorem(implies(and(A,not(implies(not(A),B))),not(equiv(C,D)))). [para(342(a,1),21135(a,1,2))].
% 113.98/114.34 22474 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),not(equiv(C,D)))). [para(342(a,1),21132(a,1,2))].
% 113.98/114.34 22822 is_a_theorem(implies(and(not(not(not(equiv(A,A)))),not(B)),C)). [resolve(21173,a,19558,a)].
% 113.98/114.34 22833 is_a_theorem(implies(implies(implies(and(not(not(A)),not(B)),A),C),implies(D,C))). [resolve(21173,a,10383,a)].
% 113.98/114.34 22987 is_a_theorem(implies(implies(implies(A,A),and(not(not(not(equiv(B,B)))),not(C))),D)). [resolve(22822,a,7531,a)].
% 113.98/114.34 25247 is_a_theorem(implies(and(A,implies(B,not(A))),implies(not(equiv(not(A),B)),C))). [para(342(a,1),21144(a,1,2,1)),rewrite([80(4)])].
% 113.98/114.34 25560 is_a_theorem(and(equiv(A,A),implies(not(implies(B,B)),C))). [resolve(21462,a,152,a),rewrite([80(6)])].
% 113.98/114.34 25813 is_a_theorem(and(implies(A,A),implies(not(equiv(B,B)),C))). [resolve(21510,a,152,a),rewrite([80(6)])].
% 113.98/114.34 28623 -is_a_theorem(implies(implies(implies(A,B),implies(not(C),B)),D)) | is_a_theorem(implies(C,D)). [resolve(629,a,69,b)].
% 113.98/114.34 47645 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),and(not(not(C)),not(D))),C)). [resolve(19422,a,21158,a)].
% 113.98/114.34 50859 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(implies(C,C)),D),A),B)). [resolve(19635,a,69,b)].
% 113.98/114.34 53143 is_a_theorem(implies(implies(not(A),and(not(not(A)),not(not(A)))),A)). [resolve(21172,a,13242,a)].
% 113.98/114.34 53208 -is_a_theorem(implies(not(A),and(not(not(A)),not(not(A))))) | is_a_theorem(A). [resolve(53143,a,69,b)].
% 113.98/114.34 53245 is_a_theorem(implies(implies(A,and(not(A),not(A))),implies(A,B))). [resolve(21558,a,13242,a)].
% 113.98/114.34 53288 is_a_theorem(implies(implies(implies(not(A),B),and(not(A),not(A))),implies(A,C))). [resolve(53245,a,19422,a)].
% 113.98/114.34 53434 is_a_theorem(implies(A,implies(and(B,not(equiv(C,C))),D))). [resolve(21859,a,16806,a)].
% 113.98/114.34 53477 is_a_theorem(implies(implies(implies(and(A,not(equiv(B,B))),C),D),implies(E,D))). [resolve(53434,a,18186,a)].
% 113.98/114.34 57920 -is_a_theorem(and(A,implies(B,not(A)))) | is_a_theorem(implies(not(equiv(not(A),B)),C)). [resolve(25247,a,69,b)].
% 113.98/114.34 59059 is_a_theorem(implies(A,implies(B,implies(not(A),C)))). [resolve(28623,a,22833,a)].
% 113.98/114.34 59068 is_a_theorem(implies(A,implies(implies(implies(not(A),B),C),implies(D,C)))). [resolve(28623,a,9512,a)].
% 113.98/114.34 59148 is_a_theorem(implies(implies(implies(A,implies(not(B),C)),D),implies(B,D))). [resolve(59059,a,132,a)].
% 113.98/114.34 63992 is_a_theorem(implies(A,implies(B,implies(C,implies(not(B),D))))). [resolve(59148,a,3356,a)].
% 113.98/114.34 64048 -is_a_theorem(implies(implies(A,implies(not(not(c34)),B)),not(and(c34,c35)))). [ur(69,b,59148,a,c,1726,a)].
% 113.98/114.34 109203 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),and(not(equiv(C,C)),not(D))),E)). [resolve(50859,a,21117,a)].
% 113.98/114.34 109992 is_a_theorem(implies(and(and(A,not(equiv(B,B))),not(C)),implies(D,E))). [resolve(53477,a,414,a)].
% 113.98/114.34 110144 is_a_theorem(implies(and(and(A,not(equiv(B,B))),not(C)),not(equiv(D,E)))). [para(342(a,1),109992(a,1,2))].
