TSTP Solution File: LCL473+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL473+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 13:47:04 EDT 2022
% Result : Theorem 120.84s 121.14s
% Output : Refutation 120.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL473+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 2 22:55:28 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.41/1.01 ============================== Prover9 ===============================
% 0.41/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.41/1.01 Process 25018 was started by sandbox on n023.cluster.edu,
% 0.41/1.01 Sat Jul 2 22:55:29 2022
% 0.41/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_24864_n023.cluster.edu".
% 0.41/1.01 ============================== end of head ===========================
% 0.41/1.01
% 0.41/1.01 ============================== INPUT =================================
% 0.41/1.01
% 0.41/1.01 % Reading from file /tmp/Prover9_24864_n023.cluster.edu
% 0.41/1.01
% 0.41/1.01 set(prolog_style_variables).
% 0.41/1.01 set(auto2).
% 0.41/1.01 % set(auto2) -> set(auto).
% 0.41/1.01 % set(auto) -> set(auto_inference).
% 0.41/1.01 % set(auto) -> set(auto_setup).
% 0.41/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.41/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.41/1.01 % set(auto) -> set(auto_limits).
% 0.41/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.41/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.41/1.01 % set(auto) -> set(auto_denials).
% 0.41/1.01 % set(auto) -> set(auto_process).
% 0.41/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.41/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.41/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.41/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.41/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.41/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.41/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.41/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.41/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.41/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.41/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.41/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.41/1.01 % set(auto2) -> assign(stats, some).
% 0.41/1.01 % set(auto2) -> clear(echo_input).
% 0.41/1.01 % set(auto2) -> set(quiet).
% 0.41/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.41/1.01 % set(auto2) -> clear(print_given).
% 0.41/1.01 assign(lrs_ticks,-1).
% 0.41/1.01 assign(sos_limit,10000).
% 0.41/1.01 assign(order,kbo).
% 0.41/1.01 set(lex_order_vars).
% 0.41/1.01 clear(print_given).
% 0.41/1.01
% 0.41/1.01 % formulas(sos). % not echoed (43 formulas)
% 0.41/1.01
% 0.41/1.01 ============================== end of input ==========================
% 0.41/1.01
% 0.41/1.01 % From the command line: assign(max_seconds, 300).
% 0.41/1.01
% 0.41/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.41/1.01
% 0.41/1.01 % Formulas that are not ordinary clauses:
% 0.41/1.01 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].
% 0.41/1.01 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].
% 0.41/1.01 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].
% 0.41/1.01 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 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].
% 0.41/1.01 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].
% 0.41/1.01 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 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].
% 0.41/1.01 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 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].
% 0.41/1.01 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].
% 0.41/1.01 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].
% 1.20/1.53 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].
% 1.20/1.53 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 1.20/1.53 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 1.20/1.53 18 kn3 <-> (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))) # label(kn3) # label(axiom) # label(non_clause). [assumption].
% 1.20/1.53 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].
% 1.20/1.53 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 1.20/1.53 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 1.20/1.53 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 1.20/1.53 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 1.20/1.53 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 1.20/1.53 25 r4 <-> (all P all Q all R is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))) # label(r4) # label(axiom) # label(non_clause). [assumption].
% 1.20/1.53 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].
% 1.20/1.53 27 op_or -> (all X all Y or(X,Y) = not(and(not(X),not(Y)))) # label(op_or) # label(axiom) # label(non_clause). [assumption].
% 1.20/1.53 28 op_and -> (all X all Y and(X,Y) = not(or(not(X),not(Y)))) # label(op_and) # label(axiom) # label(non_clause). [assumption].
% 1.20/1.53 29 op_implies_and -> (all X all Y implies(X,Y) = not(and(X,not(Y)))) # label(op_implies_and) # label(axiom) # label(non_clause). [assumption].
% 1.20/1.53 30 op_implies_or -> (all X all Y implies(X,Y) = or(not(X),Y)) # label(op_implies_or) # label(axiom) # label(non_clause). [assumption].
% 1.20/1.53 31 op_equiv -> (all X all Y equiv(X,Y) = and(implies(X,Y),implies(Y,X))) # label(op_equiv) # label(axiom) # label(non_clause). [assumption].
% 1.20/1.53
% 1.20/1.53 ============================== end of process non-clausal formulas ===
% 1.20/1.53
% 1.20/1.53 ============================== PROCESS INITIAL CLAUSES ===============
% 1.20/1.53
% 1.20/1.53 ============================== PREDICATE ELIMINATION =================
% 1.20/1.53
% 1.20/1.53 ============================== end predicate elimination =============
% 1.20/1.53
% 1.20/1.53 Auto_denials: (non-Horn, no changes).
% 1.20/1.53
% 1.20/1.53 Term ordering decisions:
% 1.20/1.53
% 1.20/1.53 % Assigning unary symbol not kb_weight 0 and highest precedence (94).
% 1.20/1.53 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.
% 1.20/1.53
% 1.20/1.53 ============================== end of process initial clauses ========
% 1.20/1.53
% 1.20/1.53 ============================== CLAUSES FOR SEARCH ====================
% 1.20/1.53
% 1.20/1.53 ============================== end of clauses for search =============
% 1.20/1.53
% 1.20/1.53 ============================== SEARCH ================================
% 1.20/1.53
% 1.20/1.53 % Starting search at 0.02 seconds.
% 1.20/1.53
% 1.20/1.53 Low Water (keep): wt=43.000, iters=3363
% 1.20/1.53
% 1.20/1.53 Low Water (keep): wt=40.000, iters=3461
% 1.20/1.53
% 1.20/1.53 Low Water (keep): wt=36.000, iters=3339
% 1.20/1.53
% 1.20/1.53 Low Water (keep): wt=33.000, iters=3370
% 1.20/1.53
% 1.20/1.53 Low Water (keep): wt=32.000, iters=3369
% 1.20/1.53
% 1.20/1.53 Low Water (keep): wt=30.000, iters=3333
% 1.20/1.53
% 1.20/1.53 Low Water (keep): wt=27.000, iters=3407
% 1.20/1.53
% 1.20/1.53 Low Water (keep): wt=25.000, iters=3391
% 1.20/1.53
% 1.20/1.53 Low Water (keep): wt=24.000, iters=3454
% 1.20/1.53
% 1.20/1.53 Low Water (keep): wt=23.000, iters=3340
% 1.20/1.53
% 120.84/121.14 Low Water (keep): wt=22.000, iters=3363
% 120.84/121.14
% 120.84/121.14 Low Water (keep): wt=21.000, iters=3344
% 120.84/121.14
% 120.84/121.14 Low Water (keep): wt=20.000, iters=3337
% 120.84/121.14
% 120.84/121.14 Low Water (keep): wt=19.000, iters=3367
% 120.84/121.14
% 120.84/121.14 Low Water (keep): wt=18.000, iters=3362
% 120.84/121.14
% 120.84/121.14 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 90 (0.00 of 1.27 sec).
