TSTP Solution File: LCL509+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL509+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 13:47:16 EDT 2022
% Result : Theorem 2.47s 2.79s
% Output : Refutation 2.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL509+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 : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 3 00:30:05 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.80/1.11 ============================== Prover9 ===============================
% 0.80/1.11 Prover9 (32) version 2009-11A, November 2009.
% 0.80/1.11 Process 24859 was started by sandbox2 on n011.cluster.edu,
% 0.80/1.11 Sun Jul 3 00:30:06 2022
% 0.80/1.11 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_24448_n011.cluster.edu".
% 0.80/1.11 ============================== end of head ===========================
% 0.80/1.11
% 0.80/1.11 ============================== INPUT =================================
% 0.80/1.11
% 0.80/1.11 % Reading from file /tmp/Prover9_24448_n011.cluster.edu
% 0.80/1.11
% 0.80/1.11 set(prolog_style_variables).
% 0.80/1.11 set(auto2).
% 0.80/1.11 % set(auto2) -> set(auto).
% 0.80/1.11 % set(auto) -> set(auto_inference).
% 0.80/1.11 % set(auto) -> set(auto_setup).
% 0.80/1.11 % set(auto_setup) -> set(predicate_elim).
% 0.80/1.11 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.80/1.11 % set(auto) -> set(auto_limits).
% 0.80/1.11 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.80/1.11 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.80/1.11 % set(auto) -> set(auto_denials).
% 0.80/1.11 % set(auto) -> set(auto_process).
% 0.80/1.11 % set(auto2) -> assign(new_constants, 1).
% 0.80/1.11 % set(auto2) -> assign(fold_denial_max, 3).
% 0.80/1.11 % set(auto2) -> assign(max_weight, "200.000").
% 0.80/1.11 % set(auto2) -> assign(max_hours, 1).
% 0.80/1.11 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.80/1.11 % set(auto2) -> assign(max_seconds, 0).
% 0.80/1.11 % set(auto2) -> assign(max_minutes, 5).
% 0.80/1.11 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.80/1.11 % set(auto2) -> set(sort_initial_sos).
% 0.80/1.11 % set(auto2) -> assign(sos_limit, -1).
% 0.80/1.11 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.80/1.11 % set(auto2) -> assign(max_megs, 400).
% 0.80/1.11 % set(auto2) -> assign(stats, some).
% 0.80/1.11 % set(auto2) -> clear(echo_input).
% 0.80/1.11 % set(auto2) -> set(quiet).
% 0.80/1.11 % set(auto2) -> clear(print_initial_clauses).
% 0.80/1.11 % set(auto2) -> clear(print_given).
% 0.80/1.11 assign(lrs_ticks,-1).
% 0.80/1.11 assign(sos_limit,10000).
% 0.80/1.11 assign(order,kbo).
% 0.80/1.11 set(lex_order_vars).
% 0.80/1.11 clear(print_given).
% 0.80/1.11
% 0.80/1.11 % formulas(sos). % not echoed (43 formulas)
% 0.80/1.11
% 0.80/1.11 ============================== end of input ==========================
% 0.80/1.11
% 0.80/1.11 % From the command line: assign(max_seconds, 300).
% 0.80/1.11
% 0.80/1.11 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.80/1.11
% 0.80/1.11 % Formulas that are not ordinary clauses:
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.11 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.11 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].
% 0.80/1.11 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.11 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.80/1.11 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].
% 0.84/1.57 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].
% 0.84/1.57 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.57 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.57 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].
% 0.84/1.57 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].
% 0.84/1.57 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.57 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.57 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.57 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.57 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.57 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].
% 0.84/1.57 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].
% 0.84/1.57 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].
% 0.84/1.57 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].
% 0.84/1.57 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].
% 0.84/1.57 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].
% 0.84/1.57 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].
% 0.84/1.57
% 0.84/1.57 ============================== end of process non-clausal formulas ===
% 0.84/1.57
% 0.84/1.57 ============================== PROCESS INITIAL CLAUSES ===============
% 0.84/1.57
% 0.84/1.57 ============================== PREDICATE ELIMINATION =================
% 0.84/1.57
% 0.84/1.57 ============================== end predicate elimination =============
% 0.84/1.57
% 0.84/1.57 Auto_denials: (non-Horn, no changes).