% 113.98/114.34 113449 is_a_theorem(implies(not(equiv(not(implies(A,A)),not(equiv(B,B)))),C)). [resolve(57920,a,25813,a)].
% 113.98/114.34 113452 is_a_theorem(implies(not(equiv(not(equiv(A,A)),not(implies(B,B)))),C)). [resolve(57920,a,25560,a)].
% 113.98/114.34 113492 is_a_theorem(equiv(not(implies(A,A)),not(equiv(B,B)))). [resolve(113449,a,53208,a)].
% 113.98/114.34 113589 not(equiv(A,A)) = not(implies(B,B)). [resolve(113492,a,61,a)].
% 113.98/114.34 113597 not(equiv(A,A)) = c_0. [new_symbol(113589)].
% 113.98/114.34 113601 not(implies(A,A)) = c_0. [back_rewrite(113589),rewrite([113597(2)]),flip(a)].
% 113.98/114.34 113612 is_a_theorem(implies(c_0,A)). [back_rewrite(113452),rewrite([113597(2),113601(3),113597(4)])].
% 113.98/114.34 113620 is_a_theorem(implies(and(and(A,c_0),not(B)),not(equiv(C,D)))). [back_rewrite(110144),rewrite([113597(2)])].
% 113.98/114.34 113634 is_a_theorem(implies(implies(implies(c_0,A),and(c_0,not(B))),C)). [back_rewrite(109203),rewrite([113601(2),113597(4)])].
% 113.98/114.34 113981 is_a_theorem(implies(implies(implies(c_0,A),and(not(not(B)),not(C))),B)). [back_rewrite(47645),rewrite([113597(2)])].
% 113.98/114.34 114188 is_a_theorem(implies(implies(implies(A,A),and(not(not(c_0)),not(B))),C)). [back_rewrite(22987),rewrite([113597(3)])].
% 113.98/114.34 114259 -is_a_theorem(not(equiv(c_0,A))) | is_a_theorem(and(A,not(c_0))). [back_rewrite(19576),rewrite([113597(2),113597(6)])].
% 113.98/114.34 114263 -is_a_theorem(implies(implies(c_0,A),B)) | is_a_theorem(B). [back_rewrite(19558),rewrite([113597(2)])].
% 113.98/114.34 116061 implies(A,equiv(B,B)) = not(and(A,c_0)). [para(113597(a,1),80(a,1,1,2)),flip(a)].
% 113.98/114.34 116190 is_a_theorem(implies(and(implies(not(A),A),not(A)),c_0)). [para(113597(a,1),22167(a,1,2))].
% 113.98/114.34 116191 is_a_theorem(implies(and(A,not(implies(not(A),B))),c_0)). [para(113597(a,1),22205(a,1,2))].
% 113.98/114.34 116213 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),c_0)). [para(113597(a,1),22474(a,1,2))].
% 113.98/114.34 117246 implies(A,implies(B,B)) = not(and(A,c_0)). [para(113601(a,1),80(a,1,1,2)),flip(a)].
% 113.98/114.34 126203 -is_a_theorem(implies(not(and(equiv(A,A),c_0)),B)) | is_a_theorem(B). [para(116061(a,1),7365(a,1,1))].
% 113.98/114.34 127292 is_a_theorem(implies(implies(c_0,A),implies(and(implies(not(B),B),not(B)),A))). [resolve(116190,a,132,a)].
% 113.98/114.34 127406 is_a_theorem(implies(implies(c_0,A),implies(and(B,not(implies(not(B),C))),A))). [resolve(116191,a,132,a)].
% 113.98/114.34 129119 is_a_theorem(and(implies(c_0,A),implies(c_0,B))). [resolve(113634,a,152,a),rewrite([80(6)])].
% 113.98/114.34 129153 is_a_theorem(implies(not(equiv(not(implies(c_0,A)),c_0)),B)). [resolve(129119,a,57920,a)].
% 113.98/114.34 129333 is_a_theorem(equiv(not(implies(c_0,A)),c_0)). [resolve(129153,a,53208,a)].
% 113.98/114.34 129426 not(implies(c_0,A)) = c_0. [resolve(129333,a,61,a),flip(a)].
% 113.98/114.34 129428 implies(A,implies(c_0,B)) = not(and(A,c_0)). [para(129426(a,1),80(a,1,1,2)),flip(a)].
% 113.98/114.34 134398 is_a_theorem(implies(and(implies(not(and(equiv(A,A),c_0)),B),not(B)),c_0)). [para(116061(a,1),116213(a,1,1,1,1))].
