TSTP Solution File: LCL462+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL462+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 13:46:59 EDT 2022
% Result : Theorem 117.39s 117.68s
% Output : Refutation 117.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL462+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 : n021.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 : Sat Jul 2 19:21:30 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.44/1.02 ============================== Prover9 ===============================
% 0.44/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.02 Process 1550 was started by sandbox2 on n021.cluster.edu,
% 0.44/1.02 Sat Jul 2 19:21:31 2022
% 0.44/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_1395_n021.cluster.edu".
% 0.44/1.02 ============================== end of head ===========================
% 0.44/1.02
% 0.44/1.02 ============================== INPUT =================================
% 0.44/1.02
% 0.44/1.02 % Reading from file /tmp/Prover9_1395_n021.cluster.edu
% 0.44/1.02
% 0.44/1.02 set(prolog_style_variables).
% 0.44/1.02 set(auto2).
% 0.44/1.02 % set(auto2) -> set(auto).
% 0.44/1.02 % set(auto) -> set(auto_inference).
% 0.44/1.02 % set(auto) -> set(auto_setup).
% 0.44/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.02 % set(auto) -> set(auto_limits).
% 0.44/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.02 % set(auto) -> set(auto_denials).
% 0.44/1.02 % set(auto) -> set(auto_process).
% 0.44/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.02 % set(auto2) -> assign(stats, some).
% 0.44/1.02 % set(auto2) -> clear(echo_input).
% 0.44/1.02 % set(auto2) -> set(quiet).
% 0.44/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.02 % set(auto2) -> clear(print_given).
% 0.44/1.02 assign(lrs_ticks,-1).
% 0.44/1.02 assign(sos_limit,10000).
% 0.44/1.02 assign(order,kbo).
% 0.44/1.02 set(lex_order_vars).
% 0.44/1.02 clear(print_given).
% 0.44/1.02
% 0.44/1.02 % formulas(sos). % not echoed (43 formulas)
% 0.44/1.02
% 0.44/1.02 ============================== end of input ==========================
% 0.44/1.02
% 0.44/1.02 % From the command line: assign(max_seconds, 300).
% 0.44/1.02
% 0.44/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.02
% 0.44/1.02 % Formulas that are not ordinary clauses:
% 0.44/1.02 1 modus_ponens <-> (all X all Y (is_a_theorem(X) & is_a_theorem(implies(X,Y)) -> is_a_theorem(Y))) # label(modus_ponens) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 2 substitution_of_equivalents <-> (all X all Y (is_a_theorem(equiv(X,Y)) -> X = Y)) # label(substitution_of_equivalents) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 3 modus_tollens <-> (all X all Y is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))) # label(modus_tollens) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 5 implies_2 <-> (all X all Y is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))) # label(implies_2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 6 implies_3 <-> (all X all Y all Z is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))) # label(implies_3) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 9 and_3 <-> (all X all Y is_a_theorem(implies(X,implies(Y,and(X,Y))))) # label(and_3) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 12 or_3 <-> (all X all Y all Z is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))) # label(or_3) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 13 equivalence_1 <-> (all X all Y is_a_theorem(implies(equiv(X,Y),implies(X,Y)))) # label(equivalence_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 14 equivalence_2 <-> (all X all Y is_a_theorem(implies(equiv(X,Y),implies(Y,X)))) # label(equivalence_2) # label(axiom) # label(non_clause). [assumption].
% 1.22/1.50 15 equivalence_3 <-> (all X all Y is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))) # label(equivalence_3) # label(axiom) # label(non_clause). [assumption].
% 1.22/1.50 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 1.22/1.50 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 1.22/1.50 18 kn3 <-> (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))) # label(kn3) # label(axiom) # label(non_clause). [assumption].
% 1.22/1.50 19 cn1 <-> (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))) # label(cn1) # label(axiom) # label(non_clause). [assumption].
% 1.22/1.50 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 1.22/1.50 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 1.22/1.50 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 1.22/1.50 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 1.22/1.50 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 1.22/1.50 25 r4 <-> (all P all Q all R is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))) # label(r4) # label(axiom) # label(non_clause). [assumption].
% 1.22/1.50 26 r5 <-> (all P all Q all R is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))) # label(r5) # label(axiom) # label(non_clause). [assumption].
% 1.22/1.50 27 op_or -> (all X all Y or(X,Y) = not(and(not(X),not(Y)))) # label(op_or) # label(axiom) # label(non_clause). [assumption].
% 1.22/1.50 28 op_and -> (all X all Y and(X,Y) = not(or(not(X),not(Y)))) # label(op_and) # label(axiom) # label(non_clause). [assumption].
% 1.22/1.50 29 op_implies_and -> (all X all Y implies(X,Y) = not(and(X,not(Y)))) # label(op_implies_and) # label(axiom) # label(non_clause). [assumption].
% 1.22/1.50 30 op_implies_or -> (all X all Y implies(X,Y) = or(not(X),Y)) # label(op_implies_or) # label(axiom) # label(non_clause). [assumption].
% 1.22/1.50 31 op_equiv -> (all X all Y equiv(X,Y) = and(implies(X,Y),implies(Y,X))) # label(op_equiv) # label(axiom) # label(non_clause). [assumption].
% 1.22/1.50
% 1.22/1.50 ============================== end of process non-clausal formulas ===
% 1.22/1.50
% 1.22/1.50 ============================== PROCESS INITIAL CLAUSES ===============
% 1.22/1.50
% 1.22/1.50 ============================== PREDICATE ELIMINATION =================
% 1.22/1.50
% 1.22/1.50 ============================== end predicate elimination =============
% 1.22/1.50
% 1.22/1.50 Auto_denials: (non-Horn, no changes).
% 1.22/1.50
% 1.22/1.50 Term ordering decisions:
% 1.22/1.50
% 1.22/1.50 % Assigning unary symbol not kb_weight 0 and highest precedence (94).
