TSTP Solution File: LCL495+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL495+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.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 13:47:12 EDT 2022
% Result : Theorem 58.54s 58.82s
% Output : Refutation 58.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL495+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jul 2 16:27:37 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.42/1.01 ============================== Prover9 ===============================
% 0.42/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.42/1.01 Process 10344 was started by sandbox on n009.cluster.edu,
% 0.42/1.01 Sat Jul 2 16:27:38 2022
% 0.42/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_10191_n009.cluster.edu".
% 0.42/1.01 ============================== end of head ===========================
% 0.42/1.01
% 0.42/1.01 ============================== INPUT =================================
% 0.42/1.01
% 0.42/1.01 % Reading from file /tmp/Prover9_10191_n009.cluster.edu
% 0.42/1.01
% 0.42/1.01 set(prolog_style_variables).
% 0.42/1.01 set(auto2).
% 0.42/1.01 % set(auto2) -> set(auto).
% 0.42/1.01 % set(auto) -> set(auto_inference).
% 0.42/1.01 % set(auto) -> set(auto_setup).
% 0.42/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.42/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/1.01 % set(auto) -> set(auto_limits).
% 0.42/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/1.01 % set(auto) -> set(auto_denials).
% 0.42/1.01 % set(auto) -> set(auto_process).
% 0.42/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.42/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.42/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.42/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.42/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.42/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.42/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.42/1.01 % set(auto2) -> assign(stats, some).
% 0.42/1.01 % set(auto2) -> clear(echo_input).
% 0.42/1.01 % set(auto2) -> set(quiet).
% 0.42/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.42/1.01 % set(auto2) -> clear(print_given).
% 0.42/1.01 assign(lrs_ticks,-1).
% 0.42/1.01 assign(sos_limit,10000).
% 0.42/1.01 assign(order,kbo).
% 0.42/1.01 set(lex_order_vars).
% 0.42/1.01 clear(print_given).
% 0.42/1.01
% 0.42/1.01 % formulas(sos). % not echoed (45 formulas)
% 0.42/1.01
% 0.42/1.01 ============================== end of input ==========================
% 0.42/1.01
% 0.42/1.01 % From the command line: assign(max_seconds, 300).
% 0.42/1.01
% 0.42/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/1.01
% 0.42/1.01 % Formulas that are not ordinary clauses:
% 0.42/1.01 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].
% 0.42/1.01 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].
% 0.42/1.01 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].
% 0.42/1.01 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.01 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].
% 0.42/1.01 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].
% 0.42/1.01 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.01 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.01 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].
% 0.42/1.01 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.01 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.01 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].
% 0.42/1.01 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].
% 0.42/1.01 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].
% 1.55/1.83 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].
% 1.55/1.83 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.83 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.83 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].
% 1.55/1.83 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].
% 1.55/1.83 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.83 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.83 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.83 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.83 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.83 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].
% 1.55/1.83 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].
% 1.55/1.83 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].
% 1.55/1.83 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].
% 1.55/1.83 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].
% 1.55/1.83 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].
% 1.55/1.83 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].
% 1.55/1.83
% 1.55/1.83 ============================== end of process non-clausal formulas ===
% 1.55/1.83
% 1.55/1.83 ============================== PROCESS INITIAL CLAUSES ===============
% 1.55/1.83
% 1.55/1.83 ============================== PREDICATE ELIMINATION =================
% 1.55/1.83
% 1.55/1.83 ============================== end predicate elimination =============
% 1.55/1.83
% 1.55/1.83 Auto_denials: (non-Horn, no changes).
% 1.55/1.83
% 1.55/1.83 Term ordering decisions:
% 1.55/1.83
% 1.55/1.83 % Assigning unary symbol not kb_weight 0 and highest precedence (93).
% 1.55/1.83 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.
% 1.55/1.83
% 1.55/1.83 ============================== end of process initial clauses ========
% 1.55/1.83
% 1.55/1.83 ============================== CLAUSES FOR SEARCH ====================
% 1.55/1.83
% 1.55/1.83 ============================== end of clauses for search =============
% 1.55/1.83
% 1.55/1.83 ============================== SEARCH ================================
% 1.55/1.83
% 1.55/1.83 % Starting search at 0.02 seconds.