% 113.98/114.34 141161 is_a_theorem(implies(and(and(A,c_0),not(B)),c_0)). [para(113597(a,1),113620(a,1,2))].
% 113.98/114.34 141240 is_a_theorem(implies(implies(c_0,A),implies(and(and(B,c_0),not(C)),A))). [resolve(141161,a,132,a)].
% 113.98/114.34 164285 is_a_theorem(implies(not(equiv(c_0,not(not(A)))),A)). [para(342(a,1),113981(a,1,1))].
% 113.98/114.34 164356 is_a_theorem(implies(implies(A,B),implies(not(equiv(c_0,not(not(A)))),B))). [resolve(164285,a,132,a)].
% 113.98/114.34 166258 is_a_theorem(and(implies(A,A),implies(not(not(c_0)),B))). [resolve(114188,a,152,a),rewrite([80(7)])].
% 113.98/114.34 166296 is_a_theorem(implies(not(equiv(c_0,not(not(c_0)))),A)). [resolve(166258,a,57920,a),rewrite([113601(2)])].
% 113.98/114.34 166366 is_a_theorem(equiv(c_0,not(not(c_0)))). [resolve(166296,a,53208,a)].
% 113.98/114.34 166459 not(not(c_0)) = c_0. [resolve(166366,a,61,a)].
% 113.98/114.34 166478 not(and(A,c_0)) = implies(A,not(c_0)). [para(166459(a,1),80(a,1,1,2))].
% 113.98/114.34 166479 is_a_theorem(not(c_0)). [para(166459(a,1),124(a,1,1)),unit_del(a,113612)].
% 113.98/114.34 166486 implies(implies(not(c_0),A),and(A,c_0)) = not(equiv(not(c_0),A)). [para(166459(a,1),342(a,1,2,2))].
% 113.98/114.34 166489 is_a_theorem(implies(A,not(c_0))). [para(166459(a,1),3431(a,1,2,2,1)),rewrite([129428(5),166478(5),117246(6),166478(3)])].
% 113.98/114.34 167118 is_a_theorem(implies(and(implies(implies(equiv(A,A),not(c_0)),B),not(B)),c_0)). [back_rewrite(134398),rewrite([166478(4)])].
% 113.98/114.34 167320 implies(A,implies(c_0,B)) = implies(A,not(c_0)). [back_rewrite(129428),rewrite([166478(6)])].
% 113.98/114.34 167554 -is_a_theorem(implies(implies(equiv(A,A),not(c_0)),B)) | is_a_theorem(B). [back_rewrite(126203),rewrite([166478(4)])].
% 113.98/114.34 167721 implies(A,implies(B,B)) = implies(A,not(c_0)). [back_rewrite(117246),rewrite([166478(5)])].
% 113.98/114.34 168080 implies(A,equiv(B,B)) = implies(A,not(c_0)). [back_rewrite(116061),rewrite([166478(5)])].
% 113.98/114.34 168624 is_a_theorem(implies(implies(not(c_0),A),implies(B,A))). [resolve(166489,a,18186,a)].
% 113.98/114.34 169688 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(not(c_0),B),C))). [resolve(168624,a,132,a)].
% 113.98/114.34 188395 is_a_theorem(implies(and(and(A,c_0),not(B)),C)). [resolve(141240,a,114263,a)].
% 113.98/114.34 199455 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(equiv(c_0,not(not(A)))),B)). [resolve(164356,a,69,b)].
% 113.98/114.34 212808 is_a_theorem(implies(A,implies(implies(not(c_0),B),B))). [resolve(169688,a,16806,a)].
% 113.98/114.34 212813 is_a_theorem(implies(implies(A,B),implies(implies(not(c_0),A),B))). [resolve(169688,a,13242,a)].
% 113.98/114.34 212839 is_a_theorem(implies(implies(not(c_0),A),A)). [resolve(212808,a,167554,a)].
% 113.98/114.34 212975 -is_a_theorem(implies(not(c_0),A)) | is_a_theorem(A). [resolve(212839,a,69,b)].
% 113.98/114.34 216852 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(c_0),A),B)). [resolve(212813,a,69,b)].
% 113.98/114.34 218343 is_a_theorem(implies(implies(not(c_0),and(and(A,c_0),not(B))),C)). [resolve(216852,a,188395,a)].
% 113.98/114.34 226079 is_a_theorem(and(not(c_0),implies(and(A,c_0),B))). [resolve(218343,a,152,a),rewrite([80(7)])].