% 1.22/1.50 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. c10=1. c11=1. c12=1. c13=1. c14=1. c15=1. c16=1. c17=1. c18=1. c19=1. c20=1. c21=1. c22=1. c23=1. c24=1. c25=1. c26=1. c27=1. c28=1. c29=1. c30=1. c31=1. c32=1. c33=1. c34=1. c35=1. c36=1. c37=1. c38=1. c39=1. c40=1. c41=1. c42=1. c43=1. c44=1. c45=1. c46=1. c47=1. c48=1. c49=1. c50=1. c51=1. c52=1. c53=1. c54=1. c55=1. implies=1. or=1. and=1. equiv=1. not=0.
% 1.22/1.50
% 1.22/1.50 ============================== end of process initial clauses ========
% 1.22/1.50
% 1.22/1.50 ============================== CLAUSES FOR SEARCH ====================
% 1.22/1.50
% 1.22/1.50 ============================== end of clauses for search =============
% 1.22/1.50
% 1.22/1.50 ============================== SEARCH ================================
% 1.22/1.50
% 1.22/1.50 % Starting search at 0.02 seconds.
% 1.22/1.50
% 1.22/1.50 Low Water (keep): wt=43.000, iters=3396
% 1.22/1.50
% 1.22/1.50 Low Water (keep): wt=40.000, iters=3382
% 1.22/1.50
% 1.22/1.50 Low Water (keep): wt=38.000, iters=3408
% 1.22/1.50
% 1.22/1.50 Low Water (keep): wt=35.000, iters=3376
% 1.22/1.50
% 1.22/1.50 Low Water (keep): wt=34.000, iters=3367
% 1.22/1.50
% 1.22/1.50 Low Water (keep): wt=33.000, iters=3369
% 1.22/1.50
% 1.22/1.50 Low Water (keep): wt=29.000, iters=3394
% 1.22/1.50
% 1.22/1.50 Low Water (keep): wt=27.000, iters=3397
% 1.22/1.50
% 1.22/1.50 Low Water (keep): wt=25.000, iters=3373
% 1.22/1.50
% 1.22/1.50 Low Water (keep): wt=24.000, iters=3377
% 1.22/1.50
% 1.22/1.50 Low Water (keep): wt=23.000, iters=3386
% 117.39/117.68
% 117.39/117.68 Low Water (keep): wt=22.000, iters=3346
% 117.39/117.68
% 117.39/117.68 Low Water (keep): wt=21.000, iters=3388
% 117.39/117.68
% 117.39/117.68 Low Water (keep): wt=20.000, iters=3337
% 117.39/117.68
% 117.39/117.68 Low Water (keep): wt=19.000, iters=3346
% 117.39/117.68
% 117.39/117.68 Low Water (keep): wt=18.000, iters=3334
% 117.39/117.68
% 117.39/117.68 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 87 (0.00 of 1.32 sec).
% 117.39/117.68
% 117.39/117.68 Low Water (displace): id=3600, wt=143.000
% 117.39/117.68
% 117.39/117.68 Low Water (displace): id=2049, wt=127.000
% 117.39/117.68
% 117.39/117.68 Low Water (displace): id=1533, wt=119.000
% 117.39/117.68
% 117.39/117.68 Low Water (displace): id=2462, wt=111.000
% 117.39/117.68
% 117.39/117.68 Low Water (displace): id=1683, wt=99.000
% 117.39/117.68
% 117.39/117.68 Low Water (displace): id=3159, wt=91.000
% 117.39/117.68
% 117.39/117.68 Low Water (displace): id=1538, wt=87.000
% 117.39/117.68
% 117.39/117.68 Low Water (displace): id=1537, wt=71.000
% 117.39/117.68
% 117.39/117.68 Low Water (displace): id=10044, wt=45.000
% 117.39/117.68
% 117.39/117.68 Low Water (displace): id=9742, wt=43.000
% 117.39/117.68
% 117.39/117.68 Low Water (displace): id=9741, wt=42.000
% 117.39/117.68
% 117.39/117.68 Low Water (displace): id=10048, wt=41.000
% 117.39/117.68
% 117.39/117.68 Low Water (displace): id=7700, wt=39.000
% 117.39/117.68
% 117.39/117.68 Low Water (displace): id=7698, wt=38.000
% 117.39/117.68
% 117.39/117.68 Low Water (displace): id=10052, wt=37.000
% 117.39/117.68
% 117.39/117.68 Low Water (displace): id=10731, wt=35.000
% 117.39/117.68
% 117.39/117.68 Low Water (displace): id=9736, wt=34.000
% 117.39/117.68
% 117.39/117.68 Low Water (displace): id=10810, wt=33.000
% 117.39/117.68
% 117.39/117.68 Low Water (displace): id=10868, wt=17.000
% 117.39/117.68
% 117.39/117.68 Low Water (displace): id=11467, wt=16.000
% 117.39/117.68
% 117.39/117.68 Low Water (displace): id=11989, wt=15.000
% 117.39/117.68
% 117.39/117.68 Low Water (displace): id=12054, wt=13.000
% 117.39/117.68
% 117.39/117.68 Low Water (keep): wt=17.000, iters=3335
% 117.39/117.68
% 117.39/117.68 Low Water (keep): wt=16.000, iters=3334
% 117.39/117.68
% 117.39/117.68 Low Water (keep): wt=15.000, iters=4258
% 117.39/117.68
% 117.39/117.68 Low Water (keep): wt=14.000, iters=3441
% 117.39/117.68
% 117.39/117.68 Low Water (displace): id=123978, wt=12.000
% 117.39/117.68
% 117.39/117.68 Low Water (displace): id=126577, wt=11.000
% 117.39/117.68
% 117.39/117.68 Low Water (keep): wt=13.000, iters=3333
% 117.39/117.68
% 117.39/117.68 ============================== PROOF =================================
% 117.39/117.68 % SZS status Theorem
% 117.39/117.68 % SZS output start Refutation
% 117.39/117.68
% 117.39/117.68 % Proof 1 at 109.81 (+ 6.86) seconds.
% 117.39/117.68 % Length of proof is 240.
% 117.39/117.68 % Level of proof is 76.
% 117.39/117.68 % Maximum clause weight is 21.000.