% 1.55/1.83
% 1.55/1.83 Low Water (keep): wt=35.000, iters=3394
% 1.55/1.83
% 1.55/1.83 Low Water (keep): wt=32.000, iters=3345
% 1.55/1.83
% 1.55/1.83 Low Water (keep): wt=30.000, iters=3378
% 1.55/1.83
% 1.55/1.83 Low Water (keep): wt=29.000, iters=3352
% 1.55/1.83
% 1.55/1.83 Low Water (keep): wt=28.000, iters=3391
% 1.55/1.83
% 1.55/1.83 Low Water (keep): wt=23.000, iters=3385
% 1.55/1.83
% 1.55/1.83 Low Water (keep): wt=22.000, iters=3358
% 1.55/1.83
% 1.55/1.83 Low Water (keep): wt=21.000, iters=3440
% 1.55/1.83
% 1.55/1.83 Low Water (keep): wt=20.000, iters=3434
% 1.55/1.83
% 1.55/1.83 Low Water (keep): wt=19.000, iters=3466
% 1.55/1.83
% 58.54/58.82 Low Water (keep): wt=18.000, iters=3349
% 58.54/58.82
% 58.54/58.82 Low Water (keep): wt=17.000, iters=3346
% 58.54/58.82
% 58.54/58.82 Low Water (keep): wt=16.000, iters=3376
% 58.54/58.82
% 58.54/58.82 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 22 (0.00 of 1.04 sec).
% 58.54/58.82
% 58.54/58.82 Low Water (keep): wt=15.000, iters=3340
% 58.54/58.82
% 58.54/58.82 Low Water (displace): id=8041, wt=40.000
% 58.54/58.82
% 58.54/58.82 Low Water (displace): id=8040, wt=37.000
% 58.54/58.82
% 58.54/58.82 Low Water (displace): id=8039, wt=36.000
% 58.54/58.82
% 58.54/58.82 Low Water (displace): id=15728, wt=14.000
% 58.54/58.82
% 58.54/58.82 Low Water (displace): id=16260, wt=13.000
% 58.54/58.82
% 58.54/58.82 Low Water (displace): id=17789, wt=12.000
% 58.54/58.82
% 58.54/58.82 Low Water (keep): wt=14.000, iters=3334
% 58.54/58.82
% 58.54/58.82 Low Water (displace): id=18440, wt=11.000
% 58.54/58.82
% 58.54/58.82 Low Water (keep): wt=13.000, iters=3337
% 58.54/58.82
% 58.54/58.82 Low Water (keep): wt=12.000, iters=3363
% 58.54/58.82
% 58.54/58.82 Low Water (keep): wt=11.000, iters=3337
% 58.54/58.82
% 58.54/58.82 ============================== PROOF =================================
% 58.54/58.82 % SZS status Theorem
% 58.54/58.82 % SZS output start Refutation
% 58.54/58.82
% 58.54/58.82 % Proof 1 at 54.62 (+ 3.20) seconds.
% 58.54/58.82 % Length of proof is 205.
% 58.54/58.82 % Level of proof is 44.
% 58.54/58.82 % Maximum clause weight is 25.000.
% 58.54/58.82 % Given clauses 5638.
% 58.54/58.82
% 58.54/58.82 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].
% 58.54/58.82 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].
% 58.54/58.82 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].
% 58.54/58.82 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 58.54/58.82 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 58.54/58.82 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 58.54/58.82 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].
% 58.54/58.82 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].
% 58.54/58.82 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].
% 58.54/58.82 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].
% 58.54/58.82 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].
% 58.54/58.82 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].
% 58.54/58.82 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].
% 58.54/58.82 32 op_implies_or # label(principia_op_implies_or) # label(axiom). [assumption].
% 58.54/58.82 33 op_and # label(principia_op_and) # label(axiom). [assumption].
% 58.54/58.82 34 op_equiv # label(principia_op_equiv) # label(axiom). [assumption].
% 58.54/58.82 35 modus_ponens # label(principia_modus_ponens) # label(axiom). [assumption].
% 58.54/58.82 36 r1 # label(principia_r1) # label(axiom). [assumption].
% 58.54/58.82 37 r2 # label(principia_r2) # label(axiom). [assumption].
% 58.54/58.82 38 r3 # label(principia_r3) # label(axiom). [assumption].
% 58.54/58.82 39 r4 # label(principia_r4) # label(axiom). [assumption].
% 58.54/58.82 40 r5 # label(principia_r5) # label(axiom). [assumption].
% 58.54/58.82 41 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom). [assumption].
% 58.54/58.82 42 op_or # label(hilbert_op_or) # label(axiom). [assumption].
% 58.54/58.82 43 op_implies_and # label(hilbert_op_implies_and) # label(axiom). [assumption].
% 58.54/58.82 44 -equivalence_3 # label(hilbert_equivalence_3) # label(negated_conjecture). [assumption].
% 58.54/58.82 59 -r1 | is_a_theorem(implies(or(A,A),A)) # label(r1) # label(axiom). [clausify(22)].
% 58.54/58.82 60 is_a_theorem(implies(or(A,A),A)). [copy(59),unit_del(a,36)].
% 58.54/58.82 62 -r2 | is_a_theorem(implies(A,or(B,A))) # label(r2) # label(axiom). [clausify(23)].