% 113.98/114.34 226113 is_a_theorem(implies(not(equiv(c_0,and(A,c_0))),B)). [resolve(226079,a,57920,a),rewrite([166459(3)])].
% 113.98/114.34 226182 is_a_theorem(equiv(c_0,and(A,c_0))). [resolve(226113,a,53208,a)].
% 113.98/114.34 226276 and(A,c_0) = c_0. [resolve(226182,a,61,a)].
% 113.98/114.34 226325 implies(implies(not(c_0),A),c_0) = not(equiv(not(c_0),A)). [back_rewrite(166486),rewrite([226276(5)])].
% 113.98/114.34 226326 implies(A,not(c_0)) = not(c_0). [back_rewrite(166478),rewrite([226276(2)]),flip(a)].
% 113.98/114.34 226347 implies(A,equiv(B,B)) = not(c_0). [back_rewrite(168080),rewrite([226326(5)])].
% 113.98/114.34 226354 implies(A,implies(B,B)) = not(c_0). [back_rewrite(167721),rewrite([226326(5)])].
% 113.98/114.34 226371 implies(A,implies(c_0,B)) = not(c_0). [back_rewrite(167320),rewrite([226326(6)])].
% 113.98/114.34 226374 is_a_theorem(implies(and(implies(not(c_0),A),not(A)),c_0)). [back_rewrite(167118),rewrite([226326(4)])].
% 113.98/114.34 226422 and(not(c_0),implies(not(c_0),A)) = equiv(A,not(c_0)). [para(226326(a,1),90(a,1,1))].
% 113.98/114.34 226423 and(implies(not(c_0),A),not(c_0)) = equiv(not(c_0),A). [para(226326(a,1),90(a,1,2))].
% 113.98/114.34 228893 is_a_theorem(implies(implies(c_0,A),implies(and(implies(not(c_0),B),not(B)),A))). [resolve(226374,a,132,a)].
% 113.98/114.34 229607 implies(not(c_0),c_0) = c_0. [para(113597(a,1),226325(a,2)),rewrite([226326(5)])].
% 113.98/114.34 229635 not(equiv(not(c_0),equiv(A,A))) = c_0. [para(226347(a,1),226325(a,1,1)),rewrite([229607(4)]),flip(a)].
% 113.98/114.34 229636 not(equiv(not(c_0),implies(A,A))) = c_0. [para(226354(a,1),226325(a,1,1)),rewrite([229607(4)]),flip(a)].
% 113.98/114.34 229637 not(equiv(not(c_0),implies(c_0,A))) = c_0. [para(226371(a,1),226325(a,1,1)),rewrite([229607(4)]),flip(a)].
% 113.98/114.34 229640 is_a_theorem(implies(implies(not(c_0),A),implies(implies(A,c_0),c_0))). [para(229607(a,1),96(a,1,2,2))].
% 113.98/114.34 229665 is_a_theorem(implies(and(implies(A,c_0),not(c_0)),implies(implies(not(c_0),A),B))). [para(229607(a,1),21147(a,1,1,2,1))].
% 113.98/114.34 229669 is_a_theorem(implies(A,implies(implies(implies(not(A),B),c_0),c_0))). [para(229607(a,1),59068(a,1,2,2))].
% 113.98/114.34 229695 implies(A,equiv(not(c_0),equiv(B,B))) = not(c_0). [para(229635(a,1),80(a,1,1,2)),rewrite([226276(2)]),flip(a)].
% 113.98/114.34 229696 is_a_theorem(equiv(not(c_0),equiv(A,A))). [para(229635(a,1),124(a,1,1)),rewrite([229695(6)]),unit_del(a,166479)].
% 113.98/114.34 229743 equiv(A,A) = not(c_0). [resolve(229696,a,61,a)].
% 113.98/114.34 230334 implies(A,equiv(not(c_0),implies(B,B))) = not(c_0). [para(229636(a,1),80(a,1,1,2)),rewrite([226276(2)]),flip(a)].
% 113.98/114.34 230335 is_a_theorem(equiv(not(c_0),implies(A,A))). [para(229636(a,1),124(a,1,1)),rewrite([230334(6)]),unit_del(a,166479)].
% 113.98/114.34 230396 implies(A,A) = not(c_0). [resolve(230335,a,61,a)].
% 113.98/114.34 231438 and(not(c_0),not(c_0)) = not(c_0). [para(230396(a,1),90(a,1,1)),rewrite([230396(3),229743(6)])].
% 113.98/114.34 231439 is_a_theorem(implies(implies(A,B),implies(not(c_0),implies(A,B)))). [para(230396(a,1),96(a,1,2,1))].