% 117.39/117.68 % Given clauses 8227.
% 117.39/117.68
% 117.39/117.68 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].
% 117.39/117.68 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].
% 117.39/117.68 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].
% 117.39/117.68 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].
% 117.39/117.68 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 117.39/117.68 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 117.39/117.68 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].
% 117.39/117.68 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].
% 117.39/117.68 34 op_equiv # label(luka_op_equiv) # label(axiom). [assumption].
% 117.39/117.68 35 modus_ponens # label(luka_modus_ponens) # label(axiom). [assumption].
% 117.39/117.68 36 cn1 # label(luka_cn1) # label(axiom). [assumption].
% 117.39/117.68 37 cn2 # label(luka_cn2) # label(axiom). [assumption].
% 117.39/117.68 38 cn3 # label(luka_cn3) # label(axiom). [assumption].
% 117.39/117.68 39 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption].
% 117.39/117.68 40 op_implies_and # label(hilbert_op_implies_and) # label(axiom). [assumption].
% 117.39/117.68 41 -modus_tollens # label(hilbert_modus_tollens) # label(negated_conjecture). [assumption].
% 117.39/117.68 60 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(2)].
% 117.39/117.68 61 -is_a_theorem(equiv(A,B)) | B = A. [copy(60),unit_del(a,39)].
% 117.39/117.68 62 -cn2 | is_a_theorem(implies(A,implies(not(A),B))) # label(cn2) # label(axiom). [clausify(20)].
% 117.39/117.68 63 is_a_theorem(implies(A,implies(not(A),B))). [copy(62),unit_del(a,37)].
% 117.39/117.68 65 -cn3 | is_a_theorem(implies(implies(not(A),A),A)) # label(cn3) # label(axiom). [clausify(21)].
% 117.39/117.68 66 is_a_theorem(implies(implies(not(A),A),A)). [copy(65),unit_del(a,38)].
% 117.39/117.68 68 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 117.39/117.68 69 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(68),unit_del(a,35)].
% 117.39/117.68 79 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 117.39/117.68 80 not(and(A,not(B))) = implies(A,B). [copy(79),unit_del(a,40)].
% 117.39/117.68 81 modus_tollens | -is_a_theorem(implies(implies(not(c6),not(c5)),implies(c5,c6))) # label(modus_tollens) # label(axiom). [clausify(3)].
% 117.39/117.68 82 -is_a_theorem(implies(implies(not(c6),not(c5)),implies(c5,c6))). [copy(81),unit_del(a,41)].
% 117.39/117.68 89 -op_equiv | and(implies(A,B),implies(B,A)) = equiv(A,B) # label(op_equiv) # label(axiom). [clausify(31)].
% 117.39/117.68 90 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(89),unit_del(a,34)].
% 117.39/117.68 95 -cn1 | is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))) # label(cn1) # label(axiom). [clausify(19)].
% 117.39/117.68 96 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))). [copy(95),unit_del(a,36)].
% 117.39/117.68 122 -is_a_theorem(implies(not(A),A)) | is_a_theorem(A). [resolve(69,b,66,a)].
% 117.39/117.68 123 -is_a_theorem(A) | is_a_theorem(implies(not(A),B)). [resolve(69,b,63,a)].
% 117.39/117.68 124 is_a_theorem(implies(and(A,not(B)),implies(implies(A,B),C))). [para(80(a,1),63(a,1,2,1))].
% 117.39/117.68 125 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))].
% 117.39/117.68 126 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(80(a,1),80(a,1,1,2))].
% 117.39/117.68 130 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(B,C),implies(A,C))). [resolve(96,a,69,b)].
% 117.39/117.68 132 -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))].
% 117.39/117.68 226 is_a_theorem(implies(implies(implies(implies(A,B),C),D),implies(and(A,not(B)),D))). [resolve(130,a,124,a)].
% 117.39/117.68 228 is_a_theorem(implies(implies(A,B),implies(implies(not(A),A),B))). [resolve(130,a,66,a)].
% 117.39/117.68 229 is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C))). [resolve(130,a,63,a)].
% 117.39/117.68 230 is_a_theorem(implies(implies(implies(implies(not(A),A),B),C),implies(implies(A,B),C))). [resolve(228,a,130,a)].
% 117.39/117.68 232 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(A),A),B)). [resolve(228,a,69,b)].
% 117.39/117.68 242 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(not(A),D),B),C))). [resolve(229,a,130,a)].
% 117.39/117.68 244 -is_a_theorem(implies(implies(not(A),B),C)) | is_a_theorem(implies(A,C)). [resolve(229,a,69,b)].
% 117.39/117.68 256 -is_a_theorem(implies(implies(implies(implies(not(A),B),C),implies(A,C)),implies(implies(not(c6),not(c5)),implies(c5,c6)))). [ur(69,a,229,a,c,82,a)].
% 117.39/117.68 257 implies(implies(A,B),and(B,not(A))) = not(equiv(A,B)). [para(90(a,1),126(a,1,1)),flip(a)].
% 117.39/117.68 346 is_a_theorem(implies(A,implies(implies(B,C),implies(not(A),C)))). [resolve(244,a,96,a)].
% 117.39/117.68 347 is_a_theorem(implies(A,A)). [resolve(244,a,66,a)].
% 117.39/117.68 349 -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))].
% 117.39/117.68 413 is_a_theorem(implies(not(implies(A,A)),B)). [resolve(347,a,123,a)].
% 117.39/117.68 433 is_a_theorem(implies(implies(A,B),implies(not(implies(C,C)),B))). [resolve(413,a,130,a)].
% 117.39/117.68 609 is_a_theorem(implies(implies(not(A),A),implies(implies(B,C),implies(not(A),C)))). [resolve(346,a,232,a)].
% 117.39/117.68 638 is_a_theorem(implies(A,implies(not(implies(B,B)),C))). [resolve(433,a,244,a)].
% 117.39/117.68 753 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),implies(D,C))). [resolve(638,a,130,a)].
% 117.39/117.68 1024 is_a_theorem(implies(not(equiv(A,A)),and(A,not(A)))). [para(257(a,1),125(a,1,1))].