% 120.84/121.14
% 120.84/121.14 Low Water (displace): id=3600, wt=127.000
% 120.84/121.14
% 120.84/121.14 Low Water (displace): id=2049, wt=111.000
% 120.84/121.14
% 120.84/121.14 Low Water (displace): id=2462, wt=103.000
% 120.84/121.14
% 120.84/121.14 Low Water (displace): id=1682, wt=91.000
% 120.84/121.14
% 120.84/121.14 Low Water (displace): id=3159, wt=83.000
% 120.84/121.14
% 120.84/121.14 Low Water (displace): id=1537, wt=71.000
% 120.84/121.14
% 120.84/121.14 Low Water (displace): id=1536, wt=63.000
% 120.84/121.14
% 120.84/121.14 Low Water (displace): id=10017, wt=45.000
% 120.84/121.14
% 120.84/121.14 Low Water (displace): id=9673, wt=43.000
% 120.84/121.14
% 120.84/121.14 Low Water (displace): id=9672, wt=42.000
% 120.84/121.14
% 120.84/121.14 Low Water (displace): id=10021, wt=41.000
% 120.84/121.14
% 120.84/121.14 Low Water (displace): id=7669, wt=39.000
% 120.84/121.14
% 120.84/121.14 Low Water (displace): id=7667, wt=38.000
% 120.84/121.14
% 120.84/121.14 Low Water (displace): id=10025, wt=37.000
% 120.84/121.14
% 120.84/121.14 Low Water (displace): id=10739, wt=35.000
% 120.84/121.14
% 120.84/121.14 Low Water (displace): id=9667, wt=34.000
% 120.84/121.14
% 120.84/121.14 Low Water (displace): id=10812, wt=17.000
% 120.84/121.14
% 120.84/121.14 Low Water (displace): id=11528, wt=16.000
% 120.84/121.14
% 120.84/121.14 Low Water (displace): id=11535, wt=15.000
% 120.84/121.14
% 120.84/121.14 Low Water (keep): wt=17.000, iters=3335
% 120.84/121.14
% 120.84/121.14 Low Water (displace): id=12939, wt=14.000
% 120.84/121.14
% 120.84/121.14 Low Water (displace): id=12966, wt=13.000
% 120.84/121.14
% 120.84/121.14 Low Water (keep): wt=16.000, iters=3333
% 120.84/121.14
% 120.84/121.14 Low Water (keep): wt=15.000, iters=4003
% 120.84/121.14
% 120.84/121.14 Low Water (keep): wt=14.000, iters=3362
% 120.84/121.14
% 120.84/121.14 Low Water (keep): wt=13.000, iters=3333
% 120.84/121.14
% 120.84/121.14 Low Water (displace): id=130243, wt=12.000
% 120.84/121.14
% 120.84/121.14 Low Water (displace): id=132879, wt=11.000
% 120.84/121.14
% 120.84/121.14 ============================== PROOF =================================
% 120.84/121.14 % SZS status Theorem
% 120.84/121.14 % SZS output start Refutation
% 120.84/121.14
% 120.84/121.14 % Proof 1 at 112.94 (+ 7.20) seconds.
% 120.84/121.14 % Length of proof is 309.
% 120.84/121.14 % Level of proof is 103.
% 120.84/121.14 % Maximum clause weight is 19.000.
% 120.84/121.14 % Given clauses 8877.
% 120.84/121.14
% 120.84/121.14 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].
% 120.84/121.14 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].
% 120.84/121.14 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].
% 120.84/121.14 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].
% 120.84/121.14 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 120.84/121.14 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 120.84/121.14 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].
% 120.84/121.14 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].
% 120.84/121.14 34 op_equiv # label(luka_op_equiv) # label(axiom). [assumption].
% 120.84/121.14 35 modus_ponens # label(luka_modus_ponens) # label(axiom). [assumption].
% 120.84/121.14 36 cn1 # label(luka_cn1) # label(axiom). [assumption].
% 120.84/121.14 37 cn2 # label(luka_cn2) # label(axiom). [assumption].
% 120.84/121.14 38 cn3 # label(luka_cn3) # label(axiom). [assumption].
% 120.84/121.14 39 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption].
% 120.84/121.14 40 op_implies_and # label(hilbert_op_implies_and) # label(axiom). [assumption].
% 120.84/121.14 41 -equivalence_2 # label(hilbert_equivalence_2) # label(negated_conjecture). [assumption].
% 120.84/121.14 60 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(2)].
% 120.84/121.14 61 -is_a_theorem(equiv(A,B)) | B = A. [copy(60),unit_del(a,39)].
% 120.84/121.14 62 -cn2 | is_a_theorem(implies(A,implies(not(A),B))) # label(cn2) # label(axiom). [clausify(20)].
% 120.84/121.14 63 is_a_theorem(implies(A,implies(not(A),B))). [copy(62),unit_del(a,37)].
% 120.84/121.14 65 -cn3 | is_a_theorem(implies(implies(not(A),A),A)) # label(cn3) # label(axiom). [clausify(21)].
% 120.84/121.14 66 is_a_theorem(implies(implies(not(A),A),A)). [copy(65),unit_del(a,38)].
% 120.84/121.14 68 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 120.84/121.14 69 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(68),unit_del(a,35)].
% 120.84/121.14 74 equivalence_2 | -is_a_theorem(implies(equiv(c29,c30),implies(c30,c29))) # label(equivalence_2) # label(axiom). [clausify(14)].
% 120.84/121.14 75 -is_a_theorem(implies(equiv(c29,c30),implies(c30,c29))). [copy(74),unit_del(a,41)].
% 120.84/121.14 79 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 120.84/121.14 80 not(and(A,not(B))) = implies(A,B). [copy(79),unit_del(a,40)].
% 120.84/121.14 89 -op_equiv | and(implies(A,B),implies(B,A)) = equiv(A,B) # label(op_equiv) # label(axiom). [clausify(31)].
% 120.84/121.14 90 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(89),unit_del(a,34)].
% 120.84/121.14 95 -cn1 | is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))) # label(cn1) # label(axiom). [clausify(19)].
% 120.84/121.14 96 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))). [copy(95),unit_del(a,36)].
% 120.84/121.14 122 -is_a_theorem(implies(not(A),A)) | is_a_theorem(A). [resolve(69,b,66,a)].
% 120.84/121.14 123 -is_a_theorem(A) | is_a_theorem(implies(not(A),B)). [resolve(69,b,63,a)].
% 120.84/121.14 125 -is_a_theorem(implies(implies(implies(not(A),A),A),implies(equiv(c29,c30),implies(c30,c29)))). [ur(69,a,66,a,c,75,a)].
% 120.84/121.14 127 is_a_theorem(implies(and(A,not(B)),implies(implies(A,B),C))). [para(80(a,1),63(a,1,2,1))].
% 120.84/121.14 128 is_a_theorem(implies(implies(implies(A,B),and(A,not(B))),and(A,not(B)))). [para(80(a,1),66(a,1,1,1))].
% 120.84/121.14 129 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(80(a,1),80(a,1,1,2))].
% 120.84/121.14 130 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(B,C),implies(A,C))). [resolve(96,a,69,b)].
% 120.84/121.14 132 -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))].
% 120.84/121.14 134 -is_a_theorem(implies(equiv(c29,c30),implies(not(implies(c30,c29)),implies(c30,c29)))). [ur(69,b,96,a,c,125,a)].
% 120.84/121.14 226 is_a_theorem(implies(implies(implies(implies(A,B),C),D),implies(and(A,not(B)),D))). [resolve(130,a,127,a)].
% 120.84/121.14 228 is_a_theorem(implies(implies(A,B),implies(implies(not(A),A),B))). [resolve(130,a,66,a)].
% 120.84/121.14 229 is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C))). [resolve(130,a,63,a)].