% 113.98/114.34 231440 implies(A,and(B,not(B))) = implies(A,c_0). [para(230396(a,1),131(a,1,1,2)),rewrite([80(4)]),flip(a)].
% 113.98/114.34 231485 implies(A,equiv(not(c_0),implies(c_0,B))) = not(c_0). [para(229637(a,1),80(a,1,1,2)),rewrite([226276(2)]),flip(a)].
% 113.98/114.34 231486 is_a_theorem(equiv(not(c_0),implies(c_0,A))). [para(229637(a,1),124(a,1,1)),rewrite([231485(7)]),unit_del(a,166479)].
% 113.98/114.34 231583 implies(c_0,A) = not(c_0). [resolve(231486,a,61,a)].
% 113.98/114.34 231790 is_a_theorem(implies(not(c_0),implies(and(implies(not(c_0),A),not(A)),B))). [back_rewrite(228893),rewrite([231583(2)])].
% 113.98/114.34 231792 is_a_theorem(implies(not(c_0),implies(and(A,not(implies(not(A),B))),C))). [back_rewrite(127406),rewrite([231583(2)])].
% 113.98/114.34 231793 is_a_theorem(implies(not(c_0),implies(and(implies(not(A),A),not(A)),B))). [back_rewrite(127292),rewrite([231583(2)])].
% 113.98/114.34 231796 and(implies(A,c_0),not(c_0)) = equiv(A,c_0). [para(231583(a,1),90(a,1,2))].
% 113.98/114.34 231797 is_a_theorem(implies(implies(A,c_0),implies(not(c_0),implies(A,B)))). [para(231583(a,1),96(a,1,2,1))].
% 113.98/114.34 231798 implies(A,and(c_0,not(B))) = implies(A,c_0). [para(231583(a,1),131(a,1,1,2)),rewrite([80(4)]),flip(a)].
% 113.98/114.34 231801 implies(not(c_0),and(A,not(c_0))) = not(equiv(c_0,A)). [para(231583(a,1),342(a,1,1))].
% 113.98/114.34 231830 is_a_theorem(implies(and(A,not(c_0)),implies(not(equiv(not(A),c_0)),B))). [para(231583(a,1),25247(a,1,1,2))].
% 113.98/114.34 231853 is_a_theorem(implies(equiv(A,c_0),implies(implies(not(c_0),A),B))). [back_rewrite(229665),rewrite([231796(5)])].
% 113.98/114.34 231861 implies(implies(A,c_0),and(and(B,not(B)),not(A))) = not(equiv(A,and(B,not(B)))). [para(231440(a,1),342(a,1,1))].
% 113.98/114.34 231887 implies(and(A,not(A)),c_0) = not(c_0). [para(231440(a,1),230396(a,1))].
% 113.98/114.34 232199 equiv(and(A,not(A)),c_0) = not(c_0). [para(231887(a,1),90(a,1,1)),rewrite([231440(6),230396(5),231438(5)]),flip(a)].
% 113.98/114.34 232219 and(A,not(A)) = c_0. [para(232199(a,1),61(a,1)),flip(b),unit_del(a,166479)].
% 113.98/114.34 232223 implies(implies(A,c_0),c_0) = not(equiv(A,c_0)). [back_rewrite(231861),rewrite([232219(4),231798(6),232219(6)])].
% 113.98/114.34 232236 is_a_theorem(implies(A,not(equiv(implies(not(A),B),c_0)))). [back_rewrite(229669),rewrite([232223(6)])].
% 113.98/114.34 232248 is_a_theorem(implies(implies(not(c_0),A),not(equiv(A,c_0)))). [back_rewrite(229640),rewrite([232223(7)])].
% 113.98/114.34 232791 is_a_theorem(implies(A,implies(not(equiv(not(A),c_0)),implies(B,c_0)))). [para(232223(a,1),59068(a,1,2,1))].
% 113.98/114.34 233135 -is_a_theorem(implies(not(c_0),A)) | is_a_theorem(not(equiv(A,c_0))). [resolve(232248,a,69,b)].
% 113.98/114.34 233623 is_a_theorem(not(equiv(implies(A,implies(B,implies(not(A),C))),c_0))). [resolve(233135,a,63992,a)].
% 113.98/114.34 233709 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(c_0),implies(A,B))). [resolve(231439,a,69,b)].