% 58.54/58.82 63 is_a_theorem(implies(A,or(B,A))). [copy(62),unit_del(a,37)].
% 58.54/58.82 65 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom). [clausify(2)].
% 58.54/58.82 66 -is_a_theorem(equiv(A,B)) | B = A. [copy(65),unit_del(a,41)].
% 58.54/58.82 71 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 58.54/58.82 72 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(71),unit_del(a,35)].
% 58.54/58.82 79 -r3 | is_a_theorem(implies(or(A,B),or(B,A))) # label(r3) # label(axiom). [clausify(24)].
% 58.54/58.82 80 is_a_theorem(implies(or(A,B),or(B,A))). [copy(79),unit_del(a,38)].
% 58.54/58.82 82 -op_implies_or | or(not(A),B) = implies(A,B) # label(op_implies_or) # label(axiom). [clausify(30)].
% 58.54/58.82 83 or(not(A),B) = implies(A,B). [copy(82),unit_del(a,32)].
% 58.54/58.82 84 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 58.54/58.82 85 not(and(A,not(B))) = implies(A,B). [copy(84),unit_del(a,43)].
% 58.54/58.82 90 -op_or | or(A,B) = not(and(not(A),not(B))) # label(op_or) # label(axiom). [clausify(27)].
% 58.54/58.82 91 or(A,B) = implies(not(A),B). [copy(90),rewrite([85(6)]),unit_del(a,42)].
% 58.54/58.82 92 -op_and | and(A,B) = not(or(not(A),not(B))) # label(op_and) # label(axiom). [clausify(28)].
% 58.54/58.82 93 not(implies(not(not(A)),not(B))) = and(A,B). [copy(92),rewrite([91(5)]),flip(b),unit_del(a,33)].
% 58.54/58.82 94 -op_equiv | and(implies(A,B),implies(B,A)) = equiv(A,B) # label(op_equiv) # label(axiom). [clausify(31)].
% 58.54/58.82 95 and(implies(A,B),implies(B,A)) = equiv(A,B). [copy(94),unit_del(a,34)].
% 58.54/58.82 98 equivalence_3 | -is_a_theorem(implies(implies(c31,c32),implies(implies(c32,c31),equiv(c31,c32)))) # label(equivalence_3) # label(axiom). [clausify(15)].
% 58.54/58.82 99 -is_a_theorem(implies(implies(c31,c32),implies(implies(c32,c31),equiv(c31,c32)))). [copy(98),unit_del(a,44)].
% 58.54/58.82 102 -r4 | is_a_theorem(implies(or(A,or(B,C)),or(B,or(A,C)))) # label(r4) # label(axiom). [clausify(25)].
% 58.54/58.82 103 is_a_theorem(implies(implies(not(A),implies(not(B),C)),implies(not(B),implies(not(A),C)))). [copy(102),rewrite([91(2),91(4),91(6),91(8)]),unit_del(a,39)].
% 58.54/58.82 105 -r5 | is_a_theorem(implies(implies(A,B),implies(or(C,A),or(C,B)))) # label(r5) # label(axiom). [clausify(26)].
% 58.54/58.82 106 is_a_theorem(implies(implies(A,B),implies(implies(not(C),A),implies(not(C),B)))). [copy(105),rewrite([91(3),91(5)]),unit_del(a,40)].
% 58.54/58.82 115 implies(not(not(A)),B) = implies(A,B). [back_rewrite(83),rewrite([91(2)])].
% 58.54/58.82 116 is_a_theorem(implies(implies(not(A),B),implies(not(B),A))). [back_rewrite(80),rewrite([91(1),91(3)])].
% 58.54/58.82 117 is_a_theorem(implies(A,implies(not(B),A))). [back_rewrite(63),rewrite([91(1)])].
% 58.54/58.82 118 is_a_theorem(implies(implies(not(A),A),A)). [back_rewrite(60),rewrite([91(1)])].
% 58.54/58.82 121 not(implies(A,not(B))) = and(A,B). [back_rewrite(93),rewrite([115(4)])].
% 58.54/58.82 124 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(85(a,1),85(a,1,1,2))].
% 58.54/58.82 125 -is_a_theorem(implies(not(A),implies(not(B),C))) | is_a_theorem(implies(not(B),implies(not(A),C))). [resolve(103,a,72,b)].
% 58.54/58.82 129 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(not(C),A),implies(not(C),B))). [resolve(106,a,72,b)].
% 58.54/58.82 133 implies(not(implies(A,B)),C) = implies(and(A,not(B)),C). [para(85(a,1),115(a,1,1,1))].
% 58.54/58.82 135 and(implies(A,not(not(B))),implies(B,A)) = equiv(A,not(not(B))). [para(115(a,1),95(a,1,2))].