% 0.84/1.57
% 0.84/1.57 Term ordering decisions:
% 0.84/1.57
% 0.84/1.57 % Assigning unary symbol not kb_weight 0 and highest precedence (93).
% 0.84/1.57 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.
% 0.84/1.57
% 0.84/1.57 ============================== end of process initial clauses ========
% 0.84/1.57
% 0.84/1.57 ============================== CLAUSES FOR SEARCH ====================
% 0.84/1.57
% 0.84/1.57 ============================== end of clauses for search =============
% 0.84/1.57
% 0.84/1.57 ============================== SEARCH ================================
% 0.84/1.57
% 0.84/1.57 % Starting search at 0.02 seconds.
% 0.84/1.57
% 0.84/1.57 Low Water (keep): wt=37.000, iters=3471
% 0.84/1.57
% 0.84/1.57 Low Water (keep): wt=31.000, iters=3380
% 0.84/1.57
% 0.84/1.57 Low Water (keep): wt=27.000, iters=3366
% 0.84/1.57
% 0.84/1.57 Low Water (keep): wt=25.000, iters=3427
% 0.84/1.57
% 0.84/1.57 Low Water (keep): wt=24.000, iters=3398
% 0.84/1.57
% 0.84/1.57 Low Water (keep): wt=23.000, iters=3340
% 0.84/1.57
% 0.84/1.57 Low Water (keep): wt=22.000, iters=3471
% 0.84/1.57
% 0.84/1.57 Low Water (keep): wt=21.000, iters=3342
% 0.84/1.57
% 0.84/1.57 Low Water (keep): wt=20.000, iters=3416
% 0.84/1.57
% 0.84/1.57 Low Water (keep): wt=19.000, iters=3368
% 2.47/2.78
% 2.47/2.78 Low Water (keep): wt=18.000, iters=3370
% 2.47/2.78
% 2.47/2.78 Low Water (keep): wt=17.000, iters=3357
% 2.47/2.78
% 2.47/2.78 Low Water (keep): wt=16.000, iters=3372
% 2.47/2.78
% 2.47/2.78 Low Water (keep): wt=15.000, iters=3424
% 2.47/2.78
% 2.47/2.78 Low Water (displace): id=3327, wt=51.000
% 2.47/2.78
% 2.47/2.78 Low Water (displace): id=3336, wt=49.000
% 2.47/2.78
% 2.47/2.78 Low Water (displace): id=1613, wt=47.000
% 2.47/2.78
% 2.47/2.78 Low Water (displace): id=2763, wt=45.000
% 2.47/2.78
% 2.47/2.78 Low Water (displace): id=3326, wt=43.000
% 2.47/2.78
% 2.47/2.78 Low Water (displace): id=3335, wt=41.000
% 2.47/2.78
% 2.47/2.78 Low Water (displace): id=3292, wt=40.000
% 2.47/2.78
% 2.47/2.78 Low Water (displace): id=3328, wt=39.000
% 2.47/2.78
% 2.47/2.78 Low Water (displace): id=3289, wt=38.000
% 2.47/2.78
% 2.47/2.78 Low Water (displace): id=3531, wt=37.000
% 2.47/2.78
% 2.47/2.78 Low Water (displace): id=3430, wt=35.000
% 2.47/2.78
% 2.47/2.78 Low Water (displace): id=1629, wt=34.000
% 2.47/2.78
% 2.47/2.78 Low Water (displace): id=3601, wt=33.000
% 2.47/2.78
% 2.47/2.78 Low Water (displace): id=3674, wt=32.000
% 2.47/2.78
% 2.47/2.78 Low Water (displace): id=3610, wt=31.000
% 2.47/2.78
% 2.47/2.78 Low Water (displace): id=10777, wt=14.000
% 2.47/2.78
% 2.47/2.78 Low Water (displace): id=11245, wt=12.000
% 2.47/2.78
% 2.47/2.78 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 114 (0.00 of 0.99 sec).
% 2.47/2.78
% 2.47/2.78 Low Water (displace): id=11889, wt=11.000
% 2.47/2.78
% 2.47/2.78 Low Water (displace): id=11984, wt=10.000
% 2.47/2.79
% 2.47/2.79 ============================== PROOF =================================
% 2.47/2.79 % SZS status Theorem
% 2.47/2.79 % SZS output start Refutation
% 2.47/2.79
% 2.47/2.79 % Proof 1 at 1.61 (+ 0.08) seconds.
% 2.47/2.79 % Length of proof is 61.