% 117.39/117.68 1210 is_a_theorem(implies(implies(and(A,not(A)),B),implies(not(equiv(A,A)),B))). [resolve(1024,a,130,a)].
% 117.39/117.68 2284 -is_a_theorem(implies(implies(not(implies(A,A)),B),C)) | is_a_theorem(implies(D,C)). [resolve(753,a,69,b)].
% 117.39/117.68 3020 is_a_theorem(implies(A,implies(B,B))). [resolve(2284,a,66,a)].
% 117.39/117.68 3027 is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))). [resolve(3020,a,130,a)].
% 117.39/117.68 3373 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(D,D),B),C))). [resolve(3027,a,130,a)].
% 117.39/117.68 3375 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(implies(C,B)). [resolve(3027,a,69,b)].
% 117.39/117.68 3446 is_a_theorem(implies(A,implies(B,implies(C,C)))). [resolve(3375,a,3027,a)].
% 117.39/117.68 3448 is_a_theorem(implies(A,implies(B,implies(not(B),C)))). [resolve(3375,a,229,a)].
% 117.39/117.68 3449 is_a_theorem(implies(A,implies(implies(not(B),B),B))). [resolve(3375,a,228,a)].
% 117.39/117.68 3455 is_a_theorem(implies(implies(implies(A,implies(B,B)),C),implies(D,C))). [resolve(3446,a,130,a)].
% 117.39/117.68 3529 is_a_theorem(implies(implies(implies(A,implies(not(A),B)),C),implies(D,C))). [resolve(3448,a,130,a)].
% 117.39/117.68 3831 is_a_theorem(implies(implies(implies(implies(not(A),A),A),B),implies(C,B))). [resolve(3449,a,130,a)].
% 117.39/117.68 5580 -is_a_theorem(implies(implies(implies(not(A),A),A),B)) | is_a_theorem(implies(C,B)). [resolve(3831,a,69,b)].
% 117.39/117.68 6868 -is_a_theorem(implies(not(A),A)) | is_a_theorem(implies(implies(B,C),implies(not(A),C))). [resolve(609,a,69,b)].
% 117.39/117.68 7414 -is_a_theorem(implies(and(A,not(A)),B)) | is_a_theorem(implies(not(equiv(A,A)),B)). [resolve(1210,a,69,b)].
% 117.39/117.68 7857 is_a_theorem(implies(A,implies(implies(implies(B,B),C),C))). [resolve(3373,a,5580,a)].
% 117.39/117.68 7867 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(implies(D,D),B),C)). [resolve(3373,a,69,b)].
% 117.39/117.68 7919 is_a_theorem(implies(implies(implies(implies(implies(A,A),B),B),C),implies(D,C))). [resolve(7857,a,130,a)].
% 117.39/117.68 7921 is_a_theorem(implies(implies(implies(A,A),B),B)). [resolve(7857,a,122,a)].
% 117.39/117.68 7963 is_a_theorem(implies(implies(A,B),implies(implies(implies(C,C),A),B))). [resolve(7921,a,130,a)].
% 117.39/117.68 7964 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(B). [resolve(7921,a,69,b)].
% 117.39/117.68 8140 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(C,C),A),B)). [resolve(7963,a,69,b)].
% 117.39/117.68 8622 is_a_theorem(implies(implies(implies(A,A),implies(implies(B,B),C)),implies(D,C))). [resolve(8140,a,3027,a)].
% 117.39/117.68 10092 is_a_theorem(implies(implies(implies(A,A),B),implies(implies(B,C),implies(D,C)))). [resolve(7867,a,96,a)].
% 117.39/117.68 10219 -is_a_theorem(implies(implies(implies(implies(A,A),B),B),C)) | is_a_theorem(implies(D,C)). [resolve(7919,a,69,b)].
% 117.39/117.68 10762 -is_a_theorem(implies(implies(A,A),implies(implies(B,B),C))) | is_a_theorem(implies(D,C)). [resolve(8622,a,69,b)].
% 117.39/117.68 10994 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(implies(implies(B,C),implies(D,C))). [resolve(10092,a,69,b)].
% 117.39/117.68 11647 is_a_theorem(implies(A,implies(and(B,not(B)),C))). [resolve(226,a,10219,a)].
% 117.39/117.68 11681 is_a_theorem(implies(and(A,not(A)),B)). [resolve(11647,a,7964,a)].
% 117.39/117.68 11739 is_a_theorem(implies(not(equiv(A,A)),B)). [back_unit_del(7414),unit_del(a,11681)].
% 117.39/117.68 11867 is_a_theorem(implies(implies(A,B),implies(not(equiv(C,C)),B))). [resolve(11739,a,6868,a)].
% 117.39/117.68 12867 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),C),implies(D,C))). [resolve(11867,a,10994,a)].
% 117.39/117.68 13277 is_a_theorem(implies(A,implies(B,equiv(C,C)))). [resolve(12867,a,5580,a)].
% 117.39/117.68 13334 is_a_theorem(implies(A,equiv(B,B))). [resolve(13277,a,10762,a)].
% 117.39/117.68 13411 is_a_theorem(implies(implies(equiv(A,A),B),implies(C,B))). [resolve(13334,a,10994,a)].
% 117.39/117.68 13749 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(equiv(D,D),B),C))). [resolve(13411,a,130,a)].
% 117.39/117.68 14178 -is_a_theorem(implies(implies(implies(not(A),A),B),C)) | is_a_theorem(implies(implies(A,B),C)). [resolve(230,a,69,b)].
% 117.39/117.68 14903 is_a_theorem(implies(A,implies(implies(implies(not(implies(B,B)),C),D),D))). [resolve(242,a,10219,a)].
% 117.39/117.68 14910 is_a_theorem(implies(A,implies(implies(implies(not(not(B)),C),B),B))). [resolve(242,a,5580,a)].
% 117.39/117.68 14954 is_a_theorem(implies(implies(implies(not(not(A)),B),A),A)). [resolve(14910,a,7964,a)].