% 58.54/58.82 139 is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))). [para(115(a,1),106(a,1,2,1)),rewrite([115(5)])].
% 58.54/58.82 140 -is_a_theorem(implies(not(A),B)) | is_a_theorem(implies(not(B),A)). [resolve(116,a,72,b)].
% 58.54/58.82 144 is_a_theorem(implies(implies(A,B),implies(not(B),not(A)))). [para(115(a,1),116(a,1,1))].
% 58.54/58.82 150 is_a_theorem(implies(A,implies(B,A))). [para(115(a,1),117(a,1,2))].
% 58.54/58.82 153 -is_a_theorem(implies(not(A),A)) | is_a_theorem(A). [resolve(118,a,72,b)].
% 58.54/58.82 157 is_a_theorem(implies(implies(A,not(A)),not(A))). [para(115(a,1),118(a,1,1))].
% 58.54/58.82 159 not(implies(A,implies(B,C))) = and(A,and(B,not(C))). [para(85(a,1),121(a,1,1,2))].
% 58.54/58.82 161 and(not(not(A)),B) = and(A,B). [para(115(a,1),121(a,1,1)),rewrite([121(3)]),flip(a)].
% 58.54/58.82 168 implies(implies(A,B),and(B,not(A))) = not(equiv(A,B)). [para(95(a,1),124(a,1,1)),flip(a)].
% 58.54/58.82 197 -is_a_theorem(A) | is_a_theorem(implies(B,A)). [resolve(150,a,72,b)].
% 58.54/58.82 202 is_a_theorem(implies(A,implies(B,not(not(A))))). [para(115(a,1),150(a,1))].
% 58.54/58.82 206 is_a_theorem(implies(not(A),implies(not(B),not(B)))). [resolve(125,a,150,a)].
% 58.54/58.82 209 -is_a_theorem(implies(not(A),implies(B,C))) | is_a_theorem(implies(B,implies(not(A),C))). [para(115(a,1),125(a,1,2)),rewrite([115(9)])].
% 58.54/58.82 229 -is_a_theorem(implies(and(implies(c31,c32),and(implies(c32,c31),not(equiv(c31,c32)))),implies(implies(c31,c32),implies(implies(c32,c31),equiv(c31,c32))))). [ur(153,b,99,a),rewrite([159(12)])].
% 58.54/58.82 247 -is_a_theorem(A) | is_a_theorem(implies(B,not(not(A)))). [resolve(202,a,72,b)].
% 58.54/58.82 350 is_a_theorem(implies(implies(not(A),implies(not(B),B)),implies(not(A),B))). [resolve(129,a,118,a)].
% 58.54/58.82 403 is_a_theorem(implies(not(A),not(A))). [resolve(206,a,153,a)].
% 58.54/58.82 444 is_a_theorem(implies(A,not(not(A)))). [para(115(a,1),403(a,1))].
% 58.54/58.82 446 is_a_theorem(implies(A,implies(B,B))). [resolve(444,a,247,a),rewrite([121(4),85(3)])].
% 58.54/58.82 472 is_a_theorem(implies(A,A)). [resolve(446,a,153,a)].
% 58.54/58.82 549 is_a_theorem(implies(A,not(not(implies(B,B))))). [resolve(472,a,247,a)].
% 58.54/58.82 760 implies(and(A,not(not(B))),C) = implies(and(A,B),C). [para(121(a,1),133(a,1,1)),flip(a)].
% 58.54/58.82 1041 equiv(A,not(not(B))) = equiv(A,B). [para(135(a,1),161(a,2)),rewrite([121(4),85(3),95(3)]),flip(a)].
% 58.54/58.82 1336 -is_a_theorem(equiv(A,B)) | not(not(B)) = A. [para(1041(a,1),66(a,1))].
% 58.54/58.82 1351 is_a_theorem(implies(and(A,not(A)),B)). [resolve(140,a,549,a),rewrite([115(5),133(3)])].
% 58.54/58.82 1356 is_a_theorem(implies(and(A,B),B)). [resolve(140,a,202,a),rewrite([121(5),760(4)])].
% 58.54/58.82 1358 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(B),not(A))). [para(115(a,1),140(a,1))].
% 58.54/58.82 1500 is_a_theorem(implies(implies(not(A),and(B,C)),implies(not(A),C))). [resolve(1356,a,129,a)].
% 58.54/58.82 1615 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(C,A),implies(C,B))). [resolve(139,a,72,b)].
% 58.54/58.82 2845 is_a_theorem(implies(implies(A,not(B)),implies(B,not(A)))). [para(115(a,1),144(a,1,2))].
% 58.54/58.82 6713 is_a_theorem(implies(A,and(A,A))). [resolve(1358,a,157,a),rewrite([121(5),115(4)])].