% 113.98/114.34 233907 is_a_theorem(implies(not(c_0),implies(equiv(A,c_0),implies(implies(not(c_0),A),B)))). [resolve(233709,a,231853,a)].
% 113.98/114.34 237490 is_a_theorem(implies(A,implies(not(equiv(not(A),c_0)),c_0))). [para(229607(a,1),232791(a,1,2,2))].
% 113.98/114.34 237543 -is_a_theorem(A) | is_a_theorem(implies(not(equiv(not(A),c_0)),c_0)). [resolve(237490,a,69,b)].
% 113.98/114.34 239868 is_a_theorem(implies(and(implies(not(c_0),A),not(A)),B)). [resolve(231790,a,212975,a)].
% 113.98/114.34 239892 is_a_theorem(implies(not(equiv(c_0,not(implies(implies(not(c_0),A),A)))),B)). [resolve(239868,a,199455,a),rewrite([80(7)])].
% 113.98/114.34 239953 is_a_theorem(implies(and(A,not(implies(not(A),B))),C)). [resolve(231792,a,212975,a)].
% 113.98/114.34 239962 is_a_theorem(implies(not(equiv(c_0,not(implies(A,implies(not(A),B))))),C)). [resolve(239953,a,199455,a),rewrite([80(6)])].
% 113.98/114.34 240000 is_a_theorem(implies(and(implies(not(A),A),not(A)),B)). [resolve(231793,a,212975,a)].
% 113.98/114.34 240007 is_a_theorem(implies(implies(not(c_0),and(implies(not(A),A),not(A))),B)). [resolve(240000,a,216852,a)].
% 113.98/114.34 240688 is_a_theorem(equiv(c_0,not(implies(implies(not(c_0),A),A)))). [resolve(239892,a,53208,a)].
% 113.98/114.34 240693 not(implies(implies(not(c_0),A),A)) = c_0. [resolve(240688,a,61,a)].
% 113.98/114.34 240695 implies(A,implies(implies(not(c_0),B),B)) = not(c_0). [para(240693(a,1),80(a,1,1,2)),rewrite([226276(2)]),flip(a)].
% 113.98/114.34 240708 equiv(implies(implies(not(c_0),A),A),not(c_0)) = not(c_0). [para(240695(a,1),226422(a,1,2)),rewrite([231438(5)]),flip(a)].
% 113.98/114.34 240729 implies(implies(not(c_0),A),A) = not(c_0). [para(240708(a,1),61(a,1)),flip(b),unit_del(a,166479)].
% 113.98/114.34 240732 and(implies(A,implies(not(c_0),A)),not(c_0)) = equiv(A,implies(not(c_0),A)). [para(240729(a,1),90(a,1,2))].
% 113.98/114.34 240963 is_a_theorem(equiv(c_0,not(implies(A,implies(not(A),B))))). [resolve(239962,a,53208,a)].
% 113.98/114.34 240972 not(implies(A,implies(not(A),B))) = c_0. [resolve(240963,a,61,a)].
% 113.98/114.34 241117 implies(A,implies(B,implies(not(B),C))) = not(c_0). [para(240972(a,1),80(a,1,1,2)),rewrite([226276(2)]),flip(a)].
% 113.98/114.34 241132 equiv(implies(A,implies(not(A),B)),not(c_0)) = not(c_0). [para(241117(a,1),226422(a,1,2)),rewrite([231438(5)]),flip(a)].
% 113.98/114.34 241138 implies(A,implies(not(A),B)) = not(c_0). [para(241132(a,1),61(a,1)),flip(b),unit_del(a,166479)].
% 113.98/114.34 241141 and(not(c_0),implies(implies(not(A),B),A)) = equiv(A,implies(not(A),B)). [para(241138(a,1),90(a,1,1))].
% 113.98/114.34 241142 and(implies(implies(not(A),B),A),not(c_0)) = equiv(implies(not(A),B),A). [para(241138(a,1),90(a,1,2))].
% 113.98/114.34 241262 is_a_theorem(equiv(A,implies(not(A),A))). [resolve(240007,a,152,a),rewrite([80(7),241141(6)])].
% 113.98/114.34 241298 implies(not(A),A) = A. [resolve(241262,a,61,a)].
% 113.98/114.34 241330 implies(A,and(not(B),not(B))) = not(and(A,B)). [para(241298(a,1),131(a,1,1,2)),flip(a)].
% 113.98/114.34 241577 -is_a_theorem(implies(implies(A,not(c34)),not(and(c34,c35)))). [para(241298(a,1),64048(a,1,1,2))].