% 117.39/117.68 14979 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(not(A)),C),A),B))). [resolve(14954,a,130,a)].
% 117.39/117.68 14980 -is_a_theorem(implies(implies(not(not(A)),B),A)) | is_a_theorem(A). [resolve(14954,a,69,b)].
% 117.39/117.68 15006 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),C)). [resolve(14903,a,14980,a)].
% 117.39/117.68 15071 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(implies(C,C)),D),A),B))). [resolve(15006,a,130,a)].
% 117.39/117.68 15072 -is_a_theorem(implies(implies(not(implies(A,A)),B),C)) | is_a_theorem(C). [resolve(15006,a,69,b)].
% 117.39/117.68 15216 is_a_theorem(implies(A,implies(implies(equiv(B,B),C),C))). [resolve(13749,a,10219,a)].
% 117.39/117.68 15232 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(equiv(D,D),B),C)). [resolve(13749,a,69,b)].
% 117.39/117.68 15241 is_a_theorem(implies(implies(equiv(A,A),B),B)). [resolve(15216,a,15072,a)].
% 117.39/117.68 15243 is_a_theorem(implies(implies(implies(implies(equiv(A,A),B),B),C),implies(D,C))). [resolve(15216,a,10994,a)].
% 117.39/117.68 15307 -is_a_theorem(implies(equiv(A,A),B)) | is_a_theorem(B). [resolve(15241,a,69,b)].
% 117.39/117.68 17098 -is_a_theorem(implies(implies(not(c6),not(c5)),implies(implies(not(c5),A),c6))). [ur(130,b,256,a)].
% 117.39/117.68 18364 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(not(A)),C),A),B)). [resolve(14979,a,69,b)].
% 117.39/117.68 18438 is_a_theorem(implies(implies(equiv(A,A),B),implies(implies(B,C),implies(D,C)))). [resolve(15232,a,10092,a)].
% 117.39/117.68 18523 -is_a_theorem(implies(implies(implies(equiv(A,A),B),B),C)) | is_a_theorem(implies(D,C)). [resolve(15243,a,69,b)].
% 117.39/117.68 20562 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),and(A,not(A))),C)). [resolve(18364,a,11681,a),rewrite([80(3)])].
% 117.39/117.68 20828 -is_a_theorem(implies(equiv(A,A),B)) | is_a_theorem(implies(implies(B,C),implies(D,C))). [resolve(18438,a,69,b)].
% 117.39/117.68 20906 is_a_theorem(implies(A,implies(implies(implies(not(equiv(B,B)),C),D),D))). [resolve(18523,a,242,a)].
% 117.39/117.68 20936 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),C),C)). [resolve(20906,a,15307,a)].
% 117.39/117.68 20992 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(equiv(C,C)),D),A),B))). [resolve(20936,a,130,a)].
% 117.39/117.68 23001 is_a_theorem(implies(and(not(equiv(A,A)),not(B)),C)). [resolve(349,a,20936,a)].
% 117.39/117.68 23003 is_a_theorem(implies(and(not(implies(A,A)),not(B)),C)). [resolve(349,a,20562,a)].
% 117.39/117.68 23011 is_a_theorem(implies(and(not(not(A)),not(B)),A)). [resolve(349,a,14954,a)].
% 117.39/117.68 23023 is_a_theorem(implies(and(implies(not(A),A),not(A)),implies(B,C))). [resolve(349,a,3831,a)].
% 117.39/117.68 23024 is_a_theorem(implies(and(A,not(implies(not(A),B))),implies(C,D))). [resolve(349,a,3529,a)].
% 117.39/117.68 23025 is_a_theorem(implies(and(A,not(implies(B,B))),implies(C,D))). [resolve(349,a,3455,a)].
% 117.39/117.68 23034 is_a_theorem(implies(and(A,not(B)),implies(implies(implies(not(A),C),B),D))). [resolve(349,a,242,a)].
% 117.39/117.68 23077 is_a_theorem(implies(implies(implies(not(not(A)),B),and(not(not(A)),not(B))),A)). [resolve(23011,a,232,a),rewrite([80(5)])].
% 117.39/117.68 23078 is_a_theorem(implies(implies(A,B),implies(and(not(not(A)),not(C)),B))). [resolve(23011,a,130,a)].
% 117.39/117.68 23395 is_a_theorem(implies(implies(implies(A,A),and(not(equiv(B,B)),not(C))),D)). [resolve(23001,a,8140,a)].
% 117.39/117.68 23435 is_a_theorem(implies(implies(implies(A,A),and(not(implies(B,B)),not(C))),D)). [resolve(23003,a,8140,a)].
% 117.39/117.68 23919 is_a_theorem(implies(implies(implies(A,B),C),implies(and(D,not(implies(E,E))),C))). [resolve(23025,a,130,a)].
% 117.39/117.68 24208 is_a_theorem(implies(and(implies(not(A),A),not(A)),not(equiv(B,C)))). [para(257(a,1),23023(a,1,2))].
% 117.39/117.68 24237 is_a_theorem(implies(and(A,not(implies(not(A),B))),not(equiv(C,D)))). [para(257(a,1),23024(a,1,2))].
% 117.39/117.68 24843 is_a_theorem(implies(and(not(not(not(implies(A,A)))),not(B)),C)). [resolve(23078,a,15072,a)].
% 117.39/117.68 24983 is_a_theorem(implies(implies(implies(A,A),and(not(not(not(implies(B,B)))),not(C))),D)). [resolve(24843,a,8140,a)].
% 117.39/117.68 27430 is_a_theorem(implies(and(A,implies(B,not(A))),implies(not(equiv(not(A),B)),C))). [para(257(a,1),23034(a,1,2,1)),rewrite([80(4)])].
% 117.39/117.68 27851 is_a_theorem(and(implies(A,A),implies(not(equiv(B,B)),C))). [resolve(23395,a,132,a),rewrite([80(6)])].
% 117.39/117.68 28116 is_a_theorem(and(implies(A,A),implies(not(implies(B,B)),C))). [resolve(23435,a,132,a),rewrite([80(6)])].