% 120.84/121.14 230 is_a_theorem(implies(implies(implies(implies(not(A),A),B),C),implies(implies(A,B),C))). [resolve(228,a,130,a)].
% 120.84/121.14 232 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(A),A),B)). [resolve(228,a,69,b)].
% 120.84/121.14 242 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(not(A),D),B),C))). [resolve(229,a,130,a)].
% 120.84/121.14 244 -is_a_theorem(implies(implies(not(A),B),C)) | is_a_theorem(implies(A,C)). [resolve(229,a,69,b)].
% 120.84/121.14 245 -is_a_theorem(implies(implies(not(equiv(c29,c30)),A),implies(not(implies(c30,c29)),implies(c30,c29)))). [ur(69,b,229,a,c,134,a)].
% 120.84/121.14 257 implies(implies(A,B),and(B,not(A))) = not(equiv(A,B)). [para(90(a,1),129(a,1,1)),flip(a)].
% 120.84/121.14 347 is_a_theorem(implies(A,implies(implies(B,C),implies(not(A),C)))). [resolve(244,a,96,a)].
% 120.84/121.14 348 is_a_theorem(implies(A,A)). [resolve(244,a,66,a)].
% 120.84/121.14 350 -is_a_theorem(implies(implies(implies(A,B),C),D)) | is_a_theorem(implies(and(A,not(B)),D)). [para(80(a,1),244(a,1,1,1))].
% 120.84/121.14 415 is_a_theorem(implies(not(implies(A,A)),B)). [resolve(348,a,123,a)].
% 120.84/121.14 435 is_a_theorem(implies(implies(A,B),implies(not(implies(C,C)),B))). [resolve(415,a,130,a)].
% 120.84/121.14 610 is_a_theorem(implies(implies(not(A),A),implies(implies(B,C),implies(not(A),C)))). [resolve(347,a,232,a)].
% 120.84/121.14 611 is_a_theorem(implies(implies(implies(implies(A,B),implies(not(C),B)),D),implies(C,D))). [resolve(347,a,130,a)].
% 120.84/121.14 639 is_a_theorem(implies(A,implies(not(implies(B,B)),C))). [resolve(435,a,244,a)].
% 120.84/121.14 756 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),implies(D,C))). [resolve(639,a,130,a)].
% 120.84/121.14 1025 is_a_theorem(implies(not(equiv(A,A)),and(A,not(A)))). [para(257(a,1),128(a,1,1))].
% 120.84/121.14 1204 is_a_theorem(implies(implies(and(A,not(A)),B),implies(not(equiv(A,A)),B))). [resolve(1025,a,130,a)].
% 120.84/121.14 2284 -is_a_theorem(implies(implies(not(implies(A,A)),B),C)) | is_a_theorem(implies(D,C)). [resolve(756,a,69,b)].
% 120.84/121.14 3020 is_a_theorem(implies(A,implies(B,B))). [resolve(2284,a,66,a)].
% 120.84/121.14 3027 is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))). [resolve(3020,a,130,a)].
% 120.84/121.14 3373 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(D,D),B),C))). [resolve(3027,a,130,a)].
% 120.84/121.14 3375 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(implies(C,B)). [resolve(3027,a,69,b)].
% 120.84/121.14 3448 is_a_theorem(implies(A,implies(B,implies(not(B),C)))). [resolve(3375,a,229,a)].
% 120.84/121.14 3449 is_a_theorem(implies(A,implies(implies(not(B),B),B))). [resolve(3375,a,228,a)].
% 120.84/121.14 3529 is_a_theorem(implies(implies(implies(A,implies(not(A),B)),C),implies(D,C))). [resolve(3448,a,130,a)].
% 120.84/121.14 3829 is_a_theorem(implies(implies(implies(implies(not(A),A),A),B),implies(C,B))). [resolve(3449,a,130,a)].
% 120.84/121.14 5537 -is_a_theorem(implies(implies(implies(not(A),A),A),B)) | is_a_theorem(implies(C,B)). [resolve(3829,a,69,b)].
% 120.84/121.14 6819 -is_a_theorem(implies(not(A),A)) | is_a_theorem(implies(implies(B,C),implies(not(A),C))). [resolve(610,a,69,b)].
% 120.84/121.14 7375 -is_a_theorem(implies(and(A,not(A)),B)) | is_a_theorem(implies(not(equiv(A,A)),B)). [resolve(1204,a,69,b)].
% 120.84/121.14 7782 is_a_theorem(implies(A,implies(implies(implies(B,B),C),C))). [resolve(3373,a,5537,a)].
% 120.84/121.14 7792 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(implies(D,D),B),C)). [resolve(3373,a,69,b)].
% 120.84/121.14 7864 is_a_theorem(implies(implies(implies(implies(implies(A,A),B),B),C),implies(D,C))). [resolve(7782,a,130,a)].
% 120.84/121.14 7866 is_a_theorem(implies(implies(implies(A,A),B),B)). [resolve(7782,a,122,a)].
% 120.84/121.14 7910 is_a_theorem(implies(implies(A,B),implies(implies(implies(C,C),A),B))). [resolve(7866,a,130,a)].
% 120.84/121.14 7911 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(B). [resolve(7866,a,69,b)].
% 120.84/121.14 8090 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(C,C),A),B)). [resolve(7910,a,69,b)].
% 120.84/121.14 8579 is_a_theorem(implies(implies(implies(A,A),implies(implies(B,B),C)),implies(D,C))). [resolve(8090,a,3027,a)].
% 120.84/121.14 10085 is_a_theorem(implies(implies(implies(A,A),B),implies(implies(B,C),implies(D,C)))). [resolve(7792,a,96,a)].
% 120.84/121.14 10156 -is_a_theorem(implies(implies(implies(implies(A,A),B),B),C)) | is_a_theorem(implies(D,C)). [resolve(7864,a,69,b)].
% 120.84/121.14 10707 -is_a_theorem(implies(implies(A,A),implies(implies(B,B),C))) | is_a_theorem(implies(D,C)). [resolve(8579,a,69,b)].
% 120.84/121.14 10955 -is_a_theorem(implies(implies(A,A),B)) | is_a_theorem(implies(implies(B,C),implies(D,C))). [resolve(10085,a,69,b)].
% 120.84/121.14 11611 is_a_theorem(implies(A,implies(and(B,not(B)),C))). [resolve(226,a,10156,a)].
% 120.84/121.14 11646 is_a_theorem(implies(and(A,not(A)),B)). [resolve(11611,a,7911,a)].
% 120.84/121.14 11706 is_a_theorem(implies(not(equiv(A,A)),B)). [back_unit_del(7375),unit_del(a,11646)].
% 120.84/121.14 11837 is_a_theorem(implies(implies(A,B),implies(not(equiv(C,C)),B))). [resolve(11706,a,6819,a)].
% 120.84/121.14 12766 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),C),implies(D,C))). [resolve(11837,a,10955,a)].
% 120.84/121.14 13179 is_a_theorem(implies(A,implies(B,equiv(C,C)))). [resolve(12766,a,5537,a)].
% 120.84/121.14 13232 is_a_theorem(implies(implies(implies(A,equiv(B,B)),C),implies(D,C))). [resolve(13179,a,10955,a)].
% 120.84/121.14 13235 is_a_theorem(implies(A,equiv(B,B))). [resolve(13179,a,10707,a)].
% 120.84/121.14 13314 is_a_theorem(implies(implies(equiv(A,A),B),implies(C,B))). [resolve(13235,a,10955,a)].