% 58.54/58.82 6730 -is_a_theorem(A) | is_a_theorem(and(A,A)). [resolve(6713,a,72,b)].
% 58.54/58.82 6859 is_a_theorem(equiv(A,A)). [resolve(6730,a,472,a),rewrite([95(3)])].
% 58.54/58.82 7046 not(not(A)) = A. [resolve(6859,a,1336,a)].
% 58.54/58.82 7110 not(and(A,B)) = implies(A,not(B)). [para(7046(a,1),85(a,1,1,2))].
% 58.54/58.82 7111 not(implies(A,B)) = and(A,not(B)). [para(85(a,1),7046(a,1,1))].
% 58.54/58.82 7233 implies(implies(not(A),B),and(B,A)) = not(equiv(not(A),B)). [para(7046(a,1),168(a,1,2,2))].
% 58.54/58.82 8898 is_a_theorem(implies(and(A,B),and(B,A))). [resolve(2845,a,1358,a),rewrite([7111(3),7046(2),7111(4),7046(3)])].
% 58.54/58.82 8900 -is_a_theorem(implies(A,not(B))) | is_a_theorem(implies(B,not(A))). [resolve(2845,a,72,b)].
% 58.54/58.82 9171 is_a_theorem(implies(A,implies(and(B,C),and(C,B)))). [resolve(8898,a,197,a)].
% 58.54/58.82 11081 -is_a_theorem(implies(A,implies(B,C))) | is_a_theorem(implies(B,implies(A,C))). [para(7046(a,1),209(a,1,1)),rewrite([7046(5)])].
% 58.54/58.82 15077 is_a_theorem(implies(implies(A,and(B,C)),implies(A,C))). [para(7046(a,1),1500(a,1,1,1)),rewrite([7046(4)])].
% 58.54/58.82 15106 -is_a_theorem(implies(A,and(B,C))) | is_a_theorem(implies(A,C)). [resolve(15077,a,72,b)].
% 58.54/58.82 15125 is_a_theorem(implies(and(A,B),A)). [resolve(15106,a,8898,a)].
% 58.54/58.82 15157 is_a_theorem(implies(A,implies(not(A),not(B)))). [resolve(15125,a,8900,a),rewrite([7110(3)])].
% 58.54/58.82 15710 is_a_theorem(implies(A,implies(not(A),B))). [para(7046(a,1),15157(a,1,2,2))].
% 58.54/58.82 15778 is_a_theorem(implies(not(A),implies(A,B))). [para(7046(a,1),15710(a,1,2,1))].
% 58.54/58.82 15910 -is_a_theorem(not(A)) | is_a_theorem(implies(A,B)). [resolve(15778,a,72,b)].
% 58.54/58.82 19882 is_a_theorem(implies(implies(A,implies(not(B),B)),implies(A,B))). [para(7046(a,1),350(a,1,1,1)),rewrite([7046(5)])].
% 58.54/58.82 21094 -is_a_theorem(implies(A,implies(not(B),B))) | is_a_theorem(implies(A,B)). [resolve(19882,a,72,b)].
% 58.54/58.82 21196 is_a_theorem(implies(implies(not(A),and(B,A)),A)). [resolve(21094,a,15077,a)].
% 58.54/58.82 21818 is_a_theorem(implies(A,and(A,implies(B,A)))). [resolve(21196,a,8900,a),rewrite([7046(2),7111(4),7110(3),7046(2)])].
% 58.54/58.82 30715 is_a_theorem(implies(implies(A,and(B,C)),implies(A,B))). [resolve(1615,a,15125,a)].
% 58.54/58.82 30799 is_a_theorem(implies(implies(A,B),implies(A,and(B,B)))). [resolve(1615,a,6713,a)].
% 58.54/58.82 30896 is_a_theorem(implies(not(equiv(A,B)),implies(implies(A,B),B))). [para(168(a,1),30715(a,1,1))].
% 58.54/58.82 31006 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(A,and(B,B))). [resolve(30799,a,72,b)].
% 58.54/58.82 32276 is_a_theorem(not(equiv(A,not(A)))). [resolve(31006,a,157,a),rewrite([168(6)])].
% 58.54/58.82 32283 is_a_theorem(not(equiv(not(A),A))). [resolve(31006,a,118,a),rewrite([7233(4)])].
% 58.54/58.82 32307 is_a_theorem(implies(equiv(A,not(A)),B)). [resolve(32276,a,15910,a)].
% 58.54/58.82 32374 is_a_theorem(implies(equiv(not(A),A),B)). [resolve(32283,a,15910,a)].
% 58.54/58.82 32449 is_a_theorem(implies(implies(A,equiv(B,not(B))),implies(A,C))). [resolve(32307,a,1615,a)].
