TSTP Solution File: LCL517+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL517+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n007.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 13:47:19 EDT 2022
% Result : Theorem 3.01s 3.30s
% Output : Refutation 3.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL517+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jul 2 15:55:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.43/1.07 ============================== Prover9 ===============================
% 0.43/1.07 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.07 Process 29403 was started by sandbox on n007.cluster.edu,
% 0.43/1.07 Sat Jul 2 15:55:41 2022
% 0.43/1.07 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_29223_n007.cluster.edu".
% 0.43/1.07 ============================== end of head ===========================
% 0.43/1.07
% 0.43/1.07 ============================== INPUT =================================
% 0.43/1.07
% 0.43/1.07 % Reading from file /tmp/Prover9_29223_n007.cluster.edu
% 0.43/1.07
% 0.43/1.07 set(prolog_style_variables).
% 0.43/1.07 set(auto2).
% 0.43/1.07 % set(auto2) -> set(auto).
% 0.43/1.07 % set(auto) -> set(auto_inference).
% 0.43/1.07 % set(auto) -> set(auto_setup).
% 0.43/1.07 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.07 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.07 % set(auto) -> set(auto_limits).
% 0.43/1.07 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.07 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.07 % set(auto) -> set(auto_denials).
% 0.43/1.07 % set(auto) -> set(auto_process).
% 0.43/1.07 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.07 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.07 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.07 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.07 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.07 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.07 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.07 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.07 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.07 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.07 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.07 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.07 % set(auto2) -> assign(stats, some).
% 0.43/1.07 % set(auto2) -> clear(echo_input).
% 0.43/1.07 % set(auto2) -> set(quiet).
% 0.43/1.07 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.07 % set(auto2) -> clear(print_given).
% 0.43/1.07 assign(lrs_ticks,-1).
% 0.43/1.07 assign(sos_limit,10000).
% 0.43/1.07 assign(order,kbo).
% 0.43/1.07 set(lex_order_vars).
% 0.43/1.07 clear(print_given).
% 0.43/1.07
% 0.43/1.07 % formulas(sos). % not echoed (43 formulas)
% 0.43/1.07
% 0.43/1.07 ============================== end of input ==========================
% 0.43/1.07
% 0.43/1.07 % From the command line: assign(max_seconds, 300).
% 0.43/1.07
% 0.43/1.07 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.07
% 0.43/1.07 % Formulas that are not ordinary clauses:
% 0.43/1.07 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].
% 0.43/1.07 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].
% 0.43/1.07 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].
% 0.43/1.07 4 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.07 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].
% 0.43/1.07 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].
% 0.43/1.07 7 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.07 8 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.07 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].
% 0.43/1.07 10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.07 11 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.07 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].
% 0.43/1.07 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].
% 0.43/1.07 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].
% 1.39/1.65 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].
% 1.39/1.65 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.65 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.65 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].
% 1.39/1.65 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].
% 1.39/1.65 20 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.65 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.65 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.65 23 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.65 24 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.65 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].
% 1.39/1.65 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].
% 1.39/1.65 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].
% 1.39/1.65 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].
% 1.39/1.65 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].
% 1.39/1.65 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].
% 1.39/1.65 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].
% 1.39/1.65
% 1.39/1.65 ============================== end of process non-clausal formulas ===
% 1.39/1.65
% 1.39/1.65 ============================== PROCESS INITIAL CLAUSES ===============
% 1.39/1.65
% 1.39/1.65 ============================== PREDICATE ELIMINATION =================
% 1.39/1.65
% 1.39/1.65 ============================== end predicate elimination =============
% 1.39/1.65
% 1.39/1.65 Auto_denials: (non-Horn, no changes).
% 1.39/1.65
% 1.39/1.65 Term ordering decisions:
% 1.39/1.65
% 1.39/1.65 % Assigning unary symbol not kb_weight 0 and highest precedence (94).
% 1.39/1.65 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.
% 1.39/1.65
% 1.39/1.65 ============================== end of process initial clauses ========
% 1.39/1.65
% 1.39/1.65 ============================== CLAUSES FOR SEARCH ====================
% 1.39/1.65
% 1.39/1.65 ============================== end of clauses for search =============
% 1.39/1.65
% 1.39/1.65 ============================== SEARCH ================================
% 1.39/1.65
% 1.39/1.65 % Starting search at 0.02 seconds.