% 120.84/121.14 13636 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(equiv(D,D),B),C))). [resolve(13314,a,130,a)].
% 120.84/121.14 14157 -is_a_theorem(implies(implies(implies(not(A),A),B),C)) | is_a_theorem(implies(implies(A,B),C)). [resolve(230,a,69,b)].
% 120.84/121.14 14899 is_a_theorem(implies(A,implies(implies(equiv(B,B),C),C))). [resolve(13636,a,10156,a)].
% 120.84/121.14 14915 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(equiv(D,D),B),C)). [resolve(13636,a,69,b)].
% 120.84/121.14 14926 is_a_theorem(implies(implies(implies(implies(equiv(A,A),B),B),C),implies(D,C))). [resolve(14899,a,10955,a)].
% 120.84/121.14 14938 is_a_theorem(implies(implies(equiv(A,A),B),B)). [resolve(14899,a,7911,a)].
% 120.84/121.14 14969 is_a_theorem(implies(A,implies(implies(implies(not(implies(B,B)),C),D),D))). [resolve(242,a,10156,a)].
% 120.84/121.14 14976 is_a_theorem(implies(A,implies(implies(implies(not(not(B)),C),B),B))). [resolve(242,a,5537,a)].
% 120.84/121.14 14986 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(implies(implies(not(A),D),B),C)). [resolve(242,a,69,b)].
% 120.84/121.14 15016 is_a_theorem(implies(implies(A,B),implies(implies(equiv(C,C),A),B))). [resolve(14938,a,130,a)].
% 120.84/121.14 15017 -is_a_theorem(implies(equiv(A,A),B)) | is_a_theorem(B). [resolve(14938,a,69,b)].
% 120.84/121.14 15146 -is_a_theorem(implies(not(implies(c30,c29)),not(equiv(c29,c30)))). [ur(130,b,245,a)].
% 120.84/121.14 15185 is_a_theorem(implies(implies(implies(not(not(A)),B),A),A)). [resolve(14976,a,15017,a)].
% 120.84/121.14 15223 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(not(A)),C),A),B))). [resolve(15185,a,130,a)].
% 120.84/121.14 15224 -is_a_theorem(implies(implies(not(not(A)),B),A)) | is_a_theorem(A). [resolve(15185,a,69,b)].
% 120.84/121.14 15368 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(equiv(C,C),A),B)). [resolve(15016,a,69,b)].
% 120.84/121.14 16917 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),C)). [resolve(14969,a,15224,a)].
% 120.84/121.14 16958 -is_a_theorem(implies(implies(not(implies(A,A)),B),C)) | is_a_theorem(C). [resolve(16917,a,69,b)].
% 120.84/121.14 18244 is_a_theorem(implies(implies(equiv(A,A),B),implies(implies(B,C),implies(D,C)))). [resolve(14915,a,10085,a)].
% 120.84/121.14 18319 -is_a_theorem(implies(implies(implies(equiv(A,A),B),B),C)) | is_a_theorem(implies(D,C)). [resolve(14926,a,69,b)].
% 120.84/121.14 18511 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(not(A)),C),A),B)). [resolve(15223,a,69,b)].
% 120.84/121.14 19832 -is_a_theorem(implies(equiv(A,A),B)) | is_a_theorem(implies(implies(B,C),implies(D,C))). [resolve(18244,a,69,b)].
% 120.84/121.14 19938 is_a_theorem(implies(A,implies(implies(implies(not(equiv(B,B)),C),D),D))). [resolve(18319,a,242,a)].
% 120.84/121.14 19962 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),C),C)). [resolve(19938,a,16958,a)].
% 120.84/121.14 20006 is_a_theorem(implies(implies(A,B),implies(implies(implies(not(equiv(C,C)),D),A),B))). [resolve(19962,a,130,a)].
% 120.84/121.14 20007 -is_a_theorem(implies(implies(not(equiv(A,A)),B),C)) | is_a_theorem(C). [resolve(19962,a,69,b)].
% 120.84/121.14 20026 -is_a_theorem(not(equiv(not(equiv(A,A)),B))) | is_a_theorem(and(B,not(not(equiv(A,A))))). [para(257(a,1),20007(a,1))].
% 120.84/121.14 20628 is_a_theorem(implies(implies(implies(not(implies(A,A)),B),and(A,not(A))),C)). [resolve(18511,a,11646,a),rewrite([80(3)])].
% 120.84/121.14 22703 is_a_theorem(implies(and(not(implies(A,A)),not(B)),C)). [resolve(350,a,20628,a)].
% 120.84/121.14 22705 is_a_theorem(implies(and(not(equiv(A,A)),not(B)),C)). [resolve(350,a,19962,a)].
% 120.84/121.14 22711 is_a_theorem(implies(and(not(not(A)),not(B)),A)). [resolve(350,a,15185,a)].
% 120.84/121.14 22715 is_a_theorem(implies(and(A,not(equiv(B,B))),implies(C,D))). [resolve(350,a,13232,a)].
% 120.84/121.14 22722 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),implies(C,D))). [resolve(350,a,7864,a)].
% 120.84/121.14 22724 is_a_theorem(implies(and(implies(not(A),A),not(A)),implies(B,C))). [resolve(350,a,3829,a)].
% 120.84/121.14 22725 is_a_theorem(implies(and(A,not(implies(not(A),B))),implies(C,D))). [resolve(350,a,3529,a)].
% 120.84/121.14 22734 is_a_theorem(implies(and(A,not(B)),implies(implies(implies(not(A),C),B),D))). [resolve(350,a,242,a)].
% 120.84/121.14 22768 is_a_theorem(implies(implies(implies(not(not(A)),B),and(not(not(A)),not(B))),A)). [resolve(22711,a,232,a),rewrite([80(5)])].
% 120.84/121.14 22769 is_a_theorem(implies(implies(A,B),implies(and(not(not(A)),not(C)),B))). [resolve(22711,a,130,a)].
% 120.84/121.14 23085 is_a_theorem(implies(implies(equiv(A,A),and(not(implies(B,B)),not(C))),D)). [resolve(22703,a,15368,a)].
% 120.84/121.14 23133 is_a_theorem(implies(implies(implies(A,A),and(not(equiv(B,B)),not(C))),D)). [resolve(22705,a,8090,a)].
% 120.84/121.14 23574 is_a_theorem(implies(implies(implies(A,B),C),implies(and(D,not(equiv(E,E))),C))). [resolve(22715,a,130,a)].
% 120.84/121.14 23878 is_a_theorem(implies(and(implies(not(A),A),not(A)),not(equiv(B,C)))). [para(257(a,1),22724(a,1,2))].
% 120.84/121.14 23907 is_a_theorem(implies(and(A,not(implies(not(A),B))),not(equiv(C,D)))). [para(257(a,1),22725(a,1,2))].
% 120.84/121.14 24168 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),not(equiv(C,D)))). [para(257(a,1),22722(a,1,2))].
% 120.84/121.14 24558 is_a_theorem(implies(and(not(not(not(equiv(A,A)))),not(B)),C)). [resolve(22769,a,20007,a)].
% 120.84/121.14 24570 is_a_theorem(implies(implies(implies(and(not(not(A)),not(B)),A),C),implies(D,C))). [resolve(22769,a,10955,a)].
% 120.84/121.14 27108 is_a_theorem(implies(and(A,implies(B,not(A))),implies(not(equiv(not(A),B)),C))). [para(257(a,1),22734(a,1,2,1)),rewrite([80(4)])].