% 117.39/117.68 45225 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(implies(C,C)),D),A),B)). [resolve(15071,a,69,b)].
% 117.39/117.68 53783 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(equiv(C,C)),D),A),B)). [resolve(20992,a,69,b)].
% 117.39/117.68 56048 is_a_theorem(implies(implies(not(A),and(not(not(A)),not(not(A)))),A)). [resolve(23077,a,14178,a)].
% 117.39/117.68 56116 -is_a_theorem(implies(not(A),and(not(not(A)),not(not(A))))) | is_a_theorem(A). [resolve(56048,a,69,b)].
% 117.39/117.68 57248 is_a_theorem(implies(A,implies(and(B,not(implies(C,C))),D))). [resolve(23919,a,18523,a)].
% 117.39/117.68 57290 is_a_theorem(implies(implies(implies(and(A,not(implies(B,B))),C),D),implies(E,D))). [resolve(57248,a,20828,a)].
% 117.39/117.68 61128 -is_a_theorem(and(A,implies(B,not(A)))) | is_a_theorem(implies(not(equiv(not(A),B)),C)). [resolve(27430,a,69,b)].
% 117.39/117.68 92015 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),and(not(not(C)),not(D))),C)). [resolve(45225,a,23011,a)].
% 117.39/117.68 115183 is_a_theorem(implies(and(and(A,not(implies(B,B))),not(C)),implies(D,E))). [resolve(57290,a,349,a)].
% 117.39/117.68 115343 is_a_theorem(implies(and(and(A,not(implies(B,B))),not(C)),not(equiv(D,E)))). [para(257(a,1),115183(a,1,2))].
% 117.39/117.68 117888 is_a_theorem(implies(not(equiv(not(implies(A,A)),not(implies(B,B)))),C)). [resolve(61128,a,28116,a)].
% 117.39/117.68 117890 is_a_theorem(implies(not(equiv(not(implies(A,A)),not(equiv(B,B)))),C)). [resolve(61128,a,27851,a)].
% 117.39/117.68 117926 is_a_theorem(equiv(not(implies(A,A)),not(implies(B,B)))). [resolve(117888,a,56116,a)].
% 117.39/117.68 118027 not(implies(A,A)) = not(implies(B,B)). [resolve(117926,a,61,a)].
% 117.39/117.68 118035 not(implies(A,A)) = c_0. [new_symbol(118027)].
% 117.39/117.68 118037 is_a_theorem(implies(not(equiv(c_0,not(equiv(A,A)))),B)). [back_rewrite(117890),rewrite([118035(2)])].
% 117.39/117.68 118052 is_a_theorem(implies(and(and(A,c_0),not(B)),not(equiv(C,D)))). [back_rewrite(115343),rewrite([118035(2)])].
% 117.39/117.68 118136 is_a_theorem(implies(implies(implies(c_0,A),and(not(not(B)),not(C))),B)). [back_rewrite(92015),rewrite([118035(2)])].
% 117.39/117.68 118522 is_a_theorem(implies(implies(implies(A,A),and(not(not(c_0)),not(B))),C)). [back_rewrite(24983),rewrite([118035(3)])].
% 117.39/117.68 118573 is_a_theorem(implies(and(c_0,not(A)),B)). [back_rewrite(23003),rewrite([118035(2)])].
% 117.39/117.68 118675 -is_a_theorem(implies(implies(c_0,A),B)) | is_a_theorem(B). [back_rewrite(15072),rewrite([118035(2)])].
% 117.39/117.68 120337 is_a_theorem(implies(c_0,A)). [back_rewrite(413),rewrite([118035(2)])].
% 117.39/117.68 120816 implies(A,implies(B,B)) = not(and(A,c_0)). [para(118035(a,1),80(a,1,1,2)),flip(a)].
% 117.39/117.68 123024 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),and(c_0,not(C))),D)). [resolve(118573,a,53783,a)].
% 117.39/117.68 126633 is_a_theorem(equiv(c_0,not(equiv(A,A)))). [resolve(118037,a,56116,a)].
% 117.39/117.68 126736 not(equiv(A,A)) = c_0. [resolve(126633,a,61,a)].
% 117.39/117.68 126802 is_a_theorem(implies(implies(implies(c_0,A),and(c_0,not(B))),C)). [back_rewrite(123024),rewrite([126736(2)])].
% 117.39/117.68 126841 implies(A,equiv(B,B)) = not(and(A,c_0)). [para(126736(a,1),80(a,1,1,2)),flip(a)].
% 117.39/117.68 126885 is_a_theorem(implies(and(implies(not(A),A),not(A)),c_0)). [para(126736(a,1),24208(a,1,2))].
% 117.39/117.68 126886 is_a_theorem(implies(and(A,not(implies(not(A),B))),c_0)). [para(126736(a,1),24237(a,1,2))].
% 117.39/117.68 130791 -is_a_theorem(implies(not(and(implies(A,A),c_0)),B)) | is_a_theorem(B). [para(120816(a,1),7964(a,1,1))].
% 117.39/117.68 133247 is_a_theorem(implies(implies(c_0,A),implies(and(implies(not(B),B),not(B)),A))). [resolve(126885,a,130,a)].
% 117.39/117.68 133320 is_a_theorem(implies(implies(c_0,A),implies(and(B,not(implies(not(B),C))),A))). [resolve(126886,a,130,a)].
% 117.39/117.68 141436 is_a_theorem(and(implies(c_0,A),implies(c_0,B))). [resolve(126802,a,132,a),rewrite([80(6)])].
% 117.39/117.68 141473 is_a_theorem(implies(not(equiv(not(implies(c_0,A)),c_0)),B)). [resolve(141436,a,61128,a)].
% 117.39/117.68 141682 is_a_theorem(equiv(not(implies(c_0,A)),c_0)). [resolve(141473,a,56116,a)].
% 117.39/117.68 141780 not(implies(c_0,A)) = c_0. [resolve(141682,a,61,a),flip(a)].
% 117.39/117.68 141840 implies(A,implies(c_0,B)) = not(and(A,c_0)). [para(141780(a,1),80(a,1,1,2)),flip(a)].