% 58.54/58.82 46111 is_a_theorem(implies(implies(not(A),equiv(B,not(B))),A)). [resolve(32449,a,21094,a)].
% 58.54/58.82 46245 -is_a_theorem(implies(not(A),equiv(B,not(B)))) | is_a_theorem(A). [resolve(46111,a,72,b)].
% 58.54/58.82 46308 -is_a_theorem(implies(A,equiv(B,not(B)))) | is_a_theorem(not(A)). [para(7046(a,1),46245(a,1,1))].
% 58.54/58.82 46976 -is_a_theorem(implies(A,equiv(not(B),B))) | is_a_theorem(not(A)). [para(7046(a,1),46308(a,1,2,2))].
% 58.54/58.82 97028 is_a_theorem(implies(implies(A,B),implies(not(equiv(A,B)),B))). [resolve(11081,a,30896,a)].
% 58.54/58.82 97153 is_a_theorem(implies(A,implies(implies(A,B),B))). [resolve(11081,a,472,a)].
% 58.54/58.82 97432 -is_a_theorem(A) | is_a_theorem(implies(implies(A,B),B)). [resolve(97153,a,72,b)].
% 58.54/58.82 99360 is_a_theorem(implies(implies(not(equiv(not(A),A)),B),B)). [resolve(97432,a,32283,a)].
% 58.54/58.82 99561 is_a_theorem(implies(implies(implies(and(A,B),A),C),C)). [resolve(97432,a,15125,a)].
% 58.54/58.82 99667 is_a_theorem(implies(implies(implies(A,and(A,A)),B),B)). [resolve(97432,a,6713,a)].
% 58.54/58.82 99699 is_a_theorem(implies(implies(implies(and(A,B),B),C),C)). [resolve(97432,a,1356,a)].
% 58.54/58.82 108498 is_a_theorem(implies(A,and(not(equiv(not(B),B)),A))). [resolve(99360,a,8900,a),rewrite([7111(6),7046(5)])].
% 58.54/58.82 108720 -is_a_theorem(implies(implies(and(A,B),A),C)) | is_a_theorem(C). [resolve(99561,a,72,b)].
% 58.54/58.82 108922 -is_a_theorem(implies(implies(A,and(A,A)),B)) | is_a_theorem(B). [resolve(99667,a,72,b)].
% 58.54/58.82 109046 -is_a_theorem(implies(implies(and(A,B),B),C)) | is_a_theorem(C). [resolve(99699,a,72,b)].
% 58.54/58.82 136760 -is_a_theorem(A) | is_a_theorem(and(not(equiv(not(B),B)),A)). [resolve(108498,a,72,b)].
% 58.54/58.82 162587 is_a_theorem(implies(not(equiv(and(A,B),B)),B)). [resolve(97028,a,109046,a)].
% 58.54/58.82 162589 is_a_theorem(implies(not(equiv(and(A,B),A)),A)). [resolve(97028,a,108720,a)].
% 58.54/58.82 162697 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(equiv(A,B)),B)). [resolve(97028,a,72,b)].
% 58.54/58.82 162839 is_a_theorem(implies(not(A),equiv(and(B,A),A))). [resolve(162587,a,1358,a),rewrite([7046(5)])].
% 58.54/58.82 162983 is_a_theorem(implies(not(A),equiv(and(A,B),A))). [resolve(162589,a,1358,a),rewrite([7046(5)])].
% 58.54/58.82 163113 -is_a_theorem(not(A)) | is_a_theorem(equiv(and(B,A),A)). [resolve(162839,a,72,b)].
% 58.54/58.82 163243 -is_a_theorem(not(A)) | is_a_theorem(equiv(and(A,B),A)). [resolve(162983,a,72,b)].
% 58.54/58.82 163272 is_a_theorem(equiv(and(A,equiv(not(B),B)),equiv(not(B),B))). [resolve(163113,a,32283,a)].
% 58.54/58.82 163300 is_a_theorem(equiv(and(equiv(not(A),A),B),equiv(not(A),A))). [resolve(163243,a,32283,a)].
% 58.54/58.82 201402 is_a_theorem(implies(not(equiv(equiv(not(A),A),B)),B)). [resolve(162697,a,32374,a)].
% 58.54/58.82 201649 is_a_theorem(implies(not(equiv(and(A,not(A)),B)),B)). [resolve(162697,a,1351,a)].
% 58.54/58.82 201671 is_a_theorem(implies(not(equiv(implies(not(A),A),A)),A)). [resolve(162697,a,118,a)].
% 58.54/58.82 201749 is_a_theorem(equiv(equiv(not(A),A),equiv(not(B),B))). [resolve(201402,a,46976,a),rewrite([7046(7)])].