% 120.84/121.14 27461 is_a_theorem(and(equiv(A,A),implies(not(implies(B,B)),C))). [resolve(23085,a,132,a),rewrite([80(6)])].
% 120.84/121.14 27755 is_a_theorem(and(implies(A,A),implies(not(equiv(B,B)),C))). [resolve(23133,a,132,a),rewrite([80(6)])].
% 120.84/121.14 30595 -is_a_theorem(implies(implies(implies(A,B),implies(not(C),B)),D)) | is_a_theorem(implies(C,D)). [resolve(611,a,69,b)].
% 120.84/121.14 53809 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(implies(not(equiv(C,C)),D),A),B)). [resolve(20006,a,69,b)].
% 120.84/121.14 56155 is_a_theorem(implies(implies(not(A),and(not(not(A)),not(not(A)))),A)). [resolve(22768,a,14157,a)].
% 120.84/121.14 56221 -is_a_theorem(implies(not(A),and(not(not(A)),not(not(A))))) | is_a_theorem(A). [resolve(56155,a,69,b)].
% 120.84/121.14 56454 is_a_theorem(implies(A,implies(and(B,not(equiv(C,C))),D))). [resolve(23574,a,18319,a)].
% 120.84/121.14 56498 is_a_theorem(implies(implies(implies(and(A,not(equiv(B,B))),C),D),implies(E,D))). [resolve(56454,a,19832,a)].
% 120.84/121.14 61387 -is_a_theorem(and(A,implies(B,not(A)))) | is_a_theorem(implies(not(equiv(not(A),B)),C)). [resolve(27108,a,69,b)].
% 120.84/121.14 62362 is_a_theorem(implies(A,implies(B,implies(not(A),C)))). [resolve(30595,a,24570,a)].
% 120.84/121.14 62371 is_a_theorem(implies(A,implies(implies(implies(not(A),B),C),implies(D,C)))). [resolve(30595,a,10085,a)].
% 120.84/121.14 62462 is_a_theorem(implies(implies(implies(A,implies(not(B),C)),D),implies(B,D))). [resolve(62362,a,130,a)].
% 120.84/121.14 67507 is_a_theorem(implies(A,implies(B,implies(C,implies(not(B),D))))). [resolve(62462,a,3375,a)].
% 120.84/121.14 113951 is_a_theorem(implies(implies(implies(not(equiv(A,A)),B),and(not(not(C)),not(D))),C)). [resolve(53809,a,22711,a)].
% 120.84/121.14 114844 is_a_theorem(implies(and(and(A,not(equiv(B,B))),not(C)),implies(D,E))). [resolve(56498,a,350,a)].
% 120.84/121.14 115025 is_a_theorem(implies(and(and(A,not(equiv(B,B))),not(C)),not(equiv(D,E)))). [para(257(a,1),114844(a,1,2))].
% 120.84/121.14 118428 is_a_theorem(implies(not(equiv(not(implies(A,A)),not(equiv(B,B)))),C)). [resolve(61387,a,27755,a)].
% 120.84/121.14 118431 is_a_theorem(implies(not(equiv(not(equiv(A,A)),not(implies(B,B)))),C)). [resolve(61387,a,27461,a)].
% 120.84/121.14 118466 is_a_theorem(equiv(not(implies(A,A)),not(equiv(B,B)))). [resolve(118428,a,56221,a)].
% 120.84/121.14 118575 not(equiv(A,A)) = not(implies(B,B)). [resolve(118466,a,61,a)].
% 120.84/121.14 118585 not(equiv(A,A)) = c_0. [new_symbol(118575)].
% 120.84/121.14 118589 not(implies(A,A)) = c_0. [back_rewrite(118575),rewrite([118585(2)]),flip(a)].
% 120.84/121.14 118600 is_a_theorem(implies(c_0,A)). [back_rewrite(118431),rewrite([118585(2),118589(3),118585(4)])].
% 120.84/121.14 118610 is_a_theorem(implies(and(and(A,c_0),not(B)),not(equiv(C,D)))). [back_rewrite(115025),rewrite([118585(2)])].
% 120.84/121.14 118627 is_a_theorem(implies(implies(implies(c_0,A),and(not(not(B)),not(C))),B)). [back_rewrite(113951),rewrite([118585(2)])].
% 120.84/121.14 119005 is_a_theorem(implies(and(not(not(c_0)),not(A)),B)). [back_rewrite(24558),rewrite([118585(2)])].
% 120.84/121.14 119040 is_a_theorem(implies(implies(implies(A,A),and(c_0,not(B))),C)). [back_rewrite(23133),rewrite([118585(3)])].
% 120.84/121.14 119059 -is_a_theorem(not(equiv(c_0,A))) | is_a_theorem(and(A,not(c_0))). [back_rewrite(20026),rewrite([118585(2),118585(6)])].
% 120.84/121.14 119064 -is_a_theorem(implies(implies(c_0,A),B)) | is_a_theorem(B). [back_rewrite(20007),rewrite([118585(2)])].
% 120.84/121.14 121030 implies(A,equiv(B,B)) = not(and(A,c_0)). [para(118585(a,1),80(a,1,1,2)),flip(a)].
% 120.84/121.14 121178 is_a_theorem(implies(and(implies(not(A),A),not(A)),c_0)). [para(118585(a,1),23878(a,1,2))].
% 120.84/121.14 121181 is_a_theorem(implies(and(A,not(implies(not(A),B))),c_0)). [para(118585(a,1),23907(a,1,2))].
% 120.84/121.14 121203 is_a_theorem(implies(and(implies(implies(A,A),B),not(B)),c_0)). [para(118585(a,1),24168(a,1,2))].
% 120.84/121.14 122279 implies(A,implies(B,B)) = not(and(A,c_0)). [para(118589(a,1),80(a,1,1,2)),flip(a)].
% 120.84/121.14 126300 is_a_theorem(implies(implies(equiv(A,A),and(not(not(c_0)),not(B))),C)). [resolve(119005,a,15368,a)].
% 120.84/121.14 130632 -is_a_theorem(implies(not(and(equiv(A,A),c_0)),B)) | is_a_theorem(B). [para(121030(a,1),7911(a,1,1))].
% 120.84/121.14 131717 is_a_theorem(implies(implies(c_0,A),implies(and(implies(not(B),B),not(B)),A))). [resolve(121178,a,130,a)].
% 120.84/121.14 131789 is_a_theorem(implies(implies(c_0,A),implies(and(B,not(implies(not(B),C))),A))). [resolve(121181,a,130,a)].
% 120.84/121.14 137186 is_a_theorem(implies(implies(implies(c_0,A),and(c_0,not(B))),C)). [resolve(119040,a,14986,a),rewrite([118589(2)])].
% 120.84/121.14 138412 is_a_theorem(implies(and(implies(not(and(equiv(A,A),c_0)),B),not(B)),c_0)). [para(121030(a,1),121203(a,1,1,1,1))].
% 120.84/121.14 143313 is_a_theorem(and(implies(c_0,A),implies(c_0,B))). [resolve(137186,a,132,a),rewrite([80(6)])].
% 120.84/121.14 143348 is_a_theorem(implies(not(equiv(not(implies(c_0,A)),c_0)),B)). [resolve(143313,a,61387,a)].
% 120.84/121.14 143534 is_a_theorem(equiv(not(implies(c_0,A)),c_0)). [resolve(143348,a,56221,a)].