% 2.47/2.79 % Level of proof is 21.
% 2.47/2.79 % Maximum clause weight is 16.000.
% 2.47/2.79 % Given clauses 767.
% 2.47/2.79
% 2.47/2.79 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].
% 2.47/2.79 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 2.47/2.79 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 2.47/2.79 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 2.47/2.79 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].
% 2.47/2.79 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].
% 2.47/2.79 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].
% 2.47/2.79 32 op_or # label(rosser_op_or) # label(axiom). [assumption].
% 2.47/2.79 33 op_implies_and # label(rosser_op_implies_and) # label(axiom). [assumption].
% 2.47/2.79 35 modus_ponens # label(rosser_modus_ponens) # label(axiom). [assumption].
% 2.47/2.79 36 kn1 # label(rosser_kn1) # label(axiom). [assumption].
% 2.47/2.79 37 kn2 # label(rosser_kn2) # label(axiom). [assumption].
% 2.47/2.79 38 kn3 # label(rosser_kn3) # label(axiom). [assumption].
% 2.47/2.79 40 -or_1 # label(hilbert_or_1) # label(negated_conjecture). [assumption].
% 2.47/2.79 47 or_1 | -is_a_theorem(implies(c20,or(c20,c21))) # label(or_1) # label(axiom). [clausify(10)].
% 2.47/2.79 48 -is_a_theorem(implies(c20,or(c20,c21))). [copy(47),unit_del(a,40)].
% 2.47/2.79 51 -kn1 | is_a_theorem(implies(A,and(A,A))) # label(kn1) # label(axiom). [clausify(16)].
% 2.47/2.79 52 is_a_theorem(implies(A,and(A,A))). [copy(51),unit_del(a,36)].
% 2.47/2.79 54 -kn2 | is_a_theorem(implies(and(A,B),A)) # label(kn2) # label(axiom). [clausify(17)].
% 2.47/2.79 55 is_a_theorem(implies(and(A,B),A)). [copy(54),unit_del(a,37)].
% 2.47/2.79 67 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 2.47/2.79 68 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(67),unit_del(a,35)].
% 2.47/2.79 78 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 2.47/2.79 79 not(and(A,not(B))) = implies(A,B). [copy(78),unit_del(a,33)].
% 2.47/2.79 84 -op_or | or(A,B) = not(and(not(A),not(B))) # label(op_or) # label(axiom). [clausify(27)].
% 2.47/2.79 85 or(A,B) = implies(not(A),B). [copy(84),rewrite([79(6)]),unit_del(a,32)].
% 2.47/2.79 108 -kn3 | is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))) # label(kn3) # label(axiom). [clausify(18)].
% 2.47/2.79 109 is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))). [copy(108),unit_del(a,38)].
% 2.47/2.79 121 -is_a_theorem(implies(c20,implies(not(c20),c21))). [back_rewrite(48),rewrite([85(4)])].
% 2.47/2.79 128 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(and(B,C)),not(and(C,A)))). [resolve(109,a,68,b)].
% 2.47/2.79 216 is_a_theorem(implies(not(and(A,B)),not(and(B,and(A,C))))). [resolve(128,a,55,a)].
% 2.47/2.79 217 is_a_theorem(implies(not(and(and(A,A),B)),not(and(B,A)))). [resolve(128,a,52,a)].
% 2.47/2.79 252 -is_a_theorem(not(and(A,B))) | is_a_theorem(not(and(B,and(A,C)))). [resolve(216,a,68,b)].
% 2.47/2.79 270 -is_a_theorem(not(and(and(A,A),B))) | is_a_theorem(not(and(B,A))). [resolve(217,a,68,b)].
% 2.47/2.79 376 -is_a_theorem(implies(and(A,A),B)) | is_a_theorem(not(and(not(B),A))). [para(79(a,1),270(a,1))].
% 2.47/2.79 565 is_a_theorem(not(and(not(A),A))). [resolve(376,a,55,a)].
% 2.47/2.79 568 is_a_theorem(not(and(A,and(not(A),B)))). [resolve(565,a,252,a)].
% 2.47/2.79 591 is_a_theorem(implies(not(not(A)),A)). [para(79(a,1),565(a,1))].
% 2.47/2.79 696 is_a_theorem(implies(not(and(A,B)),implies(B,not(A)))). [resolve(591,a,128,a),rewrite([79(6)])].