% 58.54/58.82 201791 is_a_theorem(implies(A,equiv(equiv(not(B),B),not(A)))). [resolve(201402,a,8900,a),rewrite([7046(6)])].
% 58.54/58.82 202209 is_a_theorem(equiv(and(A,not(A)),equiv(not(B),B))). [resolve(201649,a,46976,a),rewrite([7046(7)])].
% 58.54/58.82 202333 is_a_theorem(equiv(implies(not(equiv(not(A),A)),equiv(not(A),A)),equiv(not(A),A))). [resolve(201671,a,46976,a),rewrite([7046(11)])].
% 58.54/58.82 202443 equiv(not(A),A) = equiv(not(B),B). [resolve(201749,a,66,a)].
% 58.54/58.82 202448 equiv(not(A),A) = c_0. [new_symbol(202443)].
% 58.54/58.82 202460 is_a_theorem(equiv(implies(not(c_0),c_0),c_0)). [back_rewrite(202333),rewrite([202448(2),202448(4),202448(6)])].
% 58.54/58.82 202469 is_a_theorem(equiv(and(A,not(A)),c_0)). [back_rewrite(202209),rewrite([202448(4)])].
% 58.54/58.82 202557 is_a_theorem(implies(A,equiv(c_0,not(A)))). [back_rewrite(201791),rewrite([202448(2)])].
% 58.54/58.82 202766 is_a_theorem(equiv(and(c_0,A),c_0)). [back_rewrite(163300),rewrite([202448(2),202448(4)])].
% 58.54/58.82 202767 is_a_theorem(equiv(and(A,c_0),c_0)). [back_rewrite(163272),rewrite([202448(2),202448(4)])].
% 58.54/58.82 202816 -is_a_theorem(A) | is_a_theorem(and(not(c_0),A)). [back_rewrite(136760),rewrite([202448(3)])].
% 58.54/58.82 203115 is_a_theorem(not(c_0)). [back_rewrite(32283),rewrite([202448(2)])].
% 58.54/58.82 205341 and(c_0,A) = c_0. [resolve(202766,a,66,a),flip(a)].
% 58.54/58.82 205377 implies(c_0,not(A)) = not(c_0). [para(205341(a,1),7110(a,1,1)),flip(a)].
% 58.54/58.82 205517 and(A,c_0) = c_0. [resolve(202767,a,66,a),flip(a)].
% 58.54/58.82 205797 implies(A,not(c_0)) = not(c_0). [para(205517(a,1),7110(a,1,1)),flip(a)].
% 58.54/58.82 206554 implies(not(c_0),c_0) = c_0. [resolve(202460,a,66,a),flip(a)].
% 58.54/58.82 206596 and(not(c_0),not(c_0)) = not(c_0). [para(206554(a,1),7111(a,1,1)),flip(a)].
% 58.54/58.82 206867 and(A,not(A)) = c_0. [resolve(202469,a,66,a),flip(a)].
% 58.54/58.82 207235 implies(A,A) = not(c_0). [para(206867(a,1),7110(a,1,1)),rewrite([7046(4)]),flip(a)].
% 58.54/58.82 208379 is_a_theorem(equiv(c_0,and(and(A,B),not(B)))). [resolve(202557,a,109046,a),rewrite([7111(4)])].
% 58.54/58.82 208380 is_a_theorem(equiv(c_0,and(A,implies(A,not(A))))). [resolve(202557,a,108922,a),rewrite([7111(4),7110(3)])].
% 58.54/58.82 208381 is_a_theorem(equiv(c_0,and(and(A,B),not(A)))). [resolve(202557,a,108720,a),rewrite([7111(4)])].
% 58.54/58.82 209755 is_a_theorem(and(not(c_0),implies(A,and(A,implies(B,A))))). [resolve(202816,a,21818,a)].
% 58.54/58.82 211870 implies(c_0,A) = not(c_0). [para(7046(a,1),205377(a,1,2))].
% 58.54/58.82 211876 and(implies(A,c_0),not(c_0)) = equiv(A,c_0). [para(211870(a,1),95(a,1,2))].
% 58.54/58.82 211919 and(implies(not(c_0),A),not(c_0)) = equiv(not(c_0),A). [para(205797(a,1),95(a,1,2))].
% 58.54/58.82 214782 and(and(A,B),not(B)) = c_0. [resolve(208379,a,66,a)].
% 58.54/58.82 214786 implies(and(A,B),B) = not(c_0). [para(214782(a,1),7110(a,1,1)),rewrite([7046(5)]),flip(a)].
% 58.54/58.82 214806 and(A,implies(A,not(A))) = c_0. [resolve(208380,a,66,a)].
% 58.54/58.82 214842 implies(A,and(A,A)) = not(c_0). [para(214806(a,1),7110(a,1,1)),rewrite([7111(5),7046(4)]),flip(a)].