% 117.39/117.68 147642 is_a_theorem(implies(and(and(A,c_0),not(B)),c_0)). [para(126736(a,1),118052(a,1,2))].
% 117.39/117.68 147710 is_a_theorem(implies(implies(c_0,A),implies(and(and(B,c_0),not(C)),A))). [resolve(147642,a,130,a)].
% 117.39/117.68 167155 is_a_theorem(implies(not(equiv(c_0,not(not(A)))),A)). [para(257(a,1),118136(a,1,1))].
% 117.39/117.68 167226 is_a_theorem(implies(implies(A,B),implies(not(equiv(c_0,not(not(A)))),B))). [resolve(167155,a,130,a)].
% 117.39/117.68 168968 is_a_theorem(and(implies(A,A),implies(not(not(c_0)),B))). [resolve(118522,a,132,a),rewrite([80(7)])].
% 117.39/117.68 169038 is_a_theorem(implies(not(equiv(c_0,not(not(c_0)))),A)). [resolve(168968,a,61128,a),rewrite([118035(2)])].
% 117.39/117.68 169108 is_a_theorem(equiv(c_0,not(not(c_0)))). [resolve(169038,a,56116,a)].
% 117.39/117.68 169203 not(not(c_0)) = c_0. [resolve(169108,a,61,a)].
% 117.39/117.68 169206 not(and(A,c_0)) = implies(A,not(c_0)). [para(169203(a,1),80(a,1,1,2))].
% 117.39/117.68 169207 is_a_theorem(not(c_0)). [para(169203(a,1),122(a,1,1)),unit_del(a,120337)].
% 117.39/117.68 169215 implies(implies(not(c_0),A),and(A,c_0)) = not(equiv(not(c_0),A)). [para(169203(a,1),257(a,1,2,2))].
% 117.39/117.68 169217 is_a_theorem(implies(A,not(c_0))). [para(169203(a,1),3448(a,1,2,2,1)),rewrite([141840(5),169206(5),120816(6),169206(3)])].
% 117.39/117.68 169907 implies(A,implies(c_0,B)) = implies(A,not(c_0)). [back_rewrite(141840),rewrite([169206(6)])].
% 117.39/117.68 170264 -is_a_theorem(implies(implies(implies(A,A),not(c_0)),B)) | is_a_theorem(B). [back_rewrite(130791),rewrite([169206(4)])].
% 117.39/117.68 170315 implies(A,equiv(B,B)) = implies(A,not(c_0)). [back_rewrite(126841),rewrite([169206(5)])].
% 117.39/117.68 170734 implies(A,implies(B,B)) = implies(A,not(c_0)). [back_rewrite(120816),rewrite([169206(5)])].
% 117.39/117.68 171400 is_a_theorem(implies(implies(not(c_0),A),implies(B,A))). [resolve(169217,a,20828,a)].
% 117.39/117.68 172490 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(not(c_0),B),C))). [resolve(171400,a,130,a)].
% 117.39/117.68 194365 is_a_theorem(implies(and(and(A,c_0),not(B)),C)). [resolve(147710,a,118675,a)].
% 117.39/117.68 201588 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(equiv(c_0,not(not(A)))),B)). [resolve(167226,a,69,b)].
% 117.39/117.68 214767 is_a_theorem(implies(A,implies(implies(not(c_0),B),B))). [resolve(172490,a,18523,a)].
% 117.39/117.68 214774 is_a_theorem(implies(implies(A,B),implies(implies(not(c_0),A),B))). [resolve(172490,a,14178,a)].
% 117.39/117.68 214798 is_a_theorem(implies(implies(not(c_0),A),A)). [resolve(214767,a,170264,a)].
% 117.39/117.68 214932 -is_a_theorem(implies(not(c_0),A)) | is_a_theorem(A). [resolve(214798,a,69,b)].
% 117.39/117.68 218721 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(c_0),A),B)). [resolve(214774,a,69,b)].
% 117.39/117.68 220186 is_a_theorem(implies(implies(not(c_0),and(and(A,c_0),not(B))),C)). [resolve(218721,a,194365,a)].
% 117.39/117.68 227551 is_a_theorem(and(not(c_0),implies(and(A,c_0),B))). [resolve(220186,a,132,a),rewrite([80(7)])].
% 117.39/117.68 227585 is_a_theorem(implies(not(equiv(c_0,and(A,c_0))),B)). [resolve(227551,a,61128,a),rewrite([169203(3)])].
% 117.39/117.68 227654 is_a_theorem(equiv(c_0,and(A,c_0))). [resolve(227585,a,56116,a)].
% 117.39/117.68 227748 and(A,c_0) = c_0. [resolve(227654,a,61,a)].
% 117.39/117.68 227791 implies(implies(not(c_0),A),c_0) = not(equiv(not(c_0),A)). [back_rewrite(169215),rewrite([227748(5)])].
% 117.39/117.68 227792 implies(A,not(c_0)) = not(c_0). [back_rewrite(169206),rewrite([227748(2)]),flip(a)].
% 117.39/117.68 227813 implies(A,implies(B,B)) = not(c_0). [back_rewrite(170734),rewrite([227792(5)])].
% 117.39/117.68 227821 implies(A,equiv(B,B)) = not(c_0). [back_rewrite(170315),rewrite([227792(5)])].
% 117.39/117.68 227844 implies(A,implies(c_0,B)) = not(c_0). [back_rewrite(169907),rewrite([227792(6)])].
% 117.39/117.68 227858 and(not(c_0),implies(not(c_0),A)) = equiv(A,not(c_0)). [para(227792(a,1),90(a,1,1))].
% 117.39/117.68 236803 implies(not(c_0),c_0) = c_0. [para(126736(a,1),227791(a,2)),rewrite([227792(5)])].
% 117.39/117.68 236831 not(equiv(not(c_0),implies(A,A))) = c_0. [para(227813(a,1),227791(a,1,1)),rewrite([236803(4)]),flip(a)].