% 113.98/114.34 241646 is_a_theorem(implies(A,not(equiv(A,c_0)))). [para(241298(a,1),232236(a,1,2,1,1))].
% 113.98/114.34 241648 is_a_theorem(implies(implies(not(A),c_0),implies(not(c_0),A))). [para(241298(a,1),231797(a,1,2,2))].
% 113.98/114.34 241661 is_a_theorem(not(equiv(implies(A,implies(B,A)),c_0))). [para(241298(a,1),233623(a,1,1,1,2,2))].
% 113.98/114.34 241712 is_a_theorem(implies(and(A,not(c_0)),equiv(not(A),c_0))). [para(241298(a,1),231830(a,1,2))].
% 113.98/114.34 241834 is_a_theorem(implies(not(and(implies(not(A),B),A)),implies(A,C))). [back_rewrite(53288),rewrite([241330(6)])].
% 113.98/114.34 242826 -is_a_theorem(A) | is_a_theorem(not(equiv(A,c_0))). [resolve(241646,a,69,b)].
% 113.98/114.34 242888 is_a_theorem(not(equiv(implies(A,not(equiv(A,c_0))),c_0))). [resolve(242826,a,241646,a)].
% 113.98/114.34 245798 is_a_theorem(not(equiv(implies(implies(not(A),c_0),implies(not(c_0),A)),c_0))). [resolve(241648,a,242826,a)].
% 113.98/114.34 245876 is_a_theorem(implies(not(equiv(A,c_0)),not(equiv(c_0,A)))). [para(231801(a,1),241648(a,1,2)),rewrite([80(4),232223(4)])].
% 113.98/114.34 245986 -is_a_theorem(and(A,not(c_0))) | is_a_theorem(equiv(not(A),c_0)). [resolve(241712,a,69,b)].
% 113.98/114.34 246858 -is_a_theorem(not(equiv(A,c_0))) | is_a_theorem(not(equiv(c_0,A))). [resolve(245876,a,69,b)].
% 113.98/114.34 247314 is_a_theorem(not(equiv(c_0,implies(A,not(equiv(A,c_0)))))). [resolve(246858,a,242888,a)].
% 113.98/114.34 247315 is_a_theorem(not(equiv(c_0,implies(A,implies(B,A))))). [resolve(246858,a,241661,a)].
% 113.98/114.34 247358 is_a_theorem(and(implies(A,implies(B,A)),not(c_0))). [resolve(247315,a,114259,a)].
% 113.98/114.34 247373 is_a_theorem(equiv(not(implies(A,implies(B,A))),c_0)). [resolve(247358,a,245986,a)].
% 113.98/114.34 247426 not(implies(A,implies(B,A))) = c_0. [resolve(247373,a,61,a),flip(a)].
% 113.98/114.34 247491 implies(A,implies(B,implies(C,B))) = not(c_0). [para(247426(a,1),80(a,1,1,2)),rewrite([226276(2)]),flip(a)].
% 113.98/114.34 247493 implies(A,implies(B,A)) = not(c_0). [para(247426(a,1),241298(a,1,1)),rewrite([247491(4)]),flip(a)].
% 113.98/114.34 247498 equiv(A,implies(not(c_0),A)) = not(c_0). [back_rewrite(240732),rewrite([247493(4),231438(5)]),flip(a)].
% 113.98/114.34 247521 implies(not(c_0),A) = A. [para(247498(a,1),61(a,1)),unit_del(a,166479)].
% 113.98/114.34 247547 is_a_theorem(not(equiv(implies(implies(not(A),c_0),A),c_0))). [back_rewrite(245798),rewrite([247521(6)])].
% 113.98/114.34 247614 is_a_theorem(implies(equiv(A,c_0),implies(A,B))). [back_rewrite(233907),rewrite([247521(7),247521(7)])].
% 113.98/114.34 247661 not(equiv(c_0,A)) = and(A,not(c_0)). [back_rewrite(231801),rewrite([247521(6)]),flip(a)].
% 113.98/114.34 247669 equiv(not(c_0),A) = and(A,not(c_0)). [back_rewrite(226423),rewrite([247521(3)]),flip(a)].
% 113.98/114.34 247682 is_a_theorem(and(implies(A,not(equiv(A,c_0))),not(c_0))). [back_rewrite(247314),rewrite([247661(7)])].
% 113.98/114.34 247693 -is_a_theorem(not(equiv(A,c_0))) | is_a_theorem(and(A,not(c_0))). [back_rewrite(246858),rewrite([247661(7)])].