% 1.39/1.65
% 1.39/1.65 Low Water (keep): wt=37.000, iters=3438
% 1.39/1.65
% 1.39/1.65 Low Water (keep): wt=31.000, iters=3353
% 1.39/1.65
% 1.39/1.65 Low Water (keep): wt=30.000, iters=3639
% 1.39/1.65
% 1.39/1.65 Low Water (keep): wt=25.000, iters=3390
% 1.39/1.65
% 1.39/1.65 Low Water (keep): wt=24.000, iters=3402
% 1.39/1.65
% 1.39/1.65 Low Water (keep): wt=23.000, iters=3361
% 1.39/1.65
% 1.39/1.65 Low Water (keep): wt=22.000, iters=3391
% 1.39/1.65
% 1.39/1.65 Low Water (keep): wt=21.000, iters=3422
% 1.39/1.65
% 1.39/1.65 Low Water (keep): wt=20.000, iters=3555
% 1.39/1.65
% 1.39/1.65 Low Water (keep): wt=19.000, iters=3339
% 1.39/1.65
% 3.01/3.30 Low Water (keep): wt=18.000, iters=3344
% 3.01/3.30
% 3.01/3.30 Low Water (keep): wt=17.000, iters=3358
% 3.01/3.30
% 3.01/3.30 Low Water (keep): wt=16.000, iters=3364
% 3.01/3.30
% 3.01/3.30 Low Water (keep): wt=15.000, iters=3382
% 3.01/3.30
% 3.01/3.30 Low Water (displace): id=3270, wt=51.000
% 3.01/3.30
% 3.01/3.30 Low Water (displace): id=3277, wt=49.000
% 3.01/3.30
% 3.01/3.30 Low Water (displace): id=1614, wt=47.000
% 3.01/3.30
% 3.01/3.30 Low Water (displace): id=2744, wt=45.000
% 3.01/3.30
% 3.01/3.30 Low Water (displace): id=3269, wt=43.000
% 3.01/3.30
% 3.01/3.30 Low Water (displace): id=3279, wt=41.000
% 3.01/3.30
% 3.01/3.30 Low Water (displace): id=3465, wt=40.000
% 3.01/3.30
% 3.01/3.30 Low Water (displace): id=3271, wt=39.000
% 3.01/3.30
% 3.01/3.30 Low Water (displace): id=3230, wt=38.000
% 3.01/3.30
% 3.01/3.30 Low Water (displace): id=3280, wt=37.000
% 3.01/3.30
% 3.01/3.30 Low Water (displace): id=3281, wt=35.000
% 3.01/3.30
% 3.01/3.30 Low Water (displace): id=10904, wt=14.000
% 3.01/3.30
% 3.01/3.30 Low Water (displace): id=10960, wt=13.000
% 3.01/3.30
% 3.01/3.30 Low Water (displace): id=11784, wt=11.000
% 3.01/3.30
% 3.01/3.30 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 36 (0.00 of 1.16 sec).
% 3.01/3.30
% 3.01/3.30 Low Water (displace): id=12327, wt=10.000
% 3.01/3.30
% 3.01/3.30 Low Water (displace): id=12771, wt=9.000
% 3.01/3.30
% 3.01/3.30 Low Water (keep): wt=14.000, iters=3346
% 3.01/3.30
% 3.01/3.30 ============================== PROOF =================================
% 3.01/3.30 % SZS status Theorem
% 3.01/3.30 % SZS output start Refutation
% 3.01/3.30
% 3.01/3.30 % Proof 1 at 2.15 (+ 0.10) seconds.
% 3.01/3.30 % Length of proof is 60.
% 3.01/3.30 % Level of proof is 21.
% 3.01/3.30 % Maximum clause weight is 14.000.
% 3.01/3.30 % Given clauses 831.
% 3.01/3.30
% 3.01/3.30 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].
% 3.01/3.30 16 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause). [assumption].
% 3.01/3.30 17 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause). [assumption].
% 3.01/3.30 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].