% 120.84/121.14 143628 not(implies(c_0,A)) = c_0. [resolve(143534,a,61,a),flip(a)].
% 120.84/121.14 143632 implies(A,implies(c_0,B)) = not(and(A,c_0)). [para(143628(a,1),80(a,1,1,2)),flip(a)].
% 120.84/121.14 147090 is_a_theorem(implies(and(and(A,c_0),not(B)),c_0)). [para(118585(a,1),118610(a,1,2))].
% 120.84/121.14 147158 is_a_theorem(implies(implies(c_0,A),implies(and(and(B,c_0),not(C)),A))). [resolve(147090,a,130,a)].
% 120.84/121.14 166178 is_a_theorem(implies(not(equiv(c_0,not(not(A)))),A)). [para(257(a,1),118627(a,1,1))].
% 120.84/121.14 166249 is_a_theorem(implies(implies(A,B),implies(not(equiv(c_0,not(not(A)))),B))). [resolve(166178,a,130,a)].
% 120.84/121.14 180869 is_a_theorem(and(equiv(A,A),implies(not(not(c_0)),B))). [resolve(126300,a,132,a),rewrite([80(7)])].
% 120.84/121.14 180903 is_a_theorem(implies(not(equiv(c_0,not(not(c_0)))),A)). [resolve(180869,a,61387,a),rewrite([118585(2)])].
% 120.84/121.14 180968 is_a_theorem(equiv(c_0,not(not(c_0)))). [resolve(180903,a,56221,a)].
% 120.84/121.14 181063 not(not(c_0)) = c_0. [resolve(180968,a,61,a)].
% 120.84/121.14 181096 not(and(A,c_0)) = implies(A,not(c_0)). [para(181063(a,1),80(a,1,1,2))].
% 120.84/121.14 181097 is_a_theorem(not(c_0)). [para(181063(a,1),122(a,1,1)),unit_del(a,118600)].
% 120.84/121.14 181105 implies(implies(not(c_0),A),and(A,c_0)) = not(equiv(not(c_0),A)). [para(181063(a,1),257(a,1,2,2))].
% 120.84/121.14 181107 is_a_theorem(implies(A,not(c_0))). [para(181063(a,1),3448(a,1,2,2,1)),rewrite([143632(5),181096(5),122279(6),181096(3)])].
% 120.84/121.14 181864 implies(A,implies(c_0,B)) = implies(A,not(c_0)). [back_rewrite(143632),rewrite([181096(6)])].
% 120.84/121.14 181917 is_a_theorem(implies(and(implies(implies(equiv(A,A),not(c_0)),B),not(B)),c_0)). [back_rewrite(138412),rewrite([181096(4)])].
% 120.84/121.14 182138 -is_a_theorem(implies(implies(equiv(A,A),not(c_0)),B)) | is_a_theorem(B). [back_rewrite(130632),rewrite([181096(4)])].
% 120.84/121.14 182292 implies(A,implies(B,B)) = implies(A,not(c_0)). [back_rewrite(122279),rewrite([181096(5)])].
% 120.84/121.14 182636 implies(A,equiv(B,B)) = implies(A,not(c_0)). [back_rewrite(121030),rewrite([181096(5)])].
% 120.84/121.14 183256 is_a_theorem(implies(implies(not(c_0),A),implies(B,A))). [resolve(181107,a,19832,a)].
% 120.84/121.14 184328 is_a_theorem(implies(implies(implies(A,B),C),implies(implies(not(c_0),B),C))). [resolve(183256,a,130,a)].
% 120.84/121.14 197119 is_a_theorem(implies(and(and(A,c_0),not(B)),C)). [resolve(147158,a,119064,a)].
% 120.84/121.14 203093 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(equiv(c_0,not(not(A)))),B)). [resolve(166249,a,69,b)].
% 120.84/121.14 222478 is_a_theorem(implies(A,implies(implies(not(c_0),B),B))). [resolve(184328,a,18319,a)].
% 120.84/121.14 222484 is_a_theorem(implies(implies(A,B),implies(implies(not(c_0),A),B))). [resolve(184328,a,14157,a)].
% 120.84/121.14 222510 is_a_theorem(implies(implies(not(c_0),A),A)). [resolve(222478,a,182138,a)].
% 120.84/121.14 222644 -is_a_theorem(implies(not(c_0),A)) | is_a_theorem(A). [resolve(222510,a,69,b)].
% 120.84/121.14 226514 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(c_0),A),B)). [resolve(222484,a,69,b)].
% 120.84/121.14 227984 is_a_theorem(implies(implies(not(c_0),and(and(A,c_0),not(B))),C)). [resolve(226514,a,197119,a)].
% 120.84/121.14 235672 is_a_theorem(and(not(c_0),implies(and(A,c_0),B))). [resolve(227984,a,132,a),rewrite([80(7)])].
% 120.84/121.14 235707 is_a_theorem(implies(not(equiv(c_0,and(A,c_0))),B)). [resolve(235672,a,61387,a),rewrite([181063(3)])].
% 120.84/121.14 235777 is_a_theorem(equiv(c_0,and(A,c_0))). [resolve(235707,a,56221,a)].
% 120.84/121.14 235869 and(A,c_0) = c_0. [resolve(235777,a,61,a)].
% 120.84/121.14 235910 implies(implies(not(c_0),A),c_0) = not(equiv(not(c_0),A)). [back_rewrite(181105),rewrite([235869(5)])].
% 120.84/121.14 235911 implies(A,not(c_0)) = not(c_0). [back_rewrite(181096),rewrite([235869(2)]),flip(a)].
% 120.84/121.14 235939 implies(A,equiv(B,B)) = not(c_0). [back_rewrite(182636),rewrite([235911(5)])].
% 120.84/121.14 235946 implies(A,implies(B,B)) = not(c_0). [back_rewrite(182292),rewrite([235911(5)])].
% 120.84/121.14 235958 is_a_theorem(implies(and(implies(not(c_0),A),not(A)),c_0)). [back_rewrite(181917),rewrite([235911(4)])].
% 120.84/121.14 235960 implies(A,implies(c_0,B)) = not(c_0). [back_rewrite(181864),rewrite([235911(6)])].
% 120.84/121.14 236066 and(not(c_0),implies(not(c_0),A)) = equiv(A,not(c_0)). [para(235911(a,1),90(a,1,1))].
% 120.84/121.14 239053 is_a_theorem(implies(implies(c_0,A),implies(and(implies(not(c_0),B),not(B)),A))). [resolve(235958,a,130,a)].
% 120.84/121.14 245242 implies(not(c_0),c_0) = c_0. [para(118585(a,1),235910(a,2)),rewrite([235911(5)])].
% 120.84/121.14 245275 not(equiv(not(c_0),equiv(A,A))) = c_0. [para(235939(a,1),235910(a,1,1)),rewrite([245242(4)]),flip(a)].
% 120.84/121.14 245276 not(equiv(not(c_0),implies(A,A))) = c_0. [para(235946(a,1),235910(a,1,1)),rewrite([245242(4)]),flip(a)].
% 120.84/121.14 245277 not(equiv(not(c_0),implies(c_0,A))) = c_0. [para(235960(a,1),235910(a,1,1)),rewrite([245242(4)]),flip(a)].
% 120.84/121.14 245301 is_a_theorem(implies(implies(not(c_0),A),implies(implies(A,c_0),c_0))). [para(245242(a,1),96(a,1,2,2))].