% 117.39/117.68 236832 not(equiv(not(c_0),equiv(A,A))) = c_0. [para(227821(a,1),227791(a,1,1)),rewrite([236803(4)]),flip(a)].
% 117.39/117.68 236833 not(equiv(not(c_0),implies(c_0,A))) = c_0. [para(227844(a,1),227791(a,1,1)),rewrite([236803(4)]),flip(a)].
% 117.39/117.68 236894 implies(A,equiv(not(c_0),implies(B,B))) = not(c_0). [para(236831(a,1),80(a,1,1,2)),rewrite([227748(2)]),flip(a)].
% 117.39/117.68 236895 is_a_theorem(equiv(not(c_0),implies(A,A))). [para(236831(a,1),122(a,1,1)),rewrite([236894(6)]),unit_del(a,169207)].
% 117.39/117.68 236967 implies(A,A) = not(c_0). [resolve(236895,a,61,a)].
% 117.39/117.68 237987 and(not(c_0),not(c_0)) = equiv(A,A). [para(236967(a,1),90(a,1,1)),rewrite([236967(3)])].
% 117.39/117.68 238032 implies(A,equiv(not(c_0),equiv(B,B))) = not(c_0). [para(236832(a,1),80(a,1,1,2)),rewrite([227748(2)]),flip(a)].
% 117.39/117.68 238033 is_a_theorem(equiv(not(c_0),equiv(A,A))). [para(236832(a,1),122(a,1,1)),rewrite([238032(6)]),unit_del(a,169207)].
% 117.39/117.68 238078 equiv(A,A) = not(c_0). [resolve(238033,a,61,a)].
% 117.39/117.68 238294 and(not(c_0),not(c_0)) = not(c_0). [back_rewrite(237987),rewrite([238078(6)])].
% 117.39/117.68 238412 implies(A,equiv(not(c_0),implies(c_0,B))) = not(c_0). [para(236833(a,1),80(a,1,1,2)),rewrite([227748(2)]),flip(a)].
% 117.39/117.68 238413 is_a_theorem(equiv(not(c_0),implies(c_0,A))). [para(236833(a,1),122(a,1,1)),rewrite([238412(7)]),unit_del(a,169207)].
% 117.39/117.68 238461 implies(c_0,A) = not(c_0). [resolve(238413,a,61,a)].
% 117.39/117.68 238688 is_a_theorem(implies(not(c_0),implies(and(A,not(implies(not(A),B))),C))). [back_rewrite(133320),rewrite([238461(2)])].
% 117.39/117.68 238689 is_a_theorem(implies(not(c_0),implies(and(implies(not(A),A),not(A)),B))). [back_rewrite(133247),rewrite([238461(2)])].
% 117.39/117.68 247419 is_a_theorem(implies(and(A,not(implies(not(A),B))),C)). [resolve(238688,a,214932,a)].
% 117.39/117.68 247428 is_a_theorem(implies(not(equiv(c_0,not(implies(A,implies(not(A),B))))),C)). [resolve(247419,a,201588,a),rewrite([80(6)])].
% 117.39/117.68 247459 is_a_theorem(implies(and(implies(not(A),A),not(A)),B)). [resolve(238689,a,214932,a)].
% 117.39/117.68 247467 is_a_theorem(implies(implies(not(c_0),and(implies(not(A),A),not(A))),B)). [resolve(247459,a,218721,a)].
% 117.39/117.68 248296 is_a_theorem(equiv(c_0,not(implies(A,implies(not(A),B))))). [resolve(247428,a,56116,a)].
% 117.39/117.68 248305 not(implies(A,implies(not(A),B))) = c_0. [resolve(248296,a,61,a)].
% 117.39/117.68 248373 implies(A,implies(B,implies(not(B),C))) = not(c_0). [para(248305(a,1),80(a,1,1,2)),rewrite([227748(2)]),flip(a)].
% 117.39/117.68 248388 equiv(implies(A,implies(not(A),B)),not(c_0)) = not(c_0). [para(248373(a,1),227858(a,1,2)),rewrite([238294(5)]),flip(a)].
% 117.39/117.68 248404 implies(A,implies(not(A),B)) = not(c_0). [para(248388(a,1),61(a,1)),flip(b),unit_del(a,169207)].
% 117.39/117.68 248407 and(not(c_0),implies(implies(not(A),B),A)) = equiv(A,implies(not(A),B)). [para(248404(a,1),90(a,1,1))].
% 117.39/117.68 248531 is_a_theorem(equiv(A,implies(not(A),A))). [resolve(247467,a,132,a),rewrite([80(7),248407(6)])].
% 117.39/117.68 248567 implies(not(A),A) = A. [resolve(248531,a,61,a)].
% 117.39/117.68 248706 is_a_theorem(implies(implies(not(A),B),implies(implies(B,A),A))). [para(248567(a,1),96(a,1,2,2))].
% 117.39/117.68 248707 $F. [resolve(248706,a,17098,a)].
% 117.39/117.68
% 117.39/117.68 % SZS output end Refutation
% 117.39/117.68 ============================== end of proof ==========================
% 117.39/117.68
% 117.39/117.68 ============================== STATISTICS ============================
% 117.39/117.68
% 117.39/117.68 Given=8227. Generated=13239823. Kept=248656. proofs=1.
% 117.39/117.68 Usable=1583. Sos=6319. Demods=56. Limbo=4, Disabled=240821. Hints=0.
% 117.39/117.68 Megabytes=177.55.
% 117.39/117.68 User_CPU=109.82, System_CPU=6.86, Wall_clock=116.
% 117.39/117.68
% 117.39/117.68 ============================== end of statistics =====================
% 117.39/117.68
% 117.39/117.68 ============================== end of search =========================
% 117.39/117.68
% 117.39/117.68 THEOREM PROVED
% 117.39/117.68 % SZS status Theorem
% 117.39/117.68
% 117.39/117.68 Exiting with 1 proof.
% 117.39/117.68
% 117.39/117.68 Process 1550 exit (max_proofs) Sat Jul 2 19:23:27 2022
% 117.39/117.68 Prover9 interrupted
%------------------------------------------------------------------------------