% 3.01/3.30 21 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause). [assumption].
% 3.01/3.30 22 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause). [assumption].
% 3.01/3.30 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].
% 3.01/3.30 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].
% 3.01/3.30 32 op_or # label(rosser_op_or) # label(axiom). [assumption].
% 3.01/3.30 33 op_implies_and # label(rosser_op_implies_and) # label(axiom). [assumption].
% 3.01/3.30 35 modus_ponens # label(rosser_modus_ponens) # label(axiom). [assumption].
% 3.01/3.30 36 kn1 # label(rosser_kn1) # label(axiom). [assumption].
% 3.01/3.30 37 kn2 # label(rosser_kn2) # label(axiom). [assumption].
% 3.01/3.30 38 kn3 # label(rosser_kn3) # label(axiom). [assumption].
% 3.01/3.30 41 -cn3 # label(luka_cn3) # label(negated_conjecture). [assumption].
% 3.01/3.30 52 -kn1 | is_a_theorem(implies(A,and(A,A))) # label(kn1) # label(axiom). [clausify(16)].
% 3.01/3.30 53 is_a_theorem(implies(A,and(A,A))). [copy(52),unit_del(a,36)].
% 3.01/3.30 55 -kn2 | is_a_theorem(implies(and(A,B),A)) # label(kn2) # label(axiom). [clausify(17)].
% 3.01/3.30 56 is_a_theorem(implies(and(A,B),A)). [copy(55),unit_del(a,37)].
% 3.01/3.30 58 -r1 | is_a_theorem(implies(or(A,A),A)) # label(r1) # label(axiom). [clausify(22)].
% 3.01/3.30 59 r1 | -is_a_theorem(implies(or(c45,c45),c45)) # label(r1) # label(axiom). [clausify(22)].
% 3.01/3.30 66 cn3 | -is_a_theorem(implies(implies(not(c44),c44),c44)) # label(cn3) # label(axiom). [clausify(21)].
% 3.01/3.30 67 -is_a_theorem(implies(implies(not(c44),c44),c44)). [copy(66),unit_del(a,41)].
% 3.01/3.30 68 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom). [clausify(1)].
% 3.01/3.30 69 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B). [copy(68),unit_del(a,35)].
% 3.01/3.30 79 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom). [clausify(29)].
% 3.01/3.30 80 not(and(A,not(B))) = implies(A,B). [copy(79),unit_del(a,33)].
% 3.01/3.30 85 -op_or | or(A,B) = not(and(not(A),not(B))) # label(op_or) # label(axiom). [clausify(27)].
% 3.01/3.30 86 or(A,B) = implies(not(A),B). [copy(85),rewrite([80(6)]),unit_del(a,32)].
% 3.01/3.30 109 -kn3 | is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))) # label(kn3) # label(axiom). [clausify(18)].
% 3.01/3.30 110 is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))). [copy(109),unit_del(a,38)].
% 3.01/3.30 118 r1 | -is_a_theorem(implies(implies(not(c45),c45),c45)). [back_rewrite(59),rewrite([86(4)])].
% 3.01/3.30 119 -r1 | is_a_theorem(implies(implies(not(A),A),A)). [back_rewrite(58),rewrite([86(2)])].
% 3.01/3.30 129 not(and(A,implies(B,C))) = implies(A,and(B,not(C))). [para(80(a,1),80(a,1,1,2))].
% 3.01/3.30 133 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(and(B,C)),not(and(C,A)))). [resolve(110,a,69,b)].
% 3.01/3.30 139 -r1. [ur(119,b,67,a)].
% 3.01/3.30 140 -is_a_theorem(implies(implies(not(c45),c45),c45)). [back_unit_del(118),unit_del(a,139)].
% 3.01/3.30 277 is_a_theorem(implies(not(and(and(A,A),B)),not(and(B,A)))). [resolve(133,a,53,a)].
% 3.01/3.30 358 -is_a_theorem(not(and(and(A,A),B))) | is_a_theorem(not(and(B,A))). [resolve(277,a,69,b)].
% 3.01/3.30 408 -is_a_theorem(implies(and(A,A),B)) | is_a_theorem(not(and(not(B),A))). [para(80(a,1),358(a,1))].