% 120.84/121.14 245355 implies(A,equiv(not(c_0),equiv(B,B))) = not(c_0). [para(245275(a,1),80(a,1,1,2)),rewrite([235869(2)]),flip(a)].
% 120.84/121.14 245356 is_a_theorem(equiv(not(c_0),equiv(A,A))). [para(245275(a,1),122(a,1,1)),rewrite([245355(6)]),unit_del(a,181097)].
% 120.84/121.14 245405 equiv(A,A) = not(c_0). [resolve(245356,a,61,a)].
% 120.84/121.14 246399 implies(A,equiv(not(c_0),implies(B,B))) = not(c_0). [para(245276(a,1),80(a,1,1,2)),rewrite([235869(2)]),flip(a)].
% 120.84/121.14 246400 is_a_theorem(equiv(not(c_0),implies(A,A))). [para(245276(a,1),122(a,1,1)),rewrite([246399(6)]),unit_del(a,181097)].
% 120.84/121.14 246445 implies(A,A) = not(c_0). [resolve(246400,a,61,a)].
% 120.84/121.14 247052 and(not(c_0),not(c_0)) = not(c_0). [para(246445(a,1),90(a,1,1)),rewrite([246445(3),245405(6)])].
% 120.84/121.14 247054 implies(A,and(B,not(B))) = implies(A,c_0). [para(246445(a,1),129(a,1,1,2)),rewrite([80(4)]),flip(a)].
% 120.84/121.14 247173 implies(A,equiv(not(c_0),implies(c_0,B))) = not(c_0). [para(245277(a,1),80(a,1,1,2)),rewrite([235869(2)]),flip(a)].
% 120.84/121.14 247174 is_a_theorem(equiv(not(c_0),implies(c_0,A))). [para(245277(a,1),122(a,1,1)),rewrite([247173(7)]),unit_del(a,181097)].
% 120.84/121.14 247220 implies(c_0,A) = not(c_0). [resolve(247174,a,61,a)].
% 120.84/121.14 247309 is_a_theorem(implies(not(c_0),implies(and(implies(not(c_0),A),not(A)),B))). [back_rewrite(239053),rewrite([247220(2)])].
% 120.84/121.14 247311 is_a_theorem(implies(not(c_0),implies(and(A,not(implies(not(A),B))),C))). [back_rewrite(131789),rewrite([247220(2)])].
% 120.84/121.14 247312 is_a_theorem(implies(not(c_0),implies(and(implies(not(A),A),not(A)),B))). [back_rewrite(131717),rewrite([247220(2)])].
% 120.84/121.14 247317 is_a_theorem(implies(implies(A,c_0),implies(not(c_0),implies(A,B)))). [para(247220(a,1),96(a,1,2,1))].
% 120.84/121.14 247318 implies(A,and(c_0,not(B))) = implies(A,c_0). [para(247220(a,1),129(a,1,1,2)),rewrite([80(4)]),flip(a)].
% 120.84/121.14 247319 implies(not(c_0),and(A,not(c_0))) = not(equiv(c_0,A)). [para(247220(a,1),257(a,1,1))].
% 120.84/121.14 247349 is_a_theorem(implies(and(A,not(c_0)),implies(not(equiv(not(A),c_0)),B))). [para(247220(a,1),27108(a,1,1,2))].
% 120.84/121.14 247481 implies(implies(A,c_0),and(and(B,not(B)),not(A))) = not(equiv(A,and(B,not(B)))). [para(247054(a,1),257(a,1,1))].
% 120.84/121.14 247506 implies(and(A,not(A)),c_0) = not(c_0). [para(247054(a,1),246445(a,1))].
% 120.84/121.14 247508 equiv(and(A,not(A)),c_0) = not(c_0). [para(247506(a,1),90(a,1,1)),rewrite([247054(6),246445(5),247052(5)]),flip(a)].
% 120.84/121.14 247531 and(A,not(A)) = c_0. [para(247508(a,1),61(a,1)),flip(b),unit_del(a,181097)].
% 120.84/121.14 247535 implies(implies(A,c_0),c_0) = not(equiv(A,c_0)). [back_rewrite(247481),rewrite([247531(4),247318(6),247531(6)])].
% 120.84/121.14 247553 is_a_theorem(implies(implies(not(c_0),A),not(equiv(A,c_0)))). [back_rewrite(245301),rewrite([247535(7)])].
% 120.84/121.14 248763 -is_a_theorem(implies(not(c_0),A)) | is_a_theorem(not(equiv(A,c_0))). [resolve(247553,a,69,b)].
% 120.84/121.14 249262 is_a_theorem(not(equiv(implies(A,implies(B,implies(not(A),C))),c_0))). [resolve(248763,a,67507,a)].
% 120.84/121.14 249283 is_a_theorem(not(equiv(implies(implies(implies(not(not(A)),B),A),A),c_0))). [resolve(248763,a,14976,a)].
% 120.84/121.14 255730 is_a_theorem(implies(and(implies(not(c_0),A),not(A)),B)). [resolve(247309,a,222644,a)].
% 120.84/121.14 255739 is_a_theorem(implies(not(equiv(c_0,not(implies(implies(not(c_0),A),A)))),B)). [resolve(255730,a,203093,a),rewrite([80(7)])].
% 120.84/121.14 255800 is_a_theorem(implies(and(A,not(implies(not(A),B))),C)). [resolve(247311,a,222644,a)].
% 120.84/121.14 255809 is_a_theorem(implies(not(equiv(c_0,not(implies(A,implies(not(A),B))))),C)). [resolve(255800,a,203093,a),rewrite([80(6)])].
% 120.84/121.14 255843 is_a_theorem(implies(and(implies(not(A),A),not(A)),B)). [resolve(247312,a,222644,a)].
% 120.84/121.14 255870 is_a_theorem(implies(implies(not(c_0),and(implies(not(A),A),not(A))),B)). [resolve(255843,a,226514,a)].
% 120.84/121.14 256601 is_a_theorem(equiv(c_0,not(implies(implies(not(c_0),A),A)))). [resolve(255739,a,56221,a)].
% 120.84/121.14 256606 not(implies(implies(not(c_0),A),A)) = c_0. [resolve(256601,a,61,a)].
% 120.84/121.14 256608 implies(A,implies(implies(not(c_0),B),B)) = not(c_0). [para(256606(a,1),80(a,1,1,2)),rewrite([235869(2)]),flip(a)].
% 120.84/121.14 256619 equiv(implies(implies(not(c_0),A),A),not(c_0)) = not(c_0). [para(256608(a,1),236066(a,1,2)),rewrite([247052(5)]),flip(a)].
% 120.84/121.14 256628 implies(implies(not(c_0),A),A) = not(c_0). [para(256619(a,1),61(a,1)),flip(b),unit_del(a,181097)].
% 120.84/121.14 256632 and(implies(A,implies(not(c_0),A)),not(c_0)) = equiv(A,implies(not(c_0),A)). [para(256628(a,1),90(a,1,2))].
% 120.84/121.14 256715 is_a_theorem(equiv(c_0,not(implies(A,implies(not(A),B))))). [resolve(255809,a,56221,a)].
% 120.84/121.14 256721 not(implies(A,implies(not(A),B))) = c_0. [resolve(256715,a,61,a)].