% 58.54/58.82 214846 equiv(A,and(A,A)) = not(c_0). [para(214842(a,1),95(a,1,1)),rewrite([214786(4),206596(5)]),flip(a)].
% 58.54/58.82 214848 and(A,A) = A. [para(214846(a,1),66(a,1)),unit_del(a,203115)].
% 58.54/58.82 214957 and(and(A,B),not(A)) = c_0. [resolve(208381,a,66,a)].
% 58.54/58.82 214964 implies(and(A,B),A) = not(c_0). [para(214957(a,1),7110(a,1,1)),rewrite([7046(5)]),flip(a)].
% 58.54/58.82 214992 and(not(c_0),implies(A,and(A,B))) = equiv(and(A,B),A). [para(214964(a,1),95(a,1,1))].
% 58.54/58.82 215002 is_a_theorem(equiv(and(A,implies(B,A)),A)). [back_rewrite(209755),rewrite([214992(6)])].
% 58.54/58.82 215076 and(A,implies(B,A)) = A. [resolve(215002,a,66,a),flip(a)].
% 58.54/58.82 215168 and(A,not(c_0)) = A. [para(207235(a,1),215076(a,1,2))].
% 58.54/58.82 215171 equiv(not(c_0),A) = implies(not(c_0),A). [back_rewrite(211919),rewrite([215168(6)]),flip(a)].
% 58.54/58.82 215173 equiv(A,c_0) = implies(A,c_0). [back_rewrite(211876),rewrite([215168(5)]),flip(a)].
% 58.54/58.82 215269 implies(A,c_0) = not(A). [para(215168(a,1),7110(a,1,1)),rewrite([7046(4)]),flip(a)].
% 58.54/58.82 215278 equiv(A,c_0) = not(A). [back_rewrite(215173),rewrite([215269(4)])].
% 58.54/58.82 215441 -is_a_theorem(not(A)) | c_0 = A. [para(215278(a,1),66(a,1))].
% 58.54/58.82 217309 -is_a_theorem(A) | not(A) = c_0. [para(7046(a,1),215441(a,1)),flip(b)].
% 58.54/58.82 217438 and(A,and(implies(A,B),not(B))) = c_0. [resolve(217309,a,97153,a),rewrite([7111(4),7111(3)])].
% 58.54/58.82 219818 -is_a_theorem(implies(not(c_0),A)) | not(c_0) = A. [para(215171(a,1),66(a,1)),flip(b)].
% 58.54/58.82 221313 implies(and(A,B),and(B,A)) = not(c_0). [resolve(219818,a,9171,a),flip(a)].
% 58.54/58.82 225763 and(implies(A,B),and(not(equiv(A,B)),implies(B,A))) = c_0. [para(168(a,1),217438(a,1,2,1)),rewrite([7110(6),7046(5)])].
% 58.54/58.82 227213 equiv(and(A,B),and(B,A)) = not(c_0). [para(221313(a,1),95(a,1,1)),rewrite([221313(5),214848(5)]),flip(a)].
% 58.54/58.82 228351 and(A,B) = and(B,A). [para(227213(a,1),66(a,1)),unit_del(a,203115)].
% 58.54/58.82 228785 and(implies(A,B),and(implies(B,A),not(equiv(A,B)))) = c_0. [back_rewrite(225763),rewrite([228351(5)])].
% 58.54/58.82 229301 $F. [back_rewrite(229),rewrite([228785(12),211870(13)]),unit_del(a,203115)].
% 58.54/58.82
% 58.54/58.82 % SZS output end Refutation
% 58.54/58.82 ============================== end of proof ==========================
% 58.54/58.82
% 58.54/58.82 ============================== STATISTICS ============================
% 58.54/58.82
% 58.54/58.82 Given=5638. Generated=6353369. Kept=229249. proofs=1.
% 58.54/58.82 Usable=342. Sos=1293. Demods=448. Limbo=516, Disabled=227172. Hints=0.
% 58.54/58.82 Megabytes=140.04.
% 58.54/58.82 User_CPU=54.62, System_CPU=3.20, Wall_clock=57.
% 58.54/58.82
% 58.54/58.82 ============================== end of statistics =====================
% 58.54/58.82
% 58.54/58.82 ============================== end of search =========================
% 58.54/58.82
% 58.54/58.82 THEOREM PROVED
% 58.54/58.82 % SZS status Theorem
% 58.54/58.82
% 58.54/58.82 Exiting with 1 proof.
% 58.54/58.82
% 58.54/58.82 Process 10344 exit (max_proofs) Sat Jul 2 16:28:35 2022
% 58.54/58.82 Prover9 interrupted
%------------------------------------------------------------------------------