% 3.01/3.30 704 is_a_theorem(not(and(not(A),A))). [resolve(408,a,56,a)].
% 3.01/3.30 737 is_a_theorem(implies(not(not(A)),A)). [para(80(a,1),704(a,1))].
% 3.01/3.30 740 is_a_theorem(implies(not(and(A,B)),implies(B,not(A)))). [resolve(737,a,133,a),rewrite([80(6)])].
% 3.01/3.30 742 -is_a_theorem(not(not(A))) | is_a_theorem(A). [resolve(737,a,69,b)].
% 3.01/3.30 1174 -is_a_theorem(not(and(A,B))) | is_a_theorem(implies(B,not(A))). [resolve(740,a,69,b)].
% 3.01/3.30 1787 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(B),not(A))). [para(80(a,1),1174(a,1))].
% 3.01/3.30 4885 is_a_theorem(implies(not(A),not(and(A,B)))). [resolve(1787,a,56,a)].
% 3.01/3.30 4886 is_a_theorem(implies(not(and(A,A)),not(A))). [resolve(1787,a,53,a)].
% 3.01/3.30 4966 is_a_theorem(implies(not(A),implies(A,B))). [para(80(a,1),4885(a,1,2))].
% 3.01/3.30 4973 is_a_theorem(implies(not(and(implies(A,B),C)),implies(C,A))). [resolve(4966,a,133,a),rewrite([80(6)])].
% 3.01/3.30 5385 -is_a_theorem(not(and(A,A))) | is_a_theorem(not(A)). [resolve(4886,a,69,b)].
% 3.01/3.30 5487 -is_a_theorem(implies(not(A),A)) | is_a_theorem(not(not(A))). [para(80(a,1),5385(a,1))].
% 3.01/3.30 11808 -is_a_theorem(not(and(implies(A,B),C))) | is_a_theorem(implies(C,A)). [resolve(4973,a,69,b)].
% 3.01/3.30 11827 is_a_theorem(implies(implies(implies(A,B),C),implies(not(C),A))). [para(80(a,1),4973(a,1,1))].
% 3.01/3.30 14047 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(not(C),A)). [para(80(a,1),11808(a,1))].
% 3.01/3.30 15365 is_a_theorem(implies(not(implies(not(A),B)),implies(B,C))). [resolve(14047,a,11827,a)].
% 3.01/3.30 16122 is_a_theorem(not(not(implies(not(A),not(A))))). [resolve(15365,a,5487,a)].
% 3.01/3.30 16153 is_a_theorem(implies(not(A),not(A))). [resolve(16122,a,742,a)].
% 3.01/3.30 16334 is_a_theorem(implies(not(and(not(A),B)),implies(B,A))). [resolve(16153,a,133,a),rewrite([80(6)])].
% 3.01/3.30 17617 $F. [ur(69,b,16334,a,c,140,a),rewrite([129(8)]),unit_del(a,53)].
% 3.01/3.30
% 3.01/3.30 % SZS output end Refutation
% 3.01/3.30 ============================== end of proof ==========================
% 3.01/3.30
% 3.01/3.30 ============================== STATISTICS ============================
% 3.01/3.30
% 3.01/3.30 Given=831. Generated=166722. Kept=17566. proofs=1.
% 3.01/3.30 Usable=822. Sos=9999. Demods=5. Limbo=33, Disabled=6784. Hints=0.
% 3.01/3.30 Megabytes=14.49.
% 3.01/3.30 User_CPU=2.15, System_CPU=0.10, Wall_clock=2.
% 3.01/3.30
% 3.01/3.30 ============================== end of statistics =====================
% 3.01/3.30
% 3.01/3.30 ============================== end of search =========================
% 3.01/3.30
% 3.01/3.30 THEOREM PROVED
% 3.01/3.30 % SZS status Theorem
% 3.01/3.30
% 3.01/3.30 Exiting with 1 proof.
% 3.01/3.30
% 3.01/3.30 Process 29403 exit (max_proofs) Sat Jul 2 15:55:43 2022
% 3.01/3.30 Prover9 interrupted
%------------------------------------------------------------------------------