% 120.84/121.14 256723 implies(A,implies(B,implies(not(B),C))) = not(c_0). [para(256721(a,1),80(a,1,1,2)),rewrite([235869(2)]),flip(a)].
% 120.84/121.14 256738 equiv(implies(A,implies(not(A),B)),not(c_0)) = not(c_0). [para(256723(a,1),236066(a,1,2)),rewrite([247052(5)]),flip(a)].
% 120.84/121.14 256750 implies(A,implies(not(A),B)) = not(c_0). [para(256738(a,1),61(a,1)),flip(b),unit_del(a,181097)].
% 120.84/121.14 256753 and(not(c_0),implies(implies(not(A),B),A)) = equiv(A,implies(not(A),B)). [para(256750(a,1),90(a,1,1))].
% 120.84/121.14 256867 is_a_theorem(equiv(A,implies(not(A),A))). [resolve(255870,a,132,a),rewrite([80(7),256753(6)])].
% 120.84/121.14 256903 implies(not(A),A) = A. [resolve(256867,a,61,a)].
% 120.84/121.14 257218 is_a_theorem(implies(A,implies(implies(A,B),implies(C,B)))). [para(256903(a,1),62371(a,1,2,1,1))].
% 120.84/121.14 257331 is_a_theorem(implies(implies(not(A),c_0),implies(not(c_0),A))). [para(256903(a,1),247317(a,1,2,2))].
% 120.84/121.14 257340 is_a_theorem(not(equiv(implies(A,implies(B,A)),c_0))). [para(256903(a,1),249262(a,1,1,1,2,2))].
% 120.84/121.14 257375 is_a_theorem(implies(and(A,not(c_0)),equiv(not(A),c_0))). [para(256903(a,1),247349(a,1,2))].
% 120.84/121.14 260773 is_a_theorem(implies(A,implies(implies(A,B),B))). [para(256903(a,1),257218(a,1,2,2))].
% 120.84/121.14 261597 is_a_theorem(implies(not(equiv(A,c_0)),not(equiv(c_0,A)))). [para(247319(a,1),257331(a,1,2)),rewrite([80(4),247535(4)])].
% 120.84/121.14 261662 -is_a_theorem(and(A,not(c_0))) | is_a_theorem(equiv(not(A),c_0)). [resolve(257375,a,69,b)].
% 120.84/121.14 262520 -is_a_theorem(not(equiv(A,c_0))) | is_a_theorem(not(equiv(c_0,A))). [resolve(261597,a,69,b)].
% 120.84/121.14 262750 is_a_theorem(not(equiv(c_0,implies(A,implies(B,A))))). [resolve(262520,a,257340,a)].
% 120.84/121.14 262761 is_a_theorem(not(equiv(c_0,implies(implies(implies(not(not(A)),B),A),A)))). [resolve(262520,a,249283,a)].
% 120.84/121.14 262820 is_a_theorem(and(implies(A,implies(B,A)),not(c_0))). [resolve(262750,a,119059,a)].
% 120.84/121.14 262836 is_a_theorem(equiv(not(implies(A,implies(B,A))),c_0)). [resolve(262820,a,261662,a)].
% 120.84/121.14 262890 not(implies(A,implies(B,A))) = c_0. [resolve(262836,a,61,a),flip(a)].
% 120.84/121.14 262892 implies(A,implies(B,implies(C,B))) = not(c_0). [para(262890(a,1),80(a,1,1,2)),rewrite([235869(2)]),flip(a)].
% 120.84/121.14 262894 implies(A,implies(B,A)) = not(c_0). [para(262890(a,1),256903(a,1,1)),rewrite([262892(4)]),flip(a)].
% 120.84/121.14 262898 equiv(A,implies(not(c_0),A)) = not(c_0). [back_rewrite(256632),rewrite([262894(4),247052(5)]),flip(a)].
% 120.84/121.14 262921 and(implies(implies(A,B),B),not(c_0)) = equiv(implies(A,B),B). [para(262894(a,1),90(a,1,2))].
% 120.84/121.14 262944 implies(not(c_0),A) = A. [para(262898(a,1),61(a,1)),unit_del(a,181097)].
% 120.84/121.14 263087 not(equiv(c_0,A)) = and(A,not(c_0)). [back_rewrite(247319),rewrite([262944(6)]),flip(a)].
% 120.84/121.14 263101 is_a_theorem(equiv(implies(implies(not(not(A)),B),A),A)). [back_rewrite(262761),rewrite([263087(8),262921(8)])].
% 120.84/121.14 266619 implies(implies(not(not(A)),B),A) = A. [resolve(263101,a,61,a),flip(a)].
% 120.84/121.14 266703 is_a_theorem(implies(not(not(A)),A)). [para(266619(a,1),260773(a,1,2))].
% 120.84/121.14 267138 is_a_theorem(implies(implies(A,c_0),equiv(c_0,A))). [para(263087(a,1),266703(a,1,1,1)),rewrite([80(4)])].
% 120.84/121.14 267245 is_a_theorem(implies(A,equiv(c_0,not(A)))). [resolve(267138,a,244,a)].
% 120.84/121.14 267386 -is_a_theorem(A) | is_a_theorem(equiv(c_0,not(A))). [resolve(267245,a,69,b)].
% 120.84/121.14 267441 is_a_theorem(equiv(c_0,not(implies(not(not(A)),A)))). [resolve(267386,a,266703,a)].
% 120.84/121.14 267943 not(implies(not(not(A)),A)) = c_0. [resolve(267441,a,61,a)].
% 120.84/121.14 267979 implies(A,implies(not(not(B)),B)) = not(c_0). [para(267943(a,1),80(a,1,1,2)),rewrite([235869(2)]),flip(a)].
% 120.84/121.14 267986 implies(not(not(A)),A) = not(c_0). [para(267943(a,1),256903(a,1,1)),rewrite([267979(5)]),flip(a)].
% 120.84/121.14 268029 is_a_theorem(implies(not(not(A)),implies(B,A))). [para(267986(a,1),257218(a,1,2,1)),rewrite([262944(6)])].
% 120.84/121.14 268093 is_a_theorem(implies(not(implies(A,B)),not(equiv(B,A)))). [para(257(a,1),268029(a,1,2)),rewrite([80(3)])].
% 120.84/121.14 268094 $F. [resolve(268093,a,15146,a)].
% 120.84/121.14
% 120.84/121.14 % SZS output end Refutation
% 120.84/121.14 ============================== end of proof ==========================
% 120.84/121.14
% 120.84/121.14 ============================== STATISTICS ============================
% 120.84/121.14
% 120.84/121.14 Given=8877. Generated=14505328. Kept=268043. proofs=1.
% 120.84/121.14 Usable=1114. Sos=8102. Demods=83. Limbo=62, Disabled=258836. Hints=0.
% 120.84/121.14 Megabytes=188.81.
% 120.84/121.14 User_CPU=112.94, System_CPU=7.20, Wall_clock=120.
% 120.84/121.14
% 120.84/121.14 ============================== end of statistics =====================
% 120.84/121.14
% 120.84/121.14 ============================== end of search =========================
% 120.84/121.14
% 120.84/121.14 THEOREM PROVED
% 120.84/121.14 % SZS status Theorem
% 120.84/121.14
% 120.84/121.14 Exiting with 1 proof.
% 120.84/121.14
% 120.84/121.14 Process 25018 exit (max_proofs) Sat Jul 2 22:57:29 2022
% 120.84/121.14 Prover9 interrupted
%------------------------------------------------------------------------------