% 2.47/2.79 698 -is_a_theorem(not(not(A))) | is_a_theorem(A). [resolve(591,a,68,b)].
% 2.47/2.79 751 is_a_theorem(not(and(and(not(A),B),and(A,C)))). [resolve(568,a,252,a)].
% 2.47/2.79 977 -is_a_theorem(not(and(A,B))) | is_a_theorem(implies(B,not(A))). [resolve(696,a,68,b)].
% 2.47/2.79 1530 is_a_theorem(implies(and(A,B),not(and(not(A),C)))). [resolve(977,a,751,a)].
% 2.47/2.79 1537 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(B),not(A))). [para(79(a,1),977(a,1))].
% 2.47/2.79 2366 is_a_theorem(implies(and(A,B),implies(not(A),C))). [para(79(a,1),1530(a,1,2))].
% 2.47/2.79 2576 is_a_theorem(not(and(not(implies(not(A),B)),A))). [resolve(2366,a,376,a)].
% 2.47/2.79 2693 -is_a_theorem(implies(not(and(not(implies(not(A),B)),A)),implies(c20,implies(not(c20),c21)))). [ur(68,a,2576,a,c,121,a)].
% 2.47/2.79 4572 is_a_theorem(implies(not(A),not(and(A,B)))). [resolve(1537,a,55,a)].
% 2.47/2.79 4573 is_a_theorem(implies(not(and(A,A)),not(A))). [resolve(1537,a,52,a)].
% 2.47/2.79 4647 is_a_theorem(implies(not(A),implies(A,B))). [para(79(a,1),4572(a,1,2))].
% 2.47/2.79 4654 is_a_theorem(implies(not(and(implies(A,B),C)),implies(C,A))). [resolve(4647,a,128,a),rewrite([79(6)])].
% 2.47/2.79 5070 -is_a_theorem(not(and(A,A))) | is_a_theorem(not(A)). [resolve(4573,a,68,b)].
% 2.47/2.79 5420 -is_a_theorem(implies(not(A),A)) | is_a_theorem(not(not(A))). [para(79(a,1),5070(a,1))].
% 2.47/2.79 11238 -is_a_theorem(not(and(implies(A,B),C))) | is_a_theorem(implies(C,A)). [resolve(4654,a,68,b)].
% 2.47/2.79 11257 is_a_theorem(implies(implies(implies(A,B),C),implies(not(C),A))). [para(79(a,1),4654(a,1,1))].
% 2.47/2.79 13483 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(not(C),A)). [para(79(a,1),11238(a,1))].
% 2.47/2.79 14418 is_a_theorem(implies(not(implies(not(A),B)),implies(B,C))). [resolve(13483,a,11257,a)].
% 2.47/2.79 15258 is_a_theorem(not(not(implies(not(A),not(A))))). [resolve(14418,a,5420,a)].
% 2.47/2.79 15290 is_a_theorem(implies(not(A),not(A))). [resolve(15258,a,698,a)].
% 2.47/2.79 15465 is_a_theorem(implies(not(and(not(A),B)),implies(B,A))). [resolve(15290,a,128,a),rewrite([79(6)])].
% 2.47/2.79 15466 $F. [resolve(15465,a,2693,a)].
% 2.47/2.79
% 2.47/2.79 % SZS output end Refutation
% 2.47/2.79 ============================== end of proof ==========================
% 2.47/2.79
% 2.47/2.79 ============================== STATISTICS ============================
% 2.47/2.79
% 2.47/2.79 Given=767. Generated=139824. Kept=15415. proofs=1.
% 2.47/2.79 Usable=762. Sos=9999. Demods=5. Limbo=9, Disabled=4716. Hints=0.
% 2.47/2.79 Megabytes=13.58.
% 2.47/2.79 User_CPU=1.61, System_CPU=0.08, Wall_clock=1.
% 2.47/2.79
% 2.47/2.79 ============================== end of statistics =====================
% 2.47/2.79
% 2.47/2.79 ============================== end of search =========================
% 2.47/2.79
% 2.47/2.79 THEOREM PROVED
% 2.47/2.79 % SZS status Theorem
% 2.47/2.79
% 2.47/2.79 Exiting with 1 proof.
% 2.47/2.79
% 2.47/2.79 Process 24859 exit (max_proofs) Sun Jul 3 00:30:07 2022
% 2.47/2.79 Prover9 interrupted
%------------------------------------------------------------------------------