% 113.98/114.34 249492 is_a_theorem(implies(equiv(not(A),c_0),A)). [para(241298(a,1),247614(a,1,2))].
% 113.98/114.34 249503 is_a_theorem(implies(not(equiv(not(implies(equiv(not(A),c_0),A)),c_0)),c_0)). [resolve(249492,a,237543,a)].
% 113.98/114.34 250702 -is_a_theorem(and(A,not(c_0))) | not(c_0) = A. [para(247669(a,1),61(a,1)),flip(b)].
% 113.98/114.34 253414 implies(A,not(equiv(A,c_0))) = not(c_0). [resolve(247682,a,250702,a),flip(a)].
% 113.98/114.34 253418 and(implies(not(equiv(A,c_0)),A),not(c_0)) = equiv(not(equiv(A,c_0)),A). [para(253414(a,1),90(a,1,2))].
% 113.98/114.34 253767 is_a_theorem(equiv(implies(not(A),c_0),A)). [resolve(247693,a,247547,a),rewrite([241142(7)])].
% 113.98/114.34 253806 implies(not(A),c_0) = A. [resolve(253767,a,61,a),flip(a)].
% 113.98/114.34 253862 is_a_theorem(equiv(not(implies(equiv(not(A),c_0),A)),c_0)). [back_rewrite(249503),rewrite([253806(10)])].
% 113.98/114.34 253970 implies(implies(A,B),c_0) = and(A,not(B)). [para(80(a,1),253806(a,1,1))].
% 113.98/114.34 253971 equiv(not(A),c_0) = and(A,not(c_0)). [para(253806(a,1),90(a,1,1)),rewrite([231583(3)]),flip(a)].
% 113.98/114.34 253975 implies(A,and(not(B),not(c_0))) = not(and(A,B)). [para(253806(a,1),131(a,1,1,2)),flip(a)].
% 113.98/114.34 254087 not(equiv(A,c_0)) = and(A,not(c_0)). [back_rewrite(232223),rewrite([253970(4)]),flip(a)].
% 113.98/114.34 254207 is_a_theorem(and(implies(and(A,not(c_0)),A),not(c_0))). [back_rewrite(253862),rewrite([253971(3),253971(7)])].
% 113.98/114.34 255452 and(implies(and(A,not(c_0)),A),not(c_0)) = equiv(and(A,not(c_0)),A). [back_rewrite(253418),rewrite([254087(3),254087(10)])].
% 113.98/114.34 255826 is_a_theorem(equiv(and(A,not(c_0)),A)). [back_rewrite(254207),rewrite([255452(7)])].
% 113.98/114.34 257098 and(A,not(c_0)) = A. [resolve(255826,a,61,a),flip(a)].
% 113.98/114.34 257249 not(and(A,B)) = implies(A,not(B)). [back_rewrite(253975),rewrite([257098(4)]),flip(a)].
% 113.98/114.34 257988 is_a_theorem(implies(implies(implies(not(A),B),not(A)),implies(A,C))). [back_rewrite(241834),rewrite([257249(4)])].
% 113.98/114.34 258015 -is_a_theorem(implies(implies(A,not(c34)),implies(c34,not(c35)))). [back_rewrite(241577),rewrite([257249(7)])].
% 113.98/114.34 258016 $F. [resolve(258015,a,257988,a)].
% 113.98/114.34
% 113.98/114.34 % SZS output end Refutation
% 113.98/114.34 ============================== end of proof ==========================
% 113.98/114.34
% 113.98/114.34 ============================== STATISTICS ============================
% 113.98/114.34
% 113.98/114.34 Given=8696. Generated=13825012. Kept=257965. proofs=1.
% 113.98/114.34 Usable=865. Sos=4495. Demods=86. Limbo=766, Disabled=251910. Hints=0.
% 113.98/114.34 Megabytes=179.66.
% 113.98/114.34 User_CPU=106.30, System_CPU=7.03, Wall_clock=113.
% 113.98/114.34
% 113.98/114.34 ============================== end of statistics =====================
% 113.98/114.34
% 113.98/114.34 ============================== end of search =========================
% 113.98/114.34
% 113.98/114.34 THEOREM PROVED
% 113.98/114.34 % SZS status Theorem
% 113.98/114.34
% 113.98/114.34 Exiting with 1 proof.
% 113.98/114.34
% 113.98/114.34 Process 13870 exit (max_proofs) Sun Jul 3 07:16:19 2022
% 113.98/114.34 Prover9 interrupted
%------------------------------------------------------------------------------